LMFDB - Embedded newform 216.2.t.a.61.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(13,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 8]))

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

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

chi := DirichletCharacter("216.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.11
Character	$\chi$	$=$	216.61
Dual form			216.2.t.a.85.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.907362 + 1.08476i) q^{2} +(-1.73201 + 0.0113521i) q^{3} +(-0.353388 - 1.96853i) q^{4} +(-3.55522 + 0.626880i) q^{5} +(1.55925 - 1.88911i) q^{6} +(0.197520 + 0.165739i) q^{7} +(2.45603 + 1.40283i) q^{8} +(2.99974 - 0.0393239i) q^{9} +O(q^{10})$	\(q+(-0.907362 + 1.08476i) q^{2} +(-1.73201 + 0.0113521i) q^{3} +(-0.353388 - 1.96853i) q^{4} +(-3.55522 + 0.626880i) q^{5} +(1.55925 - 1.88911i) q^{6} +(0.197520 + 0.165739i) q^{7} +(2.45603 + 1.40283i) q^{8} +(2.99974 - 0.0393239i) q^{9} +(2.54586 - 4.42535i) q^{10} +(4.72909 + 0.833866i) q^{11} +(0.634419 + 3.40551i) q^{12} +(2.06615 - 5.67671i) q^{13} +(-0.359008 + 0.0638755i) q^{14} +(6.15057 - 1.12612i) q^{15} +(-3.75023 + 1.39131i) q^{16} +(-2.76368 - 4.78684i) q^{17} +(-2.67920 + 3.28967i) q^{18} +(1.75645 + 1.01409i) q^{19} +(2.49040 + 6.77702i) q^{20} +(-0.343988 - 0.284820i) q^{21} +(-5.19554 + 4.37328i) q^{22} +(-0.164150 + 0.137738i) q^{23} +(-4.26979 - 2.40184i) q^{24} +(7.54812 - 2.74729i) q^{25} +(4.28309 + 7.39210i) q^{26} +(-5.19515 + 0.102163i) q^{27} +(0.256461 - 0.447394i) q^{28} +(-0.455110 - 1.25040i) q^{29} +(-4.35922 + 7.69366i) q^{30} +(-0.00197394 + 0.00165633i) q^{31} +(1.89359 - 5.33051i) q^{32} +(-8.20031 - 1.39058i) q^{33} +(7.70020 + 1.34548i) q^{34} +(-0.806124 - 0.465416i) q^{35} +(-1.13748 - 5.89119i) q^{36} +(0.995752 - 0.574898i) q^{37} +(-2.69377 + 0.985173i) q^{38} +(-3.51416 + 9.85559i) q^{39} +(-9.61111 - 3.44774i) q^{40} +(4.72689 + 1.72045i) q^{41} +(0.621081 - 0.114709i) q^{42} +(4.99819 + 0.881316i) q^{43} +(-0.0297094 - 9.60404i) q^{44} +(-10.6401 + 2.02028i) q^{45} +(-0.000468717 - 0.303041i) q^{46} +(-1.18349 - 0.993067i) q^{47} +(6.47966 - 2.45234i) q^{48} +(-1.20399 - 6.82818i) q^{49} +(-3.86874 + 10.6806i) q^{50} +(4.84107 + 8.25949i) q^{51} +(-11.9049 - 2.06121i) q^{52} -12.4496i q^{53} +(4.60306 - 5.72816i) q^{54} -17.3357 q^{55} +(0.252610 + 0.684146i) q^{56} +(-3.05370 - 1.73647i) q^{57} +(1.76933 + 0.640886i) q^{58} +(10.3154 - 1.81887i) q^{59} +(-4.39035 - 11.7096i) q^{60} +(-5.31333 + 6.33218i) q^{61} +(-5.63643e-6 - 0.00364414i) q^{62} +(0.599026 + 0.489406i) q^{63} +(4.06412 + 6.89078i) q^{64} +(-3.78700 + 21.4771i) q^{65} +(8.94909 - 7.63357i) q^{66} +(1.10004 - 3.02234i) q^{67} +(-8.44639 + 7.13200i) q^{68} +(0.282746 - 0.240428i) q^{69} +(1.23631 - 0.452146i) q^{70} +(-3.40904 - 5.90464i) q^{71} +(7.42261 + 4.11156i) q^{72} +(1.51096 - 2.61705i) q^{73} +(-0.279884 + 1.60179i) q^{74} +(-13.0423 + 4.84403i) q^{75} +(1.37555 - 3.81599i) q^{76} +(0.795884 + 0.948498i) q^{77} +(-7.50228 - 12.7546i) q^{78} +(10.1554 - 3.69627i) q^{79} +(12.4607 - 7.29735i) q^{80} +(8.99691 - 0.235923i) q^{81} +(-6.15527 + 3.56645i) q^{82} +(-2.84189 - 7.80804i) q^{83} +(-0.439115 + 0.777804i) q^{84} +(12.8263 + 15.2857i) q^{85} +(-5.49118 + 4.62214i) q^{86} +(0.802451 + 2.16055i) q^{87} +(10.4450 + 8.68211i) q^{88} +(-0.381609 + 0.660965i) q^{89} +(7.46289 - 13.3750i) q^{90} +(1.34896 - 0.778820i) q^{91} +(0.329150 + 0.274459i) q^{92} +(0.00340009 - 0.00289120i) q^{93} +(2.15109 - 0.382727i) q^{94} +(-6.88026 - 2.50421i) q^{95} +(-3.21921 + 9.25401i) q^{96} +(-0.902281 + 5.11709i) q^{97} +(8.49936 + 4.88960i) q^{98} +(14.2188 + 2.31542i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	−0.907362	+	1.08476i	−0.641602	+	0.767038i
$2$	−0.907362	+	1.08476i	−0.641602	+	0.767038i
$3$	−1.73201	+	0.0113521i	−0.999979	+	0.00655413i
$3$	−1.73201	+	0.0113521i	−0.999979	+	0.00655413i
$4$	−0.353388	−	1.96853i	−0.176694	−	0.984266i
$5$	−3.55522	+	0.626880i	−1.58994	+	0.280349i	−0.897463	−	0.441090i	$-0.854592\pi$
$5$	−3.55522	+	0.626880i	−1.58994	+	0.280349i	−0.692478	+	0.721439i	$0.743481\pi$
$6$	1.55925	−	1.88911i	0.636561	−	0.771226i
$7$	0.197520	+	0.165739i	0.0746554	+	0.0626434i	0.679352	−	0.733813i	$-0.262261\pi$
$7$	0.197520	+	0.165739i	0.0746554	+	0.0626434i	−0.604696	+	0.796456i	$0.706706\pi$
$8$	2.45603	+	1.40283i	0.868336	+	0.495976i
$9$	2.99974	−	0.0393239i	0.999914	−	0.0131080i
$10$	2.54586	−	4.42535i	0.805071	−	1.39942i
$11$	4.72909	+	0.833866i	1.42587	+	0.251420i	0.832731	−	0.553677i	$-0.186776\pi$
$11$	4.72909	+	0.833866i	1.42587	+	0.251420i	0.593143	+	0.805097i	$0.297887\pi$
$12$	0.634419	+	3.40551i	0.183141	+	0.983087i
$13$	2.06615	−	5.67671i	0.573047	−	1.57443i	−0.226615	−	0.973984i	$-0.572766\pi$
$13$	2.06615	−	5.67671i	0.573047	−	1.57443i	0.799662	−	0.600450i	$-0.205012\pi$
$14$	−0.359008	+	0.0638755i	−0.0959489	+	0.0170714i
$15$	6.15057	−	1.12612i	1.58807	−	0.290764i
$16$	−3.75023	+	1.39131i	−0.937559	+	0.347827i
$17$	−2.76368	−	4.78684i	−0.670291	−	1.16098i	−0.977822	−	0.209440i	$-0.932836\pi$
$17$	−2.76368	−	4.78684i	−0.670291	−	1.16098i	0.307530	−	0.951538i	$-0.400497\pi$
$18$	−2.67920	+	3.28967i	−0.631493	+	0.775382i
$19$	1.75645	+	1.01409i	0.402957	+	0.232647i	0.687759	−	0.725939i	$-0.258595\pi$
$19$	1.75645	+	1.01409i	0.402957	+	0.232647i	−0.284802	+	0.958586i	$0.591928\pi$
$20$	2.49040	+	6.77702i	0.556871	+	1.51539i
$21$	−0.343988	−	0.284820i	−0.0750644	−	0.0621527i
$22$	−5.19554	+	4.37328i	−1.10769	+	0.932387i
$23$	−0.164150	+	0.137738i	−0.0342276	+	0.0287204i	−0.659741	−	0.751493i	$-0.729334\pi$
$23$	−0.164150	+	0.137738i	−0.0342276	+	0.0287204i	0.625513	+	0.780213i	$0.284890\pi$
$24$	−4.26979	−	2.40184i	−0.871568	−	0.490274i
$25$	7.54812	−	2.74729i	1.50962	−	0.549458i
$26$	4.28309	+	7.39210i	0.839982	+	1.44971i
$27$	−5.19515	+	0.102163i	−0.999807	+	0.0196613i
$28$	0.256461	−	0.447394i	0.0484666	−	0.0845495i
$29$	−0.455110	−	1.25040i	−0.0845117	−	0.232194i	0.890237	−	0.455497i	$-0.150538\pi$
$29$	−0.455110	−	1.25040i	−0.0845117	−	0.232194i	−0.974749	+	0.223303i	$0.928316\pi$
$30$	−4.35922	+	7.69366i	−0.795881	+	1.40466i
$31$	−0.00197394	+	0.00165633i	−0.000354531	+	0.000297486i	−0.642965	−	0.765896i	$-0.722296\pi$
$31$	−0.00197394	+	0.00165633i	−0.000354531	+	0.000297486i	0.642610	+	0.766193i	$0.277851\pi$
$32$	1.89359	−	5.33051i	0.334743	−	0.942310i
$33$	−8.20031	−	1.39058i	−1.42749	−	0.242069i
$34$	7.70020	+	1.34548i	1.32057	+	0.230747i
$35$	−0.806124	−	0.465416i	−0.136260	−	0.0786696i
$36$	−1.13748	−	5.89119i	−0.189580	−	0.981865i
$37$	0.995752	−	0.574898i	0.163701	−	0.0945126i	−0.415912	−	0.909405i	$-0.636537\pi$
$37$	0.995752	−	0.574898i	0.163701	−	0.0945126i	0.579612	+	0.814892i	$0.303204\pi$
$38$	−2.69377	+	0.985173i	−0.436987	+	0.159816i
$39$	−3.51416	+	9.85559i	−0.562716	+	1.57816i
$40$	−9.61111	−	3.44774i	−1.51965	−	0.545135i
$41$	4.72689	+	1.72045i	0.738217	+	0.268689i	0.683639	−	0.729821i	$-0.260396\pi$
$41$	4.72689	+	1.72045i	0.738217	+	0.268689i	0.0545779	+	0.998510i	$0.482619\pi$
$42$	0.621081	−	0.114709i	0.0958350	−	0.0176999i
$43$	4.99819	+	0.881316i	0.762217	+	0.134399i	0.541227	−	0.840877i	$-0.317960\pi$
$43$	4.99819	+	0.881316i	0.762217	+	0.134399i	0.220990	+	0.975276i	$0.429071\pi$
$44$	−0.0297094	−	9.60404i	−0.00447886	−	1.44786i
$45$	−10.6401	+	2.02028i	−1.58613	+	0.301166i
$46$	−0.000468717	−	0.303041i	−6.91085e−5	−	0.0446809i
$47$	−1.18349	−	0.993067i	−0.172630	−	0.144854i	0.552379	−	0.833593i	$-0.313720\pi$
$47$	−1.18349	−	0.993067i	−0.172630	−	0.144854i	−0.725009	+	0.688739i	$0.758165\pi$
$48$	6.47966	−	2.45234i	0.935259	−	0.353965i
$49$	−1.20399	−	6.82818i	−0.171999	−	0.975454i
$50$	−3.86874	+	10.6806i	−0.547122	+	1.51047i
$51$	4.84107	+	8.25949i	0.677886	+	1.15656i
$52$	−11.9049	−	2.06121i	−1.65092	−	0.285838i
$53$		−	12.4496i		−	1.71008i	−0.518560	−	0.855041i	$-0.673532\pi$
$53$		−	12.4496i		−	1.71008i	0.518560	−	0.855041i	$-0.326468\pi$
$54$	4.60306	−	5.72816i	0.626397	−	0.779504i
$55$	−17.3357			−2.33754
$56$	0.252610	+	0.684146i	0.0337564	+	0.0914228i
$57$	−3.05370	−	1.73647i	−0.404473	−	0.230001i
$58$	1.76933	+	0.640886i	0.232324	+	0.0841525i
$59$	10.3154	−	1.81887i	1.34294	−	0.236797i	0.544447	−	0.838795i	$-0.316740\pi$
$59$	10.3154	−	1.81887i	1.34294	−	0.236797i	0.798497	+	0.601998i	$0.205629\pi$
$60$	−4.39035	−	11.7096i	−0.566791	−	1.51171i
$61$	−5.31333	+	6.33218i	−0.680303	+	0.810753i	−0.990147	−	0.140034i	$-0.955279\pi$
$61$	−5.31333	+	6.33218i	−0.680303	+	0.810753i	0.309844	+	0.950787i	$0.399723\pi$
$62$	−5.63643e−6	−	0.00364414i	−7.15827e−7	−	0.000462806i
$63$	0.599026	+	0.489406i	0.0754702	+	0.0616594i
$64$	4.06412	+	6.89078i	0.508015	+	0.861348i
$65$	−3.78700	+	21.4771i	−0.469720	+	2.66391i
$66$	8.94909	−	7.63357i	1.10156	−	0.939627i
$67$	1.10004	−	3.02234i	0.134392	−	0.369238i	−0.854182	−	0.519973i	$-0.825942\pi$
$67$	1.10004	−	3.02234i	0.134392	−	0.369238i	0.988574	+	0.150735i	$0.0481641\pi$
$68$	−8.44639	+	7.13200i	−1.02427	+	0.864882i
$69$	0.282746	−	0.240428i	0.0340387	−	0.0289441i
$70$	1.23631	−	0.452146i	0.147767	−	0.0540418i
$71$	−3.40904	−	5.90464i	−0.404579	−	0.700751i	0.589693	−	0.807627i	$-0.299249\pi$
$71$	−3.40904	−	5.90464i	−0.404579	−	0.700751i	−0.994272	+	0.106876i	$0.965915\pi$
$72$	7.42261	+	4.11156i	0.874763	+	0.484551i
$73$	1.51096	−	2.61705i	0.176844	−	0.306303i	−0.763954	−	0.645271i	$-0.776744\pi$
$73$	1.51096	−	2.61705i	0.176844	−	0.306303i	0.940798	+	0.338968i	$0.110078\pi$
$74$	−0.279884	+	1.60179i	−0.0325359	+	0.186204i
$75$	−13.0423	+	4.84403i	−1.50599	+	0.559341i
$76$	1.37555	−	3.81599i	0.157787	−	0.437724i
$77$	0.795884	+	0.948498i	0.0906995	+	0.108091i
$78$	−7.50228	−	12.7546i	−0.849466	−	1.44417i
$79$	10.1554	−	3.69627i	1.14257	−	0.415863i	0.299732	−	0.954023i	$-0.403103\pi$
$79$	10.1554	−	3.69627i	1.14257	−	0.415863i	0.842843	+	0.538160i	$0.180880\pi$
$80$	12.4607	−	7.29735i	1.39315	−	0.815869i
$81$	8.99691	−	0.235923i	0.999656	−	0.0262137i
$82$	−6.15527	+	3.56645i	−0.679736	+	0.393849i
$83$	−2.84189	−	7.80804i	−0.311938	−	0.857044i	−0.992265	−	0.124135i	$-0.960384\pi$
$83$	−2.84189	−	7.80804i	−0.311938	−	0.857044i	0.680327	−	0.732909i	$-0.261838\pi$
$84$	−0.439115	+	0.777804i	−0.0479114	+	0.0848653i
$85$	12.8263	+	15.2857i	1.39120	+	1.65797i
$86$	−5.49118	+	4.62214i	−0.592129	+	0.498418i
$87$	0.802451	+	2.16055i	0.0860317	+	0.231635i
$88$	10.4450	+	8.68211i	1.11344	+	0.925517i
$89$	−0.381609	+	0.660965i	−0.0404504	+	0.0700622i	−0.885542	−	0.464560i	$-0.846213\pi$
$89$	−0.381609	+	0.660965i	−0.0404504	+	0.0700622i	0.845091	+	0.534622i	$0.179546\pi$
$90$	7.46289	−	13.3750i	0.786658	−	1.40985i
$91$	1.34896	−	0.778820i	0.141409	−	0.0816425i
$92$	0.329150	+	0.274459i	0.0343163	+	0.0286144i
$93$	0.00340009	−	0.00289120i	0.000352573	−	0.000299804i
$94$	2.15109	−	0.382727i	0.221868	−	0.0394752i
$95$	−6.88026	−	2.50421i	−0.705900	−	0.256927i
$96$	−3.21921	+	9.25401i	−0.328560	+	0.944483i
$97$	−0.902281	+	5.11709i	−0.0916127	+	0.519562i	0.904120	+	0.427278i	$0.140528\pi$
$97$	−0.902281	+	5.11709i	−0.0916127	+	0.519562i	−0.995733	+	0.0922832i	$0.970584\pi$
$98$	8.49936	+	4.88960i	0.858565	+	0.493924i
$99$	14.2188	+	2.31542i	1.42905	+	0.232708i
$100$	−8.07554	−	13.8879i	−0.807554	−	1.38879i
$101$	−4.68417	+	5.58238i	−0.466092	+	0.555467i	−0.946971	−	0.321320i	$-0.895873\pi$
$101$	−4.68417	+	5.58238i	−0.466092	+	0.555467i	0.480878	+	0.876787i	$0.340318\pi$
$102$	−13.3521	−	2.24297i	−1.32206	−	0.222087i
$103$	0.771419	+	4.37493i	0.0760102	+	0.431075i	0.998937	+	0.0460994i	$0.0146791\pi$
$103$	0.771419	+	4.37493i	0.0760102	+	0.431075i	−0.922927	+	0.384976i	$0.874210\pi$
$104$	13.0380	−	11.0437i	1.27848	−	1.08292i
$105$	1.40150	+	0.796955i	0.136772	+	0.0777749i
$106$	13.5048	+	11.2963i	1.31170	+	1.09719i
$107$			9.51271i			0.919629i	0.888015	+	0.459814i	$0.152084\pi$
$107$			9.51271i			0.919629i	−0.888015	+	0.459814i	$0.847916\pi$
$108$	2.03701	+	10.1907i	0.196012	+	0.980602i
$109$			7.93890i			0.760409i	0.924903	+	0.380204i	$0.124146\pi$
$109$			7.93890i			0.760409i	−0.924903	+	0.380204i	$0.875854\pi$
$110$	15.7297	−	18.8050i	1.49977	−	1.79298i
$111$	−1.71813	+	1.00703i	−0.163078	+	0.0955835i
$112$	−0.971339	−	0.346748i	−0.0917829	−	0.0327646i
$113$	−1.23440	−	7.00061i	−0.116122	−	0.658562i	−0.986188	−	0.165627i	$-0.947035\pi$
$113$	−1.23440	−	7.00061i	−0.116122	−	0.658562i	0.870066	−	0.492935i	$-0.164076\pi$
$114$	4.65446	−	1.73691i	0.435930	−	0.162677i
$115$	0.497243	−	0.592591i	0.0463682	−	0.0552594i
$116$	−2.30063	+	1.33777i	−0.213608	+	0.124209i
$117$	5.97469	−	17.1099i	0.552360	−	1.58181i
$118$	−7.38673	+	12.8400i	−0.680003	+	1.18202i
$119$	0.247483	−	1.40354i	0.0226867	−	0.128663i
$120$	16.6857	+	5.86242i	1.52319	+	0.535164i
$121$	11.3323	+	4.12463i	1.03021	+	0.374966i
$122$	−2.04775	−	11.5092i	−0.185395	−	1.04200i
$123$	−8.20657	−	2.92618i	−0.739962	−	0.263845i
$124$	0.00395811	+	0.00330044i	0.000355449	+	0.000296388i
$125$	−9.48095	+	5.47383i	−0.848002	+	0.489594i
$126$	−1.07442	+	0.205728i	−0.0957169	+	0.0183277i
$127$	−8.72390	+	15.1102i	−0.774121	+	1.34082i	0.161167	+	0.986927i	$0.448474\pi$
$127$	−8.72390	+	15.1102i	−0.774121	+	1.34082i	−0.935287	+	0.353889i	$0.884859\pi$
$128$	−11.1624	−	1.84386i	−0.986630	−	0.162976i
$129$	−8.66694	−	1.46971i	−0.763081	−	0.129401i
$130$	−19.8613	−	23.5955i	−1.74195	−	2.06946i
$131$	−9.50899	−	11.3324i	−0.830805	−	0.990114i	−0.999990	−	0.00453015i	$-0.998558\pi$
$131$	−9.50899	−	11.3324i	−0.830805	−	0.990114i	0.169185	−	0.985584i	$-0.445886\pi$
$132$	0.160483	+	16.6340i	0.0139682	+	1.44780i
$133$	0.178860	+	0.491413i	0.0155091	+	0.0426109i
$134$	2.28037	+	3.93564i	0.196994	+	0.339987i
$135$	18.4058	−	3.61995i	1.58412	−	0.311556i
$136$	−0.0725423	−	15.6336i	−0.00622045	−	1.34057i
$137$	−11.3732	+	4.13951i	−0.971678	+	0.353662i	−0.778599	−	0.627521i	$-0.784070\pi$
$137$	−11.3732	+	4.13951i	−0.971678	+	0.353662i	−0.193079	+	0.981183i	$0.561847\pi$
$138$	0.00425197	+	0.524866i	0.000361952	+	0.0446795i
$139$	−6.31955	−	7.53135i	−0.536017	−	0.638801i	0.428272	−	0.903650i	$-0.359122\pi$
$139$	−6.31955	−	7.53135i	−0.536017	−	0.638801i	−0.964290	+	0.264849i	$0.914678\pi$
$140$	−0.631312	+	1.75135i	−0.0533556	+	0.148016i
$141$	2.06110	+	1.70657i	0.173576	+	0.143719i
$142$	9.49832	+	1.65967i	0.797082	+	0.139276i
$143$	14.5046	−	25.1227i	1.21294	−	2.10087i
$144$	−11.1950	+	4.32104i	−0.932919	+	0.360087i
$145$	2.40187	+	4.16015i	0.199464	+	0.345482i
$146$	1.46788	+	4.01363i	0.121482	+	0.332171i
$147$	2.16285	+	11.8128i	0.178388	+	0.974306i
$148$	−1.48359	−	1.75701i	−0.121950	−	0.144425i
$149$	5.68507	−	15.6196i	0.465739	−	1.27961i	−0.455370	−	0.890302i	$-0.650493\pi$
$149$	5.68507	−	15.6196i	0.465739	−	1.27961i	0.921109	−	0.389305i	$-0.127285\pi$
$150$	6.57946	−	18.5429i	0.537211	−	1.51403i
$151$	0.796354	−	4.51635i	0.0648064	−	0.367535i	−0.935107	−	0.354366i	$-0.884697\pi$
$151$	0.796354	−	4.51635i	0.0648064	−	0.367535i	0.999913	−	0.0131695i	$-0.00419209\pi$
$152$	2.89129	+	4.95462i	0.234514	+	0.401873i
$153$	−8.47857	−	14.2506i	−0.685452	−	1.15209i
$154$	−1.75104	+	0.00270836i	−0.141103	+	0.000218246i
$155$	0.00597947	−	0.00712605i	0.000480282	−	0.000572378i
$156$	20.6429	+	3.43490i	1.65275	+	0.275012i
$157$	1.68663	−	0.297399i	0.134608	−	0.0237350i	−0.105938	−	0.994373i	$-0.533785\pi$
$157$	1.68663	−	0.297399i	0.134608	−	0.0237350i	0.240546	+	0.970638i	$0.422673\pi$
$158$	−5.20510	+	14.3700i	−0.414096	+	1.14322i
$159$	0.141329	+	21.5629i	0.0112081	+	1.71005i
$160$	−3.39054	+	20.1382i	−0.268045	+	1.59206i
$161$	−0.0552514			−0.00435442
$162$	−7.90753	+	9.97351i	−0.621275	+	0.783593i
$163$			12.9384i			1.01341i	0.862119	+	0.506705i	$0.169137\pi$
$163$			12.9384i			1.01341i	−0.862119	+	0.506705i	$0.830863\pi$
$164$	1.71633	−	9.91302i	0.134023	−	0.774077i
$165$	30.0256	−	0.196796i	2.33749	−	0.0153205i
$166$	11.0484	+	4.00196i	0.857525	+	0.310612i
$167$	2.50837	+	14.2257i	0.194103	+	1.10082i	0.913690	+	0.406412i	$0.133220\pi$
$167$	2.50837	+	14.2257i	0.194103	+	1.10082i	−0.719586	+	0.694403i	$0.755668\pi$
$168$	−0.445290	−	1.18208i	−0.0343549	−	0.0911996i
$169$	−17.9974	−	15.1016i	−1.38442	−	1.16166i
$170$	−28.2193	+	0.0436472i	−2.16432	+	0.00334758i
$171$	5.30877	+	2.97293i	0.405972	+	0.227345i
$172$	−0.0314000	−	10.1505i	−0.00239423	−	0.773972i
$173$	11.9612	+	2.10908i	0.909391	+	0.160350i	0.608727	−	0.793380i	$-0.291680\pi$
$173$	11.9612	+	2.10908i	0.909391	+	0.160350i	0.300664	+	0.953730i	$0.402792\pi$
$174$	−3.07178	−	1.08994i	−0.232871	−	0.0826280i
$175$	1.94623	+	0.708372i	0.147122	+	0.0535479i
$176$	−18.8954	+	3.45243i	−1.42429	+	0.260237i
$177$	−17.8457	+	3.26742i	−1.34136	+	0.245594i
$178$	−0.370728	−	1.01369i	−0.0277873	−	0.0759790i
$179$	−16.4151	+	9.47728i	−1.22692	+	0.708365i	−0.966385	−	0.257098i	$-0.917234\pi$
$179$	−16.4151	+	9.47728i	−1.22692	+	0.708365i	−0.260539	+	0.965463i	$0.583900\pi$
$180$	7.73707	+	20.2314i	0.576687	+	1.50796i
$181$	2.91223	+	1.68138i	0.216465	+	0.124976i	0.604312	−	0.796748i	$-0.293448\pi$
$181$	2.91223	+	1.68138i	0.216465	+	0.124976i	−0.387848	+	0.921723i	$0.626781\pi$
$182$	−0.379163	+	2.16996i	−0.0281054	+	0.160848i
$183$	9.13088	−	11.0277i	0.674974	−	0.815194i
$184$	−0.596380	+	0.108014i	−0.0439657	+	0.00796286i
$185$	−3.17972	+	2.66810i	−0.233778	+	0.196163i
$186$	5.11309e−5		0.00631163i	3.74910e−6		0.000462792i
$187$	−9.07811	−	24.9419i	−0.663857	−	1.82393i
$188$	−1.53665	+	2.68068i	−0.112072	+	0.195509i
$189$	−1.04308	−	0.840858i	−0.0758727	−	0.0611634i
$190$	8.95935	−	5.19117i	0.649979	−	0.376607i
$191$	5.49500	−	2.00002i	0.397604	−	0.144716i	−0.135476	−	0.990781i	$-0.543256\pi$
$191$	5.49500	−	2.00002i	0.397604	−	0.144716i	0.533081	+	0.846064i	$0.321034\pi$
$192$	−7.11734	−	11.8888i	−0.513650	−	0.858000i
$193$	5.79233	−	4.86034i	0.416941	−	0.349855i	−0.410057	−	0.912060i	$-0.634491\pi$
$193$	5.79233	−	4.86034i	0.416941	−	0.349855i	0.826998	+	0.562205i	$0.190047\pi$
$194$	−4.73209	−	5.62181i	−0.339744	−	0.403622i
$195$	6.31532	−	37.2417i	0.452250	−	2.66693i
$196$	−13.0160	+	4.78309i	−0.929715	+	0.341649i
$197$	10.5090	+	6.06740i	0.748739	+	0.432284i	0.825238	−	0.564785i	$-0.191041\pi$
$197$	10.5090	+	6.06740i	0.748739	+	0.432284i	−0.0764994	+	0.997070i	$0.524374\pi$
$198$	−15.4133	+	13.3230i	−1.09538	+	0.946827i
$199$	−6.35656	−	11.0099i	−0.450605	−	0.780470i	0.547819	−	0.836597i	$-0.315458\pi$
$199$	−6.35656	−	11.0099i	−0.450605	−	0.780470i	−0.998424	+	0.0561267i	$0.982125\pi$
$200$	22.3924	+	3.84133i	1.58338	+	0.271623i
$201$	−1.87098	+	5.24723i	−0.131969	+	0.370111i
$202$	−1.80527	−	10.1464i	−0.127019	−	0.713899i
$203$	0.117347	−	0.322409i	0.00823616	−	0.0226287i
$204$	14.5483	−	12.4486i	1.01858	−	0.871577i
$205$	−17.8836	−	3.15337i	−1.24905	−	0.220241i
$206$	−5.44569	−	3.13285i	−0.379419	−	0.218276i
$207$	−0.486991	+	0.419634i	−0.0338482	+	0.0291666i
$208$	0.149498	+	24.1636i	0.0103658	+	1.67545i
$209$	7.46079	+	6.26034i	0.516073	+	0.433037i
$210$	−2.13617	+	0.797158i	−0.147410	+	0.0550091i
$211$	−25.8007	+	4.54936i	−1.77619	+	0.313191i	−0.963140	−	0.269000i	$-0.913307\pi$
$211$	−25.8007	+	4.54936i	−1.77619	+	0.313191i	−0.813052	+	0.582191i	$0.802196\pi$
$212$	−24.5074	+	4.39953i	−1.68318	+	0.302161i
$213$	5.97154	+	10.1882i	0.409163	+	0.698085i
$214$	−10.3190	−	8.63148i	−0.705390	−	0.590036i
$215$	−18.3221			−1.24956
$216$	−12.9027	−	7.03701i	−0.877920	−	0.478808i
$217$	−0.000664411	0		−4.51032e−5	0
$218$	−8.61176	−	7.20346i	−0.583262	−	0.487880i
$219$	−2.58729	+	4.54993i	−0.174833	+	0.307456i
$220$	6.12621	+	34.1258i	0.413029	+	2.30076i
$221$	−32.8836	+	5.79827i	−2.21199	+	0.390034i
$222$	0.466580	−	2.77749i	0.0313148	−	0.186413i
$223$	3.37847	+	2.83488i	0.226239	+	0.189837i	0.748860	−	0.662728i	$-0.230601\pi$
$223$	3.37847	+	2.83488i	0.226239	+	0.189837i	−0.522621	+	0.852565i	$0.675046\pi$
$224$	1.25749	−	0.739039i	0.0840198	−	0.0493791i
$225$	22.5344	−	8.53798i	1.50229	−	0.569199i
$226$	8.71399	+	5.01307i	0.579646	+	0.333465i
$227$	−4.31991	−	0.761717i	−0.286723	−	0.0505569i	0.0284371	−	0.999596i	$-0.490947\pi$
$227$	−4.31991	−	0.761717i	−0.286723	−	0.0505569i	−0.315160	+	0.949039i	$0.602058\pi$
$228$	−2.33916	+	6.62496i	−0.154914	+	0.438749i
$229$	3.02517	−	8.31159i	0.199909	−	0.549246i	−0.798714	−	0.601711i	$-0.794486\pi$
$229$	3.02517	−	8.31159i	0.199909	−	0.549246i	0.998623	+	0.0524657i	$0.0167080\pi$
$230$	0.191637	+	1.07708i	0.0126362	+	0.0710207i
$231$	−1.38925	−	1.63378i	−0.0914059	−	0.107495i
$232$	0.636346	−	3.70946i	0.0417781	−	0.243538i
$233$	12.1136	+	20.9814i	0.793589	+	1.37454i	0.923731	+	0.383042i	$0.125123\pi$
$233$	12.1136	+	20.9814i	0.793589	+	1.37454i	−0.130142	+	0.991495i	$0.541543\pi$
$234$	13.1388	+	22.0060i	0.858913	+	1.43857i
$235$	4.83010	+	2.78866i	0.315081	+	0.181912i
$236$	−7.22583	−	19.6633i	−0.470361	−	1.27997i
$237$	−17.5474	+	6.51728i	−1.13982	+	0.423343i
$238$	1.29794	+	1.54198i	0.0841333	+	0.0999518i
$239$	16.6186	−	13.9446i	1.07497	−	0.902004i	0.0794735	−	0.996837i	$-0.474676\pi$
$239$	16.6186	−	13.9446i	1.07497	−	0.902004i	0.995493	+	0.0948328i	$0.0302316\pi$
$240$	−21.4993	+	12.7806i	−1.38777	+	0.824982i
$241$	17.1009	−	6.22423i	1.10157	−	0.400938i	0.273674	−	0.961823i	$-0.411761\pi$
$241$	17.1009	−	6.22423i	1.10157	−	0.400938i	0.827894	+	0.560885i	$0.189539\pi$
$242$	−14.7567	+	8.55027i	−0.948599	+	0.549632i
$243$	−15.5801	+	0.510756i	−0.999463	+	0.0327650i
$244$	14.3428	+	8.22175i	0.918202	+	0.526344i
$245$	8.56091	+	23.5209i	0.546936	+	1.50270i
$246$	10.6205	−	6.24702i	0.677140	−	0.398295i
$247$	9.38575	−	7.87558i	0.597201	−	0.501111i
$248$	−0.00717161	+	0.00129889i	−0.000455398	+	8.24795e-5i
$249$	5.01084	+	13.4914i	0.317549	+	0.854981i
$250$	2.66489	−	15.2512i	0.168542	−	0.964574i
$251$	12.6453	+	7.30079i	0.798167	+	0.460822i	0.842830	−	0.538180i	$-0.180888\pi$
$251$	12.6453	+	7.30079i	0.798167	+	0.460822i	−0.0446629	+	0.999002i	$0.514221\pi$
$252$	0.751724	−	1.35215i	0.0473541	−	0.0851775i
$253$	−0.891135	+	0.514497i	−0.0560252	+	0.0323461i
$254$	−8.47517	−	23.1737i	−0.531779	−	1.45405i
$255$	−22.3888	−	26.3295i	−1.40204	−	1.64882i
$256$	12.1285	−	10.4355i	0.758032	−	0.652217i
$257$	5.43741	+	1.97905i	0.339176	+	0.123450i	0.505992	−	0.862538i	$-0.331126\pi$
$257$	5.43741	+	1.97905i	0.339176	+	0.123450i	−0.166816	+	0.985988i	$0.553349\pi$
$258$	9.45833	−	8.06794i	0.588850	−	0.502288i
$259$	0.291963	+	0.0514810i	0.0181417	+	0.00319888i
$260$	43.6167	−	0.134925i	2.70499	−	0.00836771i
$261$	−1.41438	−	3.73299i	−0.0875481	−	0.231066i
$262$	20.9210	−	0.0323587i	1.29250	−	0.00199913i
$263$	3.38239	+	2.83816i	0.208567	+	0.175009i	0.741087	−	0.671409i	$-0.234310\pi$
$263$	3.38239	+	2.83816i	0.208567	+	0.175009i	−0.532520	+	0.846417i	$0.678755\pi$
$264$	−18.1894	−	14.9190i	−1.11948	−	0.918199i
$265$	7.80440	+	44.2610i	0.479421	+	2.71893i
$266$	−0.695354	−	0.251871i	−0.0426349	−	0.0154432i
$267$	0.653448	−	1.14913i	0.0399904	−	0.0703258i
$268$	−6.33832	−	1.09741i	−0.387175	−	0.0670351i
$269$		−	7.57493i		−	0.461852i	−0.972971	−	0.230926i	$-0.925825\pi$
$269$		−	7.57493i		−	0.461852i	0.972971	−	0.230926i	$-0.0741755\pi$
$270$	−12.7740	+	23.2504i	−0.777401	+	1.41498i
$271$	6.02446			0.365960			0.182980	−	0.983117i	$-0.441426\pi$
$271$	6.02446			0.365960			0.182980	+	0.983117i	$0.441426\pi$
$272$	17.0244	+	14.1066i	1.03226	+	0.855340i
$273$	−2.32757	+	1.36424i	−0.140871	+	0.0825676i
$274$	5.82926	−	16.0932i	0.352159	−	0.972224i
$275$	37.9866	−	6.69806i	2.29068	−	0.403908i
$276$	−0.573209	−	0.471631i	−0.0345031	−	0.0283888i
$277$	0.284428	−	0.338968i	0.0170896	−	0.0203666i	−0.757432	−	0.652914i	$-0.773546\pi$
$277$	0.284428	−	0.338968i	0.0170896	−	0.0203666i	0.774522	+	0.632548i	$0.217991\pi$
$278$	13.9038	−	0.0215051i	0.833894	−	0.00128979i
$279$	−0.00585618	+	0.00504620i	−0.000350601	+	0.000302108i
$280$	−1.32696	−	2.27393i	−0.0793010	−	0.135893i
$281$	3.92170	−	22.2411i	0.233949	−	1.32679i	−0.610866	−	0.791734i	$-0.709179\pi$
$281$	3.92170	−	22.2411i	0.233949	−	1.32679i	0.844816	−	0.535058i	$-0.179710\pi$
$282$	−3.72137	+	0.687307i	−0.221605	+	0.0409286i
$283$	6.72971	−	18.4897i	0.400040	−	1.09910i	−0.562224	−	0.826985i	$-0.690054\pi$
$283$	6.72971	−	18.4897i	0.400040	−	1.09910i	0.962264	−	0.272116i	$-0.0877235\pi$
$284$	−10.4188	+	8.79744i	−0.618239	+	0.522032i
$285$	11.9451	+	4.25922i	0.707569	+	0.252295i
$286$	14.0911	+	38.5294i	0.833223	+	2.27829i
$287$	0.648510	+	1.12325i	0.0382803	+	0.0663034i
$288$	5.47067	−	16.0646i	0.322362	−	0.946616i
$289$	−6.77586	+	11.7361i	−0.398580	+	0.690361i
$290$	−6.69211	−	1.16933i	−0.392974	−	0.0686654i
$291$	1.50467	−	8.87311i	0.0882055	−	0.520151i
$292$	−5.68571	−	2.04953i	−0.332731	−	0.119940i
$293$	0.454390	+	0.541521i	0.0265458	+	0.0316360i	0.779154	−	0.626833i	$-0.215649\pi$
$293$	0.454390	+	0.541521i	0.0265458	+	0.0316360i	−0.752608	+	0.658469i	$0.771205\pi$
$294$	−14.7765	−	8.37236i	−0.861784	−	0.488286i
$295$	−35.5331	+	12.9330i	−2.06882	+	0.752987i
$296$	3.25208	−	0.0150902i	0.189023	−	0.000877098i
$297$	−24.6535	−	3.84892i	−1.43054	−	0.223337i
$298$	11.7850	+	20.3395i	0.682688	+	1.17824i
$299$	0.442740	+	1.21642i	0.0256043	+	0.0703473i
$300$	14.1446	+	23.9623i	0.816639	+	1.38346i
$301$	0.841173	+	1.00247i	0.0484844	+	0.0577815i
$302$	4.17655	+	4.96181i	0.240333	+	0.285520i
$303$	8.04968	−	9.72193i	0.462442	−	0.558510i
$304$	−7.99800	−	1.35930i	−0.458717	−	0.0779610i
$305$	14.9205	−	25.8431i	0.854347	−	1.47977i
$306$	23.1515	+	3.73328i	1.32349	+	0.213418i
$307$	−16.9763	+	9.80126i	−0.968887	+	0.559387i	−0.898897	−	0.438160i	$-0.855630\pi$
$307$	−16.9763	+	9.80126i	−0.968887	+	0.559387i	−0.0699905	+	0.997548i	$0.522297\pi$
$308$	1.58589	−	1.90191i	0.0903646	−	0.108371i
$309$	−1.38577	−	7.56869i	−0.0788339	−	0.430568i
$310$	0.00230448	+	0.0129522i	0.000130886	+	0.000735634i
$311$	23.9780	+	8.72727i	1.35967	+	0.494878i	0.915951	−	0.401289i	$-0.131438\pi$
$311$	23.9780	+	8.72727i	1.35967	+	0.494878i	0.443716	+	0.896168i	$0.353660\pi$
$312$	−22.4566	+	19.2758i	−1.27135	+	1.09128i
$313$	3.61764	−	20.5167i	0.204481	−	1.15967i	−0.693773	−	0.720194i	$-0.744053\pi$
$313$	3.61764	−	20.5167i	0.204481	−	1.15967i	0.898254	−	0.439477i	$-0.144836\pi$
$314$	−1.20778	+	2.09943i	−0.0681590	+	0.118478i
$315$	−2.43647	−	1.36443i	−0.137279	−	0.0768768i
$316$	−10.8650	−	18.6851i	−0.611206	−	1.05112i
$317$	−5.72173	+	6.81889i	−0.321364	+	0.382987i	−0.902406	−	0.430887i	$-0.858201\pi$
$317$	−5.72173	+	6.81889i	−0.321364	+	0.382987i	0.581042	+	0.813874i	$0.302645\pi$
$318$	−23.5187	−	19.4120i	−1.31886	−	1.08857i
$319$	−1.10958	−	6.29277i	−0.0621248	−	0.352327i
$320$	−18.7685	−	21.9505i	−1.04919	−	1.22707i
$321$	−0.107989	−	16.4761i	−0.00602736	−	0.919609i
$322$	0.0501330	−	0.0599342i	0.00279380	−	0.00334000i
$323$		−	11.2104i		−	0.623765i
$324$	−3.64382	−	17.6273i	−0.202434	−	0.979296i
$325$		−	48.5248i		−	2.69167i
$326$	−14.0350	−	11.7398i	−0.777324	−	0.650206i
$327$	−0.0901230	−	13.7503i	−0.00498382	−	0.760392i
$328$	9.19587	+	10.8565i	0.507757	+	0.599450i
$329$	−0.0691732	−	0.392301i	−0.00381364	−	0.0216282i
$330$	−27.0306	+	32.7490i	−1.48799	+	1.80277i
$331$	5.83964	−	6.95942i	0.320976	−	0.382524i	−0.581296	−	0.813692i	$-0.697454\pi$
$331$	5.83964	−	6.95942i	0.320976	−	0.382524i	0.902272	+	0.431168i	$0.141898\pi$
$332$	−14.3661	+	8.35362i	−0.788441	+	0.458465i
$333$	2.96439	−	1.76370i	0.162448	−	0.0966502i
$334$	−17.7074	−	10.1869i	−0.968904	−	0.557401i
$335$	−2.01624	+	11.4347i	−0.110159	+	0.624743i
$336$	1.68631	+	0.589546i	0.0919957	+	0.0321624i
$337$	−8.03414	−	2.92419i	−0.437647	−	0.159291i	0.113794	−	0.993504i	$-0.463700\pi$
$337$	−8.03414	−	2.92419i	−0.437647	−	0.159291i	−0.551441	+	0.834214i	$0.685922\pi$
$338$	32.7117	−	5.82015i	1.77928	−	0.316574i
$339$	2.21746	+	12.1111i	0.120436	+	0.657787i
$340$	25.5578	−	30.6507i	1.38607	−	1.66227i
$341$	−0.0107161	+	0.00618695i	−0.000580310	+	0.000335042i
$342$	−8.04187	+	3.06119i	−0.434855	+	0.165530i
$343$	1.79633	−	3.11134i	0.0969930	−	0.167997i
$344$	11.0393	+	9.17616i	0.595201	+	0.494745i
$345$	−0.854505	+	1.03202i	−0.0460050	+	0.0555621i
$346$	−13.1410	+	11.0612i	−0.706462	+	0.594656i
$347$	18.6424	+	22.2171i	1.00077	+	1.19268i	0.981225	+	0.192868i	$0.0617790\pi$
$347$	18.6424	+	22.2171i	1.00077	+	1.19268i	0.0195503	+	0.999809i	$0.493777\pi$
$348$	3.96953	−	2.34316i	0.212789	−	0.125607i
$349$	7.61884	+	20.9326i	0.407827	+	1.12050i	0.958330	+	0.285663i	$0.0922136\pi$
$349$	7.61884	+	20.9326i	0.407827	+	1.12050i	−0.550503	+	0.834833i	$0.685564\pi$
$350$	−2.53435	+	1.46844i	−0.135467	+	0.0784914i
$351$	−10.1540	+	29.7024i	−0.541981	+	1.58540i
$352$	13.3999	−	23.6294i	0.714217	−	1.25945i
$353$	−8.48681	+	3.08895i	−0.451707	+	0.164408i	−0.557848	−	0.829943i	$-0.688373\pi$
$353$	−8.48681	+	3.08895i	−0.451707	+	0.164408i	0.106141	+	0.994351i	$0.466151\pi$
$354$	12.6481	−	22.3229i	0.672242	−	1.18645i
$355$	15.8214	+	18.8552i	0.839712	+	1.00073i
$356$	1.43599	+	0.517632i	0.0761072	+	0.0274344i
$357$	−0.412710	+	2.43377i	−0.0218429	+	0.128809i
$358$	4.61394	−	26.4057i	0.243854	−	1.39559i
$359$	−16.7721	+	29.0501i	−0.885197	+	1.53321i	−0.0397083	+	0.999211i	$0.512643\pi$
$359$	−16.7721	+	29.0501i	−0.885197	+	1.53321i	−0.845488	+	0.533994i	$0.820690\pi$
$360$	−28.9664	−	9.96438i	−1.52666	−	0.525169i
$361$	−7.44326	−	12.8921i	−0.391751	−	0.678532i
$362$	−4.46633	+	1.63344i	−0.234745	+	0.0858517i
$363$	−19.6746	−	7.01527i	−1.03265	−	0.368206i
$364$	−2.00984	−	2.38024i	−0.105344	−	0.124758i
$365$	−3.73120	+	10.2514i	−0.195300	+	0.536582i
$366$	3.67739	+	19.9109i	0.192220	+	1.04076i
$367$	0.629860	−	3.57211i	0.0328784	−	0.186463i	−0.963946	−	0.266100i	$-0.914265\pi$
$367$	0.629860	−	3.57211i	0.0328784	−	0.186463i	0.996824	+	0.0796368i	$0.0253761\pi$
$368$	0.423964	−	0.744934i	0.0221007	−	0.0388324i
$369$	14.2471	+	4.97502i	0.741675	+	0.258989i
$370$	−0.00907943	−	5.87015i	−0.000472017	−	0.305175i
$371$	2.06338	−	2.45904i	0.107125	−	0.127667i
$372$	−0.00689297	−	0.00567147i	−0.000357384	−	0.000294052i
$373$	7.64585	−	1.34817i	0.395887	−	0.0698056i	0.0278392	−	0.999612i	$-0.491137\pi$
$373$	7.64585	−	1.34817i	0.395887	−	0.0698056i	0.368048	+	0.929807i	$0.380026\pi$
$374$	35.2930	+	12.7838i	1.82496	+	0.661035i
$375$	16.3590	−	9.58837i	0.844774	−	0.495141i
$376$	−1.51358	−	4.09924i	−0.0780568	−	0.211402i
$377$	−8.03850			−0.414004
$378$	1.85857	−	0.368520i	0.0955947	−	0.0189546i
$379$			13.5768i			0.697393i	0.937236	+	0.348696i	$0.113376\pi$
$379$			13.5768i			0.697393i	−0.937236	+	0.348696i	$0.886624\pi$
$380$	−2.49822	+	14.4290i	−0.128156	+	0.740191i
$381$	14.9384	−	26.2702i	0.765316	−	1.34586i
$382$	−2.81643	+	7.77547i	−0.144101	+	0.397828i
$383$	−0.0486221	−	0.275749i	−0.00248447	−	0.0140901i	0.983540	−	0.180689i	$-0.0578327\pi$
$383$	−0.0486221	−	0.275749i	−0.00248447	−	0.0140901i	−0.986025	+	0.166599i	$0.946722\pi$
$384$	19.3544	+	3.06687i	0.987677	+	0.156506i
$385$	−3.42414	−	2.87319i	−0.174510	−	0.146431i
$386$	0.0165395	+	10.6934i	0.000841840	+	0.544277i
$387$	15.0279	+	2.44717i	0.763913	+	0.124397i
$388$	10.3920	−	0.0321469i	0.527574	−	0.00163201i
$389$	31.5106	+	5.55617i	1.59765	+	0.281709i	0.900382	−	0.435101i	$-0.143287\pi$
$389$	31.5106	+	5.55617i	1.59765	+	0.281709i	0.697269	+	0.716810i	$0.254398\pi$
$390$	34.6678	+	40.6423i	1.75547	+	2.05800i
$391$	1.11299	+	0.405094i	0.0562862	+	0.0204865i
$392$	6.62176	−	18.4592i	0.334449	−	0.932330i
$393$	16.5984	+	19.5199i	0.837276	+	0.984648i
$394$	−16.1172	+	5.89441i	−0.811971	+	0.296956i
$395$	−33.7876	+	19.5073i	−1.70004	+	0.981518i
$396$	−0.466789	−	28.8085i	−0.0234570	−	1.44768i
$397$	−30.5442	−	17.6347i	−1.53297	−	0.885061i	−0.999223	−	0.0394172i	$-0.987450\pi$
$397$	−30.5442	−	17.6347i	−1.53297	−	0.885061i	−0.533748	−	0.845644i	$-0.679217\pi$
$398$	17.7107	+	3.09464i	0.887759	+	0.155120i
$399$	−0.315366	−	0.849104i	−0.0157881	−	0.0425084i
$400$	−24.4849	+	20.8047i	−1.22424	+	1.04024i
$401$	−0.0106231	+	0.00891385i	−0.000530493	+	0.000445136i	−0.643053	−	0.765822i	$-0.722332\pi$
$401$	−0.0106231	+	0.00891385i	−0.000530493	+	0.000445136i	0.642522	+	0.766267i	$0.277888\pi$
$402$	−3.99430	−	6.79069i	−0.199218	−	0.338689i
$403$	0.00532406	+	0.0146277i	0.000265210	+	0.000728659i
$404$	12.6444	+	7.24820i	0.629083	+	0.360611i
$405$	−31.8381	+	6.47874i	−1.58205	+	0.321931i
$406$	0.243258	+	0.419834i	0.0120727	+	0.0208360i
$407$	5.18839	−	1.88842i	0.257179	−	0.0936054i
$408$	0.303118	+	27.0767i	0.0150066	+	1.34050i
$409$	−28.7699	+	24.1408i	−1.42258	+	1.19369i	−0.472642	+	0.881254i	$0.656700\pi$
$409$	−28.7699	+	24.1408i	−1.42258	+	1.19369i	−0.949940	+	0.312434i	$0.898856\pi$
$410$	19.6476	−	16.5381i	0.970324	−	0.816760i
$411$	19.6515	−	7.29879i	0.969339	−	0.360023i
$412$	8.33959	−	3.06461i	0.410862	−	0.150983i
$413$	2.33894	+	1.35039i	0.115092	+	0.0664483i
$414$	−0.0133228	−	0.909026i	−0.000654779	−	0.0446762i
$415$	14.9983	+	25.9777i	0.736235	+	1.27520i
$416$	−26.3473	−	21.7630i	−1.29178	−	1.06702i
$417$	11.0310	+	12.9727i	0.540193	+	0.635274i
$418$	−13.5606	+	2.41273i	−0.663269	+	0.118010i
$419$	−10.9340	+	30.0410i	−0.534162	+	1.46760i	0.319913	+	0.947447i	$0.396346\pi$
$419$	−10.9340	+	30.0410i	−0.534162	+	1.46760i	−0.854075	+	0.520150i	$0.825876\pi$
$420$	1.07356	−	3.04053i	0.0523843	−	0.148363i
$421$	−10.9684	−	1.93402i	−0.534566	−	0.0942585i	−0.100153	−	0.994972i	$-0.531933\pi$
$421$	−10.9684	−	1.93402i	−0.534566	−	0.0942585i	−0.434413	+	0.900714i	$0.643044\pi$
$422$	18.4756	−	32.1153i	0.899379	−	1.56335i
$423$	−3.58922	−	2.93241i	−0.174514	−	0.142578i
$424$	17.4647	−	30.5765i	0.848160	−	1.48493i
$425$	−34.0114	−	28.5390i	−1.64980	−	1.38434i
$426$	−16.4701	−	2.76674i	−0.797977	−	0.134049i
$427$	−2.09898	+	0.370106i	−0.101577	+	0.0179107i
$428$	18.7261	−	3.36167i	0.905159	−	0.162493i
$429$	−24.8370	+	43.6776i	−1.19914	+	2.10877i
$430$	16.6248	−	19.8750i	0.801719	−	0.958458i
$431$	−34.2928			−1.65182			−0.825912	−	0.563799i	$-0.809339\pi$
$431$	−34.2928			−1.65182			−0.825912	+	0.563799i	$0.809339\pi$
$432$	19.3409	−	7.61119i	0.930539	−	0.366194i
$433$	−4.97925			−0.239288			−0.119644	−	0.992817i	$-0.538175\pi$
$433$	−4.97925			−0.239288			−0.119644	+	0.992817i	$0.538175\pi$
$434$	0.000602862	0	0.000720724i	2.89383e−5	0	3.45958e-5i
$435$	−4.20729	−	7.17818i	−0.201724	−	0.344167i
$436$	15.6280	−	2.80551i	0.748444	−	0.134359i
$437$	−0.427999	+	0.0754678i	−0.0204740	+	0.00361011i
$438$	−2.58795	−	6.93501i	−0.123657	−	0.331367i
$439$	30.4090	+	25.5162i	1.45134	+	1.21782i	0.931595	+	0.363499i	$0.118418\pi$
$439$	30.4090	+	25.5162i	1.45134	+	1.21782i	0.519746	+	0.854321i	$0.326027\pi$
$440$	−42.5768	−	24.3190i	−2.02977	−	1.15936i
$441$	−3.88018	−	20.4354i	−0.184770	−	0.973116i
$442$	23.5477	−	40.9318i	1.12005	−	1.94693i
$443$	−21.6555	−	3.81846i	−1.02889	−	0.181420i	−0.366371	−	0.930469i	$-0.619400\pi$
$443$	−21.6555	−	3.81846i	−1.02889	−	0.181420i	−0.662515	+	0.749049i	$0.730511\pi$
$444$	2.58954	+	3.02632i	0.122894	+	0.143623i
$445$	0.942354	−	2.58910i	0.0446719	−	0.122735i
$446$	−6.14064	+	1.09256i	−0.290768	+	0.0517341i
$447$	−9.66930	+	27.1179i	−0.457342	+	1.28263i
$448$	−0.339326	+	2.03465i	−0.0160316	+	0.0961281i
$449$	5.92233	+	10.2578i	0.279492	+	0.484094i	0.971259	−	0.238027i	$-0.0765006\pi$
$449$	5.92233	+	10.2578i	0.279492	+	0.484094i	−0.691767	+	0.722121i	$0.743167\pi$
$450$	−11.1852	+	32.1913i	−0.527276	+	1.51751i
$451$	20.9193	+	12.0777i	0.985050	+	0.568719i
$452$	−13.3447	+	4.90388i	−0.627682	+	0.230659i
$453$	−1.32803	+	7.83142i	−0.0623961	+	0.367952i
$454$	4.74600	−	3.99489i	0.222741	−	0.187490i
$455$	−4.30760	+	3.61451i	−0.201943	+	0.169451i
$456$	−5.06400	−	8.54865i	−0.237143	−	0.400327i
$457$	−15.6430	+	5.69358i	−0.731748	+	0.266335i	−0.680905	−	0.732372i	$-0.738413\pi$
$457$	−15.6430	+	5.69358i	−0.731748	+	0.266335i	−0.0508437	+	0.998707i	$0.516191\pi$
$458$	6.27112	+	10.8232i	0.293030	+	0.505735i
$459$	14.8468	+	24.5860i	0.692988	+	1.14758i
$460$	−1.34225	−	0.769424i	−0.0625829	−	0.0358746i
$461$	−0.915935	−	2.51651i	−0.0426594	−	0.117206i	0.916534	−	0.399957i	$-0.130975\pi$
$461$	−0.915935	−	2.51651i	−0.0426594	−	0.117206i	−0.959193	+	0.282752i	$0.908753\pi$
$462$	3.03280	−	0.0245689i	0.141099	−	0.00114305i
$463$	−9.61960	+	8.07180i	−0.447061	+	0.375128i	−0.838344	−	0.545142i	$-0.816476\pi$
$463$	−9.61960	+	8.07180i	−0.447061	+	0.375128i	0.391283	+	0.920270i	$0.372031\pi$
$464$	3.44647	+	4.05611i	0.159998	+	0.188300i
$465$	−0.0102756	+	0.0124103i	−0.000476521	+	0.000575514i
$466$	−33.7511	−	5.89742i	−1.56349	−	0.273193i
$467$	20.3871	+	11.7705i	0.943402	+	0.544673i	0.891025	−	0.453954i	$-0.149987\pi$
$467$	20.3871	+	11.7705i	0.943402	+	0.544673i	0.0523766	+	0.998627i	$0.483320\pi$
$468$	−35.7928	−	5.71495i	−1.65452	−	0.264173i
$469$	0.718200	−	0.414653i	0.0331634	−	0.0191469i
$470$	−7.40767	+	2.70915i	−0.341690	+	0.124964i
$471$	−2.91789	+	0.534245i	−0.134449	+	0.0246167i
$472$	27.8863	+	10.0035i	1.28357	+	0.460449i
$473$	22.9020	+	8.33564i	1.05303	+	0.383273i
$474$	8.85217	−	24.9481i	0.406594	−	1.14591i
$475$	16.0439	+	2.82897i	0.736143	+	0.129802i
$476$	−2.85038	+	0.00881744i	−0.130647	+	0.000404147i
$477$	−0.489567	−	37.3456i	−0.0224157	−	1.70994i
$478$	0.0474530	+	30.6799i	0.00217045	+	1.40327i
$479$	−7.82522	−	6.56614i	−0.357543	−	0.300015i	0.446267	−	0.894900i	$-0.352753\pi$
$479$	−7.82522	−	6.56614i	−0.357543	−	0.300015i	−0.803811	+	0.594885i	$0.797198\pi$
$480$	5.64384	−	34.9181i	0.257605	−	1.59378i
$481$	−1.20615	−	6.84041i	−0.0549957	−	0.311896i
$482$	−8.76497	+	24.1979i	−0.399233	+	1.10219i
$483$	0.0956962		0.000627219i	0.00435433		2.85394e-5i
$484$	4.11476	−	23.7656i	0.187035	−	1.08026i
$485$		−	18.7580i		−	0.851756i
$486$	13.5827	−	17.3640i	0.616126	−	0.787648i
$487$	12.9335			0.586075			0.293037	−	0.956101i	$-0.405334\pi$
$487$	12.9335			0.586075			0.293037	+	0.956101i	$0.405334\pi$
$488$	−21.9327	+	8.09829i	−0.992845	+	0.366592i
$489$	−0.146877	−	22.4094i	−0.00664203	−	1.01339i
$490$	−33.2823	−	12.0555i	−1.50354	−	0.544611i
$491$	−23.4853	+	4.14108i	−1.05987	+	0.186885i	−0.676301	−	0.736626i	$-0.736418\pi$
$491$	−23.4853	+	4.14108i	−1.05987	+	0.186885i	−0.383574	+	0.923510i	$0.625307\pi$
$492$	−2.86018	+	17.1890i	−0.128947	+	0.774939i
$493$	−4.72770	+	5.63425i	−0.212925	+	0.253754i
$494$	0.0268002	+	17.3272i	0.00120580	+	0.779590i
$495$	−52.0025	+	0.681706i	−2.33734	+	0.0306404i
$496$	0.00509827	−	0.00895801i	0.000228919	−	0.000402226i
$497$	0.305274	−	1.73129i	0.0136934	−	0.0776591i
$498$	−19.1815	−	6.80603i	−0.859543	−	0.304985i
$499$	11.7879	−	32.3871i	0.527701	−	1.44985i	−0.334071	−	0.942548i	$-0.608422\pi$
$499$	11.7879	−	32.3871i	0.527701	−	1.44985i	0.861771	−	0.507297i	$-0.169355\pi$
$500$	14.1258	+	16.7292i	0.631727	+	0.748151i
$501$	−4.50602	−	24.6106i	−0.201314	−	1.09952i
$502$	−19.3935	+	7.09264i	−0.865573	+	0.316560i
$503$	−2.19116	−	3.79521i	−0.0976991	−	0.169220i	0.813033	−	0.582218i	$-0.197815\pi$
$503$	−2.19116	−	3.79521i	−0.0976991	−	0.169220i	−0.910732	+	0.412998i	$0.864482\pi$
$504$	0.784668	+	2.04233i	0.0349519	+	0.0909725i
$505$	13.1538	−	22.7830i	0.585334	−	1.01383i
$506$	0.250479	−	1.43350i	0.0111351	−	0.0637268i
$507$	31.3432	+	25.9519i	1.39200	+	1.15257i
$508$	32.8279	+	11.8335i	1.45650	+	0.525027i
$509$	−3.18212	−	3.79231i	−0.141045	−	0.168091i	0.690897	−	0.722953i	$-0.257216\pi$
$509$	−3.18212	−	3.79231i	−0.141045	−	0.168091i	−0.831943	+	0.554862i	$0.812771\pi$
$510$	48.8758	−	0.395946i	2.16426	−	0.0175328i
$511$	0.732191	−	0.266496i	0.0323902	−	0.0117891i
$512$	0.314972	+	22.6252i	0.0139199	+	0.999903i
$513$	−9.22861	−	5.08888i	−0.407453	−	0.224680i
$514$	−7.08049	+	4.10254i	−0.312307	+	0.180955i
$515$	−5.48512	−	15.0702i	−0.241703	−	0.664075i
$516$	0.169615	+	17.5805i	0.00746688	+	0.773939i
$517$	−4.76875	−	5.68318i	−0.209729	−	0.249946i
$518$	−0.320761	+	0.269997i	−0.0140934	+	0.0118630i
$519$	−20.7409	−	3.51717i	−0.910423	−	0.154387i
$520$	−39.4298	+	47.4359i	−1.72911	+	2.08020i
$521$	−9.74864	+	16.8851i	−0.427096	+	0.739752i	−0.996614	−	0.0822273i	$-0.973797\pi$
$521$	−9.74864	+	16.8851i	−0.427096	+	0.739752i	0.569518	+	0.821979i	$0.307130\pi$
$522$	5.33274	+	1.85292i	0.233408	+	0.0811000i
$523$	−1.05708	+	0.610304i	−0.0462227	+	0.0266867i	−0.522933	−	0.852374i	$-0.675162\pi$
$523$	−1.05708	+	0.610304i	−0.0462227	+	0.0266867i	0.476711	+	0.879060i	$0.341829\pi$
$524$	−18.9478	+	22.7235i	−0.827738	+	0.992680i
$525$	−3.37895	−	1.20482i	−0.147469	−	0.0525825i
$526$	−6.14777	+	1.09382i	−0.268055	+	0.0476930i
$527$	0.0133839	+	0.00487136i	0.000583014	+	0.000212200i
$528$	32.6878	−	6.19416i	1.42255	−	0.269566i
$529$	−3.98593	+	22.6054i	−0.173302	+	0.982842i
$530$	−55.0937	−	31.6949i	−2.39312	−	1.37674i
$531$	30.8719	−	5.86179i	1.33972	−	0.254380i
$532$	0.904156	−	0.525751i	0.0392001	−	0.0227942i
$533$	19.5330	−	23.2785i	0.846066	−	1.00830i
$534$	0.653614	+	1.75151i	0.0282846	+	0.0757953i
$535$	−5.96333	−	33.8197i	−0.257817	−	1.46216i
$536$	6.94158	−	5.87978i	0.299830	−	0.253968i
$537$	28.3236	−	16.6011i	1.22226	−	0.716391i
$538$	8.21695	+	6.87321i	0.354258	+	0.296325i
$539$		−	33.2950i		−	1.43412i
$540$	−13.6304	−	34.9532i	−0.586558	−	1.50415i
$541$			25.7027i			1.10505i	0.833497	+	0.552524i	$0.186335\pi$
$541$			25.7027i			1.10505i	−0.833497	+	0.552524i	$0.813665\pi$
$542$	−5.46636	+	6.53506i	−0.234800	+	0.280705i
$543$	−5.06311	−	2.87911i	−0.217279	−	0.123554i
$544$	−30.7495	+	5.66751i	−1.31838	+	0.242993i
$545$	−4.97674	−	28.2245i	−0.213180	−	1.20900i
$546$	0.632081	−	3.76270i	0.0270506	−	0.161029i
$547$	−1.72787	+	2.05919i	−0.0738783	+	0.0880447i	−0.801718	−	0.597703i	$-0.796080\pi$
$547$	−1.72787	+	2.05919i	−0.0738783	+	0.0880447i	0.727839	+	0.685748i	$0.240525\pi$
$548$	12.1679	+	20.9257i	0.519787	+	0.893900i
$549$	−15.6896	+	19.2039i	−0.669617	+	0.819601i
$550$	−27.2018	+	47.2837i	−1.15989	+	2.01618i
$551$	0.468640	−	2.65779i	0.0199647	−	0.113226i
$552$	1.03171	−	0.193851i	0.0439126	−	0.00825085i
$553$	2.61851	+	0.953061i	0.111351	+	0.0405283i
$554$	0.109618	+	0.616101i	0.00465722	+	0.0261756i
$555$	5.47703	−	4.65729i	0.232487	−	0.197691i
$556$	−12.5925	+	15.1017i	−0.534039	+	0.640456i
$557$	23.1240	−	13.3506i	0.979795	−	0.565685i	0.0775865	−	0.996986i	$-0.475279\pi$
$557$	23.1240	−	13.3506i	0.979795	−	0.565685i	0.902208	+	0.431301i	$0.141945\pi$
$558$	−0.000160210	−	0.0109313i	−6.78222e−6	−	0.000462757i
$559$	15.3300	−	26.5523i	0.648389	−	1.12304i
$560$	3.67069	+	0.623851i	0.155115	+	0.0263625i
$561$	16.0066	+	43.0967i	0.675797	+	1.81954i
$562$	20.5677	+	24.4348i	0.867597	+	1.03072i
$563$	−13.8007	−	16.4470i	−0.581629	−	0.693159i	0.392345	−	0.919818i	$-0.371664\pi$
$563$	−13.8007	−	16.4470i	−0.581629	−	0.693159i	−0.973974	+	0.226659i	$0.927220\pi$
$564$	2.63107	−	4.66041i	0.110788	−	0.196239i
$565$	8.77709	+	24.1149i	0.369255	+	1.01452i
$566$	13.9506	+	24.0770i	0.586385	+	1.01203i
$567$	1.81617	+	1.44454i	0.0762719	+	0.0606648i
$568$	−0.0894821	−	19.2843i	−0.00375458	−	0.809149i
$569$	15.7460	−	5.73106i	0.660105	−	0.240259i	0.00982343	−	0.999952i	$-0.496873\pi$
$569$	15.7460	−	5.73106i	0.660105	−	0.240259i	0.650282	+	0.759693i	$0.274651\pi$
$570$	−15.4588	+	9.09289i	−0.647497	+	0.380859i
$571$	−7.89328	−	9.40685i	−0.330324	−	0.393664i	0.575163	−	0.818039i	$-0.304939\pi$
$571$	−7.89328	−	9.40685i	−0.330324	−	0.393664i	−0.905487	+	0.424374i	$0.860494\pi$
$572$	−54.5807	−	19.6747i	−2.28213	−	0.822643i
$573$	−9.49471	+	3.52644i	−0.396647	+	0.147319i
$574$	−1.80689	−	0.315722i	−0.0754180	−	0.0131780i
$575$	−0.860616	+	1.49063i	−0.0358902	+	0.0621636i
$576$	12.4623	+	20.5108i	0.519262	+	0.854615i
$577$	−2.56985	−	4.45111i	−0.106984	−	0.185302i	0.807563	−	0.589781i	$-0.200786\pi$
$577$	−2.56985	−	4.45111i	−0.106984	−	0.185302i	−0.914547	+	0.404479i	$0.867453\pi$
$578$	−6.58268	−	17.9991i	−0.273803	−	0.748663i
$579$	−9.97722	+	8.48394i	−0.414639	+	0.352580i
$580$	7.34061	−	6.19830i	0.304802	−	0.257370i
$581$	0.732765	−	2.01325i	0.0304002	−	0.0835239i
$582$	8.25987	+	9.68333i	0.342383	+	0.401387i
$583$	10.3813	−	58.8752i	0.429949	−	2.43836i
$584$	7.38224	−	4.30793i	0.305479	−	0.178264i
$585$	−10.5155	+	64.5748i	−0.434761	+	2.66984i
$586$	−0.999714	+	0.00154627i	−0.0412978	+	6.38758e-5i
$587$	2.99496	−	3.56925i	0.123615	−	0.147319i	−0.700687	−	0.713469i	$-0.747123\pi$
$587$	2.99496	−	3.56925i	0.123615	−	0.147319i	0.824302	+	0.566150i	$0.191568\pi$
$588$	22.4896	−	8.43214i	0.927456	−	0.347736i
$589$	−0.00514679		0.000907518i	−0.000212070		3.73936e-5i
$590$	18.2123	−	50.2796i	0.749787	−	2.06998i
$591$	−18.2707	−	10.3895i	−0.751556	−	0.427368i
$592$	−2.93444	+	3.54140i	−0.120605	+	0.145551i
$593$	5.90755			0.242594			0.121297	−	0.992616i	$-0.461295\pi$
$593$	5.90755			0.242594			0.121297	+	0.992616i	$0.461295\pi$
$594$	26.5448	−	23.2507i	1.08915	−	0.953986i
$595$			5.14504i			0.210926i
$596$	−32.7567	−	5.67147i	−1.34177	−	0.232312i
$597$	11.1346	+	18.9971i	0.455710	+	0.777500i
$598$	−1.72124	−	0.623468i	−0.0703868	−	0.0254955i
$599$	7.47843	+	42.4123i	0.305561	+	1.73292i	0.620854	+	0.783926i	$0.286786\pi$
$599$	7.47843	+	42.4123i	0.305561	+	1.73292i	−0.315294	+	0.948994i	$0.602103\pi$
$600$	−38.8275	−	6.39904i	−1.58513	−	0.261240i
$601$	−30.3485	−	25.4654i	−1.23794	−	1.03876i	−0.997682	−	0.0680483i	$-0.978323\pi$
$601$	−30.3485	−	25.4654i	−1.23794	−	1.03876i	−0.240260	−	0.970709i	$-0.577233\pi$
$602$	−1.85068	+	0.00286247i	−0.0754283	+	0.000116666i
$603$	3.18100	−	9.10951i	0.129540	−	0.370968i
$604$	−9.17200	+	0.0283729i	−0.373203	+	0.00115448i
$605$	−42.8745	−	7.55993i	−1.74310	−	0.307355i
$606$	3.24194	+	17.5532i	0.131695	+	0.713052i
$607$	22.7963	+	8.29716i	0.925272	+	0.336771i	0.760334	−	0.649533i	$-0.225035\pi$
$607$	22.7963	+	8.29716i	0.925272	+	0.336771i	0.164938	+	0.986304i	$0.447258\pi$
$608$	8.73159	−	7.44250i	0.354113	−	0.301833i
$609$	−0.199587	+	0.559748i	−0.00808767	+	0.0226821i
$610$	14.4951	+	39.6342i	0.586890	+	1.60474i
$611$	−8.08262	+	4.66650i	−0.326988	+	0.188787i
$612$	−25.0565	+	21.7263i	−1.01285	+	0.878234i
$613$	11.1793	+	6.45437i	0.451528	+	0.260690i	0.708475	−	0.705736i	$-0.249383\pi$
$613$	11.1793	+	6.45437i	0.451528	+	0.260690i	−0.256947	+	0.966425i	$0.582717\pi$
$614$	4.77167	−	27.3084i	0.192569	−	1.10208i
$615$	31.0105	+	5.25866i	1.25046	+	0.212050i
$616$	0.624129	+	3.44603i	0.0251469	+	0.138844i
$617$	36.0968	−	30.2888i	1.45320	−	1.21938i	0.523004	−	0.852330i	$-0.324811\pi$
$617$	36.0968	−	30.2888i	1.45320	−	1.21938i	0.930200	−	0.367053i	$-0.119633\pi$
$618$	9.46757	+	5.36432i	0.380842	+	0.215785i
$619$	12.7178	+	34.9419i	0.511173	+	1.40444i	0.880016	+	0.474944i	$0.157532\pi$
$619$	12.7178	+	34.9419i	0.511173	+	1.40444i	−0.368843	+	0.929492i	$0.620246\pi$
$620$	−0.0161409	−	0.00925251i	−0.000648235	−	0.000371590i
$621$	0.838711	−	0.732340i	0.0336563	−	0.0293878i
$622$	−31.2237	+	18.0914i	−1.25196	+	0.725401i
$623$	−0.184923	+	0.0673064i	−0.00740878	+	0.00269657i
$624$	−0.533241	−	41.8500i	−0.0213467	−	1.67534i
$625$	−0.491039	+	0.412031i	−0.0196416	+	0.0164812i
$626$	18.9730	+	22.5403i	0.758316	+	0.900892i
$627$	−12.9933	−	10.7583i	−0.518900	−	0.429645i
$628$	−1.18147	−	3.21509i	−0.0471459	−	0.128296i
$629$	−5.50388	−	3.17767i	−0.219454	−	0.126702i
$630$	3.69083	−	1.40494i	0.147046	−	0.0559741i
$631$	−19.0617	−	33.0158i	−0.758833	−	1.31434i	−0.943446	−	0.331526i	$-0.892436\pi$
$631$	−19.0617	−	33.0158i	−0.758833	−	1.31434i	0.184613	−	0.982811i	$-0.440897\pi$
$632$	30.1272	+	5.16822i	1.19840	+	0.205581i
$633$	44.6355	−	8.17244i	1.77410	−	0.324825i
$634$	−2.20515	−	12.3939i	−0.0875775	−	0.492224i
$635$	21.5430	−	59.1890i	0.854909	−	2.34884i
$636$	42.3972	−	7.89826i	1.68116	−	0.313186i
$637$	−41.2492	−	7.27335i	−1.63435	−	0.288180i
$638$	7.83291	+	4.50619i	0.310108	+	0.178402i
$639$	−10.4584	−	17.5783i	−0.413730	−	0.695388i
$640$	40.8408	−	0.442199i	1.61437	−	0.0174795i
$641$	20.1927	+	16.9437i	0.797565	+	0.669236i	0.947605	−	0.319444i	$-0.103496\pi$
$641$	20.1927	+	16.9437i	0.797565	+	0.669236i	−0.150041	+	0.988680i	$0.547940\pi$
$642$	17.9706	+	14.8327i	0.709242	+	0.585400i
$643$	−36.5216	+	6.43974i	−1.44027	+	0.253959i	−0.838583	−	0.544773i	$-0.816616\pi$
$643$	−36.5216	+	6.43974i	−1.44027	+	0.253959i	−0.601687	+	0.798732i	$0.705505\pi$
$644$	0.0195252	+	0.108764i	0.000769399	+	0.00428591i
$645$	31.7342	−	0.207994i	1.24953	−	0.00818977i
$646$	12.1606	+	10.1719i	0.478452	+	0.400209i
$647$	34.9632			1.37454			0.687272	−	0.726400i	$-0.258808\pi$
$647$	34.9632			1.37454			0.687272	+	0.726400i	$0.258808\pi$
$648$	22.4276	+	12.0417i	0.881039	+	0.473043i
$649$	50.2989			1.97440
$650$	52.6375	+	44.0295i	2.06461	+	1.72698i
$651$	0.00115077		7.54245e-6i	4.51022e−5		2.95612e-7i
$652$	25.4696	−	4.57226i	0.997466	−	0.179063i
$653$	7.50466	−	1.32327i	0.293680	−	0.0517837i	−0.0248671	−	0.999691i	$-0.507916\pi$
$653$	7.50466	−	1.32327i	0.293680	−	0.0517837i	0.318547	+	0.947907i	$0.396805\pi$
$654$	14.9975	+	12.3787i	0.586447	+	0.484046i
$655$	40.9106	+	34.3280i	1.59851	+	1.34131i
$656$	−20.1206	+	0.124485i	−0.785579	+	0.00486031i
$657$	4.42957	−	7.90991i	0.172814	−	0.308595i
$658$	0.488315	+	0.280923i	0.0190365	+	0.0109515i
$659$	−21.1078	−	3.72188i	−0.822245	−	0.144984i	−0.253329	−	0.967380i	$-0.581526\pi$
$659$	−21.1078	−	3.72188i	−0.822245	−	0.144984i	−0.568915	+	0.822396i	$0.692637\pi$
$660$	−10.9981	−	59.0368i	−0.428099	−	2.29800i
$661$	−5.23825	+	14.3920i	−0.203744	+	0.559783i	−0.998913	−	0.0466051i	$-0.985160\pi$
$661$	−5.23825	+	14.3920i	−0.203744	+	0.559783i	0.795169	+	0.606388i	$0.207382\pi$
$662$	2.25059	+	12.6493i	0.0874717	+	0.491629i
$663$	56.8891	−	10.4160i	2.20939	−	0.404523i
$664$	3.97361	−	23.1634i	0.154206	−	0.898916i
$665$	−0.943943	−	1.63496i	−0.0366045	−	0.0634009i
$666$	−0.776593	+	4.81596i	−0.0300924	+	0.186614i
$667$	0.246934	+	0.142568i	0.00956134	+	0.00552024i
$668$	27.1173	−	9.96498i	1.04920	−	0.385557i
$669$	−5.88374	−	4.87169i	−0.227479	−	0.188350i
$670$	−10.5744	−	12.5625i	−0.408523	−	0.485333i
$671$	−30.4074	+	25.5148i	−1.17387	+	0.984990i
$672$	−2.16961	+	1.29430i	−0.0836944	+	0.0499287i
$673$	−6.37794	+	2.32138i	−0.245851	+	0.0894826i	−0.462007	−	0.886876i	$-0.652870\pi$
$673$	−6.37794	+	2.32138i	−0.245851	+	0.0894826i	0.216155	+	0.976359i	$0.430648\pi$
$674$	10.4619	−	6.06177i	0.402977	−	0.233491i
$675$	−38.9329	+	15.0437i	−1.49853	+	0.579033i
$676$	−23.3680	+	40.7652i	−0.898768	+	1.56789i
$677$	5.34948	+	14.6976i	0.205597	+	0.564874i	0.999042	−	0.0437688i	$-0.0139365\pi$
$677$	5.34948	+	14.6976i	0.205597	+	0.564874i	−0.793444	+	0.608643i	$0.791714\pi$
$678$	−15.1497	−	8.58379i	−0.581819	−	0.329658i
$679$	−1.02632	+	0.861183i	−0.0393865	+	0.0330492i
$680$	10.0583	+	55.5352i	0.385718	+	2.12968i
$681$	7.49079	+	1.27026i	0.287048	+	0.0486766i
$682$	0.00301207	−	0.0172382i	0.000115338	−	0.000660083i
$683$	6.24942	+	3.60810i	0.239127	+	0.138060i	0.614776	−	0.788702i	$-0.289247\pi$
$683$	6.24942	+	3.60810i	0.239127	+	0.138060i	−0.375648	+	0.926762i	$0.622580\pi$
$684$	3.97625	−	11.5011i	0.152036	−	0.439755i
$685$	37.8392	−	21.8465i	1.44576	−	0.834711i
$686$	1.74512	+	4.77170i	0.0666290	+	0.182184i
$687$	−5.14529	+	14.4301i	−0.196305	+	0.550544i
$688$	−19.9706	+	3.64889i	−0.761371	+	0.139112i
$689$	−70.6726	−	25.7227i	−2.69241	−	0.979958i
$690$	−0.344145	−	1.86335i	−0.0131014	−	0.0709363i
$691$	42.2279	+	7.44592i	1.60643	+	0.283256i	0.903687	−	0.428193i	$-0.140850\pi$
$691$	42.2279	+	7.44592i	1.60643	+	0.283256i	0.702738	+	0.711449i	$0.251961\pi$
$692$	−0.0751433	−	24.2913i	−0.00285652	−	0.923416i
$693$	2.42475	+	2.81395i	0.0921085	+	0.106893i
$694$	−41.0155	+	0.0634391i	−1.55693	+	0.00240812i
$695$	27.1886	+	22.8140i	1.03132	+	0.865383i
$696$	−1.06005	+	6.43207i	−0.0401811	+	0.243807i
$697$	−4.82812	−	27.3816i	−0.182878	−	1.03715i
$698$	−29.6198	−	10.7289i	−1.12112	−	0.406093i
$699$	−21.2191	−	36.2026i	−0.802581	−	1.36931i
$700$	0.706677	−	4.08155i	0.0267099	−	0.154268i
$701$		−	33.1261i		−	1.25116i	−0.780162	−	0.625578i	$-0.784863\pi$
$701$		−	33.1261i		−	1.25116i	0.780162	−	0.625578i	$-0.215137\pi$
$702$	−23.0065	−	37.9655i	−0.868323	−	1.43291i
$703$	2.33198			0.0879524
$704$	13.4736	+	35.9761i	0.507806	+	1.35590i
$705$	−8.39746	−	4.77517i	−0.316267	−	0.179843i
$706$	4.34986	−	12.0089i	0.163709	−	0.451961i
$707$	−1.85043	+	0.326281i	−0.0695927	+	0.0122711i
$708$	12.7385	+	33.9751i	0.478740	+	1.27686i
$709$	28.0590	−	33.4394i	1.05378	−	1.25584i	0.0880950	−	0.996112i	$-0.471922\pi$
$709$	28.0590	−	33.4394i	1.05378	−	1.25584i	0.965681	−	0.259730i	$-0.0836335\pi$
$710$	−34.8090	+	0.0538395i	−1.30636	+	0.00202056i
$711$	30.3183	−	11.4872i	1.13703	−	0.430804i
$712$	−1.86446	+	1.08801i	−0.0698737	+	0.0407751i
$713$	9.58821e−5	0	0.000543774i	3.59081e−6	0	2.03645e-5i
$714$	−2.26556	−	2.65600i	−0.0847866	−	0.0993982i
$715$	−35.8181	+	98.4095i	−1.33952	+	3.68030i
$716$	24.4572	+	28.9645i	0.914009	+	1.08246i
$717$	−28.6253	+	24.3410i	−1.06903	+	0.909030i
$718$	−16.2939	−	44.5526i	−0.608083	−	1.66269i
$719$	7.51355	+	13.0138i	0.280208	+	0.485335i	0.971436	−	0.237302i	$-0.0762632\pi$
$719$	7.51355	+	13.0138i	0.280208	+	0.485335i	−0.691228	+	0.722637i	$0.742930\pi$
$720$	37.0920	−	22.3802i	1.38234	−	0.834060i
$721$	−0.572726	+	0.991990i	−0.0213294	+	0.0369436i
$722$	20.7385	+	3.62369i	0.771807	+	0.134860i
$723$	−29.5484	+	10.9746i	−1.09892	+	0.408149i
$724$	2.28070	−	6.32700i	0.0847615	−	0.235141i
$725$	−6.87044	−	8.18787i	−0.255162	−	0.304090i
$726$	25.4618	−	14.9767i	0.944976	−	0.555837i
$727$	−25.6575	+	9.33858i	−0.951586	+	0.346349i	−0.770731	−	0.637161i	$-0.780109\pi$
$727$	−25.6575	+	9.33858i	−0.951586	+	0.346349i	−0.180855	+	0.983510i	$0.557886\pi$
$728$	4.40562	−	0.0204428i	0.163283	−	0.000757661i
$729$	26.9791	−	1.06150i	0.999227	−	0.0393149i
$730$	−7.73469	−	13.3492i	−0.286274	−	0.494074i
$731$	−9.59469	−	26.3612i	−0.354872	−	0.975004i
$732$	−24.9352	−	14.0774i	−0.921632	−	0.520314i
$733$	27.3864	+	32.6378i	1.01154	+	1.20551i	0.978541	+	0.206051i	$0.0660612\pi$
$733$	27.3864	+	32.6378i	1.01154	+	1.20551i	0.0329983	+	0.999455i	$0.489494\pi$
$734$	3.30336	+	3.92445i	0.121929	+	0.144854i
$735$	−15.0946	−	40.6413i	−0.556773	−	1.49908i
$736$	0.423381	+	1.13582i	0.0156060	+	0.0418670i
$737$	7.72243	−	13.3756i	0.284459	−	0.492698i
$738$	−18.3240	+	10.9405i	−0.674515	+	0.402725i
$739$	40.4642	−	23.3620i	1.48850	−	0.859385i	0.488585	−	0.872516i	$-0.337513\pi$
$739$	40.4642	−	23.3620i	1.48850	−	0.859385i	0.999914	+	0.0131310i	$0.00417983\pi$
$740$	6.37592	+	5.31651i	0.234383	+	0.195439i
$741$	−16.1668	+	13.7472i	−0.593904	+	0.505015i
$742$	0.795224	+	4.46950i	0.0291936	+	0.164081i
$743$	−32.7196	−	11.9089i	−1.20036	−	0.436897i	−0.337013	−	0.941500i	$-0.609417\pi$
$743$	−32.7196	−	11.9089i	−1.20036	−	0.436897i	−0.863351	+	0.504603i	$0.831639\pi$
$744$	0.0124066	−	0.00233111i	0.000454847	−	8.54625e-5i
$745$	−10.4200	+	59.0949i	−0.381760	+	2.16507i
$746$	−5.47512	+	9.51715i	−0.200458	+	0.348448i
$747$	−8.83199	−	23.3104i	−0.323146	−	0.852881i
$748$	−45.8908	+	26.6847i	−1.67794	+	0.975690i
$749$	−1.57662	+	1.87895i	−0.0576086	+	0.0686553i
$750$	−4.44249	+	26.4456i	−0.162217	+	0.965658i
$751$	6.08986	+	34.5373i	0.222222	+	1.26028i	0.867925	+	0.496695i	$0.165453\pi$
$751$	6.08986	+	34.5373i	0.222222	+	1.26028i	−0.645703	+	0.763589i	$0.723436\pi$
$752$	5.82003	+	2.07763i	0.212235	+	0.0757635i
$753$	−21.9848	−	12.5015i	−0.801170	−	0.455581i
$754$	7.29383	−	8.71980i	0.265626	−	0.317556i
$755$			16.5558i			0.602528i
$756$	−1.28665	+	2.35048i	−0.0467949	+	0.0854861i
$757$		−	11.7722i		−	0.427866i	−0.976848	−	0.213933i	$-0.931373\pi$
$757$		−	11.7722i		−	0.427866i	0.976848	−	0.213933i	$-0.0686275\pi$
$758$	−14.7275	−	12.3191i	−0.534927	−	0.447449i
$759$	1.53762	−	0.901232i	0.0558120	−	0.0327126i
$760$	−13.3851	−	15.8023i	−0.485529	−	0.573208i
$761$	−0.482495	−	2.73637i	−0.0174904	−	0.0991932i	0.974813	−	0.223024i	$-0.0715930\pi$
$761$	−0.482495	−	2.73637i	−0.0174904	−	0.0991932i	−0.992303	+	0.123831i	$0.960482\pi$
$762$	14.9422	+	40.0410i	0.541298	+	1.45053i
$763$	−1.31578	+	1.56809i	−0.0476345	+	0.0567686i
$764$	−5.87896	−	10.1103i	−0.212693	−	0.365778i
$765$	39.0766	+	45.3489i	1.41282	+	1.63959i
$766$	0.343238	+	0.197462i	0.0124017	+	0.00713458i
$767$	10.9879	−	62.3153i	0.396749	−	2.25007i
$768$	−20.8883	+	18.2121i	−0.753741	+	0.657171i
$769$	−21.8665	−	7.95874i	−0.788525	−	0.286999i	−0.0838020	−	0.996482i	$-0.526706\pi$
$769$	−21.8665	−	7.95874i	−0.788525	−	0.286999i	−0.704723	+	0.709483i	$0.748929\pi$
$770$	6.22364	−	1.10732i	0.224284	−	0.0399052i
$771$	−9.44013	−	3.36602i	−0.339978	−	0.121224i
$772$	−11.6147	−	9.68480i	−0.418021	−	0.348564i
$773$	−15.8287	+	9.13870i	−0.569319	+	0.328696i	−0.756877	−	0.653557i	$-0.773276\pi$
$773$	−15.8287	+	9.13870i	−0.569319	+	0.328696i	0.187558	+	0.982253i	$0.439943\pi$
$774$	−16.2904	+	14.0812i	−0.585545	+	0.506137i
$775$	−0.0103491	+	0.0179252i	−0.000371751	+	0.000643892i
$776$	−9.39444	+	11.3020i	−0.337241	+	0.405716i
$777$	−0.506269	−	0.0858515i	−0.0181623	−	0.00307990i
$778$	−34.6186	+	29.1398i	−1.24114	+	1.04471i
$779$	6.55786	+	7.81535i	0.234960	+	0.280014i
$780$	−75.5432	+	0.728833i	−2.70488	+	0.0260964i
$781$	−11.1980	−	30.7662i	−0.400696	−	1.10090i
$782$	−1.44931	+	0.839752i	−0.0518273	+	0.0300295i
$783$	2.49211	+	6.44953i	0.0890606	+	0.230488i
$784$	14.0154	+	23.9322i	0.500549	+	0.854720i
$785$	−5.80991	+	2.11463i	−0.207364	+	0.0754745i
$786$	−36.2350	+	0.293542i	−1.29246	+	0.0104703i
$787$	0.462707	+	0.551432i	0.0164937	+	0.0196564i	0.774228	−	0.632906i	$-0.218138\pi$
$787$	0.462707	+	0.551432i	0.0164937	+	0.0196564i	−0.757735	+	0.652563i	$0.773694\pi$
$788$	8.23010	−	22.8315i	0.293185	−	0.813340i
$789$	−5.89057	−	4.87734i	−0.209710	−	0.173638i
$790$	9.49697	−	54.3515i	0.337887	−	1.93374i
$791$	0.916455	−	1.58735i	0.0325854	−	0.0564395i
$792$	31.6737	+	25.6334i	1.12548	+	0.910842i
$793$	24.9678	+	43.2455i	0.886632	+	1.53569i
$794$	46.8440	−	17.1319i	1.66243	−	0.607989i
$795$	−14.0198	−	76.5720i	−0.497231	−	2.71573i
$796$	−19.4270	+	16.4038i	−0.688571	+	0.581419i
$797$	−10.2956	+	28.2870i	−0.364690	+	1.00198i	0.612660	+	0.790347i	$0.290099\pi$
$797$	−10.2956	+	28.2870i	−0.364690	+	1.00198i	−0.977350	+	0.211630i	$0.932123\pi$
$798$	1.20722	+	0.428350i	0.0427352	+	0.0151634i
$799$	−1.48286	+	8.40970i	−0.0524597	+	0.297514i
$800$	−0.351400	−	45.4375i	−0.0124239	−	1.60646i
$801$	−1.11874	+	1.99773i	−0.0395286	+	0.0705864i
$802$	−3.03334e−5	−	0.0196116i	−1.07111e−6	−	0.000692508i
$803$	9.32772	−	11.1163i	0.329168	−	0.392287i
$804$	10.9905	+	1.82878i	0.387606	+	0.0644960i
$805$	0.196431	−	0.0346360i	0.00692327	−	0.00122076i
$806$	−0.0206983	−	0.00749735i	−0.000729068	−	0.000264083i
$807$	0.0859913	+	13.1199i	0.00302704	+	0.461842i
$808$	−19.3356	+	7.13935i	−0.680223	+	0.251162i
$809$	−29.5119			−1.03758			−0.518792	−	0.854901i	$-0.673618\pi$
$809$	−29.5119			−1.03758			−0.518792	+	0.854901i	$0.673618\pi$
$810$	21.8608	−	40.4151i	0.768110	−	1.42004i
$811$			12.2968i			0.431800i	0.976415	+	0.215900i	$0.0692685\pi$
$811$			12.2968i			0.431800i	−0.976415	+	0.215900i	$0.930731\pi$
$812$	−0.676141	−	0.117066i	−0.0237279	−	0.00410823i
$813$	−10.4344	+	0.0683901i	−0.365952	+	0.00239855i
$814$	−2.65927	+	7.34161i	−0.0932075	+	0.257323i
$815$	−8.11081	−	45.9987i	−0.284109	−	1.61126i
$816$	−29.6467	−	24.2396i	−1.03784	−	0.848556i
$817$	7.88533	+	6.61658i	0.275873	+	0.231485i
$818$	−0.0821502	−	53.1128i	−0.00287231	−	1.85705i
$819$	4.01589	−	2.38931i	0.140327	−	0.0834891i
$820$	0.112350	+	36.3189i	0.00392343	+	1.26831i
$821$	−35.5839	−	6.27441i	−1.24189	−	0.218978i	−0.486164	−	0.873868i	$-0.661604\pi$
$821$	−35.5839	−	6.27441i	−1.24189	−	0.218978i	−0.755725	+	0.654889i	$0.772715\pi$
$822$	−9.91367	+	27.9398i	−0.345779	+	0.974511i
$823$	−32.2737	−	11.7467i	−1.12499	−	0.409463i	−0.288519	−	0.957474i	$-0.593163\pi$
$823$	−32.2737	−	11.7467i	−1.12499	−	0.409463i	−0.836471	+	0.548011i	$0.815385\pi$
$824$	−4.24268	+	11.8271i	−0.147801	+	0.412017i
$825$	−65.7173	+	12.0324i	−2.28798	+	0.418913i
$826$	−3.58711	+	1.31189i	−0.124812	+	0.0456464i
$827$	7.34810	−	4.24243i	0.255518	−	0.147524i	−0.366770	−	0.930312i	$-0.619536\pi$
$827$	7.34810	−	4.24243i	0.255518	−	0.147524i	0.622289	+	0.782788i	$0.286203\pi$
$828$	0.998159	+	0.810364i	0.0346884	+	0.0281621i
$829$	16.3678	+	9.44995i	0.568477	+	0.328210i	0.756541	−	0.653947i	$-0.226888\pi$
$829$	16.3678	+	9.44995i	0.568477	+	0.328210i	−0.188064	+	0.982157i	$0.560221\pi$
$830$	−41.7883	−	7.30179i	−1.45049	−	0.253449i
$831$	−0.488784	+	0.590325i	−0.0169557	+	0.0204782i
$832$	47.5140	−	8.83342i	1.64725	−	0.306244i
$833$	−29.3579	+	24.6342i	−1.01719	+	0.853525i
$834$	−24.0813	+	0.195084i	−0.833868	+	0.00675521i
$835$	−17.8356	−	49.0029i	−0.617226	−	1.69581i
$836$	9.68713	−	16.8991i	0.335037	−	0.584468i
$837$	0.0100857	−	0.00880657i	0.000348613	−	0.000304399i
$838$	−22.6660	−	39.1188i	−0.782983	−	1.35133i
$839$	−44.5776	+	16.2249i	−1.53899	+	0.560147i	−0.965803	−	0.259277i	$-0.916516\pi$
$839$	−44.5776	+	16.2249i	−1.53899	+	0.560147i	−0.573188	+	0.819424i	$0.694293\pi$
$840$	2.32413	+	3.92341i	0.0801900	+	0.135371i
$841$	20.8589	−	17.5027i	0.719273	−	0.603541i
$842$	12.0502	−	10.1432i	0.415279	−	0.349556i
$843$	−6.53996	+	38.5664i	−0.225248	+	1.32830i
$844$	18.0732	+	49.1818i	0.622105	+	1.69291i
$845$	73.4516	+	42.4073i	2.52681	+	1.45886i
$846$	6.43767	−	1.23267i	0.221332	−	0.0423801i
$847$	1.55475	+	2.69290i	0.0534217	+	0.0925292i
$848$	17.3212	+	46.6889i	0.594813	+	1.60330i
$849$	−11.4461	+	32.1009i	−0.392828	+	1.10170i
$850$	61.8185	−	10.9989i	2.12036	−	0.377258i
$851$	−0.0842673	+	0.231522i	−0.00288864	+	0.00793649i
$852$	17.9456	−	15.3556i	0.614804	−	0.526073i
$853$	48.7404	+	8.59425i	1.66884	+	0.294262i	0.926649	−	0.375927i	$-0.122676\pi$
$853$	48.7404	+	8.59425i	1.66884	+	0.294262i	0.742191	+	0.670188i	$0.233787\pi$
$854$	1.50306	−	2.61270i	0.0514336	−	0.0894046i
$855$	−20.7375	−	7.24143i	−0.709207	−	0.247652i
$856$	−13.3447	+	23.3635i	−0.456114	+	0.798547i
$857$	21.0814	+	17.6894i	0.720126	+	0.604257i	0.927420	−	0.374021i	$-0.122021\pi$
$857$	21.0814	+	17.6894i	0.720126	+	0.604257i	−0.207294	+	0.978279i	$0.566466\pi$
$858$	−24.8433	−	66.5735i	−0.848137	−	2.27278i
$859$	40.4643	−	7.13496i	1.38063	−	0.243442i	0.566467	−	0.824084i	$-0.308310\pi$
$859$	40.4643	−	7.13496i	1.38063	−	0.243442i	0.814159	+	0.580643i	$0.197199\pi$
$860$	6.47481	+	36.0677i	0.220789	+	1.22990i
$861$	−1.13598	−	1.93813i	−0.0387141	−	0.0660511i
$862$	31.1160	−	37.1993i	1.05981	−	1.26701i
$863$	28.7460			0.978524			0.489262	−	0.872137i	$-0.337266\pi$
$863$	28.7460			0.978524			0.489262	+	0.872137i	$0.337266\pi$
$864$	−9.29291	+	27.8862i	−0.316151	+	0.948709i
$865$	−43.8467			−1.49083
$866$	4.51799	−	5.40127i	0.153527	−	0.183543i
$867$	11.6027	−	20.4041i	0.394047	−	0.692959i
$868$	0.000234795		0.00130791i	7.96945e−6		4.43935e-5i
$869$	51.1081	−	9.01174i	1.73372	−	0.305702i
$870$	11.6041	+	1.94933i	0.393416	+	0.0660884i
$871$	−14.8841	−	12.4892i	−0.504328	−	0.423182i
$872$	−11.1369	+	19.4981i	−0.377145	+	0.660290i
$873$	−2.50539	+	15.3854i	−0.0847945	+	0.520718i
$874$	0.306486	−	0.532751i	0.0103670	−	0.0180206i
$875$	−2.77990	−	0.490171i	−0.0939777	−	0.0165708i
$876$	9.87099	+	3.48527i	0.333510	+	0.117756i
$877$	8.94594	−	24.5788i	0.302083	−	0.829966i	−0.692055	−	0.721845i	$-0.743294\pi$
$877$	8.94594	−	24.5788i	0.302083	−	0.829966i	0.994138	−	0.108121i	$-0.0344834\pi$
$878$	−55.2707	+	9.83389i	−1.86530	+	0.331878i
$879$	−0.793157	−	0.932764i	−0.0267525	−	0.0314613i
$880$	65.0128	−	24.1193i	2.19158	−	0.813060i
$881$	−3.99560	−	6.92059i	−0.134615	−	0.233160i	0.790835	−	0.612029i	$-0.209647\pi$
$881$	−3.99560	−	6.92059i	−0.134615	−	0.233160i	−0.925450	+	0.378869i	$0.876313\pi$
$882$	25.6882	+	14.3333i	0.864966	+	0.482627i
$883$	−37.6003	−	21.7085i	−1.26535	−	0.730551i	−0.291246	−	0.956648i	$-0.594070\pi$
$883$	−37.6003	−	21.7085i	−1.26535	−	0.730551i	−0.974105	+	0.226097i	$0.927403\pi$
$884$	23.0348	+	62.6834i	0.774743	+	2.10827i
$885$	61.3970	−	22.8035i	2.06384	−	0.766531i
$886$	23.7915	−	20.0262i	0.799291	−	0.672795i
$887$	−41.5415	+	34.8574i	−1.39483	+	1.17040i	−0.431484	+	0.902121i	$0.642010\pi$
$887$	−41.5415	+	34.8574i	−1.39483	+	1.17040i	−0.963342	+	0.268277i	$0.913546\pi$
$888$	−5.63247	+	0.0630542i	−0.189013	+	0.00211596i
$889$	−4.22749	+	1.53868i	−0.141786	+	0.0516057i
$890$	1.95348	+	3.37147i	0.0654808	+	0.113012i
$891$	42.7439	+	6.38651i	1.43197	+	0.213956i
$892$	4.38663	−	7.65244i	0.146875	−	0.256223i
$893$	−1.07169	−	2.94443i	−0.0358626	−	0.0985317i
$894$	−20.6427	−	35.0946i	−0.690395	−	1.17374i
$895$	52.4182	−	43.9841i	1.75215	−	1.47023i
$896$	−1.89920	−	2.21425i	−0.0634480	−	0.0739728i
$897$	−0.780641	−	2.10183i	−0.0260648	−	0.0701780i
$898$	−16.5009	−	2.88324i	−0.550641	−	0.0962150i
$899$	0.00296945	+	0.00171441i	9.90366e−5	+	5.71788e-5i
$900$	−24.7707	−	41.3424i	−0.825689	−	1.37808i
$901$	−59.5941	+	34.4067i	−1.98537	+	1.14625i
$902$	−32.0827	+	11.7334i	−1.06824	+	0.390679i
$903$	−1.46830	−	1.72674i	−0.0488621	−	0.0574625i
$904$	6.78898	−	18.9253i	0.225798	−	0.629447i
$905$	−11.4076	−	4.15204i	−0.379203	−	0.138018i
$906$	−7.29017	−	8.54652i	−0.242200	−	0.283939i
$907$	−12.0222	−	2.11983i	−0.399190	−	0.0703879i	−0.0295505	−	0.999563i	$-0.509408\pi$
$907$	−12.0222	−	2.11983i	−0.399190	−	0.0703879i	−0.369639	+	0.929175i	$0.620519\pi$
$908$	0.0271388	+	8.77306i	0.000900634	+	0.291144i
$909$	−13.8318	+	16.9299i	−0.458771	+	0.561529i
$910$	−0.0123000	−	7.95236i	−0.000407741	−	0.263618i
$911$	−8.79514	−	7.38000i	−0.291396	−	0.244510i	0.485356	−	0.874316i	$-0.338690\pi$
$911$	−8.79514	−	7.38000i	−0.291396	−	0.244510i	−0.776752	+	0.629806i	$0.783134\pi$
$912$	13.8681	+	2.26353i	0.459218	+	0.0749529i
$913$	−6.92871	−	39.2947i	−0.229307	−	1.30046i
$914$	8.01772	−	22.1350i	0.265203	−	0.732160i
$915$	−25.5492	+	44.9300i	−0.844630	+	1.48534i
$916$	−17.4307	−	3.01794i	−0.575926	−	0.0997154i
$917$		−	3.81438i		−	0.125962i
$918$	−40.1412	−	6.20328i	−1.32486	−	0.204739i
$919$	−16.5475			−0.545852			−0.272926	−	0.962035i	$-0.587991\pi$
$919$	−16.5475			−0.545852			−0.272926	+	0.962035i	$0.587991\pi$
$920$	2.05255	−	0.757870i	0.0676705	−	0.0249863i
$921$	29.2919	−	17.1686i	0.965200	−	0.565726i
$922$	3.56088	+	1.28982i	0.117271	+	0.0424780i
$923$	−40.5625	+	7.15226i	−1.33513	+	0.235420i
$924$	−2.72520	+	3.31214i	−0.0896524	+	0.108961i
$925$	5.93664	−	7.07501i	0.195196	−	0.232625i
$926$	−0.0274680	−	17.7590i	−0.000902653	−	0.583595i
$927$	2.48610	+	13.0933i	0.0816542	+	0.430042i
$928$	−7.52708	+	0.0582122i	−0.247088	+	0.00191091i
$929$	2.54299	−	14.4220i	0.0834326	−	0.473170i	−0.914251	−	0.405148i	$-0.867220\pi$
$929$	2.54299	−	14.4220i	0.0834326	−	0.473170i	0.997684	−	0.0680222i	$-0.0216689\pi$
$930$	−0.00413842	−	0.0224072i	−0.000135704	−	0.000734760i
$931$	4.80961	−	13.2143i	0.157629	−	0.433081i
$932$	37.0218	−	31.2606i	1.21269	−	1.02398i
$933$	−41.6293	−	14.8436i	−1.36288	−	0.485956i
$934$	−31.2666	+	11.4349i	−1.02307	+	0.374161i
$935$	47.9102	+	82.9830i	1.56683	+	2.71383i
$936$	38.6763	−	33.6409i	1.26418	−	1.09959i
$937$	12.7855	−	22.1452i	0.417685	−	0.723452i	−0.578021	−	0.816022i	$-0.696175\pi$
$937$	12.7855	−	22.1452i	0.417685	−	0.723452i	0.995706	+	0.0925699i	$0.0295082\pi$
$938$	−0.201871	+	1.15531i	−0.00659131	+	0.0377223i
$939$	−6.03290	+	35.5762i	−0.196876	+	1.16099i
$940$	3.78267	−	10.4937i	0.123377	−	0.342266i
$941$	−4.21884	−	5.02781i	−0.137530	−	0.163902i	0.692883	−	0.721050i	$-0.256340\pi$
$941$	−4.21884	−	5.02781i	−0.137530	−	0.163902i	−0.830413	+	0.557148i	$0.811896\pi$
$942$	2.06806	−	3.64995i	0.0673810	−	0.118922i
$943$	−1.01289	+	0.368662i	−0.0329842	+	0.0120053i
$944$	−36.1544	+	21.1730i	−1.17672	+	0.689124i
$945$	4.23548	+	2.33555i	0.137780	+	0.0759754i
$946$	−29.8225	+	17.2796i	−0.969614	+	0.561808i
$947$	16.2688	+	44.6981i	0.528664	+	1.45249i	0.860645	+	0.509206i	$0.170061\pi$
$947$	16.2688	+	44.6981i	0.528664	+	1.45249i	−0.331981	+	0.943286i	$0.607717\pi$
$948$	19.0305	+	32.2394i	0.618082	+	1.04709i
$949$	−11.7344	−	13.9845i	−0.380914	−	0.453956i
$950$	−17.6263	+	14.8368i	−0.571874	+	0.481368i
$951$	9.83270	−	11.8754i	0.318847	−	0.385085i
$952$	2.57676	−	3.09996i	0.0835133	−	0.100470i
$953$	0.186102	−	0.322338i	0.00602843	−	0.0104416i	−0.862995	−	0.505212i	$-0.831414\pi$
$953$	0.186102	−	0.322338i	0.00602843	−	0.0104416i	0.869024	+	0.494770i	$0.164748\pi$
$954$	40.9550	+	33.3549i	1.32597	+	1.07990i
$955$	−18.2821	+	10.5552i	−0.591596	+	0.341558i
$956$	−33.3233	−	27.7863i	−1.07775	−	0.898675i
$957$	1.99325	+	10.8866i	0.0644327	+	0.351913i
$958$	14.2230	−	2.53058i	0.459523	−	0.0817594i
$959$	−2.93251	−	1.06735i	−0.0946956	−	0.0344664i
$960$	32.7565	+	37.8055i	1.05721	+	1.22017i
$961$	−5.38309	+	30.5290i	−0.173648	+	0.984808i
$962$	8.51459	+	4.89836i	0.274521	+	0.157929i
$963$	0.374077	+	28.5357i	0.0120545	+	0.919550i
$964$	−18.2958	−	31.4641i	−0.589269	−	1.01339i
$965$	−17.5461	+	20.9107i	−0.564830	+	0.673138i
$966$	−0.0861507	+	0.104376i	−0.00277185	+	0.00335824i
$967$	−1.69350	−	9.60434i	−0.0544594	−	0.308855i	0.945395	−	0.325927i	$-0.105676\pi$
$967$	−1.69350	−	9.60434i	−0.0544594	−	0.308855i	−0.999854	+	0.0170726i	$0.994565\pi$
$968$	22.0463	+	26.0275i	0.708595	+	0.836557i
$969$	0.127262	+	19.4166i	0.00408824	+	0.623752i
$970$	20.3478	+	17.0203i	0.653329	+	0.546488i
$971$		−	0.0717145i		−	0.00230143i	−0.999999	−	0.00115071i	$-0.999634\pi$
$971$		−	0.0717145i		−	0.00230143i	0.999999	−	0.00115071i	$-0.000366284\pi$
$972$	6.51125	+	30.4894i	0.208848	+	0.977948i
$973$		−	2.53499i		−	0.0812679i
$974$	−11.7354	+	14.0297i	−0.376027	+	0.449542i
$975$	0.550857	+	84.0455i	0.0176415	+	2.69161i
$976$	11.1162	−	31.1397i	0.355822	−	0.996756i
$977$	8.23563	+	46.7066i	0.263481	+	1.49428i	0.773325	+	0.634010i	$0.218592\pi$
$977$	8.23563	+	46.7066i	0.263481	+	1.49428i	−0.509844	+	0.860267i	$0.670297\pi$
$978$	24.4420	+	20.1741i	0.781569	+	0.645098i
$979$	−2.35582	+	2.80755i	−0.0752922	+	0.0897298i
$980$	43.2763	−	25.1644i	1.38241	−	0.803848i
$981$	0.312189	+	23.8146i	0.00996742	+	0.760343i
$982$	16.8176	−	29.2332i	0.536670	−	0.932869i
$983$	−0.121491	+	0.689011i	−0.00387497	+	0.0219760i	−0.986684	−	0.162649i	$-0.947996\pi$
$983$	−0.121491	+	0.689011i	−0.00387497	+	0.0219760i	0.982809	+	0.184625i	$0.0591072\pi$
$984$	−16.0506	−	18.6992i	−0.511675	−	0.596109i
$985$	−41.1655	−	14.9830i	−1.31164	−	0.477398i
$986$	−1.82205	−	10.2407i	−0.0580258	−	0.326130i
$987$	0.124262	+	0.678685i	0.00395531	+	0.0216028i
$988$	−18.8201	−	15.6930i	−0.598748	−	0.499261i
$989$	−0.941843	+	0.543774i	−0.0299489	+	0.0172910i
$990$	46.4456	−	57.0286i	1.47614	−	1.81249i
$991$	−9.00116	+	15.5905i	−0.285931	+	0.495247i	−0.972835	−	0.231501i	$-0.925636\pi$
$991$	−9.00116	+	15.5905i	−0.285931	+	0.495247i	0.686903	+	0.726749i	$0.258970\pi$
$992$	0.00509126	+	0.0136585i	0.000161648	+	0.000433659i
$993$	−10.0353	+	12.1201i	−0.318462	+	0.384620i
$994$	1.60104	+	1.90206i	0.0507818	+	0.0603296i
$995$	29.5008	+	35.1577i	0.935239	+	1.11457i
$996$	24.7874	−	14.6317i	0.785420	−	0.463622i
$997$	14.7188	+	40.4396i	0.466150	+	1.28074i	0.920789	+	0.390061i	$0.127546\pi$
$997$	14.7188	+	40.4396i	0.466150	+	1.28074i	−0.454639	+	0.890676i	$0.650232\pi$
$998$	24.4361	+	42.1738i	0.773512	+	1.33499i
$999$	−5.11434	+	3.08841i	−0.161811	+	0.0977129i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.61.11	yes	204
3.2	odd	2		648.2.t.a.181.24		204
4.3	odd	2		864.2.bf.a.817.34		204
8.3	odd	2		864.2.bf.a.817.1		204
8.5	even	2	inner	216.2.t.a.61.2	✓	204
24.5	odd	2		648.2.t.a.181.33		204
27.4	even	9	inner	216.2.t.a.85.2	yes	204
27.23	odd	18		648.2.t.a.469.33		204
108.31	odd	18		864.2.bf.a.625.1		204
216.77	odd	18		648.2.t.a.469.24		204
216.85	even	18	inner	216.2.t.a.85.11	yes	204
216.139	odd	18		864.2.bf.a.625.34		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.61.2	✓	204	8.5	even	2	inner
216.2.t.a.61.11	yes	204	1.1	even	1	trivial
216.2.t.a.85.2	yes	204	27.4	even	9	inner
216.2.t.a.85.11	yes	204	216.85	even	18	inner
648.2.t.a.181.24		204	3.2	odd	2
648.2.t.a.181.33		204	24.5	odd	2
648.2.t.a.469.24		204	216.77	odd	18
648.2.t.a.469.33		204	27.23	odd	18
864.2.bf.a.625.1		204	108.31	odd	18
864.2.bf.a.625.34		204	216.139	odd	18
864.2.bf.a.817.1		204	8.3	odd	2
864.2.bf.a.817.34		204	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.907362 + 1.08476i) q^{2} +(-1.73201 + 0.0113521i) q^{3} +(-0.353388 - 1.96853i) q^{4} +(-3.55522 + 0.626880i) q^{5} +(1.55925 - 1.88911i) q^{6} +(0.197520 + 0.165739i) q^{7} +(2.45603 + 1.40283i) q^{8} +(2.99974 - 0.0393239i) q^{9} +O(q^{10})\)	\(q+(-0.907362 + 1.08476i) q^{2} +(-1.73201 + 0.0113521i) q^{3} +(-0.353388 - 1.96853i) q^{4} +(-3.55522 + 0.626880i) q^{5} +(1.55925 - 1.88911i) q^{6} +(0.197520 + 0.165739i) q^{7} +(2.45603 + 1.40283i) q^{8} +(2.99974 - 0.0393239i) q^{9} +(2.54586 - 4.42535i) q^{10} +(4.72909 + 0.833866i) q^{11} +(0.634419 + 3.40551i) q^{12} +(2.06615 - 5.67671i) q^{13} +(-0.359008 + 0.0638755i) q^{14} +(6.15057 - 1.12612i) q^{15} +(-3.75023 + 1.39131i) q^{16} +(-2.76368 - 4.78684i) q^{17} +(-2.67920 + 3.28967i) q^{18} +(1.75645 + 1.01409i) q^{19} +(2.49040 + 6.77702i) q^{20} +(-0.343988 - 0.284820i) q^{21} +(-5.19554 + 4.37328i) q^{22} +(-0.164150 + 0.137738i) q^{23} +(-4.26979 - 2.40184i) q^{24} +(7.54812 - 2.74729i) q^{25} +(4.28309 + 7.39210i) q^{26} +(-5.19515 + 0.102163i) q^{27} +(0.256461 - 0.447394i) q^{28} +(-0.455110 - 1.25040i) q^{29} +(-4.35922 + 7.69366i) q^{30} +(-0.00197394 + 0.00165633i) q^{31} +(1.89359 - 5.33051i) q^{32} +(-8.20031 - 1.39058i) q^{33} +(7.70020 + 1.34548i) q^{34} +(-0.806124 - 0.465416i) q^{35} +(-1.13748 - 5.89119i) q^{36} +(0.995752 - 0.574898i) q^{37} +(-2.69377 + 0.985173i) q^{38} +(-3.51416 + 9.85559i) q^{39} +(-9.61111 - 3.44774i) q^{40} +(4.72689 + 1.72045i) q^{41} +(0.621081 - 0.114709i) q^{42} +(4.99819 + 0.881316i) q^{43} +(-0.0297094 - 9.60404i) q^{44} +(-10.6401 + 2.02028i) q^{45} +(-0.000468717 - 0.303041i) q^{46} +(-1.18349 - 0.993067i) q^{47} +(6.47966 - 2.45234i) q^{48} +(-1.20399 - 6.82818i) q^{49} +(-3.86874 + 10.6806i) q^{50} +(4.84107 + 8.25949i) q^{51} +(-11.9049 - 2.06121i) q^{52} -12.4496i q^{53} +(4.60306 - 5.72816i) q^{54} -17.3357 q^{55} +(0.252610 + 0.684146i) q^{56} +(-3.05370 - 1.73647i) q^{57} +(1.76933 + 0.640886i) q^{58} +(10.3154 - 1.81887i) q^{59} +(-4.39035 - 11.7096i) q^{60} +(-5.31333 + 6.33218i) q^{61} +(-5.63643e-6 - 0.00364414i) q^{62} +(0.599026 + 0.489406i) q^{63} +(4.06412 + 6.89078i) q^{64} +(-3.78700 + 21.4771i) q^{65} +(8.94909 - 7.63357i) q^{66} +(1.10004 - 3.02234i) q^{67} +(-8.44639 + 7.13200i) q^{68} +(0.282746 - 0.240428i) q^{69} +(1.23631 - 0.452146i) q^{70} +(-3.40904 - 5.90464i) q^{71} +(7.42261 + 4.11156i) q^{72} +(1.51096 - 2.61705i) q^{73} +(-0.279884 + 1.60179i) q^{74} +(-13.0423 + 4.84403i) q^{75} +(1.37555 - 3.81599i) q^{76} +(0.795884 + 0.948498i) q^{77} +(-7.50228 - 12.7546i) q^{78} +(10.1554 - 3.69627i) q^{79} +(12.4607 - 7.29735i) q^{80} +(8.99691 - 0.235923i) q^{81} +(-6.15527 + 3.56645i) q^{82} +(-2.84189 - 7.80804i) q^{83} +(-0.439115 + 0.777804i) q^{84} +(12.8263 + 15.2857i) q^{85} +(-5.49118 + 4.62214i) q^{86} +(0.802451 + 2.16055i) q^{87} +(10.4450 + 8.68211i) q^{88} +(-0.381609 + 0.660965i) q^{89} +(7.46289 - 13.3750i) q^{90} +(1.34896 - 0.778820i) q^{91} +(0.329150 + 0.274459i) q^{92} +(0.00340009 - 0.00289120i) q^{93} +(2.15109 - 0.382727i) q^{94} +(-6.88026 - 2.50421i) q^{95} +(-3.21921 + 9.25401i) q^{96} +(-0.902281 + 5.11709i) q^{97} +(8.49936 + 4.88960i) q^{98} +(14.2188 + 2.31542i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26} - 12 q^{28} - 39 q^{30} - 12 q^{31} - 36 q^{32} - 36 q^{36} - 42 q^{38} - 12 q^{39} - 21 q^{40} - 24 q^{41} - 66 q^{42} + 21 q^{44} - 3 q^{46} - 12 q^{47} + 51 q^{48} - 12 q^{49} - 99 q^{50} - 33 q^{52} - 90 q^{54} - 24 q^{55} + 99 q^{56} - 30 q^{57} + 21 q^{58} + 102 q^{60} - 36 q^{62} - 72 q^{63} - 3 q^{64} - 12 q^{65} - 9 q^{66} + 75 q^{68} + 9 q^{70} - 90 q^{71} + 60 q^{72} - 6 q^{73} + 9 q^{74} - 18 q^{76} + 12 q^{78} - 12 q^{79} + 78 q^{80} - 12 q^{81} - 12 q^{82} + 102 q^{84} - 30 q^{86} - 48 q^{87} - 30 q^{88} - 6 q^{89} + 6 q^{90} + 111 q^{92} - 33 q^{94} - 42 q^{95} + 126 q^{96} - 12 q^{97} + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more