LMFDB - Embedded newform 930.2.bk.a.47.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(47,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 4]))

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

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

chi := DirichletCharacter("930.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bk (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$64$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			47.17
Character	$\chi$	$=$	930.47
Dual form			930.2.bk.a.653.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.156434 + 0.987688i) q^{2} +(0.207488 - 1.71958i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.69493 - 1.45849i) q^{5} +(1.66595 + 0.473934i) q^{6} +(0.759514 - 0.386992i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.91390 - 0.713583i) q^{9} +O(q^{10})$	\(q+(-0.156434 + 0.987688i) q^{2} +(0.207488 - 1.71958i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.69493 - 1.45849i) q^{5} +(1.66595 + 0.473934i) q^{6} +(0.759514 - 0.386992i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.91390 - 0.713583i) q^{9} +(1.17539 + 1.90223i) q^{10} +(3.43320 + 1.11551i) q^{11} +(-0.728711 + 1.57130i) q^{12} +(0.0972668 - 0.0154055i) q^{13} +(0.263413 + 0.810702i) q^{14} +(-2.15631 - 3.21719i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.69842 + 2.39396i) q^{17} +(1.16063 - 2.76639i) q^{18} +(0.759541 + 1.04542i) q^{19} +(-2.06268 + 0.863344i) q^{20} +(-0.507873 - 1.38634i) q^{21} +(-1.63885 + 3.21642i) q^{22} +(1.66161 - 3.26110i) q^{23} +(-1.43796 - 0.965545i) q^{24} +(0.745605 - 4.94409i) q^{25} +0.0984792i q^{26} +(-1.83166 + 4.86261i) q^{27} +(-0.841928 + 0.133348i) q^{28} +(1.03174 - 0.749602i) q^{29} +(3.51490 - 1.62648i) q^{30} +(-2.20598 - 5.11211i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.63056 - 5.67219i) q^{33} +(-3.09948 + 4.26608i) q^{34} +(0.722902 - 1.76367i) q^{35} +(2.55077 + 1.57910i) q^{36} +(-5.10943 - 5.10943i) q^{37} +(-1.15137 + 0.586651i) q^{38} +(-0.00630937 - 0.170454i) q^{39} +(-0.530041 - 2.17234i) q^{40} +(-1.56794 - 2.15808i) q^{41} +(1.44872 - 0.284749i) q^{42} +(0.0812549 - 0.513023i) q^{43} +(-2.92045 - 2.12183i) q^{44} +(-5.97962 + 3.04042i) q^{45} +(2.96101 + 2.15130i) q^{46} +(-1.21518 + 0.192465i) q^{47} +(1.17860 - 1.26921i) q^{48} +(-3.68740 + 5.07527i) q^{49} +(4.76659 + 1.50985i) q^{50} +(5.09147 - 7.58258i) q^{51} +(-0.0972668 - 0.0154055i) q^{52} +(4.05223 - 7.95295i) q^{53} +(-4.51621 - 2.56979i) q^{54} +(7.44601 - 3.11657i) q^{55} -0.852423i q^{56} +(1.95528 - 1.08918i) q^{57} +(0.578973 + 1.13630i) q^{58} +(-1.12082 - 0.814322i) q^{59} +(1.05661 + 3.72607i) q^{60} -12.5259 q^{61} +(5.39426 - 1.37912i) q^{62} +(-2.48930 + 0.585678i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(0.142392 - 0.167974i) q^{65} +(5.19085 + 3.48550i) q^{66} +(-1.91246 - 1.91246i) q^{67} +(-3.72869 - 3.72869i) q^{68} +(-5.26295 - 3.53391i) q^{69} +(1.62887 + 0.989901i) q^{70} +(-0.441681 + 0.143511i) q^{71} +(-1.95869 + 2.27234i) q^{72} +(6.79877 + 13.3433i) q^{73} +(5.84582 - 4.24724i) q^{74} +(-8.34705 - 2.30796i) q^{75} +(-0.399315 - 1.22896i) q^{76} +(3.03926 - 0.481371i) q^{77} +(0.169343 + 0.0204332i) q^{78} +(7.60671 - 2.47157i) q^{79} +(2.22851 - 0.183687i) q^{80} +(7.98160 + 4.15861i) q^{81} +(2.37679 - 1.21104i) q^{82} +(11.8300 + 1.87369i) q^{83} +(0.0546131 + 1.47543i) q^{84} +(11.4551 - 2.79499i) q^{85} +(0.493996 + 0.160509i) q^{86} +(-1.07493 - 1.92969i) q^{87} +(2.55257 - 2.55257i) q^{88} +(2.36200 - 7.26948i) q^{89} +(-2.06757 - 6.38163i) q^{90} +(0.0679137 - 0.0493422i) q^{91} +(-2.58802 + 2.58802i) q^{92} +(-9.24838 + 2.73266i) q^{93} -1.23032i q^{94} +(2.81211 + 0.664132i) q^{95} +(1.06921 + 1.36264i) q^{96} +(6.56292 - 3.34397i) q^{97} +(-4.43595 - 4.43595i) q^{98} +(-9.20797 - 5.70036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) $ 512 * q + 8 * q^3 - 12 * q^7	$ 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) $ 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$2$	−0.156434	+	0.987688i	−0.110616	+	0.698401i
$3$	0.207488	−	1.71958i	0.119793	−	0.992799i
$3$	0.207488	−	1.71958i	0.119793	−	0.992799i
$4$	−0.951057	−	0.309017i	−0.475528	−	0.154508i
$5$	1.69493	−	1.45849i	0.757998	−	0.652257i
$5$	1.69493	−	1.45849i	0.757998	−	0.652257i
$6$	1.66595	+	0.473934i	0.680121	+	0.193483i
$7$	0.759514	−	0.386992i	0.287069	−	0.146269i	−0.304526	−	0.952504i	$-0.598498\pi$
$7$	0.759514	−	0.386992i	0.287069	−	0.146269i	0.591596	+	0.806235i	$0.298498\pi$
$8$	0.453990	−	0.891007i	0.160510	−	0.315018i
$9$	−2.91390	−	0.713583i	−0.971299	−	0.237861i
$10$	1.17539	+	1.90223i	0.371691	+	0.601536i
$11$	3.43320	+	1.11551i	1.03515	+	0.336340i	0.776823	−	0.629718i	$-0.216830\pi$
$11$	3.43320	+	1.11551i	1.03515	+	0.336340i	0.258324	+	0.966058i	$0.416830\pi$
$12$	−0.728711	+	1.57130i	−0.210361	+	0.453595i
$13$	0.0972668	−	0.0154055i	0.0269770	−	0.00427273i	−0.142931	−	0.989733i	$-0.545653\pi$
$13$	0.0972668	−	0.0154055i	0.0269770	−	0.00427273i	0.169908	+	0.985460i	$0.445653\pi$
$14$	0.263413	+	0.810702i	0.0704001	+	0.216669i
$15$	−2.15631	−	3.21719i	−0.556757	−	0.830675i
$16$	0.809017	+	0.587785i	0.202254	+	0.146946i
$17$	4.69842	+	2.39396i	1.13953	+	0.580622i	0.918804	−	0.394713i	$-0.129156\pi$
$17$	4.69842	+	2.39396i	1.13953	+	0.580622i	0.220730	+	0.975335i	$0.429156\pi$
$18$	1.16063	−	2.76639i	0.273563	−	0.652045i
$19$	0.759541	+	1.04542i	0.174251	+	0.239836i	0.887206	−	0.461374i	$-0.152644\pi$
$19$	0.759541	+	1.04542i	0.174251	+	0.239836i	−0.712955	+	0.701210i	$0.752644\pi$
$20$	−2.06268	+	0.863344i	−0.461229	+	0.193050i
$21$	−0.507873	−	1.38634i	−0.110827	−	0.302524i
$22$	−1.63885	+	3.21642i	−0.349404	+	0.685744i
$23$	1.66161	−	3.26110i	0.346470	−	0.679986i	−0.650353	−	0.759632i	$-0.725379\pi$
$23$	1.66161	−	3.26110i	0.346470	−	0.679986i	0.996823	+	0.0796462i	$0.0253790\pi$
$24$	−1.43796	−	0.965545i	−0.293522	−	0.197091i
$25$	0.745605	−	4.94409i	0.149121	−	0.988819i
$26$			0.0984792i			0.0193134i
$27$	−1.83166	+	4.86261i	−0.352503	+	0.935811i
$28$	−0.841928	+	0.133348i	−0.159109	+	0.0252005i
$29$	1.03174	−	0.749602i	0.191589	−	0.139198i	−0.487856	−	0.872924i	$-0.662221\pi$
$29$	1.03174	−	0.749602i	0.191589	−	0.139198i	0.679445	+	0.733727i	$0.262221\pi$
$30$	3.51490	−	1.62648i	0.641731	−	0.296954i
$31$	−2.20598	−	5.11211i	−0.396207	−	0.918161i
$31$	−2.20598	−	5.11211i	−0.396207	−	0.918161i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	2.63056	−	5.67219i	0.457921	−	0.987402i
$34$	−3.09948	+	4.26608i	−0.531557	+	0.731626i
$35$	0.722902	−	1.76367i	0.122193	−	0.298115i
$36$	2.55077	+	1.57910i	0.425129	+	0.263184i
$37$	−5.10943	−	5.10943i	−0.839986	−	0.839986i	0.148871	−	0.988857i	$-0.452436\pi$
$37$	−5.10943	−	5.10943i	−0.839986	−	0.839986i	−0.988857	+	0.148871i	$0.952436\pi$
$38$	−1.15137	+	0.586651i	−0.186776	+	0.0951673i
$39$	−0.00630937	−	0.170454i	−0.00101031	−	0.0272945i
$40$	−0.530041	−	2.17234i	−0.0838069	−	0.343477i
$41$	−1.56794	−	2.15808i	−0.244871	−	0.337036i	0.668836	−	0.743410i	$-0.266793\pi$
$41$	−1.56794	−	2.15808i	−0.244871	−	0.337036i	−0.913707	+	0.406374i	$0.866793\pi$
$42$	1.44872	−	0.284749i	0.223542	−	0.0439377i
$43$	0.0812549	−	0.513023i	0.0123912	−	0.0782353i	−0.980718	−	0.195429i	$-0.937390\pi$
$43$	0.0812549	−	0.513023i	0.0123912	−	0.0782353i	0.993109	+	0.117194i	$0.0373900\pi$
$44$	−2.92045	−	2.12183i	−0.440275	−	0.319878i
$45$	−5.97962	+	3.04042i	−0.891389	+	0.453239i
$46$	2.96101	+	2.15130i	0.436578	+	0.317192i
$47$	−1.21518	+	0.192465i	−0.177252	+	0.0280739i	−0.244429	−	0.969667i	$-0.578601\pi$
$47$	−1.21518	+	0.192465i	−0.177252	+	0.0280739i	0.0671775	+	0.997741i	$0.478601\pi$
$48$	1.17860	−	1.26921i	0.170117	−	0.183195i
$49$	−3.68740	+	5.07527i	−0.526771	+	0.725038i
$50$	4.76659	+	1.50985i	0.674097	+	0.213525i
$51$	5.09147	−	7.58258i	0.712949	−	1.06177i
$52$	−0.0972668	−	0.0154055i	−0.0134885	−	0.00213637i
$53$	4.05223	−	7.95295i	0.556617	−	1.09242i	−0.425642	−	0.904892i	$-0.639952\pi$
$53$	4.05223	−	7.95295i	0.556617	−	1.09242i	0.982259	−	0.187530i	$-0.0600483\pi$
$54$	−4.51621	−	2.56979i	−0.614579	−	0.349704i
$55$	7.44601	−	3.11657i	1.00402	−	0.420238i
$56$		−	0.852423i		−	0.113910i
$57$	1.95528	−	1.08918i	0.258983	−	0.144265i
$58$	0.578973	+	1.13630i	0.0760229	+	0.149203i
$59$	−1.12082	−	0.814322i	−0.145918	−	0.106016i	0.512431	−	0.858728i	$-0.328745\pi$
$59$	−1.12082	−	0.814322i	−0.145918	−	0.106016i	−0.658349	+	0.752713i	$0.728745\pi$
$60$	1.05661	+	3.72607i	0.136408	+	0.481033i
$61$	−12.5259			−1.60378			−0.801888	−	0.597474i	$-0.796171\pi$
$61$	−12.5259			−1.60378			−0.801888	+	0.597474i	$0.796171\pi$
$62$	5.39426	−	1.37912i	0.685072	−	0.175148i
$63$	−2.48930	+	0.585678i	−0.313622	+	0.0737885i
$64$	−0.587785	−	0.809017i	−0.0734732	−	0.101127i
$65$	0.142392	−	0.167974i	0.0176616	−	0.0208346i
$66$	5.19085	+	3.48550i	0.638949	+	0.429035i
$67$	−1.91246	−	1.91246i	−0.233644	−	0.233644i	0.580568	−	0.814212i	$-0.302831\pi$
$67$	−1.91246	−	1.91246i	−0.233644	−	0.233644i	−0.814212	+	0.580568i	$0.802831\pi$
$68$	−3.72869	−	3.72869i	−0.452170	−	0.452170i
$69$	−5.26295	−	3.53391i	−0.633585	−	0.425433i
$70$	1.62887	+	0.989901i	0.194687	+	0.118316i
$71$	−0.441681	+	0.143511i	−0.0524178	+	0.0170316i	−0.335109	−	0.942180i	$-0.608773\pi$
$71$	−0.441681	+	0.143511i	−0.0524178	+	0.0170316i	0.282691	+	0.959211i	$0.408773\pi$
$72$	−1.95869	+	2.27234i	−0.230834	+	0.267798i
$73$	6.79877	+	13.3433i	0.795736	+	1.56172i	0.826995	+	0.562209i	$0.190048\pi$
$73$	6.79877	+	13.3433i	0.795736	+	1.56172i	−0.0312587	+	0.999511i	$0.509952\pi$
$74$	5.84582	−	4.24724i	0.679563	−	0.493731i
$75$	−8.34705	−	2.30796i	−0.963835	−	0.266501i
$76$	−0.399315	−	1.22896i	−0.0458045	−	0.140972i
$77$	3.03926	−	0.481371i	0.346355	−	0.0548573i
$78$	0.169343	+	0.0204332i	0.0191743	+	0.00231361i
$79$	7.60671	−	2.47157i	0.855822	−	0.278073i	0.151939	−	0.988390i	$-0.451448\pi$
$79$	7.60671	−	2.47157i	0.855822	−	0.278073i	0.703883	+	0.710316i	$0.251448\pi$
$80$	2.22851	−	0.183687i	0.249155	−	0.0205368i
$81$	7.98160	+	4.15861i	0.886844	+	0.462068i
$82$	2.37679	−	1.21104i	0.262473	−	0.133737i
$83$	11.8300	+	1.87369i	1.29851	+	0.205664i	0.767142	−	0.641477i	$-0.221678\pi$
$83$	11.8300	+	1.87369i	1.29851	+	0.205664i	0.531368	+	0.847141i	$0.321678\pi$
$84$	0.0546131	+	1.47543i	0.00595877	+	0.160983i
$85$	11.4551	−	2.79499i	1.24248	−	0.303160i
$86$	0.493996	+	0.160509i	0.0532689	+	0.0173081i
$87$	−1.07493	−	1.92969i	−0.115244	−	0.206884i
$88$	2.55257	−	2.55257i	0.272105	−	0.272105i
$89$	2.36200	−	7.26948i	0.250371	−	0.770563i	−0.744335	−	0.667806i	$-0.767234\pi$
$89$	2.36200	−	7.26948i	0.250371	−	0.770563i	0.994706	−	0.102757i	$-0.0327665\pi$
$90$	−2.06757	−	6.38163i	−0.217941	−	0.672683i
$91$	0.0679137	−	0.0493422i	0.00711929	−	0.00517247i
$92$	−2.58802	+	2.58802i	−0.269820	+	0.269820i
$93$	−9.24838	+	2.73266i	−0.959012	+	0.283364i
$94$		−	1.23032i		−	0.126898i
$95$	2.81211	+	0.664132i	0.288516	+	0.0681385i
$96$	1.06921	+	1.36264i	0.109126	+	0.139074i
$97$	6.56292	−	3.34397i	0.666363	−	0.339529i	−0.0878734	−	0.996132i	$-0.528007\pi$
$97$	6.56292	−	3.34397i	0.666363	−	0.339529i	0.754237	+	0.656603i	$0.228007\pi$
$98$	−4.43595	−	4.43595i	−0.448098	−	0.448098i
$99$	−9.20797	−	5.70036i	−0.925436	−	0.572908i
$100$	−2.23692	+	4.47171i	−0.223692	+	0.447171i
$101$	−7.03532	+	2.28591i	−0.700040	+	0.227457i	−0.637348	−	0.770576i	$-0.719969\pi$
$101$	−7.03532	+	2.28591i	−0.700040	+	0.227457i	−0.0626922	+	0.998033i	$0.519969\pi$
$102$	6.69274	+	6.21496i	0.662680	+	0.615373i
$103$	−2.89347	+	18.2686i	−0.285102	+	1.80006i	0.264231	+	0.964459i	$0.414882\pi$
$103$	−2.89347	+	18.2686i	−0.285102	+	1.80006i	−0.549333	+	0.835603i	$0.685118\pi$
$104$	0.0304318	−	0.0936593i	0.00298408	−	0.00918405i
$105$	−2.88278	−	1.60903i	−0.281330	−	0.157025i
$106$	7.22113	+	5.24646i	0.701378	+	0.509581i
$107$	3.99943	+	2.03781i	0.386639	+	0.197002i	0.636495	−	0.771280i	$-0.280383\pi$
$107$	3.99943	+	2.03781i	0.386639	+	0.197002i	−0.249856	+	0.968283i	$0.580383\pi$
$108$	3.24464	−	4.05861i	0.312216	−	0.390540i
$109$	5.18049	−	7.13033i	0.496201	−	0.682962i	−0.485316	−	0.874339i	$-0.661295\pi$
$109$	5.18049	−	7.13033i	0.496201	−	0.682962i	0.981517	+	0.191377i	$0.0612953\pi$
$110$	1.91338	+	7.84187i	0.182434	+	0.747693i
$111$	−9.84621	+	7.72593i	−0.934561	+	0.733312i
$112$	0.841928	+	0.133348i	0.0795547	+	0.0126002i
$113$	−6.83569	+	3.48296i	−0.643047	+	0.327649i	−0.744925	−	0.667148i	$-0.767515\pi$
$113$	−6.83569	+	3.48296i	−0.643047	+	0.327649i	0.101878	+	0.994797i	$0.467515\pi$
$114$	0.769897	+	2.10159i	0.0721075	+	0.196832i
$115$	−1.93996	−	7.95079i	−0.180902	−	0.741415i
$116$	−1.21288	+	0.394089i	−0.112613	+	0.0365902i
$117$	−0.294419	−	0.0245177i	−0.0272190	−	0.00226666i
$118$	0.979631	−	0.979631i	0.0901824	−	0.0901824i
$119$	4.49496			0.412052
$120$	−3.84548	+	0.460714i	−0.351043	+	0.0420572i
$121$	1.64328	+	1.19391i	0.149389	+	0.108538i
$122$	1.95948	−	12.3717i	0.177403	−	1.12008i
$123$	−4.03632	+	2.24842i	−0.363943	+	0.202733i
$124$	0.518289	+	5.54359i	0.0465437	+	0.497829i
$125$	−5.94717	−	9.46737i	−0.531931	−	0.846788i
$126$	−0.189056	−	2.55027i	−0.0168424	−	0.227196i
$127$	3.32094	+	20.9676i	0.294686	+	1.86057i	0.479150	+	0.877733i	$0.340945\pi$
$127$	3.32094	+	20.9676i	0.294686	+	1.86057i	−0.184465	+	0.982839i	$0.559055\pi$
$128$	0.891007	−	0.453990i	0.0787546	−	0.0401275i
$129$	−0.865324	−	0.246170i	−0.0761875	−	0.0216741i
$130$	0.143631	+	0.166916i	0.0125973	+	0.0146395i
$131$	9.06144	+	2.94424i	0.791702	+	0.257240i	0.676829	−	0.736141i	$-0.263354\pi$
$131$	9.06144	+	2.94424i	0.791702	+	0.257240i	0.114873	+	0.993380i	$0.463354\pi$
$132$	−4.25461	+	4.58169i	−0.370317	+	0.398785i
$133$	0.981451	+	0.500074i	0.0851026	+	0.0433619i
$134$	2.18809	−	1.58974i	0.189022	−	0.137333i
$135$	3.98754	+	10.9133i	0.343193	+	0.939265i
$136$	4.26608	−	3.09948i	0.365813	−	0.265779i
$137$	−18.6785	+	2.95839i	−1.59582	+	0.252752i	−0.890107	−	0.455751i	$-0.849371\pi$
$137$	−18.6785	+	2.95839i	−1.59582	+	0.252752i	−0.705708	+	0.708503i	$0.749371\pi$
$138$	4.31371	−	4.64533i	0.367207	−	0.395437i
$139$	−8.12403	+	11.1818i	−0.689071	+	0.948425i	−0.999998	−	0.00200910i	$-0.999360\pi$
$139$	−8.12403	+	11.1818i	−0.689071	+	0.948425i	0.310927	+	0.950434i	$0.399360\pi$
$140$	−1.23253	+	1.45396i	−0.104167	+	0.122882i
$141$	0.0788245	+	2.12953i	0.00663822	+	0.179338i
$142$	−0.0726498	−	0.458693i	−0.00609664	−	0.0384926i
$143$	0.351121	+	0.0556121i	0.0293622	+	0.00465052i
$144$	−1.93796	−	2.29005i	−0.161497	−	0.190837i
$145$	0.655441	−	2.77531i	0.0544314	−	0.230477i
$146$	−14.2426	+	4.62771i	−1.17873	+	0.382992i
$147$	7.96223	+	7.39382i	0.656714	+	0.609832i
$148$	3.28046	+	6.43826i	0.269652	+	0.529222i
$149$	5.05896			0.414446			0.207223	−	0.978294i	$-0.433557\pi$
$149$	5.05896			0.414446			0.207223	+	0.978294i	$0.433557\pi$
$150$	3.58532	−	7.88324i	0.292740	−	0.643664i
$151$	−0.976750	+	3.00613i	−0.0794868	+	0.244635i	−0.982901	−	0.184133i	$-0.941052\pi$
$151$	−0.976750	+	3.00613i	−0.0794868	+	0.244635i	0.903415	+	0.428768i	$0.141052\pi$
$152$	1.27630	−	0.202146i	0.103522	−	0.0163962i
$153$	−11.9824	−	10.3285i	−0.968721	−	0.835008i
$154$			3.07714i			0.247963i
$155$	−11.1950	−	5.44727i	−0.899201	−	0.437536i
$156$	−0.0466727	+	0.164061i	−0.00373681	+	0.0131354i
$157$	6.80699	+	1.07812i	0.543257	+	0.0860435i	0.422031	−	0.906581i	$-0.361317\pi$
$157$	6.80699	+	1.07812i	0.543257	+	0.0860435i	0.121226	+	0.992625i	$0.461317\pi$
$158$	1.25119	+	7.89970i	0.0995393	+	0.628466i
$159$	−12.8349	−	8.61827i	−1.01788	−	0.683473i
$160$	−0.167190	+	2.22981i	−0.0132175	+	0.176282i
$161$		−	3.11988i		−	0.245881i
$162$	−5.35601	+	7.23278i	−0.420808	+	0.568261i
$163$	21.5569	+	10.9838i	1.68847	+	0.860316i	0.989393	+	0.145265i	$0.0464034\pi$
$163$	21.5569	+	10.9838i	1.68847	+	0.860316i	0.699072	+	0.715051i	$0.253597\pi$
$164$	0.824315	+	2.53698i	0.0643682	+	0.198105i
$165$	−3.81422	−	13.4506i	−0.296937	−	1.04713i
$166$	−3.70124	+	11.3912i	−0.287272	+	0.884131i
$167$	0.908873	−	5.73840i	0.0703307	−	0.444051i	−0.927245	−	0.374456i	$-0.877829\pi$
$167$	0.908873	−	5.73840i	0.0703307	−	0.444051i	0.997575	−	0.0695946i	$-0.0221706\pi$
$168$	−1.46581	−	0.176867i	−0.113089	−	0.0136456i
$169$	−12.3545	+	4.01422i	−0.950347	+	0.308786i
$170$	0.968611	+	11.7513i	0.0742891	+	0.901283i
$171$	−1.46723	−	3.58824i	−0.112202	−	0.274400i
$172$	−0.235811	+	0.462805i	−0.0179804	+	0.0352885i
$173$	1.83838	+	11.6071i	0.139769	+	0.882468i	0.953537	+	0.301277i	$0.0974130\pi$
$173$	1.83838	+	11.6071i	0.139769	+	0.882468i	−0.813767	+	0.581191i	$0.802587\pi$
$174$	2.07409	−	0.759822i	0.157236	−	0.0576020i
$175$	−1.34703	−	4.04365i	−0.101826	−	0.305671i
$176$	2.12183	+	2.92045i	0.159939	+	0.220137i
$177$	−1.63285	+	1.75837i	−0.122732	+	0.132167i
$178$	6.81048	+	3.47011i	0.510467	+	0.260096i
$179$	−6.10416	+	18.7867i	−0.456246	+	1.40418i	0.413420	+	0.910541i	$0.364334\pi$
$179$	−6.10416	+	18.7867i	−0.456246	+	1.40418i	−0.869666	+	0.493641i	$0.835666\pi$
$180$	6.62650	−	1.04381i	0.493910	−	0.0778008i
$181$	2.53506			0.188429			0.0942146	−	0.995552i	$-0.469966\pi$
$181$	2.53506			0.188429			0.0942146	+	0.995552i	$0.469966\pi$
$182$	0.0381107	+	0.0747964i	0.00282495	+	0.00554428i
$183$	−2.59897	+	21.5393i	−0.192121	+	1.59223i
$184$	−2.15130	−	2.96101i	−0.158596	−	0.218289i
$185$	−16.1122	−	1.20809i	−1.18459	−	0.0888204i
$186$	−1.25225	−	9.56200i	−0.0918198	−	0.701120i
$187$	13.4601	+	13.4601i	0.984300	+	0.984300i
$188$	1.21518	+	0.192465i	0.0886259	+	0.0140370i
$189$	0.490621	+	4.40206i	0.0356874	+	0.320203i
$190$	−1.09587	+	2.67359i	−0.0795025	+	0.193963i
$191$		−	14.2768i		−	1.03304i	−0.856277	−	0.516518i	$-0.827228\pi$
$191$		−	14.2768i		−	1.03304i	0.856277	−	0.516518i	$-0.172772\pi$
$192$	−1.51313	+	0.842882i	−0.109200	+	0.0608297i
$193$	−3.28985	−	6.45670i	−0.236809	−	0.464763i	0.741765	−	0.670660i	$-0.233989\pi$
$193$	−3.28985	−	6.45670i	−0.236809	−	0.464763i	−0.978574	+	0.205897i	$0.933989\pi$
$194$	2.27614	+	7.00523i	0.163417	+	0.502946i
$195$	−0.259300	−	0.279707i	−0.0185689	−	0.0200302i
$196$	5.07527	−	3.68740i	0.362519	−	0.263386i
$197$	0.396530	+	0.778233i	0.0282516	+	0.0554468i	0.904701	−	0.426047i	$-0.140094\pi$
$197$	0.396530	+	0.778233i	0.0282516	+	0.0554468i	−0.876449	+	0.481494i	$0.840094\pi$
$198$	7.07062	−	8.20287i	0.502487	−	0.582953i
$199$	3.28390	−	4.51990i	0.232789	−	0.320407i	−0.676602	−	0.736349i	$-0.736548\pi$
$199$	3.28390	−	4.51990i	0.232789	−	0.320407i	0.909391	+	0.415942i	$0.136548\pi$
$200$	−4.06672	−	2.90891i	−0.287561	−	0.205691i
$201$	−3.68544	+	2.89181i	−0.259951	+	0.203973i
$202$	−1.15720	−	7.30630i	−0.0814206	−	0.514069i
$203$	0.493530	−	0.968607i	0.0346390	−	0.0679829i
$204$	−7.18542	+	5.63811i	−0.503080	+	0.394747i
$205$	−5.80510	−	1.37098i	−0.405446	−	0.0957536i
$206$	−17.5911	−	5.71569i	−1.22563	−	0.398231i
$207$	−7.16883	+	8.31681i	−0.498268	+	0.578058i
$208$	0.0877456	+	0.0447086i	0.00608407	+	0.00309999i
$209$	1.44148	+	4.43641i	0.0997090	+	0.306873i
$210$	2.04018	−	2.59558i	0.140786	−	0.179112i
$211$	−13.4836			−0.928251			−0.464125	−	0.885770i	$-0.653631\pi$
$211$	−13.4836			−0.928251			−0.464125	+	0.885770i	$0.653631\pi$
$212$	−6.31150	+	6.31150i	−0.433476	+	0.433476i
$213$	0.155135	+	0.789281i	0.0106296	+	0.0540806i
$214$	−2.63837	+	3.63140i	−0.180355	+	0.248238i
$215$	−0.610518	−	0.988050i	−0.0416370	−	0.0673844i
$216$	3.50107	+	3.83960i	0.238217	+	0.261252i
$217$	−3.65382	−	3.02902i	−0.248037	−	0.205623i
$218$	6.23214	+	6.23214i	0.422094	+	0.422094i
$219$	24.3556	−	8.92244i	1.64580	−	0.602923i
$220$	−8.04465	+	0.663088i	−0.542370	+	0.0447054i
$221$	0.493880	+	0.160471i	0.0332220	+	0.0107945i
$222$	−6.09052	−	10.9336i	−0.408769	−	0.733815i
$223$	−1.12718	+	1.12718i	−0.0754817	+	0.0754817i	−0.743840	−	0.668358i	$-0.766997\pi$
$223$	−1.12718	+	1.12718i	−0.0754817	+	0.0754817i	0.668358	+	0.743840i	$0.266997\pi$
$224$	−0.263413	+	0.810702i	−0.0176000	+	0.0541673i
$225$	−5.70064	+	13.8745i	−0.380042	+	0.924969i
$226$	−2.37074	−	7.29638i	−0.157699	−	0.485348i
$227$	−0.0149188	+	0.0941934i	−0.000990193	+	0.00625183i	−0.988178	−	0.153308i	$-0.951007\pi$
$227$	−0.0149188	+	0.0941934i	−0.000990193	+	0.00625183i	0.987188	+	0.159560i	$0.0510074\pi$
$228$	−2.19615	+	0.431658i	−0.145444	+	0.0285872i
$229$	−17.0744	−	23.5009i	−1.12831	−	1.55298i	−0.791242	−	0.611504i	$-0.790565\pi$
$229$	−17.0744	−	23.5009i	−1.12831	−	1.55298i	−0.337068	−	0.941480i	$-0.609435\pi$
$230$	8.15638	−	0.672298i	0.537816	−	0.0443300i
$231$	−0.197146	−	5.32612i	−0.0129713	−	0.350433i
$232$	−0.199501	−	1.25960i	−0.0130979	−	0.0826966i
$233$	−1.37663	−	8.69169i	−0.0901860	−	0.569412i	−0.990858	−	0.134911i	$-0.956925\pi$
$233$	−1.37663	−	8.69169i	−0.0901860	−	0.569412i	0.900672	−	0.434500i	$-0.143075\pi$
$234$	0.0702731	−	0.286958i	0.00459390	−	0.0187591i
$235$	−1.77894	+	2.09854i	−0.116045	+	0.136894i
$236$	0.814322	+	1.12082i	0.0530079	+	0.0729591i
$237$	−2.67176	−	13.5932i	−0.173549	−	0.882970i
$238$	−0.703167	+	4.43962i	−0.0455795	+	0.287778i
$239$	1.69864	+	5.22787i	0.109876	+	0.338163i	0.990844	−	0.135013i	$-0.0431076\pi$
$239$	1.69864	+	5.22787i	0.109876	+	0.338163i	−0.880968	+	0.473176i	$0.843108\pi$
$240$	0.146524	−	3.87021i	0.00945810	−	0.249821i
$241$	−0.608129	+	1.87163i	−0.0391731	+	0.120562i	−0.968731	−	0.248115i	$-0.920189\pi$
$241$	−0.608129	+	1.87163i	−0.0391731	+	0.120562i	0.929558	+	0.368677i	$0.120189\pi$
$242$	−1.43628	+	1.43628i	−0.0923276	+	0.0923276i
$243$	8.80715	−	12.8621i	0.564979	−	0.825106i
$244$	11.9128	+	3.87072i	0.762641	+	0.247797i
$245$	1.15234	+	13.9803i	0.0736202	+	0.893168i
$246$	−1.58932	−	4.33836i	−0.101331	−	0.276604i
$247$	0.0899834	+	0.0899834i	0.00572551	+	0.00572551i
$248$	−5.55642	−	0.355301i	−0.352833	−	0.0225616i
$249$	5.67653	−	19.9538i	0.359735	−	1.26452i
$250$	10.2812	−	4.39293i	0.650237	−	0.277833i
$251$	15.6762	−	21.5765i	0.989476	−	1.36190i	0.0579106	−	0.998322i	$-0.481556\pi$
$251$	15.6762	−	21.5765i	0.989476	−	1.36190i	0.931565	−	0.363575i	$-0.118444\pi$
$252$	2.54845	+	0.212222i	0.160537	+	0.0133687i
$253$	9.34244	−	9.34244i	0.587354	−	0.587354i
$254$	−21.2289			−1.33202
$255$	−2.42942	−	20.2778i	−0.152136	−	1.26985i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−4.57156	−	2.32933i	−0.285166	−	0.145299i	0.305557	−	0.952174i	$-0.401157\pi$
$257$	−4.57156	−	2.32933i	−0.285166	−	0.145299i	−0.590723	+	0.806874i	$0.701157\pi$
$258$	0.378506	−	0.816161i	0.0235647	−	0.0508119i
$259$	−5.85800	−	1.90338i	−0.363998	−	0.118270i
$260$	−0.187330	+	0.115751i	−0.0116177	+	0.00717860i
$261$	−3.54128	+	1.44803i	−0.219200	+	0.0896309i
$262$	−4.32551	+	8.48930i	−0.267231	+	0.524471i
$263$	4.79235	+	30.2577i	0.295509	+	1.86577i	0.472182	+	0.881501i	$0.343467\pi$
$263$	4.79235	+	30.2577i	0.295509	+	1.86577i	−0.176673	+	0.984270i	$0.556533\pi$
$264$	−3.85971	−	4.91897i	−0.237549	−	0.302741i
$265$	−4.73105	−	19.3899i	−0.290626	−	1.19111i
$266$	−0.647450	+	0.891139i	−0.0396977	+	0.0546392i
$267$	−12.0104	−	5.56997i	−0.735022	−	0.340876i
$268$	1.22787	+	2.40984i	0.0750044	+	0.147204i
$269$	−21.4155	+	15.5593i	−1.30572	+	0.948665i	−0.999994	−	0.00345328i	$-0.998901\pi$
$269$	−21.4155	+	15.5593i	−1.30572	+	0.948665i	−0.305731	+	0.952118i	$0.598901\pi$
$270$	−11.4027	+	2.23124i	−0.693946	+	0.135789i
$271$	−3.87995	−	11.9413i	−0.235690	−	0.725380i	−0.997029	−	0.0770256i	$-0.975458\pi$
$271$	−3.87995	−	11.9413i	−0.235690	−	0.725380i	0.761339	−	0.648354i	$-0.224542\pi$
$272$	2.39396	+	4.69842i	0.145155	+	0.284883i
$273$	−0.0707565	−	0.127021i	−0.00428238	−	0.00768765i
$274$		−	18.9114i		−	1.14248i
$275$	8.07501	−	16.1423i	0.486941	−	0.973418i
$276$	3.91332	+	4.98729i	0.235554	+	0.300200i
$277$	6.21181	+	0.983854i	0.373231	+	0.0591140i	0.340232	−	0.940341i	$-0.389494\pi$
$277$	6.21181	+	0.983854i	0.373231	+	0.0591140i	0.0329989	+	0.999455i	$0.489494\pi$
$278$	−9.77322	−	9.77322i	−0.586159	−	0.586159i
$279$	2.78010	+	16.4703i	0.166440	+	0.986052i
$280$	−1.24325	−	1.44480i	−0.0742985	−	0.0863433i
$281$	−1.65804	−	2.28210i	−0.0989104	−	0.136138i	0.756693	−	0.653770i	$-0.226814\pi$
$281$	−1.65804	−	2.28210i	−0.0989104	−	0.136138i	−0.855603	+	0.517632i	$0.826814\pi$
$282$	−2.11564	−	0.255277i	−0.125984	−	0.0152015i
$283$	12.5215	+	24.5748i	0.744325	+	1.46082i	0.882450	+	0.470406i	$0.155892\pi$
$283$	12.5215	+	24.5748i	0.744325	+	1.46082i	−0.138125	+	0.990415i	$0.544108\pi$
$284$	0.464410			0.0275577
$285$	1.72550	−	4.69784i	0.102210	−	0.278276i
$286$	−0.109855	+	0.338099i	−0.00649586	+	0.0199922i
$287$	−2.02603	−	1.03232i	−0.119593	−	0.0609356i
$288$	2.56502	−	1.55586i	0.151145	−	0.0916798i
$289$	6.35173	+	8.74240i	0.373631	+	0.514259i
$290$	2.63861	+	1.08152i	0.154944	+	0.0635093i
$291$	−4.38850	−	11.9793i	−0.257258	−	0.702238i
$292$	−2.34270	−	14.7912i	−0.137096	−	0.865590i
$293$	4.40175	−	8.63893i	0.257153	−	0.504691i	−0.725949	−	0.687748i	$-0.758599\pi$
$293$	4.40175	−	8.63893i	0.257153	−	0.504691i	0.983102	+	0.183057i	$0.0585993\pi$
$294$	−8.54836	+	6.70755i	−0.498551	+	0.391192i
$295$	−3.08740	+	0.254482i	−0.179755	+	0.0148165i
$296$	−6.87217	+	2.23290i	−0.399437	+	0.129785i
$297$	−11.7128	+	14.6511i	−0.679643	+	0.850141i
$298$	−0.791396	+	4.99668i	−0.0458443	+	0.289450i
$299$	0.111381	−	0.342795i	0.00644131	−	0.0198243i
$300$	7.22532	+	4.77439i	0.417154	+	0.275649i
$301$	−0.136821	−	0.421093i	−0.00788626	−	0.0242714i
$302$	−2.81632	−	1.43499i	−0.162061	−	0.0825742i
$303$	2.47106	+	12.5721i	0.141959	+	0.722247i
$304$			1.29221i			0.0741133i
$305$	−21.2306	+	18.2689i	−1.21566	+	1.04608i
$306$	12.0758	−	10.2192i	0.690326	−	0.584191i
$307$	3.02072	+	19.0721i	0.172401	+	1.08850i	0.910410	+	0.413708i	$0.135767\pi$
$307$	3.02072	+	19.0721i	0.172401	+	1.08850i	−0.738008	+	0.674792i	$0.764233\pi$
$308$	−3.03926	−	0.481371i	−0.173178	−	0.0274286i
$309$	30.8140	+	8.76606i	1.75295	+	0.498684i
$310$	7.13149	−	10.2050i	0.405041	−	0.579605i
$311$			15.1396i			0.858486i	0.903189	+	0.429243i	$0.141220\pi$
$311$			15.1396i			0.858486i	−0.903189	+	0.429243i	$0.858780\pi$
$312$	−0.154740	−	0.0717629i	−0.00876044	−	0.00406278i
$313$	3.13624	−	0.496732i	0.177271	−	0.0280769i	−0.0671679	−	0.997742i	$-0.521396\pi$
$313$	3.13624	−	0.496732i	0.177271	−	0.0280769i	0.244439	+	0.969665i	$0.421396\pi$
$314$	−2.12970	+	6.55453i	−0.120186	+	0.369894i
$315$	−3.36499	+	4.62331i	−0.189596	+	0.260494i
$316$	−7.99817			−0.449932
$317$	7.96939	+	15.6408i	0.447606	+	0.878476i	0.999021	+	0.0442446i	$0.0140881\pi$
$317$	7.96939	+	15.6408i	0.447606	+	0.878476i	−0.551415	+	0.834231i	$0.685912\pi$
$318$	10.5200	−	11.3287i	0.589932	−	0.635283i
$319$	4.37835	−	1.42261i	0.245141	−	0.0796510i
$320$	−2.17620	−	0.513951i	−0.121653	−	0.0287307i
$321$	4.33400	−	6.45450i	0.241901	−	0.360255i
$322$	3.08147	+	0.488057i	0.171724	+	0.0271983i
$323$	1.06595	+	6.73013i	0.0593109	+	0.374475i
$324$	−6.30587	−	6.42153i	−0.350326	−	0.356751i
$325$	−0.00364392	−	0.492383i	−0.000202128	−	0.0273125i
$326$	−14.2208	+	19.5732i	−0.787617	+	1.08406i
$327$	−11.1863	−	10.3877i	−0.618603	−	0.574442i
$328$	−2.63470	+	0.417295i	−0.145477	+	0.0230413i
$329$	−0.848462	+	0.616444i	−0.0467772	+	0.0339856i
$330$	13.8817	−	1.66312i	0.764163	−	0.0915518i
$331$	−16.4484	+	11.9505i	−0.904088	+	0.656859i	−0.939513	−	0.342514i	$-0.888722\pi$
$331$	−16.4484	+	11.9505i	−0.904088	+	0.656859i	0.0354246	+	0.999372i	$0.488722\pi$
$332$	−10.6720	−	5.43765i	−0.585701	−	0.298430i
$333$	11.2424	+	18.5344i	0.616078	+	1.01568i
$334$	5.52557	+	1.79537i	0.302346	+	0.0982381i
$335$	−6.03080	−	0.452187i	−0.329498	−	0.0247056i
$336$	0.403993	−	1.42009i	0.0220396	−	0.0774724i
$337$	−23.9364	+	12.1962i	−1.30390	+	0.664371i	−0.961402	−	0.275147i	$-0.911273\pi$
$337$	−23.9364	+	12.1962i	−1.30390	+	0.664371i	−0.342499	+	0.939518i	$0.611273\pi$
$338$	−2.03213	−	12.8304i	−0.110533	−	0.697880i
$339$	4.57089	+	12.4772i	0.248257	+	0.677667i
$340$	−11.7581	−	0.881621i	−0.637674	−	0.0478126i
$341$	−1.87096	−	20.0117i	−0.101318	−	1.08369i
$342$	3.77359	−	0.887845i	0.204052	−	0.0480091i
$343$	−1.76998	+	11.1752i	−0.0955700	+	0.603405i
$344$	−0.420218	−	0.305306i	−0.0226566	−	0.0164610i
$345$	−14.0745	+	1.68622i	−0.757747	+	0.0907831i
$346$	−11.7517			−0.631777
$347$	6.94708	−	6.94708i	0.372939	−	0.372939i	−0.495608	−	0.868547i	$-0.665055\pi$
$347$	6.94708	−	6.94708i	0.372939	−	0.372939i	0.868547	+	0.495608i	$0.165055\pi$
$348$	0.426009	+	2.16741i	0.0228365	+	0.116186i
$349$	−8.07279	+	2.62301i	−0.432126	+	0.140406i	−0.517000	−	0.855985i	$-0.672951\pi$
$349$	−8.07279	+	2.62301i	−0.432126	+	0.140406i	0.0848737	+	0.996392i	$0.472951\pi$
$350$	4.20459	−	0.697876i	0.224745	−	0.0373030i
$351$	−0.103248	+	0.501189i	−0.00551099	+	0.0267515i
$352$	−3.21642	+	1.63885i	−0.171436	+	0.0873510i
$353$	−5.39160	−	0.853945i	−0.286966	−	0.0454509i	0.0112921	−	0.999936i	$-0.496406\pi$
$353$	−5.39160	−	0.853945i	−0.286966	−	0.0454509i	−0.298258	+	0.954485i	$0.596406\pi$
$354$	−1.48129	−	1.88781i	−0.0787297	−	0.100336i
$355$	−0.539310	+	0.887429i	−0.0286236	+	0.0470998i
$356$	−4.49278	+	6.18379i	−0.238117	+	0.327740i
$357$	0.932649	−	7.72944i	0.0493610	−	0.409085i
$358$	−17.6005	−	8.96789i	−0.930214	−	0.473968i
$359$	13.3442	+	9.69510i	0.704278	+	0.511688i	0.881323	−	0.472515i	$-0.156654\pi$
$359$	13.3442	+	9.69510i	0.704278	+	0.511688i	−0.177045	+	0.984203i	$0.556654\pi$
$360$	−0.00565694	+	6.70820i	−0.000298147	+	0.353553i
$361$	5.35532	−	16.4820i	0.281859	−	0.867473i
$362$	−0.396570	+	2.50385i	−0.0208433	+	0.131599i
$363$	2.39399	−	2.57803i	0.125652	−	0.135311i
$364$	−0.0798373	+	0.0259407i	−0.00418461	+	0.00135966i
$365$	30.9846	+	12.7001i	1.62181	+	0.664756i
$366$	−20.8675	−	5.93646i	−1.09076	−	0.310303i
$367$	−3.86988	−	3.86988i	−0.202006	−	0.202006i	0.598853	−	0.800859i	$-0.295623\pi$
$367$	−3.86988	−	3.86988i	−0.202006	−	0.202006i	−0.800859	+	0.598853i	$0.795623\pi$
$368$	3.26110	−	1.66161i	0.169996	−	0.0866175i
$369$	3.02884	+	7.40729i	0.157675	+	0.385608i
$370$	3.71372	−	15.7249i	0.193067	−	0.817497i
$371$		−	7.60856i		−	0.395017i
$372$	9.64017	+	0.258989i	0.499820	+	0.0134280i
$373$	19.9298	−	19.9298i	1.03193	−	1.03193i	0.0324552	−	0.999473i	$-0.489667\pi$
$373$	19.9298	−	19.9298i	1.03193	−	1.03193i	0.999473	−	0.0324552i	$-0.0103326\pi$
$374$	−15.4000	+	11.1888i	−0.796315	+	0.578557i
$375$	−17.5139	+	8.26226i	−0.904412	+	0.426661i
$376$	−0.380191	+	1.17011i	−0.0196069	+	0.0603437i
$377$	0.0888059	−	0.0888059i	0.00457373	−	0.00457373i
$378$	−4.42462	−	0.204054i	−0.227578	−	0.0104954i
$379$	−13.5717	−	4.40970i	−0.697129	−	0.226511i	−0.0610499	−	0.998135i	$-0.519445\pi$
$379$	−13.5717	−	4.40970i	−0.697129	−	0.226511i	−0.636079	+	0.771624i	$0.719445\pi$
$380$	−2.46925	−	1.50062i	−0.126670	−	0.0769800i
$381$	36.7444	−	1.36010i	1.88247	−	0.0696799i
$382$	14.1011	+	2.23339i	0.721473	+	0.114270i
$383$	16.8813	−	8.60146i	0.862595	−	0.439514i	0.0340393	−	0.999420i	$-0.489163\pi$
$383$	16.8813	−	8.60146i	0.862595	−	0.439514i	0.828556	+	0.559906i	$0.189163\pi$
$384$	−0.595799	−	1.62635i	−0.0304043	−	0.0829945i
$385$	4.44926	−	5.24862i	0.226755	−	0.267494i
$386$	6.89185	−	2.23930i	0.350786	−	0.113977i
$387$	−0.602853	+	1.43691i	−0.0306447	+	0.0730425i
$388$	−7.27505	+	1.15225i	−0.369335	+	0.0584969i
$389$	9.30154	+	28.6272i	0.471607	+	1.45146i	0.850479	+	0.526008i	$0.176312\pi$
$389$	9.30154	+	28.6272i	0.471607	+	1.45146i	−0.378872	+	0.925449i	$0.623688\pi$
$390$	0.316827	−	0.212352i	0.0160431	−	0.0107529i
$391$	15.6139	−	11.3442i	0.789629	−	0.573699i
$392$	2.84805	+	5.58962i	0.143848	+	0.282318i
$393$	6.94299	−	14.9710i	0.350228	−	0.755185i
$394$	−0.830683	+	0.269905i	−0.0418492	+	0.0135976i
$395$	9.28811	−	15.2835i	0.467336	−	0.768995i
$396$	6.99579	+	8.26678i	0.351552	+	0.415422i
$397$	13.1212	+	13.1212i	0.658536	+	0.658536i	0.955034	−	0.296498i	$-0.0958187\pi$
$397$	13.1212	+	13.1212i	0.658536	+	0.658536i	−0.296498	+	0.955034i	$0.595819\pi$
$398$	3.95054	+	3.95054i	0.198023	+	0.198023i
$399$	1.06356	−	1.58392i	0.0532444	−	0.0792953i
$400$	3.50927	−	3.56160i	0.175464	−	0.178080i
$401$	4.82567	+	6.64196i	0.240982	+	0.331684i	0.912328	−	0.409461i	$-0.134283\pi$
$401$	4.82567	+	6.64196i	0.240982	+	0.331684i	−0.671345	+	0.741145i	$0.734283\pi$
$402$	−2.27968	−	4.09244i	−0.113700	−	0.204112i
$403$	−0.293324	−	0.463254i	−0.0146115	−	0.0230763i
$404$	7.39737			0.368033
$405$	19.5936	−	4.59252i	0.973613	−	0.228204i
$406$	0.879477	+	0.638978i	0.0436477	+	0.0317119i
$407$	−11.8420	−	23.2413i	−0.586989	−	1.15203i
$408$	−4.44465	−	7.97895i	−0.220043	−	0.395017i
$409$		−	2.60314i		−	0.128717i	−0.997927	−	0.0643584i	$-0.979500\pi$
$409$		−	2.60314i		−	0.128717i	0.997927	−	0.0643584i	$-0.0205001\pi$
$410$	2.26222	−	5.51916i	0.111723	−	0.272572i
$411$	1.21161	+	32.7330i	0.0597645	+	1.61460i
$412$	8.39717	−	16.4804i	0.413699	−	0.811930i
$413$	−1.16641	−	0.184742i	−0.0573955	−	0.00909055i
$414$	−7.09296	−	8.38161i	−0.348600	−	0.411934i
$415$	22.7838	−	14.0782i	1.11841	−	0.691070i
$416$	−0.0578846	+	0.0796714i	−0.00283803	+	0.00390621i
$417$	17.5423	+	16.2900i	0.859049	+	0.797723i
$418$	−4.60728	+	0.729722i	−0.225350	+	0.0356919i
$419$	9.91559	+	7.20409i	0.484408	+	0.351943i	0.803030	−	0.595939i	$-0.203220\pi$
$419$	9.91559	+	7.20409i	0.484408	+	0.351943i	−0.318622	+	0.947882i	$0.603220\pi$
$420$	2.24447	+	2.42110i	0.109519	+	0.118138i
$421$	−9.84911	−	7.15580i	−0.480016	−	0.348752i	0.321316	−	0.946972i	$-0.395875\pi$
$421$	−9.84911	−	7.15580i	−0.480016	−	0.348752i	−0.801332	+	0.598220i	$0.795875\pi$
$422$	2.10930	−	13.3176i	0.102679	−	0.648291i
$423$	3.67824	+	0.306306i	0.178842	+	0.0148931i
$424$	−5.24646	−	7.22113i	−0.254791	−	0.350689i
$425$	15.3391	−	21.4445i	0.744058	−	1.04021i
$426$	−0.803832	+	0.0297539i	−0.0389458	+	0.00144158i
$427$	−9.51360	+	4.84742i	−0.460395	+	0.234583i
$428$	−3.17396	−	3.17396i	−0.153419	−	0.153419i
$429$	0.168483	−	0.592241i	0.00813442	−	0.0285937i
$430$	1.07139	−	0.448437i	0.0516671	−	0.0216255i
$431$	−0.893804	+	1.23022i	−0.0430530	+	0.0592574i	−0.830001	−	0.557762i	$-0.811660\pi$
$431$	−0.893804	+	1.23022i	−0.0430530	+	0.0592574i	0.786948	+	0.617020i	$0.211660\pi$
$432$	−4.34002	+	2.85732i	−0.208809	+	0.137473i
$433$	−0.741401	+	0.741401i	−0.0356295	+	0.0356295i	−0.724697	−	0.689068i	$-0.758020\pi$
$433$	−0.741401	+	0.741401i	−0.0356295	+	0.0356295i	0.689068	+	0.724697i	$0.258020\pi$
$434$	3.56331	−	3.13499i	0.171044	−	0.150484i
$435$	−4.63636	−	1.70292i	−0.222297	−	0.0816489i
$436$	−7.13033	+	5.18049i	−0.341481	+	0.248101i
$437$	4.67128	−	0.739858i	0.223458	−	0.0353922i
$438$	5.00254	+	25.4515i	0.239031	+	1.21612i
$439$		−	2.55636i		−	0.122009i	−0.998138	−	0.0610043i	$-0.980570\pi$
$439$		−	2.55636i		−	0.122009i	0.998138	−	0.0610043i	$-0.0194303\pi$
$440$	0.603536	−	8.04933i	0.0287725	−	0.383737i
$441$	14.3663	−	12.1575i	0.684111	−	0.578931i
$442$	−0.235756	+	0.462697i	−0.0112138	+	0.0220082i
$443$	13.0733	−	25.6577i	0.621129	−	1.21903i	−0.339344	−	0.940662i	$-0.610205\pi$
$443$	13.0733	−	25.6577i	0.621129	−	1.21903i	0.960473	−	0.278372i	$-0.0897948\pi$
$444$	11.7517	−	4.30514i	0.557713	−	0.204313i
$445$	−6.59904	−	15.7662i	−0.312825	−	0.747392i
$446$	−0.936974	−	1.28963i	−0.0443670	−	0.0610659i
$447$	1.04967	−	8.69928i	0.0496478	−	0.411462i
$448$	−0.759514	−	0.386992i	−0.0358837	−	0.0182836i
$449$	−0.999830	−	0.726419i	−0.0471849	−	0.0342818i	0.563943	−	0.825814i	$-0.309284\pi$
$449$	−0.999830	−	0.726419i	−0.0471849	−	0.0342818i	−0.611128	+	0.791532i	$0.709284\pi$
$450$	−12.8119	−	7.80091i	−0.603961	−	0.367738i
$451$	−2.97567	−	9.15818i	−0.140119	−	0.431242i
$452$	7.57742	−	1.20014i	0.356412	−	0.0564501i
$453$	4.96661	+	2.30333i	0.233352	+	0.108220i
$454$	−0.0906999	−	0.0294702i	−0.00425676	−	0.00138310i
$455$	0.0431441	−	0.182683i	0.00202263	−	0.00856433i
$456$	−0.0827893	−	2.23664i	−0.00387697	−	0.104740i
$457$	−12.9295	+	25.3755i	−0.604815	+	1.18702i	0.362153	+	0.932119i	$0.382042\pi$
$457$	−12.9295	+	25.3755i	−0.604815	+	1.18702i	−0.966968	+	0.254898i	$0.917958\pi$
$458$	25.8826	−	13.1878i	1.20941	−	0.616228i
$459$	−20.2468	+	18.4617i	−0.945041	+	0.861717i
$460$	−0.611919	+	8.16114i	−0.0285309	+	0.380515i
$461$	18.0657	+	5.86990i	0.841404	+	0.273389i	0.697841	−	0.716253i	$-0.254144\pi$
$461$	18.0657	+	5.86990i	0.841404	+	0.273389i	0.143563	+	0.989641i	$0.454144\pi$
$462$	5.29138	+	0.638469i	0.246177	+	0.0297043i
$463$	−4.75035	+	29.9925i	−0.220767	+	1.39387i	0.589481	+	0.807783i	$0.299332\pi$
$463$	−4.75035	+	29.9925i	−0.220767	+	1.39387i	−0.810248	+	0.586087i	$0.800668\pi$
$464$	1.27530			0.0592043
$465$	−11.6898	+	18.1204i	−0.542103	+	0.840312i
$466$	8.80004			0.407654
$467$	2.40615	−	15.1918i	0.111343	−	0.702993i	−0.867355	−	0.497690i	$-0.834182\pi$
$467$	2.40615	−	15.1918i	0.111343	−	0.702993i	0.978698	−	0.205303i	$-0.0658181\pi$
$468$	0.272432	+	0.114298i	0.0125932	+	0.00528343i
$469$	−2.19265	−	0.712434i	−0.101247	−	0.0328971i
$470$	−1.79442	−	2.08532i	−0.0827703	−	0.0961886i
$471$	3.26628	−	11.4815i	0.150502	−	0.529038i
$472$	−1.23441	+	0.628962i	−0.0568182	+	0.0289503i
$473$	0.851248	−	1.67067i	0.0391404	−	0.0768174i
$474$	13.8438	−	0.512427i	0.635865	−	0.0235366i
$475$	5.73497	−	2.97578i	0.263138	−	0.136538i
$476$	−4.27496	−	1.38902i	−0.195943	−	0.0636656i
$477$	−17.4829	+	20.2825i	−0.800486	+	0.928671i
$478$	−5.42923	+	0.859906i	−0.248327	+	0.0393312i
$479$	3.71464	+	11.4325i	0.169726	+	0.522363i	0.999353	−	0.0359544i	$-0.0114471\pi$
$479$	3.71464	+	11.4325i	0.169726	+	0.522363i	−0.829627	+	0.558317i	$0.811447\pi$
$480$	3.79964	+	0.750155i	0.173429	+	0.0342397i
$481$	−0.575692	−	0.418265i	−0.0262493	−	0.0190712i
$482$	−1.75345	−	0.893430i	−0.0798677	−	0.0406946i
$483$	−5.36488	−	0.647337i	−0.244110	−	0.0294549i
$484$	−1.19391	−	1.64328i	−0.0542688	−	0.0746946i
$485$	6.24656	−	15.2398i	0.283642	−	0.692003i
$486$	11.3260	+	10.7108i	0.513759	+	0.485851i
$487$	2.78627	−	5.46837i	0.126258	−	0.247795i	−0.819221	−	0.573478i	$-0.805594\pi$
$487$	2.78627	−	5.46837i	0.126258	−	0.247795i	0.945479	+	0.325682i	$0.105594\pi$
$488$	−5.68664	+	11.1607i	−0.257422	+	0.505219i
$489$	23.3603	−	34.7897i	1.05639	−	1.57325i
$490$	−13.9884	−	1.04885i	−0.631933	−	0.0473821i
$491$		−	32.4139i		−	1.46282i	−0.681939	−	0.731409i	$-0.738863\pi$
$491$		−	32.4139i		−	1.46282i	0.681939	−	0.731409i	$-0.261137\pi$
$492$	4.53357	−	0.891081i	0.204389	−	0.0401730i
$493$	6.64206	−	1.05200i	0.299143	−	0.0473796i
$494$	−0.102952	+	0.0747991i	−0.00463203	+	0.00336537i
$495$	−23.9208	+	3.76801i	−1.07516	+	0.169360i
$496$	1.22014	−	5.43243i	0.0547860	−	0.243923i
$497$	−0.279925	+	0.279925i	−0.0125564	+	0.0125564i
$498$	18.8202	+	8.72811i	0.843351	+	0.391116i
$499$	−11.3301	+	15.5946i	−0.507206	+	0.698109i	−0.983445	−	0.181207i	$-0.942000\pi$
$499$	−11.3301	+	15.5946i	−0.507206	+	0.698109i	0.476239	+	0.879316i	$0.342000\pi$
$500$	2.73052	+	10.8418i	0.122112	+	0.484859i
$501$	−9.67905	−	2.75353i	−0.432428	−	0.123018i
$502$	18.8585	+	18.8585i	0.841698	+	0.841698i
$503$	12.5572	−	6.39824i	0.559900	−	0.285283i	−0.151050	−	0.988526i	$-0.548265\pi$
$503$	12.5572	−	6.39824i	0.559900	−	0.285283i	0.710950	+	0.703243i	$0.248265\pi$
$504$	−0.608274	+	2.48387i	−0.0270947	+	0.110640i
$505$	−8.59042	+	14.1354i	−0.382268	+	0.629018i
$506$	7.76594	+	10.6889i	0.345238	+	0.475179i
$507$	4.33936	+	22.0774i	0.192718	+	0.980494i
$508$	3.32094	−	20.9676i	0.147343	−	0.930286i
$509$	−12.6947	−	9.22324i	−0.562683	−	0.408813i	0.269757	−	0.962928i	$-0.413057\pi$
$509$	−12.6947	−	9.22324i	−0.562683	−	0.408813i	−0.832440	+	0.554115i	$0.813057\pi$
$510$	20.4082	+	0.772646i	0.903692	+	0.0342133i
$511$	10.3275	+	7.50339i	0.456863	+	0.331930i
$512$	−0.987688	+	0.156434i	−0.0436501	+	0.00691349i
$513$	−6.47469	+	1.77851i	−0.285865	+	0.0785230i
$514$	3.01580	−	4.15089i	0.133021	−	0.183088i
$515$	21.7404	+	35.1842i	0.957997	+	1.55040i
$516$	0.746901	+	0.501521i	0.0328805	+	0.0220782i
$517$	−4.38664	−	0.694775i	−0.192924	−	0.0305562i
$518$	2.79634	−	5.48812i	0.122864	−	0.241134i
$519$	20.3407	−	0.752911i	0.892857	−	0.0330491i
$520$	−0.0850215	−	0.203131i	−0.00372844	−	0.00890788i
$521$		−	18.0504i		−	0.790801i	−0.918509	−	0.395401i	$-0.870606\pi$
$521$		−	18.0504i		−	0.790801i	0.918509	−	0.395401i	$-0.129394\pi$
$522$	−0.876226	−	3.72421i	−0.0383514	−	0.163004i
$523$	6.90760	+	13.5569i	0.302048	+	0.592803i	0.991285	−	0.131733i	$-0.0420542\pi$
$523$	6.90760	+	13.5569i	0.302048	+	0.592803i	−0.689237	+	0.724536i	$0.742054\pi$
$524$	−7.70812	−	5.60028i	−0.336731	−	0.244649i
$525$	−7.23287	+	1.47731i	−0.315668	+	0.0644751i
$526$	−30.6349			−1.33574
$527$	1.87356	−	29.2999i	0.0816134	−	1.27632i
$528$	5.46220	−	3.04270i	0.237712	−	0.132416i
$529$	5.64526	+	7.77003i	0.245446	+	0.337827i
$530$	19.8913	−	1.63956i	0.864021	−	0.0712178i
$531$	2.68486	+	3.17265i	0.116513	+	0.137681i
$532$	−0.778884	−	0.778884i	−0.0337689	−	0.0337689i
$533$	−0.185755	−	0.185755i	−0.00804594	−	0.00804594i
$534$	7.38022	−	10.9911i	0.319373	−	0.475634i
$535$	9.75089	−	2.37918i	0.421568	−	0.102861i
$536$	−2.57225	+	0.835775i	−0.111104	+	0.0361000i
$537$	31.0386	+	14.3946i	1.33941	+	0.621172i
$538$	−12.0176	−	23.5858i	−0.518115	−	1.01686i
$539$	−18.3211	+	13.3110i	−0.789145	+	0.573347i
$540$	−0.419990	−	11.6114i	−0.0180735	−	0.499673i
$541$	6.45239	+	19.8584i	0.277410	+	0.853780i	0.988572	+	0.150752i	$0.0481694\pi$
$541$	6.45239	+	19.8584i	0.277410	+	0.853780i	−0.711162	+	0.703028i	$0.751831\pi$
$542$	12.4012	−	1.96416i	0.532677	−	0.0843677i
$543$	0.525993	−	4.35923i	0.0225725	−	0.187072i
$544$	−5.01507	+	1.62950i	−0.215019	+	0.0698641i
$545$	−1.61894	−	19.6412i	−0.0693478	−	0.841334i
$546$	0.136526	−	0.0500149i	0.00584276	−	0.00214044i
$547$	−20.2102	+	10.2976i	−0.864127	+	0.440295i	−0.829106	−	0.559092i	$-0.811150\pi$
$547$	−20.2102	+	10.2976i	−0.864127	+	0.440295i	−0.0350213	+	0.999387i	$0.511150\pi$
$548$	18.6785	+	2.95839i	0.797908	+	0.126376i
$549$	36.4992	+	8.93826i	1.55775	+	0.381476i
$550$	14.6804	+	10.5008i	0.625973	+	0.447756i
$551$	1.56730	+	0.509245i	0.0667691	+	0.0216946i
$552$	−5.53807	+	3.08496i	−0.235716	+	0.131305i
$553$	4.82093	−	4.82093i	0.205007	−	0.205007i
$554$	−1.94348	+	5.98142i	−0.0825706	+	0.254126i
$555$	−5.42049	+	27.4556i	−0.230087	+	1.16542i
$556$	11.1818	−	8.12403i	0.474212	−	0.344535i
$557$	−1.88571	+	1.88571i	−0.0799001	+	0.0799001i	−0.745927	−	0.666027i	$-0.767993\pi$
$557$	−1.88571	+	1.88571i	−0.0799001	+	0.0799001i	0.666027	+	0.745927i	$0.267993\pi$
$558$	−16.7024	+	0.169352i	−0.707070	+	0.00716924i
$559$		−	0.0511519i		−	0.00216349i
$560$	1.62150	−	1.00193i	0.0685209	−	0.0423392i
$561$	25.9385	−	20.3529i	1.09512	−	0.859299i
$562$	2.51337	−	1.28063i	0.106020	−	0.0540200i
$563$	2.14843	+	2.14843i	0.0905457	+	0.0905457i	0.750929	−	0.660383i	$-0.229606\pi$
$563$	2.14843	+	2.14843i	0.0905457	+	0.0905457i	−0.660383	+	0.750929i	$0.729606\pi$
$564$	0.583093	−	2.04966i	0.0245527	−	0.0863062i
$565$	−6.50618	+	15.8732i	−0.273717	+	0.667789i
$566$	−26.2310	+	8.52298i	−1.10257	+	0.358248i
$567$	7.67149	+	0.0697128i	0.322172	+	0.00292766i
$568$	−0.0726498	+	0.458693i	−0.00304832	+	0.0192463i
$569$	4.50654	−	13.8697i	0.188924	−	0.581449i	−0.811070	−	0.584949i	$-0.801114\pi$
$569$	4.50654	−	13.8697i	0.188924	−	0.581449i	0.999994	+	0.00350073i	$0.00111432\pi$
$570$	4.37007	+	2.43916i	0.183042	+	0.102165i
$571$	−30.5680	−	22.2089i	−1.27923	−	0.929415i	−0.279701	−	0.960087i	$-0.590235\pi$
$571$	−30.5680	−	22.2089i	−1.27923	−	0.929415i	−0.999530	+	0.0306719i	$0.990235\pi$
$572$	−0.316751	−	0.161393i	−0.0132440	−	0.00674817i
$573$	−24.5501	−	2.96227i	−1.02560	−	0.123750i
$574$	1.33655	−	1.83960i	0.0557864	−	0.0767834i
$575$	−14.8843	−	10.6467i	−0.620717	−	0.443996i
$576$	1.13545	+	2.77683i	0.0473102	+	0.115701i
$577$	19.3704	+	3.06797i	0.806400	+	0.127721i	0.546006	−	0.837781i	$-0.316147\pi$
$577$	19.3704	+	3.06797i	0.806400	+	0.127721i	0.260394	+	0.965502i	$0.416147\pi$
$578$	−9.62840	+	4.90591i	−0.400489	+	0.204059i
$579$	−11.7854	+	4.31747i	−0.489784	+	0.179428i
$580$	−1.48098	+	2.43693i	−0.0614943	+	0.101188i
$581$	9.71015	−	3.15502i	0.402845	−	0.130892i
$582$	12.5183	−	2.46050i	0.518901	−	0.101991i
$583$	22.7837	−	22.7837i	0.943606	−	0.943606i
$584$	14.9756			0.619694
$585$	−0.534779	+	0.387851i	−0.0221104	+	0.0160357i
$586$	7.84398	+	5.69899i	0.324032	+	0.235423i
$587$	5.05543	−	31.9187i	0.208660	−	1.31743i	−0.631622	−	0.775276i	$-0.717611\pi$
$587$	5.05543	−	31.9187i	0.208660	−	1.31743i	0.840282	−	0.542150i	$-0.182389\pi$
$588$	−5.28771	−	9.49241i	−0.218062	−	0.391460i
$589$	3.66876	−	6.18904i	0.151168	−	0.255015i
$590$	0.231627	−	3.08920i	0.00953592	−	0.127180i
$591$	1.42051	−	0.520390i	0.0584319	−	0.0214060i
$592$	−1.13037	−	7.13687i	−0.0464579	−	0.293323i
$593$	8.23845	−	4.19770i	0.338312	−	0.172379i	−0.276578	−	0.960992i	$-0.589200\pi$
$593$	8.23845	−	4.19770i	0.338312	−	0.172379i	0.614890	+	0.788613i	$0.289200\pi$
$594$	−12.6384	−	13.8605i	−0.518560	−	0.568703i
$595$	7.61866	−	6.55586i	0.312335	−	0.268764i
$596$	−4.81136	−	1.56331i	−0.197081	−	0.0640355i
$597$	−7.09095	−	6.58475i	−0.290213	−	0.269496i
$598$	0.321150	+	0.163634i	0.0131328	+	0.00669151i
$599$	−33.3215	+	24.2095i	−1.36148	+	0.989171i	−0.363128	+	0.931739i	$0.618291\pi$
$599$	−33.3215	+	24.2095i	−1.36148	+	0.989171i	−0.998349	+	0.0574321i	$0.981709\pi$
$600$	−5.84589	+	6.38949i	−0.238658	+	0.260850i
$601$	25.9117	−	18.8259i	1.05696	−	0.767925i	0.0834351	−	0.996513i	$-0.473411\pi$
$601$	25.9117	−	18.8259i	1.05696	−	0.767925i	0.973523	+	0.228588i	$0.0734109\pi$
$602$	0.437312	−	0.0692635i	0.0178235	−	0.00282297i
$603$	4.20801	+	6.93741i	0.171364	+	0.282513i
$604$	1.85789	−	2.55716i	0.0755964	−	0.104050i
$605$	4.52656	−	0.373106i	0.184031	−	0.0151689i
$606$	−12.8039	+	0.473935i	−0.520121	+	0.0192523i
$607$	−4.92063	−	31.0676i	−0.199722	−	1.26100i	−0.860124	−	0.510084i	$-0.829614\pi$
$607$	−4.92063	−	31.0676i	−0.199722	−	1.26100i	0.660402	−	0.750912i	$-0.270386\pi$
$608$	−1.27630	−	0.202146i	−0.0517608	−	0.00819810i
$609$	−1.56319	−	1.04964i	−0.0633438	−	0.0425335i
$610$	−14.7228	−	23.8271i	−0.596109	−	0.964730i
$611$	−0.115231	+	0.0374409i	−0.00466176	+	0.00151470i
$612$	8.20428	+	13.5257i	0.331639	+	0.546745i
$613$	−17.3559	−	34.0628i	−0.700996	−	1.37578i	−0.916800	−	0.399346i	$-0.869237\pi$
$613$	−17.3559	−	34.0628i	−0.700996	−	1.37578i	0.215804	−	0.976437i	$-0.430763\pi$
$614$	−19.3098			−0.779280
$615$	−3.56200	+	9.69786i	−0.143634	+	0.391056i
$616$	0.950889	−	2.92653i	0.0383124	−	0.117913i
$617$	−44.4910	+	7.04669i	−1.79114	+	0.283689i	−0.961540	−	0.274666i	$-0.911433\pi$
$617$	−44.4910	+	7.04669i	−1.79114	+	0.283689i	−0.829602	+	0.558355i	$0.811433\pi$
$618$	−13.4785	+	29.0633i	−0.542185	+	1.16910i
$619$			15.4454i			0.620802i	0.950606	+	0.310401i	$0.100463\pi$
$619$			15.4454i			0.620802i	−0.950606	+	0.310401i	$0.899537\pi$
$620$	8.96374	+	8.64010i	0.359993	+	0.346995i
$621$	12.8140	+	14.0530i	0.514206	+	0.563928i
$622$	−14.9532	−	2.36835i	−0.599567	−	0.0949621i
$623$	−1.01926	−	6.43535i	−0.0408357	−	0.257827i
$624$	0.0950861	−	0.141609i	0.00380649	−	0.00566890i
$625$	−23.8881	−	7.37268i	−0.955526	−	0.294907i
$626$			3.17533i			0.126912i
$627$	7.92784	−	1.55823i	0.316607	−	0.0622297i
$628$	−6.14068	−	3.12883i	−0.245040	−	0.124854i
$629$	−11.7745	−	36.2381i	−0.469478	−	1.44491i
$630$	−4.03998	−	4.04680i	−0.160957	−	0.161229i
$631$	−1.38064	+	4.24917i	−0.0549624	+	0.169157i	−0.974769	−	0.223214i	$-0.928345\pi$
$631$	−1.38064	+	4.24917i	−0.0549624	+	0.169157i	0.919807	+	0.392371i	$0.128345\pi$
$632$	1.25119	−	7.89970i	0.0497696	−	0.314233i
$633$	−2.79769	+	23.1861i	−0.111198	+	0.921566i
$634$	−16.6949	+	5.42451i	−0.663041	+	0.215435i
$635$	36.2098	+	30.6951i	1.43694	+	1.21810i
$636$	9.54356	+	12.1627i	0.378427	+	0.482281i
$637$	−0.280474	+	0.550461i	−0.0111128	+	0.0218101i
$638$	0.720173	+	4.54699i	0.0285119	+	0.180017i
$639$	1.38942	−	0.103000i	0.0549646	−	0.00407461i
$640$	0.848056	−	2.06901i	0.0335224	−	0.0817848i
$641$	−2.34890	−	3.23298i	−0.0927759	−	0.127695i	0.760106	−	0.649799i	$-0.225147\pi$
$641$	−2.34890	−	3.23298i	−0.0927759	−	0.127695i	−0.852882	+	0.522104i	$0.825147\pi$
$642$	5.69705	+	5.29035i	0.224845	+	0.208794i
$643$	−14.5289	−	7.40284i	−0.572964	−	0.291940i	0.143402	−	0.989665i	$-0.454196\pi$
$643$	−14.5289	−	7.40284i	−0.572964	−	0.291940i	−0.716366	+	0.697725i	$0.754196\pi$
$644$	−0.964096	+	2.96718i	−0.0379907	+	0.116923i
$645$	−1.82570	+	0.844825i	−0.0718870	+	0.0332650i
$646$	−6.81402			−0.268094
$647$	9.25587	+	18.1657i	0.363886	+	0.714166i	0.998267	−	0.0588547i	$-0.0187449\pi$
$647$	9.25587	+	18.1657i	0.363886	+	0.714166i	−0.634381	+	0.773021i	$0.718745\pi$
$648$	7.32892	−	5.22369i	0.287907	−	0.205206i
$649$	−2.93960	−	4.04602i	−0.115390	−	0.158820i
$650$	0.486891	+	0.0734266i	0.0190974	+	0.00288003i
$651$	−5.96676	+	5.65454i	−0.233856	+	0.221619i
$652$	−17.1076	−	17.1076i	−0.669987	−	0.669987i
$653$	23.0872	+	3.65666i	0.903473	+	0.143096i	0.590850	−	0.806781i	$-0.298792\pi$
$653$	23.0872	+	3.65666i	0.903473	+	0.143096i	0.312623	+	0.949877i	$0.398792\pi$
$654$	12.0097	−	9.42356i	0.469618	−	0.368490i
$655$	19.6527	−	8.22574i	0.767894	−	0.321406i
$656$		−	2.66754i		−	0.104150i
$657$	−10.2894	−	43.7326i	−0.401426	−	1.70617i
$658$	−0.476126	−	0.934449i	−0.0185613	−	0.0364286i
$659$	13.2666	+	40.8303i	0.516793	+	1.59052i	0.779997	+	0.625784i	$0.215221\pi$
$659$	13.2666	+	40.8303i	0.516793	+	1.59052i	−0.263204	+	0.964740i	$0.584779\pi$
$660$	−0.528935	+	13.9710i	−0.0205888	+	0.543820i
$661$	6.26975	−	4.55524i	0.243865	−	0.177178i	−0.459138	−	0.888365i	$-0.651842\pi$
$661$	6.26975	−	4.55524i	0.243865	−	0.177178i	0.703004	+	0.711186i	$0.251842\pi$
$662$	−9.23026	−	18.1154i	−0.358744	−	0.704075i
$663$	0.378417	−	0.815970i	0.0146965	−	0.0316897i
$664$	7.04017	−	9.68996i	0.273212	−	0.376043i
$665$	2.39285	−	0.583845i	0.0927907	−	0.0226405i
$666$	−20.0649	+	8.20454i	−0.777498	+	0.317919i
$667$	−0.730176	−	4.61015i	−0.0282725	−	0.178506i
$668$	−2.63765	+	5.17668i	−0.102054	+	0.200292i
$669$	1.70440	+	2.17215i	0.0658959	+	0.0839803i
$670$	1.39004	−	5.88581i	0.0537021	−	0.227389i
$671$	−43.0039	−	13.9728i	−1.66015	−	0.539414i
$672$	1.33941	+	0.621170i	0.0516689	+	0.0239622i
$673$	−35.5301	−	18.1035i	−1.36958	−	0.697838i	−0.394339	−	0.918965i	$-0.629026\pi$
$673$	−35.5301	−	18.1035i	−1.36958	−	0.697838i	−0.975245	+	0.221127i	$0.929026\pi$
$674$	−8.30159	−	25.5497i	−0.319765	−	0.984136i
$675$	22.6755	+	12.6815i	0.872782	+	0.488111i
$676$	12.9903			0.499627
$677$	−11.6054	+	11.6054i	−0.446030	+	0.446030i	−0.894032	−	0.448002i	$-0.852136\pi$
$677$	−11.6054	+	11.6054i	−0.446030	+	0.446030i	0.448002	+	0.894032i	$0.352136\pi$
$678$	−13.0386	+	2.56276i	−0.500744	+	0.0984222i
$679$	3.69054	−	5.07959i	0.141630	−	0.194937i
$680$	2.71014	−	11.4755i	0.103929	−	0.440064i
$681$	0.158877	+	0.0451979i	0.00608819	+	0.00173199i
$682$	20.0580	+	1.28259i	0.768060	+	0.0491130i
$683$	21.4166	+	21.4166i	0.819485	+	0.819485i	0.986033	−	0.166548i	$-0.0532622\pi$
$683$	21.4166	+	21.4166i	0.819485	+	0.819485i	−0.166548	+	0.986033i	$0.553262\pi$
$684$	0.286594	+	3.86602i	0.0109582	+	0.147821i
$685$	−27.3441	+	32.2568i	−1.04476	+	1.23247i
$686$	−10.7608	−	3.49638i	−0.410848	−	0.133492i
$687$	−43.9544	+	24.4846i	−1.67696	+	0.934147i
$688$	0.367284	−	0.367284i	0.0140026	−	0.0140026i
$689$	0.271628	−	0.835985i	0.0103482	−	0.0318485i
$690$	0.536281	−	14.1650i	0.0204159	−	0.539254i
$691$	12.7062	+	39.1058i	0.483368	+	1.48766i	0.834330	+	0.551265i	$0.185855\pi$
$691$	12.7062	+	39.1058i	0.483368	+	1.48766i	−0.350962	+	0.936390i	$0.614145\pi$
$692$	1.83838	−	11.6071i	0.0698846	−	0.441234i
$693$	−9.19958	−	0.766095i	−0.349463	−	0.0291015i
$694$	5.77479	+	7.94832i	0.219208	+	0.301714i
$695$	2.53882	+	30.8012i	0.0963028	+	1.16836i
$696$	−2.20737	+	0.0817059i	−0.0836702	+	0.00309705i
$697$	−2.20046	−	13.8932i	−0.0833484	−	0.526241i
$698$	−1.32785	−	8.38372i	−0.0502599	−	0.317329i
$699$	−15.2317	+	0.563801i	−0.576115	+	0.0213249i
$700$	0.0315412	+	4.26200i	0.00119215	+	0.161088i
$701$	11.6069	+	15.9756i	0.438388	+	0.603390i	0.969853	−	0.243691i	$-0.0783582\pi$
$701$	11.6069	+	15.9756i	0.438388	+	0.603390i	−0.531465	+	0.847080i	$0.678358\pi$
$702$	−0.478867	−	0.180380i	−0.0180737	−	0.00680802i
$703$	1.46067	−	9.22233i	0.0550903	−	0.347827i
$704$	−1.11551	−	3.43320i	−0.0420425	−	0.129393i
$705$	3.23950	+	3.49444i	0.122007	+	0.131608i
$706$	1.68686	−	5.19163i	0.0634859	−	0.195390i
$707$	−4.45879	+	4.45879i	−0.167690	+	0.167690i
$708$	2.09630	−	1.16773i	0.0787837	−	0.0438862i
$709$	−32.0888	−	10.4263i	−1.20512	−	0.391567i	−0.363477	−	0.931603i	$-0.618410\pi$
$709$	−32.0888	−	10.4263i	−1.20512	−	0.391567i	−0.841642	+	0.540037i	$0.818410\pi$
$710$	−0.792136	−	0.671495i	−0.0297283	−	0.0252008i
$711$	−23.9289	+	1.77389i	−0.897402	+	0.0665259i
$712$	−5.40483	−	5.40483i	−0.202555	−	0.202555i
$713$	−20.3366	−	1.30041i	−0.761611	−	0.0487006i
$714$	7.48837	+	2.13032i	0.280245	+	0.0797251i
$715$	0.676237	−	0.417848i	0.0252898	−	0.0156266i
$716$	11.6108	−	15.9809i	0.433916	−	0.597234i
$717$	9.34218	−	1.83622i	0.348890	−	0.0685750i
$718$	−11.6632	+	11.6632i	−0.435268	+	0.435268i
$719$	−13.6428			−0.508790			−0.254395	−	0.967100i	$-0.581876\pi$
$719$	−13.6428			−0.508790			−0.254395	+	0.967100i	$0.581876\pi$
$720$	−6.62473	−	1.05498i	−0.246889	−	0.0393168i
$721$	4.87218	+	14.9950i	0.181450	+	0.558444i
$722$	15.4413	+	7.86774i	0.574666	+	0.292807i
$723$	3.09223	+	1.43407i	0.115001	+	0.0533335i
$724$	−2.41098	−	0.783376i	−0.0896034	−	0.0291139i
$725$	−2.93683	−	5.65992i	−0.109071	−	0.210204i
$726$	2.17178	+	2.76781i	0.0806025	+	0.102723i
$727$	17.6871	−	34.7128i	0.655977	−	1.28743i	−0.288068	−	0.957610i	$-0.593013\pi$
$727$	17.6871	−	34.7128i	0.655977	−	1.28743i	0.944045	−	0.329817i	$-0.106987\pi$
$728$	−0.0131320	−	0.0829124i	−0.000486706	−	0.00307294i
$729$	−20.2900	−	17.8133i	−0.751483	−	0.659752i
$730$	−17.3908	+	28.6164i	−0.643664	+	1.05914i
$731$	1.60993	−	2.21588i	0.0595453	−	0.0819571i
$732$	9.12776	−	19.6819i	0.337372	−	0.727465i
$733$	−17.8284	−	34.9901i	−0.658506	−	1.29239i	−0.942706	−	0.333625i	$-0.891728\pi$
$733$	−17.8284	−	34.9901i	−0.658506	−	1.29239i	0.284200	−	0.958765i	$-0.408272\pi$
$734$	4.42761	−	3.21685i	0.163426	−	0.118736i
$735$	24.2793	+	0.919202i	0.895555	+	0.0339053i
$736$	1.13101	+	3.48088i	0.0416895	+	0.128307i
$737$	−4.43248	−	8.69922i	−0.163272	−	0.320440i
$738$	−7.78991	+	1.83280i	−0.286750	+	0.0674662i
$739$			43.6964i			1.60740i	0.595036	+	0.803699i	$0.297138\pi$
$739$			43.6964i			1.60740i	−0.595036	+	0.803699i	$0.702862\pi$
$740$	14.9503	+	6.12791i	0.549584	+	0.225266i
$741$	0.173404	−	0.136063i	0.00637015	−	0.00499840i
$742$	7.51489	+	1.19024i	0.275880	+	0.0436951i
$743$	−26.7468	−	26.7468i	−0.981244	−	0.981244i	0.0185832	−	0.999827i	$-0.494084\pi$
$743$	−26.7468	−	26.7468i	−0.981244	−	0.981244i	−0.999827	+	0.0185832i	$0.994084\pi$
$744$	−1.76386	+	9.48097i	−0.0646661	+	0.347589i
$745$	8.57461	−	7.37845i	0.314149	−	0.270326i
$746$	16.5668	+	22.8022i	0.606552	+	0.834848i
$747$	−33.1343	−	13.9014i	−1.21232	−	0.508626i
$748$	−8.64191	−	16.9607i	−0.315980	−	0.620145i
$749$	3.82624			0.139808
$750$	−5.42077	−	18.5907i	−0.197938	−	0.678838i
$751$	2.62735	−	8.08614i	0.0958732	−	0.295067i	−0.891607	−	0.452810i	$-0.850422\pi$
$751$	2.62735	−	8.08614i	0.0958732	−	0.295067i	0.987480	+	0.157743i	$0.0504216\pi$
$752$	−1.09623	−	0.558556i	−0.0399753	−	0.0203684i
$753$	−33.8498	−	31.4334i	−1.23356	−	1.14550i
$754$	0.0738202	+	0.101605i	0.00268837	+	0.00370023i
$755$	2.72888	+	6.51977i	0.0993142	+	0.237279i
$756$	0.893704	−	4.33822i	0.0325037	−	0.157780i
$757$	−4.03859	−	25.4987i	−0.146785	−	0.926765i	−0.945634	−	0.325233i	$-0.894557\pi$
$757$	−4.03859	−	25.4987i	−0.146785	−	0.926765i	0.798849	−	0.601532i	$-0.205443\pi$
$758$	6.47848	−	12.7147i	0.235309	−	0.461820i
$759$	−14.1266	−	18.0035i	−0.512764	−	0.653485i
$760$	1.86842	−	2.20410i	0.0677746	−	0.0799510i
$761$	−35.3984	+	11.5016i	−1.28319	+	0.416934i	−0.869703	−	0.493576i	$-0.835690\pi$
$761$	−35.3984	+	11.5016i	−1.28319	+	0.416934i	−0.413488	+	0.910510i	$0.635690\pi$
$762$	−4.40475	+	36.5048i	−0.159567	+	1.32243i
$763$	1.17528	−	7.42040i	0.0425478	−	0.268636i
$764$	−4.41178	+	13.5781i	−0.159613	+	0.491237i
$765$	−35.3734	−	0.0298300i	−1.27893	−	0.00107850i
$766$	5.85474	+	18.0190i	0.211540	+	0.651055i
$767$	−0.121564	−	0.0619397i	−0.00438940	−	0.00223651i
$768$	1.69953	−	0.334046i	0.0613266	−	0.0120539i
$769$		−	21.8002i		−	0.786137i	−0.919509	−	0.393068i	$-0.871414\pi$
$769$		−	21.8002i		−	0.786137i	0.919509	−	0.393068i	$-0.128586\pi$
$770$	4.48798	+	5.21555i	0.161736	+	0.187955i
$771$	−4.95401	+	7.37785i	−0.178414	+	0.265707i
$772$	1.13361	+	7.15730i	0.0407993	+	0.257597i
$773$	−50.2762	−	7.96297i	−1.80831	−	0.286408i	−0.841191	−	0.540738i	$-0.818145\pi$
$773$	−50.2762	−	7.96297i	−1.80831	−	0.286408i	−0.967118	+	0.254330i	$0.918145\pi$
$774$	−1.32492	−	0.820213i	−0.0476231	−	0.0294820i
$775$	−26.9195	+	7.09499i	−0.966978	+	0.254860i
$776$		−	7.36573i		−	0.264414i
$777$	−4.48847	+	9.67835i	−0.161023	+	0.347209i
$778$	−29.7298	+	4.70874i	−1.06587	+	0.168817i
$779$	1.06519	−	3.27831i	0.0381643	−	0.117458i
$780$	0.160175	+	0.346145i	0.00573518	+	0.0123940i
$781$	−1.67646			−0.0599886
$782$	8.76195	+	17.1963i	0.313327	+	0.614938i
$783$	1.75523	+	6.38996i	0.0627269	+	0.228359i
$784$	−5.96633	+	1.93858i	−0.213083	+	0.0692350i
$785$	13.1098	−	8.10060i	0.467910	−	0.289123i
$786$	13.7005	+	9.19948i	0.488681	+	0.328135i
$787$	−27.8609	−	4.41274i	−0.993135	−	0.157297i	−0.361341	−	0.932434i	$-0.617681\pi$
$787$	−27.8609	−	4.41274i	−0.993135	−	0.157297i	−0.631794	+	0.775137i	$0.717681\pi$
$788$	−0.136635	−	0.862678i	−0.00486741	−	0.0307316i
$789$	53.0249	−	1.96272i	1.88774	−	0.0698746i
$790$	13.6423	+	11.5646i	0.485372	+	0.411451i
$791$	−3.84392	+	5.29071i	−0.136674	+	0.188116i
$792$	−9.25939	+	5.61645i	−0.329018	+	0.199572i
$793$	−1.21835	+	0.192968i	−0.0432650	+	0.00685251i
$794$	−15.0123	+	10.9071i	−0.532767	+	0.387078i
$795$	−34.3240	+	4.11224i	−1.21735	+	0.145846i
$796$	−4.51990	+	3.28390i	−0.160204	+	0.116395i
$797$	3.29931	+	1.68108i	0.116867	+	0.0595469i	0.511447	−	0.859315i	$-0.329110\pi$
$797$	3.29931	+	1.68108i	0.116867	+	0.0595469i	−0.394579	+	0.918862i	$0.629110\pi$
$798$	1.39805	+	1.29824i	0.0494903	+	0.0459573i
$799$	−6.17017	−	2.00481i	−0.218285	−	0.0709250i
$800$	2.96878	+	4.02323i	0.104962	+	0.142242i
$801$	−12.0700	+	19.4970i	−0.426472	+	0.688894i
$802$	−7.31509	+	3.72722i	−0.258305	+	0.131613i
$803$	8.45685	+	53.3944i	0.298436	+	1.88425i
$804$	4.39868	−	1.61141i	0.155129	−	0.0568302i
$805$	−4.55032	−	5.28799i	−0.160378	−	0.186377i
$806$	0.503436	−	0.217244i	0.0177328	−	0.00765208i
$807$	22.3119	+	40.0539i	0.785416	+	1.40997i
$808$	−1.15720	+	7.30630i	−0.0407103	+	0.257035i
$809$	30.6970	+	22.3027i	1.07925	+	0.784120i	0.977552	−	0.210695i	$-0.0675728\pi$
$809$	30.6970	+	22.3027i	1.07925	+	0.784120i	0.101697	+	0.994815i	$0.467573\pi$
$810$	1.47086	+	20.0708i	0.0516809	+	0.705216i
$811$	28.1030			0.986829			0.493415	−	0.869794i	$-0.335749\pi$
$811$	28.1030			0.986829			0.493415	+	0.869794i	$0.335749\pi$
$812$	−0.768691	+	0.768691i	−0.0269758	+	0.0269758i
$813$	−21.3390	+	4.19421i	−0.748390	+	0.147097i
$814$	24.8077	−	8.06051i	0.869509	−	0.282521i
$815$	52.5572	−	12.8237i	1.84100	−	0.449196i
$816$	8.57602	−	3.14174i	0.300221	−	0.109983i
$817$	0.598040	−	0.304717i	0.0209228	−	0.0106607i
$818$	2.57109	+	0.407220i	0.0898960	+	0.0142381i
$819$	−0.233103	+	0.0953160i	−0.00814529	+	0.00333061i
$820$	5.09732	+	3.09776i	0.178006	+	0.108178i
$821$	−17.6627	+	24.3106i	−0.616432	+	0.848446i	−0.997087	−	0.0762714i	$-0.975698\pi$
$821$	−17.6627	+	24.3106i	−0.616432	+	0.848446i	0.380655	+	0.924717i	$0.375698\pi$
$822$	−32.5196	−	3.92388i	−1.13425	−	0.136861i
$823$	−29.2360	−	14.8965i	−1.01910	−	0.519260i	−0.137128	−	0.990553i	$-0.543787\pi$
$823$	−29.2360	−	14.8965i	−1.01910	−	0.519260i	−0.881976	+	0.471294i	$0.843787\pi$
$824$	14.9639	+	10.8719i	0.521291	+	0.378740i
$825$	−26.0825	−	17.2349i	−0.908076	−	0.600044i
$826$	0.364935	−	1.12315i	0.0126977	−	0.0390795i
$827$	−0.438718	+	2.76996i	−0.0152557	+	0.0963209i	−0.994141	−	0.108088i	$-0.965527\pi$
$827$	−0.438718	+	2.76996i	−0.0152557	+	0.0963209i	0.978886	+	0.204409i	$0.0655272\pi$
$828$	9.38800	−	5.69446i	0.326256	−	0.197896i
$829$	35.1851	−	11.4323i	1.22203	−	0.397061i	0.374208	−	0.927345i	$-0.377915\pi$
$829$	35.1851	−	11.4323i	1.22203	−	0.397061i	0.847820	+	0.530284i	$0.177915\pi$
$830$	10.3407	+	24.7056i	0.358930	+	0.857544i
$831$	2.98069	−	10.4776i	0.103399	−	0.363462i
$832$	−0.0696353	−	0.0696353i	−0.00241417	−	0.00241417i
$833$	−29.4749	+	15.0182i	−1.02125	+	0.520351i
$834$	−18.8336	+	14.7780i	−0.652155	+	0.511720i
$835$	−6.82893	−	11.0518i	−0.236325	−	0.382463i
$836$		−	4.66472i		−	0.161333i
$837$	28.8988	−	1.36322i	0.998889	−	0.0471197i
$838$	−8.66654	+	8.66654i	−0.299381	+	0.299381i
$839$	22.3962	−	16.2718i	0.773201	−	0.561764i	−0.129730	−	0.991549i	$-0.541411\pi$
$839$	22.3962	−	16.2718i	0.773201	−	0.561764i	0.902931	+	0.429786i	$0.141411\pi$
$840$	−2.74241	+	1.83809i	−0.0946220	+	0.0634201i
$841$	−8.45891	+	26.0339i	−0.291687	+	0.897719i
$842$	8.60844	−	8.60844i	0.296666	−	0.296666i
$843$	−4.26826	+	2.37762i	−0.147007	+	0.0818896i
$844$	12.8237	+	4.16667i	0.441409	+	0.143423i
$845$	−15.0854	+	24.8228i	−0.518953	+	0.853930i
$846$	−0.877938	+	3.58504i	−0.0301841	+	0.123256i
$847$	1.71013	+	0.270858i	0.0587607	+	0.00930679i
$848$	7.95295	−	4.05223i	0.273106	−	0.139154i
$849$	44.8563	−	16.4327i	1.53947	−	0.563969i
$850$	18.7809	+	18.5050i	0.644179	+	0.634715i
$851$	−25.1523	+	8.17247i	−0.862208	+	0.280148i
$852$	0.0963595	−	0.798590i	0.00330122	−	0.0273592i
$853$	31.5969	−	5.00446i	1.08186	−	0.171350i	0.410042	−	0.912067i	$-0.365514\pi$
$853$	31.5969	−	5.00446i	1.08186	−	0.171350i	0.671817	+	0.740717i	$0.265514\pi$
$854$	−3.29949	−	10.1548i	−0.112906	−	0.347489i
$855$	−7.72028	−	3.94188i	−0.264028	−	0.134810i
$856$	3.63140	−	2.63837i	0.124119	−	0.0901776i
$857$	−13.2433	−	25.9913i	−0.452381	−	0.887847i	−0.998735	−	0.0502928i	$-0.983985\pi$
$857$	−13.2433	−	25.9913i	−0.452381	−	0.887847i	0.546354	−	0.837555i	$-0.316015\pi$
$858$	0.558593	+	0.259055i	0.0190701	+	0.00884400i
$859$	11.0641	−	3.59496i	0.377504	−	0.122658i	−0.114118	−	0.993467i	$-0.536404\pi$
$859$	11.0641	−	3.59496i	0.377504	−	0.122658i	0.491622	+	0.870809i	$0.336404\pi$
$860$	0.275313	+	1.12835i	0.00938810	+	0.0384765i
$861$	−2.19552	+	3.26973i	−0.0748232	+	0.111432i
$862$	−1.07525	−	1.07525i	−0.0366231	−	0.0366231i
$863$	−20.3587	−	20.3587i	−0.693017	−	0.693017i	0.269878	−	0.962895i	$-0.413017\pi$
$863$	−20.3587	−	20.3587i	−0.693017	−	0.693017i	−0.962895	+	0.269878i	$0.913017\pi$
$864$	−2.14321	−	4.73357i	−0.0729135	−	0.161039i
$865$	20.0447	+	16.9919i	0.681541	+	0.577743i
$866$	−0.616292	−	0.848254i	−0.0209425	−	0.0288248i
$867$	16.3511	−	9.10835i	0.555314	−	0.309336i
$868$	2.53897	+	4.00986i	0.0861783	+	0.136104i
$869$	28.8724			0.979429
$870$	2.40724	−	4.31288i	0.0816132	−	0.146220i
$871$	−0.215481	−	0.156556i	−0.00730131	−	0.00530471i
$872$	−4.00128	−	7.85296i	−0.135500	−	0.265935i
$873$	−21.5099	+	5.06081i	−0.727999	+	0.171283i
$874$			4.72951i			0.159978i
$875$	−8.18076	−	4.88910i	−0.276560	−	0.165282i
$876$	−25.9207	+	0.959457i	−0.875780	+	0.0324170i
$877$	22.1406	−	43.4534i	0.747636	−	1.46732i	−0.131787	−	0.991278i	$-0.542072\pi$
$877$	22.1406	−	43.4534i	0.747636	−	1.46732i	0.879423	−	0.476040i	$-0.157928\pi$
$878$	2.52489	+	0.399903i	0.0852109	+	0.0134961i
$879$	−13.9420	−	9.36163i	−0.470252	−	0.315760i
$880$	7.85582	+	1.85530i	0.264820	+	0.0625421i
$881$	−28.2950	+	38.9448i	−0.953284	+	1.31208i	−0.00323147	+	0.999995i	$0.501029\pi$
$881$	−28.2950	+	38.9448i	−0.953284	+	1.31208i	−0.950053	+	0.312089i	$0.898971\pi$
$882$	9.76048	+	16.0913i	0.328652	+	0.541823i
$883$	9.56677	−	1.51523i	0.321947	−	0.0509915i	0.00663088	−	0.999978i	$-0.497889\pi$
$883$	9.56677	−	1.51523i	0.321947	−	0.0509915i	0.315317	+	0.948987i	$0.397889\pi$
$884$	−0.420120	−	0.305235i	−0.0141302	−	0.0102662i
$885$	−0.202996	+	5.36182i	−0.00682363	+	0.180236i
$886$	23.2967	+	16.9260i	0.782668	+	0.568642i
$887$	0.342998	−	2.16560i	0.0115167	−	0.0727139i	−0.981261	−	0.192685i	$-0.938280\pi$
$887$	0.342998	−	2.16560i	0.0115167	−	0.0727139i	0.992777	+	0.119972i	$0.0382803\pi$
$888$	2.41376	+	12.2805i	0.0810005	+	0.412108i
$889$	10.6366	+	14.6400i	0.356739	+	0.491010i
$890$	16.6045	−	4.05142i	0.556582	−	0.135804i
$891$	22.7634	+	23.1809i	0.762603	+	0.776590i
$892$	1.42033	−	0.723695i	0.0475562	−	0.0242311i
$893$	−1.12418	−	1.12418i	−0.0376194	−	0.0376194i
$894$	8.42797	+	2.39762i	0.281874	+	0.0801883i
$895$	17.0540	+	40.7450i	0.570054	+	1.36196i
$896$	0.501041	−	0.689624i	0.0167386	−	0.0230387i
$897$	−0.566352	−	0.262654i	−0.0189099	−	0.00876975i
$898$	0.873883	−	0.873883i	0.0291619	−	0.0291619i
$899$	−6.10804	−	3.62075i	−0.203715	−	0.120759i
$900$	9.70909	−	11.4339i	0.323636	−	0.381129i
$901$	38.0782	−	27.6654i	1.26857	−	0.921668i
$902$	9.51093	−	1.50638i	0.316679	−	0.0501571i
$903$	−0.752491	+	0.147904i	−0.0250413	+	0.00492192i
$904$			7.67187i			0.255163i
$905$	4.29675	−	3.69736i	0.142829	−	0.122904i
$906$	−3.05192	+	4.54514i	−0.101393	+	0.151002i
$907$	−14.5058	+	28.4692i	−0.481656	+	0.945303i	0.514482	+	0.857501i	$0.327984\pi$
$907$	−14.5058	+	28.4692i	−0.481656	+	0.945303i	−0.996138	+	0.0878020i	$0.972016\pi$
$908$	0.0432959	−	0.0849731i	0.00143683	−	0.00281993i
$909$	22.1314	−	1.64064i	0.734052	−	0.0544165i
$910$	0.173685	+	0.0711909i	0.00575760	+	0.00235995i
$911$	−18.7511	−	25.8086i	−0.621250	−	0.855078i	0.376193	−	0.926541i	$-0.377233\pi$
$911$	−18.7511	−	25.8086i	−0.621250	−	0.855078i	−0.997443	+	0.0714637i	$0.977233\pi$
$912$	2.22205	+	0.268118i	0.0735796	+	0.00887826i
$913$	38.5246	+	19.6292i	1.27498	+	0.649633i
$914$	−23.0405	−	16.7399i	−0.762112	−	0.553706i
$915$	27.0097	+	40.2982i	0.892915	+	1.33222i
$916$	8.97655	+	27.6270i	0.296594	+	0.912821i
$917$	8.02169	−	1.27051i	0.264900	−	0.0419560i
$918$	−15.0671	−	22.8856i	−0.497288	−	0.755337i
$919$	−36.5432	−	11.8736i	−1.20545	−	0.391674i	−0.363685	−	0.931522i	$-0.618482\pi$
$919$	−36.5432	−	11.8736i	−1.20545	−	0.391674i	−0.841763	+	0.539848i	$0.818482\pi$
$920$	−7.96493	−	1.88107i	−0.262596	−	0.0620170i
$921$	33.4227	−	1.23714i	1.10131	−	0.0407652i
$922$	−8.62373	+	16.9250i	−0.284008	+	0.557396i
$923$	−0.0407500	+	0.0207632i	−0.00134130	+	0.000683428i
$924$	−1.45836	+	5.12636i	−0.0479766	+	0.168645i
$925$	−29.0711	+	21.4519i	−0.955853	+	0.705334i
$926$	−28.8801	−	9.38372i	−0.949060	−	0.308368i
$927$	21.4675	−	51.1682i	0.705084	−	1.68058i
$928$	−0.199501	+	1.25960i	−0.00654893	+	0.0413483i
$929$	−13.5413			−0.444275			−0.222138	−	0.975015i	$-0.571303\pi$
$929$	−13.5413			−0.444275			−0.222138	+	0.975015i	$0.571303\pi$
$930$	−16.0686	−	14.3806i	−0.526910	−	0.471557i
$931$	−8.10651			−0.265680
$932$	−1.37663	+	8.69169i	−0.0450930	+	0.284706i
$933$	26.0337	+	3.14127i	0.852304	+	0.102841i
$934$	14.6284	+	4.75304i	0.478655	+	0.155524i
$935$	42.4454	+	3.18254i	1.38811	+	0.104080i
$936$	−0.155509	+	0.251198i	−0.00508296	+	0.00821067i
$937$	15.7930	−	8.04692i	0.515934	−	0.262881i	−0.176580	−	0.984286i	$-0.556503\pi$
$937$	15.7930	−	8.04692i	0.515934	−	0.262881i	0.692513	+	0.721405i	$0.256503\pi$
$938$	1.04667	−	2.05420i	0.0341749	−	0.0670721i
$939$	−0.203438	−	5.49608i	−0.00663893	−	0.179358i
$940$	2.34035	−	1.44611i	0.0763339	−	0.0471669i
$941$	0.327295	+	0.106345i	0.0106695	+	0.00346673i	0.314347	−	0.949308i	$-0.398214\pi$
$941$	0.327295	+	0.106345i	0.0106695	+	0.00346673i	−0.303677	+	0.952775i	$0.598214\pi$
$942$	10.8291	+	5.02216i	0.352833	+	0.163631i
$943$	−9.64303	+	1.52731i	−0.314020	+	0.0497359i
$944$	−0.428115	−	1.31760i	−0.0139339	−	0.0428843i
$945$	7.25194	+	6.74564i	0.235906	+	0.219436i
$946$	1.51693	+	1.10212i	0.0493198	+	0.0358329i
$947$	−43.0772	−	21.9489i	−1.39982	−	0.713244i	−0.418969	−	0.908000i	$-0.637609\pi$
$947$	−43.0772	−	21.9489i	−1.39982	−	0.713244i	−0.980852	+	0.194756i	$0.937609\pi$
$948$	−1.65952	+	13.7535i	−0.0538988	+	0.446692i
$949$	0.866857	+	1.19313i	0.0281394	+	0.0387305i
$950$	2.04199	+	6.12988i	0.0662510	+	0.198879i
$951$	28.5492	−	10.4587i	0.925770	−	0.339147i
$952$	2.04067	−	4.00504i	0.0661385	−	0.129804i
$953$	−12.7473	+	25.0179i	−0.412924	+	0.810410i	0.587075	+	0.809532i	$0.300279\pi$
$953$	−12.7473	+	25.0179i	−0.412924	+	0.810410i	−1.00000		0.000877443i	$0.999721\pi$
$954$	−17.2979	−	20.4405i	−0.560039	−	0.661786i
$955$	−20.8226	−	24.1983i	−0.673805	−	0.783038i
$956$		−	5.49691i		−	0.177783i
$957$	−1.53784	−	7.82409i	−0.0497113	−	0.252917i
$958$	−11.8728	+	1.88047i	−0.383593	+	0.0607552i
$959$	−13.0417	+	9.47538i	−0.421140	+	0.305976i
$960$	−1.33531	+	3.63551i	−0.0430971	+	0.117336i
$961$	−21.2673	+	22.5545i	−0.686041	+	0.727563i
$962$	0.503173	−	0.503173i	0.0162230	−	0.0162230i
$963$	−10.1998	−	8.79189i	−0.328683	−	0.283315i
$964$	1.15673	−	1.59210i	0.0372558	−	0.0512782i
$965$	−14.9931	−	6.14546i	−0.482646	−	0.197829i
$966$	1.47862	−	5.19756i	0.0475738	−	0.167229i
$967$	−22.0579	−	22.0579i	−0.709335	−	0.709335i	0.257061	−	0.966395i	$-0.417246\pi$
$967$	−22.0579	−	22.0579i	−0.709335	−	0.709335i	−0.966395	+	0.257061i	$0.917246\pi$
$968$	1.80982	−	0.922148i	0.0581698	−	0.0296390i
$969$	11.7942	−	0.436561i	0.378883	−	0.0140244i
$970$	14.0750	+	8.55368i	0.451920	+	0.274642i
$971$	24.0889	+	33.1555i	0.773048	+	1.06401i	0.996015	+	0.0891834i	$0.0284257\pi$
$971$	24.0889	+	33.1555i	0.773048	+	1.06401i	−0.222967	+	0.974826i	$0.571574\pi$
$972$	−12.3507	+	9.51105i	−0.396149	+	0.305067i
$973$	−1.84306	+	11.6366i	−0.0590859	+	0.373053i
$974$	4.96517	+	3.60741i	0.159094	+	0.115589i
$975$	−0.847447	−	0.0958974i	−0.0271400	−	0.00307117i
$976$	−10.1337	−	7.36254i	−0.324371	−	0.235669i
$977$	54.8305	−	8.68429i	1.75418	−	0.277835i	0.805163	−	0.593054i	$-0.202078\pi$
$977$	54.8305	−	8.68429i	1.75418	−	0.277835i	0.949019	+	0.315219i	$0.102078\pi$
$978$	30.7071	+	28.5150i	0.981904	+	0.911808i
$979$	16.2184	−	22.3227i	0.518342	−	0.713437i
$980$	3.22421	−	13.6521i	0.102993	−	0.436101i
$981$	−20.1835	+	17.0804i	−0.644410	+	0.545334i
$982$	32.0148	+	5.07065i	1.02163	+	0.161811i
$983$	15.8698	−	31.1463i	0.506169	−	0.993412i	−0.486629	−	0.873609i	$-0.661774\pi$
$983$	15.8698	−	31.1463i	0.506169	−	0.993412i	0.992798	−	0.119803i	$-0.0382264\pi$
$984$	0.170904	+	4.61715i	0.00544822	+	0.147189i
$985$	1.80714	+	0.740719i	0.0575802	+	0.0236013i
$986$			6.72485i			0.214163i
$987$	0.883978	+	1.58690i	0.0281373	+	0.0505116i
$988$	−0.0577729	−	0.113386i	−0.00183800	−	0.00360728i
$989$	−1.53800	−	1.11743i	−0.0489057	−	0.0355321i
$990$	0.0204209	−	24.2158i	0.000649017	−	0.769628i
$991$	−5.92711			−0.188281			−0.0941404	−	0.995559i	$-0.530010\pi$
$991$	−5.92711			−0.188281			−0.0941404	+	0.995559i	$0.530010\pi$
$992$	5.17467	+	2.05494i	0.164296	+	0.0652444i
$993$	17.1370	+	30.7640i	0.543825	+	0.976265i
$994$	−0.232689	−	0.320269i	−0.00738044	−	0.0101583i
$995$	−1.02624	−	12.4505i	−0.0325341	−	0.394707i
$996$	−11.5648	+	17.2231i	−0.366444	+	0.545734i
$997$	−4.95636	−	4.95636i	−0.156969	−	0.156969i	0.624253	−	0.781222i	$-0.285403\pi$
$997$	−4.95636	−	4.95636i	−0.156969	−	0.156969i	−0.781222	+	0.624253i	$0.785403\pi$
$998$	−13.6302	−	13.6302i	−0.431455	−	0.431455i
$999$	34.2039	−	15.4865i	1.08217	−	0.489970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bk.a.47.17	✓	512
3.2	odd	2	inner	930.2.bk.a.47.52	yes	512
5.3	odd	4	inner	930.2.bk.a.233.63	yes	512
15.8	even	4	inner	930.2.bk.a.233.4	yes	512
31.2	even	5	inner	930.2.bk.a.467.4	yes	512
93.2	odd	10	inner	930.2.bk.a.467.63	yes	512
155.33	odd	20	inner	930.2.bk.a.653.52	yes	512
465.188	even	20	inner	930.2.bk.a.653.17	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bk.a.47.17	✓	512	1.1	even	1	trivial
930.2.bk.a.47.52	yes	512	3.2	odd	2	inner
930.2.bk.a.233.4	yes	512	15.8	even	4	inner
930.2.bk.a.233.63	yes	512	5.3	odd	4	inner
930.2.bk.a.467.4	yes	512	31.2	even	5	inner
930.2.bk.a.467.63	yes	512	93.2	odd	10	inner
930.2.bk.a.653.17	yes	512	465.188	even	20	inner
930.2.bk.a.653.52	yes	512	155.33	odd	20	inner

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bk (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.156434 + 0.987688i) q^{2} +(0.207488 - 1.71958i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.69493 - 1.45849i) q^{5} +(1.66595 + 0.473934i) q^{6} +(0.759514 - 0.386992i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.91390 - 0.713583i) q^{9} +O(q^{10})\)	\(q+(-0.156434 + 0.987688i) q^{2} +(0.207488 - 1.71958i) q^{3} +(-0.951057 - 0.309017i) q^{4} +(1.69493 - 1.45849i) q^{5} +(1.66595 + 0.473934i) q^{6} +(0.759514 - 0.386992i) q^{7} +(0.453990 - 0.891007i) q^{8} +(-2.91390 - 0.713583i) q^{9} +(1.17539 + 1.90223i) q^{10} +(3.43320 + 1.11551i) q^{11} +(-0.728711 + 1.57130i) q^{12} +(0.0972668 - 0.0154055i) q^{13} +(0.263413 + 0.810702i) q^{14} +(-2.15631 - 3.21719i) q^{15} +(0.809017 + 0.587785i) q^{16} +(4.69842 + 2.39396i) q^{17} +(1.16063 - 2.76639i) q^{18} +(0.759541 + 1.04542i) q^{19} +(-2.06268 + 0.863344i) q^{20} +(-0.507873 - 1.38634i) q^{21} +(-1.63885 + 3.21642i) q^{22} +(1.66161 - 3.26110i) q^{23} +(-1.43796 - 0.965545i) q^{24} +(0.745605 - 4.94409i) q^{25} +0.0984792i q^{26} +(-1.83166 + 4.86261i) q^{27} +(-0.841928 + 0.133348i) q^{28} +(1.03174 - 0.749602i) q^{29} +(3.51490 - 1.62648i) q^{30} +(-2.20598 - 5.11211i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(2.63056 - 5.67219i) q^{33} +(-3.09948 + 4.26608i) q^{34} +(0.722902 - 1.76367i) q^{35} +(2.55077 + 1.57910i) q^{36} +(-5.10943 - 5.10943i) q^{37} +(-1.15137 + 0.586651i) q^{38} +(-0.00630937 - 0.170454i) q^{39} +(-0.530041 - 2.17234i) q^{40} +(-1.56794 - 2.15808i) q^{41} +(1.44872 - 0.284749i) q^{42} +(0.0812549 - 0.513023i) q^{43} +(-2.92045 - 2.12183i) q^{44} +(-5.97962 + 3.04042i) q^{45} +(2.96101 + 2.15130i) q^{46} +(-1.21518 + 0.192465i) q^{47} +(1.17860 - 1.26921i) q^{48} +(-3.68740 + 5.07527i) q^{49} +(4.76659 + 1.50985i) q^{50} +(5.09147 - 7.58258i) q^{51} +(-0.0972668 - 0.0154055i) q^{52} +(4.05223 - 7.95295i) q^{53} +(-4.51621 - 2.56979i) q^{54} +(7.44601 - 3.11657i) q^{55} -0.852423i q^{56} +(1.95528 - 1.08918i) q^{57} +(0.578973 + 1.13630i) q^{58} +(-1.12082 - 0.814322i) q^{59} +(1.05661 + 3.72607i) q^{60} -12.5259 q^{61} +(5.39426 - 1.37912i) q^{62} +(-2.48930 + 0.585678i) q^{63} +(-0.587785 - 0.809017i) q^{64} +(0.142392 - 0.167974i) q^{65} +(5.19085 + 3.48550i) q^{66} +(-1.91246 - 1.91246i) q^{67} +(-3.72869 - 3.72869i) q^{68} +(-5.26295 - 3.53391i) q^{69} +(1.62887 + 0.989901i) q^{70} +(-0.441681 + 0.143511i) q^{71} +(-1.95869 + 2.27234i) q^{72} +(6.79877 + 13.3433i) q^{73} +(5.84582 - 4.24724i) q^{74} +(-8.34705 - 2.30796i) q^{75} +(-0.399315 - 1.22896i) q^{76} +(3.03926 - 0.481371i) q^{77} +(0.169343 + 0.0204332i) q^{78} +(7.60671 - 2.47157i) q^{79} +(2.22851 - 0.183687i) q^{80} +(7.98160 + 4.15861i) q^{81} +(2.37679 - 1.21104i) q^{82} +(11.8300 + 1.87369i) q^{83} +(0.0546131 + 1.47543i) q^{84} +(11.4551 - 2.79499i) q^{85} +(0.493996 + 0.160509i) q^{86} +(-1.07493 - 1.92969i) q^{87} +(2.55257 - 2.55257i) q^{88} +(2.36200 - 7.26948i) q^{89} +(-2.06757 - 6.38163i) q^{90} +(0.0679137 - 0.0493422i) q^{91} +(-2.58802 + 2.58802i) q^{92} +(-9.24838 + 2.73266i) q^{93} -1.23032i q^{94} +(2.81211 + 0.664132i) q^{95} +(1.06921 + 1.36264i) q^{96} +(6.56292 - 3.34397i) q^{97} +(-4.43595 - 4.43595i) q^{98} +(-9.20797 - 5.70036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q + 8 q^{3} - 12 q^{7}+O(q^{10}) \) 512 * q + 8 * q^3 - 12 * q^7	\( 512 q + 8 q^{3} - 12 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} + 128 q^{16} + 28 q^{22} + 32 q^{25} + 44 q^{27} + 8 q^{28} + 24 q^{30} + 8 q^{31} + 28 q^{33} + 176 q^{37} + 24 q^{42} - 40 q^{45} - 24 q^{46} + 12 q^{48} - 16 q^{51} - 40 q^{55} + 40 q^{57} + 56 q^{58} + 12 q^{60} - 32 q^{61} - 224 q^{63} + 32 q^{66} + 48 q^{67} + 24 q^{70} + 40 q^{73} - 32 q^{75} + 48 q^{76} - 76 q^{78} - 96 q^{81} + 24 q^{85} - 80 q^{87} - 72 q^{88} + 16 q^{90} + 80 q^{91} - 168 q^{93} - 112 q^{97}+O(q^{100}) \) 512 * q + 8 * q^3 - 12 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 + 128 * q^16 + 28 * q^22 + 32 * q^25 + 44 * q^27 + 8 * q^28 + 24 * q^30 + 8 * q^31 + 28 * q^33 + 176 * q^37 + 24 * q^42 - 40 * q^45 - 24 * q^46 + 12 * q^48 - 16 * q^51 - 40 * q^55 + 40 * q^57 + 56 * q^58 + 12 * q^60 - 32 * q^61 - 224 * q^63 + 32 * q^66 + 48 * q^67 + 24 * q^70 + 40 * q^73 - 32 * q^75 + 48 * q^76 - 76 * q^78 - 96 * q^81 + 24 * q^85 - 80 * q^87 - 72 * q^88 + 16 * q^90 + 80 * q^91 - 168 * q^93 - 112 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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