LMFDB - Embedded newform 41.2.g.a.36.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			36.2
Character	$\chi$	$=$	41.36
Dual form			41.2.g.a.8.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415383 - 0.571726i) q^{2} +(-0.242613 + 0.242613i) q^{3} +(0.463706 - 1.42714i) q^{4} +(2.26179 + 0.734900i) q^{5} +(0.239486 + 0.0379308i) q^{6} +(-4.85225 + 0.768522i) q^{7} +(-2.35276 + 0.764458i) q^{8} +2.88228i q^{9} +O(q^{10})$	\(q+(-0.415383 - 0.571726i) q^{2} +(-0.242613 + 0.242613i) q^{3} +(0.463706 - 1.42714i) q^{4} +(2.26179 + 0.734900i) q^{5} +(0.239486 + 0.0379308i) q^{6} +(-4.85225 + 0.768522i) q^{7} +(-2.35276 + 0.764458i) q^{8} +2.88228i q^{9} +(-0.519348 - 1.59839i) q^{10} +(1.51881 + 0.773870i) q^{11} +(0.233742 + 0.458744i) q^{12} +(0.621065 - 3.92125i) q^{13} +(2.45493 + 2.45493i) q^{14} +(-0.727035 + 0.370443i) q^{15} +(-1.01364 - 0.736453i) q^{16} +(-1.24719 + 2.44775i) q^{17} +(1.64787 - 1.19725i) q^{18} +(-0.150964 - 0.953149i) q^{19} +(2.09761 - 2.88712i) q^{20} +(0.990766 - 1.36367i) q^{21} +(-0.188445 - 1.18979i) q^{22} +(5.46604 - 3.97131i) q^{23} +(0.385342 - 0.756277i) q^{24} +(0.530527 + 0.385451i) q^{25} +(-2.49986 + 1.27374i) q^{26} +(-1.42712 - 1.42712i) q^{27} +(-1.15323 + 7.28122i) q^{28} +(0.230233 + 0.451858i) q^{29} +(0.513791 + 0.261789i) q^{30} +(0.182364 + 0.561259i) q^{31} +5.83311i q^{32} +(-0.556233 + 0.180731i) q^{33} +(1.91751 - 0.303703i) q^{34} +(-11.5396 - 1.82769i) q^{35} +(4.11342 + 1.33653i) q^{36} +(1.31461 - 4.04595i) q^{37} +(-0.482233 + 0.482233i) q^{38} +(0.800668 + 1.10202i) q^{39} -5.88325 q^{40} +(-4.01905 - 4.98470i) q^{41} -1.19120 q^{42} +(3.16632 + 4.35807i) q^{43} +(1.80870 - 1.80870i) q^{44} +(-2.11819 + 6.51911i) q^{45} +(-4.54100 - 1.47546i) q^{46} +(-4.96501 - 0.786381i) q^{47} +(0.424595 - 0.0672493i) q^{48} +(16.2964 - 5.29501i) q^{49} -0.463426i q^{50} +(-0.291271 - 0.896441i) q^{51} +(-5.30819 - 2.70466i) q^{52} +(3.46320 + 6.79691i) q^{53} +(-0.223119 + 1.40872i) q^{54} +(2.86650 + 2.86650i) q^{55} +(10.8287 - 5.51749i) q^{56} +(0.267872 + 0.194620i) q^{57} +(0.162704 - 0.319325i) q^{58} +(-6.81790 + 4.95350i) q^{59} +(0.191544 + 1.20936i) q^{60} +(0.408684 - 0.562505i) q^{61} +(0.245135 - 0.337400i) q^{62} +(-2.21509 - 13.9855i) q^{63} +(1.30766 - 0.950072i) q^{64} +(4.28645 - 8.41262i) q^{65} +(0.334379 + 0.242940i) q^{66} +(-3.63545 + 1.85235i) q^{67} +(2.91496 + 2.91496i) q^{68} +(-0.362641 + 2.28962i) q^{69} +(3.74841 + 7.35666i) q^{70} +(6.47886 + 3.30115i) q^{71} +(-2.20338 - 6.78131i) q^{72} +9.72685i q^{73} +(-2.85924 + 0.929024i) q^{74} +(-0.222228 + 0.0351975i) q^{75} +(-1.43028 - 0.226534i) q^{76} +(-7.96437 - 2.58778i) q^{77} +(0.297472 - 0.915526i) q^{78} +(6.15477 - 6.15477i) q^{79} +(-1.75142 - 2.41063i) q^{80} -7.95436 q^{81} +(-1.18044 + 4.36836i) q^{82} +4.81920 q^{83} +(-1.48673 - 2.04631i) q^{84} +(-4.61974 + 4.61974i) q^{85} +(1.17638 - 3.62054i) q^{86} +(-0.165484 - 0.0537691i) q^{87} +(-4.16498 - 0.659667i) q^{88} +(-3.63773 + 0.576160i) q^{89} +(4.60700 - 1.49691i) q^{90} +19.5042i q^{91} +(-3.13298 - 9.64234i) q^{92} +(-0.180413 - 0.0919248i) q^{93} +(1.61279 + 3.16528i) q^{94} +(0.359020 - 2.26677i) q^{95} +(-1.41519 - 1.41519i) q^{96} +(-3.63700 + 1.85314i) q^{97} +(-9.79653 - 7.11760i) q^{98} +(-2.23051 + 4.37762i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.415383	−	0.571726i	−0.293720	−	0.404272i	0.636498	−	0.771279i	$-0.280382\pi$
$2$	−0.415383	−	0.571726i	−0.293720	−	0.404272i	−0.930218	+	0.367007i	$0.880382\pi$
$3$	−0.242613	+	0.242613i	−0.140073	+	0.140073i	−0.773666	−	0.633594i	$-0.781579\pi$
$3$	−0.242613	+	0.242613i	−0.140073	+	0.140073i	0.633594	+	0.773666i	$0.281579\pi$
$4$	0.463706	−	1.42714i	0.231853	−	0.713571i
$5$	2.26179	+	0.734900i	1.01150	+	0.328657i	0.767453	−	0.641105i	$-0.221524\pi$
$5$	2.26179	+	0.734900i	1.01150	+	0.328657i	0.244050	+	0.969763i	$0.421524\pi$
$6$	0.239486	+	0.0379308i	0.0977696	+	0.0154852i
$7$	−4.85225	+	0.768522i	−1.83398	+	0.290474i	−0.975110	−	0.221720i	$-0.928833\pi$
$7$	−4.85225	+	0.768522i	−1.83398	+	0.290474i	−0.858870	+	0.512194i	$0.828833\pi$
$8$	−2.35276	+	0.764458i	−0.831826	+	0.270277i
$9$			2.88228i			0.960759i
$10$	−0.519348	−	1.59839i	−0.164232	−	0.505455i
$11$	1.51881	+	0.773870i	0.457937	+	0.233331i	0.667713	−	0.744419i	$-0.267273\pi$
$11$	1.51881	+	0.773870i	0.457937	+	0.233331i	−0.209776	+	0.977750i	$0.567273\pi$
$12$	0.233742	+	0.458744i	0.0674755	+	0.132428i
$13$	0.621065	−	3.92125i	0.172253	−	1.08756i	−0.738393	−	0.674371i	$-0.764415\pi$
$13$	0.621065	−	3.92125i	0.172253	−	1.08756i	0.910645	−	0.413189i	$-0.135585\pi$
$14$	2.45493	+	2.45493i	0.656108	+	0.656108i
$15$	−0.727035	+	0.370443i	−0.187720	+	0.0956480i
$16$	−1.01364	−	0.736453i	−0.253410	−	0.184113i
$17$	−1.24719	+	2.44775i	−0.302488	+	0.593667i	−0.991353	−	0.131223i	$-0.958110\pi$
$17$	−1.24719	+	2.44775i	−0.302488	+	0.593667i	0.688864	+	0.724890i	$0.258110\pi$
$18$	1.64787	−	1.19725i	0.388408	−	0.282195i
$19$	−0.150964	−	0.953149i	−0.0346335	−	0.218667i	0.964301	−	0.264807i	$-0.0853082\pi$
$19$	−0.150964	−	0.953149i	−0.0346335	−	0.218667i	−0.998935	+	0.0461393i	$0.985308\pi$
$20$	2.09761	−	2.88712i	0.469040	−	0.645579i
$21$	0.990766	−	1.36367i	0.216203	−	0.297578i
$22$	−0.188445	−	1.18979i	−0.0401766	−	0.253665i
$23$	5.46604	−	3.97131i	1.13975	−	0.828075i	0.152664	−	0.988278i	$-0.451215\pi$
$23$	5.46604	−	3.97131i	1.13975	−	0.828075i	0.987084	+	0.160203i	$0.0512148\pi$
$24$	0.385342	−	0.756277i	0.0786577	−	0.154374i
$25$	0.530527	+	0.385451i	0.106105	+	0.0770902i
$26$	−2.49986	+	1.27374i	−0.490264	+	0.249802i
$27$	−1.42712	−	1.42712i	−0.274649	−	0.274649i
$28$	−1.15323	+	7.28122i	−0.217940	+	1.37602i
$29$	0.230233	+	0.451858i	0.0427532	+	0.0839080i	0.911395	−	0.411533i	$-0.135007\pi$
$29$	0.230233	+	0.451858i	0.0427532	+	0.0839080i	−0.868642	+	0.495441i	$0.835007\pi$
$30$	0.513791	+	0.261789i	0.0938049	+	0.0477960i
$31$	0.182364	+	0.561259i	0.0327536	+	0.100805i	0.966097	−	0.258180i	$-0.0831228\pi$
$31$	0.182364	+	0.561259i	0.0327536	+	0.100805i	−0.933343	+	0.358985i	$0.883123\pi$
$32$			5.83311i			1.03116i
$33$	−0.556233	+	0.180731i	−0.0968277	+	0.0314612i
$34$	1.91751	−	0.303703i	0.328850	−	0.0520847i
$35$	−11.5396	−	1.82769i	−1.95054	−	0.308936i
$36$	4.11342	+	1.33653i	0.685570	+	0.222755i
$37$	1.31461	−	4.04595i	0.216120	−	0.665150i	−0.782952	−	0.622082i	$-0.786287\pi$
$37$	1.31461	−	4.04595i	0.216120	−	0.665150i	0.999072	−	0.0430675i	$-0.0137130\pi$
$38$	−0.482233	+	0.482233i	−0.0782285	+	0.0782285i
$39$	0.800668	+	1.10202i	0.128209	+	0.176465i
$40$	−5.88325			−0.930223
$41$	−4.01905	−	4.98470i	−0.627670	−	0.778479i
$41$	−4.01905	−	4.98470i	−0.627670	−	0.778479i
$42$	−1.19120			−0.183805
$43$	3.16632	+	4.35807i	0.482860	+	0.664599i	0.979051	−	0.203614i	$-0.0652686\pi$
$43$	3.16632	+	4.35807i	0.482860	+	0.664599i	−0.496192	+	0.868213i	$0.665269\pi$
$44$	1.80870	−	1.80870i	0.272672	−	0.272672i
$45$	−2.11819	+	6.51911i	−0.315760	+	0.971811i
$46$	−4.54100	−	1.47546i	−0.669535	−	0.217545i
$47$	−4.96501	−	0.786381i	−0.724221	−	0.114705i	−0.216569	−	0.976267i	$-0.569487\pi$
$47$	−4.96501	−	0.786381i	−0.724221	−	0.114705i	−0.507652	+	0.861562i	$0.669487\pi$
$48$	0.424595	−	0.0672493i	0.0612850	−	0.00970660i
$49$	16.2964	−	5.29501i	2.32805	−	0.756430i
$50$		−	0.463426i		−	0.0655384i
$51$	−0.291271	−	0.896441i	−0.0407861	−	0.125527i
$52$	−5.30819	−	2.70466i	−0.736114	−	0.375069i
$53$	3.46320	+	6.79691i	0.475707	+	0.933628i	0.996785	+	0.0801188i	$0.0255300\pi$
$53$	3.46320	+	6.79691i	0.475707	+	0.933628i	−0.521078	+	0.853509i	$0.674470\pi$
$54$	−0.223119	+	1.40872i	−0.0303627	+	0.191703i
$55$	2.86650	+	2.86650i	0.386519	+	0.386519i
$56$	10.8287	−	5.51749i	1.44704	−	0.737306i
$57$	0.267872	+	0.194620i	0.0354805	+	0.0257781i
$58$	0.162704	−	0.319325i	0.0213641	−	0.0419294i
$59$	−6.81790	+	4.95350i	−0.887616	+	0.644890i	−0.935255	−	0.353974i	$-0.884830\pi$
$59$	−6.81790	+	4.95350i	−0.887616	+	0.644890i	0.0476396	+	0.998865i	$0.484830\pi$
$60$	0.191544	+	1.20936i	0.0247282	+	0.156128i
$61$	0.408684	−	0.562505i	0.0523266	−	0.0720214i	−0.782052	−	0.623213i	$-0.785827\pi$
$61$	0.408684	−	0.562505i	0.0523266	−	0.0720214i	0.834378	+	0.551192i	$0.185827\pi$
$62$	0.245135	−	0.337400i	0.0311322	−	0.0428499i
$63$	−2.21509	−	13.9855i	−0.279075	−	1.76201i
$64$	1.30766	−	0.950072i	0.163458	−	0.118759i
$65$	4.28645	−	8.41262i	0.531668	−	1.04346i
$66$	0.334379	+	0.242940i	0.0411592	+	0.0299039i
$67$	−3.63545	+	1.85235i	−0.444141	+	0.226301i	−0.661734	−	0.749738i	$-0.730179\pi$
$67$	−3.63545	+	1.85235i	−0.444141	+	0.226301i	0.217594	+	0.976039i	$0.430179\pi$
$68$	2.91496	+	2.91496i	0.353491	+	0.353491i
$69$	−0.362641	+	2.28962i	−0.0436568	+	0.275638i
$70$	3.74841	+	7.35666i	0.448020	+	0.879289i
$71$	6.47886	+	3.30115i	0.768900	+	0.391774i	0.794005	−	0.607911i	$-0.207992\pi$
$71$	6.47886	+	3.30115i	0.768900	+	0.391774i	−0.0251057	+	0.999685i	$0.507992\pi$
$72$	−2.20338	−	6.78131i	−0.259671	−	0.799185i
$73$			9.72685i			1.13844i	0.822185	+	0.569221i	$0.192755\pi$
$73$			9.72685i			1.13844i	−0.822185	+	0.569221i	$0.807245\pi$
$74$	−2.85924	+	0.929024i	−0.332380	+	0.107997i
$75$	−0.222228	+	0.0351975i	−0.0256607	+	0.00406425i
$76$	−1.43028	−	0.226534i	−0.164065	−	0.0259853i
$77$	−7.96437	−	2.58778i	−0.907624	−	0.294905i
$78$	0.297472	−	0.915526i	0.0336821	−	0.103663i
$79$	6.15477	−	6.15477i	0.692465	−	0.692465i	−0.270309	−	0.962774i	$-0.587126\pi$
$79$	6.15477	−	6.15477i	0.692465	−	0.692465i	0.962774	+	0.270309i	$0.0871257\pi$
$80$	−1.75142	−	2.41063i	−0.195815	−	0.269516i
$81$	−7.95436			−0.883818
$82$	−1.18044	+	4.36836i	−0.130358	+	0.482405i
$83$	4.81920			0.528976			0.264488	−	0.964389i	$-0.414797\pi$
$83$	4.81920			0.528976			0.264488	+	0.964389i	$0.414797\pi$
$84$	−1.48673	−	2.04631i	−0.162216	−	0.223271i
$85$	−4.61974	+	4.61974i	−0.501081	+	0.501081i
$86$	1.17638	−	3.62054i	0.126853	−	0.390413i
$87$	−0.165484	−	0.0537691i	−0.0177418	−	0.00576465i
$88$	−4.16498	−	0.659667i	−0.443988	−	0.0703208i
$89$	−3.63773	+	0.576160i	−0.385598	+	0.0610728i	−0.346224	−	0.938152i	$-0.612536\pi$
$89$	−3.63773	+	0.576160i	−0.385598	+	0.0610728i	−0.0393741	+	0.999225i	$0.512536\pi$
$90$	4.60700	−	1.49691i	0.485621	−	0.157788i
$91$			19.5042i			2.04460i
$92$	−3.13298	−	9.64234i	−0.326636	−	1.00528i
$93$	−0.180413	−	0.0919248i	−0.0187079	−	0.00953216i
$94$	1.61279	+	3.16528i	0.166346	+	0.326473i
$95$	0.359020	−	2.26677i	0.0368347	−	0.232565i
$96$	−1.41519	−	1.41519i	−0.144437	−	0.144437i
$97$	−3.63700	+	1.85314i	−0.369281	+	0.188158i	−0.628776	−	0.777586i	$-0.716444\pi$
$97$	−3.63700	+	1.85314i	−0.369281	+	0.188158i	0.259495	+	0.965744i	$0.416444\pi$
$98$	−9.79653	−	7.11760i	−0.989599	−	0.718986i
$99$	−2.23051	+	4.37762i	−0.224175	+	0.439967i
$100$	0.796102	−	0.578402i	0.0796102	−	0.0578402i
$101$	1.63009	+	10.2920i	0.162200	+	1.02409i	0.925693	+	0.378274i	$0.123482\pi$
$101$	1.63009	+	10.2920i	0.162200	+	1.02409i	−0.763494	+	0.645815i	$0.776518\pi$
$102$	−0.391530	+	0.538894i	−0.0387672	+	0.0533585i
$103$	−0.240884	+	0.331548i	−0.0237350	+	0.0326684i	−0.820720	−	0.571331i	$-0.806427\pi$
$103$	−0.240884	+	0.331548i	−0.0237350	+	0.0326684i	0.796985	+	0.604000i	$0.206427\pi$
$104$	1.53641	+	9.70054i	0.150658	+	0.951216i
$105$	3.24307	−	2.35623i	0.316491	−	0.229944i
$106$	2.44742	−	4.80333i	0.237714	−	0.466540i
$107$	11.3095	+	8.21683i	1.09333	+	0.794351i	0.979959	−	0.199202i	$-0.0638348\pi$
$107$	11.3095	+	8.21683i	1.09333	+	0.794351i	0.113372	+	0.993553i	$0.463835\pi$
$108$	−2.69846	+	1.37493i	−0.259660	+	0.132303i
$109$	−10.8428	−	10.8428i	−1.03855	−	1.03855i	−0.999226	−	0.0393244i	$-0.987479\pi$
$109$	−10.8428	−	10.8428i	−1.03855	−	1.03855i	−0.0393244	−	0.999226i	$-0.512521\pi$
$110$	0.448157	−	2.82955i	0.0427301	−	0.269787i
$111$	0.662658	+	1.30054i	0.0628967	+	0.123442i
$112$	5.48442	+	2.79445i	0.518229	+	0.264051i
$113$	−2.49191	−	7.66931i	−0.234419	−	0.721468i	−0.997198	−	0.0748085i	$-0.976165\pi$
$113$	−2.49191	−	7.66931i	−0.234419	−	0.721468i	0.762779	−	0.646660i	$-0.223835\pi$
$114$		−	0.233992i		−	0.0219153i
$115$	15.2815	−	4.96527i	1.42501	−	0.463014i
$116$	0.751626	−	0.119046i	0.0697867	−	0.0110531i
$117$	11.3021	+	1.79008i	1.04488	+	0.165493i
$118$	5.66409	+	1.84037i	0.521422	+	0.169420i
$119$	4.17054	−	12.8356i	0.382313	−	1.17664i
$120$	1.42735	−	1.42735i	0.130299	−	0.130299i
$121$	−4.75774	−	6.54847i	−0.432522	−	0.595315i
$122$	−0.491360			−0.0444856
$123$	2.18443	+	0.234279i	0.196963	+	0.0211243i
$124$	0.885560			0.0795256
$125$	−6.07264	−	8.35827i	−0.543153	−	0.747586i
$126$	−7.07579	+	7.07579i	−0.630362	+	0.630362i
$127$	3.32547	−	10.2347i	0.295087	−	0.908186i	−0.688105	−	0.725612i	$-0.741557\pi$
$127$	3.32547	−	10.2347i	0.295087	−	0.908186i	0.983192	−	0.182574i	$-0.0584430\pi$
$128$	10.0089	+	3.25208i	0.884668	+	0.287446i
$129$	−1.82551	−	0.289133i	−0.160728	−	0.0254568i
$130$	−6.59024	+	1.04379i	−0.578002	+	0.0915465i
$131$	−15.4682	+	5.02592i	−1.35146	+	0.439116i	−0.893184	−	0.449692i	$-0.851534\pi$
$131$	−15.4682	+	5.02592i	−1.35146	+	0.439116i	−0.458278	+	0.888809i	$0.651534\pi$
$132$			0.877629i			0.0763878i
$133$	1.46503	+	4.50890i	0.127034	+	0.390972i
$134$	2.56914	+	1.30904i	0.221940	+	0.113084i
$135$	−2.17905	−	4.27662i	−0.187543	−	0.368073i
$136$	1.06314	−	6.71240i	0.0911634	−	0.575583i
$137$	12.5397	+	12.5397i	1.07134	+	1.07134i	0.997252	+	0.0740834i	$0.0236031\pi$
$137$	12.5397	+	12.5397i	1.07134	+	1.07134i	0.0740834	+	0.997252i	$0.476397\pi$
$138$	1.45967	−	0.743740i	0.124256	−	0.0633114i
$139$	1.72343	+	1.25214i	0.146179	+	0.106206i	0.658471	−	0.752606i	$-0.271203\pi$
$139$	1.72343	+	1.25214i	0.146179	+	0.106206i	−0.512292	+	0.858811i	$0.671203\pi$
$140$	−7.95934	+	15.6211i	−0.672687	+	1.32022i
$141$	1.39536	−	1.01379i	0.117511	−	0.0853765i
$142$	−0.803861	−	5.07538i	−0.0674585	−	0.425916i
$143$	3.97782	−	5.47500i	0.332642	−	0.457842i
$144$	2.12266	−	2.92159i	0.176888	−	0.243466i
$145$	0.188669	+	1.19121i	0.0156681	+	0.0989243i
$146$	5.56110	−	4.04037i	0.460240	−	0.334384i
$147$	−2.66907	+	5.23834i	−0.220141	+	0.432051i
$148$	−5.16455	−	3.75226i	−0.424523	−	0.308434i
$149$	−1.35193	+	0.688843i	−0.110754	+	0.0564322i	−0.508490	−	0.861068i	$-0.669796\pi$
$149$	−1.35193	+	0.688843i	−0.110754	+	0.0564322i	0.397736	+	0.917500i	$0.369796\pi$
$150$	0.112433	+	0.112433i	0.00918013	+	0.00918013i
$151$	0.327873	−	2.07011i	0.0266819	−	0.168463i	−0.970749	−	0.240096i	$-0.922821\pi$
$151$	0.327873	−	2.07011i	0.0266819	−	0.168463i	0.997431	+	0.0716330i	$0.0228210\pi$
$152$	1.08382	+	2.12713i	0.0879098	+	0.172533i
$153$	−7.05510	−	3.59475i	−0.570371	−	0.290619i
$154$	1.82877	+	5.62836i	0.147366	+	0.453546i
$155$			1.40347i			0.112729i
$156$	1.94402	−	0.631651i	0.155646	−	0.0505725i
$157$	−6.82911	+	1.08163i	−0.545023	+	0.0863231i	−0.422874	−	0.906189i	$-0.638979\pi$
$157$	−6.82911	+	1.08163i	−0.545023	+	0.0863231i	−0.122149	+	0.992512i	$0.538979\pi$
$158$	−6.07543	−	0.962253i	−0.483335	−	0.0765528i
$159$	−2.48924	−	0.808802i	−0.197409	−	0.0641421i
$160$	−4.28675	+	13.1933i	−0.338898	+	1.04302i
$161$	−23.4706	+	23.4706i	−1.84974	+	1.84974i
$162$	3.30411	+	4.54772i	0.259595	+	0.357302i
$163$	−7.72291			−0.604905			−0.302453	−	0.953164i	$-0.597805\pi$
$163$	−7.72291			−0.604905			−0.302453	+	0.953164i	$0.597805\pi$
$164$	−8.97753	+	3.42432i	−0.701028	+	0.267394i
$165$	−1.39090			−0.108281
$166$	−2.00182	−	2.75526i	−0.155371	−	0.213850i
$167$	13.4205	−	13.4205i	1.03851	−	1.03851i	0.0392793	−	0.999228i	$-0.487494\pi$
$167$	13.4205	−	13.4205i	1.03851	−	1.03851i	0.999228	−	0.0392793i	$-0.0125062\pi$
$168$	−1.28856	+	3.96579i	−0.0994149	+	0.305968i
$169$	−2.62676	−	0.853486i	−0.202059	−	0.0656528i
$170$	4.56019	+	0.722263i	0.349750	+	0.0553950i
$171$	2.74724	−	0.435120i	0.210087	−	0.0332745i
$172$	7.68783	−	2.49793i	0.586191	−	0.190465i
$173$		−	12.9720i		−	0.986242i	−0.869961	−	0.493121i	$-0.835856\pi$
$173$		−	12.9720i		−	0.986242i	0.869961	−	0.493121i	$-0.164144\pi$
$174$	0.0379982	+	0.116946i	0.00288064	+	0.00886569i
$175$	−2.87048	−	1.46258i	−0.216988	−	0.110561i
$176$	−0.969604	−	1.90295i	−0.0730867	−	0.143441i
$177$	0.452329	−	2.85589i	0.0339991	−	0.214662i
$178$	1.84046	+	1.84046i	0.137948	+	0.137948i
$179$	0.493180	−	0.251288i	0.0368620	−	0.0187821i	−0.435462	−	0.900207i	$-0.643415\pi$
$179$	0.493180	−	0.251288i	0.0368620	−	0.0187821i	0.472324	+	0.881425i	$0.343415\pi$
$180$	8.32147	+	6.04590i	0.620246	+	0.450635i
$181$	10.9072	−	21.4065i	0.810723	−	1.59113i	0.00415439	−	0.999991i	$-0.498678\pi$
$181$	10.9072	−	21.4065i	0.810723	−	1.59113i	0.806568	−	0.591141i	$-0.201322\pi$
$182$	11.1511	−	8.10173i	0.826573	−	0.600540i
$183$	0.0373190	+	0.235623i	0.00275870	+	0.0174178i
$184$	−9.82438	+	13.5221i	−0.724263	+	0.996862i
$185$	5.94673	−	8.18497i	0.437212	−	0.601771i
$186$	0.0223846	+	0.141331i	0.00164132	+	0.0103629i
$187$	−3.78848	+	2.75249i	−0.277041	+	0.201282i
$188$	−3.42458	+	6.72112i	−0.249763	+	0.490188i
$189$	8.02150	+	5.82796i	0.583478	+	0.423922i
$190$	−1.44510	+	0.736316i	−0.104839	+	0.0534180i
$191$	8.79132	+	8.79132i	0.636118	+	0.636118i	0.949596	−	0.313478i	$-0.101494\pi$
$191$	8.79132	+	8.79132i	0.636118	+	0.636118i	−0.313478	+	0.949596i	$0.601494\pi$
$192$	−0.0867559	+	0.547755i	−0.00626107	+	0.0395308i
$193$	−1.47698	−	2.89873i	−0.106315	−	0.208655i	0.831720	−	0.555195i	$-0.187357\pi$
$193$	−1.47698	−	2.89873i	−0.106315	−	0.208655i	−0.938035	+	0.346540i	$0.887357\pi$
$194$	2.57024	+	1.30960i	0.184533	+	0.0940240i
$195$	1.00106	+	3.08096i	0.0716877	+	0.220632i
$196$		−	25.7125i		−	1.83661i
$197$	−12.8789	+	4.18462i	−0.917586	+	0.298142i	−0.729476	−	0.684006i	$-0.760236\pi$
$197$	−12.8789	+	4.18462i	−0.917586	+	0.298142i	−0.188110	+	0.982148i	$0.560236\pi$
$198$	3.42932	−	0.543150i	0.243711	−	0.0386000i
$199$	−9.16208	−	1.45113i	−0.649483	−	0.102868i	−0.177004	−	0.984210i	$-0.556641\pi$
$199$	−9.16208	−	1.45113i	−0.649483	−	0.102868i	−0.472479	+	0.881342i	$0.656641\pi$
$200$	−1.54286	−	0.501307i	−0.109097	−	0.0354478i
$201$	0.432602	−	1.33141i	0.0305134	−	0.0939105i
$202$	5.20708	−	5.20708i	0.366369	−	0.366369i
$203$	−1.46441	−	2.01559i	−0.102782	−	0.141467i
$204$	−1.41441			−0.0990287
$205$	−5.42699	−	14.2279i	−0.379037	−	0.993722i
$206$	0.289614			0.0201784
$207$	11.4464	+	15.7546i	0.795581	+	1.09502i
$208$	−3.51735	+	3.51735i	−0.243885	+	0.243885i
$209$	0.508329	−	1.56448i	0.0351618	−	0.108217i
$210$	−2.69423	−	0.875409i	−0.185920	−	0.0604090i
$211$	26.8855	+	4.25824i	1.85087	+	0.293149i	0.980095	−	0.198529i	$-0.0636163\pi$
$211$	26.8855	+	4.25824i	1.85087	+	0.293149i	0.870777	+	0.491678i	$0.163616\pi$
$212$	11.3061	−	1.79070i	0.776504	−	0.122986i
$213$	−2.37276	+	0.770955i	−0.162579	+	0.0528250i
$214$		−	9.87907i		−	0.675320i
$215$	3.95881	+	12.1840i	0.269989	+	0.830940i
$216$	4.44863	+	2.26669i	0.302691	+	0.154229i
$217$	−1.31622	−	2.58322i	−0.0893506	−	0.175360i
$218$	−1.69519	+	10.7030i	−0.114813	+	0.724900i
$219$	−2.35986	−	2.35986i	−0.159465	−	0.159465i
$220$	5.42012	−	2.76169i	0.365424	−	0.186193i
$221$	8.82366	+	6.41077i	0.593544	+	0.431235i
$222$	0.468296	−	0.919082i	0.0314299	−	0.0616847i
$223$	−7.71095	+	5.60233i	−0.516363	+	0.375160i	−0.815232	−	0.579134i	$-0.803391\pi$
$223$	−7.71095	+	5.60233i	−0.516363	+	0.375160i	0.298869	+	0.954294i	$0.403391\pi$
$224$	−4.48287	−	28.3037i	−0.299524	−	1.89112i
$225$	−1.11098	+	1.52913i	−0.0740651	+	0.101942i
$226$	−3.34965	+	4.61040i	−0.222815	+	0.306679i
$227$	−0.238184	−	1.50383i	−0.0158088	−	0.0998130i	0.978522	−	0.206141i	$-0.0660906\pi$
$227$	−0.238184	−	1.50383i	−0.0158088	−	0.0998130i	−0.994331	+	0.106328i	$0.966091\pi$
$228$	0.401965	−	0.292045i	0.0266208	−	0.0193411i
$229$	−6.69218	+	13.1341i	−0.442232	+	0.867929i	0.557066	+	0.830468i	$0.311927\pi$
$229$	−6.69218	+	13.1341i	−0.442232	+	0.867929i	−0.999298	+	0.0374606i	$0.988073\pi$
$230$	−9.18648	−	6.67437i	−0.605738	−	0.440095i
$231$	2.56009	−	1.30443i	0.168441	−	0.0858252i
$232$	−0.887110	−	0.887110i	−0.0582416	−	0.0582416i
$233$	−2.32886	+	14.7039i	−0.152569	+	0.963282i	0.786009	+	0.618215i	$0.212144\pi$
$233$	−2.32886	+	14.7039i	−0.152569	+	0.963282i	−0.938578	+	0.345067i	$0.887856\pi$
$234$	−3.67128	−	7.20530i	−0.239999	−	0.471025i
$235$	−10.6519	−	5.42741i	−0.694853	−	0.354045i
$236$	3.90784	+	12.0271i	0.254379	+	0.782897i
$237$			2.98645i			0.193991i
$238$	−9.07083	+	2.94729i	−0.587974	+	0.191044i
$239$	−13.2085	+	2.09203i	−0.854390	+	0.135322i	−0.568240	−	0.822863i	$-0.692375\pi$
$239$	−13.2085	+	2.09203i	−0.854390	+	0.135322i	−0.286150	+	0.958185i	$0.592375\pi$
$240$	1.00977	+	0.159931i	0.0651801	+	0.0103235i
$241$	−3.79971	−	1.23460i	−0.244761	−	0.0795276i	0.184068	−	0.982914i	$-0.441073\pi$
$241$	−3.79971	−	1.23460i	−0.244761	−	0.0795276i	−0.428828	+	0.903386i	$0.641073\pi$
$242$	−1.76765	+	5.44025i	−0.113629	+	0.349713i
$243$	6.21118	−	6.21118i	0.398447	−	0.398447i
$244$	−0.613265	−	0.844087i	−0.0392603	−	0.0540372i
$245$	40.7502			2.60344
$246$	−0.773431	−	1.34621i	−0.0493121	−	0.0858312i
$247$	−3.83130			−0.243780
$248$	−0.858118	−	1.18110i	−0.0544905	−	0.0749998i
$249$	−1.16920	+	1.16920i	−0.0740951	+	0.0740951i
$250$	−2.25617	+	6.94378i	−0.142693	+	0.439163i
$251$	−25.9816	−	8.44194i	−1.63995	−	0.532851i	−0.663420	−	0.748248i	$-0.730896\pi$
$251$	−25.9816	−	8.44194i	−1.63995	−	0.532851i	−0.976527	+	0.215397i	$0.930896\pi$
$252$	−20.9865	−	3.32394i	−1.32203	−	0.209388i
$253$	11.3751	−	1.80164i	0.715148	−	0.113268i
$254$	−7.23281	+	2.35008i	−0.453827	+	0.147457i
$255$		−	2.24162i		−	0.140375i
$256$	−3.29719	−	10.1477i	−0.206074	−	0.634231i
$257$	−6.68063	−	3.40395i	−0.416726	−	0.212333i	0.233039	−	0.972467i	$-0.425133\pi$
$257$	−6.68063	−	3.40395i	−0.416726	−	0.212333i	−0.649766	+	0.760135i	$0.725133\pi$
$258$	0.592984	+	1.16380i	0.0369176	+	0.0724548i
$259$	−3.26941	+	20.6423i	−0.203152	+	1.28265i
$260$	−10.0184	−	10.0184i	−0.621312	−	0.621312i
$261$	−1.30238	+	0.663596i	−0.0806153	+	0.0410756i
$262$	9.29868	+	6.75588i	0.574474	+	0.417380i
$263$	5.41178	−	10.6212i	0.333705	−	0.654933i	−0.661796	−	0.749684i	$-0.730206\pi$
$263$	5.41178	−	10.6212i	0.333705	−	0.654933i	0.995501	+	0.0947511i	$0.0302055\pi$
$264$	1.17052	−	0.850433i	0.0720406	−	0.0523405i
$265$	2.83798	+	17.9183i	0.174336	+	1.10071i
$266$	1.96931	−	2.71052i	0.120746	−	0.166193i
$267$	0.742776	−	1.02234i	0.0454572	−	0.0625664i
$268$	0.957790	+	6.04725i	0.0585063	+	0.369394i
$269$	−17.1372	+	12.4509i	−1.04488	+	0.759147i	−0.971231	−	0.238138i	$-0.923463\pi$
$269$	−17.1372	+	12.4509i	−1.04488	+	0.759147i	−0.0736443	+	0.997285i	$0.523463\pi$
$270$	−1.53992	+	3.02226i	−0.0937164	+	0.183929i
$271$	−3.10054	−	2.25267i	−0.188344	−	0.136840i	0.489617	−	0.871937i	$-0.337136\pi$
$271$	−3.10054	−	2.25267i	−0.188344	−	0.136840i	−0.677962	+	0.735097i	$0.737136\pi$
$272$	3.06686	−	1.56264i	0.185956	−	0.0947491i
$273$	−4.73197	−	4.73197i	−0.286392	−	0.286392i
$274$	1.96049	−	12.3780i	0.118437	−	0.747784i
$275$	0.507479	+	0.995984i	0.0306022	+	0.0600601i
$276$	3.09946	+	1.57925i	0.186565	+	0.0950598i
$277$	0.360907	+	1.11076i	0.0216848	+	0.0667389i	0.961313	−	0.275457i	$-0.0888293\pi$
$277$	0.360907	+	1.11076i	0.0216848	+	0.0667389i	−0.939629	+	0.342196i	$0.888829\pi$
$278$		−	1.50545i		−	0.0902909i
$279$	−1.61770	+	0.525624i	−0.0968494	+	0.0314683i
$280$	28.5470	−	4.52140i	1.70601	−	0.270205i
$281$	17.4781	+	2.76826i	1.04266	+	0.165140i	0.654196	−	0.756325i	$-0.273007\pi$
$281$	17.4781	+	2.76826i	1.04266	+	0.165140i	0.388460	+	0.921466i	$0.373007\pi$
$282$	−1.15922	−	0.376654i	−0.0690306	−	0.0224294i
$283$	2.28989	−	7.04757i	0.136120	−	0.418934i	−0.859643	−	0.510896i	$-0.829314\pi$
$283$	2.28989	−	7.04757i	0.136120	−	0.418934i	0.995763	+	0.0919616i	$0.0293137\pi$
$284$	7.71549	−	7.71549i	0.457830	−	0.457830i
$285$	0.462844	+	0.637050i	0.0274165	+	0.0377356i
$286$	−4.78252			−0.282796
$287$	23.3323	+	21.0983i	1.37726	+	1.24539i
$288$	−16.8126			−0.990695
$289$	5.55635	+	7.64766i	0.326844	+	0.449862i
$290$	0.602674	−	0.602674i	0.0353902	−	0.0353902i
$291$	0.432787	−	1.33198i	0.0253704	−	0.0780821i
$292$	13.8816	+	4.51040i	0.812359	+	0.263951i
$293$	10.2251	+	1.61950i	0.597357	+	0.0946120i	0.447789	−	0.894139i	$-0.352212\pi$
$293$	10.2251	+	1.61950i	0.597357	+	0.0946120i	0.149568	+	0.988751i	$0.452212\pi$
$294$	4.10359	−	0.649944i	0.239326	−	0.0379055i
$295$	−19.0610	+	6.19329i	−1.10977	+	0.360587i
$296$			10.5241i			0.611701i
$297$	−1.06311	−	3.27192i	−0.0616879	−	0.189856i
$298$	0.955399	+	0.486800i	0.0553448	+	0.0281996i
$299$	−12.1777	−	23.9002i	−0.704257	−	1.38218i
$300$	−0.0528168	+	0.333472i	−0.00304938	+	0.0192530i
$301$	−18.7131	−	18.7131i	−1.07860	−	1.07860i
$302$	−1.31973	+	0.672435i	−0.0759418	+	0.0386943i
$303$	−2.89245	−	2.10149i	−0.166167	−	0.120727i
$304$	−0.548926	+	1.07733i	−0.0314831	+	0.0617890i
$305$	1.33774	−	0.971927i	0.0765989	−	0.0556524i
$306$	0.875357	+	5.52679i	0.0500408	+	0.315945i
$307$	−0.807435	+	1.11134i	−0.0460827	+	0.0634274i	−0.831437	−	0.555620i	$-0.812481\pi$
$307$	−0.807435	+	1.11134i	−0.0460827	+	0.0634274i	0.785354	+	0.619047i	$0.212481\pi$
$308$	−7.38626	+	10.1663i	−0.420871	+	0.579279i
$309$	−0.0219964	−	0.138879i	−0.00125133	−	0.00790058i
$310$	0.802400	−	0.582978i	0.0455733	−	0.0331109i
$311$	5.51590	−	10.8256i	0.312778	−	0.613862i	−0.680083	−	0.733135i	$-0.738056\pi$
$311$	5.51590	−	10.8256i	0.312778	−	0.613862i	0.992861	+	0.119273i	$0.0380564\pi$
$312$	−2.72623	−	1.98072i	−0.154342	−	0.112136i
$313$	26.8319	−	13.6715i	1.51663	−	0.772761i	0.519950	−	0.854197i	$-0.325951\pi$
$313$	26.8319	−	13.6715i	1.51663	−	0.772761i	0.996679	+	0.0814357i	$0.0259505\pi$
$314$	3.45509	+	3.45509i	0.194982	+	0.194982i
$315$	5.26790	−	33.2602i	0.296813	−	1.87400i
$316$	−5.92972	−	11.6377i	−0.333573	−	0.654673i
$317$	−7.54815	−	3.84597i	−0.423946	−	0.216011i	0.228983	−	0.973430i	$-0.426460\pi$
$317$	−7.54815	−	3.84597i	−0.423946	−	0.216011i	−0.652929	+	0.757419i	$0.726460\pi$
$318$	0.571574	+	1.75912i	0.0320523	+	0.0986468i
$319$			0.864455i			0.0484002i
$320$	3.65586	−	1.18786i	0.204369	−	0.0664035i
$321$	−4.73734	+	0.750321i	−0.264413	+	0.0418788i
$322$	23.1680	+	3.66946i	1.29110	+	0.204491i
$323$	2.52135	+	0.819237i	0.140292	+	0.0455836i
$324$	−3.68849	+	11.3520i	−0.204916	+	0.630667i
$325$	1.84094	−	1.84094i	0.102117	−	0.102117i
$326$	3.20797	+	4.41539i	0.177673	+	0.244546i
$327$	5.26120			0.290945
$328$	13.2665	+	8.65541i	0.732517	+	0.477915i
$329$	24.6959			1.36153
$330$	0.577757	+	0.795214i	0.0318045	+	0.0437751i
$331$	−7.38632	+	7.38632i	−0.405989	+	0.405989i	−0.880337	−	0.474348i	$-0.842684\pi$
$331$	−7.38632	+	7.38632i	−0.405989	+	0.405989i	0.474348	+	0.880337i	$0.342684\pi$
$332$	2.23469	−	6.87768i	0.122645	−	0.377462i
$333$	11.6615	+	3.78907i	0.639049	+	0.207640i
$334$	−13.2475	−	2.09820i	−0.724870	−	0.114808i
$335$	−9.58391	+	1.51794i	−0.523625	+	0.0829341i
$336$	−2.00856	+	0.652621i	−0.109576	+	0.0356034i
$337$		−	22.8689i		−	1.24575i	−0.782321	−	0.622875i	$-0.785964\pi$
$337$		−	22.8689i		−	1.24575i	0.782321	−	0.622875i	$-0.214036\pi$
$338$	0.603152	+	1.85631i	0.0328072	+	0.100970i
$339$	2.46524	+	1.25610i	0.133894	+	0.0682222i
$340$	4.45082	+	8.73522i	0.241379	+	0.473734i
$341$	−0.157366	+	0.993570i	−0.00852184	+	0.0538048i
$342$	−1.38993	−	1.38993i	−0.0751587	−	0.0751587i
$343$	−44.3638	+	22.6045i	−2.39542	+	1.22053i
$344$	−10.7812	−	7.83297i	−0.581281	−	0.422325i
$345$	−2.50286	+	4.91214i	−0.134749	+	0.264461i
$346$	−7.41643	+	5.38835i	−0.398710	+	0.289680i
$347$	0.261536	+	1.65127i	0.0140400	+	0.0886450i	0.993713	−	0.111954i	$-0.0357110\pi$
$347$	0.261536	+	1.65127i	0.0140400	+	0.0886450i	−0.979673	+	0.200599i	$0.935711\pi$
$348$	−0.153472	+	0.211236i	−0.00822697	+	0.0113235i
$349$	−20.3042	+	27.9463i	−1.08686	+	1.49593i	−0.235116	+	0.971967i	$0.575547\pi$
$349$	−20.3042	+	27.9463i	−1.08686	+	1.49593i	−0.851741	+	0.523963i	$0.824453\pi$
$350$	0.356153	+	2.24866i	0.0190372	+	0.120196i
$351$	−6.48242	+	4.70975i	−0.346006	+	0.251388i
$352$	−4.51407	+	8.85936i	−0.240601	+	0.472206i
$353$	−20.7152	−	15.0505i	−1.10256	−	0.801055i	−0.121082	−	0.992642i	$-0.538636\pi$
$353$	−20.7152	−	15.0505i	−1.10256	−	0.801055i	−0.981476	+	0.191587i	$0.938636\pi$
$354$	−1.82068	+	0.927683i	−0.0967680	+	0.0493058i
$355$	12.2278	+	12.2278i	0.648985	+	0.648985i
$356$	−0.864577	+	5.45872i	−0.0458225	+	0.289312i
$357$	2.10226	+	4.12591i	0.111263	+	0.218366i
$358$	−0.348527	−	0.177583i	−0.0184202	−	0.00938556i
$359$	−8.16247	−	25.1215i	−0.430799	−	1.32586i	−0.897331	−	0.441358i	$-0.854497\pi$
$359$	−8.16247	−	25.1215i	−0.430799	−	1.32586i	0.466532	−	0.884504i	$-0.345503\pi$
$360$		−	16.9572i		−	0.893720i
$361$	17.1844	−	5.58354i	0.904441	−	0.293871i
$362$	−16.7693	+	2.65600i	−0.881375	+	0.139596i
$363$	2.74303	+	0.434454i	0.143972	+	0.0228029i
$364$	27.8353	+	9.04423i	1.45897	+	0.474047i
$365$	−7.14826	+	22.0001i	−0.374157	+	1.15154i
$366$	0.119210	−	0.119210i	0.00623122	−	0.00623122i
$367$	11.8091	+	16.2538i	0.616429	+	0.848442i	0.997087	−	0.0762741i	$-0.0243024\pi$
$367$	11.8091	+	16.2538i	0.616429	+	0.848442i	−0.380658	+	0.924716i	$0.624302\pi$
$368$	−8.46528			−0.441283
$369$	14.3673	−	11.5840i	0.747931	−	0.603040i
$370$	−7.14974			−0.371697
$371$	−22.0279	−	30.3188i	−1.14363	−	1.57407i
$372$	−0.214848	+	0.214848i	−0.0111394	+	0.0111394i
$373$	−2.37421	+	7.30705i	−0.122932	+	0.378345i	−0.993519	−	0.113670i	$-0.963739\pi$
$373$	−2.37421	+	7.30705i	−0.122932	+	0.378345i	0.870587	+	0.492015i	$0.163739\pi$
$374$	3.14735	+	1.02264i	0.162745	+	0.0528792i
$375$	3.50113	+	0.554524i	0.180797	+	0.0286355i
$376$	12.2826	−	1.94538i	0.633428	−	0.100325i
$377$	1.91484	−	0.622169i	0.0986193	−	0.0320433i
$378$		−	7.00694i		−	0.360398i
$379$	7.20512	+	22.1751i	0.370102	+	1.13906i	0.946724	+	0.322046i	$0.104371\pi$
$379$	7.20512	+	22.1751i	0.370102	+	1.13906i	−0.576622	+	0.817011i	$0.695629\pi$
$380$	−3.06852	−	1.56349i	−0.157412	−	0.0802052i
$381$	1.67628	+	3.28988i	0.0858783	+	0.168546i
$382$	1.37446	−	8.67800i	0.0703235	−	0.444005i
$383$	−11.5251	−	11.5251i	−0.588904	−	0.588904i	0.348430	−	0.937335i	$-0.386715\pi$
$383$	−11.5251	−	11.5251i	−0.588904	−	0.588904i	−0.937335	+	0.348430i	$0.886715\pi$
$384$	−3.21728	+	1.63929i	−0.164181	+	0.0836544i
$385$	−16.1120	−	11.7060i	−0.821142	−	0.596594i
$386$	−1.04377	+	2.04851i	−0.0531265	+	0.104267i
$387$	−12.5612	+	9.12622i	−0.638520	+	0.463912i
$388$	0.958199	+	6.04983i	0.0486452	+	0.307134i
$389$	−0.170988	+	0.235345i	−0.00866943	+	0.0119325i	−0.813330	−	0.581803i	$-0.802347\pi$
$389$	−0.170988	+	0.235345i	−0.00866943	+	0.0119325i	0.804660	+	0.593735i	$0.202347\pi$
$390$	1.34564	−	1.85211i	0.0681391	−	0.0937854i
$391$	2.90358	+	18.3325i	0.146840	+	0.927114i
$392$	−34.2936	+	24.9158i	−1.73209	+	1.25844i
$393$	2.53343	−	4.97213i	0.127795	−	0.250811i
$394$	7.74216	+	5.62500i	0.390044	+	0.283384i
$395$	18.4439	−	9.39765i	0.928014	−	0.472847i
$396$	5.21318	+	5.21318i	0.261972	+	0.261972i
$397$	4.42708	−	27.9515i	0.222189	−	1.40284i	−0.584272	−	0.811558i	$-0.698620\pi$
$397$	4.42708	−	27.9515i	0.222189	−	1.40284i	0.806461	−	0.591287i	$-0.201380\pi$
$398$	2.97613	+	5.84098i	0.149180	+	0.292782i
$399$	−1.44935	−	0.738483i	−0.0725585	−	0.0369704i
$400$	−0.253898	−	0.781417i	−0.0126949	−	0.0390708i
$401$			6.77610i			0.338382i	0.985583	+	0.169191i	$0.0541155\pi$
$401$			6.77610i			0.338382i	−0.985583	+	0.169191i	$0.945885\pi$
$402$	−0.940899	+	0.305716i	−0.0469278	+	0.0152478i
$403$	2.31410	−	0.366517i	0.115273	−	0.0182575i
$404$	15.4440	+	2.44609i	0.768367	+	0.121697i
$405$	−17.9911	−	5.84566i	−0.893984	−	0.290473i
$406$	−0.544074	+	1.67449i	−0.0270019	+	0.0831034i
$407$	5.12767	−	5.12767i	0.254169	−	0.254169i
$408$	1.37058	+	1.88645i	0.0678540	+	0.0933930i
$409$	16.9059			0.835945			0.417972	−	0.908460i	$-0.362741\pi$
$409$	16.9059			0.835945			0.417972	+	0.908460i	$0.362741\pi$
$410$	−5.88021	+	9.01280i	−0.290403	+	0.445111i
$411$	−6.08457			−0.300130
$412$	0.361467	+	0.497517i	0.0178082	+	0.0245109i
$413$	29.2753	−	29.2753i	1.44055	−	1.44055i
$414$	4.25269	−	13.0884i	0.209008	−	0.643262i
$415$	10.9000	+	3.54163i	0.535061	+	0.173852i
$416$	22.8731	+	3.62274i	1.12145	+	0.177620i
$417$	−0.721913	+	0.114340i	−0.0353522	+	0.00559924i
$418$	−1.10560	+	0.359232i	−0.0540768	+	0.0175706i
$419$		−	12.2920i		−	0.600504i	−0.953860	−	0.300252i	$-0.902929\pi$
$419$		−	12.2920i		−	0.600504i	0.953860	−	0.300252i	$-0.0970708\pi$
$420$	−1.85884	−	5.72091i	−0.0907020	−	0.279152i
$421$	25.9576	+	13.2260i	1.26509	+	0.644597i	0.952283	−	0.305218i	$-0.0987293\pi$
$421$	25.9576	+	13.2260i	1.26509	+	0.644597i	0.312811	+	0.949815i	$0.398729\pi$
$422$	−8.73323	−	17.1399i	−0.425127	−	0.834359i
$423$	2.26657	−	14.3105i	0.110204	−	0.695802i
$424$	−13.3440	−	13.3440i	−0.648043	−	0.648043i
$425$	−1.60516	+	0.817868i	−0.0778616	+	0.0396724i
$426$	1.42638	+	1.03633i	0.0691083	+	0.0502101i
$427$	−1.55074	+	3.04350i	−0.0750456	+	0.147285i
$428$	16.9709	−	12.3301i	0.820318	−	0.595996i
$429$	0.363235	+	2.29337i	0.0175371	+	0.110725i
$430$	5.32147	−	7.32437i	0.256624	−	0.353213i
$431$	5.05984	−	6.96427i	0.243724	−	0.335457i	−0.669577	−	0.742743i	$-0.733525\pi$
$431$	5.05984	−	6.96427i	0.243724	−	0.335457i	0.913301	+	0.407285i	$0.133525\pi$
$432$	0.395579	+	2.49759i	0.0190323	+	0.120165i
$433$	9.57821	−	6.95897i	0.460299	−	0.334427i	−0.333349	−	0.942803i	$-0.608179\pi$
$433$	9.57821	−	6.95897i	0.460299	−	0.334427i	0.793649	+	0.608376i	$0.208179\pi$
$434$	−0.930161	+	1.82554i	−0.0446491	+	0.0876289i
$435$	−0.334775	−	0.243229i	−0.0160513	−	0.0116619i
$436$	−20.5021	+	10.4463i	−0.981871	+	0.500288i
$437$	−4.61043	−	4.61043i	−0.220547	−	0.220547i
$438$	−0.368947	+	2.32944i	−0.0176290	+	0.111305i
$439$	−13.8074	−	27.0986i	−0.658993	−	1.29335i	−0.942445	−	0.334360i	$-0.891480\pi$
$439$	−13.8074	−	27.0986i	−0.658993	−	1.29335i	0.283453	−	0.958986i	$-0.408520\pi$
$440$	−8.93551	−	4.55287i	−0.425984	−	0.217050i
$441$	15.2617	+	46.9706i	0.726747	+	2.23670i
$442$		−	7.70765i		−	0.366615i
$443$	−12.6998	+	4.12642i	−0.603387	+	0.196052i	−0.594750	−	0.803911i	$-0.702749\pi$
$443$	−12.6998	+	4.12642i	−0.603387	+	0.196052i	−0.00863630	+	0.999963i	$0.502749\pi$
$444$	2.16333	−	0.342638i	0.102667	−	0.0162609i
$445$	−8.65119	−	1.37021i	−0.410106	−	0.0649544i
$446$	6.40600	+	2.08144i	0.303333	+	0.0985588i
$447$	0.160874	−	0.495118i	0.00760906	−	0.0234183i
$448$	−5.61496	+	5.61496i	−0.265282	+	0.265282i
$449$	14.7829	+	20.3470i	0.697649	+	0.960232i	0.999975	+	0.00702734i	$0.00223689\pi$
$449$	14.7829	+	20.3470i	0.697649	+	0.960232i	−0.302326	+	0.953205i	$0.597763\pi$
$450$	1.33572			0.0629666
$451$	−2.24664	−	10.6810i	−0.105790	−	0.502949i
$452$	−12.1007			−0.569169
$453$	0.422689	+	0.581781i	0.0198597	+	0.0273345i
$454$	−0.760844	+	0.760844i	−0.0357082	+	0.0357082i
$455$	−14.3336	+	44.1144i	−0.671972	+	2.06812i
$456$	−0.779018	−	0.253118i	−0.0364809	−	0.0118533i
$457$	−31.7784	−	5.03321i	−1.48653	−	0.235444i	−0.640245	−	0.768170i	$-0.721167\pi$
$457$	−31.7784	−	5.03321i	−1.48653	−	0.235444i	−0.846287	+	0.532727i	$0.821167\pi$
$458$	10.2890	−	1.62961i	0.480771	−	0.0761467i
$459$	5.27311	−	1.71334i	0.246128	−	0.0799718i
$460$		−	24.1114i		−	1.12420i
$461$	9.09817	+	28.0013i	0.423744	+	1.30415i	0.904192	+	0.427126i	$0.140474\pi$
$461$	9.09817	+	28.0013i	0.423744	+	1.30415i	−0.480448	+	0.877023i	$0.659526\pi$
$462$	−1.80919	−	0.921831i	−0.0841714	−	0.0428874i
$463$	9.31629	+	18.2842i	0.432965	+	0.849741i	0.999667	+	0.0258181i	$0.00821907\pi$
$463$	9.31629	+	18.2842i	0.432965	+	0.849741i	−0.566702	+	0.823923i	$0.691781\pi$
$464$	0.0993985	−	0.627578i	0.00461446	−	0.0291346i
$465$	−0.340500	−	0.340500i	−0.0157903	−	0.0157903i
$466$	9.37396	−	4.77627i	0.434240	−	0.221256i
$467$	19.9773	+	14.5143i	0.924437	+	0.671643i	0.944625	−	0.328153i	$-0.106426\pi$
$467$	19.9773	+	14.5143i	0.924437	+	0.671643i	−0.0201872	+	0.999796i	$0.506426\pi$
$468$	7.79558	−	15.2997i	0.360351	−	0.707228i
$469$	16.2165	−	11.7820i	0.748811	−	0.544043i
$470$	1.32163	+	8.34443i	0.0609621	+	0.384900i
$471$	1.39441	−	1.91925i	0.0642512	−	0.0884342i
$472$	12.2541	−	16.8664i	0.564043	−	0.776339i
$473$	1.43645	+	9.06939i	0.0660480	+	0.417011i
$474$	1.70743	−	1.24052i	0.0784250	−	0.0569791i
$475$	0.287302	−	0.563861i	0.0131823	−	0.0258717i
$476$	−16.3843	−	11.9039i	−0.750974	−	0.545615i
$477$	−19.5906	+	9.98191i	−0.896992	+	0.457040i
$478$	6.68268	+	6.68268i	0.305659	+	0.305659i
$479$	−4.53834	+	28.6540i	−0.207362	+	1.30923i	0.635917	+	0.771757i	$0.280622\pi$
$479$	−4.53834	+	28.6540i	−0.207362	+	1.30923i	−0.843279	+	0.537476i	$0.819378\pi$
$480$	−2.16084	−	4.24088i	−0.0986282	−	0.193569i
$481$	−15.0487	−	7.66771i	−0.686163	−	0.349617i
$482$	0.872483	+	2.68523i	0.0397405	+	0.122309i
$483$		−	11.3885i		−	0.518196i
$484$	−11.5518	+	3.75340i	−0.525081	+	0.170609i
$485$	−9.58800	+	1.51859i	−0.435369	+	0.0689557i
$486$	−6.13112	−	0.971073i	−0.278113	−	0.0440488i
$487$	−25.0893	−	8.15201i	−1.13691	−	0.369403i	−0.320709	−	0.947178i	$-0.603921\pi$
$487$	−25.0893	−	8.15201i	−1.13691	−	0.369403i	−0.816196	+	0.577775i	$0.803921\pi$
$488$	−0.531524	+	1.63586i	−0.0240609	+	0.0740520i
$489$	1.87368	−	1.87368i	0.0847307	−	0.0847307i
$490$	−16.9270	−	23.2980i	−0.764682	−	1.05250i
$491$	17.4748			0.788628			0.394314	−	0.918976i	$-0.370982\pi$
$491$	17.4748			0.788628			0.394314	+	0.918976i	$0.370982\pi$
$492$	1.34728	−	3.00885i	0.0607402	−	0.135649i
$493$	−1.39318			−0.0627457
$494$	1.59146	+	2.19045i	0.0716031	+	0.0985532i
$495$	−8.26205	+	8.26205i	−0.371352	+	0.371352i
$496$	0.228489	−	0.703217i	0.0102595	−	0.0315754i
$497$	−33.9741	−	11.0389i	−1.52395	−	0.495160i
$498$	1.15413	+	0.182796i	0.0517178	+	0.00819129i
$499$	6.24219	−	0.988666i	0.279439	−	0.0442588i	−0.0151419	−	0.999885i	$-0.504820\pi$
$499$	6.24219	−	0.988666i	0.279439	−	0.0442588i	0.294581	+	0.955627i	$0.404820\pi$
$500$	−14.7444	+	4.79073i	−0.659388	+	0.214248i
$501$			6.51196i			0.290933i
$502$	5.96586	+	18.3610i	0.266269	+	0.819493i
$503$	9.88764	+	5.03800i	0.440868	+	0.224634i	0.660312	−	0.750992i	$-0.270424\pi$
$503$	9.88764	+	5.03800i	0.440868	+	0.224634i	−0.219444	+	0.975625i	$0.570424\pi$
$504$	15.9029	+	31.2113i	0.708373	+	1.39026i
$505$	−3.87665	+	24.4762i	−0.172509	+	1.08918i
$506$	−5.75509	−	5.75509i	−0.255845	−	0.255845i
$507$	0.844353	−	0.430219i	0.0374990	−	0.0191067i
$508$	−13.0644	−	9.49183i	−0.579638	−	0.421132i
$509$	9.54403	−	18.7312i	0.423032	−	0.830247i	−0.576878	−	0.816830i	$-0.695729\pi$
$509$	9.54403	−	18.7312i	0.423032	−	0.830247i	0.999910	−	0.0134165i	$-0.00427073\pi$
$510$	−1.28159	+	0.931130i	−0.0567498	+	0.0412311i
$511$	−7.47530	−	47.1972i	−0.330688	−	2.08788i
$512$	7.93954	−	10.9278i	0.350881	−	0.482947i
$513$	−1.14481	+	1.57570i	−0.0505447	+	0.0695688i
$514$	0.828895	+	5.23344i	0.0365610	+	0.230837i
$515$	−0.788484	+	0.572867i	−0.0347447	+	0.0252435i
$516$	−1.25914	+	2.47120i	−0.0554304	+	0.108788i
$517$	−6.93233	−	5.03663i	−0.304884	−	0.221511i
$518$	13.1598	−	6.70525i	0.578208	−	0.294612i
$519$	3.14717	+	3.14717i	0.138146	+	0.138146i
$520$	−3.65388	+	23.0697i	−0.160233	+	1.01167i
$521$	−4.33618	−	8.51023i	−0.189971	−	0.372840i	0.776301	−	0.630363i	$-0.217094\pi$
$521$	−4.33618	−	8.51023i	−0.189971	−	0.372840i	−0.966272	+	0.257523i	$0.917094\pi$
$522$	0.920383	+	0.468958i	0.0402841	+	0.0205258i
$523$	3.08324	+	9.48924i	0.134821	+	0.414936i	0.995562	−	0.0941069i	$-0.0299996\pi$
$523$	3.08324	+	9.48924i	0.134821	+	0.414936i	−0.860741	+	0.509043i	$0.830000\pi$
$524$			24.4058i			1.06617i
$525$	1.05126	−	0.341574i	0.0458806	−	0.0149075i
$526$	−8.32040	+	1.31782i	−0.362787	+	0.0574598i
$527$	−1.60127	−	0.253616i	−0.0697522	−	0.0110477i
$528$	0.696920	+	0.226443i	0.0303295	+	0.00985467i
$529$	6.99889	−	21.5404i	0.304300	−	0.936538i
$530$	9.06551	−	9.06551i	0.393780	−	0.393780i
$531$	−14.2774	−	19.6511i	−0.619585	−	0.852785i
$532$	7.11419			0.308439
$533$	−22.0424	+	12.6639i	−0.954761	+	0.548534i
$534$	−0.893038			−0.0386455
$535$	19.5412	+	26.8961i	0.844838	+	1.16282i
$536$	7.13729	−	7.13729i	0.308284	−	0.308284i
$537$	−0.0586862	+	0.180617i	−0.00253249	+	0.00779422i
$538$	14.2370	+	4.62590i	0.613803	+	0.199437i
$539$	28.8486	+	4.56918i	1.24260	+	0.196808i
$540$	−7.11379	+	1.12671i	−0.306129	+	0.0484860i
$541$	−4.63179	+	1.50496i	−0.199136	+	0.0647032i	−0.406887	−	0.913479i	$-0.633386\pi$
$541$	−4.63179	+	1.50496i	−0.199136	+	0.0647032i	0.207751	+	0.978182i	$0.433386\pi$
$542$			2.70838i			0.116335i
$543$	2.54728	+	7.83971i	0.109314	+	0.336434i
$544$	−14.2780	−	7.27501i	−0.612164	−	0.311913i
$545$	−16.5557	−	32.4925i	−0.709170	−	1.39182i
$546$	−0.739810	+	4.67098i	−0.0316610	+	0.199899i
$547$	14.2161	+	14.2161i	0.607837	+	0.607837i	0.942380	−	0.334543i	$-0.108582\pi$
$547$	14.2161	+	14.2161i	0.607837	+	0.607837i	−0.334543	+	0.942380i	$0.608582\pi$
$548$	23.7106	−	12.0812i	1.01287	−	0.516081i
$549$	1.62130	+	1.17794i	0.0691953	+	0.0502733i
$550$	0.358632	−	0.703855i	0.0152921	−	0.0300125i
$551$	0.395931	−	0.287661i	0.0168672	−	0.0122548i
$552$	−0.897114	−	5.66416i	−0.0381837	−	0.241082i
$553$	−25.1344	+	34.5946i	−1.06882	+	1.47111i
$554$	0.485134	−	0.667730i	0.0206114	−	0.0283691i
$555$	0.543026	+	3.42853i	0.0230502	+	0.145533i
$556$	2.58615	−	1.87895i	0.109677	−	0.0796852i
$557$	9.22663	−	18.1083i	0.390945	−	0.767273i	−0.608714	−	0.793390i	$-0.708314\pi$
$557$	9.22663	−	18.1083i	0.390945	−	0.767273i	0.999659	+	0.0261171i	$0.00831428\pi$
$558$	0.972481	+	0.706549i	0.0411684	+	0.0299106i
$559$	19.0556	−	9.70931i	0.805965	−	0.410660i
$560$	10.3510	+	10.3510i	0.437408	+	0.437408i
$561$	0.251344	−	1.58693i	0.0106118	−	0.0670001i
$562$	−5.67742	−	11.1426i	−0.239488	−	0.470021i
$563$	14.3215	+	7.29719i	0.603581	+	0.307540i	0.728946	−	0.684571i	$-0.240010\pi$
$563$	14.3215	+	7.29719i	0.603581	+	0.307540i	−0.125366	+	0.992111i	$0.540010\pi$
$564$	−0.799783	−	2.46148i	−0.0336770	−	0.103647i
$565$		−	19.1777i		−	0.806811i
$566$	−4.98046	+	1.61825i	−0.209345	+	0.0680202i
$567$	38.5966	−	6.11310i	1.62090	−	0.256726i
$568$	−17.7668	−	2.81398i	−0.745478	−	0.118072i
$569$	13.6249	+	4.42700i	0.571186	+	0.185590i	0.580348	−	0.814369i	$-0.302916\pi$
$569$	13.6249	+	4.42700i	0.571186	+	0.185590i	−0.00916232	+	0.999958i	$0.502916\pi$
$570$	0.171960	−	0.529240i	0.00720263	−	0.0221674i
$571$	−5.79685	+	5.79685i	−0.242591	+	0.242591i	−0.817921	−	0.575330i	$-0.804873\pi$
$571$	−5.79685	+	5.79685i	−0.242591	+	0.242591i	0.575330	+	0.817921i	$0.304873\pi$
$572$	−5.96906	−	8.21570i	−0.249579	−	0.343516i
$573$	−4.26578			−0.178205
$574$	2.37061	−	22.1036i	0.0989472	−	0.922586i
$575$	4.43063			0.184770
$576$	2.73837	+	3.76905i	0.114099	+	0.157044i
$577$	−3.49886	+	3.49886i	−0.145660	+	0.145660i	−0.776176	−	0.630516i	$-0.782843\pi$
$577$	−3.49886	+	3.49886i	−0.145660	+	0.145660i	0.630516	+	0.776176i	$0.282843\pi$
$578$	2.06435	−	6.35342i	0.0858657	−	0.264268i
$579$	1.06160	+	0.344936i	0.0441188	+	0.0143351i
$580$	1.78751	+	0.283113i	0.0742222	+	0.0117556i
$581$	−23.3840	+	3.70366i	−0.970132	+	0.153654i
$582$	−0.941300	+	0.305847i	−0.0390182	+	0.0126778i
$583$			13.0033i			0.538540i
$584$	−7.43577	−	22.8849i	−0.307694	−	0.946986i
$585$	24.2475	+	12.3547i	1.00251	+	0.510805i
$586$	−3.32143	−	6.51867i	−0.137207	−	0.269284i
$587$	1.58441	−	10.0036i	0.0653955	−	0.412891i	−0.933174	−	0.359425i	$-0.882973\pi$
$587$	1.58441	−	10.0036i	0.0653955	−	0.412891i	0.998570	−	0.0534665i	$-0.0170270\pi$
$588$	6.23819	+	6.23819i	0.257259	+	0.257259i
$589$	0.507433	−	0.258550i	0.0209084	−	0.0106534i
$590$	11.4585	+	8.32508i	0.471738	+	0.342738i
$591$	2.10935	−	4.13984i	0.0867672	−	0.170290i
$592$	−4.31219	+	3.13299i	−0.177230	+	0.128765i
$593$	2.36683	+	14.9436i	0.0971942	+	0.613660i	0.987417	+	0.158136i	$0.0505483\pi$
$593$	2.36683	+	14.9436i	0.0971942	+	0.613660i	−0.890223	+	0.455525i	$0.849452\pi$
$594$	−1.42904	+	1.96691i	−0.0586343	+	0.0807032i
$595$	18.8658	−	25.9665i	0.773421	−	1.06452i
$596$	0.356178	+	2.24882i	0.0145896	+	0.0921151i
$597$	2.57490	−	1.87078i	0.105384	−	0.0765658i
$598$	−8.60592	+	16.8901i	−0.351922	+	0.690686i
$599$	2.65199	+	1.92679i	0.108358	+	0.0787264i	0.640644	−	0.767838i	$-0.278667\pi$
$599$	2.65199	+	1.92679i	0.108358	+	0.0787264i	−0.532287	+	0.846564i	$0.678667\pi$
$600$	0.495942	−	0.252695i	0.0202468	−	0.0103162i
$601$	−5.05364	−	5.05364i	−0.206142	−	0.206142i	0.596483	−	0.802626i	$-0.296564\pi$
$601$	−5.05364	−	5.05364i	−0.206142	−	0.206142i	−0.802626	+	0.596483i	$0.796564\pi$
$602$	−2.92566	+	18.4719i	−0.119241	+	0.752857i
$603$	−5.33900	−	10.4784i	−0.217421	−	0.426712i
$604$	−2.80230	−	1.42784i	−0.114024	−	0.0580981i
$605$	−5.94854	−	18.3077i	−0.241843	−	0.744315i
$606$			2.52661i			0.102637i
$607$	−32.2830	+	10.4894i	−1.31033	+	0.425751i	−0.879163	−	0.476522i	$-0.841897\pi$
$607$	−32.2830	+	10.4894i	−1.31033	+	0.425751i	−0.431165	+	0.902273i	$0.641897\pi$
$608$	5.55983	−	0.880590i	0.225481	−	0.0357126i
$609$	0.844294	+	0.133723i	0.0342125	+	0.00541873i
$610$	−1.11135	−	0.361100i	−0.0449973	−	0.0146205i
$611$	−6.16719	+	18.9807i	−0.249498	+	0.767876i
$612$	−8.40172	+	8.40172i	−0.339619	+	0.339619i
$613$	9.06342	+	12.4747i	0.366068	+	0.503849i	0.951827	−	0.306636i	$-0.0992034\pi$
$613$	9.06342	+	12.4747i	0.366068	+	0.503849i	−0.585759	+	0.810485i	$0.699203\pi$
$614$	0.970776			0.0391773
$615$	4.76854	+	2.13522i	0.192286	+	0.0861006i
$616$	20.7165			0.834691
$617$	−0.427082	−	0.587827i	−0.0171937	−	0.0236650i	0.800334	−	0.599555i	$-0.204656\pi$
$617$	−0.427082	−	0.587827i	−0.0171937	−	0.0236650i	−0.817527	+	0.575890i	$0.804656\pi$
$618$	−0.0702641	+	0.0702641i	−0.00282644	+	0.00282644i
$619$	7.59558	−	23.3768i	0.305292	−	0.939593i	−0.674276	−	0.738480i	$-0.735544\pi$
$619$	7.59558	−	23.3768i	0.305292	−	0.939593i	0.979568	−	0.201113i	$-0.0644559\pi$
$620$	2.00295	+	0.650798i	0.0804404	+	0.0261367i
$621$	−13.4682	−	2.13315i	−0.540460	−	0.0856005i
$622$	−8.48048	+	1.34318i	−0.340036	+	0.0538564i
$623$	17.2084	−	5.59135i	0.689440	−	0.224013i
$624$		−	1.70671i		−	0.0683231i
$625$	−8.60576	−	26.4858i	−0.344230	−	1.05943i
$626$	−18.9619	−	9.66157i	−0.757870	−	0.386154i
$627$	0.256235	+	0.502889i	0.0102330	+	0.0200835i
$628$	−1.62307	+	10.2477i	−0.0647676	+	0.408927i
$629$	8.26391	+	8.26391i	0.329503	+	0.329503i
$630$	−21.2039	+	10.8040i	−0.844786	+	0.430440i
$631$	−11.0214	−	8.00754i	−0.438756	−	0.318775i	0.346384	−	0.938093i	$-0.387409\pi$
$631$	−11.0214	−	8.00754i	−0.438756	−	0.318775i	−0.785141	+	0.619318i	$0.787409\pi$
$632$	−9.77562	+	19.1857i	−0.388853	+	0.763168i
$633$	−7.55587	+	5.48966i	−0.300319	+	0.218194i
$634$	0.936532	+	5.91303i	0.0371944	+	0.234836i
$635$	15.0430	−	20.7049i	0.596964	−	0.821650i
$636$	−2.30855	+	3.17745i	−0.0915399	+	0.125994i
$637$	−10.6420	−	67.1907i	−0.421650	−	2.66219i
$638$	0.494232	−	0.359080i	0.0195668	−	0.0142161i
$639$	−9.51482	+	18.6739i	−0.376400	+	0.738727i
$640$	20.2480	+	14.7110i	0.800373	+	0.581505i
$641$	−8.46013	+	4.31065i	−0.334155	+	0.170260i	−0.613015	−	0.790071i	$-0.710043\pi$
$641$	−8.46013	+	4.31065i	−0.334155	+	0.170260i	0.278860	+	0.960332i	$0.410043\pi$
$642$	2.39679	+	2.39679i	0.0945938	+	0.0945938i
$643$	6.20230	−	39.1598i	0.244595	−	1.54431i	−0.493579	−	0.869701i	$-0.664312\pi$
$643$	6.20230	−	39.1598i	0.244595	−	1.54431i	0.738174	−	0.674610i	$-0.235688\pi$
$644$	22.6124	+	44.3793i	0.891053	+	1.74879i
$645$	−3.91645	−	1.99553i	−0.154210	−	0.0785739i
$646$	−0.578949	−	1.78182i	−0.0227784	−	0.0701048i
$647$			40.5997i			1.59614i	0.602564	+	0.798070i	$0.294146\pi$
$647$			40.5997i			1.59614i	−0.602564	+	0.798070i	$0.705854\pi$
$648$	18.7147	−	6.08077i	0.735183	−	0.238875i
$649$	−14.1884	+	2.24723i	−0.556945	+	0.0882114i
$650$	−1.81721	−	0.287818i	−0.0712769	−	0.0112892i
$651$	0.946054	+	0.307392i	0.0370788	+	0.0120476i
$652$	−3.58117	+	11.0217i	−0.140249	+	0.431643i
$653$	−6.90831	+	6.90831i	−0.270343	+	0.270343i	−0.829238	−	0.558895i	$-0.811225\pi$
$653$	−6.90831	+	6.90831i	−0.270343	+	0.270343i	0.558895	+	0.829238i	$0.311225\pi$
$654$	−2.18542	−	3.00797i	−0.0854565	−	0.117621i
$655$	−38.6793			−1.51133
$656$	0.402874	+	8.01253i	0.0157296	+	0.312837i
$657$	−28.0355			−1.09377
$658$	−10.2582	−	14.1193i	−0.399908	−	0.550426i
$659$	−27.6241	+	27.6241i	−1.07608	+	1.07608i	−0.0792258	+	0.996857i	$0.525245\pi$
$659$	−27.6241	+	27.6241i	−1.07608	+	1.07608i	−0.996857	+	0.0792258i	$0.974755\pi$
$660$	−0.644970	+	1.98501i	−0.0251054	+	0.0772665i
$661$	35.4354	+	11.5137i	1.37828	+	0.447829i	0.902102	−	0.431522i	$-0.142023\pi$
$661$	35.4354	+	11.5137i	1.37828	+	0.447829i	0.476174	+	0.879351i	$0.342023\pi$
$662$	7.29110	+	1.15480i	0.283377	+	0.0448825i
$663$	−3.69607	+	0.585400i	−0.143543	+	0.0227350i
$664$	−11.3384	+	3.68408i	−0.440016	+	0.142970i
$665$			11.2748i			0.437220i
$666$	−2.67770	−	8.24113i	−0.103759	−	0.319337i
$667$	3.05293	+	1.55555i	0.118210	+	0.0602310i
$668$	−12.9298	−	25.3761i	−0.500267	−	0.981830i
$669$	0.511578	−	3.22997i	0.0197787	−	0.124878i
$670$	4.84885	+	4.84885i	0.187327	+	0.187327i
$671$	1.05602	−	0.538068i	0.0407671	−	0.0207719i
$672$	7.95446	+	5.77925i	0.306850	+	0.222939i
$673$	−14.5486	+	28.5532i	−0.560807	+	1.10065i	0.420337	+	0.907368i	$0.361912\pi$
$673$	−14.5486	+	28.5532i	−0.560807	+	1.10065i	−0.981144	+	0.193277i	$0.938088\pi$
$674$	−13.0748	+	9.49938i	−0.503621	+	0.365902i
$675$	−0.207041	−	1.30721i	−0.00796903	−	0.0503144i
$676$	−2.43609	+	3.35299i	−0.0936958	+	0.128961i
$677$	−21.5287	+	29.6318i	−0.827417	+	1.13884i	0.160982	+	0.986957i	$0.448534\pi$
$677$	−21.5287	+	29.6318i	−0.827417	+	1.13884i	−0.988398	+	0.151884i	$0.951466\pi$
$678$	−0.305873	−	1.93121i	−0.0117470	−	0.0741676i
$679$	16.2235	−	11.7870i	0.622600	−	0.452345i
$680$	7.33754	−	14.4007i	0.281382	−	0.552243i
$681$	0.422636	+	0.307063i	0.0161954	+	0.0117667i
$682$	0.633417	−	0.322742i	0.0242548	−	0.0123584i
$683$	−32.2175	−	32.2175i	−1.23277	−	1.23277i	−0.962896	−	0.269874i	$-0.913018\pi$
$683$	−32.2175	−	32.2175i	−1.23277	−	1.23277i	−0.269874	−	0.962896i	$-0.586982\pi$
$684$	0.652935	−	4.12247i	0.0249656	−	0.157627i
$685$	19.1467	+	37.5775i	0.731557	+	1.43576i
$686$	31.3515	+	15.9744i	1.19701	+	0.609906i
$687$	−1.56290	−	4.81012i	−0.0596285	−	0.183518i
$688$		−	6.74936i		−	0.257317i
$689$	28.8033	−	9.35875i	1.09732	−	0.356540i
$690$	3.84805	−	0.609471i	0.146493	−	0.0232021i
$691$	12.3380	+	1.95415i	0.469360	+	0.0743394i	0.386635	−	0.922233i	$-0.373637\pi$
$691$	12.3380	+	1.95415i	0.469360	+	0.0743394i	0.0827257	+	0.996572i	$0.473637\pi$
$692$	−18.5129	−	6.01520i	−0.703754	−	0.228663i
$693$	7.45870	−	22.9555i	0.283333	−	0.872008i
$694$	0.835439	−	0.835439i	0.0317128	−	0.0317128i
$695$	2.97783	+	4.09864i	0.112956	+	0.155470i
$696$	0.430449			0.0163161
$697$	17.2138	−	3.62076i	0.652020	−	0.137146i
$698$	24.4116			0.923994
$699$	−3.00234	−	4.13236i	−0.113559	−	0.156300i
$700$	−3.41838	+	3.41838i	−0.129202	+	0.129202i
$701$	10.2823	−	31.6458i	0.388358	−	1.19524i	−0.545656	−	0.838009i	$-0.683720\pi$
$701$	10.2823	−	31.6458i	0.388358	−	1.19524i	0.934015	−	0.357235i	$-0.116280\pi$
$702$	5.38538	+	1.74982i	0.203258	+	0.0660425i
$703$	−4.05485	−	0.642225i	−0.152932	−	0.0242220i
$704$	2.72132	−	0.431014i	0.102564	−	0.0162445i
$705$	3.90105	−	1.26753i	0.146922	−	0.0477378i
$706$			18.0951i			0.681019i
$707$	−15.8192	−	48.6865i	−0.594943	−	1.83105i
$708$	−3.86602	−	1.96983i	−0.145294	−	0.0740309i
$709$	12.6452	+	24.8176i	0.474901	+	0.932046i	0.996868	+	0.0790803i	$0.0251983\pi$
$709$	12.6452	+	24.8176i	0.474901	+	0.932046i	−0.521967	+	0.852966i	$0.674802\pi$
$710$	1.91173	−	12.0702i	0.0717460	−	0.452986i
$711$	17.7397	+	17.7397i	0.665292	+	0.665292i
$712$	8.11825	−	4.13646i	0.304244	−	0.155020i
$713$	3.22574	+	2.34364i	0.120805	+	0.0877700i
$714$	1.48565	−	2.91575i	0.0555990	−	0.109119i
$715$	13.0206	−	9.45999i	0.486941	−	0.353784i
$716$	−0.129932	−	0.820361i	−0.00485580	−	0.0306583i
$717$	2.69701	−	3.71212i	0.100722	−	0.138632i
$718$	−10.9721	+	15.1018i	−0.409474	+	0.563593i
$719$	4.62484	+	29.2001i	0.172477	+	1.08898i	0.910289	+	0.413973i	$0.135859\pi$
$719$	4.62484	+	29.2001i	0.172477	+	1.08898i	−0.737812	+	0.675006i	$0.764141\pi$
$720$	6.94809	−	5.04808i	0.258940	−	0.188131i
$721$	0.914029	−	1.79388i	0.0340402	−	0.0668077i
$722$	−10.3304	−	7.50545i	−0.384456	−	0.279324i
$723$	1.22139	−	0.622329i	0.0454239	−	0.0231447i
$724$	−25.4924	−	25.4924i	−0.947417	−	0.947417i
$725$	−0.0520240	+	0.328467i	−0.00193212	+	0.0121989i
$726$	−0.891022	−	1.74873i	−0.0330689	−	0.0649014i
$727$	12.9250	+	6.58561i	0.479361	+	0.244247i	0.676937	−	0.736041i	$-0.263307\pi$
$727$	12.9250	+	6.58561i	0.479361	+	0.244247i	−0.197576	+	0.980288i	$0.563307\pi$
$728$	−14.9102	−	45.8887i	−0.552607	−	1.70075i
$729$		−	20.8493i		−	0.772195i
$730$	15.5473	−	5.05162i	0.575431	−	0.186969i
$731$	−14.6165	+	2.31502i	−0.540610	+	0.0856242i
$732$	0.353573	+	0.0560004i	0.0130684	+	0.00206983i
$733$	42.4622	+	13.7968i	1.56838	+	0.509596i	0.959029	−	0.283307i	$-0.0914316\pi$
$733$	42.4622	+	13.7968i	1.56838	+	0.509596i	0.609347	+	0.792904i	$0.291432\pi$
$734$	4.38743	−	13.5031i	0.161943	−	0.498410i
$735$	−9.88653	+	9.88653i	−0.364670	+	0.364670i
$736$	23.1651	+	31.8840i	0.853877	+	1.17526i
$737$	−6.95502			−0.256191
$738$	−12.5908	−	3.40235i	−0.463475	−	0.125242i
$739$	−2.65655			−0.0977228			−0.0488614	−	0.998806i	$-0.515559\pi$
$739$	−2.65655			−0.0977228			−0.0488614	+	0.998806i	$0.515559\pi$
$740$	−8.92358	−	12.2823i	−0.328037	−	0.451505i
$741$	0.929522	−	0.929522i	0.0341468	−	0.0341468i
$742$	−8.18403	+	25.1879i	−0.300445	+	0.924676i
$743$	−29.1554	−	9.47315i	−1.06961	−	0.347536i	−0.279272	−	0.960212i	$-0.590093\pi$
$743$	−29.1554	−	9.47315i	−1.06961	−	0.347536i	−0.790334	+	0.612676i	$0.790093\pi$
$744$	0.494740	+	0.0783591i	0.0181380	+	0.00287278i
$745$	−3.56401	+	0.564484i	−0.130575	+	0.0206811i
$746$	5.16384	−	1.67783i	0.189062	−	0.0614298i
$747$			13.8903i			0.508219i
$748$	2.17146	+	6.68305i	0.0793963	+	0.244357i
$749$	−61.1914	−	31.1786i	−2.23588	−	1.13924i
$750$	−1.13727	−	2.23203i	−0.0415274	−	0.0815020i
$751$	7.92192	−	50.0170i	0.289075	−	1.82515i	−0.233268	−	0.972412i	$-0.574942\pi$
$751$	7.92192	−	50.0170i	0.289075	−	1.82515i	0.522343	−	0.852735i	$-0.325058\pi$
$752$	4.45360	+	4.45360i	0.162406	+	0.162406i
$753$	8.35160	−	4.25535i	0.304349	−	0.155074i
$754$	−1.15110	−	0.836325i	−0.0419207	−	0.0304572i
$755$	2.26290	−	4.44120i	0.0823554	−	0.161632i
$756$	12.0370	−	8.74536i	0.437780	−	0.318066i
$757$	4.53435	+	28.6288i	0.164804	+	1.04053i	0.921957	+	0.387293i	$0.126590\pi$
$757$	4.53435	+	28.6288i	0.164804	+	1.04053i	−0.757153	+	0.653238i	$0.773410\pi$
$758$	9.68519	−	13.3305i	0.351782	−	0.484186i
$759$	−2.32265	+	3.19686i	−0.0843069	+	0.116039i
$760$	0.888158	+	5.60761i	0.0322169	+	0.203409i
$761$	31.5410	−	22.9159i	1.14336	−	0.830700i	0.155777	−	0.987792i	$-0.450212\pi$
$761$	31.5410	−	22.9159i	1.14336	−	0.830700i	0.987584	+	0.157092i	$0.0502119\pi$
$762$	1.18461	−	2.32493i	0.0429140	−	0.0842235i
$763$	60.9449	+	44.2791i	2.20635	+	1.60301i
$764$	16.6231	−	8.46987i	0.601401	−	0.306429i
$765$	−13.3154	−	13.3154i	−0.481418	−	0.481418i
$766$	−1.80186	+	11.3765i	−0.0651040	+	0.411051i
$767$	15.1895	+	29.8112i	0.548463	+	1.07642i
$768$	3.26190	+	1.66202i	0.117704	+	0.0599730i
$769$	−0.817089	−	2.51474i	−0.0294650	−	0.0906839i	0.935243	−	0.354008i	$-0.115181\pi$
$769$	−0.817089	−	2.51474i	−0.0294650	−	0.0906839i	−0.964708	+	0.263324i	$0.915181\pi$
$770$			14.0741i			0.507196i
$771$	2.44665	−	0.794965i	0.0881139	−	0.0286299i
$772$	−4.82179	+	0.763696i	−0.173540	+	0.0274860i
$773$	−20.6803	−	3.27543i	−0.743817	−	0.117809i	−0.226988	−	0.973898i	$-0.572888\pi$
$773$	−20.6803	−	3.27543i	−0.743817	−	0.117809i	−0.516829	+	0.856089i	$0.672888\pi$
$774$	10.4354	+	3.39067i	0.375093	+	0.121875i
$775$	−0.119589	+	0.368056i	−0.00429575	+	0.0132210i
$776$	7.14034	−	7.14034i	0.256323	−	0.256323i
$777$	−4.21488	−	5.80128i	−0.151208	−	0.208120i
$778$	0.205578			0.00737034
$779$	−4.14443	+	4.58326i	−0.148490	+	0.164213i
$780$	4.86116			0.174058
$781$	7.28548	+	10.0276i	0.260695	+	0.358816i
$782$	9.27507	−	9.27507i	0.331676	−	0.331676i
$783$	0.316285	−	0.973424i	0.0113031	−	0.0347873i
$784$	−20.4182	−	6.63427i	−0.729220	−	0.236938i
$785$	−16.2409	−	2.57231i	−0.579663	−	0.0918095i
$786$	−3.89504	+	0.616914i	−0.138932	+	0.0220046i
$787$	21.2772	−	6.91338i	0.758450	−	0.246435i	0.0958369	−	0.995397i	$-0.469447\pi$
$787$	21.2772	−	6.91338i	0.758450	−	0.246435i	0.662613	+	0.748962i	$0.269447\pi$
$788$			20.3205i			0.723888i
$789$	1.26388	+	3.88981i	0.0449952	+	0.138481i
$790$	−13.0342	−	6.64125i	−0.463735	−	0.236285i
$791$	17.9854	+	35.2984i	0.639488	+	1.25507i
$792$	1.90134	−	12.0046i	0.0675613	−	0.426566i
$793$	−1.95191	−	1.95191i	−0.0693142	−	0.0693142i
$794$	−17.8195	+	9.07951i	−0.632392	+	0.322220i
$795$	−5.03574	−	3.65868i	−0.178599	−	0.129760i
$796$	−6.31948	+	12.4027i	−0.223988	+	0.439602i
$797$	−16.2691	+	11.8202i	−0.576279	+	0.418691i	−0.837381	−	0.546620i	$-0.815914\pi$
$797$	−16.2691	+	11.8202i	−0.576279	+	0.418691i	0.261101	+	0.965311i	$0.415914\pi$
$798$	0.179828	+	1.13539i	0.00636583	+	0.0401923i
$799$	8.11718	−	11.1723i	0.287165	−	0.395249i
$800$	−2.24838	+	3.09463i	−0.0794921	+	0.109412i
$801$	−1.66065	−	10.4849i	−0.0586763	−	0.370467i
$802$	3.87407	−	2.81468i	0.136798	−	0.0993897i
$803$	−7.52732	+	14.7732i	−0.265633	+	0.521335i
$804$	−1.69951	−	1.23477i	−0.0599372	−	0.0435469i
$805$	−70.3340	+	35.8370i	−2.47895	+	1.26309i
$806$	−1.17079	−	1.17079i	−0.0412392	−	0.0412392i
$807$	1.13696	−	7.17847i	0.0400228	−	0.252694i
$808$	−11.7030	−	22.9684i	−0.411710	−	0.808026i
$809$	−8.18594	−	4.17095i	−0.287802	−	0.146643i	0.304129	−	0.952631i	$-0.401635\pi$
$809$	−8.18594	−	4.17095i	−0.287802	−	0.146643i	−0.591932	+	0.805988i	$0.701635\pi$
$810$	4.13108	+	12.7142i	0.145151	+	0.446730i
$811$			18.4060i			0.646324i	0.946344	+	0.323162i	$0.104746\pi$
$811$			18.4060i			0.646324i	−0.946344	+	0.323162i	$0.895254\pi$
$812$	−3.55559	+	1.15528i	−0.124777	+	0.0405425i
$813$	1.29876	−	0.205703i	0.0455494	−	0.00721432i
$814$	−5.06158	−	0.801675i	−0.177408	−	0.0280987i
$815$	−17.4676	−	5.67557i	−0.611863	−	0.198806i
$816$	−0.364942	+	1.12318i	−0.0127755	+	0.0393190i
$817$	3.67589	−	3.67589i	0.128603	−	0.128603i
$818$	−7.02245	−	9.66557i	−0.245534	−	0.337949i
$819$	−56.2166			−1.96437
$820$	−22.8218	+	1.14749i	−0.796972	+	0.0400722i
$821$	18.0353			0.629436			0.314718	−	0.949185i	$-0.398090\pi$
$821$	18.0353			0.629436			0.314718	+	0.949185i	$0.398090\pi$
$822$	2.52743	+	3.47871i	0.0881542	+	0.121334i
$823$	−31.4518	+	31.4518i	−1.09634	+	1.09634i	−0.101506	+	0.994835i	$0.532366\pi$
$823$	−31.4518	+	31.4518i	−1.09634	+	1.09634i	−0.994835	+	0.101506i	$0.967634\pi$
$824$	0.313287	−	0.964199i	0.0109139	−	0.0335895i
$825$	−0.364760	−	0.118518i	−0.0126993	−	0.00412625i
$826$	−28.8980	−	4.57699i	−1.00549	−	0.159254i
$827$	44.3599	−	7.02591i	1.54254	−	0.244315i	0.673551	−	0.739141i	$-0.264768\pi$
$827$	44.3599	−	7.02591i	1.54254	−	0.244315i	0.868992	+	0.494826i	$0.164768\pi$
$828$	27.7919	−	9.03013i	0.965835	−	0.313819i
$829$			45.0253i			1.56379i	0.623409	+	0.781896i	$0.285747\pi$
$829$			45.0253i			1.56379i	−0.623409	+	0.781896i	$0.714253\pi$
$830$	−2.50284	−	7.70296i	−0.0868750	−	0.267374i
$831$	−0.357044	−	0.181923i	−0.0123857	−	0.00631085i
$832$	−2.91333	−	5.71773i	−0.101001	−	0.198227i
$833$	−7.36382	+	46.4933i	−0.255141	+	1.61090i
$834$	0.365242	+	0.365242i	0.0126473	+	0.0126473i
$835$	40.2170	−	20.4916i	1.39177	−	0.709140i
$836$	−1.99701	−	1.45091i	−0.0690681	−	0.0501809i
$837$	0.540727	−	1.06124i	0.0186903	−	0.0366817i
$838$	−7.02766	+	5.10590i	−0.242767	+	0.176380i
$839$	1.71160	+	10.8066i	0.0590911	+	0.373087i	0.999458	+	0.0329242i	$0.0104820\pi$
$839$	1.71160	+	10.8066i	0.0590911	+	0.373087i	−0.940367	+	0.340162i	$0.889518\pi$
$840$	−5.82892	+	8.02282i	−0.201117	+	0.276814i
$841$	16.8946	−	23.2534i	0.582573	−	0.801842i
$842$	−3.22067	−	20.3345i	−0.110992	−	0.700773i
$843$	−4.91202	+	3.56879i	−0.169179	+	0.122916i
$844$	18.5441	−	36.3948i	0.638314	−	1.25276i
$845$	−5.31395	−	3.86081i	−0.182806	−	0.132816i
$846$	−9.12321	+	4.64851i	−0.313662	+	0.159819i
$847$	28.1184	+	28.1184i	0.966160	+	0.966160i
$848$	1.49517	−	9.44011i	0.0513442	−	0.324175i
$849$	1.15427	+	2.26539i	0.0396146	+	0.0777479i
$850$	1.13435	+	0.577982i	0.0389080	+	0.0198246i
$851$	−8.88201	−	27.3360i	−0.304471	−	0.937067i
$852$			3.74376i			0.128259i
$853$	15.9051	−	5.16789i	0.544581	−	0.176945i	−0.0237905	−	0.999717i	$-0.507573\pi$
$853$	15.9051	−	5.16789i	0.544581	−	0.176945i	0.568372	+	0.822772i	$0.307573\pi$
$854$	2.38420	−	0.377621i	0.0815857	−	0.0129219i
$855$	6.53345	+	1.03480i	0.223439	+	0.0353893i
$856$	−32.8900	−	10.6866i	−1.12416	−	0.365260i
$857$	3.43704	−	10.5781i	0.117407	−	0.361341i	−0.875034	−	0.484061i	$-0.839161\pi$
$857$	3.43704	−	10.5781i	0.117407	−	0.361341i	0.992441	+	0.122719i	$0.0391614\pi$
$858$	1.16030	−	1.16030i	0.0396120	−	0.0396120i
$859$	−27.8427	−	38.3222i	−0.949981	−	1.30754i	−0.951536	−	0.307538i	$-0.900495\pi$
$859$	−27.8427	−	38.3222i	−0.949981	−	1.30754i	0.00155429	−	0.999999i	$-0.499505\pi$
$860$	19.2240			0.655532
$861$	−10.7794	+	0.541995i	−0.367362	+	0.0184712i
$862$	−6.08343			−0.207203
$863$	−8.28362	−	11.4014i	−0.281978	−	0.388109i	0.644410	−	0.764680i	$-0.277103\pi$
$863$	−8.28362	−	11.4014i	−0.281978	−	0.388109i	−0.926388	+	0.376571i	$0.877103\pi$
$864$	8.32453	−	8.32453i	0.283206	−	0.283206i
$865$	9.53311	−	29.3399i	0.324136	−	0.997587i
$866$	−7.95726	−	2.58547i	−0.270399	−	0.0878578i
$867$	−3.20346	−	0.507379i	−0.108795	−	0.0172315i
$868$	−4.29696	+	0.680572i	−0.145848	+	0.0231001i
$869$	14.1109	−	4.58490i	0.478679	−	0.155532i
$870$			0.292433i			0.00991441i
$871$	5.00569	+	15.4059i	0.169611	+	0.522010i
$872$	33.7993	+	17.2216i	1.14459	+	0.583198i
$873$	−5.34128	−	10.4828i	−0.180775	−	0.354791i
$874$	−0.720807	+	4.55100i	−0.0243817	+	0.153940i
$875$	35.8895	+	35.8895i	1.21329	+	1.21329i
$876$	−4.46214	+	2.27357i	−0.150762	+	0.0768169i
$877$	28.6207	+	20.7942i	0.966453	+	0.702169i	0.954640	−	0.297761i	$-0.0962398\pi$
$877$	28.6207	+	20.7942i	0.966453	+	0.702169i	0.0118127	+	0.999930i	$0.496240\pi$
$878$	−9.75761	+	19.1504i	−0.329303	+	0.646294i
$879$	−2.87365	+	2.08783i	−0.0969259	+	0.0704208i
$880$	−0.794558	−	5.01664i	−0.0267846	−	0.169111i
$881$	−12.7504	+	17.5494i	−0.429572	+	0.591256i	−0.967855	−	0.251509i	$-0.919073\pi$
$881$	−12.7504	+	17.5494i	−0.429572	+	0.591256i	0.538283	+	0.842764i	$0.319073\pi$
$882$	20.5149	−	28.2363i	0.690772	−	0.950767i
$883$	−0.504234	−	3.18361i	−0.0169688	−	0.107137i	0.977750	−	0.209773i	$-0.0672724\pi$
$883$	−0.504234	−	3.18361i	−0.0169688	−	0.107137i	−0.994719	+	0.102636i	$0.967272\pi$
$884$	13.2407	−	9.61990i	0.445332	−	0.323552i
$885$	3.12187	−	6.12701i	0.104940	−	0.205957i
$886$	7.63448	+	5.54677i	0.256485	+	0.186347i
$887$	−12.8950	+	6.57032i	−0.432971	+	0.220610i	−0.656872	−	0.754002i	$-0.728121\pi$
$887$	−12.8950	+	6.57032i	−0.432971	+	0.220610i	0.223901	+	0.974612i	$0.428121\pi$
$888$	−2.55328	−	2.55328i	−0.0856826	−	0.0856826i
$889$	−8.27040	+	52.2172i	−0.277380	+	1.75131i
$890$	2.81018	+	5.51528i	0.0941973	+	0.184873i
$891$	−12.0811	−	6.15564i	−0.404733	−	0.206222i
$892$	4.41971	+	13.6025i	0.147983	+	0.455444i
$893$			4.85111i			0.162336i
$894$	−0.349896	+	0.113688i	−0.0117023	+	0.00380230i
$895$	1.30014	−	0.205922i	0.0434589	−	0.00688321i
$896$	−51.0649	−	8.08789i	−1.70596	−	0.270197i
$897$	8.75296	+	2.84401i	0.292253	+	0.0949588i
$898$	5.49230	−	16.9036i	0.183281	−	0.564080i
$899$	−0.211623	+	0.211623i	−0.00705803	+	0.00705803i
$900$	1.66712	+	2.29459i	0.0555705	+	0.0764862i
$901$	−20.9564			−0.698160
$902$	−5.17340	+	5.72118i	−0.172255	+	0.190495i
$903$	9.08007			0.302166
$904$	11.7257	+	16.1391i	0.389992	+	0.536778i
$905$	40.4013	−	40.4013i	1.34299	−	1.34299i
$906$	0.157042	−	0.483325i	0.00521736	−	0.0160574i
$907$	−40.1252	−	13.0375i	−1.33233	−	0.432902i	−0.445621	−	0.895222i	$-0.647017\pi$
$907$	−40.1252	−	13.0375i	−1.33233	−	0.432902i	−0.886713	+	0.462320i	$0.847017\pi$
$908$	−2.25663	−	0.357415i	−0.0748890	−	0.0118612i
$909$	−29.6643	+	4.69837i	−0.983904	+	0.155835i
$910$	31.1753	−	10.1295i	1.03345	−	0.335789i
$911$		−	46.8754i		−	1.55305i	−0.630087	−	0.776525i	$-0.716981\pi$
$911$		−	46.8754i		−	1.55305i	0.630087	−	0.776525i	$-0.283019\pi$
$912$	−0.128197	−	0.394550i	−0.00424503	−	0.0130649i
$913$	7.31943	+	3.72944i	0.242238	+	0.123426i
$914$	10.3226	+	20.2593i	0.341442	+	0.670118i
$915$	−0.0887516	+	0.560355i	−0.00293404	+	0.0185248i
$916$	15.6411	+	15.6411i	0.516796	+	0.516796i
$917$	71.1930	−	36.2747i	2.35100	−	1.19790i
$918$	−3.16993	−	2.30309i	−0.104623	−	0.0760131i
$919$	11.8130	−	23.1843i	0.389675	−	0.764780i	−0.609942	−	0.792446i	$-0.708807\pi$
$919$	11.8130	−	23.1843i	0.389675	−	0.764780i	0.999617	+	0.0276656i	$0.00880735\pi$
$920$	−32.1581	+	23.3642i	−1.06022	+	0.770295i
$921$	−0.0737310	−	0.465519i	−0.00242952	−	0.0153394i
$922$	12.2298	−	16.8329i	0.402768	−	0.554363i
$923$	16.9684	−	23.3550i	0.558522	−	0.768740i
$924$	−0.674477	−	4.25848i	−0.0221887	−	0.140094i
$925$	2.25695	−	1.63977i	0.0742080	−	0.0539153i
$926$	6.58375	−	12.9213i	0.216355	−	0.424622i
$927$	−0.955615	−	0.694295i	−0.0313865	−	0.0228036i
$928$	−2.63574	+	1.34298i	−0.0865224	+	0.0440853i
$929$	25.6662	+	25.6662i	0.842079	+	0.842079i	0.989129	−	0.147050i	$-0.0469778\pi$
$929$	25.6662	+	25.6662i	0.842079	+	0.842079i	−0.147050	+	0.989129i	$0.546978\pi$
$930$	−0.0532347	+	0.336111i	−0.00174563	+	0.0110215i
$931$	−7.50710	−	14.7335i	−0.246035	−	0.482871i
$932$	19.9046	+	10.1419i	0.651997	+	0.332209i
$933$	1.28819	+	3.96465i	0.0421736	+	0.129797i
$934$		−	17.4505i		−	0.570999i
$935$	−10.5916	+	3.44141i	−0.346381	+	0.112546i
$936$	−27.9597	+	4.42837i	−0.913890	+	0.144746i
$937$	11.0570	+	1.75125i	0.361216	+	0.0572110i	0.334405	−	0.942430i	$-0.391465\pi$
$937$	11.0570	+	1.75125i	0.361216	+	0.0572110i	0.0268112	+	0.999641i	$0.491465\pi$
$938$	−13.4722	−	4.37737i	−0.439882	−	0.142926i
$939$	−3.19287	+	9.82666i	−0.104196	+	0.320681i
$940$	−12.6850	+	12.6850i	−0.413740	+	0.413740i
$941$	−9.08708	−	12.5073i	−0.296230	−	0.407726i	0.634795	−	0.772681i	$-0.281085\pi$
$941$	−9.08708	−	12.5073i	−0.296230	−	0.407726i	−0.931025	+	0.364954i	$0.881085\pi$
$942$	−1.67650			−0.0546234
$943$	−41.7641	−	11.2857i	−1.36003	−	0.367512i
$944$	10.5589			0.343664
$945$	13.8600	+	19.0766i	0.450865	+	0.620563i
$946$	4.58853	−	4.58853i	0.149186	−	0.149186i
$947$	−11.7171	+	36.0615i	−0.380755	+	1.17184i	0.558758	+	0.829330i	$0.311278\pi$
$947$	−11.7171	+	36.0615i	−0.380755	+	1.17184i	−0.939513	+	0.342512i	$0.888722\pi$
$948$	4.26209	+	1.38484i	0.138426	+	0.0449774i
$949$	38.1414	+	6.04101i	1.23812	+	0.196100i
$950$	−0.441715	+	0.0699607i	−0.0143311	+	0.00226983i
$951$	2.76436	−	0.898195i	0.0896405	−	0.0291260i
$952$			33.3873i			1.08209i
$953$	−10.8163	−	33.2891i	−0.350373	−	1.07834i	−0.958644	−	0.284609i	$-0.908136\pi$
$953$	−10.8163	−	33.2891i	−0.350373	−	1.07834i	0.608270	−	0.793730i	$-0.291864\pi$
$954$	13.8445	+	7.05414i	0.448233	+	0.228386i
$955$	13.4234	+	26.3449i	0.434370	+	0.852499i
$956$	−3.13927	+	19.8205i	−0.101531	+	0.641042i
$957$	−0.209728	−	0.209728i	−0.00677954	−	0.00677954i
$958$	18.2674	−	9.30769i	0.590192	−	0.300718i
$959$	−70.4826	−	51.2086i	−2.27600	−	1.65361i
$960$	−0.598769	+	1.17515i	−0.0193252	+	0.0379278i
$961$	24.7978	−	18.0166i	0.799928	−	0.581182i
$962$	1.86716	+	11.7888i	0.0601997	+	0.380086i
$963$	−23.6832	+	32.5971i	−0.763180	+	1.05043i
$964$	−3.52390	+	4.85023i	−0.113497	+	0.156215i
$965$	−1.21034	−	7.64176i	−0.0389621	−	0.245997i
$966$	−6.51112	+	4.73061i	−0.209492	+	0.152205i
$967$	8.63244	−	16.9421i	0.277601	−	0.544822i	−0.709542	−	0.704663i	$-0.751098\pi$
$967$	8.63244	−	16.9421i	0.277601	−	0.544822i	0.987143	+	0.159841i	$0.0510982\pi$
$968$	16.1999	+	11.7699i	0.520683	+	0.378298i
$969$	−0.810471	+	0.412955i	−0.0260361	+	0.0132660i
$970$	4.85092	+	4.85092i	0.155754	+	0.155754i
$971$	−5.92738	+	37.4240i	−0.190219	+	1.20099i	0.689067	+	0.724698i	$0.258021\pi$
$971$	−5.92738	+	37.4240i	−0.190219	+	1.20099i	−0.879286	+	0.476295i	$0.841979\pi$
$972$	−5.98407	−	11.7444i	−0.191939	−	0.376702i
$973$	−9.32482	−	4.75123i	−0.298940	−	0.152318i
$974$	5.76097	+	17.7304i	0.184593	+	0.568120i
$975$			0.893272i			0.0286076i
$976$	−0.828517	+	0.269202i	−0.0265202	+	0.00861693i
$977$	21.7408	−	3.44341i	0.695551	−	0.110164i	0.201359	−	0.979517i	$-0.435464\pi$
$977$	21.7408	−	3.44341i	0.695551	−	0.110164i	0.494191	+	0.869353i	$0.335464\pi$
$978$	−1.84953	−	0.292936i	−0.0591413	−	0.00936707i
$979$	−5.97088	−	1.94006i	−0.190830	−	0.0620044i
$980$	18.8961	−	58.1563i	0.603615	−	1.85774i
$981$	31.2519	−	31.2519i	0.997797	−	0.997797i
$982$	−7.25876	−	9.99082i	−0.231636	−	0.318820i
$983$	−12.0990			−0.385900			−0.192950	−	0.981209i	$-0.561805\pi$
$983$	−12.0990			−0.385900			−0.192950	+	0.981209i	$0.561805\pi$
$984$	−5.31853	+	1.11870i	−0.169548	+	0.0356628i
$985$	−32.2047			−1.02613
$986$	0.578705	+	0.796518i	0.0184297	+	0.0253663i
$987$	−5.99153	+	5.99153i	−0.190713	+	0.190713i
$988$	−1.77660	+	5.46780i	−0.0565211	+	0.173954i
$989$	34.6145	+	11.2469i	1.10068	+	0.357632i
$990$	8.15555	+	1.29171i	0.259201	+	0.0410533i
$991$	−37.0961	+	5.87545i	−1.17840	+	0.186640i	−0.714750	−	0.699380i	$-0.753459\pi$
$991$	−37.0961	+	5.87545i	−1.17840	+	0.186640i	−0.463647	+	0.886020i	$0.653459\pi$
$992$	−3.27389	+	1.06375i	−0.103946	+	0.0337741i
$993$		−	3.58403i		−	0.113736i
$994$	7.80108	+	24.0092i	0.247435	+	0.761527i
$995$	−19.6563	−	10.0154i	−0.623145	−	0.317508i
$996$	1.12645	+	2.21078i	0.0356929	+	0.0700513i
$997$	−1.20345	+	7.59830i	−0.0381137	+	0.240641i	−0.999389	−	0.0349491i	$-0.988873\pi$
$997$	−1.20345	+	7.59830i	−0.0381137	+	0.240641i	0.961275	+	0.275590i	$0.0888731\pi$
$998$	−3.15815	−	3.15815i	−0.0999694	−	0.0999694i
$999$	−7.65014	+	3.89794i	−0.242040	+	0.123325i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.36.2	yes	24
3.2	odd	2		369.2.u.a.118.2		24
4.3	odd	2		656.2.bs.d.241.2		24
41.7	odd	40		1681.2.a.m.1.14		24
41.8	even	20	inner	41.2.g.a.8.2	✓	24
41.34	odd	40		1681.2.a.m.1.13		24
123.8	odd	20		369.2.u.a.172.2		24
164.131	odd	20		656.2.bs.d.49.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.8.2	✓	24	41.8	even	20	inner
41.2.g.a.36.2	yes	24	1.1	even	1	trivial
369.2.u.a.118.2		24	3.2	odd	2
369.2.u.a.172.2		24	123.8	odd	20
656.2.bs.d.49.2		24	164.131	odd	20
656.2.bs.d.241.2		24	4.3	odd	2
1681.2.a.m.1.13		24	41.34	odd	40
1681.2.a.m.1.14		24	41.7	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.415383 - 0.571726i) q^{2} +(-0.242613 + 0.242613i) q^{3} +(0.463706 - 1.42714i) q^{4} +(2.26179 + 0.734900i) q^{5} +(0.239486 + 0.0379308i) q^{6} +(-4.85225 + 0.768522i) q^{7} +(-2.35276 + 0.764458i) q^{8} +2.88228i q^{9} +O(q^{10})\)	\(q+(-0.415383 - 0.571726i) q^{2} +(-0.242613 + 0.242613i) q^{3} +(0.463706 - 1.42714i) q^{4} +(2.26179 + 0.734900i) q^{5} +(0.239486 + 0.0379308i) q^{6} +(-4.85225 + 0.768522i) q^{7} +(-2.35276 + 0.764458i) q^{8} +2.88228i q^{9} +(-0.519348 - 1.59839i) q^{10} +(1.51881 + 0.773870i) q^{11} +(0.233742 + 0.458744i) q^{12} +(0.621065 - 3.92125i) q^{13} +(2.45493 + 2.45493i) q^{14} +(-0.727035 + 0.370443i) q^{15} +(-1.01364 - 0.736453i) q^{16} +(-1.24719 + 2.44775i) q^{17} +(1.64787 - 1.19725i) q^{18} +(-0.150964 - 0.953149i) q^{19} +(2.09761 - 2.88712i) q^{20} +(0.990766 - 1.36367i) q^{21} +(-0.188445 - 1.18979i) q^{22} +(5.46604 - 3.97131i) q^{23} +(0.385342 - 0.756277i) q^{24} +(0.530527 + 0.385451i) q^{25} +(-2.49986 + 1.27374i) q^{26} +(-1.42712 - 1.42712i) q^{27} +(-1.15323 + 7.28122i) q^{28} +(0.230233 + 0.451858i) q^{29} +(0.513791 + 0.261789i) q^{30} +(0.182364 + 0.561259i) q^{31} +5.83311i q^{32} +(-0.556233 + 0.180731i) q^{33} +(1.91751 - 0.303703i) q^{34} +(-11.5396 - 1.82769i) q^{35} +(4.11342 + 1.33653i) q^{36} +(1.31461 - 4.04595i) q^{37} +(-0.482233 + 0.482233i) q^{38} +(0.800668 + 1.10202i) q^{39} -5.88325 q^{40} +(-4.01905 - 4.98470i) q^{41} -1.19120 q^{42} +(3.16632 + 4.35807i) q^{43} +(1.80870 - 1.80870i) q^{44} +(-2.11819 + 6.51911i) q^{45} +(-4.54100 - 1.47546i) q^{46} +(-4.96501 - 0.786381i) q^{47} +(0.424595 - 0.0672493i) q^{48} +(16.2964 - 5.29501i) q^{49} -0.463426i q^{50} +(-0.291271 - 0.896441i) q^{51} +(-5.30819 - 2.70466i) q^{52} +(3.46320 + 6.79691i) q^{53} +(-0.223119 + 1.40872i) q^{54} +(2.86650 + 2.86650i) q^{55} +(10.8287 - 5.51749i) q^{56} +(0.267872 + 0.194620i) q^{57} +(0.162704 - 0.319325i) q^{58} +(-6.81790 + 4.95350i) q^{59} +(0.191544 + 1.20936i) q^{60} +(0.408684 - 0.562505i) q^{61} +(0.245135 - 0.337400i) q^{62} +(-2.21509 - 13.9855i) q^{63} +(1.30766 - 0.950072i) q^{64} +(4.28645 - 8.41262i) q^{65} +(0.334379 + 0.242940i) q^{66} +(-3.63545 + 1.85235i) q^{67} +(2.91496 + 2.91496i) q^{68} +(-0.362641 + 2.28962i) q^{69} +(3.74841 + 7.35666i) q^{70} +(6.47886 + 3.30115i) q^{71} +(-2.20338 - 6.78131i) q^{72} +9.72685i q^{73} +(-2.85924 + 0.929024i) q^{74} +(-0.222228 + 0.0351975i) q^{75} +(-1.43028 - 0.226534i) q^{76} +(-7.96437 - 2.58778i) q^{77} +(0.297472 - 0.915526i) q^{78} +(6.15477 - 6.15477i) q^{79} +(-1.75142 - 2.41063i) q^{80} -7.95436 q^{81} +(-1.18044 + 4.36836i) q^{82} +4.81920 q^{83} +(-1.48673 - 2.04631i) q^{84} +(-4.61974 + 4.61974i) q^{85} +(1.17638 - 3.62054i) q^{86} +(-0.165484 - 0.0537691i) q^{87} +(-4.16498 - 0.659667i) q^{88} +(-3.63773 + 0.576160i) q^{89} +(4.60700 - 1.49691i) q^{90} +19.5042i q^{91} +(-3.13298 - 9.64234i) q^{92} +(-0.180413 - 0.0919248i) q^{93} +(1.61279 + 3.16528i) q^{94} +(0.359020 - 2.26677i) q^{95} +(-1.41519 - 1.41519i) q^{96} +(-3.63700 + 1.85314i) q^{97} +(-9.79653 - 7.11760i) q^{98} +(-2.23051 + 4.37762i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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