LMFDB - Embedded newform 756.2.bt.a.367.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(103,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14, 15]))

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

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

chi := DirichletCharacter("756.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bt (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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$840$
Relative dimension:	$140$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			367.8
Character	$\chi$	$=$	756.367
Dual form			756.2.bt.a.103.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39646 - 0.223410i) q^{2} +(0.897457 - 1.48141i) q^{3} +(1.90018 + 0.623965i) q^{4} +(-1.37715 + 0.242829i) q^{5} +(-1.58422 + 1.86822i) q^{6} +(-1.27459 - 2.31850i) q^{7} +(-2.51411 - 1.29586i) q^{8} +(-1.38914 - 2.65900i) q^{9} +O(q^{10})$	\(q+(-1.39646 - 0.223410i) q^{2} +(0.897457 - 1.48141i) q^{3} +(1.90018 + 0.623965i) q^{4} +(-1.37715 + 0.242829i) q^{5} +(-1.58422 + 1.86822i) q^{6} +(-1.27459 - 2.31850i) q^{7} +(-2.51411 - 1.29586i) q^{8} +(-1.38914 - 2.65900i) q^{9} +(1.97738 - 0.0314303i) q^{10} +(-4.43886 - 0.782690i) q^{11} +(2.62967 - 2.25495i) q^{12} +(-1.32849 - 1.58323i) q^{13} +(1.26193 + 3.52243i) q^{14} +(-0.876208 + 2.25806i) q^{15} +(3.22134 + 2.37129i) q^{16} +7.45773i q^{17} +(1.34582 + 4.02353i) q^{18} +2.98154 q^{19} +(-2.76835 - 0.397877i) q^{20} +(-4.57853 - 0.192568i) q^{21} +(6.02380 + 2.08468i) q^{22} +(3.92885 + 4.68222i) q^{23} +(-4.17600 + 2.56145i) q^{24} +(-2.86088 + 1.04127i) q^{25} +(1.50147 + 2.50771i) q^{26} +(-5.18576 - 0.328457i) q^{27} +(-0.975280 - 5.20085i) q^{28} +(1.56570 + 1.31378i) q^{29} +(1.72806 - 2.95752i) q^{30} +(1.57365 + 0.572762i) q^{31} +(-3.96868 - 4.03107i) q^{32} +(-5.14317 + 5.87333i) q^{33} +(1.66613 - 10.4144i) q^{34} +(2.31830 + 2.88342i) q^{35} +(-0.980488 - 5.91934i) q^{36} +(-2.43730 + 4.22153i) q^{37} +(-4.16359 - 0.666106i) q^{38} +(-3.53768 + 0.547152i) q^{39} +(3.77699 + 1.17410i) q^{40} +(-4.22870 - 5.03957i) q^{41} +(6.35069 + 1.29180i) q^{42} +(-1.40080 - 3.84866i) q^{43} +(-7.94624 - 4.25694i) q^{44} +(2.55874 + 3.32453i) q^{45} +(-4.44041 - 7.41626i) q^{46} +(-9.51207 + 3.46211i) q^{47} +(6.40385 - 2.64399i) q^{48} +(-3.75085 + 5.91025i) q^{49} +(4.22772 - 0.814944i) q^{50} +(11.0479 + 6.69299i) q^{51} +(-1.53648 - 3.83735i) q^{52} +(7.07518 - 12.2546i) q^{53} +(7.16830 + 1.61723i) q^{54} +6.30305 q^{55} +(0.200013 + 7.48064i) q^{56} +(2.67581 - 4.41688i) q^{57} +(-1.89292 - 2.18442i) q^{58} +(-3.24290 + 2.72111i) q^{59} +(-3.07390 + 3.74398i) q^{60} +(1.28096 + 3.51941i) q^{61} +(-2.06957 - 1.15141i) q^{62} +(-4.39431 + 6.60985i) q^{63} +(4.64151 + 6.51586i) q^{64} +(2.21399 + 1.85776i) q^{65} +(8.49437 - 7.05280i) q^{66} +(-5.50023 + 0.969838i) q^{67} +(-4.65336 + 14.1710i) q^{68} +(10.4623 - 1.61814i) q^{69} +(-2.59322 - 4.54450i) q^{70} +(-5.69937 + 3.29053i) q^{71} +(0.0467655 + 8.48515i) q^{72} +(5.51115 - 3.18187i) q^{73} +(4.34672 - 5.35067i) q^{74} +(-1.02496 + 5.17262i) q^{75} +(5.66545 + 1.86038i) q^{76} +(3.84305 + 11.2891i) q^{77} +(5.06245 + 0.0262798i) q^{78} +(-0.993400 - 0.175163i) q^{79} +(-5.01209 - 2.48339i) q^{80} +(-5.14058 + 7.38745i) q^{81} +(4.77930 + 7.98227i) q^{82} +(-11.6449 - 9.77122i) q^{83} +(-8.57985 - 3.22275i) q^{84} +(-1.81096 - 10.2704i) q^{85} +(1.09632 + 5.68743i) q^{86} +(3.35139 - 1.14038i) q^{87} +(10.1455 + 7.71989i) q^{88} +0.187713i q^{89} +(-2.83044 - 5.21421i) q^{90} +(-1.97744 + 5.09807i) q^{91} +(4.54397 + 11.3485i) q^{92} +(2.26078 - 1.81719i) q^{93} +(14.0566 - 2.70959i) q^{94} +(-4.10604 + 0.724006i) q^{95} +(-9.53339 + 2.26152i) q^{96} +(-4.61209 - 12.6716i) q^{97} +(6.55831 - 7.41543i) q^{98} +(4.08502 + 12.8902i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	$ 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) $ 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.39646	−	0.223410i	−0.987443	−	0.157975i
$2$	−1.39646	−	0.223410i	−0.987443	−	0.157975i
$3$	0.897457	−	1.48141i	0.518147	−	0.855291i
$3$	0.897457	−	1.48141i	0.518147	−	0.855291i
$4$	1.90018	+	0.623965i	0.950088	+	0.311982i
$5$	−1.37715	+	0.242829i	−0.615882	+	0.108597i	−0.472882	−	0.881126i	$-0.656786\pi$
$5$	−1.37715	+	0.242829i	−0.615882	+	0.108597i	−0.143000	+	0.989723i	$0.545675\pi$
$6$	−1.58422	+	1.86822i	−0.646756	+	0.762697i
$7$	−1.27459	−	2.31850i	−0.481749	−	0.876309i
$7$	−1.27459	−	2.31850i	−0.481749	−	0.876309i
$8$	−2.51411	−	1.29586i	−0.888872	−	0.458155i
$9$	−1.38914	−	2.65900i	−0.463047	−	0.886334i
$10$	1.97738	−	0.0314303i	0.625304	−	0.00993913i
$11$	−4.43886	−	0.782690i	−1.33837	−	0.235990i	−0.541782	−	0.840519i	$-0.682250\pi$
$11$	−4.43886	−	0.782690i	−1.33837	−	0.235990i	−0.796583	+	0.604529i	$0.793361\pi$
$12$	2.62967	−	2.25495i	0.759121	−	0.650949i
$13$	−1.32849	−	1.58323i	−0.368457	−	0.439110i	0.549679	−	0.835376i	$-0.314750\pi$
$13$	−1.32849	−	1.58323i	−0.368457	−	0.439110i	−0.918136	+	0.396266i	$0.870306\pi$
$14$	1.26193	+	3.52243i	0.337265	+	0.941410i
$15$	−0.876208	+	2.25806i	−0.226236	+	0.583028i
$16$	3.22134	+	2.37129i	0.805334	+	0.592821i
$17$			7.45773i			1.80876i	0.426723	+	0.904382i	$0.359668\pi$
$17$			7.45773i			1.80876i	−0.426723	+	0.904382i	$0.640332\pi$
$18$	1.34582	+	4.02353i	0.317214	+	0.948354i
$19$	2.98154			0.684012			0.342006	−	0.939698i	$-0.388894\pi$
$19$	2.98154			0.684012			0.342006	+	0.939698i	$0.388894\pi$
$20$	−2.76835	−	0.397877i	−0.619022	−	0.0889680i
$21$	−4.57853	−	0.192568i	−0.999117	−	0.0420218i
$22$	6.02380	+	2.08468i	1.28428	+	0.444455i
$23$	3.92885	+	4.68222i	0.819222	+	0.976311i	0.999974	−	0.00721764i	$-0.00229747\pi$
$23$	3.92885	+	4.68222i	0.819222	+	0.976311i	−0.180752	+	0.983529i	$0.557853\pi$
$24$	−4.17600	+	2.56145i	−0.852423	+	0.522853i
$25$	−2.86088	+	1.04127i	−0.572175	+	0.208255i
$26$	1.50147	+	2.50771i	0.294462	+	0.491803i
$27$	−5.18576	−	0.328457i	−0.998000	−	0.0632117i
$28$	−0.975280	−	5.20085i	−0.184311	−	0.982868i
$29$	1.56570	+	1.31378i	0.290743	+	0.243962i	0.776479	−	0.630143i	$-0.217004\pi$
$29$	1.56570	+	1.31378i	0.290743	+	0.243962i	−0.485736	+	0.874106i	$0.661448\pi$
$30$	1.72806	−	2.95752i	0.315499	−	0.539967i
$31$	1.57365	+	0.572762i	0.282636	+	0.102871i	0.479448	−	0.877570i	$-0.340837\pi$
$31$	1.57365	+	0.572762i	0.282636	+	0.102871i	−0.196812	+	0.980441i	$0.563059\pi$
$32$	−3.96868	−	4.03107i	−0.701571	−	0.712600i
$33$	−5.14317	+	5.87333i	−0.895311	+	1.02241i
$34$	1.66613	−	10.4144i	0.285739	−	1.78605i
$35$	2.31830	+	2.88342i	0.391865	+	0.487387i
$36$	−0.980488	−	5.91934i	−0.163415	−	0.986557i
$37$	−2.43730	+	4.22153i	−0.400690	+	0.694016i	−0.993809	−	0.111099i	$-0.964563\pi$
$37$	−2.43730	+	4.22153i	−0.400690	+	0.694016i	0.593119	+	0.805115i	$0.297896\pi$
$38$	−4.16359	−	0.666106i	−0.675423	−	0.108057i
$39$	−3.53768	+	0.547152i	−0.566482	+	0.0876144i
$40$	3.77699	+	1.17410i	0.597195	+	0.185641i
$41$	−4.22870	−	5.03957i	−0.660412	−	0.787049i	0.327033	−	0.945013i	$-0.393951\pi$
$41$	−4.22870	−	5.03957i	−0.660412	−	0.787049i	−0.987445	+	0.157964i	$0.949507\pi$
$42$	6.35069	+	1.29180i	0.979933	+	0.199329i
$43$	−1.40080	−	3.84866i	−0.213619	−	0.586915i	0.785886	−	0.618372i	$-0.212207\pi$
$43$	−1.40080	−	3.84866i	−0.213619	−	0.586915i	−0.999505	+	0.0314573i	$0.989985\pi$
$44$	−7.94624	−	4.25694i	−1.19794	−	0.641758i
$45$	2.55874	+	3.32453i	0.381435	+	0.495592i
$46$	−4.44041	−	7.41626i	−0.654703	−	1.09347i
$47$	−9.51207	+	3.46211i	−1.38748	+	0.505000i	−0.924436	−	0.381336i	$-0.875464\pi$
$47$	−9.51207	+	3.46211i	−1.38748	+	0.505000i	−0.463041	+	0.886337i	$0.653242\pi$
$48$	6.40385	−	2.64399i	0.924317	−	0.381627i
$49$	−3.75085	+	5.91025i	−0.535836	+	0.844322i
$50$	4.22772	−	0.814944i	0.597890	−	0.115250i
$51$	11.0479	+	6.69299i	1.54702	+	0.937207i
$52$	−1.53648	−	3.83735i	−0.213072	−	0.532145i
$53$	7.07518	−	12.2546i	0.971851	−	1.68330i	0.281893	−	0.959446i	$-0.409038\pi$
$53$	7.07518	−	12.2546i	0.971851	−	1.68330i	0.689958	−	0.723850i	$-0.257629\pi$
$54$	7.16830	+	1.61723i	0.975483	+	0.220077i
$55$	6.30305			0.849903
$56$	0.200013	+	7.48064i	0.0267278	+	0.999643i
$57$	2.67581	−	4.41688i	0.354419	−	0.585030i
$58$	−1.89292	−	2.18442i	−0.248552	−	0.286829i
$59$	−3.24290	+	2.72111i	−0.422189	+	0.354259i	−0.828995	−	0.559256i	$-0.811087\pi$
$59$	−3.24290	+	2.72111i	−0.422189	+	0.354259i	0.406806	+	0.913515i	$0.366643\pi$
$60$	−3.07390	+	3.74398i	−0.396838	+	0.483346i
$61$	1.28096	+	3.51941i	0.164010	+	0.450614i	0.994287	−	0.106737i	$-0.0340401\pi$
$61$	1.28096	+	3.51941i	0.164010	+	0.450614i	−0.830277	+	0.557351i	$0.811818\pi$
$62$	−2.06957	−	1.15141i	−0.262836	−	0.146229i
$63$	−4.39431	+	6.60985i	−0.553631	+	0.832762i
$64$	4.64151	+	6.51586i	0.580188	+	0.814482i
$65$	2.21399	+	1.85776i	0.274612	+	0.230427i
$66$	8.49437	−	7.05280i	1.04558	−	0.868140i
$67$	−5.50023	+	0.969838i	−0.671960	+	0.118485i	−0.499210	−	0.866481i	$-0.666376\pi$
$67$	−5.50023	+	0.969838i	−0.671960	+	0.118485i	−0.172750	+	0.984966i	$0.555265\pi$
$68$	−4.65336	+	14.1710i	−0.564303	+	1.71849i
$69$	10.4623	−	1.61814i	1.25951	−	0.194801i
$70$	−2.59322	−	4.54450i	−0.309949	−	0.543172i
$71$	−5.69937	+	3.29053i	−0.676390	+	0.390514i	−0.798494	−	0.602003i	$-0.794369\pi$
$71$	−5.69937	+	3.29053i	−0.676390	+	0.390514i	0.122103	+	0.992517i	$0.461036\pi$
$72$	0.0467655	+	8.48515i	0.00551137	+	0.999985i
$73$	5.51115	−	3.18187i	0.645032	−	0.372409i	−0.141518	−	0.989936i	$-0.545198\pi$
$73$	5.51115	−	3.18187i	0.645032	−	0.372409i	0.786550	+	0.617526i	$0.211865\pi$
$74$	4.34672	−	5.35067i	0.505296	−	0.622002i
$75$	−1.02496	+	5.17262i	−0.118353	+	0.597283i
$76$	5.66545	+	1.86038i	0.649872	+	0.213400i
$77$	3.84305	+	11.2891i	0.437956	+	1.28651i
$78$	5.06245	+	0.0262798i	0.573210	+	0.00297560i
$79$	−0.993400	−	0.175163i	−0.111766	−	0.0197074i	0.117485	−	0.993075i	$-0.462517\pi$
$79$	−0.993400	−	0.175163i	−0.111766	−	0.0197074i	−0.229251	+	0.973367i	$0.573628\pi$
$80$	−5.01209	−	2.48339i	−0.560369	−	0.277651i
$81$	−5.14058	+	7.38745i	−0.571175	+	0.820828i
$82$	4.77930	+	7.98227i	0.527786	+	0.881494i
$83$	−11.6449	−	9.77122i	−1.27819	−	1.07253i	−0.993491	−	0.113914i	$-0.963661\pi$
$83$	−11.6449	−	9.77122i	−1.27819	−	1.07253i	−0.284701	−	0.958616i	$-0.591894\pi$
$84$	−8.57985	−	3.22275i	−0.936139	−	0.351631i
$85$	−1.81096	−	10.2704i	−0.196426	−	1.11399i
$86$	1.09632	+	5.68743i	0.118219	+	0.613291i
$87$	3.35139	−	1.14038i	0.359306	−	0.122262i
$88$	10.1455	+	7.71989i	1.08152	+	0.822944i
$89$			0.187713i			0.0198975i	0.999951	+	0.00994874i	$0.00316684\pi$
$89$			0.187713i			0.0198975i	−0.999951	+	0.00994874i	$0.996833\pi$
$90$	−2.83044	−	5.21421i	−0.298354	−	0.549626i
$91$	−1.97744	+	5.09807i	−0.207292	+	0.534423i
$92$	4.54397	+	11.3485i	0.473741	+	1.18316i
$93$	2.26078	−	1.81719i	0.234432	−	0.188434i
$94$	14.0566	−	2.70959i	1.44983	−	0.279473i
$95$	−4.10604	+	0.724006i	−0.421271	+	0.0742814i
$96$	−9.53339	+	2.26152i	−0.972997	+	0.230816i
$97$	−4.61209	−	12.6716i	−0.468286	−	1.28661i	−0.919113	−	0.393995i	$-0.871093\pi$
$97$	−4.61209	−	12.6716i	−0.468286	−	1.28661i	0.450826	−	0.892612i	$-0.351129\pi$
$98$	6.55831	−	7.41543i	0.662490	−	0.749071i
$99$	4.08502	+	12.8902i	0.410560	+	1.29551i
$100$	−6.08589	+	0.193518i	−0.608589	+	0.0193518i
$101$	3.88271	−	4.62723i	0.386344	−	0.460427i	−0.537462	−	0.843288i	$-0.680617\pi$
$101$	3.88271	−	4.62723i	0.386344	−	0.460427i	0.923806	+	0.382861i	$0.125061\pi$
$102$	−13.9327	−	11.8147i	−1.37954	−	1.16983i
$103$	0.180736	+	1.02500i	0.0178084	+	0.100996i	0.992416	−	0.122921i	$-0.0392263\pi$
$103$	0.180736	+	1.02500i	0.0178084	+	0.100996i	−0.974608	+	0.223918i	$0.928115\pi$
$104$	1.28833	+	5.70196i	0.126331	+	0.559123i
$105$	6.35210	−	0.846605i	0.619901	−	0.0826202i
$106$	−12.6180	+	15.5323i	−1.22557	+	1.50863i
$107$	−12.2690	+	7.08350i	−1.18609	+	0.684788i	−0.957415	−	0.288716i	$-0.906772\pi$
$107$	−12.2690	+	7.08350i	−1.18609	+	0.684788i	−0.228672	+	0.973503i	$0.573438\pi$
$108$	−9.64891	−	3.85986i	−0.928467	−	0.371415i
$109$	−6.04584	+	10.4717i	−0.579086	+	1.00301i	0.416498	+	0.909136i	$0.363257\pi$
$109$	−6.04584	+	10.4717i	−0.579086	+	1.00301i	−0.995584	+	0.0938699i	$0.970076\pi$
$110$	−8.80193	−	1.40816i	−0.839231	−	0.134263i
$111$	4.06644	+	7.39929i	0.385969	+	0.702309i
$112$	1.39194	−	10.4911i	0.131526	−	0.991313i
$113$	−10.4584	−	3.80655i	−0.983844	−	0.358090i	−0.200510	−	0.979692i	$-0.564260\pi$
$113$	−10.4584	−	3.80655i	−0.983844	−	0.358090i	−0.783333	+	0.621602i	$0.786482\pi$
$114$	−4.72342	+	5.57017i	−0.442389	+	0.521694i
$115$	−6.54762	−	5.49410i	−0.610568	−	0.512328i
$116$	2.15535	+	3.47335i	0.200119	+	0.322492i
$117$	−2.36436	+	5.73179i	−0.218585	+	0.529904i
$118$	5.13649	−	3.07542i	0.472852	−	0.283115i
$119$	17.2907	−	9.50552i	1.58504	−	0.871370i
$120$	5.12900	−	4.54156i	0.468212	−	0.414586i
$121$	8.75422	+	3.18628i	0.795838	+	0.289661i
$122$	−1.00253	−	5.20088i	−0.0907650	−	0.470865i
$123$	−11.2607	+	1.74163i	−1.01535	+	0.157038i
$124$	2.63283	+	2.07025i	0.236435	+	0.185914i
$125$	9.74226	−	5.62470i	0.871374	−	0.503088i
$126$	7.61316	−	8.24862i	0.678234	−	0.734846i
$127$	−6.54161	−	3.77680i	−0.580474	−	0.335137i	0.180848	−	0.983511i	$-0.442116\pi$
$127$	−6.54161	−	3.77680i	−0.580474	−	0.335137i	−0.761322	+	0.648374i	$0.775449\pi$
$128$	−5.02595	−	10.1361i	−0.444235	−	0.895910i
$129$	−6.95859	−	1.37885i	−0.612669	−	0.121401i
$130$	−2.67670	−	3.08891i	−0.234762	−	0.270915i
$131$	8.48627	−	7.12082i	0.741449	−	0.622149i	−0.191778	−	0.981438i	$-0.561425\pi$
$131$	8.48627	−	7.12082i	0.741449	−	0.622149i	0.933226	+	0.359289i	$0.116981\pi$
$132$	−13.4377	+	7.95120i	−1.16960	+	0.692063i
$133$	−3.80023	−	6.91269i	−0.329522	−	0.599406i
$134$	7.89749	−	0.125530i	0.682240	−	0.0108441i
$135$	7.22135	−	0.806919i	0.621515	−	0.0694485i
$136$	9.66415	−	18.7496i	0.828694	−	1.60776i
$137$	−13.4919	+	4.91066i	−1.15269	+	0.419546i	−0.846482	−	0.532418i	$-0.821283\pi$
$137$	−13.4919	+	4.91066i	−1.15269	+	0.419546i	−0.306211	+	0.951964i	$0.599061\pi$
$138$	−14.9716	−	0.0777193i	−1.27447	−	0.00661591i
$139$	1.40145	+	7.94803i	0.118870	+	0.674143i	0.984761	+	0.173911i	$0.0556407\pi$
$139$	1.40145	+	7.94803i	0.118870	+	0.674143i	−0.865892	+	0.500232i	$0.833248\pi$
$140$	2.60603	+	6.92554i	0.220250	+	0.585315i
$141$	−3.40788	+	17.1983i	−0.286995	+	1.44836i
$142$	8.69405	−	3.32178i	0.729589	−	0.278758i
$143$	4.65780	+	8.06754i	0.389505	+	0.674642i
$144$	1.83036	−	11.8596i	0.152530	−	0.988299i
$145$	−2.47523	−	1.42908i	−0.205557	−	0.118678i
$146$	−8.40694	+	3.21209i	−0.695763	+	0.265834i
$147$	5.38926	+	10.8607i	0.444499	+	0.895779i
$148$	−7.26539	+	6.50086i	−0.597212	+	0.534368i
$149$	18.3012	+	6.66110i	1.49929	+	0.545698i	0.955878	−	0.293765i	$-0.0949082\pi$
$149$	18.3012	+	6.66110i	1.49929	+	0.545698i	0.543416	+	0.839463i	$0.317130\pi$
$150$	2.58693	−	6.99435i	0.211222	−	0.571086i
$151$	6.95419	+	1.22621i	0.565924	+	0.0997877i	0.449288	−	0.893387i	$-0.351678\pi$
$151$	6.95419	+	1.22621i	0.565924	+	0.0997877i	0.116636	+	0.993175i	$0.462789\pi$
$152$	−7.49592	−	3.86365i	−0.608000	−	0.313383i
$153$	19.8301	−	10.3598i	1.60317	−	0.837542i
$154$	−2.84455	−	16.6233i	−0.229220	−	1.33954i
$155$	−2.30624	−	0.406653i	−0.185242	−	0.0326632i
$156$	−7.06361	−	1.16770i	−0.565542	−	0.0934909i
$157$	−1.08854	−	1.29727i	−0.0868747	−	0.103533i	0.720856	−	0.693085i	$-0.243749\pi$
$157$	−1.08854	−	1.29727i	−0.0868747	−	0.103533i	−0.807731	+	0.589552i	$0.799304\pi$
$158$	1.34811	+	0.466543i	0.107250	+	0.0371162i
$159$	−11.8044	−	21.4792i	−0.936146	−	1.70341i
$160$	6.44435	+	4.58770i	0.509471	+	0.362689i
$161$	5.84806	−	15.0769i	0.460891	−	1.18823i
$162$	8.82902	−	9.16779i	0.693673	−	0.720290i
$163$	−2.06859	+	1.19430i	−0.162024	+	0.0935447i	−0.578820	−	0.815456i	$-0.696486\pi$
$163$	−2.06859	+	1.19430i	−0.162024	+	0.0935447i	0.416795	+	0.909000i	$0.363153\pi$
$164$	−4.89076	−	12.2146i	−0.381904	−	0.953802i
$165$	5.65672	−	9.33739i	0.440375	−	0.726915i
$166$	14.0786	+	16.2467i	1.09271	+	1.26098i
$167$	−9.39849	−	3.42077i	−0.727277	−	0.264707i	−0.0482653	−	0.998835i	$-0.515369\pi$
$167$	−9.39849	−	3.42077i	−0.727277	−	0.264707i	−0.679012	+	0.734127i	$0.737592\pi$
$168$	11.2614	+	6.41726i	0.868835	+	0.495102i
$169$	1.51569	−	8.59588i	0.116591	−	0.661222i
$170$	0.234398	+	14.7468i	0.0179775	+	1.13103i
$171$	−4.14178	−	7.92792i	−0.316730	−	0.606263i
$172$	−0.260334	−	8.18717i	−0.0198503	−	0.624266i
$173$	11.5109	−	13.7182i	0.875157	−	1.04297i	−0.123560	−	0.992337i	$-0.539431\pi$
$173$	11.5109	−	13.7182i	0.875157	−	1.04297i	0.998717	−	0.0506346i	$-0.0161244\pi$
$174$	−4.93484	+	0.843755i	−0.374109	+	0.0639649i
$175$	6.06063	+	5.30574i	0.458140	+	0.401076i
$176$	−12.4431	−	13.0471i	−0.937931	−	0.983462i
$177$	1.12072	+	7.24614i	0.0842383	+	0.544653i
$178$	0.0419369	−	0.262132i	0.00314330	−	0.0196476i
$179$		−	4.83106i		−	0.361090i	−0.983567	−	0.180545i	$-0.942214\pi$
$179$		−	4.83106i		−	0.361090i	0.983567	−	0.180545i	$-0.0577862\pi$
$180$	2.78767	+	7.91376i	0.207781	+	0.589857i
$181$	−14.1614	−	8.17608i	−1.05261	−	0.607723i	−0.129229	−	0.991615i	$-0.541250\pi$
$181$	−14.1614	−	8.17608i	−1.05261	−	0.607723i	−0.923378	+	0.383891i	$0.874584\pi$
$182$	3.90037	−	6.67745i	0.289115	−	0.494965i
$183$	6.36329	+	1.26090i	0.470388	+	0.0932080i
$184$	−3.81008	−	16.8629i	−0.280883	−	1.24315i
$185$	2.33143	−	6.40555i	0.171410	−	0.470945i
$186$	−3.56306	+	2.03254i	−0.261256	+	0.149033i
$187$	5.83709	−	33.1038i	0.426850	−	2.42079i
$188$	−20.2348	+	0.643423i	−1.47578	+	0.0469264i
$189$	5.84818	+	12.4418i	0.425392	+	0.905009i
$190$	5.89565	−	0.0937106i	0.427716	−	0.00679849i
$191$	−5.02110	−	0.885355i	−0.363314	−	0.0640620i	−0.0109885	−	0.999940i	$-0.503498\pi$
$191$	−5.02110	−	0.885355i	−0.363314	−	0.0640620i	−0.352325	+	0.935878i	$0.614609\pi$
$192$	13.8182	−	1.02826i	0.997243	−	0.0742083i
$193$	−8.41406	−	3.06247i	−0.605657	−	0.220441i	0.0209446	−	0.999781i	$-0.493333\pi$
$193$	−8.41406	−	3.06247i	−0.605657	−	0.220441i	−0.626602	+	0.779339i	$0.715555\pi$
$194$	3.60961	+	18.7257i	0.259155	+	1.34443i
$195$	4.73906	−	1.61256i	0.339371	−	0.115478i
$196$	−10.8151	+	8.89012i	−0.772505	+	0.635009i
$197$	9.92764	−	17.1952i	0.707315	−	1.22511i	−0.258534	−	0.966002i	$-0.583239\pi$
$197$	9.92764	−	17.1952i	0.707315	−	1.22511i	0.965849	−	0.259104i	$-0.0834272\pi$
$198$	−2.82475	−	18.9132i	−0.200746	−	1.34410i
$199$	6.25389			0.443327			0.221663	−	0.975123i	$-0.428851\pi$
$199$	6.25389			0.443327			0.221663	+	0.975123i	$0.428851\pi$
$200$	8.54190	+	1.08941i	0.604004	+	0.0770329i
$201$	−3.49949	+	9.01847i	−0.246835	+	0.636114i
$202$	−6.45580	+	5.59429i	−0.454229	+	0.393613i
$203$	1.05037	−	5.30459i	0.0737214	−	0.372309i
$204$	16.8168	+	19.6114i	1.17741	+	1.37307i
$205$	7.04733	+	5.91341i	0.492207	+	0.413010i
$206$	−0.0233933	−	1.47175i	−0.00162989	−	0.102542i
$207$	6.99231	−	16.9511i	0.485999	−	1.17818i
$208$	−0.525217	−	8.25036i	−0.0364173	−	0.572059i
$209$	−13.2346	−	2.33362i	−0.915458	−	0.161420i
$210$	−9.05956	−	0.236877i	−0.625169	−	0.0163461i
$211$	−8.58633	+	23.5908i	−0.591107	+	1.62405i	0.177346	+	0.984149i	$0.443249\pi$
$211$	−8.58633	+	23.5908i	−0.591107	+	1.62405i	−0.768453	+	0.639906i	$0.778973\pi$
$212$	21.0905	−	18.8712i	1.44850	−	1.29608i
$213$	−0.240320	+	11.3962i	−0.0164665	+	0.780855i
$214$	18.7156	−	7.15078i	1.27937	−	0.488817i
$215$	2.86368	+	4.96004i	0.195301	+	0.338272i
$216$	12.6119	+	7.54578i	0.858134	+	0.513426i
$217$	−0.677809	−	4.37854i	−0.0460126	−	0.297235i
$218$	10.7822	−	13.2726i	0.730264	−	0.898931i
$219$	0.232384	−	11.0199i	0.0157030	−	0.744653i
$220$	11.9769	+	3.93288i	0.807482	+	0.265155i
$221$	11.8073	−	9.90752i	0.794246	−	0.666452i
$222$	−4.02552	−	11.2413i	−0.270175	−	0.754464i
$223$	−1.99606	+	11.3202i	−0.133666	+	0.758058i	0.842113	+	0.539301i	$0.181311\pi$
$223$	−1.99606	+	11.3202i	−0.133666	+	0.758058i	−0.975779	+	0.218757i	$0.929800\pi$
$224$	−4.28760	+	14.3393i	−0.286477	+	0.958087i
$225$	6.74291	+	6.16060i	0.449527	+	0.410707i
$226$	13.7543	+	7.65219i	0.914921	+	0.509016i
$227$	3.05130	−	17.3048i	0.202522	−	1.14856i	−0.698770	−	0.715346i	$-0.746269\pi$
$227$	3.05130	−	17.3048i	0.202522	−	1.14856i	0.901292	−	0.433212i	$-0.142620\pi$
$228$	7.84048	−	6.72324i	0.519248	−	0.445257i
$229$	−6.04219	+	16.6008i	−0.399279	+	1.09701i	0.563357	+	0.826214i	$0.309510\pi$
$229$	−6.04219	+	16.6008i	−0.399279	+	1.09701i	−0.962636	+	0.270798i	$0.912713\pi$
$230$	7.91602	+	9.13507i	0.521967	+	0.602349i
$231$	20.1727	+	4.43835i	1.32727	+	0.292022i
$232$	−2.23387	−	5.33190i	−0.146661	−	0.350057i
$233$	−3.83503	+	6.64247i	−0.251241	+	0.435163i	−0.963868	−	0.266381i	$-0.914172\pi$
$233$	−3.83503	+	6.64247i	−0.251241	+	0.435163i	0.712627	+	0.701544i	$0.247505\pi$
$234$	4.58226	−	7.47597i	0.299552	−	0.488719i
$235$	12.2589	−	7.07767i	0.799681	−	0.461696i
$236$	−7.85996	+	3.14714i	−0.511640	+	0.204862i
$237$	−1.15102	+	1.31443i	−0.0747669	+	0.0853813i
$238$	−26.2693	+	9.41112i	−1.70279	+	0.610032i
$239$	24.5892	−	4.33574i	1.59054	−	0.280456i	0.692852	−	0.721080i	$-0.256354\pi$
$239$	24.5892	−	4.33574i	1.59054	−	0.280456i	0.897692	+	0.440624i	$0.145243\pi$
$240$	−8.17705	+	5.19622i	−0.527827	+	0.335415i
$241$	0.235009	+	0.645681i	0.0151382	+	0.0415920i	0.947032	−	0.321140i	$-0.104066\pi$
$241$	0.235009	+	0.645681i	0.0151382	+	0.0415920i	−0.931893	+	0.362732i	$0.881844\pi$
$242$	−11.5130	−	6.40527i	−0.740086	−	0.411747i
$243$	6.33038	+	14.2452i	0.406094	+	0.913831i
$244$	0.238063	+	7.48677i	0.0152404	+	0.479291i
$245$	3.73032	−	9.05015i	0.238321	−	0.578193i
$246$	16.1142	+	0.0836508i	1.02741	+	0.00533338i
$247$	−3.96095	−	4.72047i	−0.252029	−	0.300357i
$248$	−3.21412	−	3.47922i	−0.204097	−	0.220930i
$249$	−24.9259	+	8.48157i	−1.57962	+	0.537498i
$250$	−14.8612	+	5.67812i	−0.939908	+	0.359116i
$251$	−3.68129	+	6.37619i	−0.232361	+	0.402461i	−0.958503	−	0.285084i	$-0.907978\pi$
$251$	−3.68129	+	6.37619i	−0.232361	+	0.402461i	0.726141	+	0.687545i	$0.241312\pi$
$252$	−12.4743	+	9.81798i	−0.785805	+	0.618475i
$253$	−13.7749	−	23.8588i	−0.866019	−	1.49999i
$254$	8.29129	+	6.73559i	0.520242	+	0.422629i
$255$	−16.8400	−	6.53452i	−1.05456	−	0.409207i
$256$	4.75401	+	15.2774i	0.297126	+	0.954838i
$257$	4.82664	−	13.2611i	0.301077	−	0.827203i	−0.693236	−	0.720711i	$-0.743816\pi$
$257$	4.82664	−	13.2611i	0.301077	−	0.827203i	0.994313	−	0.106493i	$-0.0339621\pi$
$258$	9.40930	+	3.48013i	0.585798	+	0.216663i
$259$	12.8942	+	0.270167i	0.801205	+	0.0167874i
$260$	3.04780	+	4.91152i	0.189016	+	0.304600i
$261$	1.31836	−	5.98821i	0.0816045	−	0.370661i
$262$	−13.4416	+	8.04800i	−0.830422	+	0.497207i
$263$	−10.0731	+	12.0046i	−0.621133	+	0.740238i	−0.981265	−	0.192664i	$-0.938287\pi$
$263$	−10.0731	+	12.0046i	−0.621133	+	0.740238i	0.360132	+	0.932902i	$0.382732\pi$
$264$	20.5415	−	8.10138i	1.26424	−	0.498606i
$265$	−6.76784	+	18.5945i	−0.415745	+	1.14225i
$266$	3.76249	+	10.5023i	0.230693	+	0.643936i
$267$	0.278079	+	0.168464i	0.0170181	+	0.0103098i
$268$	−11.0565	−	1.58908i	−0.675386	−	0.0970687i
$269$	−21.8240	−	12.6001i	−1.33063	−	0.768240i	−0.345234	−	0.938517i	$-0.612200\pi$
$269$	−21.8240	−	12.6001i	−1.33063	−	0.768240i	−0.985396	+	0.170277i	$0.945534\pi$
$270$	−10.2646	−	0.486497i	−0.624682	−	0.0296072i
$271$	5.88220	+	10.1883i	0.357318	+	0.618894i	0.987512	−	0.157544i	$-0.0503578\pi$
$271$	5.88220	+	10.1883i	0.357318	+	0.618894i	−0.630193	+	0.776438i	$0.717024\pi$
$272$	−17.6844	+	24.0238i	−1.07227	+	1.45666i
$273$	5.77765	+	7.50470i	0.349679	+	0.454205i
$274$	19.9380	−	3.84328i	1.20450	−	0.232181i
$275$	13.5140	−	2.38289i	0.814926	−	0.143693i
$276$	20.8898	+	3.45334i	1.25742	+	0.207866i
$277$	6.90899	+	5.79733i	0.415121	+	0.348328i	0.826303	−	0.563225i	$-0.190440\pi$
$277$	6.90899	+	5.79733i	0.415121	+	0.348328i	−0.411182	+	0.911553i	$0.634884\pi$
$278$	−0.181395	−	11.4122i	−0.0108793	−	0.684456i
$279$	−0.663047	−	4.97999i	−0.0396956	−	0.298144i
$280$	−2.09197	−	10.2534i	−0.125019	−	0.612759i
$281$	−18.1955	+	6.62264i	−1.08546	+	0.395073i	−0.821935	−	0.569581i	$-0.807106\pi$
$281$	−18.1955	+	6.62264i	−1.08546	+	0.395073i	−0.263520	+	0.964654i	$0.584883\pi$
$282$	8.60124	−	23.2554i	0.512196	−	1.38484i
$283$	−5.22844	−	29.6519i	−0.310798	−	1.76262i	−0.594871	−	0.803821i	$-0.702797\pi$
$283$	−5.22844	−	29.6519i	−0.310798	−	1.76262i	0.284072	−	0.958803i	$-0.408314\pi$
$284$	−12.8830	+	2.69638i	−0.764464	+	0.160001i
$285$	−2.61245	+	6.73249i	−0.154748	+	0.398798i
$286$	−4.70204	−	12.3066i	−0.278037	−	0.727702i
$287$	−6.29438	+	16.2276i	−0.371545	+	0.957885i
$288$	−5.20557	+	16.1525i	−0.306741	+	0.951793i
$289$	−38.6177			−2.27163
$290$	3.13728	+	2.54863i	0.184227	+	0.149661i
$291$	−22.9110	−	4.53984i	−1.34306	−	0.266130i
$292$	12.4575	−	2.60734i	0.729022	−	0.152583i
$293$	13.2294	−	2.33271i	0.772872	−	0.136278i	0.226715	−	0.973961i	$-0.427201\pi$
$293$	13.2294	−	2.33271i	0.772872	−	0.136278i	0.546157	+	0.837683i	$0.316090\pi$
$294$	−5.09947	−	16.3706i	−0.297407	−	0.954751i
$295$	3.80520	−	4.53486i	0.221547	−	0.264030i
$296$	11.5982	−	7.45501i	0.674129	−	0.433313i
$297$	22.7618	+	5.51682i	1.32077	+	0.320118i
$298$	−24.0687	−	13.3906i	−1.39426	−	0.775697i
$299$	2.19361	−	12.4406i	0.126860	−	0.719457i
$300$	−5.17515	+	9.18935i	−0.298787	+	0.530548i
$301$	−7.13766	+	8.15319i	−0.411408	+	0.469942i
$302$	−9.43727	−	3.26599i	−0.543054	−	0.187936i
$303$	−3.37025	−	9.90462i	−0.193616	−	0.569006i
$304$	9.60454	+	7.07008i	0.550858	+	0.405497i
$305$	−2.61870	−	4.53571i	−0.149946	−	0.259714i
$306$	−30.0064	+	10.0368i	−1.71535	+	0.573765i
$307$	−9.32841	−	16.1573i	−0.532401	−	0.922145i	−0.999284	−	0.0378262i	$-0.987957\pi$
$307$	−9.32841	−	16.1573i	−0.532401	−	0.922145i	0.466884	−	0.884319i	$-0.345377\pi$
$308$	0.258475	+	23.8492i	0.0147280	+	1.35893i
$309$	1.68065	+	0.652153i	0.0956088	+	0.0370997i
$310$	3.12972	+	1.08311i	0.177756	+	0.0615166i
$311$	1.79437	+	10.1764i	0.101749	+	0.577050i	0.992469	+	0.122496i	$0.0390900\pi$
$311$	1.79437	+	10.1764i	0.101749	+	0.577050i	−0.890720	+	0.454553i	$0.849799\pi$
$312$	9.60315	+	3.20873i	0.543671	+	0.181658i
$313$	2.19857	−	2.62015i	0.124270	−	0.148100i	−0.700322	−	0.713827i	$-0.746960\pi$
$313$	2.19857	−	2.62015i	0.124270	−	0.148100i	0.824592	+	0.565728i	$0.191405\pi$
$314$	1.23027	+	2.05477i	0.0694282	+	0.115957i
$315$	4.44657	−	10.1698i	0.250536	−	0.573006i
$316$	−1.77834	−	0.952687i	−0.100039	−	0.0535928i
$317$	−12.5385	+	4.56364i	−0.704231	+	0.256319i	−0.669216	−	0.743067i	$-0.733370\pi$
$317$	−12.5385	+	4.56364i	−0.704231	+	0.256319i	−0.0350150	+	0.999387i	$0.511148\pi$
$318$	11.6856	+	32.6320i	0.655295	+	1.82991i
$319$	−5.92163	−	7.05712i	−0.331548	−	0.395123i
$320$	−7.97431	−	7.84625i	−0.445778	−	0.438618i
$321$	−0.517335	+	24.5325i	−0.0288748	+	1.36927i
$322$	−11.5349	+	19.7478i	−0.642814	+	1.10050i
$323$			22.2355i			1.23722i
$324$	−14.3775	+	10.8299i	−0.798751	+	0.601662i
$325$	5.44923	+	3.14611i	0.302269	+	0.174515i
$326$	3.15551	−	1.20564i	0.174767	−	0.0667744i
$327$	10.0870	+	18.3542i	0.557811	+	1.01499i
$328$	4.10086	+	18.1498i	0.226432	+	1.00216i
$329$	20.1508	+	17.6409i	1.11095	+	0.972576i
$330$	−9.98542	+	11.7755i	−0.549679	+	0.648219i
$331$	−1.74848	−	4.80391i	−0.0961053	−	0.264047i	0.882319	−	0.470651i	$-0.155981\pi$
$331$	−1.74848	−	4.80391i	−0.0961053	−	0.264047i	−0.978425	+	0.206604i	$0.933759\pi$
$332$	−16.0304	−	25.8330i	−0.879784	−	1.41777i
$333$	14.6108	+	0.616492i	0.800668	+	0.0337836i
$334$	12.3603	+	6.87667i	0.676328	+	0.376275i
$335$	7.33915	−	2.67123i	0.400981	−	0.145945i
$336$	−14.2923	−	11.4773i	−0.779711	−	0.626139i
$337$	−22.7707	+	19.1069i	−1.24040	+	1.04082i	−0.242904	+	0.970050i	$0.578100\pi$
$337$	−22.7707	+	19.1069i	−1.24040	+	1.04082i	−0.997493	+	0.0707665i	$0.977455\pi$
$338$	−4.03699	+	11.6651i	−0.219584	+	0.634500i
$339$	−15.0250	+	12.0769i	−0.816047	+	0.655930i
$340$	2.96726	−	20.6456i	0.160922	−	1.11967i
$341$	−6.53692	−	3.77409i	−0.353994	−	0.204378i
$342$	4.01263	+	11.9963i	0.216978	+	0.648686i
$343$	18.4837	+	1.16321i	0.998026	+	0.0628074i
$344$	−1.46555	+	11.4912i	−0.0790173	+	0.619563i
$345$	−14.0152	+	4.76897i	−0.754554	+	0.256753i
$346$	−19.1392	+	16.5851i	−1.02893	+	0.891622i
$347$	−0.708517	+	1.94663i	−0.0380352	+	0.104501i	−0.957256	−	0.289241i	$-0.906597\pi$
$347$	−0.708517	+	1.94663i	−0.0380352	+	0.104501i	0.919221	+	0.393741i	$0.128819\pi$
$348$	7.07978	−	0.0757740i	0.379516	−	0.00406191i
$349$	22.5076	−	26.8235i	1.20480	−	1.43583i	0.335153	−	0.942164i	$-0.391212\pi$
$349$	22.5076	−	26.8235i	1.20480	−	1.43583i	0.869651	−	0.493666i	$-0.164344\pi$
$350$	−7.27804	−	8.76323i	−0.389028	−	0.468414i
$351$	6.36921	+	8.64662i	0.339963	+	0.461523i
$352$	14.4613	+	20.9996i	0.770792	+	1.11928i
$353$	9.07875	+	24.9437i	0.483213	+	1.32762i	0.906724	+	0.421726i	$0.138575\pi$
$353$	9.07875	+	24.9437i	0.483213	+	1.32762i	−0.423511	+	0.905891i	$0.639202\pi$
$354$	0.0538282	−	10.3693i	0.00286094	−	0.551122i
$355$	7.04987	−	5.91554i	0.374168	−	0.313964i
$356$	−0.117126	+	0.356687i	−0.00620766	+	0.0189044i
$357$	1.43612	−	34.1454i	0.0760076	−	1.80717i
$358$	−1.07931	+	6.74635i	−0.0570431	+	0.356556i
$359$		−	27.3403i		−	1.44297i	−0.692432	−	0.721483i	$-0.743461\pi$
$359$		−	27.3403i		−	1.44297i	0.692432	−	0.721483i	$-0.256539\pi$
$360$	−2.12485	−	11.6740i	−0.111989	−	0.615274i
$361$	−10.1104			−0.532127
$362$	17.9491	+	14.5813i	0.943385	+	0.766378i
$363$	12.5767	−	10.1090i	0.660106	−	0.530586i
$364$	−6.93851	+	8.45337i	−0.363677	+	0.443077i
$365$	−6.81706	+	5.72019i	−0.356821	+	0.299408i
$366$	−8.60435	−	3.18241i	−0.449757	−	0.166347i
$367$	2.86521	−	16.2494i	0.149563	−	0.848213i	−0.814027	−	0.580827i	$-0.802729\pi$
$367$	2.86521	−	16.2494i	0.149563	−	0.848213i	0.963590	−	0.267385i	$-0.0861597\pi$
$368$	1.55327	+	24.3994i	0.0809696	+	1.27191i
$369$	−7.52597	+	18.2448i	−0.391786	+	0.949786i
$370$	−4.68680	+	8.42420i	−0.243655	+	0.437953i
$371$	−37.4301	−	0.784261i	−1.94328	−	0.0407168i
$372$	5.42974	−	2.04233i	0.281519	−	0.105890i
$373$	2.91439	+	16.5283i	0.150901	+	0.855804i	0.962438	+	0.271502i	$0.0875204\pi$
$373$	2.91439	+	16.5283i	0.150901	+	0.855804i	−0.811537	+	0.584302i	$0.801369\pi$
$374$	−15.5470	+	44.9239i	−0.803914	+	2.32296i
$375$	0.410793	−	19.4802i	0.0212133	−	1.00595i
$376$	28.4008	+	3.62216i	1.46466	+	0.186798i
$377$		−	4.22421i		−	0.217558i
$378$	−5.38709	−	18.6810i	−0.277082	−	0.960846i
$379$			14.1494i			0.726808i	0.931632	+	0.363404i	$0.118386\pi$
$379$			14.1494i			0.726808i	−0.931632	+	0.363404i	$0.881614\pi$
$380$	−8.25395	−	1.18629i	−0.423419	−	0.0608552i
$381$	−11.4658	+	6.30128i	−0.587411	+	0.322824i
$382$	6.81394	+	2.35812i	0.348632	+	0.120652i
$383$	2.65583	+	15.0620i	0.135707	+	0.769630i	0.974365	+	0.224973i	$0.0722293\pi$
$383$	2.65583	+	15.0620i	0.135707	+	0.769630i	−0.838658	+	0.544658i	$0.816660\pi$
$384$	−19.5262	−	1.65121i	−0.996444	−	0.0842627i
$385$	−8.03379	−	14.6136i	−0.409440	−	0.744778i
$386$	11.0657	+	6.15639i	0.563228	+	0.313352i
$387$	−8.28768	+	9.07104i	−0.421286	+	0.461107i
$388$	−0.857143	−	26.9560i	−0.0435148	−	1.36849i
$389$	0.900293	−	5.10582i	0.0456467	−	0.258875i	−0.953441	−	0.301579i	$-0.902486\pi$
$389$	0.900293	−	5.10582i	0.0456467	−	0.258875i	0.999088	+	0.0427041i	$0.0135973\pi$
$390$	−6.97815	+	1.19312i	−0.353353	+	0.0604160i
$391$	−34.9187	+	29.3003i	−1.76592	+	1.48178i
$392$	17.0889	−	9.99846i	0.863120	−	0.504998i
$393$	−2.93278	−	18.9623i	−0.147939	−	0.956520i
$394$	−17.7051	+	21.7944i	−0.891969	+	1.09798i
$395$	1.41060			0.0709749
$396$	−0.280770	+	27.0425i	−0.0141092	+	1.35894i
$397$		−	20.8079i		−	1.04432i	−0.852848	−	0.522160i	$-0.825126\pi$
$397$		−	20.8079i		−	1.04432i	0.852848	−	0.522160i	$-0.174874\pi$
$398$	−8.73328	−	1.39718i	−0.437760	−	0.0700344i
$399$	−13.6511	−	0.574150i	−0.683408	−	0.0287434i
$400$	−11.6850	−	3.42966i	−0.584250	−	0.171483i
$401$	6.58745	−	5.52752i	0.328961	−	0.276031i	−0.463315	−	0.886194i	$-0.653340\pi$
$401$	6.58745	−	5.52752i	0.328961	−	0.276031i	0.792277	+	0.610162i	$0.208896\pi$
$402$	6.90170	−	11.8121i	0.344226	−	0.589132i
$403$	−1.18376	−	3.25237i	−0.0589675	−	0.162012i
$404$	10.2651	−	6.36988i	0.510706	−	0.316914i
$405$	5.28548	−	11.4219i	0.262638	−	0.567561i
$406$	−2.65189	+	7.17296i	−0.131611	+	0.355988i
$407$	14.1230	−	16.8311i	0.700051	−	0.834288i
$408$	−19.1026	−	31.1435i	−0.945718	−	1.54183i
$409$	8.62693	−	23.7023i	0.426574	−	1.17200i	−0.521304	−	0.853371i	$-0.674554\pi$
$409$	8.62693	−	23.7023i	0.426574	−	1.17200i	0.947878	−	0.318632i	$-0.103223\pi$
$410$	−8.52016	−	9.83226i	−0.420781	−	0.485581i
$411$	−4.83374	+	24.3941i	−0.238431	+	1.20327i
$412$	−0.296136	+	2.06046i	−0.0145896	+	0.101511i
$413$	10.4423	+	4.05035i	0.513830	+	0.199305i
$414$	−13.5515	+	22.1093i	−0.666020	+	1.08661i
$415$	18.4095	+	10.6287i	0.903688	+	0.521745i
$416$	−1.10977	+	11.6386i	−0.0544110	+	0.570629i
$417$	13.0320	+	5.05690i	0.638181	+	0.247637i
$418$	17.9602	+	6.21555i	0.878463	+	0.304012i
$419$	23.6940	−	19.8817i	1.15753	−	0.971282i	0.157660	−	0.987493i	$-0.449605\pi$
$419$	23.6940	−	19.8817i	1.15753	−	0.971282i	0.999869	+	0.0162112i	$0.00516040\pi$
$420$	12.5984	+	2.35479i	0.614737	+	0.114902i
$421$	−4.49853	+	1.63733i	−0.219245	+	0.0797986i	−0.449307	−	0.893377i	$-0.648329\pi$
$421$	−4.49853	+	1.63733i	−0.219245	+	0.0797986i	0.230062	+	0.973176i	$0.426107\pi$
$422$	17.2608	−	31.0252i	0.840245	−	1.51028i
$423$	22.4193	+	20.4832i	1.09007	+	0.995929i
$424$	−33.6680	+	21.6409i	−1.63506	+	1.05098i
$425$	−7.76554	−	21.3356i	−0.376684	−	1.03493i
$426$	2.88162	−	15.8606i	0.139615	−	0.768448i
$427$	6.52704	−	7.45570i	0.315866	−	0.360806i
$428$	−27.7331	+	5.80449i	−1.34053	+	0.280570i
$429$	16.1315	+	0.340177i	0.778836	+	0.0164239i
$430$	−2.89088	−	7.56625i	−0.139410	−	0.364877i
$431$	35.2314	+	20.3408i	1.69703	+	0.979783i	0.948548	+	0.316634i	$0.102553\pi$
$431$	35.2314	+	20.3408i	1.69703	+	0.979783i	0.748487	+	0.663150i	$0.230781\pi$
$432$	−15.9262	−	13.3550i	−0.766250	−	0.642542i
$433$			16.3077i			0.783696i	0.920030	+	0.391848i	$0.128164\pi$
$433$			16.3077i			0.783696i	−0.920030	+	0.391848i	$0.871836\pi$
$434$	−0.0316809	+	6.26587i	−0.00152073	+	0.300771i
$435$	−4.33846	+	2.38429i	−0.208013	+	0.114318i
$436$	−18.0221	+	16.1257i	−0.863103	+	0.772280i
$437$	11.7140	+	13.9602i	0.560358	+	0.667809i
$438$	−2.78646	+	15.3368i	−0.133142	+	0.732822i
$439$	−6.57558	+	2.39332i	−0.313835	+	0.114227i	−0.494135	−	0.869385i	$-0.664515\pi$
$439$	−6.57558	+	2.39332i	−0.313835	+	0.114227i	0.180300	+	0.983612i	$0.442293\pi$
$440$	−15.8466	−	8.16785i	−0.755455	−	0.389387i
$441$	20.9258	+	1.76336i	0.996468	+	0.0839694i
$442$	−18.7018	+	11.1975i	−0.889556	+	0.532612i
$443$	−13.2467	+	15.7868i	−0.629368	+	0.750051i	−0.982651	−	0.185465i	$-0.940621\pi$
$443$	−13.2467	+	15.7868i	−0.629368	+	0.750051i	0.353283	+	0.935516i	$0.385065\pi$
$444$	3.11005	+	16.5973i	0.147597	+	0.787671i
$445$	−0.0455821	−	0.258509i	−0.00216080	−	0.0122545i
$446$	5.31646	−	15.3622i	0.251742	−	0.727423i
$447$	26.2924	−	21.1335i	1.24359	−	0.999581i
$448$	9.19099	−	19.0663i	0.434233	−	0.900800i
$449$	3.19469	+	5.53336i	0.150767	+	0.261136i	0.931510	−	0.363717i	$-0.118492\pi$
$449$	3.19469	+	5.53336i	0.150767	+	0.261136i	−0.780743	+	0.624852i	$0.785159\pi$
$450$	−8.03983	−	10.1094i	−0.379001	−	0.476563i
$451$	14.8262	+	25.6797i	0.698137	+	1.20921i
$452$	−17.4977	−	13.7588i	−0.823020	−	0.647159i
$453$	8.05761	−	9.20152i	0.378579	−	0.432325i
$454$	−8.12707	+	23.4837i	−0.381422	+	1.10214i
$455$	1.48528	−	7.50101i	0.0696312	−	0.351653i
$456$	−12.4509	+	7.63706i	−0.583068	+	0.357638i
$457$	−5.34985	+	30.3405i	−0.250255	+	1.41927i	0.557708	+	0.830037i	$0.311681\pi$
$457$	−5.34985	+	30.3405i	−0.250255	+	1.41927i	−0.807964	+	0.589232i	$0.799430\pi$
$458$	12.1464	−	21.8324i	0.567566	−	1.02016i
$459$	2.44955	−	38.6740i	0.114335	−	1.80515i
$460$	−9.01350	−	14.5252i	−0.420256	−	0.677243i
$461$	4.15851	−	4.95592i	0.193681	−	0.230820i	−0.660460	−	0.750861i	$-0.729639\pi$
$461$	4.15851	−	4.95592i	0.193681	−	0.230820i	0.854141	+	0.520041i	$0.174083\pi$
$462$	−27.1787	−	10.7047i	−1.26447	−	0.498030i
$463$	−40.9842	+	7.22662i	−1.90470	+	0.335849i	−0.996564	−	0.0828321i	$-0.973603\pi$
$463$	−40.9842	+	7.22662i	−1.90470	+	0.335849i	−0.908133	+	0.418681i	$0.862492\pi$
$464$	1.92830	+	7.94483i	0.0895191	+	0.368830i
$465$	−2.67217	+	3.05153i	−0.123919	+	0.141512i
$466$	6.83944	−	8.41913i	0.316831	−	0.390008i
$467$	23.7060			1.09698			0.548491	−	0.836156i	$-0.315202\pi$
$467$	23.7060			1.09698			0.548491	+	0.836156i	$0.315202\pi$
$468$	−8.06914	+	9.41613i	−0.372996	+	0.435261i
$469$	9.25909	+	11.5161i	0.427545	+	0.531765i
$470$	−18.7002	+	7.14489i	−0.862576	+	0.329569i
$471$	−2.89870	+	0.448325i	−0.133565	+	0.0206577i
$472$	11.6792	−	2.63885i	0.537578	−	0.121463i
$473$	3.20563	+	18.1800i	0.147395	+	0.835918i
$474$	1.90101	−	1.57839i	0.0873162	−	0.0724979i
$475$	−8.52982	+	3.10460i	−0.391375	+	0.142449i
$476$	38.7865	−	7.27337i	1.77778	−	0.333374i
$477$	−42.4134	−	1.78960i	−1.94197	−	0.0819401i
$478$	−35.3064	+	0.561191i	−1.61488	+	0.0256683i
$479$	0.550764	+	0.462146i	0.0251650	+	0.0211160i	0.655283	−	0.755383i	$-0.272549\pi$
$479$	0.550764	+	0.462146i	0.0251650	+	0.0211160i	−0.630118	+	0.776499i	$0.716994\pi$
$480$	12.5798	−	5.42945i	0.574186	−	0.247819i
$481$	9.92161	−	1.74945i	0.452386	−	0.0797679i
$482$	−0.183927	−	0.954168i	−0.00837766	−	0.0434612i
$483$	−17.0867	−	22.1943i	−0.777472	−	1.00987i
$484$	14.6464	+	11.5168i	0.665747	+	0.523491i
$485$	9.42859	+	16.3308i	0.428130	+	0.741543i
$486$	−5.65757	−	21.3071i	−0.256632	−	0.966509i
$487$	10.5040	+	6.06448i	0.475981	+	0.274808i	0.718740	−	0.695279i	$-0.244719\pi$
$487$	10.5040	+	6.06448i	0.475981	+	0.274808i	−0.242759	+	0.970087i	$0.578052\pi$
$488$	1.34018	−	10.5081i	0.0606669	−	0.475680i
$489$	−0.0872242	+	4.13625i	−0.00394442	+	0.187048i
$490$	−7.23112	+	11.8047i	−0.326669	+	0.533284i
$491$	12.8946	−	35.4276i	0.581924	−	1.59882i	−0.202964	−	0.979186i	$-0.565057\pi$
$491$	12.8946	−	35.4276i	0.581924	−	1.59882i	0.784888	−	0.619638i	$-0.212720\pi$
$492$	−22.4841	−	3.71689i	−1.01366	−	0.167571i
$493$	−9.79779	+	11.6766i	−0.441270	+	0.525885i
$494$	4.47669	+	7.47685i	0.201416	+	0.336399i
$495$	−8.75582	−	16.7598i	−0.393545	−	0.753298i
$496$	3.71108	+	5.57664i	0.166632	+	0.250398i
$497$	14.8934	+	9.01990i	0.668062	+	0.404598i
$498$	36.7028	−	6.27543i	1.64469	−	0.281209i
$499$	7.60078	−	20.8830i	0.340257	−	0.934850i	−0.645062	−	0.764130i	$-0.723169\pi$
$499$	7.60078	−	20.8830i	0.340257	−	0.934850i	0.985320	−	0.170720i	$-0.0546092\pi$
$500$	22.0216	−	4.60909i	0.984837	−	0.206125i
$501$	−13.5023	+	10.8530i	−0.603238	+	0.484876i
$502$	6.56527	−	8.08162i	0.293022	−	0.360701i
$503$	−12.1719	−	21.0823i	−0.542717	−	0.940013i	−0.998747	−	0.0500486i	$-0.984062\pi$
$503$	−12.1719	−	21.0823i	−0.542717	−	0.940013i	0.456030	−	0.889964i	$-0.349271\pi$
$504$	19.6132	−	10.9235i	0.873641	−	0.486571i
$505$	−4.22346	+	7.31525i	−0.187942	+	0.325524i
$506$	13.9057	+	36.3952i	0.618184	+	1.61796i
$507$	−11.3737	−	9.95979i	−0.505126	−	0.442330i
$508$	−10.0736	−	11.2583i	−0.446945	−	0.499507i
$509$	6.54024	+	7.79436i	0.289891	+	0.345479i	0.891260	−	0.453493i	$-0.149822\pi$
$509$	6.54024	+	7.79436i	0.289891	+	0.345479i	−0.601369	+	0.798972i	$0.705378\pi$
$510$	22.0564	+	12.8874i	0.976673	+	0.570663i
$511$	−14.4016	−	8.72202i	−0.637089	−	0.385840i
$512$	−3.22564	−	22.3963i	−0.142555	−	0.989787i
$513$	−15.4616	−	0.979309i	−0.682644	−	0.0432375i
$514$	−9.70284	+	17.4402i	−0.427974	+	0.769254i
$515$	−0.497801	−	1.36770i	−0.0219358	−	0.0602680i
$516$	−12.3622	−	6.96198i	−0.544215	−	0.306484i
$517$	44.9324	−	7.92280i	1.97613	−	0.348444i
$518$	−17.9458	−	3.25796i	−0.788492	−	0.143147i
$519$	−9.99164	−	29.3638i	−0.438584	−	1.28893i
$520$	−3.15883	−	7.53963i	−0.138524	−	0.330635i
$521$	−17.7680	+	10.2584i	−0.778431	+	0.449427i	−0.835874	−	0.548922i	$-0.815039\pi$
$521$	−17.7680	+	10.2584i	−0.778431	+	0.449427i	0.0574432	+	0.998349i	$0.481705\pi$
$522$	−3.17886	+	8.06774i	−0.139135	+	0.353115i
$523$	−2.89320	+	5.01117i	−0.126511	+	0.219123i	−0.922322	−	0.386421i	$-0.873711\pi$
$523$	−2.89320	+	5.01117i	−0.126511	+	0.219123i	0.795812	+	0.605544i	$0.207044\pi$
$524$	20.5685	−	8.23569i	0.898541	−	0.359778i
$525$	13.2991	−	4.21659i	0.580421	−	0.184027i
$526$	16.7486	−	14.5135i	0.730273	−	0.632819i
$527$	−4.27150	+	11.7359i	−0.186070	+	0.511222i
$528$	−30.4952	+	6.72404i	−1.32713	+	0.292626i
$529$	−2.49343	+	14.1410i	−0.108410	+	0.614824i
$530$	13.6052	−	24.4544i	0.590972	−	1.06223i
$531$	11.7403	+	4.84286i	0.509485	+	0.210162i
$532$	−2.90784	−	15.5065i	−0.126071	−	0.672294i
$533$	−2.36103	+	13.3900i	−0.102267	+	0.579987i
$534$	−0.350688	−	0.297378i	−0.0151758	−	0.0128688i
$535$	15.1762	−	12.7343i	0.656124	−	0.550554i
$536$	15.0850	+	4.68923i	0.651571	+	0.202544i
$537$	−7.15677	−	4.33567i	−0.308837	−	0.187098i
$538$	27.6612	+	22.4711i	1.19256	+	0.968799i
$539$	21.2754	−	23.2990i	0.916396	−	1.00356i
$540$	14.2253	+	2.97258i	0.612160	+	0.127919i
$541$	15.7812	+	27.3339i	0.678487	+	1.17517i	0.975436	+	0.220281i	$0.0706975\pi$
$541$	15.7812	+	27.3339i	0.678487	+	1.17517i	−0.296949	+	0.954893i	$0.595969\pi$
$542$	−5.93807	−	15.5416i	−0.255062	−	0.667570i
$543$	−24.8214	+	13.6411i	−1.06519	+	0.585396i
$544$	30.0626	−	29.5974i	1.28893	−	1.26898i
$545$	5.78321	−	15.8892i	0.247726	−	0.680620i
$546$	−6.39160	−	11.7708i	−0.273535	−	0.503742i
$547$	40.0249	+	7.05747i	1.71134	+	0.301755i	0.941633	−	0.336642i	$-0.109291\pi$
$547$	40.0249	+	7.05747i	1.71134	+	0.301755i	0.769707	+	0.638397i	$0.220402\pi$
$548$	−28.7011	+	0.912631i	−1.22605	+	0.0389857i
$549$	7.57868	−	8.29503i	0.323450	−	0.354023i
$550$	−19.4041	+	0.308425i	−0.827393	+	0.0131513i
$551$	4.66819	+	3.91708i	0.198872	+	0.166873i
$552$	−28.4002	−	9.48942i	−1.20879	−	0.403897i
$553$	0.860060	+	2.52646i	0.0365735	+	0.107436i
$554$	−8.35292	−	9.63925i	−0.354881	−	0.409533i
$555$	−7.39688	−	9.20251i	−0.313980	−	0.390625i
$556$	−2.29628	+	15.9771i	−0.0973841	+	0.677580i
$557$	−2.95486			−0.125201			−0.0626007	−	0.998039i	$-0.519939\pi$
$557$	−2.95486			−0.125201			−0.0626007	+	0.998039i	$0.519939\pi$
$558$	−0.186665	+	7.10246i	−0.00790216	+	0.300671i
$559$	−4.23238	+	7.33069i	−0.179010	+	0.310055i
$560$	0.630621	+	14.7858i	0.0266486	+	0.624815i
$561$	−43.8017	−	38.3563i	−1.84931	−	1.61941i
$562$	26.8888	−	5.18315i	1.13424	−	0.218638i
$563$	27.9239	+	10.1635i	1.17685	+	0.428338i	0.855088	−	0.518482i	$-0.173503\pi$
$563$	27.9239	+	10.1635i	1.17685	+	0.428338i	0.321762	+	0.946821i	$0.395725\pi$
$564$	−17.2067	+	30.5535i	−0.724534	+	1.28653i
$565$	15.3272	+	2.70259i	0.644819	+	0.113699i
$566$	0.676735	+	42.5757i	0.0284453	+	1.78959i
$567$	23.6799	+	2.50246i	0.994462	+	0.105094i
$568$	18.5929	−	0.887193i	0.780141	−	0.0372258i
$569$	1.15117	−	6.52860i	0.0482595	−	0.273693i	−0.951124	−	0.308810i	$-0.900069\pi$
$569$	1.15117	−	6.52860i	0.0482595	−	0.273693i	0.999383	+	0.0351169i	$0.0111803\pi$
$570$	5.15227	−	8.81797i	0.215805	−	0.369344i
$571$	−4.46287	+	12.2616i	−0.186765	+	0.513133i	−0.997371	−	0.0724584i	$-0.976916\pi$
$571$	−4.46287	+	12.2616i	−0.186765	+	0.513133i	0.810606	+	0.585592i	$0.199138\pi$
$572$	3.81677	+	18.2360i	0.159587	+	0.762487i
$573$	−5.81779	+	6.64373i	−0.243042	+	0.277546i
$574$	12.4152	−	21.2549i	0.518202	−	0.887162i
$575$	−16.1154	−	9.30425i	−0.672060	−	0.388014i
$576$	10.8780	−	21.3932i	0.453249	−	0.891384i
$577$		−	29.6107i		−	1.23271i	−0.787469	−	0.616355i	$-0.788609\pi$
$577$		−	29.6107i		−	1.23271i	0.787469	−	0.616355i	$-0.211391\pi$
$578$	53.9279	+	8.62759i	2.24310	+	0.358860i
$579$	−12.0880	+	9.71623i	−0.502361	+	0.403793i
$580$	−3.81168	−	4.25995i	−0.158271	−	0.176885i
$581$	−7.81211	+	39.4529i	−0.324101	+	1.63678i
$582$	30.9799	+	11.4582i	1.28416	+	0.474959i
$583$	−40.9973	+	48.8586i	−1.69793	+	2.02352i
$584$	−17.9789	+	0.857895i	−0.743972	+	0.0354999i
$585$	1.86424	−	8.46770i	0.0770769	−	0.350096i
$586$	−18.9955	+	0.301931i	−0.784696	+	0.0124726i
$587$	−4.25679	+	24.1415i	−0.175697	+	0.996425i	0.761640	+	0.648000i	$0.224395\pi$
$587$	−4.25679	+	24.1415i	−0.175697	+	0.996425i	−0.937337	+	0.348425i	$0.886717\pi$
$588$	3.46383	+	24.0000i	0.142846	+	0.989745i
$589$	4.69190	+	1.70771i	0.193327	+	0.0703651i
$590$	−6.32693	+	5.48262i	−0.260476	+	0.225716i
$591$	−16.5634	−	30.1388i	−0.681329	−	1.23975i
$592$	−17.8618	+	7.81944i	−0.734117	+	0.321377i
$593$	8.43651	−	4.87082i	0.346446	−	0.200021i	−0.316673	−	0.948535i	$-0.602566\pi$
$593$	8.43651	−	4.87082i	0.346446	−	0.200021i	0.663119	+	0.748514i	$0.269232\pi$
$594$	−30.5533	−	12.7892i	−1.25362	−	0.524747i
$595$	−21.5038	+	17.2893i	−0.881568	+	0.708791i
$596$	30.6192	+	24.0766i	1.25421	+	0.986215i
$597$	5.61260	−	9.26456i	0.229708	−	0.379173i
$598$	−5.84263	+	16.8826i	−0.238923	+	0.690383i
$599$	−5.96105	−	7.10410i	−0.243562	−	0.290266i	0.630390	−	0.776279i	$-0.282895\pi$
$599$	−5.96105	−	7.10410i	−0.243562	−	0.290266i	−0.873951	+	0.486013i	$0.838451\pi$
$600$	9.27985	−	11.6763i	0.378848	−	0.476685i
$601$	21.4389	+	3.78025i	0.874510	+	0.154200i	0.592848	−	0.805314i	$-0.298003\pi$
$601$	21.4389	+	3.78025i	0.874510	+	0.154200i	0.281662	+	0.959514i	$0.409114\pi$
$602$	11.7889	−	9.79094i	0.480481	−	0.399049i
$603$	10.2194	+	13.2779i	0.416166	+	0.540717i
$604$	12.4491	+	6.66919i	0.506545	+	0.271365i
$605$	−12.8296	−	2.26221i	−0.521599	−	0.0919719i
$606$	2.49362	+	14.5843i	0.101296	+	0.592447i
$607$	−15.1826	−	5.52603i	−0.616245	−	0.224295i	0.0149887	−	0.999888i	$-0.495229\pi$
$607$	−15.1826	−	5.52603i	−0.616245	−	0.224295i	−0.631233	+	0.775593i	$0.717451\pi$
$608$	−11.8328	−	12.0188i	−0.479883	−	0.487427i
$609$	−6.91560	−	6.31667i	−0.280234	−	0.255964i
$610$	2.64357	+	6.91896i	0.107035	+	0.280141i
$611$	18.1180	+	10.4604i	0.732976	+	0.423184i
$612$	44.1449	−	7.31221i	1.78445	−	0.295579i
$613$	−11.2224	−	19.4378i	−0.453269	−	0.785085i	0.545318	−	0.838229i	$-0.316409\pi$
$613$	−11.2224	−	19.4378i	−0.453269	−	0.785085i	−0.998587	+	0.0531442i	$0.983076\pi$
$614$	9.41701	+	24.6470i	0.380040	+	0.994672i
$615$	15.0849	−	5.13293i	0.608280	−	0.206980i
$616$	4.96720	−	33.3620i	0.200134	−	1.34419i
$617$	−2.10885	−	11.9599i	−0.0848992	−	0.481488i	−0.997378	−	0.0723641i	$-0.976946\pi$
$617$	−2.10885	−	11.9599i	−0.0848992	−	0.481488i	0.912479	−	0.409123i	$-0.134165\pi$
$618$	−2.20125	−	1.28618i	−0.0885474	−	0.0517376i
$619$	28.1987	−	10.2635i	1.13340	−	0.412524i	0.293875	−	0.955844i	$-0.405055\pi$
$619$	28.1987	−	10.2635i	1.13340	−	0.412524i	0.839526	+	0.543319i	$0.182833\pi$
$620$	−4.12853	−	2.21173i	−0.165806	−	0.0888251i
$621$	−18.8362	−	25.5714i	−0.755870	−	1.02614i
$622$	−0.232252	−	14.6117i	−0.00931245	−	0.585878i
$623$	0.435211	−	0.239256i	0.0174364	−	0.00958559i
$624$	−12.6935	−	6.62628i	−0.508147	−	0.265264i
$625$	−0.389711	+	0.327006i	−0.0155884	+	0.0130802i
$626$	−3.65557	+	3.16774i	−0.146106	+	0.126608i
$627$	−15.3346	+	17.5116i	−0.612403	+	0.699344i
$628$	−1.25896	−	3.14424i	−0.0502380	−	0.125469i
$629$	−31.4830	−	18.1767i	−1.25531	−	0.724754i
$630$	−8.48148	+	13.2083i	−0.337910	+	0.526232i
$631$	−17.4816	+	10.0930i	−0.695930	+	0.401795i	−0.805830	−	0.592147i	$-0.798280\pi$
$631$	−17.4816	+	10.0930i	−0.695930	+	0.401795i	0.109900	+	0.993943i	$0.464947\pi$
$632$	2.27053	+	1.72768i	0.0903169	+	0.0687236i
$633$	27.2417	+	33.8916i	1.08276	+	1.34707i
$634$	18.5290	−	3.57169i	0.735881	−	0.141850i
$635$	9.92592	+	3.61274i	0.393898	+	0.143367i
$636$	−9.02809	−	48.1797i	−0.357987	−	1.91045i
$637$	14.3403	−	1.91324i	0.568183	−	0.0758052i
$638$	6.69266	+	11.1779i	0.264965	+	0.442538i
$639$	16.6667	+	10.5836i	0.659326	+	0.418681i
$640$	9.38284	+	12.7385i	0.370889	+	0.503532i
$641$	−4.63002	−	3.88505i	−0.182875	−	0.153450i	0.546755	−	0.837293i	$-0.315863\pi$
$641$	−4.63002	−	3.88505i	−0.182875	−	0.153450i	−0.729630	+	0.683843i	$0.760307\pi$
$642$	6.20325	−	34.1430i	0.244823	−	1.34752i
$643$	9.95980	+	3.62507i	0.392776	+	0.142959i	0.530856	−	0.847462i	$-0.321871\pi$
$643$	9.95980	+	3.62507i	0.392776	+	0.142959i	−0.138079	+	0.990421i	$0.544093\pi$
$644$	20.5198	−	24.9998i	0.808594	−	0.985132i
$645$	9.91787	+	0.209145i	0.390516	+	0.00823509i
$646$	4.96764	−	31.0509i	0.195449	−	1.22168i
$647$	−7.24480	+	12.5484i	−0.284822	+	0.493327i	−0.972566	−	0.232627i	$-0.925268\pi$
$647$	−7.24480	+	12.5484i	−0.284822	+	0.493327i	0.687744	+	0.725954i	$0.258601\pi$
$648$	22.4971	−	11.9114i	0.883768	−	0.467925i
$649$	16.5245	−	9.54045i	0.648645	−	0.374495i
$650$	−6.90673	−	5.61082i	−0.270904	−	0.220074i
$651$	−7.09471	−	2.92544i	−0.278064	−	0.114657i
$652$	−4.67588	+	0.978653i	−0.183122	+	0.0383270i
$653$	−4.30156	−	24.3954i	−0.168333	−	0.954664i	−0.945561	−	0.325445i	$-0.894486\pi$
$653$	−4.30156	−	24.3954i	−0.168333	−	0.954664i	0.777228	−	0.629219i	$-0.216625\pi$
$654$	−9.98548	−	27.8844i	−0.390463	−	1.09037i
$655$	−9.95775	+	11.8672i	−0.389082	+	0.463689i
$656$	−1.67181	−	26.2616i	−0.0652733	−	1.02534i
$657$	−16.1164	−	10.2341i	−0.628759	−	0.399271i
$658$	−24.1986	−	29.1367i	−0.943359	−	1.13587i
$659$	6.11947	+	16.8131i	0.238381	+	0.654945i	0.999976	+	0.00689282i	$0.00219407\pi$
$659$	6.11947	+	16.8131i	0.238381	+	0.654945i	−0.761596	+	0.648053i	$0.775584\pi$
$660$	16.5750	−	14.2131i	0.645179	−	0.553244i
$661$	−2.81189	+	0.495812i	−0.109370	+	0.0192848i	−0.228065	−	0.973646i	$-0.573240\pi$
$661$	−2.81189	+	0.495812i	−0.109370	+	0.0192848i	0.118695	+	0.992931i	$0.462129\pi$
$662$	1.36843	+	7.09908i	0.0531857	+	0.275914i
$663$	−4.08051	−	26.3830i	−0.158474	−	1.02463i
$664$	16.6144	+	39.6560i	0.644765	+	1.53895i
$665$	6.91211	+	8.59703i	0.268040	+	0.333379i
$666$	−20.2656	−	4.12511i	−0.785277	−	0.159845i
$667$			12.4926i			0.483715i
$668$	−15.7243	−	12.3644i	−0.608393	−	0.478393i
$669$	14.9785	+	13.1164i	0.579102	+	0.507109i
$670$	−10.8456	+	2.09062i	−0.419001	+	0.0807676i
$671$	−2.93139	−	16.6247i	−0.113165	−	0.641791i
$672$	17.3945	+	19.2206i	0.671006	+	0.741452i
$673$	−10.2848	−	8.63001i	−0.396452	−	0.332663i	0.422668	−	0.906284i	$-0.361093\pi$
$673$	−10.2848	−	8.63001i	−0.396452	−	0.332663i	−0.819120	+	0.573622i	$0.805538\pi$
$674$	36.0669	−	21.5947i	1.38924	−	0.831796i
$675$	15.1778	−	4.46012i	0.584195	−	0.171670i
$676$	8.24359	−	15.3879i	0.317061	−	0.591844i
$677$	−19.2324	−	3.39119i	−0.739162	−	0.130334i	−0.208625	−	0.977996i	$-0.566899\pi$
$677$	−19.2324	−	3.39119i	−0.739162	−	0.130334i	−0.530537	+	0.847662i	$0.678010\pi$
$678$	23.6799	−	13.5082i	0.909420	−	0.518778i
$679$	−23.5006	+	26.8442i	−0.901869	+	1.03018i
$680$	−8.75608	+	28.1678i	−0.335780	+	1.08018i
$681$	−22.8970	−	20.0505i	−0.877416	−	0.768338i
$682$	8.28534	+	6.73076i	0.317262	+	0.257734i
$683$	−25.3892	+	14.6585i	−0.971491	+	0.560891i	−0.899690	−	0.436528i	$-0.856208\pi$
$683$	−25.3892	+	14.6585i	−0.971491	+	0.560891i	−0.0718005	+	0.997419i	$0.522874\pi$
$684$	−2.92336	−	17.6488i	−0.111778	−	0.674817i
$685$	17.3880	−	10.0390i	0.664361	−	0.383569i
$686$	−25.5518	−	5.75382i	−0.975572	−	0.219682i
$687$	19.1699	+	23.8495i	0.731379	+	0.909914i
$688$	4.61382	−	15.7195i	0.175900	−	0.599300i
$689$	−28.8012	+	5.07842i	−1.09724	+	0.193472i
$690$	20.6371	−	3.52851i	0.785639	−	0.134328i
$691$	−4.06013	−	3.40686i	−0.154455	−	0.129603i	0.562285	−	0.826943i	$-0.309922\pi$
$691$	−4.06013	−	3.40686i	−0.154455	−	0.129603i	−0.716740	+	0.697340i	$0.754367\pi$
$692$	30.4324	−	18.8845i	1.15686	−	0.717881i
$693$	24.6792	−	25.9008i	0.937484	−	0.983889i
$694$	1.42431	−	2.56010i	0.0540661	−	0.0971800i
$695$	−3.86003	−	10.6053i	−0.146419	−	0.402284i
$696$	−9.90353	−	1.47588i	−0.375392	−	0.0559431i
$697$	37.5837	−	31.5365i	1.42359	−	1.19453i
$698$	−37.4235	+	32.4294i	−1.41650	+	1.22747i
$699$	6.39843	+	11.6426i	0.242011	+	0.440363i
$700$	8.20566	+	13.8635i	0.310145	+	0.523989i
$701$	2.90479			0.109712			0.0548561	−	0.998494i	$-0.482530\pi$
$701$	2.90479			0.109712			0.0548561	+	0.998494i	$0.482530\pi$
$702$	−6.96257	−	13.4976i	−0.262785	−	0.509433i
$703$	−7.26692	+	12.5867i	−0.274077	+	0.474715i
$704$	−15.5031	−	32.5558i	−0.584295	−	1.22699i
$705$	0.516909	−	24.5123i	0.0194679	−	0.923187i
$706$	−7.10540	−	36.8610i	−0.267415	−	1.38728i
$707$	−15.6771	−	3.10424i	−0.589597	−	0.116747i
$708$	−2.39177	+	14.4682i	−0.0898884	+	0.543749i
$709$	−19.1021	+	6.95259i	−0.717394	+	0.261110i	−0.674819	−	0.737983i	$-0.735778\pi$
$709$	−19.1021	+	6.95259i	−0.717394	+	0.261110i	−0.0425751	+	0.999093i	$0.513556\pi$
$710$	−11.1664	+	6.68578i	−0.419068	+	0.250913i
$711$	0.914212	+	2.88478i	0.0342856	+	0.108188i
$712$	0.243249	−	0.471930i	0.00911613	−	0.0176863i
$713$	3.50084	+	9.61849i	0.131108	+	0.360215i
$714$	−9.63391	+	47.3617i	−0.360540	+	1.77247i
$715$	−8.37354	−	9.97920i	−0.313153	−	0.373201i
$716$	3.01441	−	9.17986i	0.112654	−	0.343067i
$717$	15.6448	−	40.3178i	0.584265	−	1.50570i
$718$	−6.10810	+	38.1795i	−0.227952	+	1.42485i
$719$	−23.6729	+	41.0027i	−0.882851	+	1.52914i	−0.0346933	+	0.999398i	$0.511045\pi$
$719$	−23.6729	+	41.0027i	−0.882851	+	1.52914i	−0.848157	+	0.529744i	$0.822288\pi$
$720$	0.359164	+	16.7769i	0.0133853	+	0.625240i
$721$	2.14610	−	1.72549i	0.0799250	−	0.0642606i
$722$	14.1187	+	2.25877i	0.525445	+	0.0840627i
$723$	1.16743	+	0.231327i	0.0434171	+	0.00860316i
$724$	−21.8075	−	24.3722i	−0.810471	−	0.905785i
$725$	−5.84727	−	2.12823i	−0.217162	−	0.0790406i
$726$	−19.8213	+	11.3070i	−0.735637	+	0.419644i
$727$	19.5544	+	16.4081i	0.725233	+	0.608543i	0.928828	−	0.370512i	$-0.120818\pi$
$727$	19.5544	+	16.4081i	0.725233	+	0.608543i	−0.203594	+	0.979055i	$0.565262\pi$
$728$	11.5779	−	10.2546i	0.429105	−	0.380062i
$729$	26.7842	+	3.40660i	0.992009	+	0.126170i
$730$	10.7977	−	6.46499i	0.399639	−	0.239280i
$731$	28.7022	−	10.4468i	1.06159	−	0.386387i
$732$	11.3046	+	6.36639i	0.417830	+	0.235309i
$733$	−12.4957	−	14.8918i	−0.461540	−	0.550042i	0.484204	−	0.874955i	$-0.339109\pi$
$733$	−12.4957	−	14.8918i	−0.461540	−	0.550042i	−0.945744	+	0.324913i	$0.894665\pi$
$734$	−7.63142	+	22.0515i	−0.281681	+	0.813935i
$735$	−10.0592	−	13.6482i	−0.371038	−	0.503423i
$736$	3.28202	−	34.4198i	0.120977	−	1.26873i
$737$	25.1738			0.927289
$738$	14.5857	−	23.7967i	0.536909	−	0.875967i
$739$			4.24290i			0.156078i	0.996950	+	0.0780388i	$0.0248658\pi$
$739$			4.24290i			0.156078i	−0.996950	+	0.0780388i	$0.975134\pi$
$740$	8.42696	−	10.7169i	0.309781	−	0.393963i
$741$	−10.5477	+	1.63136i	−0.387481	+	0.0599294i
$742$	52.0943	+	9.45746i	1.91244	+	0.347194i
$743$	−16.0409	−	19.1168i	−0.588483	−	0.701327i	0.386830	−	0.922151i	$-0.373570\pi$
$743$	−16.0409	−	19.1168i	−0.588483	−	0.701327i	−0.975314	+	0.220824i	$0.929125\pi$
$744$	−8.03867	+	1.63897i	−0.294712	+	0.0600875i
$745$	−26.8211	−	4.72928i	−0.982649	−	0.173268i
$746$	−0.377220	−	23.7322i	−0.0138110	−	0.868896i
$747$	−9.80531	+	44.5373i	−0.358757	+	1.62954i
$748$	31.7471	−	59.2609i	1.16079	−	2.16679i
$749$	32.0610	+	19.4171i	1.17148	+	0.709484i
$750$	−4.92573	+	27.1114i	−0.179862	+	0.989970i
$751$	−20.1505	+	3.55307i	−0.735301	+	0.129653i	−0.528744	−	0.848781i	$-0.677337\pi$
$751$	−20.1505	+	3.55307i	−0.735301	+	0.129653i	−0.206557	+	0.978435i	$0.566226\pi$
$752$	−38.8512	−	11.4032i	−1.41676	−	0.415832i
$753$	6.14193	+	11.1759i	0.223824	+	0.407271i
$754$	−0.943731	+	5.89892i	−0.0343686	+	0.214826i
$755$	−9.87475			−0.359379
$756$	3.34931	+	27.2907i	0.121813	+	0.992553i
$757$	−7.56015			−0.274778			−0.137389	−	0.990517i	$-0.543871\pi$
$757$	−7.56015			−0.274778			−0.137389	+	0.990517i	$0.543871\pi$
$758$	3.16113	−	19.7591i	0.114817	−	0.717682i
$759$	−47.7070	−	1.00603i	−1.73165	−	0.0365166i
$760$	11.2612	+	3.50061i	0.408488	+	0.126981i
$761$	−47.1950	+	8.32175i	−1.71082	+	0.301663i	−0.941452	−	0.337146i	$-0.890538\pi$
$761$	−47.1950	+	8.32175i	−1.71082	+	0.301663i	−0.769365	+	0.638810i	$0.779427\pi$
$762$	17.4192	−	6.23788i	0.631033	−	0.225974i
$763$	31.9845	+	0.670161i	1.15792	+	0.0242615i
$764$	−8.98854	−	4.81532i	−0.325194	−	0.174212i
$765$	−24.7934	+	19.0824i	−0.896409	+	0.689926i
$766$	−0.343754	−	21.6267i	−0.0124203	−	0.781405i
$767$	8.61632	+	1.51929i	0.311117	+	0.0548584i
$768$	26.8986	+	6.66819i	0.970620	+	0.240618i
$769$	−12.8432	−	15.3060i	−0.463139	−	0.551948i	0.483037	−	0.875600i	$-0.339534\pi$
$769$	−12.8432	−	15.3060i	−0.463139	−	0.551948i	−0.946176	+	0.323652i	$0.895089\pi$
$770$	7.95400	+	22.2021i	0.286642	+	0.800107i
$771$	−15.3134	−	19.0515i	−0.551497	−	0.686122i
$772$	−14.0773	−	11.0693i	−0.506654	−	0.398393i
$773$			8.92667i			0.321070i	0.987030	+	0.160535i	$0.0513220\pi$
$773$			8.92667i			0.321070i	−0.987030	+	0.160535i	$0.948678\pi$
$774$	13.5999	−	10.8158i	0.488840	−	0.388764i
$775$	−5.09842			−0.183141
$776$	−4.82529	+	37.8344i	−0.173218	+	1.35818i
$777$	11.9722	−	18.8591i	0.429500	−	0.676565i
$778$	−2.39791	+	6.92891i	−0.0859693	+	0.248414i
$779$	−12.6080	−	15.0257i	−0.451730	−	0.538351i
$780$	10.0112	−	0.107149i	0.358460	−	0.00383655i
$781$	27.8741	−	10.1454i	0.997415	−	0.363029i
$782$	55.3085	−	33.1154i	1.97783	−	1.18420i
$783$	−7.68782	−	7.32720i	−0.274740	−	0.261853i
$784$	−26.0977	+	10.1446i	−0.932059	+	0.362306i
$785$	1.81410	+	1.52221i	0.0647479	+	0.0543299i
$786$	−0.140862	+	27.1352i	−0.00502438	+	0.967879i
$787$	−33.0852	−	12.0420i	−1.17936	−	0.429252i	−0.323384	−	0.946268i	$-0.604821\pi$
$787$	−33.0852	−	12.0420i	−1.17936	−	0.429252i	−0.855976	+	0.517016i	$0.827043\pi$
$788$	29.5935	−	26.4794i	1.05422	−	0.943288i
$789$	8.74360	+	25.6960i	0.311280	+	0.914802i
$790$	−1.96984	−	0.315142i	−0.0700837	−	0.0112123i
$791$	4.50468	+	29.0995i	0.160168	+	1.03466i
$792$	6.43366	−	37.7010i	0.228610	−	1.33965i
$793$	3.87030	−	6.70356i	0.137438	−	0.238050i
$794$	−4.64870	+	29.0573i	−0.164976	+	1.03121i
$795$	21.4722	+	26.7137i	0.761540	+	0.947438i
$796$	11.8835	+	3.90221i	0.421199	+	0.138310i
$797$	−7.69568	−	9.17136i	−0.272595	−	0.324866i	0.612328	−	0.790604i	$-0.290233\pi$
$797$	−7.69568	−	9.17136i	−0.272595	−	0.324866i	−0.884923	+	0.465738i	$0.845789\pi$
$798$	18.9348	+	3.85156i	0.670286	+	0.136344i
$799$	−25.8195	−	70.9384i	−0.913427	−	2.50962i
$800$	15.5514	+	7.39992i	0.549824	+	0.261627i
$801$	0.499128	−	0.260759i	0.0176358	−	0.00921347i
$802$	−10.4340	+	6.24724i	−0.368437	+	0.220598i
$803$	−26.9536	+	9.81032i	−0.951173	+	0.346199i
$804$	−12.2769	+	14.9531i	−0.432971	+	0.527356i
$805$	−4.39255	+	22.1833i	−0.154817	+	0.781860i
$806$	0.926463	+	4.80625i	0.0326333	+	0.169293i
$807$	−38.2519	+	21.0222i	−1.34653	+	0.740015i
$808$	−15.7578	+	6.60194i	−0.554357	+	0.232255i
$809$	−22.2229	+	38.4913i	−0.781317	+	1.35328i	0.149858	+	0.988708i	$0.452118\pi$
$809$	−22.2229	+	38.4913i	−0.781317	+	1.35328i	−0.931175	+	0.364573i	$0.881215\pi$
$810$	−9.93271	+	14.7694i	−0.349000	+	0.518944i
$811$	−13.7763			−0.483750			−0.241875	−	0.970307i	$-0.577762\pi$
$811$	−13.7763			−0.483750			−0.241875	+	0.970307i	$0.577762\pi$
$812$	5.30576	−	9.42426i	0.186196	−	0.330727i
$813$	20.3720	+	0.429600i	0.714478	+	0.0150667i
$814$	−23.4824	+	20.3487i	−0.823057	+	0.713222i
$815$	2.55875	−	2.14705i	0.0896292	−	0.0752078i
$816$	19.7181	+	47.7582i	0.690273	+	1.67187i
$817$	−4.17653	−	11.4749i	−0.146118	−	0.401457i
$818$	−17.3425	+	31.1719i	−0.606365	+	1.08990i
$819$	16.3027	−	1.82391i	0.569663	−	0.0637325i
$820$	9.70140	+	15.6338i	0.338788	+	0.545956i
$821$	15.3304	+	12.8637i	0.535035	+	0.448947i	0.869836	−	0.493341i	$-0.164225\pi$
$821$	15.3304	+	12.8637i	0.535035	+	0.448947i	−0.334801	+	0.942289i	$0.608669\pi$
$822$	12.2000	−	32.9854i	0.425524	−	1.15050i
$823$	43.1896	−	7.61549i	1.50549	−	0.265459i	0.640781	−	0.767724i	$-0.278611\pi$
$823$	43.1896	−	7.61549i	1.50549	−	0.265459i	0.864714	+	0.502265i	$0.167500\pi$
$824$	0.873868	−	2.81118i	0.0304426	−	0.0979320i
$825$	8.59823	−	22.1583i	0.299352	−	0.771453i
$826$	−13.6773	−	7.98904i	−0.475892	−	0.277974i
$827$	−25.1541	+	14.5228i	−0.874695	+	0.505006i	−0.868906	−	0.494978i	$-0.835176\pi$
$827$	−25.1541	+	14.5228i	−0.874695	+	0.505006i	−0.00578955	+	0.999983i	$0.501843\pi$
$828$	23.8635	−	27.8471i	0.829314	−	0.967753i
$829$	−5.18021	+	2.99080i	−0.179916	+	0.103875i	−0.587253	−	0.809403i	$-0.699791\pi$
$829$	−5.18021	+	2.99080i	−0.179916	+	0.103875i	0.407337	+	0.913278i	$0.366457\pi$
$830$	−23.3335	−	18.9555i	−0.809918	−	0.657953i
$831$	14.7887	−	5.03218i	0.513016	−	0.174564i
$832$	4.14993	−	16.0048i	0.143873	−	0.554868i
$833$	−44.0771	−	27.9728i	−1.52718	−	0.969202i
$834$	−17.0689	−	9.97321i	−0.591047	−	0.345344i
$835$	13.7738	+	2.42870i	0.476663	+	0.0840486i
$836$	−23.6920	−	12.6922i	−0.819406	−	0.438970i
$837$	−7.97245	−	3.48709i	−0.275568	−	0.120531i
$838$	−37.5294	+	22.4704i	−1.29643	+	0.776226i
$839$	3.50248	+	2.93893i	0.120919	+	0.101463i	0.701242	−	0.712923i	$-0.252629\pi$
$839$	3.50248	+	2.93893i	0.120919	+	0.101463i	−0.580323	+	0.814386i	$0.697074\pi$
$840$	−17.0670	−	6.10296i	−0.588866	−	0.210572i
$841$	−4.31040	−	24.4455i	−0.148634	−	0.842947i
$842$	6.64779	−	1.28144i	0.229098	−	0.0441614i
$843$	−6.51890	+	32.8986i	−0.224523	+	1.13309i
$844$	−31.0353	+	39.4690i	−1.06828	+	1.35858i
$845$			12.2059i			0.419896i
$846$	−26.7315	−	33.6126i	−0.919046	−	1.15563i
$847$	−3.77065	−	24.3578i	−0.129561	−	0.836945i
$848$	51.8506	−	22.6988i	1.78056	−	0.779481i
$849$	−48.6189	−	18.8659i	−1.66860	−	0.647476i
$850$	6.07763	+	31.5292i	0.208461	+	1.08144i
$851$	−29.3420	+	5.17378i	−1.00583	+	0.177355i
$852$	−7.56748	+	21.5048i	−0.259257	+	0.736744i
$853$	2.06828	+	5.68255i	0.0708165	+	0.194567i	0.970052	−	0.242899i	$-0.0780983\pi$
$853$	2.06828	+	5.68255i	0.0708165	+	0.194567i	−0.899235	+	0.437466i	$0.855876\pi$
$854$	−10.7804	+	8.95334i	−0.368898	+	0.306377i
$855$	7.62900	+	9.91222i	0.260906	+	0.338991i
$856$	40.0248	−	1.90985i	1.36802	−	0.0652775i
$857$	12.3306	−	14.6950i	0.421204	−	0.501972i	−0.513159	−	0.858294i	$-0.671525\pi$
$857$	12.3306	−	14.6950i	0.421204	−	0.501972i	0.934363	+	0.356322i	$0.115969\pi$
$858$	−22.4509	−	4.07898i	−0.766462	−	0.139254i
$859$	5.27162	+	29.8968i	0.179865	+	1.02007i	0.932377	+	0.361488i	$0.117731\pi$
$859$	5.27162	+	29.8968i	0.179865	+	1.02007i	−0.752512	+	0.658579i	$0.771158\pi$
$860$	2.34661	+	11.2118i	0.0800186	+	0.382318i
$861$	18.3908	+	23.8881i	0.626756	+	0.814105i
$862$	−44.6547	−	36.2761i	−1.52094	−	1.23557i
$863$	−5.63036	+	3.25069i	−0.191660	+	0.110655i	−0.592759	−	0.805380i	$-0.701961\pi$
$863$	−5.63036	+	3.25069i	−0.191660	+	0.110655i	0.401100	+	0.916034i	$0.368628\pi$
$864$	19.2566	+	22.2077i	0.655123	+	0.755522i
$865$	−12.5211	+	21.6872i	−0.425730	+	0.737387i
$866$	3.64330	−	22.7729i	0.123804	−	0.773855i
$867$	−34.6577	+	57.2086i	−1.17704	+	1.94290i
$868$	1.44410	−	8.74293i	0.0490159	−	0.296754i
$869$	4.27246	+	1.55505i	0.144933	+	0.0527514i
$870$	6.59114	−	2.36030i	0.223461	−	0.0800218i
$871$	8.84248	+	7.41972i	0.299616	+	0.251408i
$872$	28.7697	−	18.4925i	0.974266	−	0.626234i
$873$	−27.2870	+	29.8662i	−0.923524	+	1.01082i
$874$	−13.2393	−	22.1119i	−0.447825	−	0.747946i
$875$	−25.4582	−	15.4182i	−0.860644	−	0.521231i
$876$	7.31757	−	20.7947i	0.247238	−	0.702587i
$877$	−11.4878	−	4.18123i	−0.387917	−	0.141190i	0.140697	−	0.990053i	$-0.455066\pi$
$877$	−11.4878	−	4.18123i	−0.387917	−	0.141190i	−0.528614	+	0.848863i	$0.677288\pi$
$878$	9.71720	−	1.87311i	0.327940	−	0.0632143i
$879$	8.41717	−	21.6917i	0.283904	−	0.731643i
$880$	20.3042	+	14.9463i	0.684456	+	0.503840i
$881$	9.01177	−	5.20295i	0.303614	−	0.175292i	−0.340451	−	0.940262i	$-0.610580\pi$
$881$	9.01177	−	5.20295i	0.303614	−	0.175292i	0.644065	+	0.764970i	$0.277246\pi$
$882$	−28.8280	−	7.13749i	−0.970691	−	0.240332i
$883$	7.07432	+	4.08436i	0.238070	+	0.137450i	0.614289	−	0.789081i	$-0.289443\pi$
$883$	7.07432	+	4.08436i	0.238070	+	0.137450i	−0.376219	+	0.926531i	$0.622776\pi$
$884$	28.6179	−	11.4587i	0.962525	−	0.385397i
$885$	−3.30298	−	9.70691i	−0.111028	−	0.326294i
$886$	22.0253	−	19.0861i	0.739954	−	0.641209i
$887$	9.77722	−	8.20406i	0.328287	−	0.275465i	−0.463714	−	0.885985i	$-0.653484\pi$
$887$	9.77722	−	8.20406i	0.328287	−	0.275465i	0.792001	+	0.610519i	$0.209039\pi$
$888$	−0.635054	−	23.8722i	−0.0213110	−	0.801097i
$889$	−0.418646	+	19.9806i	−0.0140409	+	0.670127i
$890$	0.00589986	+	0.371180i	0.000197764	+	0.0124420i
$891$	28.6004	−	28.7684i	0.958149	−	0.963776i
$892$	−10.8563	+	20.2649i	−0.363495	+	0.678520i
$893$	−28.3606	+	10.3224i	−0.949051	+	0.345426i
$894$	−41.4376	+	23.6380i	−1.38588	+	0.790574i
$895$	1.17312	+	6.65311i	0.0392132	+	0.222389i
$896$	−17.0944	+	24.5719i	−0.571085	+	0.820891i
$897$	−16.4609	−	14.4145i	−0.549614	−	0.481287i
$898$	−3.22503	−	8.44082i	−0.107621	−	0.281674i
$899$	1.71138	+	2.96420i	0.0570778	+	0.0988616i
$900$	8.96871	+	15.9136i	0.298957	+	0.530452i
$901$	91.3913	+	52.7648i	3.04469	+	1.75785i
$902$	−14.9670	−	39.1729i	−0.498346	−	1.30431i
$903$	5.67246	+	17.8909i	0.188767	+	0.595373i
$904$	21.3608	+	23.1227i	0.710451	+	0.769049i
$905$	21.4878	+	7.82092i	0.714279	+	0.259976i
$906$	−13.3078	+	11.0494i	−0.442122	+	0.367090i
$907$	27.1708	+	4.79095i	0.902192	+	0.159081i	0.605456	−	0.795879i	$-0.292991\pi$
$907$	27.1708	+	4.79095i	0.902192	+	0.159081i	0.296736	+	0.954960i	$0.404102\pi$
$908$	16.5956	−	30.9782i	0.550744	−	1.02805i
$909$	−17.6974	−	3.89626i	−0.586987	−	0.129231i
$910$	−3.74993	+	10.1430i	−0.124309	+	0.336237i
$911$	0.410832	+	0.0724408i	0.0136115	+	0.00240007i	0.180450	−	0.983584i	$-0.442245\pi$
$911$	0.410832	+	0.0724408i	0.0136115	+	0.00240007i	−0.166838	+	0.985984i	$0.553356\pi$
$912$	19.0933	−	7.88315i	0.632244	−	0.261037i
$913$	44.0421	+	52.4874i	1.45758	+	1.73708i
$914$	14.2492	−	41.1740i	0.471322	−	1.36191i
$915$	−9.06941	−	0.191253i	−0.299825	−	0.00632264i
$916$	−21.8395	+	27.7743i	−0.721599	+	0.917689i
$917$	−27.3261	−	10.5993i	−0.902387	−	0.350019i
$918$	−12.0608	+	53.4593i	−0.398067	+	1.76442i
$919$	9.33883	−	5.39178i	0.308060	−	0.177858i	−0.337998	−	0.941147i	$-0.609750\pi$
$919$	9.33883	−	5.39178i	0.308060	−	0.177858i	0.646058	+	0.763288i	$0.276416\pi$
$920$	9.34186	+	22.2976i	0.307992	+	0.735129i
$921$	−32.3074	−	0.681290i	−1.06456	−	0.0224493i
$922$	−6.91438	+	5.99167i	−0.227713	+	0.197325i
$923$	12.7812	+	4.65199i	0.420699	+	0.153122i
$924$	35.5623	+	21.0207i	1.16991	+	0.691530i
$925$	2.57705	−	14.6152i	0.0847329	−	0.480544i
$926$	58.8471	−	0.935367i	1.93384	−	0.0307381i
$927$	2.47442	−	1.90445i	0.0812705	−	0.0625503i
$928$	−0.917830	−	11.5254i	−0.0301293	−	0.378340i
$929$	−10.2965	+	12.2709i	−0.337818	+	0.402595i	−0.908032	−	0.418900i	$-0.862416\pi$
$929$	−10.2965	+	12.2709i	−0.337818	+	0.402595i	0.570215	+	0.821496i	$0.306860\pi$
$930$	4.41332	−	3.66434i	0.144718	−	0.120158i
$931$	−11.1833	+	17.6217i	−0.366519	+	0.577526i
$932$	−11.4319	+	10.2289i	−0.374464	+	0.335060i
$933$	16.6857	+	6.47468i	0.546267	+	0.211971i
$934$	−33.1044	−	5.29616i	−1.08321	−	0.173296i
$935$			47.0064i			1.53727i
$936$	13.3718	−	11.3465i	0.437073	−	0.370871i
$937$	25.9661	+	14.9915i	0.848275	+	0.489752i	0.860069	−	0.510179i	$-0.170421\pi$
$937$	25.9661	+	14.9915i	0.848275	+	0.489752i	−0.0117933	+	0.999930i	$0.503754\pi$
$938$	−10.3571	−	18.1503i	−0.338171	−	0.592629i
$939$	−1.90839	−	5.60845i	−0.0622780	−	0.183025i
$940$	27.7102	−	5.79970i	0.903808	−	0.189165i
$941$	−13.8128	+	37.9503i	−0.450284	+	1.23715i	0.482241	+	0.876039i	$0.339823\pi$
$941$	−13.8128	+	37.9503i	−0.450284	+	1.23715i	−0.932525	+	0.361106i	$0.882399\pi$
$942$	4.14806	+	0.0215331i	0.135151	+	0.000701586i
$943$	6.98245	−	39.5994i	0.227380	−	1.28954i
$944$	−16.8990	+	1.07579i	−0.550016	+	0.0350140i
$945$	−11.0751	−	15.7142i	−0.360272	−	0.511183i
$946$	−0.414916	−	26.1038i	−0.0134901	−	0.848706i
$947$	−12.5454	−	2.21210i	−0.407672	−	0.0718835i	−0.0339481	−	0.999424i	$-0.510808\pi$
$947$	−12.5454	−	2.21210i	−0.407672	−	0.0718835i	−0.373724	+	0.927540i	$0.621919\pi$
$948$	−3.00730	+	1.77945i	−0.0976726	+	0.0577938i
$949$	−12.3592	−	4.49836i	−0.401195	−	0.146023i
$950$	12.6051	−	2.42979i	0.408964	−	0.0788327i
$951$	−4.49215	+	22.6703i	−0.145668	+	0.735134i
$952$	−55.7886	+	1.49164i	−1.80812	+	0.0483443i
$953$	10.2014	−	17.6694i	0.330456	−	0.572367i	−0.652145	−	0.758094i	$-0.726131\pi$
$953$	10.2014	−	17.6694i	0.330456	−	0.572367i	0.982601	+	0.185727i	$0.0594641\pi$
$954$	58.8286	+	11.9747i	1.90464	+	0.387694i
$955$	7.12981			0.230715
$956$	49.4292	+	7.10413i	1.59865	+	0.229764i
$957$	−15.7689	+	2.43888i	−0.509736	+	0.0788379i
$958$	−0.665869	−	0.768412i	−0.0215132	−	0.0248263i
$959$	28.5820	+	25.0219i	0.922960	+	0.808000i
$960$	−18.7801	+	4.77154i	−0.606125	+	0.154001i
$961$	−21.5991	−	18.1238i	−0.696744	−	0.584637i
$962$	−14.2459	+	0.226437i	−0.459307	+	0.00730063i
$963$	35.8784	+	22.7833i	1.15616	+	0.734181i
$964$	0.0436757	+	1.37354i	0.00140670	+	0.0442389i
$965$	12.3311	+	2.17431i	0.396953	+	0.0699935i
$966$	18.9024	+	34.8106i	0.608175	+	1.12001i
$967$	17.8216	−	48.9645i	0.573104	−	1.57459i	−0.226466	−	0.974019i	$-0.572717\pi$
$967$	17.8216	−	48.9645i	0.573104	−	1.57459i	0.799571	−	0.600572i	$-0.205060\pi$
$968$	−17.8801	−	19.3549i	−0.574689	−	0.622089i
$969$	32.9399	+	19.9554i	1.05818	+	0.641061i
$970$	−9.51814	−	24.9117i	−0.305609	−	0.799866i
$971$	−12.6030	−	21.8291i	−0.404450	−	0.700528i	0.589807	−	0.807544i	$-0.299204\pi$
$971$	−12.6030	−	21.8291i	−0.404450	−	0.700528i	−0.994257	+	0.107016i	$0.965870\pi$
$972$	3.14032	+	31.0184i	0.100726	+	0.994914i
$973$	16.6412	−	13.3797i	0.533493	−	0.428934i
$974$	−13.3135	−	10.8155i	−0.426591	−	0.346550i
$975$	9.55113	−	5.24903i	0.305881	−	0.168103i
$976$	−4.21912	+	14.3747i	−0.135051	+	0.460124i
$977$	−32.1231	+	26.9545i	−1.02771	+	0.862352i	−0.990577	−	0.136959i	$-0.956267\pi$
$977$	−32.1231	+	26.9545i	−1.02771	+	0.862352i	−0.0371338	+	0.999310i	$0.511823\pi$
$978$	1.04589	−	5.75661i	0.0334437	−	0.184076i
$979$	0.146921	−	0.833229i	0.00469561	−	0.0266301i
$980$	12.7352	−	14.8693i	0.406812	−	0.474982i
$981$	36.2428	+	1.52924i	1.15714	+	0.0488247i
$982$	−25.9216	+	46.5922i	−0.827191	+	1.48682i
$983$	−5.39962	+	30.6227i	−0.172221	+	0.976714i	0.769082	+	0.639150i	$0.220714\pi$
$983$	−5.39962	+	30.6227i	−0.172221	+	0.976714i	−0.941303	+	0.337563i	$0.890397\pi$
$984$	30.5677	+	10.2137i	0.974461	+	0.325599i
$985$	−9.49640	+	26.0911i	−0.302580	+	0.831333i
$986$	16.2908	−	14.1169i	0.518806	−	0.449572i
$987$	44.2179	−	14.0196i	1.40747	−	0.446250i
$988$	−4.58109	−	11.4412i	−0.145744	−	0.363994i
$989$	12.5167	−	21.6796i	0.398009	−	0.689372i
$990$	8.48280	+	25.3605i	0.269601	+	0.806009i
$991$	38.4837	−	22.2185i	1.22247	−	0.705795i	0.257029	−	0.966404i	$-0.417256\pi$
$991$	38.4837	−	22.2185i	1.22247	−	0.705795i	0.965445	+	0.260608i	$0.0839231\pi$
$992$	−3.93648	−	8.61662i	−0.124983	−	0.273578i
$993$	−8.68575	−	1.72109i	−0.275634	−	0.0546173i
$994$	−18.7829	−	15.9232i	−0.595757	−	0.505054i
$995$	−8.61257	+	1.51863i	−0.273037	+	0.0481438i
$996$	−52.6559	+	0.563569i	−1.66847	+	0.0178574i
$997$	−7.38923	−	20.3018i	−0.234019	−	0.642963i	−1.00000		9.93028e-5i	$-0.999968\pi$
$997$	−7.38923	−	20.3018i	−0.234019	−	0.642963i	0.765981	−	0.642864i	$-0.222254\pi$
$998$	−15.2796	+	27.4640i	−0.483668	+	0.869359i
$999$	14.0259	−	21.0913i	0.443759	−	0.667300i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bt.a.367.8	yes	840
4.3	odd	2	inner	756.2.bt.a.367.133	yes	840
7.5	odd	6		756.2.cd.a.691.87	yes	840
27.22	even	9		756.2.cd.a.535.56	yes	840
28.19	even	6		756.2.cd.a.691.56	yes	840
108.103	odd	18		756.2.cd.a.535.87	yes	840
189.103	odd	18	inner	756.2.bt.a.103.133	yes	840
756.103	even	18	inner	756.2.bt.a.103.8	✓	840

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.bt.a.103.8	✓	840	756.103	even	18	inner
756.2.bt.a.103.133	yes	840	189.103	odd	18	inner
756.2.bt.a.367.8	yes	840	1.1	even	1	trivial
756.2.bt.a.367.133	yes	840	4.3	odd	2	inner
756.2.cd.a.535.56	yes	840	27.22	even	9
756.2.cd.a.535.87	yes	840	108.103	odd	18
756.2.cd.a.691.56	yes	840	28.19	even	6
756.2.cd.a.691.87	yes	840	7.5	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bt (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39646 - 0.223410i) q^{2} +(0.897457 - 1.48141i) q^{3} +(1.90018 + 0.623965i) q^{4} +(-1.37715 + 0.242829i) q^{5} +(-1.58422 + 1.86822i) q^{6} +(-1.27459 - 2.31850i) q^{7} +(-2.51411 - 1.29586i) q^{8} +(-1.38914 - 2.65900i) q^{9} +O(q^{10})\)	\(q+(-1.39646 - 0.223410i) q^{2} +(0.897457 - 1.48141i) q^{3} +(1.90018 + 0.623965i) q^{4} +(-1.37715 + 0.242829i) q^{5} +(-1.58422 + 1.86822i) q^{6} +(-1.27459 - 2.31850i) q^{7} +(-2.51411 - 1.29586i) q^{8} +(-1.38914 - 2.65900i) q^{9} +(1.97738 - 0.0314303i) q^{10} +(-4.43886 - 0.782690i) q^{11} +(2.62967 - 2.25495i) q^{12} +(-1.32849 - 1.58323i) q^{13} +(1.26193 + 3.52243i) q^{14} +(-0.876208 + 2.25806i) q^{15} +(3.22134 + 2.37129i) q^{16} +7.45773i q^{17} +(1.34582 + 4.02353i) q^{18} +2.98154 q^{19} +(-2.76835 - 0.397877i) q^{20} +(-4.57853 - 0.192568i) q^{21} +(6.02380 + 2.08468i) q^{22} +(3.92885 + 4.68222i) q^{23} +(-4.17600 + 2.56145i) q^{24} +(-2.86088 + 1.04127i) q^{25} +(1.50147 + 2.50771i) q^{26} +(-5.18576 - 0.328457i) q^{27} +(-0.975280 - 5.20085i) q^{28} +(1.56570 + 1.31378i) q^{29} +(1.72806 - 2.95752i) q^{30} +(1.57365 + 0.572762i) q^{31} +(-3.96868 - 4.03107i) q^{32} +(-5.14317 + 5.87333i) q^{33} +(1.66613 - 10.4144i) q^{34} +(2.31830 + 2.88342i) q^{35} +(-0.980488 - 5.91934i) q^{36} +(-2.43730 + 4.22153i) q^{37} +(-4.16359 - 0.666106i) q^{38} +(-3.53768 + 0.547152i) q^{39} +(3.77699 + 1.17410i) q^{40} +(-4.22870 - 5.03957i) q^{41} +(6.35069 + 1.29180i) q^{42} +(-1.40080 - 3.84866i) q^{43} +(-7.94624 - 4.25694i) q^{44} +(2.55874 + 3.32453i) q^{45} +(-4.44041 - 7.41626i) q^{46} +(-9.51207 + 3.46211i) q^{47} +(6.40385 - 2.64399i) q^{48} +(-3.75085 + 5.91025i) q^{49} +(4.22772 - 0.814944i) q^{50} +(11.0479 + 6.69299i) q^{51} +(-1.53648 - 3.83735i) q^{52} +(7.07518 - 12.2546i) q^{53} +(7.16830 + 1.61723i) q^{54} +6.30305 q^{55} +(0.200013 + 7.48064i) q^{56} +(2.67581 - 4.41688i) q^{57} +(-1.89292 - 2.18442i) q^{58} +(-3.24290 + 2.72111i) q^{59} +(-3.07390 + 3.74398i) q^{60} +(1.28096 + 3.51941i) q^{61} +(-2.06957 - 1.15141i) q^{62} +(-4.39431 + 6.60985i) q^{63} +(4.64151 + 6.51586i) q^{64} +(2.21399 + 1.85776i) q^{65} +(8.49437 - 7.05280i) q^{66} +(-5.50023 + 0.969838i) q^{67} +(-4.65336 + 14.1710i) q^{68} +(10.4623 - 1.61814i) q^{69} +(-2.59322 - 4.54450i) q^{70} +(-5.69937 + 3.29053i) q^{71} +(0.0467655 + 8.48515i) q^{72} +(5.51115 - 3.18187i) q^{73} +(4.34672 - 5.35067i) q^{74} +(-1.02496 + 5.17262i) q^{75} +(5.66545 + 1.86038i) q^{76} +(3.84305 + 11.2891i) q^{77} +(5.06245 + 0.0262798i) q^{78} +(-0.993400 - 0.175163i) q^{79} +(-5.01209 - 2.48339i) q^{80} +(-5.14058 + 7.38745i) q^{81} +(4.77930 + 7.98227i) q^{82} +(-11.6449 - 9.77122i) q^{83} +(-8.57985 - 3.22275i) q^{84} +(-1.81096 - 10.2704i) q^{85} +(1.09632 + 5.68743i) q^{86} +(3.35139 - 1.14038i) q^{87} +(10.1455 + 7.71989i) q^{88} +0.187713i q^{89} +(-2.83044 - 5.21421i) q^{90} +(-1.97744 + 5.09807i) q^{91} +(4.54397 + 11.3485i) q^{92} +(2.26078 - 1.81719i) q^{93} +(14.0566 - 2.70959i) q^{94} +(-4.10604 + 0.724006i) q^{95} +(-9.53339 + 2.26152i) q^{96} +(-4.61209 - 12.6716i) q^{97} +(6.55831 - 7.41543i) q^{98} +(4.08502 + 12.8902i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9}+O(q^{10}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9	\( 840 q - 3 q^{2} - 3 q^{4} - 18 q^{5} - 6 q^{8} - 6 q^{9} - 9 q^{12} - 21 q^{14} - 3 q^{16} - 3 q^{18} - 12 q^{21} - 12 q^{22} - 9 q^{24} - 6 q^{25} - 18 q^{26} - 12 q^{28} - 36 q^{29} - 39 q^{30} + 27 q^{32} - 18 q^{33} + 18 q^{34} + 18 q^{36} + 6 q^{37} - 99 q^{38} + 36 q^{40} + 9 q^{42} + 3 q^{44} - 18 q^{45} + 3 q^{46} - 12 q^{49} + 3 q^{50} - 9 q^{52} - 12 q^{53} - 135 q^{54} + 15 q^{56} - 42 q^{57} - 3 q^{58} - 33 q^{60} - 18 q^{61} - 99 q^{62} - 6 q^{64} + 18 q^{65} - 9 q^{66} - 54 q^{68} + 72 q^{69} - 36 q^{70} - 111 q^{72} - 18 q^{73} + 93 q^{74} - 36 q^{76} - 36 q^{77} + 6 q^{78} - 18 q^{80} - 30 q^{81} - 18 q^{82} + 84 q^{84} + 6 q^{85} + 135 q^{86} - 51 q^{88} + 81 q^{90} + 48 q^{92} - 6 q^{93} - 9 q^{94} - 9 q^{96} - 117 q^{98}+O(q^{100}) \) 840 * q - 3 * q^2 - 3 * q^4 - 18 * q^5 - 6 * q^8 - 6 * q^9 - 9 * q^12 - 21 * q^14 - 3 * q^16 - 3 * q^18 - 12 * q^21 - 12 * q^22 - 9 * q^24 - 6 * q^25 - 18 * q^26 - 12 * q^28 - 36 * q^29 - 39 * q^30 + 27 * q^32 - 18 * q^33 + 18 * q^34 + 18 * q^36 + 6 * q^37 - 99 * q^38 + 36 * q^40 + 9 * q^42 + 3 * q^44 - 18 * q^45 + 3 * q^46 - 12 * q^49 + 3 * q^50 - 9 * q^52 - 12 * q^53 - 135 * q^54 + 15 * q^56 - 42 * q^57 - 3 * q^58 - 33 * q^60 - 18 * q^61 - 99 * q^62 - 6 * q^64 + 18 * q^65 - 9 * q^66 - 54 * q^68 + 72 * q^69 - 36 * q^70 - 111 * q^72 - 18 * q^73 + 93 * q^74 - 36 * q^76 - 36 * q^77 + 6 * q^78 - 18 * q^80 - 30 * q^81 - 18 * q^82 + 84 * q^84 + 6 * q^85 + 135 * q^86 - 51 * q^88 + 81 * q^90 + 48 * q^92 - 6 * q^93 - 9 * q^94 - 9 * q^96 - 117 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more