LMFDB - Embedded newform 342.2.x.b.281.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(29,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([3, 17]))

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

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

chi := DirichletCharacter("342.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.x (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:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			281.3
Character	$\chi$	$=$	342.281
Dual form			342.2.x.b.185.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.444535 - 1.67403i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.266390 + 0.731901i) q^{5} +(1.41658 + 0.996642i) q^{6} +(2.00201 + 3.46759i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.60478 + 1.48833i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.444535 - 1.67403i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.266390 + 0.731901i) q^{5} +(1.41658 + 0.996642i) q^{6} +(2.00201 + 3.46759i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.60478 + 1.48833i) q^{9} +(-0.266390 - 0.731901i) q^{10} -2.32068i q^{11} +(-1.72579 + 0.147089i) q^{12} +(1.40450 + 3.85884i) q^{13} +(-3.76255 - 1.36946i) q^{14} +(1.34365 + 0.120590i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.79778 - 4.93936i) q^{17} +(1.03869 - 2.81445i) q^{18} +(2.17044 + 3.78010i) q^{19} +(0.674524 + 0.389436i) q^{20} +(4.91489 - 4.89290i) q^{21} +(1.49170 + 1.77774i) q^{22} +(6.65933 + 1.17422i) q^{23} +(1.22749 - 1.22200i) q^{24} +(3.36551 + 2.82400i) q^{25} +(-3.55633 - 2.05325i) q^{26} +(3.64944 + 3.69887i) q^{27} +(3.76255 - 1.36946i) q^{28} +(-1.09631 + 6.21746i) q^{29} +(-1.10681 + 0.771302i) q^{30} -7.02134i q^{31} +(0.939693 - 0.342020i) q^{32} +(-3.88490 + 1.03162i) q^{33} +(1.79778 + 4.93936i) q^{34} +(-3.07125 + 0.541544i) q^{35} +(1.01341 + 2.82365i) q^{36} -9.84250i q^{37} +(-4.09246 - 1.50059i) q^{38} +(5.83548 - 4.06658i) q^{39} +(-0.767040 + 0.135250i) q^{40} +(-1.92636 + 1.61641i) q^{41} +(-0.619931 + 6.90741i) q^{42} +(1.72125 + 9.76171i) q^{43} +(-2.28542 - 0.402982i) q^{44} +(-0.395426 - 2.30292i) q^{45} +(-5.85612 + 3.38103i) q^{46} +(0.0572179 + 0.0100891i) q^{47} +(-0.154827 + 1.72512i) q^{48} +(-4.51611 + 7.82213i) q^{49} -4.39336 q^{50} +(-9.06783 - 0.813825i) q^{51} +(4.04411 - 0.713085i) q^{52} +(-9.91021 - 8.31565i) q^{53} +(-5.17322 - 0.487685i) q^{54} +(1.69851 + 0.618207i) q^{55} +(-2.00201 + 3.46759i) q^{56} +(5.36318 - 5.31378i) q^{57} +(-3.15669 - 5.46754i) q^{58} +(1.88846 + 10.7100i) q^{59} +(0.352080 - 1.30229i) q^{60} +(5.70469 - 2.07634i) q^{61} +(4.51323 + 5.37866i) q^{62} +(-10.3757 - 6.05263i) q^{63} +(-0.500000 + 0.866025i) q^{64} -3.19844 q^{65} +(2.31289 - 3.28743i) q^{66} +(-6.35785 + 7.57699i) q^{67} +(-4.55214 - 2.62818i) q^{68} +(-0.994624 - 11.6699i) q^{69} +(2.00461 - 2.38901i) q^{70} +(0.245401 - 0.205916i) q^{71} +(-2.59132 - 1.51164i) q^{72} +(-1.58780 - 9.00484i) q^{73} +(6.32664 + 7.53979i) q^{74} +(3.23138 - 6.88934i) q^{75} +(4.09957 - 1.48106i) q^{76} +(8.04716 - 4.64603i) q^{77} +(-1.85629 + 6.86615i) q^{78} +(1.68811 - 4.63804i) q^{79} +(0.500650 - 0.596651i) q^{80} +(4.56973 - 7.75355i) q^{81} +(0.436671 - 2.47649i) q^{82} +(-3.94762 + 2.27916i) q^{83} +(-3.96510 - 5.68987i) q^{84} +(3.13621 + 2.63159i) q^{85} +(-7.59326 - 6.37151i) q^{86} +(10.8956 - 0.928626i) q^{87} +(2.00977 - 1.16034i) q^{88} +(-0.627903 + 3.56102i) q^{89} +(1.78320 + 1.50996i) q^{90} +(-10.5690 + 12.5957i) q^{91} +(2.31276 - 6.35426i) q^{92} +(-11.7540 + 3.12123i) q^{93} +(-0.0503166 + 0.0290503i) q^{94} +(-3.34485 + 0.581566i) q^{95} +(-0.990280 - 1.42104i) q^{96} +(-7.45026 - 8.87888i) q^{97} +(-1.56843 - 8.89500i) q^{98} +(3.45395 + 6.04486i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	$ 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) $ 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{11}{18}\right)$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.444535	−	1.67403i	−0.256652	−	0.966504i
$3$	−0.444535	−	1.67403i	−0.256652	−	0.966504i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.266390	+	0.731901i	−0.119133	+	0.327316i	−0.984898	−	0.173135i	$-0.944610\pi$
$5$	−0.266390	+	0.731901i	−0.119133	+	0.327316i	0.865765	+	0.500451i	$0.166833\pi$
$6$	1.41658	+	0.996642i	0.578317	+	0.406878i
$7$	2.00201	+	3.46759i	0.756690	+	1.31062i	0.944530	+	0.328425i	$0.106518\pi$
$7$	2.00201	+	3.46759i	0.756690	+	1.31062i	−0.187840	+	0.982200i	$0.560149\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−2.60478	+	1.48833i	−0.868259	+	0.496111i
$10$	−0.266390	−	0.731901i	−0.0842400	−	0.231447i
$11$		−	2.32068i		−	0.699712i	−0.936804	−	0.349856i	$-0.886231\pi$
$11$		−	2.32068i		−	0.699712i	0.936804	−	0.349856i	$-0.113769\pi$
$12$	−1.72579	+	0.147089i	−0.498194	+	0.0424609i
$13$	1.40450	+	3.85884i	0.389539	+	1.07025i	0.967209	+	0.253980i	$0.0817397\pi$
$13$	1.40450	+	3.85884i	0.389539	+	1.07025i	−0.577670	+	0.816270i	$0.696038\pi$
$14$	−3.76255	−	1.36946i	−1.00558	−	0.366003i
$15$	1.34365	+	0.120590i	0.346928	+	0.0311363i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.79778	−	4.93936i	0.436026	−	1.19797i	−0.506030	−	0.862516i	$-0.668888\pi$
$17$	1.79778	−	4.93936i	0.436026	−	1.19797i	0.942056	−	0.335455i	$-0.108890\pi$
$18$	1.03869	−	2.81445i	0.244822	−	0.663372i
$19$	2.17044	+	3.78010i	0.497933	+	0.867215i
$19$	2.17044	+	3.78010i	0.497933	+	0.867215i
$20$	0.674524	+	0.389436i	0.150828	+	0.0870806i
$21$	4.91489	−	4.89290i	1.07252	−	1.06772i
$22$	1.49170	+	1.77774i	0.318033	+	0.379016i
$23$	6.65933	+	1.17422i	1.38857	+	0.244842i	0.817437	−	0.576018i	$-0.195394\pi$
$23$	6.65933	+	1.17422i	1.38857	+	0.244842i	0.571130	+	0.820860i	$0.306505\pi$
$24$	1.22749	−	1.22200i	0.250560	−	0.249439i
$25$	3.36551	+	2.82400i	0.673101	+	0.564799i
$26$	−3.55633	−	2.05325i	−0.697453	−	0.402675i
$27$	3.64944	+	3.69887i	0.702334	+	0.711847i
$28$	3.76255	−	1.36946i	0.711056	−	0.258803i
$29$	−1.09631	+	6.21746i	−0.203579	+	1.15455i	0.696082	+	0.717963i	$0.254925\pi$
$29$	−1.09631	+	6.21746i	−0.203579	+	1.15455i	−0.899660	+	0.436590i	$0.856186\pi$
$30$	−1.10681	+	0.771302i	−0.202074	+	0.140820i
$31$		−	7.02134i		−	1.26107i	−0.776161	−	0.630535i	$-0.782835\pi$
$31$		−	7.02134i		−	1.26107i	0.776161	−	0.630535i	$-0.217165\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−3.88490	+	1.03162i	−0.676274	+	0.179583i
$34$	1.79778	+	4.93936i	0.308317	+	0.847094i
$35$	−3.07125	+	0.541544i	−0.519136	+	0.0915376i
$36$	1.01341	+	2.82365i	0.168901	+	0.470609i
$37$		−	9.84250i		−	1.61810i	−0.587742	−	0.809048i	$-0.699983\pi$
$37$		−	9.84250i		−	1.61810i	0.587742	−	0.809048i	$-0.300017\pi$
$38$	−4.09246	−	1.50059i	−0.663884	−	0.243429i
$39$	5.83548	−	4.06658i	0.934425	−	0.651173i
$40$	−0.767040	+	0.135250i	−0.121280	+	0.0213849i
$41$	−1.92636	+	1.61641i	−0.300848	+	0.252441i	−0.780697	−	0.624910i	$-0.785136\pi$
$41$	−1.92636	+	1.61641i	−0.300848	+	0.252441i	0.479849	+	0.877351i	$0.340691\pi$
$42$	−0.619931	+	6.90741i	−0.0956574	+	1.06584i
$43$	1.72125	+	9.76171i	0.262489	+	1.48865i	0.776092	+	0.630620i	$0.217199\pi$
$43$	1.72125	+	9.76171i	0.262489	+	1.48865i	−0.513603	+	0.858028i	$0.671690\pi$
$44$	−2.28542	−	0.402982i	−0.344541	−	0.0607518i
$45$	−0.395426	−	2.30292i	−0.0589466	−	0.343299i
$46$	−5.85612	+	3.38103i	−0.863438	+	0.498506i
$47$	0.0572179	+	0.0100891i	0.00834609	+	0.00147164i	0.177820	−	0.984063i	$-0.443096\pi$
$47$	0.0572179	+	0.0100891i	0.00834609	+	0.00147164i	−0.169474	+	0.985535i	$0.554207\pi$
$48$	−0.154827	+	1.72512i	−0.0223473	+	0.248999i
$49$	−4.51611	+	7.82213i	−0.645158	+	1.11745i
$50$	−4.39336			−0.621315
$51$	−9.06783	−	0.813825i	−1.26975	−	0.113958i
$52$	4.04411	−	0.713085i	0.560817	−	0.0988871i
$53$	−9.91021	−	8.31565i	−1.36127	−	1.14224i	−0.975587	−	0.219612i	$-0.929521\pi$
$53$	−9.91021	−	8.31565i	−1.36127	−	1.14224i	−0.385685	−	0.922631i	$-0.626035\pi$
$54$	−5.17322	−	0.487685i	−0.703986	−	0.0663656i
$55$	1.69851	+	0.618207i	0.229027	+	0.0833590i
$56$	−2.00201	+	3.46759i	−0.267530	+	0.463376i
$57$	5.36318	−	5.31378i	0.710371	−	0.703828i
$58$	−3.15669	−	5.46754i	−0.414493	−	0.717923i
$59$	1.88846	+	10.7100i	0.245856	+	1.39432i	0.818496	+	0.574513i	$0.194808\pi$
$59$	1.88846	+	10.7100i	0.245856	+	1.39432i	−0.572639	+	0.819807i	$0.694080\pi$
$60$	0.352080	−	1.30229i	0.0454534	−	0.168125i
$61$	5.70469	−	2.07634i	0.730411	−	0.265848i	0.0500724	−	0.998746i	$-0.484055\pi$
$61$	5.70469	−	2.07634i	0.730411	−	0.265848i	0.680339	+	0.732898i	$0.261833\pi$
$62$	4.51323	+	5.37866i	0.573181	+	0.683091i
$63$	−10.3757	−	6.05263i	−1.30722	−	0.762560i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−3.19844			−0.396717
$66$	2.31289	−	3.28743i	0.284697	−	0.404655i
$67$	−6.35785	+	7.57699i	−0.776735	+	0.925676i	−0.998781	−	0.0493598i	$-0.984282\pi$
$67$	−6.35785	+	7.57699i	−0.776735	+	0.925676i	0.222046	+	0.975036i	$0.428726\pi$
$68$	−4.55214	−	2.62818i	−0.552028	−	0.318714i
$69$	−0.994624	−	11.6699i	−0.119739	−	1.40489i
$70$	2.00461	−	2.38901i	0.239597	−	0.285541i
$71$	0.245401	−	0.205916i	0.0291238	−	0.0244378i	−0.628110	−	0.778125i	$-0.716171\pi$
$71$	0.245401	−	0.205916i	0.0291238	−	0.0244378i	0.657233	+	0.753687i	$0.271727\pi$
$72$	−2.59132	−	1.51164i	−0.305390	−	0.178148i
$73$	−1.58780	−	9.00484i	−0.185838	−	1.05394i	−0.924875	−	0.380272i	$-0.875830\pi$
$73$	−1.58780	−	9.00484i	−0.185838	−	1.05394i	0.739037	−	0.673665i	$-0.235281\pi$
$74$	6.32664	+	7.53979i	0.735456	+	0.876483i
$75$	3.23138	−	6.88934i	0.373127	−	0.795512i
$76$	4.09957	−	1.48106i	0.470253	−	0.169889i
$77$	8.04716	−	4.64603i	0.917059	−	0.529465i
$78$	−1.85629	+	6.86615i	−0.210184	+	0.777439i
$79$	1.68811	−	4.63804i	0.189927	−	0.521821i	−0.807781	−	0.589482i	$-0.799332\pi$
$79$	1.68811	−	4.63804i	0.189927	−	0.521821i	0.997708	+	0.0676619i	$0.0215539\pi$
$80$	0.500650	−	0.596651i	0.0559743	−	0.0667076i
$81$	4.56973	−	7.75355i	0.507747	−	0.861506i
$82$	0.436671	−	2.47649i	0.0482223	−	0.273482i
$83$	−3.94762	+	2.27916i	−0.433307	+	0.250170i	−0.700755	−	0.713402i	$-0.747153\pi$
$83$	−3.94762	+	2.27916i	−0.433307	+	0.250170i	0.267447	+	0.963572i	$0.413820\pi$
$84$	−3.96510	−	5.68987i	−0.432628	−	0.620815i
$85$	3.13621	+	2.63159i	0.340170	+	0.285437i
$86$	−7.59326	−	6.37151i	−0.818803	−	0.687057i
$87$	10.8956	−	0.928626i	1.16813	−	0.0995591i
$88$	2.00977	−	1.16034i	0.214242	−	0.123693i
$89$	−0.627903	+	3.56102i	−0.0665576	+	0.377467i	0.933275	+	0.359163i	$0.116938\pi$
$89$	−0.627903	+	3.56102i	−0.0665576	+	0.377467i	−0.999832	+	0.0183040i	$0.994173\pi$
$90$	1.78320	+	1.50996i	0.187966	+	0.159164i
$91$	−10.5690	+	12.5957i	−1.10794	+	1.32039i
$92$	2.31276	−	6.35426i	0.241122	−	0.662478i
$93$	−11.7540	+	3.12123i	−1.21883	+	0.323657i
$94$	−0.0503166	+	0.0290503i	−0.00518976	+	0.00299631i
$95$	−3.34485	+	0.581566i	−0.343174	+	0.0596674i
$96$	−0.990280	−	1.42104i	−0.101070	−	0.145034i
$97$	−7.45026	−	8.87888i	−0.756460	−	0.901513i	0.241159	−	0.970486i	$-0.422472\pi$
$97$	−7.45026	−	8.87888i	−0.756460	−	0.901513i	−0.997619	+	0.0689722i	$0.978028\pi$
$98$	−1.56843	−	8.89500i	−0.158435	−	0.898530i
$99$	3.45395	+	6.04486i	0.347135	+	0.607531i
$100$	3.36551	−	2.82400i	0.336551	−	0.282400i
$101$	−6.47182	+	7.71282i	−0.643970	+	0.767454i	−0.984992	−	0.172602i	$-0.944783\pi$
$101$	−6.47182	+	7.71282i	−0.643970	+	0.767454i	0.341021	+	0.940056i	$0.389227\pi$
$102$	7.46948	−	5.20526i	0.739589	−	0.515398i
$103$	−3.73332	−	2.15543i	−0.367855	−	0.212381i	0.304666	−	0.952459i	$-0.401455\pi$
$103$	−3.73332	−	2.15543i	−0.367855	−	0.212381i	−0.672521	+	0.740078i	$0.734789\pi$
$104$	−2.63960	+	3.14576i	−0.258834	+	0.308467i
$105$	2.27184	+	4.90064i	0.221709	+	0.478253i
$106$	12.9369			1.25654
$107$	−0.0364312	+	0.0631007i	−0.00352194	+	0.00610017i	−0.867781	−	0.496947i	$-0.834454\pi$
$107$	−0.0364312	+	0.0631007i	−0.00352194	+	0.00610017i	0.864259	+	0.503047i	$0.167788\pi$
$108$	4.27639	−	2.95169i	0.411496	−	0.284027i
$109$	−3.74813	−	4.46685i	−0.359006	−	0.427847i	0.556065	−	0.831139i	$-0.312310\pi$
$109$	−3.74813	−	4.46685i	−0.359006	−	0.427847i	−0.915071	+	0.403292i	$0.867866\pi$
$110$	−1.69851	+	0.618207i	−0.161946	+	0.0589437i
$111$	−16.4767	+	4.37534i	−1.56390	+	0.415289i
$112$	−0.695292	−	3.94319i	−0.0656989	−	0.372597i
$113$	−5.15038	−	8.92071i	−0.484507	−	0.839190i	0.515335	−	0.856989i	$-0.327667\pi$
$113$	−5.15038	−	8.92071i	−0.484507	−	0.839190i	−0.999842	+	0.0177989i	$0.994334\pi$
$114$	−0.692804	+	7.51798i	−0.0648870	+	0.704123i
$115$	−2.63339	+	4.56117i	−0.245565	+	0.425332i
$116$	5.93263	+	2.15930i	0.550831	+	0.200486i
$117$	−9.40166	−	7.96105i	−0.869184	−	0.736000i
$118$	−8.33088	−	6.99044i	−0.766920	−	0.643522i
$119$	20.7268	−	3.65470i	1.90003	−	0.335026i
$120$	0.567389	+	1.22393i	0.0517953	+	0.111729i
$121$	5.61444			0.510404
$122$	−3.03540	+	5.25748i	−0.274813	+	0.475989i
$123$	3.56226	+	2.50625i	0.321199	+	0.225981i
$124$	−6.91467	−	1.21924i	−0.620956	−	0.109491i
$125$	−6.33604	+	3.65812i	−0.566713	+	0.327192i
$126$	11.8388	−	2.03280i	1.05469	−	0.181096i
$127$	8.86849	+	1.56375i	0.786951	+	0.138761i	0.552661	−	0.833406i	$-0.313612\pi$
$127$	8.86849	+	1.56375i	0.786951	+	0.138761i	0.234290	+	0.972167i	$0.424724\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	15.5763	−	7.22086i	1.37141	−	0.635761i
$130$	2.45014	−	2.05592i	0.214892	−	0.180316i
$131$	2.56940	−	0.453054i	0.224489	−	0.0395835i	−0.0602720	−	0.998182i	$-0.519197\pi$
$131$	2.56940	−	0.453054i	0.224489	−	0.0395835i	0.284761	+	0.958598i	$0.408086\pi$
$132$	0.341346	+	4.00502i	0.0297104	+	0.348592i
$133$	−8.76259	+	15.0940i	−0.759813	+	1.30882i
$134$		−	9.89105i		−	0.854457i
$135$	−3.67938	+	1.68568i	−0.316671	+	0.145081i
$136$	5.17650	−	0.912757i	0.443881	−	0.0782683i
$137$	−2.35948	−	6.48262i	−0.201584	−	0.553848i	0.797170	−	0.603755i	$-0.206330\pi$
$137$	−2.35948	−	6.48262i	−0.201584	−	0.553848i	−0.998754	+	0.0499074i	$0.984107\pi$
$138$	8.26321	+	8.30035i	0.703411	+	0.706573i
$139$	−10.1055	+	3.67810i	−0.857137	+	0.311972i	−0.732947	−	0.680286i	$-0.761855\pi$
$139$	−10.1055	+	3.67810i	−0.857137	+	0.311972i	−0.124190	+	0.992258i	$0.539633\pi$
$140$			3.11863i			0.263572i
$141$	−0.00854595	−	0.100270i	−0.000719698	−	0.00844423i
$142$	−0.0556280	+	0.315482i	−0.00466820	+	0.0264747i
$143$	8.95514	−	3.25940i	0.748867	−	0.272565i
$144$	2.95673	−	0.507690i	0.246394	−	0.0423075i
$145$	−4.25852	−	2.45866i	−0.353651	−	0.204180i
$146$	7.00453	+	5.87750i	0.579699	+	0.486425i
$147$	15.1021	+	4.08291i	1.24560	+	0.336752i
$148$	−9.69297	−	1.70913i	−0.796757	−	0.140490i
$149$	6.27886	+	7.48286i	0.514385	+	0.613020i	0.959243	−	0.282581i	$-0.0911906\pi$
$149$	6.27886	+	7.48286i	0.514385	+	0.613020i	−0.444859	+	0.895601i	$0.646746\pi$
$150$	1.95300	+	7.35463i	0.159462	+	0.600503i
$151$	7.00709	+	4.04554i	0.570229	+	0.329222i	0.757241	−	0.653136i	$-0.226547\pi$
$151$	7.00709	+	4.04554i	0.570229	+	0.329222i	−0.187012	+	0.982358i	$0.559880\pi$
$152$	−2.18844	+	3.76971i	−0.177506	+	0.305764i
$153$	2.66860	+	15.5416i	0.215743	+	1.25647i
$154$	−3.17807	+	8.73168i	−0.256096	+	0.703619i
$155$	5.13893	+	1.87042i	0.412769	+	0.150236i
$156$	−2.99148	−	6.45298i	−0.239510	−	0.516652i
$157$	−8.82530	−	3.21215i	−0.704336	−	0.256357i	−0.0350748	−	0.999385i	$-0.511167\pi$
$157$	−8.82530	−	3.21215i	−0.704336	−	0.256357i	−0.669261	+	0.743027i	$0.733389\pi$
$158$	1.68811	+	4.63804i	0.134299	+	0.368983i
$159$	−9.51525	+	20.2866i	−0.754608	+	1.60883i
$160$			0.778873i			0.0615753i
$161$	9.26036	+	25.4426i	0.729819	+	2.00516i
$162$	1.48327	+	8.87693i	0.116537	+	0.697438i
$163$	−3.41583	−	5.91638i	−0.267548	−	0.463407i	0.700680	−	0.713476i	$-0.252880\pi$
$163$	−3.41583	−	5.91638i	−0.267548	−	0.463407i	−0.968228	+	0.250069i	$0.919547\pi$
$164$	1.25734	+	2.17779i	0.0981821	+	0.170056i
$165$	0.279852	−	3.11818i	0.0217864	−	0.242750i
$166$	1.55904	−	4.28342i	0.121005	−	0.332458i
$167$	1.78521	−	10.1245i	0.138144	−	0.783454i	−0.834475	−	0.551046i	$-0.814229\pi$
$167$	1.78521	−	10.1245i	0.138144	−	0.783454i	0.972619	−	0.232407i	$-0.0746602\pi$
$168$	6.69482	+	1.80997i	0.516517	+	0.139642i
$169$	−2.95945	+	2.48328i	−0.227650	+	0.191021i
$170$	−4.09403			−0.313998
$171$	−11.2796	−	6.61599i	−0.862570	−	0.505937i
$172$	9.91230			0.755806
$173$	12.9538	−	10.8695i	0.984855	−	0.826392i	4.06597e−5	−	1.00000i	$-0.499987\pi$
$173$	12.9538	−	10.8695i	0.984855	−	0.826392i	0.984815	+	0.173608i	$0.0555426\pi$
$174$	−7.74959	+	7.71491i	−0.587495	+	0.584866i
$175$	−3.05466	+	17.3239i	−0.230911	+	1.30956i
$176$	−0.793720	+	2.18073i	−0.0598289	+	0.164378i
$177$	17.0894	−	7.92230i	1.28452	−	0.595477i
$178$	−1.80798	−	3.13151i	−0.135514	−	0.234716i
$179$	−1.41852	−	2.45695i	−0.106025	−	0.183641i	0.808131	−	0.589002i	$-0.200479\pi$
$179$	−1.41852	−	2.45695i	−0.106025	−	0.183641i	−0.914157	+	0.405361i	$0.867146\pi$
$180$	−2.33659	−	0.0104789i	−0.174160	−	0.000781052i
$181$	−0.752463	−	2.06737i	−0.0559301	−	0.153667i	0.908581	−	0.417708i	$-0.137167\pi$
$181$	−0.752463	−	2.06737i	−0.0559301	−	0.153667i	−0.964511	+	0.264042i	$0.914944\pi$
$182$		−	16.4425i		−	1.21880i
$183$	−6.01180	−	8.62685i	−0.444405	−	0.637715i
$184$	2.31276	+	6.35426i	0.170499	+	0.468442i
$185$	7.20373	+	2.62194i	0.529629	+	0.192769i
$186$	6.99777	−	9.94631i	0.513101	−	0.729299i
$187$	−11.4627	−	4.17208i	−0.838234	−	0.305092i
$188$	0.0198716	−	0.0545967i	0.00144928	−	0.00398187i
$189$	−5.51993	+	20.0599i	−0.401516	+	1.45914i
$190$	2.18848	−	2.59553i	0.158769	−	0.188300i
$191$	−18.0625	−	10.4284i	−1.30695	−	0.754570i	−0.325367	−	0.945588i	$-0.605488\pi$
$191$	−18.0625	−	10.4284i	−1.30695	−	0.754570i	−0.981587	+	0.191018i	$0.938821\pi$
$192$	1.67202	+	0.452038i	0.120668	+	0.0326230i
$193$	−9.51945	−	11.3448i	−0.685225	−	0.816620i	0.305544	−	0.952178i	$-0.401162\pi$
$193$	−9.51945	−	11.3448i	−0.685225	−	0.816620i	−0.990769	+	0.135558i	$0.956717\pi$
$194$	11.4145	+	2.01268i	0.819511	+	0.144502i
$195$	1.42182	+	5.35429i	0.101818	+	0.383429i
$196$	6.91908	+	5.80580i	0.494220	+	0.414700i
$197$	15.1166	+	8.72756i	1.07701	+	0.621813i	0.930089	−	0.367335i	$-0.119730\pi$
$197$	15.1166	+	8.72756i	1.07701	+	0.621813i	0.146923	+	0.989148i	$0.453063\pi$
$198$	−6.53144	−	2.41047i	−0.464169	−	0.171305i
$199$	11.5157	−	4.19138i	0.816329	−	0.297119i	0.100093	−	0.994978i	$-0.468086\pi$
$199$	11.5157	−	4.19138i	0.816329	−	0.297119i	0.716235	+	0.697859i	$0.245864\pi$
$200$	−0.762898	+	4.32661i	−0.0539451	+	0.305938i
$201$	15.5104	+	7.27501i	1.09402	+	0.513140i
$202$		−	10.0684i		−	0.708408i
$203$	−23.7544	+	8.64589i	−1.66723	+	0.606823i
$204$	−2.37607	+	8.78875i	−0.166358	+	0.615336i
$205$	−0.669889	−	1.84050i	−0.0467871	−	0.128546i
$206$	4.24537	−	0.748574i	0.295789	−	0.0521556i
$207$	−19.0937	+	6.85273i	−1.32710	+	0.476298i
$208$		−	4.10649i		−	0.284734i
$209$	8.77241	−	5.03690i	0.606801	−	0.348410i
$210$	−4.89040	−	2.29379i	−0.337470	−	0.158287i
$211$	13.4513	−	2.37183i	0.926026	−	0.163283i	0.309754	−	0.950817i	$-0.399753\pi$
$211$	13.4513	−	2.37183i	0.926026	−	0.163283i	0.616272	+	0.787533i	$0.288642\pi$
$212$	−9.91021	+	8.31565i	−0.680636	+	0.571121i
$213$	−0.453800	−	0.319273i	−0.0310939	−	0.0218762i
$214$	−0.0126524	−	0.0717555i	−0.000864902	−	0.00490510i
$215$	−7.60313	−	1.34064i	−0.518529	−	0.0914307i
$216$	−1.37860	+	5.00994i	−0.0938016	+	0.340883i
$217$	24.3471	−	14.0568i	1.65279	−	0.954239i
$218$	5.74247	+	1.01255i	0.388929	+	0.0685788i
$219$	−14.3686	+	6.66100i	−0.970939	+	0.450108i
$220$	0.903758	−	1.56535i	0.0609313	−	0.105536i
$221$	21.5852			1.45198
$222$	9.80945	−	13.9427i	0.658367	−	0.935773i
$223$	4.39972	−	0.775789i	0.294627	−	0.0519507i	−0.0243809	−	0.999703i	$-0.507761\pi$
$223$	4.39972	−	0.775789i	0.294627	−	0.0519507i	0.319008	+	0.947752i	$0.396650\pi$
$224$	3.06726	+	2.57374i	0.204940	+	0.171965i
$225$	−12.9694	−	2.34688i	−0.864629	−	0.156459i
$226$	9.67954	+	3.52306i	0.643873	+	0.234351i
$227$	3.78795	−	6.56093i	0.251415	−	0.435464i	−0.712500	−	0.701672i	$-0.752437\pi$
$227$	3.78795	−	6.56093i	0.251415	−	0.435464i	0.963916	+	0.266208i	$0.0857707\pi$
$228$	−4.30175	−	6.20443i	−0.284890	−	0.410899i
$229$	−4.91688	−	8.51629i	−0.324917	−	0.562772i	0.656579	−	0.754258i	$-0.272003\pi$
$229$	−4.91688	−	8.51629i	−0.324917	−	0.562772i	−0.981496	+	0.191485i	$0.938670\pi$
$230$	−0.914568	−	5.18677i	−0.0603048	−	0.342006i
$231$	−11.3549	−	11.4059i	−0.747095	−	0.750453i
$232$	−5.93263	+	2.15930i	−0.389496	+	0.141765i
$233$	13.7635	+	16.4027i	0.901677	+	1.07458i	0.996865	+	0.0791170i	$0.0252101\pi$
$233$	13.7635	+	16.4027i	0.901677	+	1.07458i	−0.0951888	+	0.995459i	$0.530345\pi$
$234$	12.3194	+	0.0552485i	0.805342	+	0.00361171i
$235$	−0.0226265	+	0.0391902i	−0.00147599	+	0.00255649i
$236$	10.8752			0.707915
$237$	−8.51466	−	0.764179i	−0.553087	−	0.0496388i
$238$	−13.5285	+	16.1226i	−0.876922	+	1.04507i
$239$	6.42431	+	3.70907i	0.415554	+	0.239920i	0.693173	−	0.720771i	$-0.256212\pi$
$239$	6.42431	+	3.70907i	0.415554	+	0.239920i	−0.277619	+	0.960691i	$0.589545\pi$
$240$	−1.22137	−	0.572872i	−0.0788391	−	0.0369787i
$241$	−0.111878	+	0.133331i	−0.00720668	+	0.00858859i	−0.769636	−	0.638483i	$-0.779562\pi$
$241$	−0.111878	+	0.133331i	−0.00720668	+	0.00858859i	0.762429	+	0.647072i	$0.224007\pi$
$242$	−4.30091	+	3.60889i	−0.276473	+	0.231988i
$243$	−15.0111	−	4.20315i	−0.962963	−	0.269632i
$244$	−1.05419	−	5.97858i	−0.0674873	−	0.382739i
$245$	−4.52198	−	5.38908i	−0.288899	−	0.344296i
$246$	−4.33984	+	0.369883i	−0.276698	+	0.0235829i
$247$	−11.5384	+	13.6846i	−0.734173	+	0.870728i
$248$	6.08066	−	3.51067i	0.386122	−	0.222928i
$249$	5.57024	+	5.59528i	0.353000	+	0.354586i
$250$	2.50230	−	6.87501i	0.158259	−	0.434814i
$251$	7.33464	−	8.74108i	0.462958	−	0.551732i	−0.483169	−	0.875527i	$-0.660514\pi$
$251$	7.33464	−	8.74108i	0.462958	−	0.551732i	0.946127	+	0.323795i	$0.104959\pi$
$252$	−7.76240	+	9.16706i	−0.488985	+	0.577471i
$253$	2.72499	−	15.4542i	0.171319	−	0.971597i
$254$	−7.79882	+	4.50265i	−0.489341	+	0.282521i
$255$	3.01122	−	6.41996i	0.188570	−	0.402034i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−4.92005	−	4.12841i	−0.306904	−	0.257523i	0.476307	−	0.879279i	$-0.341975\pi$
$257$	−4.92005	−	4.12841i	−0.306904	−	0.257523i	−0.783211	+	0.621756i	$0.786420\pi$
$258$	−7.29064	+	15.5437i	−0.453896	+	0.967711i
$259$	34.1297	−	19.7048i	2.12072	−	1.22440i
$260$	−0.555403	+	3.14984i	−0.0344446	+	0.195345i
$261$	−6.39802	−	17.8268i	−0.396027	−	1.10345i
$262$	−1.67705	+	1.99864i	−0.103609	+	0.123476i
$263$	0.331497	−	0.910781i	0.0204410	−	0.0561612i	−0.929052	−	0.369948i	$-0.879376\pi$
$263$	0.331497	−	0.910781i	0.0204410	−	0.0561612i	0.949493	+	0.313787i	$0.101598\pi$
$264$	−2.83586	−	2.84861i	−0.174535	−	0.175320i
$265$	8.72622	−	5.03808i	0.536047	−	0.309487i
$266$	−2.98971	−	17.1952i	−0.183311	−	1.05430i
$267$	6.24039	−	0.531866i	0.381905	−	0.0325497i
$268$	6.35785	+	7.57699i	0.388367	+	0.462838i
$269$	−4.57807	−	25.9635i	−0.279130	−	1.58302i	−0.725530	−	0.688191i	$-0.758405\pi$
$269$	−4.57807	−	25.9635i	−0.279130	−	1.58302i	0.446400	−	0.894833i	$-0.352706\pi$
$270$	1.73503	−	3.65637i	0.105591	−	0.222519i
$271$	4.11482	−	3.45275i	0.249958	−	0.209739i	−0.509196	−	0.860650i	$-0.670057\pi$
$271$	4.11482	−	3.45275i	0.249958	−	0.209739i	0.759154	+	0.650911i	$0.225613\pi$
$272$	−3.37872	+	4.02660i	−0.204865	+	0.244149i
$273$	25.7839	+	12.0937i	1.56051	+	0.731944i
$274$	5.97442	+	3.44933i	0.360928	+	0.208382i
$275$	6.55359	−	7.81027i	0.395197	−	0.470977i
$276$	−11.6654	−	1.04695i	−0.702172	−	0.0630189i
$277$	−28.6237			−1.71983			−0.859915	−	0.510437i	$-0.829484\pi$
$277$	−28.6237			−1.71983			−0.859915	+	0.510437i	$0.829484\pi$
$278$	5.37702	−	9.31327i	0.322492	−	0.558573i
$279$	10.4501	+	18.2890i	0.625631	+	1.09494i
$280$	−2.00461	−	2.38901i	−0.119799	−	0.142770i
$281$	−27.6123	+	10.0501i	−1.64721	+	0.599536i	−0.988278	−	0.152666i	$-0.951214\pi$
$281$	−27.6123	+	10.0501i	−1.64721	+	0.599536i	−0.658933	+	0.752202i	$0.728992\pi$
$282$	0.0709987	+	0.0713178i	0.00422791	+	0.00424691i
$283$	−3.77025	−	21.3822i	−0.224118	−	1.27104i	−0.864364	−	0.502867i	$-0.832279\pi$
$283$	−3.77025	−	21.3822i	−0.224118	−	1.27104i	0.640246	−	0.768170i	$-0.278833\pi$
$284$	−0.160174	−	0.277430i	−0.00950460	−	0.0164624i
$285$	2.46046	+	5.34086i	0.145745	+	0.316365i
$286$	−4.76493	+	8.25310i	−0.281756	+	0.488016i
$287$	−9.46165	−	3.44376i	−0.558504	−	0.203279i
$288$	−1.93865	+	2.28946i	−0.114236	+	0.134908i
$289$	−8.14252	−	6.83239i	−0.478972	−	0.401905i
$290$	4.84261	−	0.853883i	0.284368	−	0.0501417i
$291$	−11.5516	+	16.4190i	−0.677169	+	0.962497i
$292$	−9.14376			−0.535098
$293$	2.26940	−	3.93072i	0.132580	−	0.229635i	−0.792090	−	0.610404i	$-0.791007\pi$
$293$	2.26940	−	3.93072i	0.132580	−	0.229635i	0.924670	+	0.380769i	$0.124341\pi$
$294$	−14.1933	+	6.57974i	−0.827770	+	0.383738i
$295$	−8.34171	−	1.47087i	−0.485673	−	0.0856373i
$296$	8.52385	−	4.92125i	0.495439	−	0.286042i
$297$	8.58389	−	8.46917i	0.498088	−	0.491431i
$298$	−9.61978	−	1.69623i	−0.557259	−	0.0982598i
$299$	4.82193	+	27.3465i	0.278859	+	1.58149i
$300$	−6.22355	−	4.37861i	−0.359317	−	0.252799i
$301$	−30.4036	+	25.5117i	−1.75244	+	1.47047i
$302$	−7.96817	+	1.40500i	−0.458516	+	0.0808488i
$303$	15.7885	+	7.40543i	0.907024	+	0.425431i
$304$	−0.746676	−	4.29447i	−0.0428248	−	0.246305i
$305$			4.72839i			0.270747i
$306$	−12.0342	−	10.1902i	−0.687951	−	0.582537i
$307$	3.43441	−	0.605580i	0.196012	−	0.0345623i	−0.0747800	−	0.997200i	$-0.523825\pi$
$307$	3.43441	−	0.605580i	0.196012	−	0.0345623i	0.270792	+	0.962638i	$0.412714\pi$
$308$	−3.17807	−	8.73168i	−0.181088	−	0.497534i
$309$	−1.94868	+	7.20787i	−0.110856	+	0.410041i
$310$	−5.13893	+	1.87042i	−0.291872	+	0.106233i
$311$		−	27.9324i		−	1.58390i	−0.610586	−	0.791950i	$-0.709066\pi$
$311$		−	27.9324i		−	1.58390i	0.610586	−	0.791950i	$-0.290934\pi$
$312$	6.43950	+	3.02039i	0.364565	+	0.170996i
$313$	2.52667	−	14.3295i	0.142816	−	0.809949i	−0.826279	−	0.563261i	$-0.809547\pi$
$313$	2.52667	−	14.3295i	0.142816	−	0.809949i	0.969095	−	0.246688i	$-0.0793423\pi$
$314$	8.82530	−	3.21215i	0.498041	−	0.181272i
$315$	7.19392	−	5.98164i	0.405331	−	0.337027i
$316$	−4.27444	−	2.46785i	−0.240456	−	0.138827i
$317$	−13.1781	−	11.0578i	−0.740158	−	0.621066i	0.192722	−	0.981253i	$-0.438268\pi$
$317$	−13.1781	−	11.0578i	−0.740158	−	0.621066i	−0.932880	+	0.360187i	$0.882713\pi$
$318$	−5.75089	−	21.6567i	−0.322494	−	1.21445i
$319$	14.4287	+	2.54418i	0.807854	+	0.142446i
$320$	−0.500650	−	0.596651i	−0.0279872	−	0.0333538i
$321$	0.121828	+	0.0329366i	0.00679976	+	0.00183834i
$322$	−23.4481	−	13.5377i	−1.30671	−	0.754429i
$323$	22.5733	−	3.92480i	1.25601	−	0.218382i
$324$	−6.84224	−	5.84669i	−0.380124	−	0.324816i
$325$	−6.17049	+	16.9533i	−0.342277	+	0.940398i
$326$	6.41965	+	2.33656i	0.355552	+	0.129410i
$327$	−5.81148	+	8.26018i	−0.321376	+	0.456789i
$328$	−2.36304	−	0.860075i	−0.130477	−	0.0474897i
$329$	0.0795663	+	0.218607i	0.00438663	+	0.0120522i
$330$	1.78995	+	2.56855i	0.0985333	+	0.141394i
$331$			19.7490i			1.08551i	0.839893	+	0.542753i	$0.182618\pi$
$331$			19.7490i			1.08551i	−0.839893	+	0.542753i	$0.817382\pi$
$332$	1.55904	+	4.28342i	0.0855632	+	0.235083i
$333$	14.6489	+	25.6375i	0.802756	+	1.40493i
$334$	5.14032	+	8.90329i	0.281266	+	0.487167i
$335$	−3.85194	−	6.67175i	−0.210454	−	0.364517i
$336$	−6.29196	+	2.91683i	−0.343255	+	0.159126i
$337$	3.89886	−	10.7120i	0.212385	−	0.583522i	−0.787059	−	0.616878i	$-0.788397\pi$
$337$	3.89886	−	10.7120i	0.212385	−	0.583522i	0.999444	+	0.0333560i	$0.0106195\pi$
$338$	0.670854	−	3.80460i	0.0364896	−	0.206943i
$339$	−12.6440	+	12.5875i	−0.686730	+	0.683658i
$340$	3.13621	−	2.63159i	0.170085	−	0.142718i
$341$	−16.2943			−0.882386
$342$	12.8933	−	2.18223i	0.697191	−	0.118001i
$343$	−8.13705			−0.439359
$344$	−7.59326	+	6.37151i	−0.409401	+	0.343529i
$345$	8.80619	+	2.38079i	0.474109	+	0.128177i
$346$	−2.93638	+	16.6530i	−0.157861	+	0.895272i
$347$	0.0497255	−	0.136620i	0.00266941	−	0.00733414i	−0.938351	−	0.345685i	$-0.887647\pi$
$347$	0.0497255	−	0.136620i	0.00266941	−	0.00733414i	0.941020	+	0.338350i	$0.109869\pi$
$348$	0.977479	−	10.8913i	0.0523984	−	0.583835i
$349$	−6.40836	−	11.0996i	−0.343032	−	0.594149i	0.641962	−	0.766736i	$-0.278121\pi$
$349$	−6.40836	−	11.0996i	−0.343032	−	0.594149i	−0.984994	+	0.172588i	$0.944787\pi$
$350$	−8.79556	−	15.2344i	−0.470142	−	0.814310i
$351$	−9.14770	+	19.2777i	−0.488268	+	1.02897i
$352$	−0.793720	−	2.18073i	−0.0423054	−	0.116233i
$353$			11.9441i			0.635722i	0.948137	+	0.317861i	$0.102965\pi$
$353$			11.9441i			0.635722i	−0.948137	+	0.317861i	$0.897035\pi$
$354$	−7.99886	+	17.0537i	−0.425135	+	0.906393i
$355$	0.0853378	+	0.234464i	0.00452926	+	0.0124440i
$356$	3.39788	+	1.23673i	0.180087	+	0.0655465i
$357$	−15.3319	−	33.0728i	−0.811451	−	1.75040i
$358$	2.66595	+	0.970326i	0.140900	+	0.0512833i
$359$	−6.73681	+	18.5092i	−0.355555	+	0.976880i	0.624998	+	0.780626i	$0.285100\pi$
$359$	−6.73681	+	18.5092i	−0.355555	+	0.976880i	−0.980553	+	0.196253i	$0.937123\pi$
$360$	1.79667	−	1.49391i	0.0946929	−	0.0787358i
$361$	−9.57837	+	16.4090i	−0.504125	+	0.863631i
$362$	1.90530	+	1.10003i	0.100141	+	0.0578161i
$363$	−2.49582	−	9.39876i	−0.130996	−	0.493307i
$364$	10.5690	+	12.5957i	0.553968	+	0.660193i
$365$	7.01363	+	1.23669i	0.367110	+	0.0647314i
$366$	10.1505	+	2.74424i	0.530577	+	0.143444i
$367$	13.9312	+	11.6897i	0.727202	+	0.610195i	0.929367	−	0.369156i	$-0.120353\pi$
$367$	13.9312	+	11.6897i	0.727202	+	0.610195i	−0.202165	+	0.979351i	$0.564798\pi$
$368$	−5.85612	−	3.38103i	−0.305271	−	0.176249i
$369$	2.61199	−	7.07746i	0.135975	−	0.368438i
$370$	−7.20373	+	2.62194i	−0.374504	+	0.136308i
$371$	8.99489	−	51.0126i	0.466991	−	2.64844i
$372$	1.03276	+	12.1174i	0.0535461	+	0.628257i
$373$		−	7.79822i		−	0.403777i	−0.979409	−	0.201888i	$-0.935292\pi$
$373$		−	7.79822i		−	0.403777i	0.979409	−	0.201888i	$-0.0647078\pi$
$374$	11.4627	−	4.17208i	0.592721	−	0.215733i
$375$	8.94040	+	8.98059i	0.461680	+	0.463755i
$376$	0.0198716	+	0.0545967i	0.00102480	+	0.00281561i
$377$	−25.5319	+	4.50197i	−1.31496	+	0.231863i
$378$	−8.66575	−	18.9149i	−0.445718	−	0.972879i
$379$			25.2399i			1.29649i	0.761433	+	0.648244i	$0.224496\pi$
$379$			25.2399i			1.29649i	−0.761433	+	0.648244i	$0.775504\pi$
$380$	−0.00809571	+	3.39502i	−0.000415301	+	0.174161i
$381$	−1.32458	−	15.5413i	−0.0678602	−	0.796204i
$382$	20.5399	−	3.62173i	1.05091	−	0.185304i
$383$	13.3913	−	11.2366i	0.684263	−	0.574165i	−0.232985	−	0.972480i	$-0.574849\pi$
$383$	13.3913	−	11.2366i	0.684263	−	0.574165i	0.917249	+	0.398315i	$0.130405\pi$
$384$	−1.57141	+	0.728475i	−0.0801906	+	0.0371748i
$385$	1.25675	+	7.12739i	0.0640499	+	0.363245i
$386$	14.5847	+	2.57167i	0.742339	+	0.130894i
$387$	−19.0122	−	22.8653i	−0.966443	−	1.16231i
$388$	−10.0377	+	5.79528i	−0.509588	+	0.294211i
$389$	−3.67508	−	0.648015i	−0.186334	−	0.0328557i	0.0797025	−	0.996819i	$-0.474603\pi$
$389$	−3.67508	−	0.648015i	−0.186334	−	0.0328557i	−0.266036	+	0.963963i	$0.585714\pi$
$390$	−4.53085	−	3.18770i	−0.229428	−	0.161415i
$391$	17.7719	−	30.7819i	0.898765	−	1.55671i
$392$	−9.03222			−0.456196
$393$	−1.90061	−	4.09986i	−0.0958733	−	0.206810i
$394$	−17.1899	+	3.03105i	−0.866017	+	0.152702i
$395$	2.94489	+	2.47106i	0.148174	+	0.124332i
$396$	6.55279	−	2.35180i	0.329290	−	0.118182i
$397$	30.8259	+	11.2197i	1.54711	+	0.563101i	0.967737	−	0.251962i	$-0.0810759\pi$
$397$	30.8259	+	11.2197i	1.54711	+	0.563101i	0.579371	+	0.815064i	$0.303298\pi$
$398$	−6.12739	+	10.6130i	−0.307139	+	0.531980i
$399$	29.1632	+	7.95905i	1.45998	+	0.398451i
$400$	−2.19668	−	3.80476i	−0.109834	−	0.190238i
$401$	4.08401	+	23.1616i	0.203946	+	1.15663i	0.899090	+	0.437763i	$0.144229\pi$
$401$	4.08401	+	23.1616i	0.203946	+	1.15663i	−0.695145	+	0.718870i	$0.744660\pi$
$402$	−16.5580	+	4.39692i	−0.825836	+	0.219298i
$403$	27.0943	−	9.86150i	1.34966	−	0.491236i
$404$	6.47182	+	7.71282i	0.321985	+	0.383727i
$405$	4.45750	+	5.41006i	0.221495	+	0.268828i
$406$	12.6394	−	21.8922i	0.627285	−	1.08649i
$407$	−22.8413			−1.13220
$408$	−3.82912	−	8.25989i	−0.189570	−	0.408925i
$409$	−5.75151	+	6.85439i	−0.284394	+	0.338928i	−0.889262	−	0.457398i	$-0.848781\pi$
$409$	−5.75151	+	6.85439i	−0.284394	+	0.338928i	0.604868	+	0.796326i	$0.293226\pi$
$410$	1.69622	+	0.979312i	0.0837702	+	0.0483648i
$411$	−9.80326	+	6.83161i	−0.483559	+	0.336978i
$412$	−2.77097	+	3.30232i	−0.136516	+	0.162693i
$413$	−33.3571	+	27.9899i	−1.64139	+	1.37729i
$414$	10.2218	−	17.5227i	0.502373	−	0.861194i
$415$	−0.616511	−	3.49641i	−0.0302634	−	0.171632i
$416$	2.63960	+	3.14576i	0.129417	+	0.154233i
$417$	10.6495	+	15.2819i	0.521509	+	0.748357i
$418$	−3.48240	+	9.49729i	−0.170330	+	0.464528i
$419$	−19.9509	+	11.5187i	−0.974666	+	0.562724i	−0.900656	−	0.434534i	$-0.856913\pi$
$419$	−19.9509	+	11.5187i	−0.974666	+	0.562724i	−0.0740108	+	0.997257i	$0.523580\pi$
$420$	5.22069	−	1.38634i	0.254743	−	0.0676464i
$421$	9.17391	−	25.2051i	0.447109	−	1.22842i	−0.487618	−	0.873057i	$-0.662134\pi$
$421$	9.17391	−	25.2051i	0.447109	−	1.22842i	0.934727	−	0.355366i	$-0.115644\pi$
$422$	−8.77971	+	10.4633i	−0.427390	+	0.509343i
$423$	−0.164056	+	0.0588796i	−0.00797667	+	0.00286282i
$424$	2.24646	−	12.7403i	0.109098	−	0.618725i
$425$	19.9992	−	11.5465i	0.970103	−	0.560089i
$426$	0.552856	−	0.0471197i	0.0267860	−	0.00228296i
$427$	18.6208	+	15.6247i	0.901122	+	0.756131i
$428$	0.0558158	+	0.0468351i	0.00269796	+	0.00226386i
$429$	−9.43723	−	13.5423i	−0.455634	−	0.653828i
$430$	6.68608	−	3.86021i	0.322432	−	0.186156i
$431$	−6.16114	+	34.9416i	−0.296772	+	1.68308i	0.363141	+	0.931734i	$0.381704\pi$
$431$	−6.16114	+	34.9416i	−0.296772	+	1.68308i	−0.659913	+	0.751342i	$0.729407\pi$
$432$	−2.16426	−	4.72398i	−0.104128	−	0.227283i
$433$	−7.83317	+	9.33521i	−0.376438	+	0.448622i	−0.920687	−	0.390303i	$-0.872370\pi$
$433$	−7.83317	+	9.33521i	−0.376438	+	0.448622i	0.544249	+	0.838924i	$0.316815\pi$
$434$	−9.61543	+	26.4182i	−0.461555	+	1.26811i
$435$	−2.22281	+	8.22186i	−0.106576	+	0.394208i
$436$	−5.04985	+	2.91553i	−0.241844	+	0.139629i
$437$	10.0150	+	27.7216i	0.479083	+	1.32610i
$438$	6.72537	−	14.3386i	0.321350	−	0.685123i
$439$	−9.36684	−	11.1630i	−0.447055	−	0.532779i	0.494707	−	0.869060i	$-0.335275\pi$
$439$	−9.36684	−	11.1630i	−0.447055	−	0.532779i	−0.941762	+	0.336280i	$0.890831\pi$
$440$	0.313872	+	1.78006i	0.0149632	+	0.0848608i
$441$	0.121519	−	27.0964i	0.00578661	−	1.29030i
$442$	−16.5352	+	13.8747i	−0.786500	+	0.659952i
$443$	3.38191	−	4.03041i	0.160680	−	0.191490i	−0.679698	−	0.733492i	$-0.737889\pi$
$443$	3.38191	−	4.03041i	0.160680	−	0.191490i	0.840377	+	0.542002i	$0.182333\pi$
$444$	1.44772	+	16.9861i	0.0687058	+	0.806126i
$445$	−2.43904	−	1.40818i	−0.115622	−	0.0667543i
$446$	−2.87171	+	3.42237i	−0.135980	+	0.162054i
$447$	9.73538	−	13.8374i	0.460468	−	0.654488i
$448$	−4.00403			−0.189172
$449$	−14.7680	+	25.5789i	−0.696945	+	1.20714i	0.272576	+	0.962134i	$0.412125\pi$
$449$	−14.7680	+	25.5789i	−0.696945	+	1.20714i	−0.969521	+	0.245010i	$0.921209\pi$
$450$	11.4437	−	6.53878i	0.539462	−	0.308241i
$451$	3.75118	+	4.47048i	0.176636	+	0.210507i
$452$	−9.67954	+	3.52306i	−0.455287	+	0.165711i
$453$	3.65748	−	13.5285i	0.171843	−	0.635624i
$454$	1.31554	+	7.46081i	0.0617414	+	0.350153i
$455$	−6.40331	−	11.0909i	−0.300192	−	0.519947i
$456$	7.28346	+	1.98776i	0.341079	+	0.0930855i
$457$	−3.86942	+	6.70203i	−0.181004	+	0.313508i	−0.942223	−	0.334987i	$-0.891268\pi$
$457$	−3.86942	+	6.70203i	−0.181004	+	0.313508i	0.761219	+	0.648495i	$0.224601\pi$
$458$	9.24072	+	3.36335i	0.431790	+	0.157159i
$459$	24.8309	−	11.3761i	1.15901	−	0.530992i
$460$	4.03459	+	3.38543i	0.188114	+	0.157846i
$461$	3.93805	−	0.694385i	0.183413	−	0.0323407i	−0.0811870	−	0.996699i	$-0.525871\pi$
$461$	3.93805	−	0.694385i	0.183413	−	0.0323407i	0.264600	+	0.964358i	$0.414760\pi$
$462$	16.0299	+	1.43866i	0.745778	+	0.0669326i
$463$	29.5589			1.37372			0.686859	−	0.726791i	$-0.258989\pi$
$463$	29.5589			1.37372			0.686859	+	0.726791i	$0.258989\pi$
$464$	3.15669	−	5.46754i	0.146545	−	0.253824i
$465$	0.846707	−	9.43420i	0.0392651	−	0.437501i
$466$	−21.0869	−	3.71819i	−0.976832	−	0.172242i
$467$	32.7712	−	18.9205i	1.51647	−	0.875534i	0.516657	−	0.856193i	$-0.327176\pi$
$467$	32.7712	−	18.9205i	1.51647	−	0.875534i	0.999813	−	0.0193414i	$-0.00615695\pi$
$468$	−9.47269	+	7.87641i	−0.437875	+	0.364087i
$469$	−39.0024	−	6.87717i	−1.80096	−	0.317558i
$470$	−0.00785810	−	0.0445655i	−0.000362467	−	0.00205565i
$471$	−1.45409	+	16.2018i	−0.0670007	+	0.746538i
$472$	−8.33088	+	6.99044i	−0.383460	+	0.321761i
$473$	22.6538	−	3.99448i	1.04162	−	0.183666i
$474$	7.01382	−	4.88772i	0.322155	−	0.224501i
$475$	−3.37036	+	18.8513i	−0.154643	+	0.864956i
$476$		−	21.0466i		−	0.964669i
$477$	38.1904	+	6.91073i	1.74862	+	0.316420i
$478$	−7.30545	+	1.28815i	−0.334144	+	0.0589185i
$479$	−3.12316	−	8.58080i	−0.142701	−	0.392067i	0.847667	−	0.530528i	$-0.178006\pi$
$479$	−3.12316	−	8.58080i	−0.142701	−	0.392067i	−0.990368	+	0.138462i	$0.955784\pi$
$480$	1.30386	−	0.346236i	0.0595128	−	0.0158035i
$481$	37.9806	−	13.8238i	1.73177	−	0.630312i
$482$		−	0.174051i		−	0.00792780i
$483$	38.4753	−	26.8123i	1.75068	−	1.22000i
$484$	0.974937	−	5.52914i	0.0443153	−	0.251325i
$485$	8.48314	−	3.08761i	0.385199	−	0.140201i
$486$	14.2009	−	6.42916i	0.644166	−	0.291633i
$487$	−14.8891	−	8.59624i	−0.674691	−	0.389533i	0.123161	−	0.992387i	$-0.460697\pi$
$487$	−14.8891	−	8.59624i	−0.674691	−	0.389533i	−0.797852	+	0.602854i	$0.794030\pi$
$488$	4.65051	+	3.90224i	0.210519	+	0.176646i
$489$	−8.38577	+	8.34825i	−0.379218	+	0.377521i
$490$	6.92807	+	1.22161i	0.312978	+	0.0551865i
$491$	−16.1657	−	19.2656i	−0.729550	−	0.869444i	0.265971	−	0.963981i	$-0.414307\pi$
$491$	−16.1657	−	19.2656i	−0.729550	−	0.869444i	−0.995521	+	0.0945372i	$0.969863\pi$
$492$	3.08675	−	3.07294i	0.139162	−	0.138539i
$493$	28.7394	+	16.5927i	1.29436	+	0.747296i
$494$	0.0426835	−	17.8997i	0.00192042	−	0.805347i
$495$	−5.34433	+	0.917657i	−0.240210	+	0.0412456i
$496$	−2.40144	+	6.59790i	−0.107828	+	0.296255i
$497$	1.20533	+	0.438704i	0.0540664	+	0.0196786i
$498$	−7.86363	−	0.705750i	−0.352378	−	0.0316254i
$499$	−31.3792	−	11.4211i	−1.40473	−	0.511279i	−0.475150	−	0.879905i	$-0.657606\pi$
$499$	−31.3792	−	11.4211i	−1.40473	−	0.511279i	−0.929578	+	0.368626i	$0.879828\pi$
$500$	2.50230	+	6.87501i	0.111906	+	0.307460i
$501$	−17.7423	+	1.51217i	−0.792666	+	0.0675586i
$502$			11.4107i			0.509283i
$503$	−7.82769	−	21.5064i	−0.349020	−	0.958924i	−0.982680	−	0.185312i	$-0.940670\pi$
$503$	−7.82769	−	21.5064i	−0.349020	−	0.958924i	0.633660	−	0.773612i	$-0.281552\pi$
$504$	0.0538699	−	12.0120i	0.00239956	−	0.535055i
$505$	−3.92099	−	6.79135i	−0.174482	−	0.302211i
$506$	7.84630	+	13.5902i	0.348810	+	0.604157i
$507$	5.47267	+	3.85032i	0.243050	+	0.170999i
$508$	3.07999	−	8.46221i	0.136653	−	0.375450i
$509$	−3.33275	+	18.9010i	−0.147722	+	0.837771i	0.817420	+	0.576042i	$0.195404\pi$
$509$	−3.33275	+	18.9010i	−0.147722	+	0.837771i	−0.965142	+	0.261729i	$0.915707\pi$
$510$	1.81994	+	6.85355i	0.0805884	+	0.303480i
$511$	28.0463	−	23.5336i	1.24070	−	1.04107i
$512$	−1.00000			−0.0441942
$513$	−6.06122	+	21.8234i	−0.267609	+	0.963528i
$514$	6.42267			0.283292
$515$	2.57208	−	2.15823i	0.113340	−	0.0951032i
$516$	−4.40637	−	16.5935i	−0.193979	−	0.730489i
$517$	0.0234135	−	0.132785i	0.00102972	−	0.00583986i
$518$	−13.4789	+	37.0329i	−0.592228	+	1.62713i
$519$	−23.9543	−	16.8531i	−1.05148	−	0.739771i
$520$	−1.59922	−	2.76993i	−0.0701304	−	0.121469i
$521$	−12.8575	−	22.2699i	−0.563299	−	0.975662i	−0.997206	−	0.0747041i	$-0.976199\pi$
$521$	−12.8575	−	22.2699i	−0.563299	−	0.975662i	0.433907	−	0.900958i	$-0.357135\pi$
$522$	16.3600	+	9.54352i	0.716057	+	0.417709i
$523$	−6.53300	−	17.9493i	−0.285668	−	0.784867i	−0.996660	−	0.0816664i	$-0.973976\pi$
$523$	−6.53300	−	17.9493i	−0.285668	−	0.784867i	0.710991	−	0.703201i	$-0.248246\pi$
$524$		−	2.60903i		−	0.113976i
$525$	30.3586	−	2.58745i	1.32496	−	0.112926i
$526$	0.331497	+	0.910781i	0.0144540	+	0.0397120i
$527$	−34.6810	−	12.6228i	−1.51073	−	0.549859i
$528$	4.00345	+	0.359304i	0.174228	+	0.0156367i
$529$	21.3550	+	7.77259i	0.928479	+	0.337939i
$530$	−3.44625	+	9.46850i	−0.149696	+	0.411285i
$531$	−20.8590	−	25.0864i	−0.905205	−	1.08866i
$532$	13.3431	+	11.2505i	0.578496	+	0.487772i
$533$	−8.94306	−	5.16328i	−0.387367	−	0.223646i
$534$	−4.43854	+	4.41868i	−0.192074	+	0.191215i
$535$	−0.0364786	−	0.0434734i	−0.00157711	−	0.00187952i
$536$	−9.74079	−	1.71756i	−0.420738	−	0.0741874i
$537$	−3.48244	+	3.46685i	−0.150278	+	0.149606i
$538$	20.1960	+	16.9465i	0.870713	+	0.730615i
$539$	18.1527	+	10.4804i	0.781891	+	0.451425i
$540$	1.02116	+	3.91620i	0.0439436	+	0.168526i
$541$	−5.60184	+	2.03890i	−0.240842	+	0.0876592i	−0.459621	−	0.888115i	$-0.652015\pi$
$541$	−5.60184	+	2.03890i	−0.240842	+	0.0876592i	0.218779	+	0.975774i	$0.429793\pi$
$542$	−0.932754	+	5.28991i	−0.0400652	+	0.227221i
$543$	−3.12636	+	2.17867i	−0.134165	+	0.0934956i
$544$		−	5.25636i		−	0.225365i
$545$	4.26776	−	1.55334i	0.182811	−	0.0665377i
$546$	−27.5253	+	7.30927i	−1.17797	+	0.312808i
$547$	9.49608	+	26.0903i	0.406023	+	1.11554i	0.959262	+	0.282517i	$0.0911693\pi$
$547$	9.49608	+	26.0903i	0.406023	+	1.11554i	−0.553239	+	0.833022i	$0.686609\pi$
$548$	−6.79386	+	1.19794i	−0.290219	+	0.0511735i
$549$	−11.7692	+	13.8989i	−0.502296	+	0.593190i
$550$			10.1956i			0.434741i
$551$	−25.8821	+	9.35048i	−1.10261	+	0.398344i
$552$	9.60915	−	6.69634i	0.408992	−	0.285015i
$553$	19.4624	−	3.43175i	0.827627	−	0.145933i
$554$	21.9270	−	18.3989i	0.931590	−	0.781696i
$555$	1.18691	−	13.2248i	0.0503816	−	0.561363i
$556$	1.86742	+	10.5907i	0.0791962	+	0.449144i
$557$	−41.9117	−	7.39016i	−1.77586	−	0.313131i	−0.812822	−	0.582512i	$-0.802070\pi$
$557$	−41.9117	−	7.39016i	−1.77586	−	0.313131i	−0.963034	+	0.269381i	$0.913181\pi$
$558$	−19.7612	−	7.29302i	−0.836559	−	0.308738i
$559$	−35.2514	+	20.3524i	−1.49098	+	0.860815i
$560$	3.07125	+	0.541544i	0.129784	+	0.0228844i
$561$	−1.88863	+	21.0435i	−0.0797380	+	0.888459i
$562$	14.6922	−	25.4476i	0.619753	−	1.07344i
$563$	8.66385			0.365138			0.182569	−	0.983193i	$-0.441559\pi$
$563$	8.66385			0.365138			0.182569	+	0.983193i	$0.441559\pi$
$564$	−0.100230	−	0.00899553i	−0.00422046	−	0.000378780i
$565$	7.90109	−	1.39317i	0.332401	−	0.0586113i
$566$	16.6324	+	13.9562i	0.699110	+	0.586623i
$567$	36.0348	+	0.323216i	1.51332	+	0.0135738i
$568$	0.301029	+	0.109566i	0.0126309	+	0.00459728i
$569$	−22.0182	+	38.1367i	−0.923052	+	1.59877i	−0.128389	+	0.991724i	$0.540981\pi$
$569$	−22.0182	+	38.1367i	−0.923052	+	1.59877i	−0.794664	+	0.607050i	$0.792353\pi$
$570$	−5.31786	−	2.50978i	−0.222741	−	0.105123i
$571$	−1.43824	−	2.49110i	−0.0601883	−	0.104249i	0.834361	−	0.551218i	$-0.185837\pi$
$571$	−1.43824	−	2.49110i	−0.0601883	−	0.104249i	−0.894549	+	0.446969i	$0.852503\pi$
$572$	−1.65484	−	9.38508i	−0.0691925	−	0.392410i
$573$	−9.42804	+	34.8729i	−0.393862	+	1.45684i
$574$	9.46165	−	3.44376i	0.394922	−	0.143740i
$575$	19.0960	+	22.7578i	0.796360	+	0.949065i
$576$	0.0134539	−	2.99997i	0.000560581	−	0.124999i
$577$	−0.321477	+	0.556815i	−0.0133833	+	0.0231805i	−0.872639	−	0.488365i	$-0.837593\pi$
$577$	−0.321477	+	0.556815i	−0.0133833	+	0.0231805i	0.859256	+	0.511545i	$0.170927\pi$
$578$	10.6293			0.442121
$579$	−14.7599	+	20.9791i	−0.613401	+	0.871860i
$580$	−3.16079	+	3.76688i	−0.131245	+	0.156411i
$581$	−15.8064	−	9.12581i	−0.655758	−	0.378602i
$582$	−1.70484	−	20.0029i	−0.0706679	−	0.829147i
$583$	−19.2980	+	22.9984i	−0.799241	+	0.952498i
$584$	7.00453	−	5.87750i	0.289849	−	0.243212i
$585$	8.33121	−	4.76034i	0.344453	−	0.196816i
$586$	0.788156	+	4.46985i	0.0325584	+	0.184648i
$587$	13.9250	+	16.5952i	0.574748	+	0.684958i	0.972598	−	0.232493i	$-0.0746882\pi$
$587$	13.9250	+	16.5952i	0.574748	+	0.684958i	−0.397851	+	0.917450i	$0.630244\pi$
$588$	6.64333	−	14.1637i	0.273966	−	0.584099i
$589$	26.5414	−	15.2394i	1.09362	−	0.627929i
$590$	7.33558	−	4.23520i	0.302001	−	0.174360i
$591$	7.89038	−	29.1854i	0.324567	−	1.20053i
$592$	−3.36633	+	9.24892i	−0.138355	+	0.380128i
$593$	14.5774	−	17.3726i	0.598621	−	0.713408i	−0.378618	−	0.925553i	$-0.623600\pi$
$593$	14.5774	−	17.3726i	0.598621	−	0.713408i	0.977238	+	0.212145i	$0.0680449\pi$
$594$	−1.13176	+	12.0054i	−0.0464368	+	0.492587i
$595$	−2.84655	+	16.1436i	−0.116697	+	0.661822i
$596$	8.45949	−	4.88409i	0.346514	−	0.200060i
$597$	−12.1357	−	17.4145i	−0.496680	−	0.712728i
$598$	−21.2718	−	17.8492i	−0.869869	−	0.729907i
$599$	22.9167	+	19.2294i	0.936350	+	0.785691i	0.976946	−	0.213485i	$-0.0684814\pi$
$599$	22.9167	+	19.2294i	0.936350	+	0.785691i	−0.0405967	+	0.999176i	$0.512926\pi$
$600$	7.58203	−	0.646213i	0.309535	−	0.0263816i
$601$	−25.7353	+	14.8583i	−1.04976	+	0.606081i	−0.922583	−	0.385799i	$-0.873926\pi$
$601$	−25.7353	+	14.8583i	−1.04976	+	0.606081i	−0.127180	+	0.991880i	$0.540593\pi$
$602$	6.89194	−	39.0861i	0.280895	−	1.59303i
$603$	5.28369	−	29.1990i	0.215169	−	1.18907i
$604$	5.20085	−	6.19813i	0.211620	−	0.252198i
$605$	−1.49563	+	4.10921i	−0.0608061	+	0.167063i
$606$	−16.8548	+	4.47574i	−0.684679	+	0.181815i
$607$	8.19329	−	4.73040i	0.332555	−	0.192001i	−0.324420	−	0.945913i	$-0.605169\pi$
$607$	8.19329	−	4.73040i	0.332555	−	0.192001i	0.656975	+	0.753912i	$0.271836\pi$
$608$	3.33242	+	2.80980i	0.135147	+	0.113952i
$609$	25.0332	+	35.9223i	1.01440	+	1.45564i
$610$	−3.03935	−	3.62216i	−0.123060	−	0.146657i
$611$	0.0414307	+	0.234965i	0.00167611	+	0.00950567i
$612$	15.7689	+	0.0707187i	0.637421	+	0.00285863i
$613$	4.46412	−	3.74584i	0.180304	−	0.151293i	−0.548169	−	0.836368i	$-0.684675\pi$
$613$	4.46412	−	3.74584i	0.180304	−	0.151293i	0.728473	+	0.685075i	$0.240230\pi$
$614$	−2.24165	+	2.67150i	−0.0904658	+	0.107813i
$615$	−2.78328	+	1.93958i	−0.112233	+	0.0782116i
$616$	8.04716	+	4.64603i	0.324229	+	0.187194i
$617$	−16.7785	+	19.9958i	−0.675477	+	0.805002i	−0.989518	−	0.144407i	$-0.953872\pi$
$617$	−16.7785	+	19.9958i	−0.675477	+	0.805002i	0.314042	+	0.949409i	$0.398317\pi$
$618$	−3.14036	−	6.77413i	−0.126324	−	0.272496i
$619$	−47.1174			−1.89381			−0.946903	−	0.321518i	$-0.895807\pi$
$619$	−47.1174			−1.89381			−0.946903	+	0.321518i	$0.895807\pi$
$620$	2.73437	−	4.73606i	0.109815	−	0.190205i
$621$	19.9595	+	28.9172i	0.800948	+	1.16041i
$622$	17.9546	+	21.3974i	0.719913	+	0.857959i
$623$	−13.6052	+	4.95189i	−0.545081	+	0.198393i
$624$	−6.87441	+	1.82548i	−0.275197	+	0.0730777i
$625$	2.82497	+	16.0212i	0.112999	+	0.640849i
$626$	7.27526	+	12.6011i	0.290778	+	0.503642i
$627$	−12.3316	−	12.4462i	−0.492476	−	0.497055i
$628$	−4.69584	+	8.13344i	−0.187385	+	0.324560i
$629$	−48.6157	−	17.6947i	−1.93843	−	0.705532i
$630$	−1.66594	+	9.20636i	−0.0663725	+	0.366790i
$631$	28.7347	+	24.1113i	1.14391	+	0.959855i	0.999560	−	0.0296714i	$-0.00944610\pi$
$631$	28.7347	+	24.1113i	1.14391	+	0.959855i	0.144351	+	0.989527i	$0.453891\pi$
$632$	4.86072	−	0.857076i	0.193349	−	0.0340926i
$633$	−9.95010	−	21.4636i	−0.395481	−	0.853100i
$634$	17.2028			0.683212
$635$	−3.50699	+	6.07429i	−0.139171	+	0.241051i
$636$	18.3261	+	12.8934i	0.726678	+	0.511258i
$637$	−36.5273	−	6.44074i	−1.44726	−	0.255191i
$638$	−12.6884	+	7.32566i	−0.502339	+	0.290026i
$639$	−0.332744	+	0.901605i	−0.0131631	+	0.0356669i
$640$	0.767040	+	0.135250i	0.0303199	+	0.00534622i
$641$	−1.21755	−	6.90505i	−0.0480902	−	0.272733i	0.951276	−	0.308342i	$-0.0997741\pi$
$641$	−1.21755	−	6.90505i	−0.0480902	−	0.272733i	−0.999366	+	0.0356088i	$0.988663\pi$
$642$	−0.114497	+	0.0530784i	−0.00451882	+	0.00209484i
$643$	−8.07977	+	6.77974i	−0.318635	+	0.267367i	−0.788050	−	0.615611i	$-0.788909\pi$
$643$	−8.07977	+	6.77974i	−0.318635	+	0.267367i	0.469415	+	0.882978i	$0.344465\pi$
$644$	26.6641	−	4.70161i	1.05071	−	0.185269i
$645$	1.13559	+	13.3239i	0.0447137	+	0.524626i
$646$	−14.7693	+	17.5164i	−0.581091	+	0.689173i
$647$			1.24857i			0.0490862i	0.999699	+	0.0245431i	$0.00781309\pi$
$647$			1.24857i			0.0490862i	−0.999699	+	0.0245431i	$0.992187\pi$
$648$	8.99964	+	0.0807228i	0.353539	+	0.00317109i
$649$	24.8544	−	4.38251i	0.975622	−	0.172028i
$650$	−6.17049	−	16.9533i	−0.242026	−	0.664962i
$651$	−34.3547	−	34.5091i	−1.34647	−	1.35252i
$652$	−6.41965	+	2.33656i	−0.251413	+	0.0915068i
$653$			35.1454i			1.37535i	0.726021	+	0.687673i	$0.241368\pi$
$653$			35.1454i			1.37535i	−0.726021	+	0.687673i	$0.758632\pi$
$654$	−0.857684	−	10.0632i	−0.0335381	−	0.393503i
$655$	−0.352871	+	2.00123i	−0.0137878	+	0.0781946i
$656$	2.36304	−	0.860075i	0.0922610	−	0.0335803i
$657$	17.5381	+	21.0924i	0.684225	+	0.822895i
$658$	−0.201469	−	0.116318i	−0.00785408	−	0.00453455i
$659$	28.6581	+	24.0470i	1.11636	+	0.936738i	0.998415	−	0.0562818i	$-0.0179245\pi$
$659$	28.6581	+	24.0470i	1.11636	+	0.936738i	0.117946	+	0.993020i	$0.462369\pi$
$660$	−3.02221	−	0.817066i	−0.117639	−	0.0318042i
$661$	8.01577	+	1.41340i	0.311777	+	0.0549747i	0.327347	−	0.944904i	$-0.393845\pi$
$661$	8.01577	+	1.41340i	0.311777	+	0.0549747i	−0.0155702	+	0.999879i	$0.504956\pi$
$662$	−12.6944	−	15.1286i	−0.493383	−	0.587991i
$663$	−9.59538	−	36.1344i	−0.372654	−	1.40334i
$664$	−3.94762	−	2.27916i	−0.153197	−	0.0884485i
$665$	−8.71305	−	10.4342i	−0.337878	−	0.404623i
$666$	−27.7012	−	10.2233i	−1.07340	−	0.396146i
$667$	−14.6013	+	40.1168i	−0.565366	+	1.55333i
$668$	−9.66064	−	3.51618i	−0.373781	−	0.136045i
$669$	−3.25453	−	7.02041i	−0.125827	−	0.271425i
$670$	7.23927	+	2.63488i	0.279677	+	0.101794i
$671$	−4.81852	−	13.2388i	−0.186017	−	0.511077i
$672$	2.94502	−	6.27882i	0.113607	−	0.242211i
$673$		−	47.8894i		−	1.84600i	−0.384799	−	0.923001i	$-0.625729\pi$
$673$		−	47.8894i		−	1.84600i	0.384799	−	0.923001i	$-0.374271\pi$
$674$	3.89886	+	10.7120i	0.150179	+	0.412612i
$675$	1.83661	+	22.7546i	0.0706913	+	0.875823i
$676$	1.93165	+	3.34571i	0.0742941	+	0.128681i
$677$	13.0246	+	22.5592i	0.500574	+	0.867020i	1.00000		0.000663410i	$0.000211170\pi$
$677$	13.0246	+	22.5592i	0.500574	+	0.867020i	−0.499425	+	0.866357i	$0.666455\pi$
$678$	1.59483	−	17.7700i	0.0612492	−	0.682453i
$679$	15.8728	−	43.6101i	0.609141	−	1.67360i
$680$	−0.710922	+	4.03184i	−0.0272626	+	0.154614i
$681$	−12.6671	−	3.42460i	−0.485404	−	0.131231i
$682$	12.4822	−	10.4738i	0.477966	−	0.401061i
$683$	−19.0405			−0.728563			−0.364282	−	0.931289i	$-0.618685\pi$
$683$	−19.0405			−0.728563			−0.364282	+	0.931289i	$0.618685\pi$
$684$	−8.47415	+	9.95936i	−0.324017	+	0.380805i
$685$	5.37318			0.205299
$686$	6.23334	−	5.23039i	0.237990	−	0.199697i
$687$	−12.0708	+	12.0168i	−0.460531	+	0.458470i
$688$	1.72125	−	9.76171i	0.0656222	−	0.372162i
$689$	18.1699	−	49.9213i	0.692217	−	1.90185i
$690$	−8.27628	+	3.83672i	−0.315072	+	0.146061i
$691$	−17.2383	−	29.8576i	−0.655775	−	1.13584i	−0.981699	−	0.190440i	$-0.939008\pi$
$691$	−17.2383	−	29.8576i	−0.655775	−	1.13584i	0.325923	−	0.945396i	$-0.394325\pi$
$692$	−8.45496	−	14.6444i	−0.321409	−	0.556697i
$693$	−14.0462	+	24.0787i	−0.533572	+	0.914676i
$694$	0.0497255	+	0.136620i	0.00188756	+	0.00518602i
$695$		−	8.37603i		−	0.317721i
$696$	6.25200	+	8.97154i	0.236982	+	0.340065i
$697$	4.52086	+	12.4210i	0.171240	+	0.470477i
$698$	12.0438	+	4.38358i	0.455864	+	0.165921i
$699$	21.3403	−	30.3321i	0.807164	−	1.14727i
$700$	16.5302	+	6.01651i	0.624784	+	0.227403i
$701$	−0.849841	+	2.33492i	−0.0320980	+	0.0881887i	−0.954707	−	0.297549i	$-0.903831\pi$
$701$	−0.849841	+	2.33492i	−0.0320980	+	0.0881887i	0.922608	+	0.385738i	$0.126053\pi$
$702$	−5.38390	−	20.6476i	−0.203202	−	0.779293i
$703$	37.2057	−	21.3626i	1.40324	−	0.805705i
$704$	2.00977	+	1.16034i	0.0757460	+	0.0437320i
$705$	0.0756640	+	0.0204561i	0.00284967	+	0.000770420i
$706$	−7.67754	−	9.14973i	−0.288948	−	0.344355i
$707$	−39.7015	−	7.00045i	−1.49313	−	0.263279i
$708$	−4.83441	−	18.2054i	−0.181688	−	0.684202i
$709$	4.75726	+	3.99181i	0.178663	+	0.149916i	0.727733	−	0.685860i	$-0.240574\pi$
$709$	4.75726	+	3.99181i	0.178663	+	0.149916i	−0.549071	+	0.835776i	$0.685018\pi$
$710$	−0.216083	−	0.124755i	−0.00810944	−	0.00468199i
$711$	2.50581	+	14.5935i	0.0939750	+	0.547300i
$712$	−3.39788	+	1.23673i	−0.127341	+	0.0463483i
$713$	8.24460	−	46.7575i	0.308763	−	1.75108i
$714$	33.0037	+	15.4801i	1.23513	+	0.579327i
$715$			7.42255i			0.277588i
$716$	−2.66595	+	0.970326i	−0.0996312	+	0.0362628i
$717$	3.35329	−	12.4033i	0.125231	−	0.463210i
$718$	−6.73681	−	18.5092i	−0.251415	−	0.690758i
$719$	−10.9755	+	1.93527i	−0.409316	+	0.0721735i	−0.374515	−	0.927221i	$-0.622191\pi$
$719$	−10.9755	+	1.93527i	−0.409316	+	0.0721735i	−0.0348011	+	0.999394i	$0.511080\pi$
$720$	−0.416065	+	2.29928i	−0.0155058	+	0.0856890i
$721$		−	17.2608i		−	0.642826i
$722$	−3.21004	−	18.7269i	−0.119465	−	0.696942i
$723$	0.272934	+	0.128017i	0.0101505	+	0.00476100i
$724$	−2.16663	+	0.382035i	−0.0805222	+	0.0141982i
$725$	−21.2477	+	17.8289i	−0.789120	+	0.662150i
$726$	7.95331	+	5.59559i	0.295175	+	0.207672i
$727$	−3.39142	−	19.2337i	−0.125781	−	0.713339i	−0.980841	−	0.194810i	$-0.937591\pi$
$727$	−3.39142	−	19.2337i	−0.125781	−	0.713339i	0.855060	−	0.518529i	$-0.173520\pi$
$728$	−16.1927	−	2.85521i	−0.600142	−	0.105821i
$729$	−0.363247	+	26.9976i	−0.0134536	+	0.999909i
$730$	−6.16768	+	3.56091i	−0.228276	+	0.131795i
$731$	51.3111	+	9.04753i	1.89781	+	0.334635i
$732$	−9.53972	+	4.42243i	−0.352598	+	0.163458i
$733$	−19.3946	+	33.5924i	−0.716355	+	1.24076i	0.246080	+	0.969250i	$0.420858\pi$
$733$	−19.3946	+	33.5924i	−0.716355	+	1.24076i	−0.962435	+	0.271514i	$0.912476\pi$
$734$	−18.1859			−0.671253
$735$	−7.01133	+	9.96558i	−0.258617	+	0.367586i
$736$	6.65933	−	1.17422i	0.245466	−	0.0432823i
$737$	17.5838	+	14.7545i	0.647706	+	0.543490i
$738$	2.54841	+	7.10061i	0.0938081	+	0.261377i
$739$	12.4867	+	4.54480i	0.459332	+	0.167183i	0.561314	−	0.827603i	$-0.310296\pi$
$739$	12.4867	+	4.54480i	0.459332	+	0.167183i	−0.101982	+	0.994786i	$0.532518\pi$
$740$	3.83303	−	6.63900i	0.140905	−	0.244054i
$741$	28.0377	+	13.2325i	1.02999	+	0.486106i
$742$	25.8998	+	44.8597i	0.950810	+	1.64685i
$743$	−3.58543	−	20.3340i	−0.131537	−	0.745982i	−0.977209	−	0.212279i	$-0.931911\pi$
$743$	−3.58543	−	20.3340i	−0.131537	−	0.745982i	0.845672	−	0.533702i	$-0.179200\pi$
$744$	−8.58005	−	8.61861i	−0.314560	−	0.315974i
$745$	−7.14934	+	2.60215i	−0.261932	+	0.0953353i
$746$	5.01260	+	5.97378i	0.183524	+	0.218716i
$747$	6.89052	−	11.8121i	0.252111	−	0.432181i
$748$	−6.09917	+	10.5641i	−0.223008	+	0.386260i
$749$	−0.291743			−0.0106601
$750$	−12.6214	−	1.13275i	−0.460867	−	0.0413621i
$751$	−9.63829	+	11.4865i	−0.351706	+	0.419147i	−0.912673	−	0.408691i	$-0.865985\pi$
$751$	−9.63829	+	11.4865i	−0.351706	+	0.419147i	0.560966	+	0.827839i	$0.310430\pi$
$752$	−0.0503166	−	0.0290503i	−0.00183486	−	0.00105936i
$753$	−17.8934	−	8.39271i	−0.652070	−	0.305847i
$754$	16.6648	−	19.8603i	0.606896	−	0.723271i
$755$	−4.82756	+	4.05080i	−0.175693	+	0.147424i
$756$	18.7966	+	8.91944i	0.683627	+	0.324397i
$757$	2.01713	+	11.4397i	0.0733139	+	0.415784i	0.999272	+	0.0381570i	$0.0121487\pi$
$757$	2.01713	+	11.4397i	0.0733139	+	0.415784i	−0.925958	+	0.377627i	$0.876740\pi$
$758$	−16.2239	−	19.3349i	−0.589279	−	0.702275i
$759$	−27.0822	+	2.30820i	−0.983021	+	0.0837825i
$760$	−2.17607	−	2.60594i	−0.0789345	−	0.0945273i
$761$	−7.40115	+	4.27305i	−0.268291	+	0.154898i	−0.628111	−	0.778124i	$-0.716172\pi$
$761$	−7.40115	+	4.27305i	−0.268291	+	0.154898i	0.359820	+	0.933022i	$0.382838\pi$
$762$	11.0044	+	11.0539i	0.398649	+	0.400440i
$763$	7.98539	−	21.9397i	0.289091	−	0.794270i
$764$	−13.4064	+	15.9772i	−0.485028	+	0.578034i
$765$	−12.0858	−	2.18699i	−0.436964	−	0.0790707i
$766$	−3.03556	+	17.2155i	−0.109679	+	0.622022i
$767$	−38.6758	+	22.3295i	−1.39650	+	0.806270i
$768$	0.735514	−	1.56813i	0.0265406	−	0.0565849i
$769$	−23.9501	−	20.0965i	−0.863662	−	0.724699i	0.0990915	−	0.995078i	$-0.468406\pi$
$769$	−23.9501	−	20.0965i	−0.863662	−	0.724699i	−0.962754	+	0.270380i	$0.912851\pi$
$770$	−5.54412	−	4.65207i	−0.199796	−	0.167649i
$771$	−4.72397	+	10.0716i	−0.170130	+	0.362718i
$772$	−12.8255	+	7.40482i	−0.461601	+	0.266505i
$773$	9.13277	−	51.7945i	0.328483	−	1.86292i	−0.155491	−	0.987837i	$-0.549696\pi$
$773$	9.13277	−	51.7945i	0.328483	−	1.86292i	0.483974	−	0.875083i	$-0.339193\pi$
$774$	29.2617	+	5.29504i	1.05179	+	0.190326i
$775$	19.8282	−	23.6304i	0.712251	−	0.848828i
$776$	3.96420	−	10.8916i	0.142307	−	0.390984i
$777$	−48.1584	−	48.3748i	−1.72767	−	1.73544i
$778$	3.23181	−	1.86589i	0.115866	−	0.0668952i
$779$	−10.2913	−	3.77353i	−0.368723	−	0.135201i
$780$	5.51984	−	0.470454i	0.197642	−	0.0168450i
$781$	−0.477866	−	0.569498i	−0.0170994	−	0.0203782i
$782$	6.17212	+	35.0038i	0.220715	+	1.25174i
$783$	−26.9984	+	18.6351i	−0.964846	+	0.665965i
$784$	6.91908	−	5.80580i	0.247110	−	0.207350i
$785$	4.70195	−	5.60356i	0.167820	−	0.200000i
$786$	4.09129	+	1.91898i	0.145932	+	0.0684478i
$787$	11.0742	+	6.39367i	0.394751	+	0.227910i	0.684217	−	0.729279i	$-0.260144\pi$
$787$	11.0742	+	6.39367i	0.394751	+	0.227910i	−0.289466	+	0.957188i	$0.593478\pi$
$788$	11.2199	−	13.3714i	0.399694	−	0.476337i
$789$	−1.67204	−	0.150063i	−0.0595262	−	0.00534240i
$790$	−3.84428			−0.136773
$791$	20.6222	−	35.7188i	0.733242	−	1.27001i
$792$	−3.50803	+	6.01363i	−0.124652	+	0.213685i
$793$	16.0245	+	19.0973i	0.569048	+	0.678165i
$794$	−30.8259	+	11.2197i	−1.09397	+	0.398173i
$795$	−12.3130	−	12.3684i	−0.436698	−	0.438661i
$796$	−2.12802	−	12.0686i	−0.0754257	−	0.427761i
$797$	8.74681	+	15.1499i	0.309828	+	0.536638i	0.978325	−	0.207077i	$-0.0663952\pi$
$797$	8.74681	+	15.1499i	0.309828	+	0.536638i	−0.668497	+	0.743715i	$0.733062\pi$
$798$	−27.4563	+	12.6487i	−0.971941	+	0.447760i
$799$	0.152699	−	0.264482i	0.00540210	−	0.00935670i
$800$	4.12841	+	1.50262i	0.145961	+	0.0531255i
$801$	−3.66443	−	10.2102i	−0.129476	−	0.360759i
$802$	−18.0165	−	15.1176i	−0.636185	−	0.533822i
$803$	−20.8974	+	3.68477i	−0.737452	+	0.130033i
$804$	9.85784	−	14.0115i	0.347659	−	0.494147i
$805$	−21.0884			−0.743267
$806$	−14.4166	+	24.9702i	−0.507801	+	0.879538i
$807$	−41.4287	+	19.2055i	−1.45836	+	0.676067i
$808$	−9.91540	−	1.74835i	−0.348823	−	0.0615069i
$809$	46.0512	−	26.5877i	1.61907	−	0.934773i	0.631914	−	0.775039i	$-0.282270\pi$
$809$	46.0512	−	26.5877i	1.61907	−	0.934773i	0.987160	−	0.159734i	$-0.0510636\pi$
$810$	−6.89216	−	1.27912i	−0.242166	−	0.0449436i
$811$	−51.0811	−	9.00698i	−1.79370	−	0.316278i	−0.825116	−	0.564963i	$-0.808891\pi$
$811$	−51.0811	−	9.00698i	−1.79370	−	0.316278i	−0.968584	+	0.248685i	$0.920002\pi$
$812$	4.38963	+	24.8949i	0.154046	+	0.873638i
$813$	−7.60919	−	5.35348i	−0.266866	−	0.187755i
$814$	17.4974	−	14.6821i	0.613285	−	0.514607i
$815$	5.24015	−	0.923980i	0.183554	−	0.0323656i
$816$	8.24263	+	3.86613i	0.288550	+	0.135342i
$817$	−33.1644	+	27.6937i	−1.16028	+	0.968882i
$818$		−	8.94777i		−	0.312851i
$819$	8.78340	−	48.5392i	0.306917	−	1.69610i
$820$	−1.92887	+	0.340111i	−0.0673590	+	0.0118772i
$821$	−2.27012	−	6.23710i	−0.0792277	−	0.217676i	0.893754	−	0.448556i	$-0.148062\pi$
$821$	−2.27012	−	6.23710i	−0.0792277	−	0.217676i	−0.972982	+	0.230880i	$0.925839\pi$
$822$	3.11846	−	11.5347i	0.108769	−	0.402320i
$823$	6.38344	−	2.32338i	0.222513	−	0.0809881i	−0.228358	−	0.973577i	$-0.573336\pi$
$823$	6.38344	−	2.32338i	0.222513	−	0.0809881i	0.450871	+	0.892589i	$0.351113\pi$
$824$		−	4.31087i		−	0.150176i
$825$	−15.9880	−	7.49900i	−0.556629	−	0.261082i
$826$	7.56143	−	42.8830i	0.263096	−	1.49209i
$827$	5.14382	−	1.87220i	0.178868	−	0.0651027i	−0.251033	−	0.967978i	$-0.580770\pi$
$827$	5.14382	−	1.87220i	0.178868	−	0.0651027i	0.429902	+	0.902876i	$0.358548\pi$
$828$	3.43303	+	19.9936i	0.119306	+	0.694826i
$829$	28.3927	+	16.3925i	0.986118	+	0.569335i	0.904112	−	0.427296i	$-0.140534\pi$
$829$	28.3927	+	16.3925i	0.986118	+	0.569335i	0.0820063	+	0.996632i	$0.473867\pi$
$830$	2.71972	+	2.28212i	0.0944030	+	0.0792135i
$831$	12.7242	+	47.9170i	0.441399	+	1.66222i
$832$	−4.04411	−	0.713085i	−0.140204	−	0.0247218i
$833$	30.5174	+	36.3692i	1.05736	+	1.26012i
$834$	−17.9810	−	4.86124i	−0.622631	−	0.168331i
$835$	6.93453	+	4.00365i	0.239979	+	0.138552i
$836$	−3.43707	−	9.51379i	−0.118873	−	0.329041i
$837$	25.9710	−	25.6239i	0.897690	−	0.885693i
$838$	7.87924	−	21.6480i	0.272184	−	0.747818i
$839$	14.4001	+	5.24120i	0.497146	+	0.180946i	0.578410	−	0.815746i	$-0.303673\pi$
$839$	14.4001	+	5.24120i	0.497146	+	0.180946i	−0.0812640	+	0.996693i	$0.525896\pi$
$840$	−3.10816	+	4.41779i	−0.107242	+	0.152428i
$841$	−10.2038	−	3.71388i	−0.351855	−	0.128065i
$842$	9.17391	+	25.2051i	0.316154	+	0.868626i
$843$	29.0988	+	41.7563i	1.00221	+	1.43816i
$844$		−	13.6588i		−	0.470156i
$845$	−1.02914	−	2.82755i	−0.0354036	−	0.0972706i
$846$	0.0878270	−	0.150557i	0.00301955	−	0.00517627i
$847$	11.2402	+	19.4686i	0.386217	+	0.668948i
$848$	6.46843	+	11.2036i	0.222127	+	0.384735i
$849$	−34.1184	+	15.8166i	−1.17094	+	0.542826i
$850$	−7.89829	+	21.7004i	−0.270909	+	0.744317i
$851$	11.5573	−	65.5445i	0.396178	−	2.24684i
$852$	−0.393224	+	0.391465i	−0.0134716	+	0.0134114i
$853$	−14.0740	+	11.8095i	−0.481886	+	0.404350i	−0.851108	−	0.524991i	$-0.824069\pi$
$853$	−14.0740	+	11.8095i	−0.481886	+	0.404350i	0.369222	+	0.929341i	$0.379624\pi$
$854$	−24.3077			−0.831791
$855$	7.84701	−	6.49310i	0.268362	−	0.222059i
$856$	−0.0728624			−0.00249039
$857$	−3.17905	+	2.66754i	−0.108594	+	0.0911215i	−0.695468	−	0.718557i	$-0.744803\pi$
$857$	−3.17905	+	2.66754i	−0.108594	+	0.0911215i	0.586874	+	0.809678i	$0.300359\pi$
$858$	15.9342	+	4.30786i	0.543983	+	0.147068i
$859$	0.284319	−	1.61245i	0.00970083	−	0.0550162i	−0.979573	−	0.201089i	$-0.935552\pi$
$859$	0.284319	−	1.61245i	0.00970083	−	0.0550162i	0.989274	+	0.146072i	$0.0466632\pi$
$860$	−2.64054	+	7.25482i	−0.0900417	+	0.247387i
$861$	−1.55893	+	17.3700i	−0.0531283	+	0.591968i
$862$	−17.7403	−	30.7271i	−0.604237	−	1.04657i
$863$	−0.254136	−	0.440177i	−0.00865090	−	0.0149838i	0.861668	−	0.507473i	$-0.169420\pi$
$863$	−0.254136	−	0.440177i	−0.00865090	−	0.0149838i	−0.870318	+	0.492489i	$0.836087\pi$
$864$	4.69443	+	2.22762i	0.159708	+	0.0757851i
$865$	4.50464	+	12.3764i	0.153162	+	0.420810i
$866$		−	12.1863i		−	0.414106i
$867$	−7.81801	+	16.6681i	−0.265513	+	0.566078i
$868$	−9.61543	−	26.4182i	−0.326369	−	0.896691i
$869$	−10.7634	−	3.91756i	−0.365124	−	0.132894i
$870$	−3.58214	−	7.72711i	−0.121446	−	0.261974i
$871$	−38.1680	−	13.8920i	−1.29327	−	0.470713i
$872$	1.99434	−	5.47941i	0.0675369	−	0.185556i
$873$	32.6210	+	12.0390i	1.10405	+	0.407459i
$874$	−25.4910	−	14.7984i	−0.862247	−	0.500564i
$875$	−25.3697	−	14.6472i	−0.857651	−	0.495165i
$876$	4.06472	+	15.3070i	0.137334	+	0.517174i
$877$	0.558564	+	0.665671i	0.0188614	+	0.0224781i	0.775393	−	0.631479i	$-0.217552\pi$
$877$	0.558564	+	0.665671i	0.0188614	+	0.0224781i	−0.756531	+	0.653957i	$0.773108\pi$
$878$	14.3508	+	2.53044i	0.484317	+	0.0853982i
$879$	−7.58899	−	2.05171i	−0.255970	−	0.0692026i
$880$	−1.38464	−	1.16185i	−0.0466761	−	0.0391659i
$881$	6.78210	+	3.91565i	0.228495	+	0.131921i	0.609877	−	0.792496i	$-0.291219\pi$
$881$	6.78210	+	3.91565i	0.228495	+	0.131921i	−0.381383	+	0.924417i	$0.624552\pi$
$882$	17.3241	+	20.8351i	0.583334	+	0.701556i
$883$	−6.97969	+	2.54040i	−0.234885	+	0.0854913i	−0.456781	−	0.889579i	$-0.650998\pi$
$883$	−6.97969	+	2.54040i	−0.234885	+	0.0854913i	0.221896	+	0.975070i	$0.428776\pi$
$884$	3.74823	−	21.2573i	0.126067	−	0.714960i
$885$	1.24590	+	14.6182i	0.0418805	+	0.491384i
$886$			5.26132i			0.176758i
$887$	−2.55153	+	0.928682i	−0.0856721	+	0.0311821i	−0.384501	−	0.923125i	$-0.625626\pi$
$887$	−2.55153	+	0.928682i	−0.0856721	+	0.0311821i	0.298829	+	0.954307i	$0.403404\pi$
$888$	−12.0275	−	12.0815i	−0.403616	−	0.405430i
$889$	12.3324	+	33.8829i	0.413614	+	1.13640i
$890$	2.77358	−	0.489057i	0.0929706	−	0.0163932i
$891$	−17.9935	−	10.6049i	−0.602806	−	0.355277i
$892$		−	4.46759i		−	0.149586i
$893$	0.0860505	+	0.238187i	0.00287957	+	0.00797064i
$894$	1.43679	+	16.8579i	0.0480534	+	0.563811i
$895$	2.17613	−	0.383710i	0.0727399	−	0.0128260i
$896$	3.06726	−	2.57374i	0.102470	−	0.0859825i
$897$	43.6355	−	20.2286i	1.45695	−	0.675412i
$898$	−5.12887	−	29.0873i	−0.171153	−	0.970655i
$899$	43.6549	+	7.69754i	1.45597	+	0.256727i
$900$	−4.56335	+	12.3649i	−0.152112	+	0.412163i
$901$	−58.8904	+	34.0004i	−1.96192	+	1.13272i
$902$	−5.74713	−	1.01337i	−0.191359	−	0.0337417i
$903$	56.2229	+	39.5559i	1.87098	+	1.31634i
$904$	5.15038	−	8.92071i	0.171299	−	0.296698i
$905$	1.71356			0.0569607
$906$	5.89415	+	12.7144i	0.195820	+	0.422408i
$907$	25.7103	−	4.53343i	0.853698	−	0.150530i	0.270360	−	0.962759i	$-0.412857\pi$
$907$	25.7103	−	4.53343i	0.853698	−	0.150530i	0.583338	+	0.812229i	$0.301746\pi$
$908$	−5.80348	−	4.86970i	−0.192595	−	0.161607i
$909$	5.37841	−	29.7224i	0.178391	−	0.985830i
$910$	12.0343	+	4.38012i	0.398933	+	0.145200i
$911$	20.0425	−	34.7147i	0.664039	−	1.15015i	−0.315506	−	0.948924i	$-0.602174\pi$
$911$	20.0425	−	34.7147i	0.664039	−	1.15015i	0.979545	−	0.201226i	$-0.0644925\pi$
$912$	−6.85716	+	3.15900i	−0.227063	+	0.104605i
$913$	5.28920	+	9.16116i	0.175047	+	0.303190i
$914$	−1.34383	−	7.62126i	−0.0444501	−	0.252089i
$915$	7.91548	−	2.10193i	0.261678	−	0.0694878i
$916$	−9.24072	+	3.36335i	−0.305322	+	0.111128i
$917$	6.71497	+	8.00259i	0.221748	+	0.264269i
$918$	−11.7092	+	24.6756i	−0.386460	+	0.814417i
$919$	3.53692	−	6.12613i	0.116672	−	0.202082i	−0.801775	−	0.597626i	$-0.796111\pi$
$919$	3.53692	−	6.12613i	0.116672	−	0.202082i	0.918447	+	0.395544i	$0.129444\pi$
$920$	−5.26679			−0.173641
$921$	−2.54048	−	5.48012i	−0.0837116	−	0.180576i
$922$	−2.57038	+	3.06326i	−0.0846510	+	0.100883i
$923$	1.13927	+	0.657755i	0.0374994	+	0.0216503i
$924$	−13.2044	+	9.20174i	−0.434392	+	0.302715i
$925$	27.7952	−	33.1250i	0.913900	−	1.08914i
$926$	−22.6434	+	19.0001i	−0.744109	+	0.624382i
$927$	12.9325	+	0.0579981i	0.424758	+	0.00190491i
$928$	1.09631	+	6.21746i	0.0359880	+	0.204098i
$929$	19.0005	+	22.6439i	0.623386	+	0.742922i	0.981649	−	0.190699i	$-0.0610753\pi$
$929$	19.0005	+	22.6439i	0.623386	+	0.742922i	−0.358263	+	0.933621i	$0.616631\pi$
$930$	5.41557	+	7.77127i	0.177584	+	0.254830i
$931$	−39.3704	−	0.0938821i	−1.29031	−	0.00307686i
$932$	18.5435	−	10.7061i	0.607413	−	0.350690i
$933$	−46.7597	+	12.4169i	−1.53084	+	0.406512i
$934$	−12.9424	+	35.5588i	−0.423487	+	1.16352i
$935$	6.10709	−	7.27815i	0.199723	−	0.238021i
$936$	2.19364	−	12.1226i	0.0717015	−	0.396240i
$937$	5.05351	−	28.6599i	0.165091	−	0.936277i	−0.783880	−	0.620913i	$-0.786762\pi$
$937$	5.05351	−	28.6599i	0.165091	−	0.936277i	0.948971	−	0.315365i	$-0.102127\pi$
$938$	34.2981	−	19.8020i	1.11987	−	0.646559i
$939$	−25.1112	+	2.14022i	−0.819473	+	0.0698433i
$940$	0.0346658	+	0.0290881i	0.00113067	+	0.000948748i
$941$	13.4504	+	11.2862i	0.438469	+	0.367919i	0.835136	−	0.550043i	$-0.185389\pi$
$941$	13.4504	+	11.2862i	0.438469	+	0.367919i	−0.396667	+	0.917963i	$0.629833\pi$
$942$	−9.30040	−	13.3459i	−0.303023	−	0.434834i
$943$	−14.7263	+	8.50225i	−0.479555	+	0.276871i
$944$	1.88846	−	10.7100i	0.0614641	−	0.348580i
$945$	−13.2114	−	9.38381i	−0.429767	−	0.305255i
$946$	−14.7862	+	17.6215i	−0.480742	+	0.572926i
$947$	12.8220	−	35.2282i	0.416660	−	1.14476i	−0.536923	−	0.843631i	$-0.680413\pi$
$947$	12.8220	−	35.2282i	0.416660	−	1.14476i	0.953583	−	0.301132i	$-0.0973644\pi$
$948$	−2.23113	+	8.25261i	−0.0724636	+	0.268032i
$949$	32.5182	−	18.7744i	1.05559	−	0.609443i
$950$	−9.53553	−	16.6073i	−0.309373	−	0.538813i
$951$	−12.6529	+	26.9762i	−0.410299	+	0.874763i
$952$	13.5285	+	16.1226i	0.438461	+	0.522537i
$953$	4.15908	+	23.5873i	0.134726	+	0.764068i	0.975050	+	0.221984i	$0.0712534\pi$
$953$	4.15908	+	23.5873i	0.134726	+	0.764068i	−0.840324	+	0.542084i	$0.817636\pi$
$954$	−33.6976	+	19.2544i	−1.09100	+	0.623383i
$955$	12.4442	−	10.4419i	0.402685	−	0.337893i
$956$	4.76829	−	5.68263i	0.154218	−	0.183789i
$957$	−2.15504	−	25.2852i	−0.0696627	−	0.817353i
$958$	7.90811	+	4.56575i	0.255499	+	0.147513i
$959$	17.7554	−	21.1600i	0.573350	−	0.683292i
$960$	−0.776258	+	1.10334i	−0.0250536	+	0.0356100i
$961$	−18.2993			−0.590299
$962$	−20.2091	+	35.0032i	−0.651567	+	1.12855i
$963$	0.000980286	−	0.218585i	3.15893e−5	−	0.00704380i
$964$	0.111878	+	0.133331i	0.00360334	+	0.00429430i
$965$	10.8392	−	3.94514i	0.348926	−	0.126999i
$966$	−12.2391	+	45.2708i	−0.393788	+	1.45657i
$967$	3.72882	+	21.1472i	0.119911	+	0.680048i	0.984201	+	0.177054i	$0.0566568\pi$
$967$	3.72882	+	21.1472i	0.119911	+	0.680048i	−0.864290	+	0.502993i	$0.832232\pi$
$968$	2.80722	+	4.86225i	0.0902275	+	0.156279i
$969$	−16.6049	−	36.0437i	−0.533425	−	1.15789i
$970$	−4.51378	+	7.81810i	−0.144929	+	0.251024i
$971$	48.7579	+	17.7464i	1.56471	+	0.569510i	0.971810	−	0.235764i	$-0.0757591\pi$
$971$	48.7579	+	17.7464i	1.56471	+	0.569510i	0.592904	+	0.805273i	$0.297981\pi$
$972$	−6.74595	+	14.0532i	−0.216376	+	0.450756i
$973$	−32.9855	−	27.6781i	−1.05747	−	0.887319i
$974$	16.9313	−	2.98544i	0.542514	−	0.0956598i
$975$	31.1233	+	2.79328i	0.996745	+	0.0894564i
$976$	−6.07081			−0.194322
$977$	0.490402	−	0.849401i	0.0156893	−	0.0271747i	−0.858074	−	0.513526i	$-0.828339\pi$
$977$	0.490402	−	0.849401i	0.0156893	−	0.0271747i	0.873763	+	0.486351i	$0.161672\pi$
$978$	1.05772	−	11.7854i	0.0338223	−	0.376855i
$979$	8.26398	+	1.45716i	0.264118	+	0.0465711i
$980$	−6.09244	+	3.51747i	−0.194616	+	0.112362i
$981$	16.4112	+	6.05668i	0.523970	+	0.193375i
$982$	24.7674	+	4.36715i	0.790358	+	0.139361i
$983$	7.95646	+	45.1233i	0.253772	+	1.43921i	0.799206	+	0.601057i	$0.205254\pi$
$983$	7.95646	+	45.1233i	0.253772	+	1.43921i	−0.545434	+	0.838154i	$0.683635\pi$
$984$	−0.389341	+	4.33813i	−0.0124118	+	0.138295i
$985$	−10.4146	+	8.73891i	−0.331837	+	0.278445i
$986$	−32.6812	+	5.76257i	−1.04078	+	0.183518i
$987$	0.330585	−	0.230375i	0.0105226	−	0.00733292i
$988$	11.4730	+	13.7394i	0.365006	+	0.437110i
$989$			67.0276i			2.13136i
$990$	3.50414	−	4.13824i	0.111369	−	0.131522i
$991$	−14.1269	+	2.49096i	−0.448757	+	0.0791280i	−0.393460	−	0.919342i	$-0.628722\pi$
$991$	−14.1269	+	2.49096i	−0.448757	+	0.0791280i	−0.0552975	+	0.998470i	$0.517611\pi$
$992$	−2.40144	−	6.59790i	−0.0762458	−	0.209484i
$993$	33.0606	−	8.77914i	1.04914	−	0.278598i
$994$	−1.20533	+	0.438704i	−0.0382307	+	0.0139148i
$995$			9.54492i			0.302594i
$996$	6.47754	−	4.51401i	0.205249	−	0.143032i
$997$	9.36032	−	53.0850i	0.296444	−	1.68122i	−0.364830	−	0.931074i	$-0.618873\pi$
$997$	9.36032	−	53.0850i	0.296444	−	1.68122i	0.661274	−	0.750144i	$-0.270016\pi$
$998$	31.3792	−	11.4211i	0.993293	−	0.361529i
$999$	36.4061	−	35.9196i	1.15184	−	1.13644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.x.b.281.3	yes	48
9.5	odd	6		342.2.bf.b.167.4	yes	48
19.14	odd	18		342.2.bf.b.299.4	yes	48
171.14	even	18	inner	342.2.x.b.185.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.x.b.185.3	✓	48	171.14	even	18	inner
342.2.x.b.281.3	yes	48	1.1	even	1	trivial
342.2.bf.b.167.4	yes	48	9.5	odd	6
342.2.bf.b.299.4	yes	48	19.14	odd	18

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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.444535 - 1.67403i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.266390 + 0.731901i) q^{5} +(1.41658 + 0.996642i) q^{6} +(2.00201 + 3.46759i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.60478 + 1.48833i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.444535 - 1.67403i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.266390 + 0.731901i) q^{5} +(1.41658 + 0.996642i) q^{6} +(2.00201 + 3.46759i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-2.60478 + 1.48833i) q^{9} +(-0.266390 - 0.731901i) q^{10} -2.32068i q^{11} +(-1.72579 + 0.147089i) q^{12} +(1.40450 + 3.85884i) q^{13} +(-3.76255 - 1.36946i) q^{14} +(1.34365 + 0.120590i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(1.79778 - 4.93936i) q^{17} +(1.03869 - 2.81445i) q^{18} +(2.17044 + 3.78010i) q^{19} +(0.674524 + 0.389436i) q^{20} +(4.91489 - 4.89290i) q^{21} +(1.49170 + 1.77774i) q^{22} +(6.65933 + 1.17422i) q^{23} +(1.22749 - 1.22200i) q^{24} +(3.36551 + 2.82400i) q^{25} +(-3.55633 - 2.05325i) q^{26} +(3.64944 + 3.69887i) q^{27} +(3.76255 - 1.36946i) q^{28} +(-1.09631 + 6.21746i) q^{29} +(-1.10681 + 0.771302i) q^{30} -7.02134i q^{31} +(0.939693 - 0.342020i) q^{32} +(-3.88490 + 1.03162i) q^{33} +(1.79778 + 4.93936i) q^{34} +(-3.07125 + 0.541544i) q^{35} +(1.01341 + 2.82365i) q^{36} -9.84250i q^{37} +(-4.09246 - 1.50059i) q^{38} +(5.83548 - 4.06658i) q^{39} +(-0.767040 + 0.135250i) q^{40} +(-1.92636 + 1.61641i) q^{41} +(-0.619931 + 6.90741i) q^{42} +(1.72125 + 9.76171i) q^{43} +(-2.28542 - 0.402982i) q^{44} +(-0.395426 - 2.30292i) q^{45} +(-5.85612 + 3.38103i) q^{46} +(0.0572179 + 0.0100891i) q^{47} +(-0.154827 + 1.72512i) q^{48} +(-4.51611 + 7.82213i) q^{49} -4.39336 q^{50} +(-9.06783 - 0.813825i) q^{51} +(4.04411 - 0.713085i) q^{52} +(-9.91021 - 8.31565i) q^{53} +(-5.17322 - 0.487685i) q^{54} +(1.69851 + 0.618207i) q^{55} +(-2.00201 + 3.46759i) q^{56} +(5.36318 - 5.31378i) q^{57} +(-3.15669 - 5.46754i) q^{58} +(1.88846 + 10.7100i) q^{59} +(0.352080 - 1.30229i) q^{60} +(5.70469 - 2.07634i) q^{61} +(4.51323 + 5.37866i) q^{62} +(-10.3757 - 6.05263i) q^{63} +(-0.500000 + 0.866025i) q^{64} -3.19844 q^{65} +(2.31289 - 3.28743i) q^{66} +(-6.35785 + 7.57699i) q^{67} +(-4.55214 - 2.62818i) q^{68} +(-0.994624 - 11.6699i) q^{69} +(2.00461 - 2.38901i) q^{70} +(0.245401 - 0.205916i) q^{71} +(-2.59132 - 1.51164i) q^{72} +(-1.58780 - 9.00484i) q^{73} +(6.32664 + 7.53979i) q^{74} +(3.23138 - 6.88934i) q^{75} +(4.09957 - 1.48106i) q^{76} +(8.04716 - 4.64603i) q^{77} +(-1.85629 + 6.86615i) q^{78} +(1.68811 - 4.63804i) q^{79} +(0.500650 - 0.596651i) q^{80} +(4.56973 - 7.75355i) q^{81} +(0.436671 - 2.47649i) q^{82} +(-3.94762 + 2.27916i) q^{83} +(-3.96510 - 5.68987i) q^{84} +(3.13621 + 2.63159i) q^{85} +(-7.59326 - 6.37151i) q^{86} +(10.8956 - 0.928626i) q^{87} +(2.00977 - 1.16034i) q^{88} +(-0.627903 + 3.56102i) q^{89} +(1.78320 + 1.50996i) q^{90} +(-10.5690 + 12.5957i) q^{91} +(2.31276 - 6.35426i) q^{92} +(-11.7540 + 3.12123i) q^{93} +(-0.0503166 + 0.0290503i) q^{94} +(-3.34485 + 0.581566i) q^{95} +(-0.990280 - 1.42104i) q^{96} +(-7.45026 - 8.87888i) q^{97} +(-1.56843 - 8.89500i) q^{98} +(3.45395 + 6.04486i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8}+O(q^{10}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8	\( 48 q - 6 q^{3} - 9 q^{5} - 9 q^{6} + 9 q^{7} + 24 q^{8} - 9 q^{10} - 6 q^{12} + 15 q^{13} - 6 q^{14} + 12 q^{15} - 27 q^{17} - 9 q^{18} - 12 q^{19} - 9 q^{20} - 15 q^{21} + 18 q^{22} - 3 q^{24} - 9 q^{25} + 18 q^{26} - 12 q^{27} + 6 q^{28} + 45 q^{29} - 27 q^{34} - 18 q^{35} - 3 q^{36} + 24 q^{39} + 27 q^{41} - 3 q^{42} - 15 q^{43} - 9 q^{44} - 63 q^{45} + 27 q^{46} - 27 q^{47} - 9 q^{48} - 33 q^{49} - 6 q^{50} - 42 q^{51} + 21 q^{52} + 9 q^{55} - 9 q^{56} + 36 q^{57} - 9 q^{58} - 9 q^{60} + 69 q^{61} - 3 q^{62} + 3 q^{63} - 24 q^{64} + 18 q^{65} - 6 q^{66} + 21 q^{67} + 36 q^{68} - 12 q^{69} + 27 q^{71} - 9 q^{72} + 66 q^{73} - 15 q^{74} + 24 q^{75} - 27 q^{77} + 63 q^{78} + 33 q^{79} - 9 q^{80} - 9 q^{82} - 81 q^{83} + 6 q^{84} + 18 q^{85} - 30 q^{86} - 72 q^{87} + 9 q^{88} - 18 q^{89} + 60 q^{90} + 51 q^{91} - 18 q^{92} - 84 q^{93} - 54 q^{94} - 27 q^{95} - 3 q^{96} - 108 q^{97} + 42 q^{98} + 15 q^{99}+O(q^{100}) \) 48 * q - 6 * q^3 - 9 * q^5 - 9 * q^6 + 9 * q^7 + 24 * q^8 - 9 * q^10 - 6 * q^12 + 15 * q^13 - 6 * q^14 + 12 * q^15 - 27 * q^17 - 9 * q^18 - 12 * q^19 - 9 * q^20 - 15 * q^21 + 18 * q^22 - 3 * q^24 - 9 * q^25 + 18 * q^26 - 12 * q^27 + 6 * q^28 + 45 * q^29 - 27 * q^34 - 18 * q^35 - 3 * q^36 + 24 * q^39 + 27 * q^41 - 3 * q^42 - 15 * q^43 - 9 * q^44 - 63 * q^45 + 27 * q^46 - 27 * q^47 - 9 * q^48 - 33 * q^49 - 6 * q^50 - 42 * q^51 + 21 * q^52 + 9 * q^55 - 9 * q^56 + 36 * q^57 - 9 * q^58 - 9 * q^60 + 69 * q^61 - 3 * q^62 + 3 * q^63 - 24 * q^64 + 18 * q^65 - 6 * q^66 + 21 * q^67 + 36 * q^68 - 12 * q^69 + 27 * q^71 - 9 * q^72 + 66 * q^73 - 15 * q^74 + 24 * q^75 - 27 * q^77 + 63 * q^78 + 33 * q^79 - 9 * q^80 - 9 * q^82 - 81 * q^83 + 6 * q^84 + 18 * q^85 - 30 * q^86 - 72 * q^87 + 9 * q^88 - 18 * q^89 + 60 * q^90 + 51 * q^91 - 18 * q^92 - 84 * q^93 - 54 * q^94 - 27 * q^95 - 3 * q^96 - 108 * q^97 + 42 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more