LMFDB - Embedded newform 156.2.w.c.19.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [156,2,Mod(7,156)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(156, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 11]))

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

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

chi := DirichletCharacter("156.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 156 = 2^{2} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	156.w (of order $12$, degree $4$, 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:	$1.24566627153$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			19.5
Character	$\chi$	$=$	156.19
Dual form			156.2.w.c.115.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12047 - 0.862866i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.510925 - 1.93364i) q^{4} +(0.756294 - 0.756294i) q^{5} +(-1.40179 + 0.187026i) q^{6} +(-0.936058 - 0.250816i) q^{7} +(-1.09599 - 2.60745i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.12047 - 0.862866i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.510925 - 1.93364i) q^{4} +(0.756294 - 0.756294i) q^{5} +(-1.40179 + 0.187026i) q^{6} +(-0.936058 - 0.250816i) q^{7} +(-1.09599 - 2.60745i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.194828 - 1.49999i) q^{10} +(0.0537393 + 0.200558i) q^{11} +(-1.40929 + 1.41912i) q^{12} +(2.80701 + 2.26289i) q^{13} +(-1.26525 + 0.526659i) q^{14} +(-1.03312 + 0.276823i) q^{15} +(-3.47791 - 1.97589i) q^{16} +(2.04199 - 1.17894i) q^{17} +(1.30750 + 0.538926i) q^{18} +(-1.16450 + 4.34597i) q^{19} +(-1.07599 - 1.84881i) q^{20} +(0.685242 + 0.685242i) q^{21} +(0.233268 + 0.178350i) q^{22} +(1.03470 - 1.79216i) q^{23} +(-0.354570 + 2.80611i) q^{24} +3.85604i q^{25} +(5.09776 + 0.113439i) q^{26} -1.00000i q^{27} +(-0.963243 + 1.68185i) q^{28} +(-1.36433 + 2.36308i) q^{29} +(-0.918720 + 1.20161i) q^{30} +(6.27093 + 6.27093i) q^{31} +(-5.60184 + 0.787036i) q^{32} +(0.0537393 - 0.200558i) q^{33} +(1.27073 - 3.08294i) q^{34} +(-0.897626 + 0.518245i) q^{35} +(1.93004 - 0.524344i) q^{36} +(-8.14910 + 2.18354i) q^{37} +(2.44520 + 5.87435i) q^{38} +(-1.29950 - 3.36323i) q^{39} +(-2.80089 - 1.14311i) q^{40} +(-1.42366 - 5.31316i) q^{41} +(1.35907 + 0.176524i) q^{42} +(1.45084 + 2.51293i) q^{43} +(0.415263 - 0.00144226i) q^{44} +(1.03312 + 0.276823i) q^{45} +(-0.387033 - 2.90087i) q^{46} +(8.57257 - 8.57257i) q^{47} +(2.02401 + 3.45013i) q^{48} +(-5.24888 - 3.03044i) q^{49} +(3.32724 + 4.32059i) q^{50} -2.35789 q^{51} +(5.80979 - 4.27157i) q^{52} +0.760728 q^{53} +(-0.862866 - 1.12047i) q^{54} +(0.192323 + 0.111038i) q^{55} +(0.371920 + 2.71562i) q^{56} +(3.18147 - 3.18147i) q^{57} +(0.510331 + 3.82501i) q^{58} +(-9.45707 - 2.53401i) q^{59} +(0.00742940 + 2.13911i) q^{60} +(-6.05404 - 10.4859i) q^{61} +(12.4374 + 1.61544i) q^{62} +(-0.250816 - 0.936058i) q^{63} +(-5.59761 + 5.71549i) q^{64} +(3.83434 - 0.411514i) q^{65} +(-0.112841 - 0.271089i) q^{66} +(-3.30788 + 0.886345i) q^{67} +(-1.23635 - 4.55082i) q^{68} +(-1.79216 + 1.03470i) q^{69} +(-0.558591 + 1.35521i) q^{70} +(-1.78713 + 6.66967i) q^{71} +(1.71012 - 2.25288i) q^{72} +(1.62491 + 1.62491i) q^{73} +(-7.24675 + 9.47818i) q^{74} +(1.92802 - 3.33943i) q^{75} +(7.80856 + 4.47219i) q^{76} -0.201212i q^{77} +(-4.35807 - 2.64712i) q^{78} -4.17160i q^{79} +(-4.12468 + 1.13597i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.17971 - 4.72483i) q^{82} +(-4.68375 - 4.68375i) q^{83} +(1.67512 - 0.974902i) q^{84} +(0.652717 - 2.43597i) q^{85} +(3.79394 + 1.56379i) q^{86} +(2.36308 - 1.36433i) q^{87} +(0.464047 - 0.359932i) q^{88} +(-13.3705 + 3.58262i) q^{89} +(1.39644 - 0.581269i) q^{90} +(-2.05996 - 2.82224i) q^{91} +(-2.93672 - 2.91640i) q^{92} +(-2.29532 - 8.56625i) q^{93} +(2.20837 - 17.0023i) q^{94} +(2.40613 + 4.16754i) q^{95} +(5.24485 + 2.11932i) q^{96} +(8.29124 + 2.22163i) q^{97} +(-8.49610 + 1.13355i) q^{98} +(-0.146818 + 0.146818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/156\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	1.12047	−	0.862866i	0.792295	−	0.610138i
$2$	1.12047	−	0.862866i	0.792295	−	0.610138i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.510925	−	1.93364i	0.255463	−	0.966819i
$5$	0.756294	−	0.756294i	0.338225	−	0.338225i	−0.517474	−	0.855699i	$-0.673128\pi$
$5$	0.756294	−	0.756294i	0.338225	−	0.338225i	0.855699	+	0.517474i	$0.173128\pi$
$6$	−1.40179	+	0.187026i	−0.572279	+	0.0763532i
$7$	−0.936058	−	0.250816i	−0.353797	−	0.0947995i	0.0775434	−	0.996989i	$-0.475292\pi$
$7$	−0.936058	−	0.250816i	−0.353797	−	0.0947995i	−0.431340	+	0.902189i	$0.641959\pi$
$8$	−1.09599	−	2.60745i	−0.387491	−	0.921873i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.194828	−	1.49999i	0.0616100	−	0.474338i
$11$	0.0537393	+	0.200558i	0.0162030	+	0.0604704i	0.973554	−	0.228457i	$-0.0733680\pi$
$11$	0.0537393	+	0.200558i	0.0162030	+	0.0604704i	−0.957351	+	0.288927i	$0.906701\pi$
$12$	−1.40929	+	1.41912i	−0.406828	+	0.409664i
$13$	2.80701	+	2.26289i	0.778525	+	0.627614i
$13$	2.80701	+	2.26289i	0.778525	+	0.627614i
$14$	−1.26525	+	0.526659i	−0.338152	+	0.140756i
$15$	−1.03312	+	0.276823i	−0.266750	+	0.0714754i
$16$	−3.47791	−	1.97589i	−0.869478	−	0.493972i
$17$	2.04199	−	1.17894i	0.495255	−	0.285936i	−0.231497	−	0.972836i	$-0.574362\pi$
$17$	2.04199	−	1.17894i	0.495255	−	0.285936i	0.726752	+	0.686900i	$0.241029\pi$
$18$	1.30750	+	0.538926i	0.308181	+	0.127026i
$19$	−1.16450	+	4.34597i	−0.267154	+	0.997034i	0.693764	+	0.720202i	$0.255951\pi$
$19$	−1.16450	+	4.34597i	−0.267154	+	0.997034i	−0.960918	+	0.276832i	$0.910716\pi$
$20$	−1.07599	−	1.84881i	−0.240599	−	0.413406i
$21$	0.685242	+	0.685242i	0.149532	+	0.149532i
$22$	0.233268	+	0.178350i	0.0497329	+	0.0380243i
$23$	1.03470	−	1.79216i	0.215750	−	0.373690i	−0.737754	−	0.675069i	$-0.764114\pi$
$23$	1.03470	−	1.79216i	0.215750	−	0.373690i	0.953504	+	0.301379i	$0.0974470\pi$
$24$	−0.354570	+	2.80611i	−0.0723763	+	0.572796i
$25$			3.85604i			0.771208i
$26$	5.09776	+	0.113439i	0.999753	+	0.0222472i
$27$		−	1.00000i		−	0.192450i
$28$	−0.963243	+	1.68185i	−0.182036	+	0.317839i
$29$	−1.36433	+	2.36308i	−0.253349	+	0.438814i	−0.964446	−	0.264281i	$-0.914866\pi$
$29$	−1.36433	+	2.36308i	−0.253349	+	0.438814i	0.711097	+	0.703094i	$0.248199\pi$
$30$	−0.918720	+	1.20161i	−0.167735	+	0.219384i
$31$	6.27093	+	6.27093i	1.12629	+	1.12629i	0.990775	+	0.135517i	$0.0432695\pi$
$31$	6.27093	+	6.27093i	1.12629	+	1.12629i	0.135517	+	0.990775i	$0.456731\pi$
$32$	−5.60184	+	0.787036i	−0.990274	+	0.139130i
$33$	0.0537393	−	0.200558i	0.00935480	−	0.0349126i
$34$	1.27073	−	3.08294i	0.217928	−	0.528720i
$35$	−0.897626	+	0.518245i	−0.151726	+	0.0875993i
$36$	1.93004	−	0.524344i	0.321674	−	0.0873907i
$37$	−8.14910	+	2.18354i	−1.33970	+	0.358973i	−0.856324	−	0.516438i	$-0.827258\pi$
$37$	−8.14910	+	2.18354i	−1.33970	+	0.358973i	−0.483379	+	0.875411i	$0.660591\pi$
$38$	2.44520	+	5.87435i	0.396663	+	0.952946i
$39$	−1.29950	−	3.36323i	−0.208086	−	0.538548i
$40$	−2.80089	−	1.14311i	−0.442860	−	0.180741i
$41$	−1.42366	−	5.31316i	−0.222338	−	0.829776i	−0.983454	−	0.181160i	$-0.942015\pi$
$41$	−1.42366	−	5.31316i	−0.222338	−	0.829776i	0.761116	−	0.648616i	$-0.224652\pi$
$42$	1.35907	+	0.176524i	0.209709	+	0.0272383i
$43$	1.45084	+	2.51293i	0.221251	+	0.383218i	0.955188	−	0.296000i	$-0.0956527\pi$
$43$	1.45084	+	2.51293i	0.221251	+	0.383218i	−0.733937	+	0.679217i	$0.762319\pi$
$44$	0.415263	−	0.00144226i	0.0626032	−	0.000217429i
$45$	1.03312	+	0.276823i	0.154008	+	0.0412663i
$46$	−0.387033	−	2.90087i	−0.0570649	−	0.427710i
$47$	8.57257	−	8.57257i	1.25044	−	1.25044i	0.294915	−	0.955524i	$-0.404709\pi$
$47$	8.57257	−	8.57257i	1.25044	−	1.25044i	0.955524	−	0.294915i	$-0.0952913\pi$
$48$	2.02401	+	3.45013i	0.292141	+	0.497983i
$49$	−5.24888	−	3.03044i	−0.749840	−	0.432921i
$50$	3.32724	+	4.32059i	0.470543	+	0.611024i
$51$	−2.35789			−0.330170
$52$	5.80979	−	4.27157i	0.805673	−	0.592361i
$53$	0.760728			0.104494			0.0522470	−	0.998634i	$-0.483362\pi$
$53$	0.760728			0.104494			0.0522470	+	0.998634i	$0.483362\pi$
$54$	−0.862866	−	1.12047i	−0.117421	−	0.152477i
$55$	0.192323	+	0.111038i	0.0259329	+	0.0149724i
$56$	0.371920	+	2.71562i	0.0497000	+	0.362890i
$57$	3.18147	−	3.18147i	0.421396	−	0.421396i
$58$	0.510331	+	3.82501i	0.0670097	+	0.502248i
$59$	−9.45707	−	2.53401i	−1.23121	−	0.329901i	−0.416157	−	0.909293i	$-0.636623\pi$
$59$	−9.45707	−	2.53401i	−1.23121	−	0.329901i	−0.815049	+	0.579392i	$0.803290\pi$
$60$	0.00742940	+	2.13911i	0.000959132	+	0.276158i
$61$	−6.05404	−	10.4859i	−0.775141	−	1.34258i	−0.934715	−	0.355397i	$-0.884346\pi$
$61$	−6.05404	−	10.4859i	−0.775141	−	1.34258i	0.159575	−	0.987186i	$-0.448988\pi$
$62$	12.4374	+	1.61544i	1.57955	+	0.205162i
$63$	−0.250816	−	0.936058i	−0.0315998	−	0.117932i
$64$	−5.59761	+	5.71549i	−0.699701	+	0.714436i
$65$	3.83434	−	0.411514i	0.475591	−	0.0510421i
$66$	−0.112841	−	0.271089i	−0.0138898	−	0.0333688i
$67$	−3.30788	+	0.886345i	−0.404122	+	0.108284i	−0.455154	−	0.890413i	$-0.650416\pi$
$67$	−3.30788	+	0.886345i	−0.404122	+	0.108284i	0.0510316	+	0.998697i	$0.483749\pi$
$68$	−1.23635	−	4.55082i	−0.149929	−	0.551868i
$69$	−1.79216	+	1.03470i	−0.215750	+	0.124563i
$70$	−0.558591	+	1.35521i	−0.0667644	+	0.161979i
$71$	−1.78713	+	6.66967i	−0.212094	+	0.791544i	0.775076	+	0.631868i	$0.217712\pi$
$71$	−1.78713	+	6.66967i	−0.212094	+	0.791544i	−0.987169	+	0.159676i	$0.948955\pi$
$72$	1.71012	−	2.25288i	0.201540	−	0.265505i
$73$	1.62491	+	1.62491i	0.190181	+	0.190181i	0.795775	−	0.605593i	$-0.207064\pi$
$73$	1.62491	+	1.62491i	0.190181	+	0.190181i	−0.605593	+	0.795775i	$0.707064\pi$
$74$	−7.24675	+	9.47818i	−0.842418	+	1.10182i
$75$	1.92802	−	3.33943i	0.222628	−	0.385604i
$76$	7.80856	+	4.47219i	0.895703	+	0.512995i
$77$		−	0.201212i		−	0.0229303i
$78$	−4.35807	−	2.64712i	−0.493454	−	0.299727i
$79$		−	4.17160i		−	0.469342i	−0.972075	−	0.234671i	$-0.924599\pi$
$79$		−	4.17160i		−	0.469342i	0.972075	−	0.234671i	$-0.0754013\pi$
$80$	−4.12468	+	1.13597i	−0.461153	+	0.127005i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−6.17971	−	4.72483i	−0.682435	−	0.521770i
$83$	−4.68375	−	4.68375i	−0.514109	−	0.514109i	0.401674	−	0.915783i	$-0.368428\pi$
$83$	−4.68375	−	4.68375i	−0.514109	−	0.514109i	−0.915783	+	0.401674i	$0.868428\pi$
$84$	1.67512	−	0.974902i	0.182770	−	0.106371i
$85$	0.652717	−	2.43597i	0.0707972	−	0.264219i
$86$	3.79394	+	1.56379i	0.409111	+	0.168628i
$87$	2.36308	−	1.36433i	0.253349	−	0.146271i
$88$	0.464047	−	0.359932i	0.0494675	−	0.0383689i
$89$	−13.3705	+	3.58262i	−1.41727	+	0.379756i	−0.884515	−	0.466513i	$-0.845510\pi$
$89$	−13.3705	+	3.58262i	−1.41727	+	0.379756i	−0.532756	+	0.846269i	$0.678844\pi$
$90$	1.39644	−	0.581269i	0.147198	−	0.0612711i
$91$	−2.05996	−	2.82224i	−0.215942	−	0.295851i
$92$	−2.93672	−	2.91640i	−0.306175	−	0.304055i
$93$	−2.29532	−	8.56625i	−0.238013	−	0.888278i
$94$	2.20837	−	17.0023i	0.227776	−	1.75366i
$95$	2.40613	+	4.16754i	0.246864	+	0.427580i
$96$	5.24485	+	2.11932i	0.535300	+	0.216303i
$97$	8.29124	+	2.22163i	0.841848	+	0.225572i	0.653876	−	0.756602i	$-0.273142\pi$
$97$	8.29124	+	2.22163i	0.841848	+	0.225572i	0.187972	+	0.982174i	$0.439809\pi$
$98$	−8.49610	+	1.13355i	−0.858236	+	0.114505i
$99$	−0.146818	+	0.146818i	−0.0147558	+	0.0147558i
$100$	7.45618	+	1.97015i	0.745618	+	0.197015i
$101$	12.2195	+	7.05491i	1.21588	+	0.701989i	0.964034	−	0.265778i	$-0.0856287\pi$
$101$	12.2195	+	7.05491i	1.21588	+	0.701989i	0.251847	+	0.967767i	$0.418962\pi$
$102$	−2.64195	+	2.03454i	−0.261592	+	0.201450i
$103$	15.8765			1.56436			0.782181	−	0.623052i	$-0.214107\pi$
$103$	15.8765			1.56436			0.782181	+	0.623052i	$0.214107\pi$
$104$	2.82392	−	9.79926i	0.276909	−	0.960896i
$105$	1.03649			0.101151
$106$	0.852376	−	0.656406i	0.0827901	−	0.0637558i
$107$	−6.75261	−	3.89862i	−0.652800	−	0.376894i	0.136728	−	0.990609i	$-0.456341\pi$
$107$	−6.75261	−	3.89862i	−0.652800	−	0.376894i	−0.789528	+	0.613714i	$0.789675\pi$
$108$	−1.93364	−	0.510925i	−0.186064	−	0.0491638i
$109$	−5.34486	+	5.34486i	−0.511944	+	0.511944i	−0.915122	−	0.403177i	$-0.867906\pi$
$109$	−5.34486	+	5.34486i	−0.511944	+	0.511944i	0.403177	+	0.915122i	$0.367906\pi$
$110$	0.311304	−	0.0415341i	0.0296817	−	0.00396012i
$111$	8.14910	+	2.18354i	0.773478	+	0.207253i
$112$	2.75994	+	2.72186i	0.260790	+	0.257192i
$113$	−7.97724	−	13.8170i	−0.750436	−	1.29979i	−0.947612	−	0.319424i	$-0.896510\pi$
$113$	−7.97724	−	13.8170i	−0.750436	−	1.29979i	0.197176	−	0.980368i	$-0.436823\pi$
$114$	0.819574	−	6.30994i	0.0767602	−	0.590980i
$115$	−0.572858	−	2.13794i	−0.0534193	−	0.199364i
$116$	3.87228	+	3.84547i	0.359532	+	0.357043i
$117$	−0.556217	+	3.56239i	−0.0514223	+	0.329343i
$118$	−12.7829	+	5.32088i	−1.17676	+	0.489827i
$119$	−2.20712	+	0.591396i	−0.202326	+	0.0542132i
$120$	1.85409	+	2.39041i	0.169254	+	0.218213i
$121$	9.48894	−	5.47844i	0.862631	−	0.498040i
$122$	−15.8313	−	6.52537i	−1.43330	−	0.590779i
$123$	−1.42366	+	5.31316i	−0.128367	+	0.479071i
$124$	15.3297	−	8.92173i	1.37665	−	0.801195i
$125$	6.69777	+	6.69777i	0.599067	+	0.599067i
$126$	−1.08872	−	0.832408i	−0.0969913	−	0.0741568i
$127$	5.47085	−	9.47579i	0.485459	−	0.840840i	−0.514401	−	0.857550i	$-0.671986\pi$
$127$	5.47085	−	9.47579i	0.485459	−	0.840840i	0.999860	+	0.0167093i	$0.00531900\pi$
$128$	−1.34028	+	11.2340i	−0.118465	+	0.992958i
$129$		−	2.90168i		−	0.255478i
$130$	3.94120	−	3.76961i	0.345666	−	0.330617i
$131$			13.6503i			1.19263i	0.802751	+	0.596315i	$0.203369\pi$
$131$			13.6503i			1.19263i	−0.802751	+	0.596315i	$0.796631\pi$
$132$	−0.360349	−	0.206382i	−0.0313644	−	0.0179633i
$133$	2.18008	−	3.77600i	0.189037	−	0.327421i
$134$	−2.94160	+	3.84739i	−0.254116	+	0.332363i
$135$	−0.756294	−	0.756294i	−0.0650915	−	0.0650915i
$136$	−5.31204	−	4.03228i	−0.455504	−	0.345765i
$137$	−5.55695	+	20.7388i	−0.474763	+	1.77184i	0.147534	+	0.989057i	$0.452866\pi$
$137$	−5.55695	+	20.7388i	−0.474763	+	1.77184i	−0.622297	+	0.782781i	$0.713800\pi$
$138$	−1.11526	+	2.70575i	−0.0949369	+	0.230328i
$139$	−5.02536	+	2.90139i	−0.426246	+	0.246093i	−0.697746	−	0.716345i	$-0.745814\pi$
$139$	−5.02536	+	2.90139i	−0.426246	+	0.246093i	0.271500	+	0.962438i	$0.412480\pi$
$140$	0.543477	+	2.00047i	0.0459322	+	0.169070i
$141$	−11.7104	+	3.13778i	−0.986190	+	0.264249i
$142$	3.75259	+	9.01525i	0.314911	+	0.756543i
$143$	−0.302994	+	0.684574i	−0.0253376	+	0.0572469i
$144$	−0.0277847	−	3.99990i	−0.00231539	−	0.333325i
$145$	0.755354	+	2.81902i	0.0627288	+	0.234107i
$146$	3.22275	+	0.418591i	0.266717	+	0.0346428i
$147$	3.03044	+	5.24888i	0.249947	+	0.432921i
$148$	0.0586022	+	16.8730i	0.00481707	+	1.38696i
$149$	−1.47453	−	0.395100i	−0.120798	−	0.0323678i	0.197913	−	0.980220i	$-0.436584\pi$
$149$	−1.47453	−	0.395100i	−0.120798	−	0.0323678i	−0.318712	+	0.947852i	$0.603250\pi$
$150$	−0.721181	−	5.40536i	−0.0588842	−	0.441346i
$151$	−9.65347	+	9.65347i	−0.785588	+	0.785588i	−0.980768	−	0.195179i	$-0.937471\pi$
$151$	−9.65347	+	9.65347i	−0.785588	+	0.785588i	0.195179	+	0.980768i	$0.437471\pi$
$152$	12.6082	−	1.72677i	1.02266	−	0.140059i
$153$	2.04199	+	1.17894i	0.165085	+	0.0953120i
$154$	−0.173619	−	0.225453i	−0.0139906	−	0.0181675i
$155$	9.48533			0.761880
$156$	−7.16721	+	0.794398i	−0.573836	+	0.0636027i
$157$	14.6190			1.16672			0.583361	−	0.812213i	$-0.301737\pi$
$157$	14.6190			1.16672			0.583361	+	0.812213i	$0.301737\pi$
$158$	−3.59953	−	4.67417i	−0.286363	−	0.371857i
$159$	−0.658810	−	0.380364i	−0.0522470	−	0.0301648i
$160$	−3.64141	+	4.83187i	−0.287878	+	0.381993i
$161$	−1.41804	+	1.41804i	−0.111757	+	0.111757i
$162$	0.187026	+	1.40179i	0.0146942	+	0.110135i
$163$	−19.0881	−	5.11464i	−1.49509	−	0.400609i	−0.583641	−	0.812012i	$-0.698372\pi$
$163$	−19.0881	−	5.11464i	−1.49509	−	0.400609i	−0.911454	+	0.411403i	$0.865039\pi$
$164$	−11.0011	+	0.0382082i	−0.859042	+	0.00298356i
$165$	−0.111038	−	0.192323i	−0.00864429	−	0.0149724i
$166$	−9.28947	−	1.20657i	−0.721003	−	0.0936484i
$167$	1.33738	+	4.99116i	0.103489	+	0.386227i	0.998169	−	0.0604801i	$-0.0192632\pi$
$167$	1.33738	+	4.99116i	0.103489	+	0.386227i	−0.894680	+	0.446707i	$0.852597\pi$
$168$	1.03572	−	2.53775i	0.0799072	−	0.195792i
$169$	2.75863	+	12.7039i	0.212202	+	0.977226i
$170$	−1.37057	−	3.29265i	−0.105118	−	0.252535i
$171$	−4.34597	+	1.16450i	−0.332345	+	0.0890515i
$172$	5.60036	−	1.52148i	0.427023	−	0.116012i
$173$	18.4027	−	10.6248i	1.39913	−	0.807789i	0.404829	−	0.914392i	$-0.367331\pi$
$173$	18.4027	−	10.6248i	1.39913	−	0.807789i	0.994302	+	0.106603i	$0.0339975\pi$
$174$	1.47054	−	3.56772i	0.111482	−	0.270468i
$175$	0.967156	−	3.60947i	0.0731101	−	0.272851i
$176$	0.209379	−	0.803704i	0.0157826	−	0.0605815i
$177$	6.92305	+	6.92305i	0.520369	+	0.520369i
$178$	−11.8900	+	15.5512i	−0.891192	+	1.16561i
$179$	−10.6242	+	18.4016i	−0.794089	+	1.37540i	0.129327	+	0.991602i	$0.458718\pi$
$179$	−10.6242	+	18.4016i	−0.794089	+	1.37540i	−0.923416	+	0.383800i	$0.874615\pi$
$180$	1.06312	−	1.85624i	0.0792404	−	0.138356i
$181$			3.87797i			0.288247i	0.989560	+	0.144124i	$0.0460363\pi$
$181$			3.87797i			0.288247i	−0.989560	+	0.144124i	$0.953964\pi$
$182$	−4.74334	−	1.38478i	−0.351600	−	0.102647i
$183$			12.1081i			0.895055i
$184$	−5.80698	−	0.733748i	−0.428096	−	0.0540926i
$185$	−4.51172	+	7.81452i	−0.331708	+	0.574535i
$186$	−9.96337	−	7.61771i	−0.730549	−	0.558557i
$187$	0.346181	+	0.346181i	0.0253153	+	0.0253153i
$188$	−12.1963	−	20.9562i	−0.889507	−	1.52839i
$189$	−0.250816	+	0.936058i	−0.0182442	+	0.0680882i
$190$	6.29203	+	2.59345i	0.456472	+	0.188149i
$191$	19.5643	−	11.2954i	1.41562	−	0.817310i	0.419712	−	0.907657i	$-0.362131\pi$
$191$	19.5643	−	11.2954i	1.41562	−	0.817310i	0.995910	+	0.0903478i	$0.0287979\pi$
$192$	7.70541	−	2.15095i	0.556090	−	0.155232i
$193$	−1.65633	+	0.443812i	−0.119225	+	0.0319463i	−0.317938	−	0.948111i	$-0.602990\pi$
$193$	−1.65633	+	0.443812i	−0.119225	+	0.0319463i	0.198713	+	0.980058i	$0.436324\pi$
$194$	11.2071	−	4.66495i	0.804622	−	0.334924i
$195$	−3.52639	−	1.56079i	−0.252530	−	0.111770i
$196$	−8.54157	+	8.60111i	−0.610112	+	0.614365i
$197$	−0.601959	−	2.24654i	−0.0428878	−	0.160059i	0.941161	−	0.337959i	$-0.109736\pi$
$197$	−0.601959	−	2.24654i	−0.0428878	−	0.160059i	−0.984049	+	0.177899i	$0.943070\pi$
$198$	−0.0378217	+	0.291191i	−0.00268787	+	0.0206940i
$199$	−8.67133	−	15.0192i	−0.614694	−	1.06468i	−0.990438	−	0.137958i	$-0.955946\pi$
$199$	−8.67133	−	15.0192i	−0.614694	−	1.06468i	0.375744	−	0.926724i	$-0.377387\pi$
$200$	10.0544	−	4.22618i	0.710956	−	0.298836i
$201$	3.30788	+	0.886345i	0.233320	+	0.0625179i
$202$	19.7790	−	2.63891i	1.39165	−	0.185673i
$203$	1.86979	−	1.86979i	0.131233	−	0.131233i
$204$	−1.20470	+	4.55930i	−0.0843462	+	0.319215i
$205$	−5.09501	−	2.94161i	−0.355851	−	0.205451i
$206$	17.7893	−	13.6993i	1.23944	−	0.954477i
$207$	2.06940			0.143833
$208$	−5.29131	−	13.4165i	−0.366886	−	0.930266i
$209$	−0.934197			−0.0646198
$210$	1.16136	−	0.894351i	0.0801414	−	0.0617161i
$211$	−0.547380	−	0.316030i	−0.0376832	−	0.0217564i	0.481040	−	0.876699i	$-0.340259\pi$
$211$	−0.547380	−	0.316030i	−0.0376832	−	0.0217564i	−0.518723	+	0.854942i	$0.673592\pi$
$212$	0.388675	−	1.47097i	0.0266943	−	0.101027i
$213$	4.88254	−	4.88254i	0.334546	−	0.334546i
$214$	−10.9301	+	1.45829i	−0.747168	+	0.0996868i
$215$	2.99777	+	0.803251i	0.204446	+	0.0547812i
$216$	−2.60745	+	1.09599i	−0.177415	+	0.0745727i
$217$	−4.29710	−	7.44280i	−0.291706	−	0.505250i
$218$	−1.37688	+	10.6007i	−0.0932541	+	0.717968i
$219$	−0.594759	−	2.21967i	−0.0401901	−	0.149991i
$220$	0.312970	−	0.315152i	0.0211004	−	0.0212475i
$221$	8.39972	+	1.31150i	0.565026	+	0.0882208i
$222$	11.0150	−	4.58497i	0.739276	−	0.307723i
$223$	10.7115	−	2.87013i	0.717292	−	0.192198i	0.118329	−	0.992974i	$-0.462246\pi$
$223$	10.7115	−	2.87013i	0.717292	−	0.192198i	0.598963	+	0.800777i	$0.295580\pi$
$224$	5.44104	+	0.668318i	0.363545	+	0.0446539i
$225$	−3.33943	+	1.92802i	−0.222628	+	0.128535i
$226$	−20.8605	−	8.59829i	−1.38762	−	0.571950i
$227$	5.04441	−	18.8260i	0.334809	−	1.24952i	−0.569267	−	0.822153i	$-0.692773\pi$
$227$	5.04441	−	18.8260i	0.334809	−	1.24952i	0.904076	−	0.427372i	$-0.140560\pi$
$228$	−4.52632	−	7.77731i	−0.299763	−	0.515065i
$229$	−4.18560	−	4.18560i	−0.276592	−	0.276592i	0.555155	−	0.831747i	$-0.312659\pi$
$229$	−4.18560	−	4.18560i	−0.276592	−	0.276592i	−0.831747	+	0.555155i	$0.812659\pi$
$230$	−2.48663	−	1.90120i	−0.163963	−	0.125362i
$231$	−0.100606	+	0.174255i	−0.00661940	+	0.0114651i
$232$	7.65692	+	0.967498i	0.502701	+	0.0635194i
$233$		−	27.9305i		−	1.82979i	−0.403691	−	0.914895i	$-0.632273\pi$
$233$		−	27.9305i		−	1.82979i	0.403691	−	0.914895i	$-0.367727\pi$
$234$	2.45064	+	4.47151i	0.160203	+	0.292312i
$235$		−	12.9668i		−	0.845859i
$236$	−9.73172	+	16.9919i	−0.633481	+	1.10608i
$237$	−2.08580	+	3.61271i	−0.135487	+	0.234671i
$238$	−1.96273	+	2.56709i	−0.127225	+	0.166400i
$239$	−3.01097	−	3.01097i	−0.194763	−	0.194763i	0.602987	−	0.797751i	$-0.293977\pi$
$239$	−3.01097	−	3.01097i	−0.194763	−	0.194763i	−0.797751	+	0.602987i	$0.793977\pi$
$240$	4.14006	+	1.07856i	0.267240	+	0.0696208i
$241$	1.78646	−	6.66715i	0.115076	−	0.429469i	−0.884217	−	0.467077i	$-0.845307\pi$
$241$	1.78646	−	6.66715i	0.115076	−	0.429469i	0.999293	+	0.0376078i	$0.0119738\pi$
$242$	5.90496	−	14.3261i	0.379585	−	0.920919i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−23.3691	+	6.34881i	−1.49605	+	0.406441i
$245$	−6.26161	+	1.67779i	−0.400039	+	0.107190i
$246$	2.98937	+	7.18168i	0.190595	+	0.457887i
$247$	−13.1032	+	9.56405i	−0.833738	+	0.608546i
$248$	9.47826	−	23.2240i	0.601870	−	1.47473i
$249$	1.71437	+	6.39812i	0.108644	+	0.405465i
$250$	13.2840	+	1.72540i	0.840151	+	0.109124i
$251$	6.92033	+	11.9864i	0.436807	+	0.756573i	0.997441	−	0.0714913i	$-0.0227758\pi$
$251$	6.92033	+	11.9864i	0.436807	+	0.756573i	−0.560634	+	0.828064i	$0.689442\pi$
$252$	−1.93814	+	0.00673142i	−0.122092	+	0.000424040i
$253$	0.415035	+	0.111208i	0.0260930	+	0.00699160i
$254$	−2.04639	−	15.3380i	−0.128402	−	0.962391i
$255$	−1.78326	+	1.78326i	−0.111672	+	0.111672i
$256$	8.19172	+	13.7439i	0.511983	+	0.858996i
$257$	−0.595375	−	0.343740i	−0.0371385	−	0.0214419i	0.481316	−	0.876547i	$-0.340159\pi$
$257$	−0.595375	−	0.343740i	−0.0371385	−	0.0214419i	−0.518454	+	0.855105i	$0.673492\pi$
$258$	−2.50376	−	3.25125i	−0.155877	−	0.202414i
$259$	8.17570			0.508013
$260$	1.16334	−	7.62448i	0.0721475	−	0.472850i
$261$	−2.72865			−0.168899
$262$	11.7783	+	15.2948i	0.727669	+	0.944914i
$263$	−1.05599	−	0.609675i	−0.0651150	−	0.0375942i	0.467089	−	0.884210i	$-0.345303\pi$
$263$	−1.05599	−	0.609675i	−0.0651150	−	0.0375942i	−0.532204	+	0.846616i	$0.678636\pi$
$264$	−0.581842	+	0.0796869i	−0.0358099	+	0.00490439i
$265$	0.575334	−	0.575334i	0.0353425	−	0.0353425i
$266$	−0.815464	−	6.11203i	−0.0499993	−	0.374753i
$267$	13.3705	+	3.58262i	0.818261	+	0.219252i
$268$	0.0237878	+	6.84910i	0.00145307	+	0.418376i
$269$	−4.67240	−	8.09283i	−0.284881	−	0.493428i	0.687699	−	0.725996i	$-0.258621\pi$
$269$	−4.67240	−	8.09283i	−0.284881	−	0.493428i	−0.972580	+	0.232567i	$0.925287\pi$
$270$	−1.49999	−	0.194828i	−0.0912864	−	0.0118569i
$271$	−3.96927	−	14.8135i	−0.241116	−	0.899857i	−0.975296	−	0.220902i	$-0.929100\pi$
$271$	−3.96927	−	14.8135i	−0.241116	−	0.899857i	0.734180	−	0.678955i	$-0.237567\pi$
$272$	−9.43132	+	0.0655131i	−0.571858	+	0.00397232i
$273$	0.372853	+	3.47411i	0.0225661	+	0.210263i
$274$	11.6684	+	28.0322i	0.704914	+	1.69349i
$275$	−0.773358	+	0.207221i	−0.0466352	+	0.0124959i
$276$	1.08508	+	3.99404i	0.0653142	+	0.240413i
$277$	5.01436	−	2.89504i	0.301284	−	0.173946i	−0.341736	−	0.939796i	$-0.611015\pi$
$277$	5.01436	−	2.89504i	0.301284	−	0.173946i	0.643019	+	0.765850i	$0.277681\pi$
$278$	−3.12728	+	7.58715i	−0.187562	+	0.455047i
$279$	−2.29532	+	8.56625i	−0.137417	+	0.512848i
$280$	2.33509	+	1.77252i	0.139548	+	0.105929i
$281$	−16.3631	−	16.3631i	−0.976138	−	0.976138i	0.0235837	−	0.999722i	$-0.492492\pi$
$281$	−16.3631	−	16.3631i	−0.976138	−	0.976138i	−0.999722	+	0.0235837i	$0.992492\pi$
$282$	−10.4137	+	13.6203i	−0.620125	+	0.811075i
$283$	6.08717	−	10.5433i	0.361844	−	0.626733i	−0.626420	−	0.779486i	$-0.715480\pi$
$283$	6.08717	−	10.5433i	0.361844	−	0.626733i	0.988264	+	0.152753i	$0.0488138\pi$
$284$	11.9836	+	6.86337i	0.711098	+	0.407266i
$285$		−	4.81226i		−	0.285054i
$286$	0.251199	+	1.02849i	0.0148537	+	0.0608159i
$287$			5.33050i			0.314649i
$288$	−3.48251	−	4.45781i	−0.205209	−	0.262679i
$289$	−5.72018	+	9.90765i	−0.336481	+	0.582803i
$290$	3.27879	+	2.50687i	0.192537	+	0.147209i
$291$	−6.06961	−	6.06961i	−0.355807	−	0.355807i
$292$	3.97220	−	2.31178i	0.232455	−	0.135287i
$293$	−4.32931	+	16.1572i	−0.252921	+	0.943915i	0.716314	+	0.697778i	$0.245828\pi$
$293$	−4.32931	+	16.1572i	−0.252921	+	0.943915i	−0.969235	+	0.246137i	$0.920839\pi$
$294$	7.92462	+	3.26637i	0.462173	+	0.190499i
$295$	−9.06879	+	5.23587i	−0.528005	+	0.304844i
$296$	14.6248	+	18.8552i	0.850051	+	1.09594i
$297$	0.200558	−	0.0537393i	0.0116375	−	0.00311827i
$298$	−1.99309	+	0.829625i	−0.115457	+	0.0480589i
$299$	6.95988	−	2.68918i	0.402500	−	0.155520i
$300$	−5.47217	−	5.43429i	−0.315936	−	0.313749i
$301$	−0.727787	−	2.71614i	−0.0419489	−	0.156555i
$302$	−2.48682	+	19.1461i	−0.143100	+	1.10174i
$303$	−7.05491	−	12.2195i	−0.405294	−	0.701989i
$304$	12.6372	−	12.8140i	0.724792	−	0.734932i
$305$	−12.5091	−	3.35180i	−0.716267	−	0.191923i
$306$	3.30527	−	0.440987i	0.188950	−	0.0252096i
$307$	−15.2409	+	15.2409i	−0.869842	+	0.869842i	−0.992455	−	0.122613i	$-0.960873\pi$
$307$	−15.2409	+	15.2409i	−0.869842	+	0.869842i	0.122613	+	0.992455i	$0.460873\pi$
$308$	−0.389072	−	0.102804i	−0.0221694	−	0.00585783i
$309$	−13.7495	−	7.93827i	−0.782181	−	0.451592i
$310$	10.6281	−	8.18457i	0.603634	−	0.464852i
$311$	−16.1902			−0.918062			−0.459031	−	0.888420i	$-0.651803\pi$
$311$	−16.1902			−0.918062			−0.459031	+	0.888420i	$0.651803\pi$
$312$	−7.34522	+	7.07444i	−0.415841	+	0.400512i
$313$	10.8287			0.612077			0.306038	−	0.952019i	$-0.400996\pi$
$313$	10.8287			0.612077			0.306038	+	0.952019i	$0.400996\pi$
$314$	16.3802	−	12.6142i	0.924387	−	0.711861i
$315$	−0.897626	−	0.518245i	−0.0505755	−	0.0291998i
$316$	−8.06637	−	2.13138i	−0.453769	−	0.119899i
$317$	4.10335	−	4.10335i	0.230467	−	0.230467i	−0.582421	−	0.812888i	$-0.697894\pi$
$317$	4.10335	−	4.10335i	0.230467	−	0.230467i	0.812888	+	0.582421i	$0.197894\pi$
$318$	−1.06638	+	0.142276i	−0.0597998	+	0.00797846i
$319$	−0.547253	−	0.146636i	−0.0306403	−	0.00821003i
$320$	0.0891514	+	8.55603i	0.00498371	+	0.478297i
$321$	3.89862	+	6.75261i	0.217600	+	0.376894i
$322$	−0.365300	+	2.81246i	−0.0203574	+	0.156732i
$323$	2.74576	+	10.2473i	0.152778	+	0.570176i
$324$	1.41912	+	1.40929i	0.0788398	+	0.0782941i
$325$	−8.72580	+	10.8239i	−0.484020	+	0.600404i
$326$	−25.8010	+	10.7396i	−1.42898	+	0.594813i
$327$	7.30121	−	1.95635i	0.403758	−	0.108187i
$328$	−12.2935	+	9.53529i	−0.678794	+	0.526498i
$329$	−10.1746	+	5.87429i	−0.560942	+	0.323860i
$330$	−0.290364	−	0.119683i	−0.0159840	−	0.00658831i
$331$	3.99964	−	14.9269i	0.219840	−	0.820455i	−0.764566	−	0.644545i	$-0.777047\pi$
$331$	3.99964	−	14.9269i	0.219840	−	0.820455i	0.984406	−	0.175909i	$-0.0562866\pi$
$332$	−11.4497	+	6.66363i	−0.628385	+	0.365714i
$333$	−5.96556	−	5.96556i	−0.326910	−	0.326910i
$334$	5.80519	+	4.43849i	0.317646	+	0.242863i
$335$	−1.83140	+	3.17207i	−0.100060	+	0.173309i
$336$	−1.02925	−	3.73717i	−0.0561501	−	0.203879i
$337$		−	12.5145i		−	0.681708i	−0.940116	−	0.340854i	$-0.889284\pi$
$337$		−	12.5145i		−	0.681708i	0.940116	−	0.340854i	$-0.110716\pi$
$338$	14.0528	+	11.8541i	0.764370	+	0.644778i
$339$			15.9545i			0.866528i
$340$	−4.37680	−	2.50672i	−0.237365	−	0.135946i
$341$	−0.920687	+	1.59468i	−0.0498580	+	0.0863566i
$342$	−3.86474	+	5.05478i	−0.208981	+	0.273331i
$343$	8.94987	+	8.94987i	0.483247	+	0.483247i
$344$	4.96223	−	6.53713i	0.267545	−	0.352459i
$345$	−0.572858	+	2.13794i	−0.0308417	+	0.115103i
$346$	11.4520	−	27.7839i	0.615662	−	1.49367i
$347$	29.1626	−	16.8370i	1.56553	−	0.903858i	0.568848	−	0.822443i	$-0.307389\pi$
$347$	29.1626	−	16.8370i	1.56553	−	0.903858i	0.996680	−	0.0814151i	$-0.0259439\pi$
$348$	−1.43076	−	5.26642i	−0.0766965	−	0.282310i
$349$	−18.8550	+	5.05220i	−1.00929	+	0.270438i	−0.725332	−	0.688400i	$-0.758314\pi$
$349$	−18.8550	+	5.05220i	−1.00929	+	0.270438i	−0.283956	+	0.958837i	$0.591647\pi$
$350$	−2.03082	−	4.87885i	−0.108552	−	0.260785i
$351$	2.26289	−	2.80701i	0.120784	−	0.149827i
$352$	−0.458885	−	1.08120i	−0.0244586	−	0.0576280i
$353$	1.63463	+	6.10052i	0.0870025	+	0.324698i	0.995686	−	0.0927882i	$-0.0295779\pi$
$353$	1.63463	+	6.10052i	0.0870025	+	0.324698i	−0.908683	+	0.417486i	$0.862911\pi$
$354$	13.7308	+	1.78344i	0.729782	+	0.0947887i
$355$	3.69264	+	6.39583i	0.195985	+	0.339456i
$356$	0.0961506	+	27.6842i	0.00509597	+	1.46726i
$357$	2.20712	+	0.591396i	0.116813	+	0.0313000i
$358$	3.97401	+	29.7858i	0.210033	+	1.57423i
$359$	−7.03807	+	7.03807i	−0.371455	+	0.371455i	−0.868007	−	0.496552i	$-0.834599\pi$
$359$	−7.03807	+	7.03807i	−0.371455	+	0.371455i	0.496552	+	0.868007i	$0.334599\pi$
$360$	−0.410485	−	2.99720i	−0.0216344	−	0.157966i
$361$	−1.07692	−	0.621757i	−0.0566798	−	0.0327241i
$362$	3.34617	+	4.34517i	0.175871	+	0.228377i
$363$	−10.9569			−0.575088
$364$	−6.50968	+	2.54125i	−0.341200	+	0.133198i
$365$	2.45782			0.128648
$366$	10.4477	+	13.5668i	0.546108	+	0.709148i
$367$	12.8682	+	7.42944i	0.671713	+	0.387814i	0.796725	−	0.604341i	$-0.206564\pi$
$367$	12.8682	+	7.42944i	0.671713	+	0.387814i	−0.125012	+	0.992155i	$0.539897\pi$
$368$	−7.13970	+	4.18850i	−0.372183	+	0.218341i
$369$	3.88950	−	3.88950i	0.202479	−	0.202479i
$370$	1.68762	+	12.6490i	0.0877352	+	0.657589i
$371$	−0.712085	−	0.190803i	−0.0369696	−	0.00990598i
$372$	−17.7368	+	0.0616020i	−0.919608	+	0.00319391i
$373$	−2.30954	−	4.00024i	−0.119583	−	0.207124i	0.800019	−	0.599974i	$-0.204823\pi$
$373$	−2.30954	−	4.00024i	−0.119583	−	0.207124i	−0.919603	+	0.392850i	$0.871489\pi$
$374$	0.686595	+	0.0891793i	0.0355030	+	0.00461135i
$375$	−2.45155	−	9.14933i	−0.126598	−	0.472469i
$376$	−31.7480	−	12.9571i	−1.63728	−	0.668212i
$377$	−9.17709	+	3.54588i	−0.472644	+	0.182622i
$378$	0.526659	+	1.26525i	0.0270884	+	0.0650774i
$379$	26.9351	−	7.21724i	1.38356	−	0.370725i	0.511150	−	0.859492i	$-0.329220\pi$
$379$	26.9351	−	7.21724i	1.38356	−	0.370725i	0.872415	+	0.488767i	$0.162553\pi$
$380$	9.28786	−	2.52328i	0.476457	−	0.129442i
$381$	−9.47579	+	5.47085i	−0.485459	+	0.280280i
$382$	12.1748	−	29.5376i	0.622918	−	1.51128i
$383$	−0.692428	+	2.58418i	−0.0353814	+	0.132045i	−0.981358	−	0.192191i	$-0.938441\pi$
$383$	−0.692428	+	2.58418i	−0.0353814	+	0.132045i	0.945976	+	0.324236i	$0.105107\pi$
$384$	6.77773	−	9.05883i	0.345875	−	0.462281i
$385$	−0.152176	−	0.152176i	−0.00775559	−	0.00775559i
$386$	−1.47293	+	1.92647i	−0.0749699	+	0.0980548i
$387$	−1.45084	+	2.51293i	−0.0737502	+	0.127739i
$388$	8.53204	−	14.8972i	0.433149	−	0.756289i
$389$			9.87086i			0.500472i	0.968185	+	0.250236i	$0.0805083\pi$
$389$			9.87086i			0.500472i	−0.968185	+	0.250236i	$0.919492\pi$
$390$	−5.29798	+	1.29398i	−0.268274	+	0.0655233i
$391$		−	4.87942i		−	0.246763i
$392$	−2.14901	+	17.0075i	−0.108541	+	0.859011i
$393$	6.82513	−	11.8215i	0.344283	−	0.596315i
$394$	−2.61294	−	1.99778i	−0.131638	−	0.100647i
$395$	−3.15496	−	3.15496i	−0.158743	−	0.158743i
$396$	0.208880	+	0.358907i	0.0104966	+	0.0180357i
$397$	1.55616	−	5.80766i	0.0781013	−	0.291478i	−0.915817	−	0.401595i	$-0.868456\pi$
$397$	1.55616	−	5.80766i	0.0781013	−	0.291478i	0.993919	+	0.110117i	$0.0351226\pi$
$398$	−22.6755	−	9.34641i	−1.13662	−	0.468493i
$399$	−3.77600	+	2.18008i	−0.189037	+	0.109140i
$400$	7.61910	−	13.4110i	0.380955	−	0.670548i
$401$	30.2548	−	8.10676i	1.51085	−	0.404832i	0.594136	−	0.804365i	$-0.297494\pi$
$401$	30.2548	−	8.10676i	1.51085	−	0.404832i	0.916719	+	0.399532i	$0.130827\pi$
$402$	4.47119	−	1.86113i	0.223003	−	0.0928249i
$403$	3.41213	+	31.7930i	0.169970	+	1.58372i
$404$	19.8849	−	20.0235i	0.989309	−	0.996205i
$405$	0.276823	+	1.03312i	0.0137554	+	0.0513360i
$406$	0.481674	−	3.70843i	0.0239051	−	0.184046i
$407$	−0.875853	−	1.51702i	−0.0434144	−	0.0751960i
$408$	2.58422	+	6.14808i	0.127938	+	0.304375i
$409$	32.0766	+	8.59489i	1.58608	+	0.424990i	0.940802	−	0.338956i	$-0.110074\pi$
$409$	32.0766	+	8.59489i	1.58608	+	0.424990i	0.645281	+	0.763945i	$0.276740\pi$
$410$	−8.24704	+	1.10032i	−0.407293	+	0.0543408i
$411$	15.1819	−	15.1819i	0.748867	−	0.748867i
$412$	8.11173	−	30.6995i	0.399636	−	1.51245i
$413$	8.21679	+	4.74397i	0.404322	+	0.233435i
$414$	2.31871	−	1.78562i	0.113959	−	0.0877583i
$415$	−7.08459			−0.347769
$416$	−17.5054	−	10.4671i	−0.858273	−	0.513194i
$417$	5.80279			0.284164
$418$	−1.04674	+	0.806087i	−0.0511979	+	0.0394270i
$419$	−18.8313	−	10.8723i	−0.919971	−	0.531146i	−0.0363455	−	0.999339i	$-0.511572\pi$
$419$	−18.8313	−	10.8723i	−0.919971	−	0.531146i	−0.883626	+	0.468194i	$0.844905\pi$
$420$	0.529569	−	2.00419i	0.0258403	−	0.0977947i
$421$	2.51722	−	2.51722i	0.122682	−	0.122682i	−0.643100	−	0.765782i	$-0.722352\pi$
$421$	2.51722	−	2.51722i	0.122682	−	0.122682i	0.765782	+	0.643100i	$0.222352\pi$
$422$	−0.886017	+	0.118212i	−0.0431306	+	0.00575447i
$423$	11.7104	+	3.13778i	0.569377	+	0.152564i
$424$	−0.833751	−	1.98356i	−0.0404905	−	0.0963303i
$425$	4.54605	+	7.87399i	0.220516	+	0.381945i
$426$	1.25778	−	9.68373i	0.0609398	−	0.469178i
$427$	3.03690	+	11.3339i	0.146966	+	0.548484i
$428$	−10.9886	+	11.0652i	−0.531154	+	0.534857i
$429$	0.604687	−	0.441362i	0.0291946	−	0.0213091i
$430$	4.05202	−	1.68665i	0.195406	−	0.0813376i
$431$	−15.0480	+	4.03211i	−0.724839	+	0.194220i	−0.602330	−	0.798247i	$-0.705761\pi$
$431$	−15.0480	+	4.03211i	−0.724839	+	0.194220i	−0.122509	+	0.992467i	$0.539094\pi$
$432$	−1.97589	+	3.47791i	−0.0950650	+	0.167331i
$433$	−3.33820	+	1.92731i	−0.160424	+	0.0926207i	−0.578063	−	0.815992i	$-0.696191\pi$
$433$	−3.33820	+	1.92731i	−0.160424	+	0.0926207i	0.417639	+	0.908613i	$0.362858\pi$
$434$	−11.2369	−	4.63164i	−0.539390	−	0.222326i
$435$	0.755354	−	2.81902i	0.0362165	−	0.135162i
$436$	7.60419	+	13.0658i	0.364175	+	0.625740i
$437$	6.58375	+	6.58375i	0.314943	+	0.314943i
$438$	−2.58169	−	1.97389i	−0.123358	−	0.0943159i
$439$	3.99676	−	6.92259i	0.190755	−	0.330397i	−0.754746	−	0.656017i	$-0.772240\pi$
$439$	3.99676	−	6.92259i	0.190755	−	0.330397i	0.945501	+	0.325620i	$0.105573\pi$
$440$	0.0787414	−	0.623170i	0.00375385	−	0.0297085i
$441$		−	6.06089i		−	0.288614i
$442$	10.5433	−	5.77833i	0.501494	−	0.274847i
$443$		−	12.5584i		−	0.596666i	−0.954462	−	0.298333i	$-0.903569\pi$
$443$		−	12.5584i		−	0.596666i	0.954462	−	0.298333i	$-0.0964305\pi$
$444$	8.38577	−	14.6418i	0.397971	−	0.694868i
$445$	−7.40252	+	12.8215i	−0.350913	+	0.607800i
$446$	9.52538	−	12.4584i	0.451040	−	0.589925i
$447$	1.07943	+	1.07943i	0.0510554	+	0.0510554i
$448$	6.67322	−	3.94606i	0.315280	−	0.186434i
$449$	−3.83620	+	14.3169i	−0.181042	+	0.675656i	0.814402	+	0.580301i	$0.197065\pi$
$449$	−3.83620	+	14.3169i	−0.181042	+	0.675656i	−0.995443	+	0.0953549i	$0.969601\pi$
$450$	−2.07812	+	5.04177i	−0.0979635	+	0.237671i
$451$	0.989088	−	0.571050i	0.0465743	−	0.0268897i
$452$	−30.7928	+	8.36564i	−1.44837	+	0.393487i
$453$	13.1869	−	3.53342i	0.619574	−	0.166014i
$454$	−10.5922	−	25.4467i	−0.497115	−	1.19427i
$455$	−3.69238	−	0.576513i	−0.173101	−	0.0270273i
$456$	−11.7824	−	4.80867i	−0.551761	−	0.225187i
$457$	−0.880872	−	3.28746i	−0.0412054	−	0.153781i	0.942258	−	0.334888i	$-0.108699\pi$
$457$	−0.880872	−	3.28746i	−0.0412054	−	0.153781i	−0.983463	+	0.181107i	$0.942032\pi$
$458$	−8.30147	−	1.07825i	−0.387902	−	0.0503832i
$459$	−1.17894	−	2.04199i	−0.0550284	−	0.0953120i
$460$	−4.42668	+	0.0153744i	−0.206395	+	0.000716836i
$461$	32.5542	+	8.72286i	1.51620	+	0.406264i	0.918488	−	0.395448i	$-0.129411\pi$
$461$	32.5542	+	8.72286i	1.51620	+	0.406264i	0.597710	+	0.801712i	$0.296077\pi$
$462$	0.0376320	+	0.282058i	0.00175080	+	0.0131225i
$463$	−8.67901	+	8.67901i	−0.403348	+	0.403348i	−0.879411	−	0.476063i	$-0.842063\pi$
$463$	−8.67901	+	8.67901i	−0.403348	+	0.403348i	0.476063	+	0.879411i	$0.342063\pi$
$464$	9.41420	−	5.52284i	0.437043	−	0.256391i
$465$	−8.21454	−	4.74267i	−0.380940	−	0.219936i
$466$	−24.1003	−	31.2955i	−1.11643	−	1.44973i
$467$	−34.6585			−1.60381			−0.801903	−	0.597454i	$-0.796179\pi$
$467$	−34.6585			−1.60381			−0.801903	+	0.597454i	$0.796179\pi$
$468$	6.60419	+	2.89564i	0.305279	+	0.133851i
$469$	3.31868			0.153242
$470$	−11.1886	−	14.5289i	−0.516091	−	0.670170i
$471$	−12.6604	−	7.30949i	−0.583361	−	0.336803i
$472$	3.75754	+	27.4361i	0.172955	+	1.26285i
$473$	−0.426019	+	0.426019i	−0.0195884	+	0.0195884i
$474$	0.780200	+	5.84772i	0.0358358	+	0.268595i
$475$	−16.7582	−	4.49035i	−0.768920	−	0.206032i
$476$	0.0158719	+	4.56993i	0.000727489	+	0.209462i
$477$	0.380364	+	0.658810i	0.0174157	+	0.0301648i
$478$	−5.97177	−	0.775651i	−0.273142	−	0.0354774i
$479$	−8.74492	−	32.6365i	−0.399566	−	1.49120i	−0.813862	−	0.581058i	$-0.802639\pi$
$479$	−8.74492	−	32.6365i	−0.399566	−	1.49120i	0.414296	−	0.910142i	$-0.364028\pi$
$480$	5.56949	−	2.36382i	0.254211	−	0.107893i
$481$	−27.8157	−	12.3113i	−1.26829	−	0.561347i
$482$	−3.75118	−	9.01185i	−0.170861	−	0.410478i
$483$	1.93708	−	0.519039i	0.0881402	−	0.0236171i
$484$	−5.74518	−	21.1473i	−0.261145	−	0.961239i
$485$	7.95083	−	4.59041i	0.361028	−	0.208440i
$486$	0.538926	−	1.30750i	0.0244462	−	0.0593094i
$487$	−9.67315	+	36.1007i	−0.438332	+	1.63588i	0.294631	+	0.955611i	$0.404803\pi$
$487$	−9.67315	+	36.1007i	−0.438332	+	1.63588i	−0.732964	+	0.680268i	$0.761864\pi$
$488$	−20.7063	+	27.2781i	−0.937331	+	1.23482i
$489$	13.9734	+	13.9734i	0.631901	+	0.631901i
$490$	−5.56826	+	7.28285i	−0.251548	+	0.329006i
$491$	−8.43356	+	14.6074i	−0.380601	+	0.659221i	−0.991148	−	0.132759i	$-0.957616\pi$
$491$	−8.43356	+	14.6074i	−0.380601	+	0.659221i	0.610547	+	0.791980i	$0.290950\pi$
$492$	9.54634	+	5.46746i	0.430382	+	0.246492i
$493$			6.43386i			0.289767i
$494$	−6.42934	+	22.0226i	−0.289270	+	0.990844i
$495$			0.222076i			0.00998157i
$496$	−9.41906	−	34.2004i	−0.422928	−	1.53564i
$497$	3.34572	−	5.79496i	0.150076	−	0.259939i
$498$	7.44163	+	5.68966i	0.333468	+	0.254960i
$499$	13.6838	+	13.6838i	0.612572	+	0.612572i	0.943616	−	0.331043i	$-0.107401\pi$
$499$	13.6838	+	13.6838i	0.612572	+	0.612572i	−0.331043	+	0.943616i	$0.607401\pi$
$500$	16.3731	−	9.52900i	0.732228	−	0.426150i
$501$	1.33738	−	4.99116i	0.0597496	−	0.222988i
$502$	18.0967	+	7.45910i	0.807694	+	0.332916i
$503$	−28.3756	+	16.3827i	−1.26521	+	0.730467i	−0.974077	−	0.226217i	$-0.927364\pi$
$503$	−28.3756	+	16.3827i	−1.26521	+	0.730467i	−0.291129	+	0.956684i	$0.594031\pi$
$504$	−2.16583	+	1.67990i	−0.0964739	+	0.0748287i
$505$	14.5771	−	3.90592i	0.648672	−	0.173811i
$506$	0.560993	−	0.233513i	0.0249392	−	0.0103809i
$507$	3.96292	−	12.3812i	0.176000	−	0.549870i
$508$	−15.5276	−	15.4201i	−0.688924	−	0.684155i
$509$	4.71810	+	17.6082i	0.209126	+	0.780469i	0.988152	+	0.153478i	$0.0490473\pi$
$509$	4.71810	+	17.6082i	0.209126	+	0.780469i	−0.779026	+	0.626992i	$0.784286\pi$
$510$	−0.459382	+	3.53681i	−0.0203418	+	0.156612i
$511$	−1.11346	−	1.92856i	−0.0492564	−	0.0853147i
$512$	21.0378	+	8.33137i	0.929747	+	0.368198i
$513$	4.34597	+	1.16450i	0.191879	+	0.0514139i
$514$	−0.963704	+	0.128577i	−0.0425072	+	0.00567129i
$515$	12.0073	−	12.0073i	0.529106	−	0.529106i
$516$	−5.61079	−	1.48254i	−0.247001	−	0.0652652i
$517$	2.17998	+	1.25861i	0.0958754	+	0.0553537i
$518$	9.16066	−	7.05453i	0.402496	−	0.309958i
$519$	−21.2496			−0.932754
$520$	−5.27541	−	9.54684i	−0.231342	−	0.418657i
$521$	−0.873256			−0.0382581			−0.0191290	−	0.999817i	$-0.506089\pi$
$521$	−0.873256			−0.0382581			−0.0191290	+	0.999817i	$0.506089\pi$
$522$	−3.05739	+	2.35446i	−0.133818	+	0.103052i
$523$	37.7113	+	21.7726i	1.64900	+	0.952050i	0.977471	+	0.211071i	$0.0676950\pi$
$523$	37.7113	+	21.7726i	1.64900	+	0.952050i	0.671528	+	0.740979i	$0.265638\pi$
$524$	26.3947	+	6.97427i	1.15306	+	0.304672i
$525$	−2.64232	+	2.64232i	−0.115320	+	0.115320i
$526$	−1.70928	+	0.228051i	−0.0745280	+	0.00994349i
$527$	20.1982	+	5.41210i	0.879849	+	0.235755i
$528$	−0.583180	+	0.591339i	−0.0253797	+	0.0257347i
$529$	9.35878	+	16.2099i	0.406904	+	0.704778i
$530$	0.148211	−	1.14108i	0.00643788	−	0.0495655i
$531$	−2.53401	−	9.45707i	−0.109967	−	0.410402i
$532$	−6.18757	−	6.14474i	−0.268265	−	0.266408i
$533$	8.02689	−	18.1357i	0.347683	−	0.785543i
$534$	18.0726	−	7.52272i	0.782079	−	0.325540i
$535$	−8.05547	+	2.15846i	−0.348268	+	0.0933182i
$536$	5.93651	+	7.65372i	0.256418	+	0.330590i
$537$	18.4016	−	10.6242i	0.794089	−	0.458467i
$538$	−12.2183	−	5.03616i	−0.526769	−	0.217124i
$539$	0.325708	−	1.21556i	0.0140292	−	0.0523578i
$540$	−1.84881	+	1.07599i	−0.0795601	+	0.0463032i
$541$	−7.17836	−	7.17836i	−0.308622	−	0.308622i	0.535753	−	0.844375i	$-0.320028\pi$
$541$	−7.17836	−	7.17836i	−0.308622	−	0.308622i	−0.844375	+	0.535753i	$0.820028\pi$
$542$	−17.2295	−	13.1732i	−0.740072	−	0.565838i
$543$	1.93898	−	3.35842i	0.0832098	−	0.144124i
$544$	−10.5110	+	8.21137i	−0.450657	+	0.352060i
$545$			8.08457i			0.346305i
$546$	3.41546	+	3.57093i	0.146168	+	0.152822i
$547$		−	31.1122i		−	1.33026i	−0.746728	−	0.665130i	$-0.768376\pi$
$547$		−	31.1122i		−	1.33026i	0.746728	−	0.665130i	$-0.231624\pi$
$548$	37.2622	+	21.3411i	1.59176	+	0.911648i
$549$	6.05404	−	10.4859i	0.258380	−	0.447528i
$550$	−0.687724	+	0.899489i	−0.0293247	+	0.0383544i
$551$	−8.68114	−	8.68114i	−0.369829	−	0.369829i
$552$	4.66212	+	3.53894i	0.198433	+	0.150627i
$553$	−1.04630	+	3.90486i	−0.0444934	+	0.166052i
$554$	3.12043	−	7.57054i	0.132574	−	0.321641i
$555$	7.81452	−	4.51172i	0.331708	−	0.191512i
$556$	3.04266	+	11.1996i	0.129038	+	0.474970i
$557$	9.88590	−	2.64892i	0.418879	−	0.112238i	−0.0432222	−	0.999065i	$-0.513762\pi$
$557$	9.88590	−	2.64892i	0.418879	−	0.112238i	0.462101	+	0.886827i	$0.347096\pi$
$558$	4.81967	+	11.5788i	0.204033	+	0.490170i
$559$	−1.61396	+	10.3369i	−0.0682633	+	0.437204i
$560$	4.14586	−	0.0287985i	0.175194	−	0.00121696i
$561$	−0.126711	−	0.472892i	−0.00534975	−	0.0199655i
$562$	−32.4535	−	4.21526i	−1.36897	−	0.177810i
$563$	13.6290	+	23.6061i	0.574394	+	0.994880i	0.996107	+	0.0881508i	$0.0280957\pi$
$563$	13.6290	+	23.6061i	0.574394	+	0.994880i	−0.421713	+	0.906729i	$0.638571\pi$
$564$	0.0842120	+	24.2468i	0.00354597	+	1.02097i
$565$	−16.4828	−	4.41657i	−0.693439	−	0.185806i
$566$	−2.27692	−	17.0659i	−0.0957062	−	0.717332i
$567$	0.685242	−	0.685242i	0.0287775	−	0.0287775i
$568$	19.3495	−	2.65004i	0.811888	−	0.111193i
$569$	−29.6972	−	17.1457i	−1.24497	−	0.718784i	−0.274869	−	0.961482i	$-0.588634\pi$
$569$	−29.6972	−	17.1457i	−1.24497	−	0.718784i	−0.970102	+	0.242698i	$0.921968\pi$
$570$	−4.15233	−	5.39201i	−0.173922	−	0.225846i
$571$	13.2725			0.555436			0.277718	−	0.960663i	$-0.410422\pi$
$571$	13.2725			0.555436			0.277718	+	0.960663i	$0.410422\pi$
$572$	1.16891	+	0.935646i	0.0488746	+	0.0391213i
$573$	−22.5909			−0.943748
$574$	4.59950	+	5.97269i	0.191980	+	0.249295i
$575$	6.91062	+	3.98985i	0.288193	+	0.166388i
$576$	−7.74856	−	1.98993i	−0.322857	−	0.0829136i
$577$	6.89117	−	6.89117i	0.286883	−	0.286883i	−0.548963	−	0.835846i	$-0.684977\pi$
$577$	6.89117	−	6.89117i	0.286883	−	0.286883i	0.835846	+	0.548963i	$0.184977\pi$
$578$	2.13965	+	16.0370i	0.0889978	+	0.667052i
$579$	1.65633	+	0.443812i	0.0688347	+	0.0184442i
$580$	5.83689	−	0.0202723i	0.242364	−	0.000841760i
$581$	3.20950	+	5.55902i	0.133153	+	0.230627i
$582$	−12.0381	−	1.56358i	−0.498995	−	0.0648126i
$583$	0.0408810	+	0.152570i	0.00169312	+	0.00631880i
$584$	2.45599	−	6.01777i	0.101630	−	0.249017i
$585$	2.27355	+	3.11488i	0.0939998	+	0.128784i
$586$	9.09063	+	21.8394i	0.375530	+	0.902176i
$587$	21.4271	−	5.74136i	0.884389	−	0.236971i	0.212089	−	0.977250i	$-0.431973\pi$
$587$	21.4271	−	5.74136i	0.884389	−	0.236971i	0.672300	+	0.740279i	$0.265307\pi$
$588$	11.6978	−	3.17799i	0.482408	−	0.131058i
$589$	−34.5558	+	19.9508i	−1.42384	+	0.822057i
$590$	−5.64349	+	13.6918i	−0.232339	+	0.563683i
$591$	−0.601959	+	2.24654i	−0.0247613	+	0.0924104i
$592$	32.6563	+	8.50755i	1.34216	+	0.349658i
$593$	−8.09792	−	8.09792i	−0.332542	−	0.332542i	0.521009	−	0.853551i	$-0.325556\pi$
$593$	−8.09792	−	8.09792i	−0.332542	−	0.332542i	−0.853551	+	0.521009i	$0.825556\pi$
$594$	0.178350	−	0.233268i	0.00731779	−	0.00957109i
$595$	−1.22196	+	2.11650i	−0.0500956	+	0.0867681i
$596$	−1.51736	+	2.64935i	−0.0621533	+	0.108521i
$597$			17.3427i			0.709788i
$598$	5.47796	−	9.01860i	0.224010	−	0.368798i
$599$		−	1.92350i		−	0.0785919i	−0.999228	−	0.0392960i	$-0.987488\pi$
$599$		−	1.92350i		−	0.0785919i	0.999228	−	0.0392960i	$-0.0125115\pi$
$600$	−10.8205	−	1.36723i	−0.441744	−	0.0558171i
$601$	−11.0135	+	19.0760i	−0.449251	+	0.778126i	−0.998337	−	0.0576400i	$-0.981642\pi$
$601$	−11.0135	+	19.0760i	−0.449251	+	0.778126i	0.549086	+	0.835766i	$0.314976\pi$
$602$	−3.15913	−	2.41538i	−0.128756	−	0.0984435i
$603$	−2.42154	−	2.42154i	−0.0986127	−	0.0986127i
$604$	13.7341	+	23.5985i	0.558833	+	0.960210i
$605$	3.03312	−	11.3198i	0.123314	−	0.460213i
$606$	−18.4486	−	7.60415i	−0.749423	−	0.308898i
$607$	−28.5516	+	16.4843i	−1.15887	+	0.669076i	−0.951034	−	0.309086i	$-0.899977\pi$
$607$	−28.5516	+	16.4843i	−1.15887	+	0.669076i	−0.207840	+	0.978163i	$0.566643\pi$
$608$	3.10290	−	25.2619i	0.125839	−	1.02451i
$609$	−2.55418	+	0.684390i	−0.103501	+	0.0277329i
$610$	−16.9082	+	7.03805i	−0.684595	+	0.284962i
$611$	43.4621	−	4.66450i	1.75829	−	0.188705i
$612$	3.32296	−	3.34612i	0.134323	−	0.135259i
$613$	−0.738497	−	2.75611i	−0.0298276	−	0.111318i	0.949407	−	0.314048i	$-0.101685\pi$
$613$	−0.738497	−	2.75611i	−0.0298276	−	0.111318i	−0.979235	+	0.202730i	$0.935019\pi$
$614$	−3.92618	+	30.2278i	−0.158448	+	1.21990i
$615$	2.94161	+	5.09501i	0.118617	+	0.205451i
$616$	−0.524651	+	0.220527i	−0.0211388	+	0.00888528i
$617$	−32.2374	−	8.63799i	−1.29783	−	0.347752i	−0.457200	−	0.889364i	$-0.651148\pi$
$617$	−32.2374	−	8.63799i	−1.29783	−	0.347752i	−0.840629	+	0.541612i	$0.817814\pi$
$618$	−22.2556	+	2.96933i	−0.895252	+	0.119444i
$619$	12.9345	−	12.9345i	0.519883	−	0.519883i	−0.397653	−	0.917536i	$-0.630175\pi$
$619$	12.9345	−	12.9345i	0.519883	−	0.519883i	0.917536	+	0.397653i	$0.130175\pi$
$620$	4.84630	−	18.3412i	0.194632	−	0.736600i
$621$	−1.79216	−	1.03470i	−0.0719167	−	0.0415211i
$622$	−18.1407	+	13.9700i	−0.727376	+	0.560145i
$623$	13.4141			0.537426
$624$	−2.12583	+	14.2647i	−0.0851015	+	0.571044i
$625$	−9.14921			−0.365969
$626$	12.1333	−	9.34375i	0.484945	−	0.373452i
$627$	0.809038	+	0.467098i	0.0323099	+	0.0186541i
$628$	7.46921	−	28.2678i	0.298054	−	1.12801i
$629$	−14.0661	+	14.0661i	−0.560853	+	0.560853i
$630$	−1.45294	+	0.193851i	−0.0578866	+	0.00772321i
$631$	4.45197	+	1.19290i	0.177230	+	0.0474887i	0.346343	−	0.938108i	$-0.387423\pi$
$631$	4.45197	+	1.19290i	0.177230	+	0.0474887i	−0.169113	+	0.985597i	$0.554090\pi$
$632$	−10.8772	+	4.57204i	−0.432674	+	0.181866i
$633$	0.316030	+	0.547380i	0.0125611	+	0.0217564i
$634$	1.05706	−	8.13834i	0.0419812	−	0.323215i
$635$	−3.02891	−	11.3041i	−0.120199	−	0.448588i
$636$	−1.07209	+	1.07956i	−0.0425111	+	0.0428074i
$637$	−7.87611	−	20.3842i	−0.312063	−	0.807649i
$638$	−0.739710	+	0.307904i	−0.0292854	+	0.0121900i
$639$	−6.66967	+	1.78713i	−0.263848	+	0.0706979i
$640$	7.48260	+	9.50989i	0.295776	+	0.375911i
$641$	−8.33515	+	4.81230i	−0.329219	+	0.190075i	−0.655494	−	0.755200i	$-0.727540\pi$
$641$	−8.33515	+	4.81230i	−0.329219	+	0.190075i	0.326275	+	0.945275i	$0.394206\pi$
$642$	10.1949	+	4.20214i	0.402361	+	0.165845i
$643$	6.75429	−	25.2073i	0.266363	−	0.994081i	−0.695048	−	0.718964i	$-0.744617\pi$
$643$	6.75429	−	25.2073i	0.266363	−	0.994081i	0.961411	−	0.275117i	$-0.0887166\pi$
$644$	2.01747	+	3.46649i	0.0794993	+	0.136599i
$645$	−2.19452	−	2.19452i	−0.0864092	−	0.0864092i
$646$	11.9186	+	9.11263i	0.468931	+	0.358532i
$647$	−4.32891	+	7.49790i	−0.170187	+	0.294773i	−0.938485	−	0.345319i	$-0.887771\pi$
$647$	−4.32891	+	7.49790i	−0.170187	+	0.294773i	0.768298	+	0.640092i	$0.221104\pi$
$648$	2.80611	+	0.354570i	0.110235	+	0.0139288i
$649$		−	2.03286i		−	0.0797969i
$650$	−0.437425	+	19.6571i	−0.0171572	+	0.771017i
$651$			8.59420i			0.336833i
$652$	−19.6424	+	34.2962i	−0.769258	+	1.34314i
$653$	7.25999	−	12.5747i	0.284105	−	0.492085i	−0.688287	−	0.725439i	$-0.741637\pi$
$653$	7.25999	−	12.5747i	0.284105	−	0.492085i	0.972392	+	0.233354i	$0.0749702\pi$
$654$	6.49275	−	8.49201i	0.253886	−	0.332064i
$655$	10.3236	+	10.3236i	0.403377	+	0.403377i
$656$	−5.54686	+	21.2917i	−0.216569	+	0.831300i
$657$	−0.594759	+	2.21967i	−0.0232038	+	0.0865976i
$658$	−6.33161	+	15.3613i	−0.246832	+	0.598845i
$659$	−3.42298	+	1.97626i	−0.133341	+	0.0769842i	−0.565186	−	0.824963i	$-0.691196\pi$
$659$	−3.42298	+	1.97626i	−0.133341	+	0.0769842i	0.431846	+	0.901947i	$0.357862\pi$
$660$	−0.428616	+	0.116444i	−0.0166838	+	0.00453259i
$661$	29.2920	−	7.84876i	1.13933	−	0.305281i	0.360645	−	0.932703i	$-0.382556\pi$
$661$	29.2920	−	7.84876i	1.13933	−	0.305281i	0.778680	+	0.627422i	$0.215890\pi$
$662$	−8.39838	−	20.1763i	−0.326412	−	0.784175i
$663$	−6.61862	−	5.33565i	−0.257046	−	0.207219i
$664$	−7.07931	+	17.3460i	−0.274730	+	0.673156i
$665$	−1.20699	−	4.50455i	−0.0468051	−	0.174679i
$666$	−11.8317	−	1.53678i	−0.458470	−	0.0595489i
$667$	2.82334	+	4.89017i	0.109320	+	0.189348i
$668$	10.3344	−	0.0358926i	0.399849	−	0.00138873i
$669$	−10.7115	−	2.87013i	−0.414129	−	0.110965i
$670$	0.685039	+	5.13447i	0.0264654	+	0.198362i
$671$	1.77769	−	1.77769i	0.0686270	−	0.0686270i
$672$	−4.37792	−	3.29930i	−0.168882	−	0.127273i
$673$	20.7235	+	11.9647i	0.798833	+	0.461206i	0.843063	−	0.537815i	$-0.180750\pi$
$673$	20.7235	+	11.9647i	0.798833	+	0.461206i	−0.0442300	+	0.999021i	$0.514083\pi$
$674$	−10.7983	−	14.0222i	−0.415936	−	0.540114i
$675$	3.85604			0.148419
$676$	25.9743	+	1.15657i	0.999010	+	0.0444834i
$677$	−29.0912			−1.11807			−0.559034	−	0.829145i	$-0.688828\pi$
$677$	−29.0912			−1.11807			−0.559034	+	0.829145i	$0.688828\pi$
$678$	13.7666	+	17.8766i	0.528702	+	0.686546i
$679$	−7.20386	−	4.15915i	−0.276459	−	0.159614i
$680$	−7.06706	+	0.967877i	−0.271009	+	0.0371164i
$681$	−13.7816	+	13.7816i	−0.528111	+	0.528111i
$682$	0.344386	+	2.58122i	0.0131872	+	0.0988402i
$683$	1.45823	+	0.390733i	0.0557978	+	0.0149510i	0.286610	−	0.958047i	$-0.407472\pi$
$683$	1.45823	+	0.390733i	0.0557978	+	0.0149510i	−0.230812	+	0.972998i	$0.574138\pi$
$684$	0.0312529	+	8.99850i	0.00119499	+	0.344066i
$685$	11.4820	+	19.8874i	0.438704	+	0.759857i
$686$	17.7506	+	2.30556i	0.677722	+	0.0880268i
$687$	1.53204	+	5.71764i	0.0584509	+	0.218142i
$688$	−0.0806221	−	11.6064i	−0.00307369	−	0.442491i
$689$	2.13537	+	1.72145i	0.0813512	+	0.0655819i
$690$	1.20288	+	2.88980i	0.0457928	+	0.110013i
$691$	−23.9475	+	6.41671i	−0.911005	+	0.244103i	−0.683736	−	0.729729i	$-0.739646\pi$
$691$	−23.9475	+	6.41671i	−0.911005	+	0.244103i	−0.227269	+	0.973832i	$0.572980\pi$
$692$	−11.1421	−	41.0126i	−0.423560	−	1.55907i
$693$	0.174255	−	0.100606i	0.00661940	−	0.00382171i
$694$	18.1478	−	44.0288i	0.688882	−	1.67131i
$695$	−1.60635	+	5.99496i	−0.0609322	+	0.227402i
$696$	−6.14734	−	4.66634i	−0.233014	−	0.176877i
$697$	−9.17101	−	9.17101i	−0.347377	−	0.347377i
$698$	−16.7672	+	21.9302i	−0.634649	+	0.830071i
$699$	−13.9653	+	24.1886i	−0.528215	+	0.914895i
$700$	−6.48527	−	3.71430i	−0.245120	−	0.140387i
$701$		−	17.4851i		−	0.660402i	−0.943911	−	0.330201i	$-0.892883\pi$
$701$		−	17.4851i		−	0.660402i	0.943911	−	0.330201i	$-0.107117\pi$
$702$	0.113439	−	5.09776i	0.00428148	−	0.192402i
$703$		−	37.9585i		−	1.43163i
$704$	−1.44710	−	0.815497i	−0.0545395	−	0.0307352i
$705$	−6.48339	+	11.2296i	−0.244179	+	0.422930i
$706$	7.09549	+	5.42501i	0.267042	+	0.204173i
$707$	−9.66863	−	9.66863i	−0.363626	−	0.363626i
$708$	16.9238	−	9.84952i	0.636037	−	0.370167i
$709$	9.57204	−	35.7233i	0.359486	−	1.34162i	−0.515259	−	0.857034i	$-0.672304\pi$
$709$	9.57204	−	35.7233i	0.359486	−	1.34162i	0.874745	−	0.484584i	$-0.161029\pi$
$710$	9.65625	+	3.98012i	0.362393	+	0.149371i
$711$	3.61271	−	2.08580i	0.135487	−	0.0782236i
$712$	23.9954	+	30.9364i	0.899267	+	1.15939i
$713$	17.7270	−	4.74994i	0.663882	−	0.177887i
$714$	2.98332	−	1.24180i	0.111648	−	0.0464733i
$715$	0.288587	+	0.746892i	0.0107925	+	0.0279322i
$716$	30.1539	+	29.9452i	1.12690	+	1.11910i
$717$	1.10209	+	4.11306i	0.0411583	+	0.153605i
$718$	−1.81307	+	13.9589i	−0.0676631	+	0.520941i
$719$	−10.4012	−	18.0154i	−0.387899	−	0.671860i	0.604268	−	0.796781i	$-0.293466\pi$
$719$	−10.4012	−	18.0154i	−0.387899	−	0.671860i	−0.992167	+	0.124921i	$0.960132\pi$
$720$	−3.04612	−	3.00409i	−0.113522	−	0.111956i
$721$	−14.8614	−	3.98209i	−0.553466	−	0.148301i
$722$	−1.74315	+	0.232570i	−0.0648733	+	0.00865537i
$723$	−4.88070	+	4.88070i	−0.181515	+	0.181515i
$724$	7.49859	+	1.98135i	0.278683	+	0.0736364i
$725$	−9.11214	−	5.26090i	−0.338416	−	0.195385i
$726$	−12.2769	+	9.45432i	−0.455639	+	0.350883i
$727$	−17.2942			−0.641408			−0.320704	−	0.947179i	$-0.603919\pi$
$727$	−17.2942			−0.641408			−0.320704	+	0.947179i	$0.603919\pi$
$728$	−5.10117	+	8.46439i	−0.189062	+	0.313711i
$729$	−1.00000			−0.0370370
$730$	2.75393	−	2.12077i	0.101927	−	0.0784933i
$731$	5.92520	+	3.42091i	0.219151	+	0.126527i
$732$	23.4127	+	6.18633i	0.865357	+	0.228653i
$733$	0.0809148	−	0.0809148i	0.00298865	−	0.00298865i	−0.705611	−	0.708600i	$-0.749327\pi$
$733$	0.0809148	−	0.0809148i	0.00298865	−	0.00298865i	0.708600	+	0.705611i	$0.249327\pi$
$734$	20.8291	−	2.77901i	0.768815	−	0.102575i
$735$	6.26161	+	1.67779i	0.230963	+	0.0618863i
$736$	−4.38574	+	10.8537i	−0.161660	+	0.400073i
$737$	−0.355526	−	0.615790i	−0.0130960	−	0.0226829i
$738$	1.00197	−	7.71420i	0.0368830	−	0.283964i
$739$	4.75477	+	17.7450i	0.174907	+	0.652761i	0.996567	+	0.0827844i	$0.0263813\pi$
$739$	4.75477	+	17.7450i	0.174907	+	0.652761i	−0.821661	+	0.569977i	$0.806952\pi$
$740$	12.8053	+	12.7167i	0.470732	+	0.467474i
$741$	16.1298	−	1.73110i	0.592541	−	0.0635935i
$742$	−0.962510	+	0.400644i	−0.0353349	+	0.0147081i
$743$	2.40766	−	0.645132i	0.0883286	−	0.0236676i	−0.214384	−	0.976749i	$-0.568774\pi$
$743$	2.40766	−	0.645132i	0.0883286	−	0.0236676i	0.302713	+	0.953082i	$0.402108\pi$
$744$	−19.8204	+	15.3735i	−0.726652	+	0.563618i
$745$	−1.41399	+	0.816369i	−0.0518047	+	0.0299095i
$746$	−6.03945	−	2.48934i	−0.221120	−	0.0911413i
$747$	1.71437	−	6.39812i	0.0627256	−	0.234095i
$748$	0.846262	−	0.492516i	0.0309424	−	0.0180082i
$749$	5.34300	+	5.34300i	0.195229	+	0.195229i
$750$	−10.6415	−	8.13622i	−0.388574	−	0.297093i
$751$	24.3048	−	42.0972i	0.886895	−	1.53615i	0.0433685	−	0.999059i	$-0.486191\pi$
$751$	24.3048	−	42.0972i	0.886895	−	1.53615i	0.843526	−	0.537088i	$-0.180476\pi$
$752$	−46.7531	+	12.8762i	−1.70491	+	0.469546i
$753$		−	13.8407i		−	0.504382i
$754$	−7.22308	+	11.8917i	−0.263049	+	0.433069i
$755$			14.6017i			0.531411i
$756$	1.68185	+	0.963243i	0.0611682	+	0.0350328i
$757$	8.09649	−	14.0235i	0.294272	−	0.509694i	−0.680543	−	0.732708i	$-0.738256\pi$
$757$	8.09649	−	14.0235i	0.294272	−	0.509694i	0.974815	+	0.223014i	$0.0715895\pi$
$758$	23.9526	−	31.3281i	0.869998	−	1.13789i
$759$	−0.303826	−	0.303826i	−0.0110282	−	0.0110282i
$760$	8.22956	−	10.8414i	0.298517	−	0.393261i
$761$	6.70436	−	25.0210i	0.243033	−	0.907012i	−0.731329	−	0.682025i	$-0.761100\pi$
$761$	6.70436	−	25.0210i	0.243033	−	0.907012i	0.974362	−	0.224987i	$-0.0722338\pi$
$762$	−5.89677	+	14.3063i	−0.213617	+	0.518262i
$763$	6.34367	−	3.66252i	0.229656	−	0.132592i
$764$	−11.8454	−	43.6014i	−0.428552	−	1.57744i
$765$	2.43597	−	0.652717i	0.0880729	−	0.0235991i
$766$	1.45395	+	3.49298i	0.0525334	+	0.126206i
$767$	−20.8119	−	28.5133i	−0.751474	−	1.02956i
$768$	−0.222272	−	15.9985i	−0.00802055	−	0.577295i
$769$	9.30929	+	34.7428i	0.335702	+	1.25286i	0.903106	+	0.429417i	$0.141281\pi$
$769$	9.30929	+	34.7428i	0.335702	+	1.25286i	−0.567405	+	0.823439i	$0.692052\pi$
$770$	−0.301816	−	0.0392018i	−0.0108767	−	0.00141273i
$771$	0.343740	+	0.595375i	0.0123795	+	0.0214419i
$772$	0.0119111	+	3.42950i	0.000428689	+	0.123430i
$773$	−34.2389	−	9.17429i	−1.23149	−	0.329976i	−0.416330	−	0.909214i	$-0.636684\pi$
$773$	−34.2389	−	9.17429i	−1.23149	−	0.329976i	−0.815159	+	0.579237i	$0.803351\pi$
$774$	0.542690	+	4.06755i	0.0195066	+	0.146205i
$775$	−24.1809	+	24.1809i	−0.868605	+	0.868605i
$776$	−3.29433	−	24.0539i	−0.118260	−	0.863485i
$777$	−7.08036	−	4.08785i	−0.254007	−	0.146651i
$778$	8.51723	+	11.0600i	0.305357	+	0.396522i
$779$	24.7487			0.886713
$780$	−4.81972	+	6.02132i	−0.172574	+	0.215598i
$781$	−1.43369			−0.0513016
$782$	−4.21029	−	5.46727i	−0.150559	−	0.195509i
$783$	2.36308	+	1.36433i	0.0844497	+	0.0487571i
$784$	12.2673	+	20.9108i	0.438119	+	0.746815i
$785$	11.0562	−	11.0562i	0.394614	−	0.394614i
$786$	−2.55296	−	19.1348i	−0.0910611	−	0.682517i
$787$	−39.5723	−	10.6034i	−1.41060	−	0.377970i	−0.528462	−	0.848957i	$-0.677231\pi$
$787$	−39.5723	−	10.6034i	−1.41060	−	0.377970i	−0.882140	+	0.470988i	$0.843898\pi$
$788$	−4.65155	+	0.0161554i	−0.165705	+	0.000575513i
$789$	0.609675	+	1.05599i	0.0217050	+	0.0375942i
$790$	−6.25736	−	0.812745i	−0.222627	−	0.0289162i
$791$	4.00164	+	14.9343i	0.142282	+	0.531003i
$792$	0.543733	+	0.221910i	0.0193207	+	0.00788524i
$793$	6.73472	−	43.1337i	0.239157	−	1.53172i
$794$	−3.26759	−	7.85008i	−0.115963	−	0.278589i
$795$	−0.785921	+	0.210587i	−0.0278738	+	0.00746875i
$796$	−33.4721	+	9.09353i	−1.18639	+	0.322311i
$797$	8.69682	−	5.02111i	0.308057	−	0.177857i	−0.338000	−	0.941146i	$-0.609750\pi$
$797$	8.69682	−	5.02111i	0.308057	−	0.177857i	0.646057	+	0.763289i	$0.276417\pi$
$798$	−2.34980	+	5.70090i	−0.0831821	+	0.201810i
$799$	7.39853	−	27.6117i	0.261741	−	0.976832i
$800$	−3.03484	−	21.6009i	−0.107298	−	0.763707i
$801$	−9.78789	−	9.78789i	−0.345838	−	0.345838i
$802$	26.9047	−	35.1893i	0.950039	−	1.24258i
$803$	−0.238567	+	0.413210i	−0.00841884	+	0.0145819i
$804$	3.40395	−	5.94339i	0.120048	−	0.209607i
$805$			2.14491i			0.0755983i
$806$	31.2563	+	32.6790i	1.10096	+	1.15107i
$807$			9.34479i			0.328952i
$808$	5.00291	−	39.5938i	0.176002	−	1.39290i
$809$	7.22179	−	12.5085i	0.253905	−	0.439776i	−0.710693	−	0.703502i	$-0.751618\pi$
$809$	7.22179	−	12.5085i	0.253905	−	0.439776i	0.964597	+	0.263727i	$0.0849517\pi$
$810$	1.20161	+	0.918720i	0.0422204	+	0.0322805i
$811$	−14.7205	−	14.7205i	−0.516908	−	0.516908i	0.399727	−	0.916634i	$-0.369105\pi$
$811$	−14.7205	−	14.7205i	−0.516908	−	0.516908i	−0.916634	+	0.399727i	$0.869105\pi$
$812$	−2.66017	−	4.57082i	−0.0933537	−	0.160404i
$813$	−3.96927	+	14.8135i	−0.139208	+	0.519532i
$814$	−2.29036	−	0.944041i	−0.0802770	−	0.0330886i
$815$	−18.3044	+	10.5680i	−0.641175	+	0.370182i
$816$	8.20052	+	4.65893i	0.287076	+	0.163095i
$817$	−12.6106	+	3.37900i	−0.441189	+	0.118216i
$818$	43.3572	−	18.0474i	1.51595	−	0.631013i
$819$	1.41416	−	3.19509i	0.0494146	−	0.111646i
$820$	−8.29118	+	8.34897i	−0.289540	+	0.291559i
$821$	−2.78031	−	10.3763i	−0.0970335	−	0.362134i	0.900286	−	0.435298i	$-0.143357\pi$
$821$	−2.78031	−	10.3763i	−0.0970335	−	0.362134i	−0.997320	+	0.0731641i	$0.976690\pi$
$822$	3.91098	−	30.1108i	0.136411	−	1.05024i
$823$	−11.5354	−	19.9799i	−0.402099	−	0.696455i	0.591880	−	0.806026i	$-0.298386\pi$
$823$	−11.5354	−	19.9799i	−0.402099	−	0.696455i	−0.993979	+	0.109570i	$0.965052\pi$
$824$	−17.4005	−	41.3973i	−0.606177	−	1.44214i
$825$	0.773358	+	0.207221i	0.0269249	+	0.00721450i
$826$	13.3001	−	1.77449i	0.462770	−	0.0617426i
$827$	23.4122	−	23.4122i	0.814123	−	0.814123i	−0.171126	−	0.985249i	$-0.554741\pi$
$827$	23.4122	−	23.4122i	0.814123	−	0.814123i	0.985249	+	0.171126i	$0.0547406\pi$
$828$	1.05731	−	4.00148i	0.0367441	−	0.139061i
$829$	42.5932	+	24.5912i	1.47932	+	0.854088i	0.999726	−	0.0234012i	$-0.00744951\pi$
$829$	42.5932	+	24.5912i	1.47932	+	0.854088i	0.479597	+	0.877489i	$0.340783\pi$
$830$	−7.93810	+	6.11305i	−0.275536	+	0.212187i
$831$	−5.79008			−0.200856
$832$	−28.6461	+	3.37665i	−0.993124	+	0.117064i
$833$	−14.2909			−0.495150
$834$	6.50188	−	5.00703i	0.225142	−	0.173379i
$835$	4.78623	+	2.76333i	0.165634	+	0.0956291i
$836$	−0.477305	+	1.80640i	−0.0165079	+	0.0624756i
$837$	6.27093	−	6.27093i	0.216755	−	0.216755i
$838$	−30.4814	+	4.06681i	−1.05296	+	0.140486i
$839$	39.5245	+	10.5905i	1.36454	+	0.365626i	0.865480	−	0.500944i	$-0.167014\pi$
$839$	39.5245	+	10.5905i	1.36454	+	0.365626i	0.499056	+	0.866570i	$0.333680\pi$
$840$	−1.13598	−	2.70260i	−0.0391951	−	0.0932484i
$841$	10.7772	+	18.6667i	0.371628	+	0.643679i
$842$	0.648459	−	4.99251i	0.0223474	−	0.172053i
$843$	5.98929	+	22.3524i	0.206282	+	0.769856i
$844$	−0.890758	+	0.896967i	−0.0306612	+	0.0308749i
$845$	11.6943	+	7.52158i	0.402295	+	0.258750i
$846$	15.8286	−	6.58866i	0.544200	−	0.226523i
$847$	−10.2563	+	2.74816i	−0.352410	+	0.0944280i
$848$	−2.64574	−	1.50311i	−0.0908552	−	0.0516172i
$849$	−10.5433	+	6.08717i	−0.361844	+	0.208911i
$850$	11.8879	+	4.89997i	0.407753	+	0.168068i
$851$	−4.51863	+	16.8638i	−0.154897	+	0.578083i
$852$	−6.94645	−	11.9357i	−0.237981	−	0.408909i
$853$	19.3286	+	19.3286i	0.661800	+	0.661800i	0.955804	−	0.294004i	$-0.0949880\pi$
$853$	19.3286	+	19.3286i	0.661800	+	0.661800i	−0.294004	+	0.955804i	$0.594988\pi$
$854$	13.1824	+	10.0789i	0.451092	+	0.344892i
$855$	−2.40613	+	4.16754i	−0.0822879	+	0.142527i
$856$	−2.76467	+	21.8800i	−0.0944944	+	0.747842i
$857$			53.6157i			1.83148i	0.401775	+	0.915738i	$0.368393\pi$
$857$			53.6157i			1.83148i	−0.401775	+	0.915738i	$0.631607\pi$
$858$	0.296701	−	1.01630i	0.0101292	−	0.0346958i
$859$		−	26.5789i		−	0.906861i	−0.891292	−	0.453430i	$-0.850200\pi$
$859$		−	26.5789i		−	0.906861i	0.891292	−	0.453430i	$-0.149800\pi$
$860$	3.08483	−	5.38620i	0.105192	−	0.183668i
$861$	2.66525	−	4.61635i	0.0908314	−	0.157325i
$862$	−13.3818	+	17.5023i	−0.455785	+	0.596131i
$863$	9.63899	+	9.63899i	0.328115	+	0.328115i	0.851869	−	0.523754i	$-0.175469\pi$
$863$	9.63899	+	9.63899i	0.328115	+	0.328115i	−0.523754	+	0.851869i	$0.675469\pi$
$864$	0.787036	+	5.60184i	0.0267755	+	0.190578i
$865$	5.88238	−	21.9533i	0.200007	−	0.746436i
$866$	−2.07736	+	5.03993i	−0.0705915	+	0.171264i
$867$	9.90765	−	5.72018i	0.336481	−	0.194268i
$868$	−16.5872	+	4.50632i	−0.563005	+	0.152955i
$869$	0.836647	−	0.224179i	0.0283813	−	0.00760475i
$870$	−1.58608	−	3.81041i	−0.0537732	−	0.129185i
$871$	−11.2910	−	4.99741i	−0.382580	−	0.169331i
$872$	19.7944	+	8.07854i	0.670322	+	0.273574i
$873$	2.22163	+	8.29124i	0.0751908	+	0.280616i
$874$	13.0578	+	1.69603i	0.441687	+	0.0573691i
$875$	−4.58959	−	7.94941i	−0.155157	−	0.268739i
$876$	−4.59592	+	0.0159622i	−0.155282	+	0.000539313i
$877$	−38.7626	−	10.3864i	−1.30892	−	0.350724i	−0.464104	−	0.885781i	$-0.653623\pi$
$877$	−38.7626	−	10.3864i	−1.30892	−	0.350724i	−0.844816	+	0.535057i	$0.820290\pi$
$878$	−1.49500	−	11.2052i	−0.0504538	−	0.378159i
$879$	11.8279	−	11.8279i	0.398945	−	0.398945i
$880$	−0.449485	−	0.766190i	−0.0151521	−	0.0258282i
$881$	29.2445	+	16.8843i	0.985271	+	0.568846i	0.903857	−	0.427834i	$-0.140723\pi$
$881$	29.2445	+	16.8843i	0.985271	+	0.568846i	0.0814136	+	0.996680i	$0.474057\pi$
$882$	−5.22973	−	6.79107i	−0.176094	−	0.228667i
$883$	20.9088			0.703636			0.351818	−	0.936068i	$-0.385564\pi$
$883$	20.9088			0.703636			0.351818	+	0.936068i	$0.385564\pi$
$884$	6.82759	−	15.5719i	0.229637	−	0.523741i
$885$	10.4717			0.352004
$886$	−10.8362	−	14.0713i	−0.364049	−	0.472735i
$887$	3.71344	+	2.14396i	0.124685	+	0.0719870i	0.561045	−	0.827785i	$-0.310399\pi$
$887$	3.71344	+	2.14396i	0.124685	+	0.0719870i	−0.436360	+	0.899772i	$0.643733\pi$
$888$	−3.23785	−	23.6415i	−0.108655	−	0.793358i
$889$	−7.49771	+	7.49771i	−0.251465	+	0.251465i
$890$	2.76894	+	20.7536i	0.0928149	+	0.695662i
$891$	−0.200558	−	0.0537393i	−0.00671893	−	0.00180033i
$892$	−0.0770287	−	22.1785i	−0.00257911	−	0.742591i
$893$	27.2734	+	47.2389i	0.912669	+	1.58079i
$894$	2.14088	+	0.278071i	0.0716018	+	0.00930009i
$895$	5.88204	+	21.9521i	0.196615	+	0.733776i
$896$	4.07225	−	10.1795i	0.136044	−	0.340075i
$897$	−7.37202	−	1.15104i	−0.246145	−	0.0384320i
$898$	8.05520	+	19.3518i	0.268805	+	0.645780i
$899$	−23.3743	+	6.26313i	−0.779577	+	0.208887i
$900$	2.02189	+	7.44232i	0.0673964	+	0.248077i
$901$	1.55340	−	0.896856i	0.0517512	−	0.0298786i
$902$	0.615508	−	1.49330i	0.0204942	−	0.0497214i
$903$	−0.727787	+	2.71614i	−0.0242192	+	0.0903874i
$904$	−27.2841	+	35.9436i	−0.907457	+	1.19546i
$905$	2.93289	+	2.93289i	0.0974925	+	0.0974925i
$906$	11.7267	−	15.3376i	0.389594	−	0.509558i
$907$	−28.2167	+	48.8727i	−0.936919	+	1.62279i	−0.165745	+	0.986169i	$0.553003\pi$
$907$	−28.2167	+	48.8727i	−0.936919	+	1.62279i	−0.771175	+	0.636623i	$0.780331\pi$
$908$	−33.8253	−	19.3727i	−1.12253	−	0.642907i
$909$			14.1098i			0.467993i
$910$	−4.63467	+	2.54006i	−0.153638	+	0.0842021i
$911$			59.4025i			1.96809i	0.177912	+	0.984046i	$0.443066\pi$
$911$			59.4025i			1.96809i	−0.177912	+	0.984046i	$0.556934\pi$
$912$	−17.3511	+	4.77864i	−0.574553	+	0.158236i
$913$	0.687661	−	1.19106i	0.0227583	−	0.0394185i
$914$	−3.82363	−	2.92344i	−0.126474	−	0.0966987i
$915$	9.15728	+	9.15728i	0.302730	+	0.302730i
$916$	−10.2320	+	5.95491i	−0.338074	+	0.196756i
$917$	3.42370	−	12.7774i	0.113061	−	0.421948i
$918$	−3.08294	−	1.27073i	−0.101752	−	0.0419403i
$919$	2.85503	−	1.64835i	0.0941788	−	0.0543742i	−0.452171	−	0.891931i	$-0.649350\pi$
$919$	2.85503	−	1.64835i	0.0941788	−	0.0543742i	0.546350	+	0.837557i	$0.316017\pi$
$920$	−4.94672	+	3.83686i	−0.163088	+	0.126498i
$921$	20.8194	−	5.57854i	0.686023	−	0.183819i
$922$	44.0028	−	18.3161i	1.44915	−	0.603209i
$923$	−20.1093	+	14.6778i	−0.661904	+	0.483124i
$924$	0.285544	+	0.283567i	0.00939370	+	0.00932867i
$925$	−8.41983	−	31.4232i	−0.276842	−	1.03319i
$926$	−2.23579	+	17.2134i	−0.0734725	+	0.565668i
$927$	7.93827	+	13.7495i	0.260727	+	0.451592i
$928$	5.78291	−	14.3114i	0.189833	−	0.469794i
$929$	32.6709	+	8.75413i	1.07190	+	0.287214i	0.751272	−	0.659993i	$-0.229441\pi$
$929$	32.6709	+	8.75413i	1.07190	+	0.287214i	0.320624	+	0.947206i	$0.396107\pi$
$930$	−13.2965	+	1.77401i	−0.436008	+	0.0581720i
$931$	19.2825	−	19.2825i	0.631960	−	0.631960i
$932$	−54.0076	−	14.2704i	−1.76908	−	0.467443i
$933$	14.0211	+	8.09510i	0.459031	+	0.265022i
$934$	−38.8340	+	29.9057i	−1.27069	+	0.978543i
$935$	0.523630			0.0171245
$936$	9.89837	−	2.45404i	0.323538	−	0.0802128i
$937$	18.1789			0.593880			0.296940	−	0.954896i	$-0.404034\pi$
$937$	18.1789			0.593880			0.296940	+	0.954896i	$0.404034\pi$
$938$	3.71849	−	2.86357i	0.121413	−	0.0934990i
$939$	−9.37797	−	5.41437i	−0.306038	−	0.176691i
$940$	−25.0731	−	6.62506i	−0.817793	−	0.216086i
$941$	−15.7580	+	15.7580i	−0.513697	+	0.513697i	−0.915657	−	0.401960i	$-0.868329\pi$
$941$	−15.7580	+	15.7580i	−0.513697	+	0.513697i	0.401960	+	0.915657i	$0.368329\pi$
$942$	−20.4928	+	2.73414i	−0.667690	+	0.0890829i
$943$	−10.9951	−	2.94612i	−0.358049	−	0.0959388i
$944$	27.8839	+	27.4992i	0.907544	+	0.895023i
$945$	0.518245	+	0.897626i	0.0168585	+	0.0291998i
$946$	−0.109746	+	0.844941i	−0.00356816	+	0.0274714i
$947$	11.2282	+	41.9042i	0.364867	+	1.36170i	0.867601	+	0.497262i	$0.165661\pi$
$947$	11.2282	+	41.9042i	0.364867	+	1.36170i	−0.502733	+	0.864441i	$0.667672\pi$
$948$	5.91999	+	5.87901i	0.192272	+	0.190941i
$949$	0.884145	+	8.23815i	0.0287006	+	0.267422i
$950$	−22.6517	+	9.42877i	−0.734919	+	0.305910i
$951$	−5.60528	+	1.50193i	−0.181764	+	0.0487034i
$952$	3.96102	+	5.10679i	0.128377	+	0.165512i
$953$	−50.7124	+	29.2788i	−1.64274	+	0.948434i	−0.662880	+	0.748726i	$0.730666\pi$
$953$	−50.7124	+	29.2788i	−1.64274	+	0.948434i	−0.979856	+	0.199708i	$0.936001\pi$
$954$	0.994652	+	0.409976i	0.0322031	+	0.0132735i
$955$	6.25368	−	23.3390i	0.202364	−	0.755234i
$956$	−7.36050	+	4.28374i	−0.238056	+	0.138546i
$957$	0.400617	+	0.400617i	0.0129501	+	0.0129501i
$958$	−37.9594	−	29.0227i	−1.22641	−	0.937680i
$959$	10.4033	−	18.0190i	0.335939	−	0.581863i
$960$	4.20081	−	7.45431i	0.135580	−	0.240587i
$961$			47.6491i			1.53707i
$962$	−41.7898	+	10.2068i	−1.34736	+	0.329079i
$963$		−	7.79725i		−	0.251263i
$964$	−11.9791	−	6.86078i	−0.385821	−	0.220971i
$965$	−0.917021	+	1.58833i	−0.0295199	+	0.0511300i
$966$	1.72259	−	2.25301i	0.0554234	−	0.0724894i
$967$	−2.43403	−	2.43403i	−0.0782732	−	0.0782732i	0.666886	−	0.745159i	$-0.267627\pi$
$967$	−2.43403	−	2.43403i	−0.0782732	−	0.0782732i	−0.745159	+	0.666886i	$0.767627\pi$
$968$	−24.6846	−	18.7376i	−0.793392	−	0.602250i
$969$	2.74576	−	10.2473i	0.0882065	−	0.329191i
$970$	4.94779	−	12.0039i	0.158864	−	0.385423i
$971$	−16.8468	+	9.72650i	−0.540639	+	0.312138i	−0.745338	−	0.666687i	$-0.767712\pi$
$971$	−16.8468	+	9.72650i	−0.540639	+	0.312138i	0.204699	+	0.978825i	$0.434379\pi$
$972$	−0.524344	−	1.93004i	−0.0168184	−	0.0619061i
$973$	5.43175	−	1.45543i	0.174134	−	0.0466590i
$974$	20.3115	+	48.7965i	0.650824	+	1.56354i
$975$	12.9687	−	5.01091i	0.415332	−	0.160478i
$976$	0.336419	+	48.4312i	0.0107685	+	1.55024i
$977$	−0.132867	−	0.495868i	−0.00425080	−	0.0158642i	0.963768	−	0.266742i	$-0.0859473\pi$
$977$	−0.132867	−	0.495868i	−0.00425080	−	0.0158642i	−0.968019	+	0.250878i	$0.919281\pi$
$978$	27.7141	+	3.59968i	0.886199	+	0.115105i
$979$	−1.43704	−	2.48903i	−0.0459281	−	0.0795497i
$980$	0.0450288	+	12.9649i	0.00143839	+	0.414149i
$981$	−7.30121	−	1.95635i	−0.233110	−	0.0624615i
$982$	3.15460	+	23.6442i	0.100667	+	0.754517i
$983$	−15.5041	+	15.5041i	−0.494504	+	0.494504i	−0.909722	−	0.415218i	$-0.863705\pi$
$983$	−15.5041	+	15.5041i	−0.494504	+	0.494504i	0.415218	+	0.909722i	$0.363705\pi$
$984$	15.4141	−	2.11106i	0.491384	−	0.0672981i
$985$	−2.15431	−	1.24379i	−0.0686419	−	0.0396304i
$986$	5.55156	+	7.20898i	0.176798	+	0.229581i
$987$	11.7486			0.373961
$988$	11.7986	+	30.2234i	0.375365	+	0.961535i
$989$	6.00474			0.190940
$990$	0.191622	+	0.248830i	0.00609014	+	0.00790835i
$991$	36.8516	+	21.2763i	1.17063	+	0.675864i	0.953828	−	0.300352i	$-0.0971041\pi$
$991$	36.8516	+	21.2763i	1.17063	+	0.675864i	0.216802	+	0.976216i	$0.430437\pi$
$992$	−40.0642	−	30.1933i	−1.27204	−	0.958637i
$993$	−10.9272	+	10.9272i	−0.346765	+	0.346765i
$994$	−1.25148	−	9.38001i	−0.0396944	−	0.297516i
$995$	−17.9170	−	4.80085i	−0.568007	−	0.152197i
$996$	13.2476	−	0.0460105i	0.419765	−	0.00145790i
$997$	−4.45802	−	7.72151i	−0.141187	−	0.244543i	0.786757	−	0.617263i	$-0.211758\pi$
$997$	−4.45802	−	7.72151i	−0.141187	−	0.244543i	−0.927944	+	0.372720i	$0.878425\pi$
$998$	27.1397	+	3.52507i	0.859092	+	0.111584i
$999$	2.18354	+	8.14910i	0.0690843	+	0.257826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	156.2.w.c.19.5	✓	24
3.2	odd	2		468.2.cb.h.19.2		24
4.3	odd	2		156.2.w.d.19.1	yes	24
12.11	even	2		468.2.cb.g.19.6		24
13.11	odd	12		156.2.w.d.115.1	yes	24
39.11	even	12		468.2.cb.g.271.6		24
52.11	even	12	inner	156.2.w.c.115.5	yes	24
156.11	odd	12		468.2.cb.h.271.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
156.2.w.c.19.5	✓	24	1.1	even	1	trivial
156.2.w.c.115.5	yes	24	52.11	even	12	inner
156.2.w.d.19.1	yes	24	4.3	odd	2
156.2.w.d.115.1	yes	24	13.11	odd	12
468.2.cb.g.19.6		24	12.11	even	2
468.2.cb.g.271.6		24	39.11	even	12
468.2.cb.h.19.2		24	3.2	odd	2
468.2.cb.h.271.2		24	156.11	odd	12

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:	\( N \)	\(=\)	\( 156 = 2^{2} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	156.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12047 - 0.862866i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.510925 - 1.93364i) q^{4} +(0.756294 - 0.756294i) q^{5} +(-1.40179 + 0.187026i) q^{6} +(-0.936058 - 0.250816i) q^{7} +(-1.09599 - 2.60745i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.12047 - 0.862866i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.510925 - 1.93364i) q^{4} +(0.756294 - 0.756294i) q^{5} +(-1.40179 + 0.187026i) q^{6} +(-0.936058 - 0.250816i) q^{7} +(-1.09599 - 2.60745i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.194828 - 1.49999i) q^{10} +(0.0537393 + 0.200558i) q^{11} +(-1.40929 + 1.41912i) q^{12} +(2.80701 + 2.26289i) q^{13} +(-1.26525 + 0.526659i) q^{14} +(-1.03312 + 0.276823i) q^{15} +(-3.47791 - 1.97589i) q^{16} +(2.04199 - 1.17894i) q^{17} +(1.30750 + 0.538926i) q^{18} +(-1.16450 + 4.34597i) q^{19} +(-1.07599 - 1.84881i) q^{20} +(0.685242 + 0.685242i) q^{21} +(0.233268 + 0.178350i) q^{22} +(1.03470 - 1.79216i) q^{23} +(-0.354570 + 2.80611i) q^{24} +3.85604i q^{25} +(5.09776 + 0.113439i) q^{26} -1.00000i q^{27} +(-0.963243 + 1.68185i) q^{28} +(-1.36433 + 2.36308i) q^{29} +(-0.918720 + 1.20161i) q^{30} +(6.27093 + 6.27093i) q^{31} +(-5.60184 + 0.787036i) q^{32} +(0.0537393 - 0.200558i) q^{33} +(1.27073 - 3.08294i) q^{34} +(-0.897626 + 0.518245i) q^{35} +(1.93004 - 0.524344i) q^{36} +(-8.14910 + 2.18354i) q^{37} +(2.44520 + 5.87435i) q^{38} +(-1.29950 - 3.36323i) q^{39} +(-2.80089 - 1.14311i) q^{40} +(-1.42366 - 5.31316i) q^{41} +(1.35907 + 0.176524i) q^{42} +(1.45084 + 2.51293i) q^{43} +(0.415263 - 0.00144226i) q^{44} +(1.03312 + 0.276823i) q^{45} +(-0.387033 - 2.90087i) q^{46} +(8.57257 - 8.57257i) q^{47} +(2.02401 + 3.45013i) q^{48} +(-5.24888 - 3.03044i) q^{49} +(3.32724 + 4.32059i) q^{50} -2.35789 q^{51} +(5.80979 - 4.27157i) q^{52} +0.760728 q^{53} +(-0.862866 - 1.12047i) q^{54} +(0.192323 + 0.111038i) q^{55} +(0.371920 + 2.71562i) q^{56} +(3.18147 - 3.18147i) q^{57} +(0.510331 + 3.82501i) q^{58} +(-9.45707 - 2.53401i) q^{59} +(0.00742940 + 2.13911i) q^{60} +(-6.05404 - 10.4859i) q^{61} +(12.4374 + 1.61544i) q^{62} +(-0.250816 - 0.936058i) q^{63} +(-5.59761 + 5.71549i) q^{64} +(3.83434 - 0.411514i) q^{65} +(-0.112841 - 0.271089i) q^{66} +(-3.30788 + 0.886345i) q^{67} +(-1.23635 - 4.55082i) q^{68} +(-1.79216 + 1.03470i) q^{69} +(-0.558591 + 1.35521i) q^{70} +(-1.78713 + 6.66967i) q^{71} +(1.71012 - 2.25288i) q^{72} +(1.62491 + 1.62491i) q^{73} +(-7.24675 + 9.47818i) q^{74} +(1.92802 - 3.33943i) q^{75} +(7.80856 + 4.47219i) q^{76} -0.201212i q^{77} +(-4.35807 - 2.64712i) q^{78} -4.17160i q^{79} +(-4.12468 + 1.13597i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-6.17971 - 4.72483i) q^{82} +(-4.68375 - 4.68375i) q^{83} +(1.67512 - 0.974902i) q^{84} +(0.652717 - 2.43597i) q^{85} +(3.79394 + 1.56379i) q^{86} +(2.36308 - 1.36433i) q^{87} +(0.464047 - 0.359932i) q^{88} +(-13.3705 + 3.58262i) q^{89} +(1.39644 - 0.581269i) q^{90} +(-2.05996 - 2.82224i) q^{91} +(-2.93672 - 2.91640i) q^{92} +(-2.29532 - 8.56625i) q^{93} +(2.20837 - 17.0023i) q^{94} +(2.40613 + 4.16754i) q^{95} +(5.24485 + 2.11932i) q^{96} +(8.29124 + 2.22163i) q^{97} +(-8.49610 + 1.13355i) q^{98} +(-0.146818 + 0.146818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9	\( 24 q - 4 q^{2} + 4 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} - 4 q^{8} + 12 q^{9} + 12 q^{10} + 4 q^{11} - 4 q^{12} - 22 q^{14} - 4 q^{15} + 12 q^{16} - 2 q^{18} - 22 q^{19} - 4 q^{20} + 10 q^{21} - 34 q^{22} + 2 q^{24} - 4 q^{26} - 14 q^{28} + 8 q^{29} - 16 q^{30} - 2 q^{31} - 34 q^{32} + 4 q^{33} + 20 q^{34} + 24 q^{35} - 4 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} + 28 q^{40} - 36 q^{41} + 6 q^{42} + 10 q^{43} + 20 q^{44} + 4 q^{45} - 2 q^{46} + 20 q^{47} + 32 q^{48} - 54 q^{49} - 24 q^{50} + 36 q^{51} + 4 q^{52} - 36 q^{53} - 4 q^{54} - 24 q^{55} + 70 q^{56} - 32 q^{57} + 48 q^{58} - 36 q^{59} - 28 q^{60} - 2 q^{61} + 64 q^{62} + 8 q^{63} - 8 q^{64} + 16 q^{65} + 20 q^{66} - 16 q^{67} - 10 q^{68} + 12 q^{69} + 36 q^{71} - 2 q^{72} - 40 q^{73} - 30 q^{74} - 8 q^{75} + 58 q^{76} + 24 q^{78} - 48 q^{80} - 12 q^{81} - 30 q^{82} - 24 q^{83} - 26 q^{84} + 18 q^{85} + 30 q^{86} + 6 q^{87} - 78 q^{88} + 66 q^{89} + 12 q^{90} + 42 q^{91} + 36 q^{92} - 10 q^{93} + 6 q^{94} - 28 q^{95} + 8 q^{96} + 4 q^{97} + 44 q^{98} - 4 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 + 4 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 - 4 * q^8 + 12 * q^9 + 12 * q^10 + 4 * q^11 - 4 * q^12 - 22 * q^14 - 4 * q^15 + 12 * q^16 - 2 * q^18 - 22 * q^19 - 4 * q^20 + 10 * q^21 - 34 * q^22 + 2 * q^24 - 4 * q^26 - 14 * q^28 + 8 * q^29 - 16 * q^30 - 2 * q^31 - 34 * q^32 + 4 * q^33 + 20 * q^34 + 24 * q^35 - 4 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 + 28 * q^40 - 36 * q^41 + 6 * q^42 + 10 * q^43 + 20 * q^44 + 4 * q^45 - 2 * q^46 + 20 * q^47 + 32 * q^48 - 54 * q^49 - 24 * q^50 + 36 * q^51 + 4 * q^52 - 36 * q^53 - 4 * q^54 - 24 * q^55 + 70 * q^56 - 32 * q^57 + 48 * q^58 - 36 * q^59 - 28 * q^60 - 2 * q^61 + 64 * q^62 + 8 * q^63 - 8 * q^64 + 16 * q^65 + 20 * q^66 - 16 * q^67 - 10 * q^68 + 12 * q^69 + 36 * q^71 - 2 * q^72 - 40 * q^73 - 30 * q^74 - 8 * q^75 + 58 * q^76 + 24 * q^78 - 48 * q^80 - 12 * q^81 - 30 * q^82 - 24 * q^83 - 26 * q^84 + 18 * q^85 + 30 * q^86 + 6 * q^87 - 78 * q^88 + 66 * q^89 + 12 * q^90 + 42 * q^91 + 36 * q^92 - 10 * q^93 + 6 * q^94 - 28 * q^95 + 8 * q^96 + 4 * q^97 + 44 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more