LMFDB - Embedded newform 570.2.bh.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-0.538816 - 2.17018i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.793037 + 2.95965i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-0.538816 - 2.17018i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.793037 + 2.95965i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(0.347622 + 2.20888i) q^{10} +(-1.44519 - 2.50314i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(0.455168 - 0.976112i) q^{13} +(-0.532068 - 3.01751i) q^{14} +(1.40549 + 1.73914i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.258633 + 2.95619i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(3.21906 - 2.93899i) q^{19} +(-0.153782 - 2.23077i) q^{20} +(-1.96954 - 2.34721i) q^{21} +(1.22153 + 2.61957i) q^{22} +(4.56487 - 3.19636i) q^{23} +(0.984808 - 0.173648i) q^{24} +(-4.41935 + 2.33865i) q^{25} +(-0.538510 + 0.932727i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(0.267050 + 3.05240i) q^{28} +(-4.28911 - 3.59899i) q^{29} +(-1.24857 - 1.85502i) q^{30} +(-1.15090 - 0.664472i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(2.36766 + 1.65785i) q^{33} +(0.515298 - 2.92240i) q^{34} +(5.99568 - 3.31574i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-2.45087 - 2.45087i) q^{37} +(-3.46296 + 2.64724i) q^{38} +1.07702i q^{39} +(-0.0412275 + 2.23569i) q^{40} +(3.72962 - 10.2470i) q^{41} +(1.75747 + 2.50993i) q^{42} +(6.89364 - 9.84514i) q^{43} +(-0.988567 - 2.71606i) q^{44} +(-2.00880 - 0.982207i) q^{45} +(-4.82609 + 2.78634i) q^{46} +(8.29119 - 0.725385i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(-2.06846 + 1.19423i) q^{49} +(4.60637 - 1.94458i) q^{50} +(-1.01494 - 2.78852i) q^{51} +(0.617753 - 0.882243i) q^{52} +(-1.14239 - 1.63150i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-4.65357 + 4.48505i) q^{55} -3.06406i q^{56} +(-1.67539 + 4.02406i) q^{57} +(3.95912 + 3.95912i) q^{58} +(4.79584 - 4.02419i) q^{59} +(1.08214 + 1.95678i) q^{60} +(1.11889 - 6.34556i) q^{61} +(1.08861 + 0.762251i) q^{62} +(2.77698 + 1.29493i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-2.36359 - 0.461852i) q^{65} +(-2.21416 - 1.85790i) q^{66} +(0.242677 + 2.77381i) q^{67} +(-0.768041 + 2.86637i) q^{68} +(-2.78634 + 4.82609i) q^{69} +(-6.26185 + 2.78057i) q^{70} +(10.1390 - 1.78778i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(3.00396 + 6.44202i) q^{73} +(2.22794 + 2.65516i) q^{74} +(3.01694 - 3.98724i) q^{75} +(3.68051 - 2.33535i) q^{76} +(6.26234 - 6.26234i) q^{77} +(0.0938685 - 1.07292i) q^{78} +(-1.53318 - 0.558033i) q^{79} +(0.235924 - 2.22359i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.60851 + 9.88299i) q^{82} +(-8.46000 + 2.26685i) q^{83} +(-1.53203 - 2.65355i) q^{84} +(6.55482 - 1.03156i) q^{85} +(-7.72547 + 9.20686i) q^{86} +(5.40825 + 1.44914i) q^{87} +(0.748084 + 2.79189i) q^{88} +(-12.6365 + 4.59931i) q^{89} +(1.91555 + 1.15355i) q^{90} +(3.24992 + 0.573048i) q^{91} +(5.05057 - 2.35512i) q^{92} +(1.32389 + 0.115825i) q^{93} -8.32286 q^{94} +(-8.11261 - 5.40237i) q^{95} +1.00000 q^{96} +(0.244230 + 0.0213673i) q^{97} +(2.16468 - 1.00941i) q^{98} +(-2.84646 - 0.501908i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	−0.538816	−	2.17018i	−0.240966	−	0.970534i
$5$	−0.538816	−	2.17018i	−0.240966	−	0.970534i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	0.793037	+	2.95965i	0.299740	+	1.11864i	0.937380	+	0.348309i	$0.113244\pi$
$7$	0.793037	+	2.95965i	0.299740	+	1.11864i	−0.637640	+	0.770335i	$0.720089\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	0.347622	+	2.20888i	0.109928	+	0.698510i
$11$	−1.44519	−	2.50314i	−0.435741	−	0.754725i	0.561615	−	0.827399i	$-0.310180\pi$
$11$	−1.44519	−	2.50314i	−0.435741	−	0.754725i	−0.997356	+	0.0726738i	$0.976847\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	0.455168	−	0.976112i	0.126241	−	0.270725i	−0.833022	−	0.553240i	$-0.813391\pi$
$13$	0.455168	−	0.976112i	0.126241	−	0.270725i	0.959263	+	0.282516i	$0.0911689\pi$
$14$	−0.532068	−	3.01751i	−0.142201	−	0.806463i
$15$	1.40549	+	1.73914i	0.362896	+	0.449043i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−0.258633	+	2.95619i	−0.0627277	+	0.716981i	0.898092	+	0.439808i	$0.144953\pi$
$17$	−0.258633	+	2.95619i	−0.0627277	+	0.716981i	−0.960820	+	0.277174i	$0.910602\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	3.21906	−	2.93899i	0.738504	−	0.674250i
$19$	3.21906	−	2.93899i	0.738504	−	0.674250i
$20$	−0.153782	−	2.23077i	−0.0343868	−	0.498816i
$21$	−1.96954	−	2.34721i	−0.429789	−	0.512202i
$22$	1.22153	+	2.61957i	0.260430	+	0.558494i
$23$	4.56487	−	3.19636i	0.951842	−	0.666487i	0.00908210	−	0.999959i	$-0.497109\pi$
$23$	4.56487	−	3.19636i	0.951842	−	0.666487i	0.942760	+	0.333472i	$0.108220\pi$
$24$	0.984808	−	0.173648i	0.201023	−	0.0354458i
$25$	−4.41935	+	2.33865i	−0.883871	+	0.467731i
$26$	−0.538510	+	0.932727i	−0.105611	+	0.182923i
$27$	−0.258819	+	0.965926i	−0.0498097	+	0.185893i
$28$	0.267050	+	3.05240i	0.0504678	+	0.576849i
$29$	−4.28911	−	3.59899i	−0.796468	−	0.668316i	0.150869	−	0.988554i	$-0.451793\pi$
$29$	−4.28911	−	3.59899i	−0.796468	−	0.668316i	−0.947337	+	0.320238i	$0.896237\pi$
$30$	−1.24857	−	1.85502i	−0.227956	−	0.338678i
$31$	−1.15090	−	0.664472i	−0.206708	−	0.119343i	0.393073	−	0.919507i	$-0.371412\pi$
$31$	−1.15090	−	0.664472i	−0.206708	−	0.119343i	−0.599780	+	0.800165i	$0.704745\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	2.36766	+	1.65785i	0.412156	+	0.288595i
$34$	0.515298	−	2.92240i	0.0883729	−	0.501187i
$35$	5.99568	−	3.31574i	1.01345	−	0.560462i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−2.45087	−	2.45087i	−0.402921	−	0.402921i	0.476340	−	0.879261i	$-0.341963\pi$
$37$	−2.45087	−	2.45087i	−0.402921	−	0.402921i	−0.879261	+	0.476340i	$0.841963\pi$
$38$	−3.46296	+	2.64724i	−0.561767	+	0.429439i
$39$			1.07702i			0.172461i
$40$	−0.0412275	+	2.23569i	−0.00651864	+	0.353493i
$41$	3.72962	−	10.2470i	0.582468	−	1.60032i	−0.201480	−	0.979493i	$-0.564575\pi$
$41$	3.72962	−	10.2470i	0.582468	−	1.60032i	0.783948	−	0.620826i	$-0.213203\pi$
$42$	1.75747	+	2.50993i	0.271184	+	0.387291i
$43$	6.89364	−	9.84514i	1.05127	−	1.50137i	0.197790	−	0.980244i	$-0.436623\pi$
$43$	6.89364	−	9.84514i	1.05127	−	1.50137i	0.853480	−	0.521125i	$-0.174488\pi$
$44$	−0.988567	−	2.71606i	−0.149032	−	0.409462i
$45$	−2.00880	−	0.982207i	−0.299454	−	0.146419i
$46$	−4.82609	+	2.78634i	−0.711567	+	0.410824i
$47$	8.29119	−	0.725385i	1.20939	−	0.105808i	0.535435	−	0.844577i	$-0.320148\pi$
$47$	8.29119	−	0.725385i	1.20939	−	0.105808i	0.673960	+	0.738768i	$0.264592\pi$
$48$	−0.996195	+	0.0871557i	−0.143788	+	0.0125798i
$49$	−2.06846	+	1.19423i	−0.295495	+	0.170604i
$50$	4.60637	−	1.94458i	0.651438	−	0.275006i
$51$	−1.01494	−	2.78852i	−0.142120	−	0.390471i
$52$	0.617753	−	0.882243i	0.0856670	−	0.122345i
$53$	−1.14239	−	1.63150i	−0.156919	−	0.224104i	0.732992	−	0.680237i	$-0.238123\pi$
$53$	−1.14239	−	1.63150i	−0.156919	−	0.224104i	−0.889912	+	0.456133i	$0.849234\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	−4.65357	+	4.48505i	−0.627487	+	0.604764i
$56$		−	3.06406i		−	0.409452i
$57$	−1.67539	+	4.02406i	−0.221911	+	0.533000i
$58$	3.95912	+	3.95912i	0.519858	+	0.519858i
$59$	4.79584	−	4.02419i	0.624366	−	0.523905i	−0.274807	−	0.961499i	$-0.588614\pi$
$59$	4.79584	−	4.02419i	0.624366	−	0.523905i	0.899172	+	0.437594i	$0.144169\pi$
$60$	1.08214	+	1.95678i	0.139704	+	0.252619i
$61$	1.11889	−	6.34556i	0.143260	−	0.812465i	−0.825489	−	0.564419i	$-0.809100\pi$
$61$	1.11889	−	6.34556i	0.143260	−	0.812465i	0.968748	−	0.248046i	$-0.0797886\pi$
$62$	1.08861	+	0.762251i	0.138253	+	0.0968059i
$63$	2.77698	+	1.29493i	0.349867	+	0.163145i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−2.36359	−	0.461852i	−0.293167	−	0.0572857i
$66$	−2.21416	−	1.85790i	−0.272544	−	0.228691i
$67$	0.242677	+	2.77381i	0.0296477	+	0.338875i	0.996503	+	0.0835516i	$0.0266263\pi$
$67$	0.242677	+	2.77381i	0.0296477	+	0.338875i	−0.966856	+	0.255323i	$0.917818\pi$
$68$	−0.768041	+	2.86637i	−0.0931386	+	0.347598i
$69$	−2.78634	+	4.82609i	−0.335436	+	0.580992i
$70$	−6.26185	+	2.78057i	−0.748434	+	0.332341i
$71$	10.1390	−	1.78778i	1.20328	−	0.212171i	0.464164	−	0.885749i	$-0.346355\pi$
$71$	10.1390	−	1.78778i	1.20328	−	0.212171i	0.739116	+	0.673578i	$0.235244\pi$
$72$	−0.819152	+	0.573576i	−0.0965380	+	0.0675966i
$73$	3.00396	+	6.44202i	0.351587	+	0.753981i	0.999973	−	0.00733080i	$-0.00233349\pi$
$73$	3.00396	+	6.44202i	0.351587	+	0.753981i	−0.648386	+	0.761312i	$0.724556\pi$
$74$	2.22794	+	2.65516i	0.258993	+	0.308656i
$75$	3.01694	−	3.98724i	0.348366	−	0.460407i
$76$	3.68051	−	2.33535i	0.422183	−	0.267883i
$77$	6.26234	−	6.26234i	0.713660	−	0.713660i
$78$	0.0938685	−	1.07292i	0.0106285	−	0.121484i
$79$	−1.53318	−	0.558033i	−0.172497	−	0.0627836i	0.254328	−	0.967118i	$-0.418146\pi$
$79$	−1.53318	−	0.558033i	−0.172497	−	0.0627836i	−0.426825	+	0.904334i	$0.640368\pi$
$80$	0.235924	−	2.22359i	0.0263771	−	0.248605i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−4.60851	+	9.88299i	−0.508925	+	1.09139i
$83$	−8.46000	+	2.26685i	−0.928606	+	0.248819i	−0.691260	−	0.722606i	$-0.742944\pi$
$83$	−8.46000	+	2.26685i	−0.928606	+	0.248819i	−0.237346	+	0.971425i	$0.576277\pi$
$84$	−1.53203	−	2.65355i	−0.167158	−	0.289526i
$85$	6.55482	−	1.03156i	0.710970	−	0.111889i
$86$	−7.72547	+	9.20686i	−0.833059	+	0.992801i
$87$	5.40825	+	1.44914i	0.579826	+	0.155364i
$88$	0.748084	+	2.79189i	0.0797461	+	0.297616i
$89$	−12.6365	+	4.59931i	−1.33946	+	0.487525i	−0.909644	−	0.415389i	$-0.863646\pi$
$89$	−12.6365	+	4.59931i	−1.33946	+	0.487525i	−0.429821	+	0.902914i	$0.641423\pi$
$90$	1.91555	+	1.15355i	0.201917	+	0.121595i
$91$	3.24992	+	0.573048i	0.340684	+	0.0600718i
$92$	5.05057	−	2.35512i	0.526558	−	0.245538i
$93$	1.32389	+	0.115825i	0.137281	+	0.0120105i
$94$	−8.32286			−0.858438
$95$	−8.11261	−	5.40237i	−0.832336	−	0.554271i
$96$	1.00000			0.102062
$97$	0.244230	+	0.0213673i	0.0247977	+	0.00216952i	0.0995479	−	0.995033i	$-0.468260\pi$
$97$	0.244230	+	0.0213673i	0.0247977	+	0.00216952i	−0.0747501	+	0.997202i	$0.523816\pi$
$98$	2.16468	−	1.00941i	0.218665	−	0.101965i
$99$	−2.84646	−	0.501908i	−0.286080	−	0.0504437i
$100$	−4.75832	+	1.53571i	−0.475832	+	0.153571i
$101$	−7.24698	+	2.63768i	−0.721101	+	0.262459i	−0.676393	−	0.736541i	$-0.736458\pi$
$101$	−7.24698	+	2.63768i	−0.721101	+	0.262459i	−0.0447080	+	0.999000i	$0.514236\pi$
$102$	0.768041	+	2.86637i	0.0760474	+	0.283813i
$103$	−3.18860	−	0.854383i	−0.314182	−	0.0841849i	0.0982821	−	0.995159i	$-0.468665\pi$
$103$	−3.18860	−	0.854383i	−0.314182	−	0.0841849i	−0.412464	+	0.910974i	$0.635332\pi$
$104$	−0.692295	+	0.825045i	−0.0678851	+	0.0809024i
$105$	−4.03264	+	5.53896i	−0.393545	+	0.540548i
$106$	0.995848	+	1.72486i	0.0967253	+	0.167533i
$107$	−17.5010	+	4.68937i	−1.69188	+	0.453338i	−0.970874	−	0.239589i	$-0.922987\pi$
$107$	−17.5010	+	4.68937i	−1.69188	+	0.453338i	−0.721008	+	0.692927i	$0.756321\pi$
$108$	−0.422618	+	0.906308i	−0.0406665	+	0.0872095i
$109$	−0.322290	−	1.82780i	−0.0308698	−	0.175071i	0.965475	−	0.260496i	$-0.0838862\pi$
$109$	−0.322290	−	1.82780i	−0.0308698	−	0.175071i	−0.996345	+	0.0854252i	$0.972775\pi$
$110$	5.02676	−	4.06240i	0.479283	−	0.387334i
$111$	3.25703	+	1.18546i	0.309144	+	0.112519i
$112$	−0.267050	+	3.05240i	−0.0252339	+	0.288425i
$113$	−5.68472	+	5.68472i	−0.534773	+	0.534773i	−0.921989	−	0.387216i	$-0.873437\pi$
$113$	−5.68472	+	5.68472i	−0.534773	+	0.534773i	0.387216	+	0.921989i	$0.373437\pi$
$114$	2.01974	−	3.86273i	0.189166	−	0.361778i
$115$	−9.39630	−	8.18435i	−0.876210	−	0.763194i
$116$	−3.59899	−	4.28911i	−0.334158	−	0.398234i
$117$	−0.455168	−	0.976112i	−0.0420803	−	0.0902416i
$118$	−5.12833	+	3.59089i	−0.472101	+	0.330568i
$119$	−8.95440	+	1.57890i	−0.820849	+	0.144738i
$120$	−0.907478	−	2.04364i	−0.0828410	−	0.186558i
$121$	1.32286	−	2.29127i	0.120260	−	0.208297i
$122$	−1.66769	+	6.22389i	−0.150985	+	0.563485i
$123$	0.950405	+	10.8632i	0.0856951	+	0.979500i
$124$	−1.01803	−	0.854229i	−0.0914218	−	0.0767120i
$125$	7.45652	+	8.33069i	0.666931	+	0.745119i
$126$	−2.65355	−	1.53203i	−0.236397	−	0.136484i
$127$	1.83171	+	0.854141i	0.162538	+	0.0757928i	0.502185	−	0.864760i	$-0.332530\pi$
$127$	1.83171	+	0.854141i	0.162538	+	0.0757928i	−0.339647	+	0.940553i	$0.610307\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	−2.08702	+	11.8361i	−0.183752	+	1.04211i
$130$	2.31434	+	0.666095i	0.202981	+	0.0584204i
$131$	14.9632	−	12.5556i	1.30734	−	1.09699i	0.318510	−	0.947920i	$-0.396818\pi$
$131$	14.9632	−	12.5556i	1.30734	−	1.09699i	0.988827	−	0.149066i	$-0.0476268\pi$
$132$	2.04380	+	2.04380i	0.177890	+	0.177890i
$133$	11.2512	+	7.19659i	0.975604	+	0.624023i
$134$		−	2.78441i		−	0.240536i
$135$	2.23569	+	0.0412275i	0.192417	+	0.00354830i
$136$	1.01494	−	2.78852i	0.0870303	−	0.239114i
$137$	5.92979	+	8.46861i	0.506616	+	0.723522i	0.988249	−	0.152850i	$-0.0488452\pi$
$137$	5.92979	+	8.46861i	0.506616	+	0.723522i	−0.481633	+	0.876373i	$0.659956\pi$
$138$	3.19636	−	4.56487i	0.272092	−	0.388588i
$139$	4.74025	+	13.0237i	0.402063	+	1.10466i	0.961265	+	0.275627i	$0.0888854\pi$
$139$	4.74025	+	13.0237i	0.402063	+	1.10466i	−0.559202	+	0.829031i	$0.688892\pi$
$140$	6.48036	−	2.22423i	0.547691	−	0.187982i
$141$	−7.20781	+	4.16143i	−0.607007	+	0.350456i
$142$	−10.2563	+	0.897306i	−0.860685	+	0.0753002i
$143$	−3.10115	+	0.271315i	−0.259331	+	0.0226885i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−5.49942	+	11.2473i	−0.456702	+	0.934040i
$146$	−2.43107	−	6.67931i	−0.201197	−	0.552784i
$147$	1.36996	−	1.95651i	0.112993	−	0.161370i
$148$	−1.98805	−	2.83923i	−0.163417	−	0.233383i
$149$	−5.60505	+	15.3997i	−0.459183	+	1.26160i	0.466911	+	0.884304i	$0.345367\pi$
$149$	−5.60505	+	15.3997i	−0.459183	+	1.26160i	−0.926094	+	0.377292i	$0.876855\pi$
$150$	−3.35297	+	3.70912i	−0.273769	+	0.302849i
$151$			14.9062i			1.21305i	0.795064	+	0.606525i	$0.207437\pi$
$151$			14.9062i			1.21305i	−0.795064	+	0.606525i	$0.792563\pi$
$152$	−3.87004	+	2.00569i	−0.313902	+	0.162683i
$153$	2.09833	+	2.09833i	0.169640	+	0.169640i
$154$	−6.78431	+	5.69271i	−0.546695	+	0.458731i
$155$	−0.821900	+	2.85568i	−0.0660166	+	0.229374i
$156$	−0.187023	+	1.06066i	−0.0149738	+	0.0849206i
$157$	−7.59225	−	5.31615i	−0.605927	−	0.424275i	0.229941	−	0.973204i	$-0.426147\pi$
$157$	−7.59225	−	5.31615i	−0.605927	−	0.424275i	−0.835869	+	0.548930i	$0.815035\pi$
$158$	1.47871	+	0.689535i	0.117640	+	0.0548565i
$159$	1.72486	+	0.995848i	0.136790	+	0.0789759i
$160$	−0.428824	+	2.19456i	−0.0339015	+	0.173495i
$161$	13.0802	+	10.9756i	1.03087	+	0.865000i
$162$	0.0871557	+	0.996195i	0.00684760	+	0.0782684i
$163$	4.45295	−	16.6186i	0.348782	−	1.30167i	−0.539350	−	0.842082i	$-0.681330\pi$
$163$	4.45295	−	16.6186i	0.348782	−	1.30167i	0.888131	−	0.459590i	$-0.152003\pi$
$164$	5.45234	−	9.44372i	0.425756	−	0.737431i
$165$	2.32210	−	6.03152i	0.180775	−	0.469553i
$166$	8.62538	−	1.52089i	0.669459	−	0.118044i
$167$	−10.0643	+	7.04708i	−0.778797	+	0.545320i	−0.894024	−	0.448020i	$-0.852129\pi$
$167$	−10.0643	+	7.04708i	−0.778797	+	0.545320i	0.115227	+	0.993339i	$0.463241\pi$
$168$	1.29493	+	2.77698i	0.0999058	+	0.214249i
$169$	7.61062	+	9.06999i	0.585433	+	0.697691i
$170$	−6.61978	+	0.456347i	−0.507714	+	0.0350002i
$171$	−0.182220	−	4.35509i	−0.0139347	−	0.333042i
$172$	8.49850	−	8.49850i	0.648005	−	0.648005i
$173$	0.661641	−	7.56259i	0.0503036	−	0.574973i	−0.928659	−	0.370934i	$-0.879038\pi$
$173$	0.661641	−	7.56259i	0.0503036	−	0.574973i	0.978963	−	0.204039i	$-0.0654069\pi$
$174$	−5.26137	−	1.91498i	−0.398864	−	0.145175i
$175$	−10.4263	−	11.2251i	−0.788155	−	0.848539i
$176$	−0.501908	−	2.84646i	−0.0378328	−	0.214560i
$177$	−2.64581	+	5.67397i	−0.198872	+	0.426482i
$178$	12.9893	−	3.48046i	0.973586	−	0.260872i
$179$	−1.50968	−	2.61485i	−0.112839	−	0.195443i	0.804075	−	0.594528i	$-0.202661\pi$
$179$	−1.50968	−	2.61485i	−0.112839	−	0.195443i	−0.916914	+	0.399085i	$0.869328\pi$
$180$	−1.80772	−	1.31611i	−0.134740	−	0.0980970i
$181$	−1.14841	+	1.36862i	−0.0853604	+	0.101729i	−0.807034	−	0.590505i	$-0.798929\pi$
$181$	−1.14841	+	1.36862i	−0.0853604	+	0.101729i	0.721674	+	0.692233i	$0.243373\pi$
$182$	−3.18761	−	0.854117i	−0.236281	−	0.0633113i
$183$	1.66769	+	6.22389i	0.123279	+	0.460083i
$184$	−5.23661	+	1.90597i	−0.386048	+	0.140510i
$185$	−3.99827	+	6.63941i	−0.293958	+	0.488139i
$186$	−1.30875	−	0.230769i	−0.0959625	−	0.0169208i
$187$	7.77353	−	3.62486i	0.568457	−	0.265076i
$188$	8.29119	+	0.725385i	0.604697	+	0.0529041i
$189$	−3.06406			−0.222877
$190$	7.61089	+	6.08887i	0.552152	+	0.441733i
$191$	15.9698			1.15553			0.577767	−	0.816201i	$-0.303924\pi$
$191$	15.9698			1.15553			0.577767	+	0.816201i	$0.303924\pi$
$192$	−0.996195	−	0.0871557i	−0.0718942	−	0.00628992i
$193$	1.37071	−	0.639173i	0.0986660	−	0.0460087i	−0.372659	−	0.927968i	$-0.621554\pi$
$193$	1.37071	−	0.639173i	0.0986660	−	0.0460087i	0.471325	+	0.881960i	$0.343776\pi$
$194$	−0.241438	−	0.0425720i	−0.0173342	−	0.00305649i
$195$	2.33733	−	0.580316i	0.167379	−	0.0415573i
$196$	−2.24442	+	0.816900i	−0.160315	+	0.0583500i
$197$	6.96591	+	25.9971i	0.496301	+	1.85222i	0.522619	+	0.852566i	$0.324955\pi$
$197$	6.96591	+	25.9971i	0.496301	+	1.85222i	−0.0263186	+	0.999654i	$0.508378\pi$
$198$	2.79189	+	0.748084i	0.198411	+	0.0531640i
$199$	10.3365	−	12.3186i	0.732736	−	0.873240i	−0.263066	−	0.964778i	$-0.584734\pi$
$199$	10.3365	−	12.3186i	0.732736	−	0.873240i	0.995802	+	0.0915375i	$0.0291781\pi$
$200$	4.87406	−	1.11515i	0.344648	−	0.0788532i
$201$	−1.39220	−	2.41137i	−0.0981984	−	0.170085i
$202$	7.44929	−	1.99603i	0.524130	−	0.140440i
$203$	7.25035	−	15.5484i	0.508874	−	1.09128i
$204$	−0.515298	−	2.92240i	−0.0360781	−	0.204609i
$205$	−24.2475	−	2.57267i	−1.69352	−	0.179683i
$206$	3.10200	+	1.12904i	0.216127	+	0.0786638i
$207$	0.485691	−	5.55148i	0.0337579	−	0.385854i
$208$	0.761568	−	0.761568i	0.0528053	−	0.0528053i
$209$	−12.0088	−	3.81037i	−0.830669	−	0.263569i
$210$	4.50004	−	5.16642i	0.310533	−	0.356517i
$211$	17.5662	+	20.9346i	1.20931	+	1.44120i	0.864579	+	0.502497i	$0.167585\pi$
$211$	17.5662	+	20.9346i	1.20931	+	1.44120i	0.344731	+	0.938702i	$0.387970\pi$
$212$	−0.841727	−	1.80509i	−0.0578101	−	0.123974i
$213$	−8.43352	+	5.90521i	−0.577855	+	0.404619i
$214$	17.8431	−	3.14622i	1.21973	−	0.215071i
$215$	−25.0801	−	9.65572i	−1.71045	−	0.658515i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	1.05390	−	3.93321i	0.0715435	−	0.267004i
$218$	0.161761	+	1.84893i	0.0109558	+	0.125225i
$219$	−5.44503	−	4.56892i	−0.367941	−	0.308739i
$220$	−5.36169	+	3.60883i	−0.361485	+	0.243307i
$221$	2.76785	+	1.59802i	0.186186	+	0.107494i
$222$	−3.14132	−	1.46482i	−0.210831	−	0.0983123i
$223$	−13.7085	−	9.59882i	−0.917992	−	0.642785i	0.0160798	−	0.999871i	$-0.494881\pi$
$223$	−13.7085	−	9.59882i	−0.917992	−	0.642785i	−0.934072	+	0.357086i	$0.883770\pi$
$224$	0.532068	−	3.01751i	0.0355503	−	0.201616i
$225$	−1.04919	+	4.88868i	−0.0699462	+	0.325912i
$226$	6.15854	−	5.16763i	0.409660	−	0.343746i
$227$	−4.00735	−	4.00735i	−0.265977	−	0.265977i	0.561500	−	0.827477i	$-0.310224\pi$
$227$	−4.00735	−	4.00735i	−0.265977	−	0.265977i	−0.827477	+	0.561500i	$0.810224\pi$
$228$	−2.34871	+	3.67200i	−0.155547	+	0.243184i
$229$		−	18.8204i		−	1.24368i	−0.783143	−	0.621842i	$-0.786385\pi$
$229$		−	18.8204i		−	1.24368i	0.783143	−	0.621842i	$-0.213615\pi$
$230$	8.64723	+	8.97214i	0.570182	+	0.591606i
$231$	−3.02903	+	8.32218i	−0.199295	+	0.547559i
$232$	3.21148	+	4.58646i	0.210844	+	0.301116i
$233$	0.657516	−	0.939031i	0.0430753	−	0.0615179i	−0.797037	−	0.603931i	$-0.793600\pi$
$233$	0.657516	−	0.939031i	0.0430753	−	0.0615179i	0.840112	+	0.542413i	$0.182489\pi$
$234$	0.368363	+	1.01207i	0.0240806	+	0.0661610i
$235$	−6.04164	−	17.6025i	−0.394113	−	1.14826i
$236$	5.42178	−	3.13027i	0.352928	−	0.203763i
$237$	1.62537	−	0.142202i	0.105579	−	0.00923698i
$238$	9.05794	−	0.792467i	0.587139	−	0.0513680i
$239$	−7.47057	+	4.31313i	−0.483231	+	0.278993i	−0.721762	−	0.692141i	$-0.756667\pi$
$239$	−7.47057	+	4.31313i	−0.483231	+	0.278993i	0.238531	+	0.971135i	$0.423334\pi$
$240$	0.725909	+	2.11496i	0.0468572	+	0.136520i
$241$	−7.42516	−	20.4005i	−0.478297	−	1.31411i	−0.910938	−	0.412544i	$-0.864640\pi$
$241$	−7.42516	−	20.4005i	−0.478297	−	1.31411i	0.432641	−	0.901566i	$-0.357582\pi$
$242$	−1.51753	+	2.16725i	−0.0975503	+	0.139316i
$243$	0.573576	+	0.819152i	0.0367949	+	0.0525486i
$244$	2.20379	−	6.05486i	0.141083	−	0.387623i
$245$	3.70621	+	3.84547i	0.236781	+	0.245678i
$246$		−	10.9047i		−	0.695257i
$247$	−1.40356	−	4.47990i	−0.0893066	−	0.285049i
$248$	0.939705	+	0.939705i	0.0596713	+	0.0596713i
$249$	6.70935	−	5.62982i	0.425188	−	0.356775i
$250$	−6.70208	−	8.94887i	−0.423876	−	0.565976i
$251$	1.98753	−	11.2719i	0.125452	−	0.711473i	−0.855587	−	0.517660i	$-0.826803\pi$
$251$	1.98753	−	11.2719i	0.125452	−	0.711473i	0.981038	−	0.193813i	$-0.0620856\pi$
$252$	2.50993	+	1.75747i	0.158111	+	0.110710i
$253$	−14.5980	−	6.80718i	−0.917771	−	0.427963i
$254$	−1.75030	−	1.01054i	−0.109824	−	0.0634066i
$255$	−5.50473	+	3.70510i	−0.344719	+	0.232022i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.0587537	+	0.671558i	0.00366495	+	0.0418906i	0.997807	−	0.0661912i	$-0.0210847\pi$
$257$	0.0587537	+	0.671558i	0.00366495	+	0.0418906i	−0.994142	+	0.108082i	$0.965529\pi$
$258$	3.11067	−	11.6092i	0.193662	−	0.722755i
$259$	5.31011	−	9.19737i	0.329954	−	0.571497i
$260$	−2.24748	−	0.865269i	−0.139383	−	0.0536617i
$261$	−5.51398	+	0.972263i	−0.341306	+	0.0601815i
$262$	−16.0005	+	11.2037i	−0.988515	+	0.692165i
$263$	−8.21846	−	17.6245i	−0.506772	−	1.08678i	−0.978730	−	0.205155i	$-0.934230\pi$
$263$	−8.21846	−	17.6245i	−0.506772	−	1.08678i	0.471958	−	0.881621i	$-0.343548\pi$
$264$	−1.85790	−	2.21416i	−0.114346	−	0.136272i
$265$	−2.92511	+	3.35827i	−0.179688	+	0.206297i
$266$	−10.5812	−	8.14981i	−0.648774	−	0.499697i
$267$	9.50880	−	9.50880i	0.581929	−	0.581929i
$268$	−0.242677	+	2.77381i	−0.0148239	+	0.169437i
$269$	14.5544	+	5.29738i	0.887400	+	0.322987i	0.745192	−	0.666850i	$-0.232358\pi$
$269$	14.5544	+	5.29738i	0.887400	+	0.322987i	0.142208	+	0.989837i	$0.454580\pi$
$270$	−2.22359	−	0.235924i	−0.135323	−	0.0143579i
$271$	2.18803	+	12.4089i	0.132913	+	0.753789i	0.976290	+	0.216467i	$0.0694532\pi$
$271$	2.18803	+	12.4089i	0.132913	+	0.753789i	−0.843377	+	0.537323i	$0.819436\pi$
$272$	−1.25411	+	2.68945i	−0.0760417	+	0.163072i
$273$	−3.18761	+	0.854117i	−0.192923	+	0.0516935i
$274$	−5.16913	−	8.95320i	−0.312279	−	0.540883i
$275$	12.2408	+	7.68246i	0.738146	+	0.463270i
$276$	−3.58205	+	4.26892i	−0.215614	+	0.256959i
$277$	−9.41092	−	2.52165i	−0.565448	−	0.151511i	−0.0352397	−	0.999379i	$-0.511219\pi$
$277$	−9.41092	−	2.52165i	−0.565448	−	0.151511i	−0.530208	+	0.847868i	$0.677886\pi$
$278$	−3.58712	−	13.3873i	−0.215141	−	0.802918i
$279$	−1.24880	+	0.454525i	−0.0747636	+	0.0272117i
$280$	−6.64956	+	1.65096i	−0.397387	+	0.0986639i
$281$	−25.8369	−	4.55574i	−1.54130	−	0.271773i	−0.662536	−	0.749030i	$-0.730520\pi$
$281$	−25.8369	−	4.55574i	−1.54130	−	0.271773i	−0.878763	+	0.477258i	$0.841631\pi$
$282$	7.54307	−	3.51739i	0.449183	−	0.209458i
$283$	−9.17351	−	0.802578i	−0.545309	−	0.0477083i	−0.188826	−	0.982010i	$-0.560468\pi$
$283$	−9.17351	−	0.802578i	−0.545309	−	0.0477083i	−0.356482	+	0.934302i	$0.616024\pi$
$284$	10.2954			0.610921
$285$	9.63566	+	1.46767i	0.570767	+	0.0869375i
$286$	3.11299			0.184075
$287$	33.2854	+	2.91210i	1.96478	+	0.171896i
$288$	−0.906308	+	0.422618i	−0.0534047	+	0.0249030i
$289$	8.06956	+	1.42288i	0.474680	+	0.0836989i
$290$	6.45876	−	10.7252i	0.379271	−	0.629807i
$291$	−0.230377	+	0.0838505i	−0.0135050	+	0.00491540i
$292$	1.83968	+	6.86578i	0.107659	+	0.401789i
$293$	22.2975	+	5.97459i	1.30263	+	0.349039i	0.842445	−	0.538783i	$-0.181116\pi$
$293$	22.2975	+	5.97459i	1.30263	+	0.349039i	0.460187	+	0.887822i	$0.347782\pi$
$294$	−1.53527	+	1.82966i	−0.0895388	+	0.106708i
$295$	−11.3173	−	8.23954i	−0.658918	−	0.479725i
$296$	1.73303	+	3.00170i	0.100730	+	0.174470i
$297$	2.79189	−	0.748084i	0.162002	−	0.0434083i
$298$	6.92589	−	14.8526i	0.401206	−	0.860390i
$299$	−1.04222	−	5.91071i	−0.0602730	−	0.341825i
$300$	3.66348	−	3.40278i	0.211511	−	0.196460i
$301$	34.6051	+	12.5952i	1.99461	+	0.725977i
$302$	1.29916	−	14.8495i	0.0747584	−	0.854492i
$303$	5.45326	−	5.45326i	0.313282	−	0.313282i
$304$	4.03012	−	1.66076i	0.231143	−	0.0952511i
$305$	−14.3739	+	0.990889i	−0.823045	+	0.0567381i
$306$	−1.90746	−	2.27322i	−0.109042	−	0.129952i
$307$	9.97914	+	21.4003i	0.569539	+	1.22138i	0.954434	+	0.298421i	$0.0964599\pi$
$307$	9.97914	+	21.4003i	0.569539	+	1.22138i	−0.384895	+	0.922960i	$0.625762\pi$
$308$	7.25464	−	5.07975i	0.413372	−	0.289446i
$309$	3.25093	−	0.573227i	0.184939	−	0.0326098i
$310$	1.06766	−	2.77318i	0.0606391	−	0.157506i
$311$	−14.4020	+	24.9449i	−0.816660	+	1.41450i	0.0914695	+	0.995808i	$0.470844\pi$
$311$	−14.4020	+	24.9449i	−0.816660	+	1.41450i	−0.908130	+	0.418689i	$0.862490\pi$
$312$	0.278753	−	1.04032i	0.0157813	−	0.0588966i
$313$	−2.91482	−	33.3165i	−0.164755	−	1.88316i	−0.407694	−	0.913119i	$-0.633667\pi$
$313$	−2.91482	−	33.3165i	−0.164755	−	1.88316i	0.242939	−	0.970042i	$-0.421889\pi$
$314$	7.10002	+	5.95763i	0.400677	+	0.336208i
$315$	1.31394	−	6.72427i	0.0740323	−	0.378870i
$316$	−1.41299	−	0.815790i	−0.0794869	−	0.0458918i
$317$	−1.26938	−	0.591923i	−0.0712957	−	0.0332457i	0.386643	−	0.922229i	$-0.373634\pi$
$317$	−1.26938	−	0.591923i	−0.0712957	−	0.0332457i	−0.457939	+	0.888984i	$0.651412\pi$
$318$	−1.63150	−	1.14239i	−0.0914901	−	0.0640620i
$319$	−2.81020	+	15.9375i	−0.157341	+	0.892326i
$320$	0.618461	−	2.14884i	0.0345730	−	0.120124i
$321$	13.8794	−	11.6462i	0.774675	−	0.650030i
$322$	−12.0739	−	12.0739i	−0.672850	−	0.672850i
$323$	7.85564	+	10.2763i	0.437100	+	0.571787i
$324$		−	1.00000i		−	0.0555556i
$325$	0.271237	+	5.37827i	0.0150455	+	0.298333i
$326$	−5.88441	+	16.1673i	−0.325907	+	0.895423i
$327$	1.06455	+	1.52034i	0.0588700	+	0.0840751i
$328$	−6.25466	+	8.93259i	−0.345356	+	0.493219i
$329$	8.72211	+	23.9638i	0.480865	+	1.32117i
$330$	−2.83895	+	5.80618i	−0.156279	+	0.319620i
$331$	−12.9357	+	7.46842i	−0.711009	+	0.410501i	−0.811435	−	0.584443i	$-0.801313\pi$
$331$	−12.9357	+	7.46842i	−0.711009	+	0.410501i	0.100425	+	0.994945i	$0.467980\pi$
$332$	−8.72511	+	0.763348i	−0.478853	+	0.0418942i
$333$	−3.45287	+	0.302087i	−0.189216	+	0.0165543i
$334$	10.6402	−	6.14311i	0.582204	−	0.336136i
$335$	5.88891	−	2.02123i	0.321745	−	0.110431i
$336$	−1.04797	−	2.87927i	−0.0571714	−	0.157077i
$337$	7.15617	−	10.2201i	0.389822	−	0.556723i	−0.575495	−	0.817805i	$-0.695191\pi$
$337$	7.15617	−	10.2201i	0.389822	−	0.556723i	0.965316	+	0.261083i	$0.0840795\pi$
$338$	−6.79116	−	9.69878i	−0.369390	−	0.527544i
$339$	2.74964	−	7.55457i	0.149340	−	0.410308i
$340$	6.63436	+	0.122342i	0.359799	+	0.00663492i
$341$			3.84115i			0.208010i
$342$	−0.198044	+	4.35440i	−0.0107090	+	0.235459i
$343$	9.99145	+	9.99145i	0.539487	+	0.539487i
$344$	−9.20686	+	7.72547i	−0.496400	+	0.416529i
$345$	11.9748	+	3.44649i	0.644701	+	0.185553i
$346$	−1.31825	+	7.47615i	−0.0708693	+	0.401920i
$347$	−6.16998	−	4.32027i	−0.331222	−	0.231924i	0.396121	−	0.918198i	$-0.370356\pi$
$347$	−6.16998	−	4.32027i	−0.331222	−	0.231924i	−0.727343	+	0.686274i	$0.759245\pi$
$348$	5.07445	+	2.36626i	0.272019	+	0.126845i
$349$	−19.1637	−	11.0642i	−1.02581	−	0.592252i	−0.110029	−	0.993928i	$-0.535094\pi$
$349$	−19.1637	−	11.0642i	−1.02581	−	0.592252i	−0.915782	+	0.401676i	$0.868428\pi$
$350$	9.40831	+	12.0911i	0.502895	+	0.646298i
$351$	0.825045	+	0.692295i	0.0440377	+	0.0369520i
$352$	0.251913	+	2.87938i	0.0134270	+	0.153471i
$353$	−3.73508	+	13.9395i	−0.198798	+	0.741925i	0.792453	+	0.609934i	$0.208804\pi$
$353$	−3.73508	+	13.9395i	−0.198798	+	0.741925i	−0.991251	+	0.131992i	$0.957863\pi$
$354$	3.13027	−	5.42178i	0.166372	−	0.288164i
$355$	−9.34287	−	21.0402i	−0.495868	−	1.11670i
$356$	−13.2432	+	2.33513i	−0.701887	+	0.123762i
$357$	7.44817	−	5.21527i	0.394199	−	0.276021i
$358$	1.27604	+	2.73647i	0.0674407	+	0.144627i
$359$	20.7686	+	24.7511i	1.09612	+	1.30631i	0.948327	+	0.317293i	$0.102774\pi$
$359$	20.7686	+	24.7511i	1.09612	+	1.30631i	0.147797	+	0.989018i	$0.452782\pi$
$360$	1.68614	+	1.46865i	0.0888672	+	0.0774049i
$361$	1.72472	−	18.9216i	0.0907749	−	0.995871i
$362$	1.26332	−	1.26332i	0.0663986	−	0.0663986i
$363$	−0.230590	+	2.63566i	−0.0121029	+	0.138336i
$364$	3.10104	+	1.12868i	0.162538	+	0.0591592i
$365$	12.3617	−	9.99019i	0.647043	−	0.522911i
$366$	−1.11889	−	6.34556i	−0.0584855	−	0.331688i
$367$	−1.89629	+	4.06662i	−0.0989858	+	0.212276i	−0.949564	−	0.313572i	$-0.898474\pi$
$367$	−1.89629	+	4.06662i	−0.0989858	+	0.212276i	0.850579	+	0.525848i	$0.176252\pi$
$368$	5.38280	−	1.44232i	0.280598	−	0.0751859i
$369$	−5.45234	−	9.44372i	−0.283837	−	0.491621i
$370$	4.56171	−	6.26567i	0.237152	−	0.325737i
$371$	3.92272	−	4.67492i	0.203658	−	0.242710i
$372$	1.28366	+	0.343956i	0.0665547	+	0.0178333i
$373$	7.28281	+	27.1798i	0.377090	+	1.40732i	0.850267	+	0.526351i	$0.176440\pi$
$373$	7.28281	+	27.1798i	0.377090	+	1.40732i	−0.473178	+	0.880967i	$0.656893\pi$
$374$	−8.05987	+	2.93355i	−0.416766	+	0.151690i
$375$	−10.2786	−	4.39891i	−0.530785	−	0.227159i
$376$	−8.19642	−	1.44525i	−0.422698	−	0.0745331i
$377$	−5.46529	+	2.54850i	−0.281477	+	0.131255i
$378$	3.05240	+	0.267050i	0.156998	+	0.0137356i
$379$	30.0921			1.54573			0.772863	−	0.634573i	$-0.218824\pi$
$379$	30.0921			1.54573			0.772863	+	0.634573i	$0.218824\pi$
$380$	−7.05125	−	6.72903i	−0.361721	−	0.345192i
$381$	−2.02107			−0.103543
$382$	−15.9090	−	1.39186i	−0.813977	−	0.0712138i
$383$	0.695035	−	0.324100i	0.0355146	−	0.0165607i	−0.404780	−	0.914414i	$-0.632652\pi$
$383$	0.695035	−	0.324100i	0.0355146	−	0.0165607i	0.440294	+	0.897853i	$0.354874\pi$
$384$	0.984808	+	0.173648i	0.0502558	+	0.00886145i
$385$	−16.9646	−	10.2161i	−0.864598	−	0.520663i
$386$	−1.42120	+	0.517276i	−0.0723373	+	0.0263286i
$387$	−3.11067	−	11.6092i	−0.158124	−	0.590127i
$388$	0.236809	+	0.0634527i	0.0120221	+	0.00322132i
$389$	−11.2228	+	13.3748i	−0.569018	+	0.678130i	−0.971429	−	0.237329i	$-0.923728\pi$
$389$	−11.2228	+	13.3748i	−0.569018	+	0.678130i	0.402411	+	0.915459i	$0.368172\pi$
$390$	−2.37901	+	0.374396i	−0.120466	+	0.0189583i
$391$	8.26842	+	14.3213i	0.418152	+	0.724260i
$392$	2.30707	−	0.618178i	0.116525	−	0.0312227i
$393$	−8.25501	+	17.7029i	−0.416410	+	0.892994i
$394$	−4.67361	−	26.5053i	−0.235453	−	1.33532i
$395$	−0.384928	+	3.62796i	−0.0193678	+	0.182542i
$396$	−2.71606	−	0.988567i	−0.136487	−	0.0496773i
$397$	3.18986	−	36.4602i	0.160094	−	1.82989i	−0.314012	−	0.949419i	$-0.601673\pi$
$397$	3.18986	−	36.4602i	0.160094	−	1.82989i	0.474107	−	0.880467i	$-0.342771\pi$
$398$	−11.3708	+	11.3708i	−0.569967	+	0.569967i
$399$	−13.2385	−	1.76735i	−0.662753	−	0.0884783i
$400$	−4.95270	+	0.686108i	−0.247635	+	0.0343054i
$401$	−14.9577	−	17.8259i	−0.746952	−	0.890183i	0.249996	−	0.968247i	$-0.419571\pi$
$401$	−14.9577	−	17.8259i	−0.746952	−	0.890183i	−0.996948	+	0.0780637i	$0.975126\pi$
$402$	1.17674	+	2.52353i	0.0586905	+	0.125862i
$403$	−1.17245	+	0.820959i	−0.0584040	+	0.0408949i
$404$	−7.59491	+	1.33919i	−0.377861	+	0.0666271i
$405$	−2.04364	+	0.907478i	−0.101550	+	0.0450929i
$406$	−8.57789	+	14.8573i	−0.425714	+	0.737357i
$407$	−2.59290	+	9.67685i	−0.128526	+	0.479664i
$408$	0.258633	+	2.95619i	0.0128042	+	0.146353i
$409$	11.8547	+	9.94730i	0.586178	+	0.491862i	0.886970	−	0.461828i	$-0.152806\pi$
$409$	11.8547	+	9.94730i	0.586178	+	0.491862i	−0.300791	+	0.953690i	$0.597251\pi$
$410$	23.9310	+	4.67619i	1.18187	+	0.230940i
$411$	−8.95320	−	5.16913i	−0.441629	−	0.254975i
$412$	−2.99180	−	1.39510i	−0.147395	−	0.0687316i
$413$	15.7135	+	11.0027i	0.773210	+	0.541408i
$414$	−0.967686	+	5.48802i	−0.0475592	+	0.269722i
$415$	9.47786	+	17.1383i	0.465250	+	0.841286i
$416$	−0.825045	+	0.692295i	−0.0404512	+	0.0339426i
$417$	−9.80019	−	9.80019i	−0.479917	−	0.479917i
$418$	11.6310	+	4.84251i	0.568893	+	0.236855i
$419$			6.79590i			0.332002i	0.986126	+	0.166001i	$0.0530854\pi$
$419$			6.79590i			0.332002i	−0.986126	+	0.166001i	$0.946915\pi$
$420$	−4.93320	+	4.75455i	−0.240716	+	0.231999i
$421$	−12.4372	+	34.1709i	−0.606151	+	1.66539i	0.132405	+	0.991196i	$0.457730\pi$
$421$	−12.4372	+	34.1709i	−0.606151	+	1.66539i	−0.738557	+	0.674192i	$0.764492\pi$
$422$	−15.6748	−	22.3860i	−0.763038	−	1.08973i
$423$	4.77380	−	6.81769i	0.232110	−	0.331487i
$424$	0.681200	+	1.87158i	0.0330820	+	0.0908921i
$425$	−5.77051	−	13.6693i	−0.279911	−	0.663059i
$426$	8.91610	−	5.14771i	0.431987	−	0.249408i
$427$	19.6680	−	1.72072i	0.951800	−	0.0832717i
$428$	−18.0494	+	1.57912i	−0.872450	+	0.0763295i
$429$	2.69593	−	1.55650i	0.130161	−	0.0751484i
$430$	24.1431	+	11.8049i	1.16429	+	0.569281i
$431$	−8.53866	−	23.4598i	−0.411293	−	1.13002i	−0.956504	−	0.291719i	$-0.905773\pi$
$431$	−8.53866	−	23.4598i	−0.411293	−	1.13002i	0.545212	−	0.838298i	$-0.316449\pi$
$432$	−0.573576	+	0.819152i	−0.0275962	+	0.0394115i
$433$	−18.9616	−	27.0800i	−0.911237	−	1.30138i	−0.953225	−	0.302263i	$-0.902258\pi$
$433$	−18.9616	−	27.0800i	−0.911237	−	1.30138i	0.0419875	−	0.999118i	$-0.486631\pi$
$434$	−1.39269	+	3.82639i	−0.0668514	+	0.183673i
$435$	0.230834	−	12.5177i	0.0110677	−	0.600178i
$436$		−	1.85599i		−	0.0888860i
$437$	5.30056	−	23.7054i	0.253560	−	1.13398i
$438$	5.02610	+	5.02610i	0.240156	+	0.240156i
$439$	14.9354	−	12.5323i	0.712828	−	0.598134i	−0.212563	−	0.977147i	$-0.568181\pi$
$439$	14.9354	−	12.5323i	0.712828	−	0.598134i	0.925391	+	0.379014i	$0.123737\pi$
$440$	5.65582	−	3.12779i	0.269631	−	0.149112i
$441$	−0.414751	+	2.35217i	−0.0197501	+	0.112008i
$442$	−2.61804	−	1.83317i	−0.124528	−	0.0871951i
$443$	23.0039	+	10.7269i	1.09295	+	0.509650i	0.883625	−	0.468196i	$-0.155096\pi$
$443$	23.0039	+	10.7269i	1.09295	+	0.509650i	0.209324	+	0.977846i	$0.432874\pi$
$444$	3.00170	+	1.73303i	0.142454	+	0.0822460i
$445$	16.7901	+	24.9453i	0.795925	+	1.18252i
$446$	12.8198	+	10.7571i	0.607034	+	0.509362i
$447$	−1.42831	−	16.3257i	−0.0675569	−	0.772179i
$448$	−0.793037	+	2.95965i	−0.0374675	+	0.139830i
$449$	8.23151	−	14.2574i	0.388469	−	0.672848i	−0.603775	−	0.797155i	$-0.706337\pi$
$449$	8.23151	−	14.2574i	0.388469	−	0.672848i	0.992244	+	0.124307i	$0.0396707\pi$
$450$	1.47128	−	4.77863i	0.0693567	−	0.225267i
$451$	−31.0398	+	5.47315i	−1.46161	+	0.257720i
$452$	−6.58550	+	4.61122i	−0.309756	+	0.216893i
$453$	−6.29964	−	13.5096i	−0.295983	−	0.634737i
$454$	3.64283	+	4.34136i	0.170967	+	0.203750i
$455$	−0.507490	−	7.36167i	−0.0237915	−	0.345120i
$456$	2.65981	−	3.45332i	0.124557	−	0.161717i
$457$	−1.74915	+	1.74915i	−0.0818217	+	0.0818217i	−0.746833	−	0.665011i	$-0.768427\pi$
$457$	−1.74915	+	1.74915i	−0.0818217	+	0.0818217i	0.665011	+	0.746833i	$0.268427\pi$
$458$	−1.64030	+	18.7487i	−0.0766463	+	0.876071i
$459$	−2.78852	−	1.01494i	−0.130157	−	0.0473733i
$460$	−7.83235	−	9.69166i	−0.365185	−	0.451876i
$461$	0.197813	+	1.12185i	0.00921308	+	0.0522500i	0.989068	−	0.147462i	$-0.0471104\pi$
$461$	0.197813	+	1.12185i	0.00921308	+	0.0522500i	−0.979855	+	0.199712i	$0.935999\pi$
$462$	3.74283	−	8.02652i	0.174132	−	0.373427i
$463$	−22.7095	+	6.08499i	−1.05540	+	0.282793i	−0.744481	−	0.667643i	$-0.767303\pi$
$463$	−22.7095	+	6.08499i	−1.05540	+	0.282793i	−0.310918	+	0.950437i	$0.600636\pi$
$464$	−2.79952	−	4.84891i	−0.129964	−	0.225105i
$465$	−0.461970	−	2.93548i	−0.0214233	−	0.136130i
$466$	−0.736856	+	0.878151i	−0.0341342	+	0.0406796i
$467$	−15.0417	−	4.03041i	−0.696046	−	0.186505i	−0.106587	−	0.994303i	$-0.533992\pi$
$467$	−15.0417	−	4.03041i	−0.696046	−	0.186505i	−0.589459	+	0.807798i	$0.700659\pi$
$468$	−0.278753	−	1.04032i	−0.0128854	−	0.0480889i
$469$	−8.01707	+	2.91797i	−0.370194	+	0.134739i
$470$	4.48449	+	18.0621i	0.206854	+	0.833142i
$471$	9.12761	+	1.60944i	0.420578	+	0.0741593i
$472$	−5.67397	+	2.64581i	−0.261166	+	0.121783i
$473$	−34.6064	−	3.02766i	−1.59120	−	0.139212i
$474$	−1.63158			−0.0749409
$475$	−7.35291	+	20.5167i	−0.337375	+	0.941371i
$476$	−9.09254			−0.416756
$477$	−1.98412	−	0.173588i	−0.0908465	−	0.00794804i
$478$	7.81806	−	3.64562i	0.357590	−	0.166747i
$479$	−2.85836	−	0.504007i	−0.130602	−	0.0230287i	0.107965	−	0.994155i	$-0.465567\pi$
$479$	−2.85836	−	0.504007i	−0.130602	−	0.0230287i	−0.238567	+	0.971126i	$0.576678\pi$
$480$	−0.538816	−	2.17018i	−0.0245935	−	0.0990547i
$481$	−3.50789	+	1.27677i	−0.159946	+	0.0582156i
$482$	5.61889	+	20.9700i	0.255933	+	0.955157i
$483$	−16.4932	−	4.41934i	−0.750467	−	0.201087i
$484$	1.70064	−	2.02674i	0.0773019	−	0.0921248i
$485$	−0.0852238	−	0.541535i	−0.00386982	−	0.0245898i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−2.25171	+	0.603345i	−0.102035	+	0.0273402i	−0.309475	−	0.950908i	$-0.600153\pi$
$487$	−2.25171	+	0.603345i	−0.102035	+	0.0273402i	0.207440	+	0.978248i	$0.433487\pi$
$488$	−2.72312	+	5.83975i	−0.123270	+	0.264353i
$489$	2.98759	+	16.9435i	0.135104	+	0.766211i
$490$	−3.35695	−	4.15385i	−0.151652	−	0.187652i
$491$	0.669697	+	0.243750i	0.0302230	+	0.0110003i	0.357087	−	0.934071i	$-0.383770\pi$
$491$	0.669697	+	0.243750i	0.0302230	+	0.0110003i	−0.326864	+	0.945071i	$0.605992\pi$
$492$	−0.950405	+	10.8632i	−0.0428476	+	0.489750i
$493$	11.7486	−	11.7486i	0.529131	−	0.529131i
$494$	1.00777	+	4.58518i	0.0453419	+	0.206297i
$495$	0.444489	+	6.44777i	0.0199783	+	0.289806i
$496$	−0.854229	−	1.01803i	−0.0383560	−	0.0457109i
$497$	13.3318	+	28.5902i	0.598014	+	1.28245i
$498$	−7.17449	+	5.02363i	−0.321497	+	0.225114i
$499$	4.96348	−	0.875195i	0.222196	−	0.0391791i	−0.0614418	−	0.998111i	$-0.519570\pi$
$499$	4.96348	−	0.875195i	0.222196	−	0.0391791i	0.283638	+	0.958932i	$0.408459\pi$
$500$	5.89663	+	9.49894i	0.263705	+	0.424805i
$501$	6.14311	−	10.6402i	0.274454	−	0.475368i
$502$	−2.96238	+	11.0557i	−0.132217	+	0.493442i
$503$	3.56815	+	40.7842i	0.159096	+	1.81848i	0.486597	+	0.873627i	$0.338238\pi$
$503$	3.56815	+	40.7842i	0.159096	+	1.81848i	−0.327501	+	0.944851i	$0.606206\pi$
$504$	−2.34721	−	1.96954i	−0.104553	−	0.0877302i
$505$	9.62903	+	14.3060i	0.428486	+	0.636609i
$506$	13.9492	+	8.05357i	0.620118	+	0.358025i
$507$	−10.7307	−	5.00381i	−0.476568	−	0.222227i
$508$	1.65556	+	1.15924i	0.0734538	+	0.0514329i
$509$	−2.46116	+	13.9579i	−0.109089	+	0.618675i	0.880419	+	0.474197i	$0.157261\pi$
$509$	−2.46116	+	13.9579i	−0.109089	+	0.618675i	−0.989508	+	0.144478i	$0.953850\pi$
$510$	5.80670	−	3.21123i	0.257125	−	0.142196i
$511$	−16.6839	+	13.9994i	−0.738052	+	0.619299i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	2.00569	+	3.87004i	0.0885533	+	0.170866i
$514$		−	0.674123i		−	0.0297343i
$515$	−0.136095	+	7.38019i	−0.00599708	+	0.325210i
$516$	−4.11064	+	11.2939i	−0.180961	+	0.497185i
$517$	−13.7981	−	19.7057i	−0.606838	−	0.866655i
$518$	−6.09150	+	8.69957i	−0.267645	+	0.382237i
$519$	2.59644	+	7.13365i	0.113971	+	0.313133i
$520$	2.16352	+	1.05786i	0.0948764	+	0.0463901i
$521$	11.4941	−	6.63613i	0.503567	−	0.290734i	−0.226619	−	0.973984i	$-0.572767\pi$
$521$	11.4941	−	6.63613i	0.503567	−	0.290734i	0.730185	+	0.683249i	$0.239434\pi$
$522$	5.57773	−	0.487988i	0.244131	−	0.0213587i
$523$	32.0495	−	2.80397i	1.40143	−	0.122609i	0.638762	−	0.769404i	$-0.279447\pi$
$523$	32.0495	−	2.80397i	1.40143	−	0.122609i	0.762664	+	0.646795i	$0.223891\pi$
$524$	16.9161	−	9.76651i	0.738983	−	0.426652i
$525$	14.1934	+	5.76706i	0.619450	+	0.251695i
$526$	6.65111	+	18.2738i	0.290002	+	0.796774i
$527$	2.26197	−	3.23042i	0.0985328	−	0.140719i
$528$	1.65785	+	2.36766i	0.0721487	+	0.103039i
$529$	2.75490	−	7.56904i	0.119778	−	0.329089i
$530$	3.20668	−	3.09055i	0.139289	−	0.134245i
$531$		−	6.26053i		−	0.271684i
$532$	9.83061	+	9.04101i	0.426211	+	0.391977i
$533$	−8.30465	−	8.30465i	−0.359714	−	0.359714i
$534$	−10.3014	+	8.64387i	−0.445783	+	0.374057i
$535$	19.6066	+	35.4535i	0.847666	+	1.53279i
$536$	0.483507	−	2.74210i	0.0208843	−	0.118441i
$537$	2.47332	+	1.73184i	0.106732	+	0.0747343i
$538$	−14.0374	−	6.54573i	−0.605194	−	0.282206i
$539$	5.97864	+	3.45177i	0.257518	+	0.148678i
$540$	2.19456	+	0.428824i	0.0944390	+	0.0184537i
$541$	−1.98871	−	1.66873i	−0.0855013	−	0.0717441i	0.599035	−	0.800723i	$-0.295551\pi$
$541$	−1.98871	−	1.66873i	−0.0855013	−	0.0717441i	−0.684537	+	0.728979i	$0.739995\pi$
$542$	−1.09819	−	12.5524i	−0.0471715	−	0.539173i
$543$	0.462407	−	1.72573i	0.0198438	−	0.0740580i
$544$	1.48374	−	2.56991i	0.0636149	−	0.110184i
$545$	−3.79299	+	1.68427i	−0.162474	+	0.0721463i
$546$	3.24992	−	0.573048i	0.139084	−	0.0245242i
$547$	−21.2871	+	14.9054i	−0.910169	+	0.637307i	−0.932002	−	0.362454i	$-0.881939\pi$
$547$	−21.2871	+	14.9054i	−0.910169	+	0.637307i	0.0218324	+	0.999762i	$0.493050\pi$
$548$	4.36914	+	9.36965i	0.186640	+	0.400252i
$549$	−4.14177	−	4.93597i	−0.176766	−	0.210662i
$550$	−11.5246	−	8.72008i	−0.491412	−	0.371826i
$551$	−24.3843	+	1.02026i	−1.03881	+	0.0434645i
$552$	3.94048	−	3.94048i	0.167718	−	0.167718i
$553$	0.435714	−	4.98023i	0.0185284	−	0.211781i
$554$	9.15534	+	3.33227i	0.388973	+	0.141575i
$555$	0.817726	−	7.70709i	0.0347105	−	0.327148i
$556$	2.40669	+	13.6490i	0.102066	+	0.578847i
$557$	−10.1091	+	21.6791i	−0.428337	+	0.918573i	0.567144	+	0.823619i	$0.308048\pi$
$557$	−10.1091	+	21.6791i	−0.428337	+	0.918573i	−0.995482	+	0.0949541i	$0.969730\pi$
$558$	1.28366	−	0.343956i	0.0543417	−	0.0145608i
$559$	−6.47219	−	11.2102i	−0.273744	−	0.474139i
$560$	6.76814	−	1.06513i	0.286006	−	0.0450101i
$561$	−5.51328	+	6.57047i	−0.232771	+	0.277405i
$562$	25.3415	+	6.79023i	1.06897	+	0.286429i
$563$	0.559645	+	2.08862i	0.0235862	+	0.0880250i	0.976716	−	0.214538i	$-0.0688245\pi$
$563$	0.559645	+	2.08862i	0.0235862	+	0.0880250i	−0.953129	+	0.302563i	$0.902158\pi$
$564$	−7.82093	+	2.84659i	−0.329321	+	0.119863i
$565$	15.3999	+	9.27384i	0.647878	+	0.390154i
$566$	9.06865	+	1.59905i	0.381184	+	0.0672130i
$567$	2.77698	−	1.29493i	0.116622	−	0.0543818i
$568$	−10.2563	−	0.897306i	−0.430343	−	0.0376501i
$569$	−27.3070			−1.14477			−0.572384	−	0.819986i	$-0.693981\pi$
$569$	−27.3070			−1.14477			−0.572384	+	0.819986i	$0.693981\pi$
$570$	−9.47108	−	2.30189i	−0.396700	−	0.0964156i
$571$	43.7427			1.83058			0.915288	−	0.402801i	$-0.131963\pi$
$571$	43.7427			1.83058			0.915288	+	0.402801i	$0.131963\pi$
$572$	−3.10115	−	0.271315i	−0.129665	−	0.0113443i
$573$	−14.4736	+	6.74913i	−0.604642	+	0.281949i
$574$	−32.9049	−	5.80203i	−1.37343	−	0.242172i
$575$	−12.6986	+	24.8015i	−0.529569	+	1.03429i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	0.0853619	+	0.318575i	0.00355366	+	0.0132624i	0.967680	−	0.252182i	$-0.0811481\pi$
$577$	0.0853619	+	0.318575i	0.00355366	+	0.0132624i	−0.964126	+	0.265444i	$0.914481\pi$
$578$	−7.91484	−	2.12078i	−0.329214	−	0.0882127i
$579$	−0.972160	+	1.15858i	−0.0404016	+	0.0481487i
$580$	−7.36895	+	10.1215i	−0.305979	+	0.420272i
$581$	−13.4182	−	23.2410i	−0.556680	−	0.964198i
$582$	0.236809	−	0.0634527i	0.00981604	−	0.00263020i
$583$	−2.43291	+	5.21739i	−0.100761	+	0.216082i
$584$	−1.23429	−	6.99999i	−0.0510752	−	0.289662i
$585$	−1.87309	+	1.51374i	−0.0774426	+	0.0625855i
$586$	−21.6919	−	7.89521i	−0.896084	−	0.326148i
$587$	3.34584	−	38.2432i	0.138098	−	1.57846i	−0.538830	−	0.842415i	$-0.681133\pi$
$587$	3.34584	−	38.2432i	0.138098	−	1.57846i	0.676927	−	0.736050i	$-0.263311\pi$
$588$	1.68889	−	1.68889i	0.0696488	−	0.0696488i
$589$	−5.65769	+	1.24350i	−0.233121	+	0.0512375i
$590$	10.5561	+	9.19456i	0.434588	+	0.378534i
$591$	−17.3001	−	20.6175i	−0.711632	−	0.848090i
$592$	−1.46482	−	3.14132i	−0.0602037	−	0.129107i
$593$	−3.13405	+	2.19448i	−0.128700	+	0.0901166i	−0.636154	−	0.771562i	$-0.719476\pi$
$593$	−3.13405	+	2.19448i	−0.128700	+	0.0901166i	0.507454	+	0.861679i	$0.330587\pi$
$594$	−2.84646	+	0.501908i	−0.116792	+	0.0205936i
$595$	8.25128	+	18.5819i	0.338269	+	0.761785i
$596$	−8.19403	+	14.1925i	−0.335641	+	0.581347i
$597$	−4.16201	+	15.5328i	−0.170340	+	0.635716i
$598$	0.523099	+	5.97905i	0.0213911	+	0.244502i
$599$	4.23891	+	3.55687i	0.173197	+	0.145330i	0.725266	−	0.688469i	$-0.241717\pi$
$599$	4.23891	+	3.55687i	0.173197	+	0.145330i	−0.552069	+	0.833799i	$0.686161\pi$
$600$	−3.94611	+	3.07054i	−0.161099	+	0.125354i
$601$	27.9465	+	16.1349i	1.13996	+	0.658157i	0.946421	−	0.322935i	$-0.104669\pi$
$601$	27.9465	+	16.1349i	1.13996	+	0.658157i	0.193541	+	0.981092i	$0.438003\pi$
$602$	−33.3757	−	15.5633i	−1.36029	−	0.634314i
$603$	2.28085	+	1.59707i	0.0928835	+	0.0650377i
$604$	−2.58844	+	14.6798i	−0.105322	+	0.597311i
$605$	−5.68524	−	1.63628i	−0.231138	−	0.0665242i
$606$	−5.90779	+	4.95722i	−0.239988	+	0.201373i
$607$	−26.9251	−	26.9251i	−1.09286	−	1.09286i	−0.995222	−	0.0976333i	$-0.968873\pi$
$607$	−26.9251	−	26.9251i	−1.09286	−	1.09286i	−0.0976333	−	0.995222i	$-0.531127\pi$
$608$	−4.15953	+	1.30319i	−0.168691	+	0.0528514i
$609$			17.1558i			0.695187i
$610$	14.4055	+	0.265647i	0.583263	+	0.0107557i
$611$	3.06583	−	8.42330i	0.124030	−	0.340770i
$612$	1.70208	+	2.43082i	0.0688024	+	0.0982600i
$613$	−4.89957	+	6.99730i	−0.197892	+	0.282618i	−0.905817	−	0.423668i	$-0.860742\pi$
$613$	−4.89957	+	6.99730i	−0.197892	+	0.282618i	0.707926	+	0.706287i	$0.249631\pi$
$614$	−8.07600	−	22.1886i	−0.325921	−	0.895460i
$615$	23.0629	−	7.91580i	0.929988	−	0.319196i
$616$	−7.66976	+	4.42814i	−0.309024	+	0.178415i
$617$	43.3715	−	3.79451i	1.74607	−	0.152761i	0.831057	−	0.556187i	$-0.187736\pi$
$617$	43.3715	−	3.79451i	1.74607	−	0.152761i	0.915012	+	0.403426i	$0.132181\pi$
$618$	−3.28852	+	0.287708i	−0.132284	+	0.0115733i
$619$	−31.3818	+	18.1183i	−1.26134	+	0.728236i	−0.973334	−	0.229392i	$-0.926326\pi$
$619$	−31.3818	+	18.1183i	−1.26134	+	0.728236i	−0.288007	+	0.957628i	$0.592993\pi$
$620$	−1.30530	+	2.66958i	−0.0524220	+	0.107213i
$621$	1.90597	+	5.23661i	0.0764839	+	0.210138i
$622$	16.5212	−	23.5948i	0.662442	−	0.946065i
$623$	−23.6335	−	33.7522i	−0.946858	−	1.35225i
$624$	−0.368363	+	1.01207i	−0.0147463	+	0.0405151i
$625$	14.0614	−	20.6707i	0.562456	−	0.826827i
$626$			33.4438i			1.33668i
$627$	12.4940	−	1.62178i	0.498964	−	0.0647678i
$628$	−6.55376	−	6.55376i	−0.261524	−	0.261524i
$629$	7.87913	−	6.61137i	0.314161	−	0.263613i
$630$	−1.89500	+	6.58417i	−0.0754987	+	0.262319i
$631$	−1.06245	+	6.02544i	−0.0422954	+	0.239869i	−0.998625	−	0.0524211i	$-0.983306\pi$
$631$	−1.06245	+	6.02544i	−0.0422954	+	0.239869i	0.956330	+	0.292290i	$0.0944173\pi$
$632$	1.33651	+	0.935836i	0.0531636	+	0.0372255i
$633$	−24.7678	−	11.5494i	−0.984431	−	0.459047i
$634$	1.21296	+	0.700305i	0.0481729	+	0.0278127i
$635$	0.866684	−	4.43537i	0.0343933	−	0.176012i
$636$	1.52573	+	1.28024i	0.0604990	+	0.0507647i
$637$	0.224201	+	2.56263i	0.00888316	+	0.101535i
$638$	4.18855	−	15.6319i	0.165826	−	0.618872i
$639$	5.14771	−	8.91610i	0.203640	−	0.352716i
$640$	−0.803391	+	2.08676i	−0.0317568	+	0.0824864i
$641$	13.2767	−	2.34104i	0.524397	−	0.0924654i	0.0948182	−	0.995495i	$-0.469773\pi$
$641$	13.2767	−	2.34104i	0.524397	−	0.0924654i	0.429579	+	0.903029i	$0.358662\pi$
$642$	−14.8417	+	10.3922i	−0.585754	+	0.410149i
$643$	9.66876	+	20.7347i	0.381299	+	0.817697i	0.999498	+	0.0316763i	$0.0100846\pi$
$643$	9.66876	+	20.7347i	0.381299	+	0.817697i	−0.618200	+	0.786021i	$0.712138\pi$
$644$	10.9756	+	13.0802i	0.432500	+	0.515433i
$645$	26.8110	−	1.84826i	1.05568	−	0.0727753i
$646$	−6.93011	−	10.9218i	−0.272662	−	0.429714i
$647$	20.5372	−	20.5372i	0.807400	−	0.807400i	−0.176839	−	0.984240i	$-0.556587\pi$
$647$	20.5372	−	20.5372i	0.807400	−	0.807400i	0.984240	+	0.176839i	$0.0565873\pi$
$648$	−0.0871557	+	0.996195i	−0.00342380	+	0.0391342i
$649$	−17.0040	−	6.18895i	−0.667466	−	0.242938i
$650$	0.198542	−	5.38144i	0.00778745	−	0.211077i
$651$	0.707089	+	4.01010i	0.0277130	+	0.157168i
$652$	7.27109	−	15.5929i	0.284758	−	0.610665i
$653$	−26.9056	+	7.20935i	−1.05290	+	0.282124i	−0.743449	−	0.668792i	$-0.766812\pi$
$653$	−26.9056	+	7.20935i	−1.05290	+	0.282124i	−0.309450	+	0.950916i	$0.600145\pi$
$654$	−0.927997	−	1.60734i	−0.0362876	−	0.0628519i
$655$	−35.3102	−	25.7076i	−1.37969	−	1.00448i
$656$	7.00939	−	8.35346i	0.273671	−	0.326148i
$657$	6.86578	+	1.83968i	0.267860	+	0.0717728i
$658$	−6.60033	−	24.6328i	−0.257308	−	0.960286i
$659$	30.6280	−	11.1477i	1.19310	−	0.434253i	0.332288	−	0.943178i	$-0.392179\pi$
$659$	30.6280	−	11.1477i	1.19310	−	0.434253i	0.860811	+	0.508925i	$0.169957\pi$
$660$	3.33419	−	5.53666i	0.129783	−	0.215514i
$661$	28.8826	+	5.09278i	1.12340	+	0.198086i	0.704335	−	0.709868i	$-0.251245\pi$
$661$	28.8826	+	5.09278i	1.12340	+	0.198086i	0.419069	+	0.907954i	$0.362357\pi$
$662$	13.5374	−	6.31258i	0.526145	−	0.245345i
$663$	−3.18388	−	0.278553i	−0.123652	−	0.0108181i
$664$	8.75844			0.339893
$665$	9.55555	−	28.2948i	0.370548	−	1.09722i
$666$	3.46606			0.134307
$667$	−31.0829	−	2.71940i	−1.20354	−	0.105296i
$668$	−11.1351	+	5.19238i	−0.430830	+	0.200899i
$669$	16.4808	+	2.90601i	0.637184	+	0.112353i
$670$	−6.04266	+	1.50028i	−0.233448	+	0.0579610i
$671$	−17.5008	+	6.36978i	−0.675612	+	0.245903i
$672$	0.793037	+	2.95965i	0.0305921	+	0.114171i
$673$	4.07228	+	1.09116i	0.156975	+	0.0420613i	0.336451	−	0.941701i	$-0.390773\pi$
$673$	4.07228	+	1.09116i	0.156975	+	0.0420613i	−0.179476	+	0.983762i	$0.557440\pi$
$674$	−8.01968	+	9.55748i	−0.308906	+	0.368140i
$675$	−1.11515	−	4.87406i	−0.0429223	−	0.187603i
$676$	5.92001	+	10.2538i	0.227693	+	0.394376i
$677$	−31.0858	+	8.32942i	−1.19472	+	0.320126i	−0.800752	−	0.598996i	$-0.795566\pi$
$677$	−31.0858	+	8.32942i	−1.19472	+	0.320126i	−0.393973	+	0.919122i	$0.628900\pi$
$678$	−3.39760	+	7.28618i	−0.130484	+	0.279824i
$679$	0.130443	+	0.739780i	0.00500595	+	0.0283901i
$680$	−6.59846	−	0.700099i	−0.253039	−	0.0268476i
$681$	5.32547	+	1.93831i	0.204072	+	0.0742762i
$682$	0.334778	−	3.82653i	0.0128193	−	0.146525i
$683$	24.9849	−	24.9849i	0.956022	−	0.956022i	−0.0430506	−	0.999073i	$-0.513708\pi$
$683$	24.9849	−	24.9849i	0.956022	−	0.956022i	0.999073	+	0.0430506i	$0.0137077\pi$
$684$	0.576801	−	4.32057i	0.0220545	−	0.165201i
$685$	15.1833	−	17.4317i	0.580126	−	0.666032i
$686$	−9.08261	−	10.8242i	−0.346776	−	0.413271i
$687$	7.95382	+	17.0570i	0.303457	+	0.650766i
$688$	9.84514	−	6.89364i	0.375342	−	0.262818i
$689$	−2.11251	+	0.372492i	−0.0804802	+	0.0141908i
$690$	−11.6288	−	4.47705i	−0.442703	−	0.170438i
$691$	−1.72473	+	2.98732i	−0.0656118	+	0.113643i	−0.896965	−	0.442101i	$-0.854233\pi$
$691$	−1.72473	+	2.98732i	−0.0656118	+	0.113643i	0.831353	+	0.555744i	$0.187567\pi$
$692$	1.96482	−	7.33280i	0.0746912	−	0.278751i
$693$	−0.771876	−	8.82258i	−0.0293211	−	0.335142i
$694$	5.76997	+	4.84158i	0.219025	+	0.183784i
$695$	25.7097	−	17.3046i	0.975225	−	0.656400i
$696$	−4.84891	−	2.79952i	−0.183797	−	0.106115i
$697$	29.3276	+	13.6757i	1.11086	+	0.518003i
$698$	18.1265	+	12.6923i	0.686098	+	0.480411i
$699$	−0.199061	+	1.12893i	−0.00752917	+	0.0427000i
$700$	−8.31870	−	12.8651i	−0.314417	−	0.486255i
$701$	31.8075	−	26.6897i	1.20135	−	1.00805i	0.201762	−	0.979435i	$-0.435333\pi$
$701$	31.8075	−	26.6897i	1.20135	−	1.00805i	0.999590	−	0.0286198i	$-0.00911121\pi$
$702$	−0.761568	−	0.761568i	−0.0287435	−	0.0287435i
$703$	−15.0926	−	0.686432i	−0.569228	−	0.0258893i
$704$		−	2.89038i		−	0.108935i
$705$	12.9147	+	13.4000i	0.486397	+	0.504673i
$706$	4.93578	−	13.5609i	0.185760	−	0.510373i
$707$	−13.5538	−	19.3568i	−0.509741	−	0.727986i
$708$	−3.59089	+	5.12833i	−0.134954	+	0.192734i
$709$	6.81397	+	18.7212i	0.255904	+	0.703091i	0.999409	+	0.0343608i	$0.0109395\pi$
$709$	6.81397	+	18.7212i	0.255904	+	0.703091i	−0.743505	+	0.668730i	$0.766838\pi$
$710$	7.47354	+	21.7744i	0.280477	+	0.817179i
$711$	−1.41299	+	0.815790i	−0.0529912	+	0.0305945i
$712$	13.3963	−	1.17202i	0.502047	−	0.0439235i
$713$	−7.37760	+	0.645456i	−0.276293	+	0.0241725i
$714$	−7.87437	+	4.54627i	−0.294691	+	0.170140i
$715$	2.25975	+	6.58386i	0.0845099	+	0.246222i
$716$	−1.03268	−	2.83727i	−0.0385932	−	0.106034i
$717$	4.94782	−	7.06623i	0.184780	−	0.263893i
$718$	−18.5324	−	26.4670i	−0.691622	−	0.987739i
$719$	−2.01194	+	5.52776i	−0.0750327	+	0.206151i	−0.971539	−	0.236881i	$-0.923875\pi$
$719$	−2.01194	+	5.52776i	−0.0750327	+	0.206151i	0.896506	+	0.443032i	$0.146097\pi$
$720$	−1.55172	−	1.61002i	−0.0578291	−	0.0600020i
$721$		−	10.1147i		−	0.376692i
$722$	−3.36728	+	18.6992i	−0.125317	+	0.695913i
$723$	15.3511	+	15.3511i	0.570913	+	0.570913i
$724$	−1.36862	+	1.14841i	−0.0508643	+	0.0426802i
$725$	27.3719	+	5.87447i	1.01657	+	0.218172i
$726$	0.459426	−	2.60553i	0.0170509	−	0.0967004i
$727$	−34.1481	−	23.9107i	−1.26648	−	0.886800i	−0.269391	−	0.963031i	$-0.586822\pi$
$727$	−34.1481	−	23.9107i	−1.26648	−	0.886800i	−0.997090	+	0.0762311i	$0.975711\pi$
$728$	−2.99086	−	1.39466i	−0.110849	−	0.0516896i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	−13.1854	+	8.87478i	−0.488014	+	0.328470i
$731$	27.3212	+	22.9252i	1.01051	+	0.847919i
$732$	0.561583	+	6.41893i	0.0207567	+	0.237250i
$733$	−2.31507	+	8.63998i	−0.0855092	+	0.319125i	−0.995410	−	0.0957009i	$-0.969491\pi$
$733$	−2.31507	+	8.63998i	−0.0855092	+	0.319125i	0.909901	+	0.414826i	$0.136157\pi$
$734$	2.24351	−	3.88587i	0.0828094	−	0.143430i
$735$	−4.98413	−	1.91887i	−0.183843	−	0.0707784i
$736$	−5.48802	+	0.967686i	−0.202291	+	0.0356694i
$737$	6.59252	−	4.61613i	0.242839	−	0.170037i
$738$	4.60851	+	9.88299i	0.169642	+	0.363798i
$739$	9.87312	+	11.7663i	0.363188	+	0.432831i	0.916433	−	0.400188i	$-0.131055\pi$
$739$	9.87312	+	11.7663i	0.363188	+	0.432831i	−0.553245	+	0.833019i	$0.686611\pi$
$740$	−5.09044	+	5.84425i	−0.187128	+	0.214839i
$741$	3.16535	+	3.46700i	0.116282	+	0.127363i
$742$	−4.31524	+	4.31524i	−0.158418	+	0.158418i
$743$	−0.295710	+	3.37998i	−0.0108485	+	0.123999i	−0.999688	−	0.0249871i	$-0.992046\pi$
$743$	−0.295710	+	3.37998i	−0.0108485	+	0.123999i	0.988839	+	0.148986i	$0.0476011\pi$
$744$	−1.24880	−	0.454525i	−0.0457832	−	0.0166637i
$745$	36.4403	+	3.86633i	1.33507	+	0.141651i
$746$	−4.88622	−	27.7111i	−0.178897	−	1.01458i
$747$	−3.70148	+	7.93784i	−0.135430	+	0.290430i
$748$	8.28488	−	2.21993i	0.302925	−	0.0811686i
$749$	−27.7578	−	48.0779i	−1.01425	−	1.75673i
$750$	9.85610	+	5.27801i	0.359894	+	0.192726i
$751$	−26.3788	+	31.4370i	−0.962576	+	1.14715i	0.0264856	+	0.999649i	$0.491568\pi$
$751$	−26.3788	+	31.4370i	−0.962576	+	1.14715i	−0.989061	+	0.147504i	$0.952876\pi$
$752$	8.03927	+	2.15411i	0.293162	+	0.0785525i
$753$	2.96238	+	11.0557i	0.107955	+	0.402893i
$754$	5.66661	−	2.06248i	0.206366	−	0.0751109i
$755$	32.3492	−	8.03171i	1.17731	−	0.292304i
$756$	−3.01751	−	0.532068i	−0.109746	−	0.0193511i
$757$	−25.3949	+	11.8419i	−0.922995	+	0.430400i	−0.825222	−	0.564809i	$-0.808950\pi$
$757$	−25.3949	+	11.8419i	−0.922995	+	0.430400i	−0.0977733	+	0.995209i	$0.531172\pi$
$758$	−29.9776	−	2.62270i	−1.08883	−	0.0952606i
$759$	16.1071			0.584652
$760$	6.43794	+	7.31799i	0.233529	+	0.265451i
$761$	−33.1353			−1.20115			−0.600577	−	0.799567i	$-0.705062\pi$
$761$	−33.1353			−1.20115			−0.600577	+	0.799567i	$0.705062\pi$
$762$	2.01338	+	0.176148i	0.0729371	+	0.00638117i
$763$	5.15406	−	2.40338i	0.186589	−	0.0870081i
$764$	15.7272	+	2.77313i	0.568990	+	0.100328i
$765$	3.42313	−	5.68436i	0.123764	−	0.205518i
$766$	−0.720637	+	0.262291i	−0.0260377	+	0.00947694i
$767$	−1.74514	−	6.51297i	−0.0630135	−	0.235170i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	11.1139	−	13.2451i	0.400778	−	0.477629i	−0.527479	−	0.849568i	$-0.676863\pi$
$769$	11.1139	−	13.2451i	0.400778	−	0.477629i	0.928257	+	0.371939i	$0.121307\pi$
$770$	16.0097	+	11.6558i	0.576949	+	0.420047i
$771$	−0.337061	−	0.583808i	−0.0121390	−	0.0210253i
$772$	1.46088	−	0.391441i	0.0525782	−	0.0140883i
$773$	−11.3283	+	24.2936i	−0.407451	+	0.873781i	0.590328	+	0.807164i	$0.298999\pi$
$773$	−11.3283	+	24.2936i	−0.407451	+	0.873781i	−0.997779	+	0.0666176i	$0.978779\pi$
$774$	2.08702	+	11.8361i	0.0750166	+	0.425440i
$775$	6.64020	+	0.244982i	0.238523	+	0.00880003i
$776$	−0.230377	−	0.0838505i	−0.00827006	−	0.00301006i
$777$	−0.925612	+	10.5798i	−0.0332062	+	0.379548i
$778$	12.3458	−	12.3458i	0.442618	−	0.442618i
$779$	−18.1100	−	43.9472i	−0.648859	−	1.57457i
$780$	2.40259	−	0.165627i	0.0860265	−	0.00593039i
$781$	−19.1279	−	22.7957i	−0.684448	−	0.815694i
$782$	−6.98877	−	14.9875i	−0.249918	−	0.535951i
$783$	4.58646	−	3.21148i	0.163907	−	0.114769i
$784$	−2.35217	+	0.414751i	−0.0840061	+	0.0148125i
$785$	−7.44617	+	19.3410i	−0.265765	+	0.690308i
$786$	9.76651	−	16.9161i	0.348360	−	0.603377i
$787$	5.94567	−	22.1895i	0.211940	−	0.790972i	−0.775281	−	0.631616i	$-0.782392\pi$
$787$	5.94567	−	22.1895i	0.211940	−	0.790972i	0.987221	−	0.159355i	$-0.0509415\pi$
$788$	2.34573	+	26.8118i	0.0835631	+	0.955131i
$789$	14.8969	+	12.5000i	0.530344	+	0.445011i
$790$	0.699661	−	3.58061i	0.0248928	−	0.127392i
$791$	−21.3330	−	12.3166i	−0.758514	−	0.437928i
$792$	2.61957	+	1.22153i	0.0930824	+	0.0434050i
$793$	−5.68469	−	3.98046i	−0.201869	−	0.141350i
$794$	−6.35544	+	36.0435i	−0.225546	+	1.27913i
$795$	1.23179	−	4.27983i	0.0436870	−	0.151790i
$796$	12.3186	−	10.3365i	0.436620	−	0.366368i
$797$	−5.83550	−	5.83550i	−0.206704	−	0.206704i	0.596161	−	0.802865i	$-0.296692\pi$
$797$	−5.83550	−	5.83550i	−0.206704	−	0.206704i	−0.802865	+	0.596161i	$0.796692\pi$
$798$	13.0341	+	2.91444i	0.461401	+	0.103170i
$799$			24.6979i			0.873750i
$800$	4.99365	−	0.251840i	0.176552	−	0.00890390i
$801$	−4.59931	+	12.6365i	−0.162508	+	0.446488i
$802$	13.3472	+	19.0617i	0.471305	+	0.673093i
$803$	11.7840	−	16.8293i	0.415847	−	0.593892i
$804$	−0.952323	−	2.61649i	−0.0335858	−	0.0922763i
$805$	16.7712	−	34.3003i	0.591108	−	1.20893i
$806$	1.23954	−	0.715650i	0.0436610	−	0.0252077i
$807$	−15.4296	+	1.34991i	−0.543147	+	0.0475192i
$808$	7.68273	−	0.672151i	0.270277	−	0.0236462i
$809$	17.0387	−	9.83727i	0.599047	−	0.345860i	−0.169620	−	0.985510i	$-0.554254\pi$
$809$	17.0387	−	9.83727i	0.599047	−	0.345860i	0.768667	+	0.639650i	$0.220921\pi$
$810$	2.11496	−	0.725909i	0.0743121	−	0.0255058i
$811$	−12.7852	−	35.1270i	−0.448949	−	1.23348i	−0.933457	−	0.358690i	$-0.883224\pi$
$811$	−12.7852	−	35.1270i	−0.448949	−	1.23348i	0.484508	−	0.874787i	$-0.338999\pi$
$812$	9.84015	−	14.0532i	0.345322	−	0.493170i
$813$	−7.22727	−	10.3216i	−0.253472	−	0.361995i
$814$	3.42643	−	9.41404i	0.120096	−	0.329962i
$815$	−38.4647	−	0.709314i	−1.34736	−	0.0248462i
$816$		−	2.96748i		−	0.103883i
$817$	−6.74367	−	51.9524i	−0.235931	−	1.81759i
$818$	−10.9427	−	10.9427i	−0.382601	−	0.382601i
$819$	2.52799	−	2.12123i	0.0883350	−	0.0741219i
$820$	−23.4324	−	6.74412i	−0.818294	−	0.235515i
$821$	−1.09497	+	6.20988i	−0.0382147	+	0.216726i	−0.997935	−	0.0642307i	$-0.979541\pi$
$821$	−1.09497	+	6.20988i	−0.0382147	+	0.216726i	0.959720	+	0.280957i	$0.0906518\pi$
$822$	8.46861	+	5.92979i	0.295377	+	0.206825i
$823$	36.7470	+	17.1354i	1.28092	+	0.597303i	0.939481	−	0.342600i	$-0.111308\pi$
$823$	36.7470	+	17.1354i	1.28092	+	0.597303i	0.341440	+	0.939904i	$0.389085\pi$
$824$	2.85882	+	1.65054i	0.0995918	+	0.0574994i
$825$	−14.3407	−	1.78950i	−0.499278	−	0.0623025i
$826$	−14.6947	−	12.3304i	−0.511296	−	0.429028i
$827$	2.08101	+	23.7861i	0.0723639	+	0.827123i	0.942477	+	0.334271i	$0.108490\pi$
$827$	2.08101	+	23.7861i	0.0723639	+	0.827123i	−0.870113	+	0.492852i	$0.835954\pi$
$828$	1.44232	−	5.38280i	0.0501240	−	0.187065i
$829$	−6.61517	+	11.4578i	−0.229754	+	0.397946i	−0.957735	−	0.287651i	$-0.907126\pi$
$829$	−6.61517	+	11.4578i	−0.229754	+	0.397946i	0.727981	+	0.685597i	$0.240459\pi$
$830$	−7.94809	−	17.8991i	−0.275882	−	0.621288i
$831$	9.59489	−	1.69184i	0.332843	−	0.0586892i
$832$	0.882243	−	0.617753i	0.0305863	−	0.0214167i
$833$	−2.99539	−	6.42364i	−0.103784	−	0.222566i
$834$	8.90876	+	10.6170i	0.308485	+	0.367638i
$835$	20.7162	+	18.0442i	0.716914	+	0.624445i
$836$	−11.1647	−	5.83780i	−0.386140	−	0.201904i
$837$	0.939705	−	0.939705i	0.0324810	−	0.0324810i
$838$	0.592302	−	6.77004i	0.0204607	−	0.233867i
$839$	−5.56360	−	2.02498i	−0.192077	−	0.0699102i	0.244191	−	0.969727i	$-0.421478\pi$
$839$	−5.56360	−	2.02498i	−0.192077	−	0.0699102i	−0.436268	+	0.899817i	$0.643700\pi$
$840$	5.32882	−	4.30651i	0.183862	−	0.148589i
$841$	0.407937	+	2.31353i	0.0140668	+	0.0797767i
$842$	15.3680	−	32.9569i	0.529618	−	1.13577i
$843$	25.3415	−	6.79023i	0.872808	−	0.233868i
$844$	13.6641	+	23.6669i	0.470338	+	0.814649i
$845$	15.5828	−	21.4035i	0.536064	−	0.736302i
$846$	−5.34983	+	6.37568i	−0.183931	+	0.219200i
$847$	7.83044	+	2.09816i	0.269057	+	0.0720936i
$848$	−0.515489	−	1.92383i	−0.0177020	−	0.0660646i
$849$	8.65321	−	3.14951i	0.296977	−	0.108091i
$850$	4.55720	+	14.1202i	0.156311	+	0.484320i
$851$	−19.0218	−	3.35406i	−0.652059	−	0.114976i
$852$	−9.33083	+	4.35104i	−0.319669	+	0.149064i
$853$	−47.2783	−	4.13631i	−1.61878	−	0.141625i	−0.758578	−	0.651583i	$-0.774105\pi$
$853$	−47.2783	−	4.13631i	−1.61878	−	0.141625i	−0.860199	+	0.509958i	$0.829661\pi$
$854$	−19.7431			−0.675595
$855$	−9.35314	+	2.74204i	−0.319871	+	0.0937759i
$856$	18.1183			0.619272
$857$	20.1826	+	1.76575i	0.689425	+	0.0603169i	0.426484	−	0.904495i	$-0.359752\pi$
$857$	20.1826	+	1.76575i	0.689425	+	0.0603169i	0.262941	+	0.964812i	$0.415308\pi$
$858$	−2.82133	+	1.31561i	−0.0963186	+	0.0449141i
$859$	3.73101	+	0.657878i	0.127300	+	0.0224465i	0.236935	−	0.971525i	$-0.423857\pi$
$859$	3.73101	+	0.657878i	0.127300	+	0.0224465i	−0.109635	+	0.993972i	$0.534968\pi$
$860$	−23.0224	−	13.8641i	−0.785057	−	0.472763i
$861$	−31.3975	+	11.4278i	−1.07003	+	0.389457i
$862$	6.46151	+	24.1147i	0.220080	+	0.821349i
$863$	21.6439	+	5.79945i	0.736765	+	0.197416i	0.607640	−	0.794213i	$-0.292116\pi$
$863$	21.6439	+	5.79945i	0.736765	+	0.197416i	0.129125	+	0.991628i	$0.458783\pi$
$864$	0.642788	−	0.766044i	0.0218681	−	0.0260614i
$865$	−16.7687	+	2.63896i	−0.570152	+	0.0897275i
$866$	16.5293	+	28.6296i	0.561688	+	0.972872i
$867$	−7.91484	+	2.12078i	−0.268802	+	0.0720253i
$868$	1.72089	−	3.69045i	0.0584107	−	0.125262i
$869$	0.818904	+	4.64423i	0.0277794	+	0.157545i
$870$	−1.32095	+	12.4499i	−0.0447842	+	0.422093i
$871$	2.81801	+	1.02567i	0.0954845	+	0.0347535i
$872$	−0.161761	+	1.84893i	−0.00547790	+	0.0626127i
$873$	0.173356	−	0.173356i	0.00586721	−	0.00586721i
$874$	−7.34645	+	23.1532i	−0.248497	+	0.783169i
$875$	−18.7427	+	28.6752i	−0.633617	+	0.969400i
$876$	−4.56892	−	5.44503i	−0.154370	−	0.183970i
$877$	7.94780	+	17.0441i	0.268378	+	0.575538i	0.993597	−	0.112979i	$-0.0360394\pi$
$877$	7.94780	+	17.0441i	0.268378	+	0.575538i	−0.725219	+	0.688518i	$0.758262\pi$
$878$	−15.9708	+	11.1829i	−0.538989	+	0.377404i
$879$	−22.7333	+	4.00850i	−0.766776	+	0.135203i
$880$	−5.90690	+	2.62295i	−0.199122	+	0.0884197i
$881$	8.35173	−	14.4656i	0.281377	−	0.487359i	−0.690347	−	0.723478i	$-0.742542\pi$
$881$	8.35173	−	14.4656i	0.281377	−	0.487359i	0.971724	+	0.236119i	$0.0758756\pi$
$882$	0.618178	−	2.30707i	0.0208151	−	0.0776832i
$883$	1.17389	+	13.4176i	0.0395045	+	0.451538i	0.990027	+	0.140881i	$0.0449935\pi$
$883$	1.17389	+	13.4176i	0.0395045	+	0.451538i	−0.950522	+	0.310657i	$0.899451\pi$
$884$	2.44831	+	2.05437i	0.0823455	+	0.0690961i
$885$	13.7391	+	2.68467i	0.461836	+	0.0902441i
$886$	−21.9815	−	12.6910i	−0.738481	−	0.426362i
$887$	13.3977	+	6.24744i	0.449850	+	0.209768i	0.634321	−	0.773069i	$-0.281280\pi$
$887$	13.3977	+	6.24744i	0.449850	+	0.209768i	−0.184472	+	0.982838i	$0.559057\pi$
$888$	−2.83923	−	1.98805i	−0.0952783	−	0.0667146i
$889$	−1.07535	+	6.09860i	−0.0360660	+	0.204540i
$890$	−14.5520	−	26.3137i	−0.487786	−	0.882037i
$891$	−2.21416	+	1.85790i	−0.0741770	+	0.0622419i
$892$	−11.8335	−	11.8335i	−0.396213	−	0.396213i
$893$	24.5580	−	26.7027i	0.821801	−	0.893573i
$894$			16.3881i			0.548099i
$895$	−4.86124	+	4.68520i	−0.162493	+	0.156609i
$896$	1.04797	−	2.87927i	0.0350102	−	0.0961898i
$897$	3.44254	+	4.91646i	0.114943	+	0.164156i
$898$	−9.44280	+	13.4857i	−0.315110	+	0.450024i
$899$	2.54491	+	6.99207i	0.0848773	+	0.233199i
$900$	−1.88216	+	4.63222i	−0.0627388	+	0.154407i
$901$	5.11849	−	2.95516i	0.170522	−	0.0984507i
$902$	31.3987	−	2.74703i	1.04546	−	0.0914660i
$903$	−36.6859	+	3.20960i	−1.22083	+	0.106809i
$904$	6.96233	−	4.01970i	0.231564	−	0.133693i
$905$	3.58893	+	1.75482i	0.119300	+	0.0583320i
$906$	5.09823	+	14.0073i	0.169377	+	0.465360i
$907$	2.18367	−	3.11861i	0.0725077	−	0.103552i	−0.781260	−	0.624205i	$-0.785423\pi$
$907$	2.18367	−	3.11861i	0.0725077	−	0.103552i	0.853768	+	0.520654i	$0.174312\pi$
$908$	−3.25060	−	4.64233i	−0.107875	−	0.154061i
$909$	−2.63768	+	7.24698i	−0.0874865	+	0.240367i
$910$	−0.136053	+	7.37789i	−0.00451011	+	0.244575i
$911$			37.0026i			1.22595i	0.790102	+	0.612976i	$0.210028\pi$
$911$			37.0026i			1.22595i	−0.790102	+	0.612976i	$0.789972\pi$
$912$	−2.95066	+	3.20836i	−0.0977062	+	0.106239i
$913$	17.9005	+	17.9005i	0.592421	+	0.592421i
$914$	1.89494	−	1.59004i	0.0626791	−	0.0525940i
$915$	12.6084	−	6.97271i	0.416820	−	0.230511i
$916$	3.26812	−	18.5344i	0.107982	−	0.612395i
$917$	49.0265	+	34.3287i	1.61900	+	1.13363i
$918$	2.68945	+	1.25411i	0.0887651	+	0.0413919i
$919$	0.972703	+	0.561590i	0.0320865	+	0.0185252i	0.515957	−	0.856614i	$-0.327436\pi$
$919$	0.972703	+	0.561590i	0.0320865	+	0.0185252i	−0.483871	+	0.875139i	$0.660770\pi$
$920$	6.95786	+	10.3374i	0.229394	+	0.340814i
$921$	−18.0883	−	15.1779i	−0.596031	−	0.500129i
$922$	−0.0992844	−	1.13483i	−0.00326976	−	0.0373735i
$923$	2.86988	−	10.7106i	0.0944634	−	0.352542i
$924$	−4.42814	+	7.66976i	−0.145675	+	0.252317i
$925$	16.5630	+	5.09954i	0.544589	+	0.167672i
$926$	23.1534	−	4.08257i	0.760868	−	0.134162i
$927$	−2.70409	+	1.89342i	−0.0888140	+	0.0621882i
$928$	2.36626	+	5.07445i	0.0776761	+	0.166577i
$929$	−20.4276	−	24.3446i	−0.670206	−	0.798721i	0.318606	−	0.947887i	$-0.396785\pi$
$929$	−20.4276	−	24.3446i	−0.670206	−	0.798721i	−0.988812	+	0.149167i	$0.952341\pi$
$930$	0.204368	+	2.96457i	0.00670150	+	0.0972122i
$931$	−3.14869	+	9.92348i	−0.103194	+	0.325229i
$932$	0.810588	−	0.810588i	0.0265517	−	0.0265517i
$933$	2.51043	−	28.6943i	0.0821877	−	0.939410i
$934$	14.6332	+	5.32604i	0.478812	+	0.174273i
$935$	−12.0551	−	14.9168i	−0.394243	−	0.487832i
$936$	0.187023	+	1.06066i	0.00611302	+	0.0346687i
$937$	−2.16668	+	4.64647i	−0.0707824	+	0.151793i	−0.938516	−	0.345237i	$-0.887799\pi$
$937$	−2.16668	+	4.64647i	−0.0707824	+	0.151793i	0.867733	+	0.497030i	$0.165576\pi$
$938$	8.24088	−	2.20814i	0.269074	−	0.0720982i
$939$	16.7219	+	28.9632i	0.545698	+	0.945177i
$940$	−2.89321	−	18.3842i	−0.0943661	−	0.599627i
$941$	−13.4848	+	16.0705i	−0.439591	+	0.523884i	−0.939664	−	0.342099i	$-0.888862\pi$
$941$	−13.4848	+	16.0705i	−0.439591	+	0.523884i	0.500073	+	0.865983i	$0.333306\pi$
$942$	−8.95261	−	2.39884i	−0.291692	−	0.0781586i
$943$	−15.7280	−	58.6977i	−0.512174	−	1.91146i
$944$	5.88297	−	2.14123i	0.191475	−	0.0696910i
$945$	1.65096	+	6.64956i	0.0537058	+	0.216310i
$946$	34.2108	+	6.03229i	1.11229	+	0.196127i
$947$	10.1106	−	4.71463i	0.328549	−	0.153205i	−0.251343	−	0.967898i	$-0.580872\pi$
$947$	10.1106	−	4.71463i	0.328549	−	0.153205i	0.579892	+	0.814693i	$0.303095\pi$
$948$	1.62537	+	0.142202i	0.0527896	+	0.00461849i
$949$	7.65544			0.248506
$950$	9.11308	−	19.7978i	0.295667	−	0.642325i
$951$	1.40061			0.0454179
$952$	9.05794	+	0.792467i	0.293570	+	0.0256840i
$953$	1.46265	−	0.682043i	0.0473798	−	0.0220935i	−0.398784	−	0.917045i	$-0.630568\pi$
$953$	1.46265	−	0.682043i	0.0473798	−	0.0220935i	0.446164	+	0.894951i	$0.352790\pi$
$954$	1.96144	+	0.345854i	0.0635039	+	0.0111974i
$955$	−8.60479	−	34.6573i	−0.278444	−	1.12149i
$956$	−8.10604	+	2.95036i	−0.262168	+	0.0954214i
$957$	−4.18855	−	15.6319i	−0.135397	−	0.505307i
$958$	2.80356	+	0.751212i	0.0905789	+	0.0242705i
$959$	−20.3616	+	24.2660i	−0.657511	+	0.783591i
$960$	0.347622	+	2.20888i	0.0112195	+	0.0712914i
$961$	−14.6170	−	25.3173i	−0.471515	−	0.816687i
$962$	3.60582	−	0.966176i	0.116256	−	0.0311508i
$963$	−7.65714	+	16.4208i	−0.246748	+	0.529152i
$964$	−3.76985	−	21.3799i	−0.121419	−	0.688600i
$965$	−2.12568	−	2.63029i	−0.0684281	−	0.0846721i
$966$	16.0453	+	5.84000i	0.516248	+	0.187899i
$967$	−4.64023	+	53.0381i	−0.149220	+	1.70559i	0.440312	+	0.897845i	$0.354868\pi$
$967$	−4.64023	+	53.0381i	−0.149220	+	1.70559i	−0.589532	+	0.807745i	$0.700688\pi$
$968$	−1.87081	+	1.87081i	−0.0601302	+	0.0601302i
$969$	−11.4626	−	5.99353i	−0.368231	−	0.192540i
$970$	0.0377017	+	0.546902i	0.00121053	+	0.0175600i
$971$	25.7155	+	30.6465i	0.825249	+	0.983494i	0.999999	−	0.00111887i	$-0.000356146\pi$
$971$	25.7155	+	30.6465i	0.825249	+	0.983494i	−0.174750	+	0.984613i	$0.555912\pi$
$972$	0.422618	+	0.906308i	0.0135555	+	0.0290698i
$973$	−34.7865	+	24.3578i	−1.11521	+	0.780875i
$974$	2.29573	−	0.404799i	0.0735599	−	0.0129706i
$975$	−2.51878	−	4.75973i	−0.0806654	−	0.152433i
$976$	3.22172	−	5.58019i	0.103125	−	0.178617i
$977$	5.42330	−	20.2400i	0.173507	−	0.647536i	−0.823294	−	0.567615i	$-0.807866\pi$
$977$	5.42330	−	20.2400i	0.173507	−	0.647536i	0.996801	−	0.0799217i	$-0.0254670\pi$
$978$	−1.49950	−	17.1394i	−0.0479488	−	0.548058i
$979$	29.7748	+	24.9840i	0.951607	+	0.798493i
$980$	2.98215	+	4.43062i	0.0952612	+	0.141531i
$981$	−1.60734	−	0.927997i	−0.0513184	−	0.0296287i
$982$	−0.645905	−	0.301190i	−0.0206116	−	0.00961137i
$983$	37.6752	+	26.3804i	1.20165	+	0.841405i	0.990696	−	0.136090i	$-0.0434538\pi$
$983$	37.6752	+	26.3804i	1.20165	+	0.841405i	0.210955	+	0.977496i	$0.432343\pi$
$984$	1.89358	−	10.7390i	0.0603650	−	0.342347i
$985$	52.6651	−	29.1250i	1.67805	−	0.927998i
$986$	−12.7279	+	10.6799i	−0.405338	+	0.340119i
$987$	−18.0325	−	18.0325i	−0.573979	−	0.573979i
$988$	−0.604314	−	4.65556i	−0.0192258	−	0.148113i
$989$		−	66.9764i		−	2.12973i
$990$	0.119163	−	6.46198i	0.00378725	−	0.205375i
$991$	−17.6073	+	48.3756i	−0.559313	+	1.53670i	0.261324	+	0.965251i	$0.415841\pi$
$991$	−17.6073	+	48.3756i	−0.559313	+	1.53670i	−0.820637	+	0.571449i	$0.806381\pi$
$992$	0.762251	+	1.08861i	0.0242015	+	0.0345633i
$993$	8.56742	−	12.2355i	0.271879	−	0.388283i
$994$	−10.7893	−	29.6434i	−0.342216	−	0.940230i
$995$	−32.3030	−	15.7946i	−1.02407	−	0.500724i
$996$	7.58503	−	4.37922i	0.240341	−	0.138761i
$997$	2.60337	−	0.227765i	0.0824495	−	0.00721340i	−0.0458563	−	0.998948i	$-0.514602\pi$
$997$	2.60337	−	0.227765i	0.0824495	−	0.00721340i	0.128306	+	0.991735i	$0.459046\pi$
$998$	−5.02087	+	0.439269i	−0.158933	+	0.0139048i
$999$	3.00170	−	1.73303i	0.0949695	−	0.0548306i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.13.2	✓	120
5.2	odd	4	inner	570.2.bh.a.127.8	yes	120
19.3	odd	18	inner	570.2.bh.a.193.8	yes	120
95.22	even	36	inner	570.2.bh.a.307.2	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.13.2	✓	120	1.1	even	1	trivial
570.2.bh.a.127.8	yes	120	5.2	odd	4	inner
570.2.bh.a.193.8	yes	120	19.3	odd	18	inner
570.2.bh.a.307.2	yes	120	95.22	even	36	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-0.538816 - 2.17018i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.793037 + 2.95965i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-0.538816 - 2.17018i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.793037 + 2.95965i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(0.347622 + 2.20888i) q^{10} +(-1.44519 - 2.50314i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(0.455168 - 0.976112i) q^{13} +(-0.532068 - 3.01751i) q^{14} +(1.40549 + 1.73914i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-0.258633 + 2.95619i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(3.21906 - 2.93899i) q^{19} +(-0.153782 - 2.23077i) q^{20} +(-1.96954 - 2.34721i) q^{21} +(1.22153 + 2.61957i) q^{22} +(4.56487 - 3.19636i) q^{23} +(0.984808 - 0.173648i) q^{24} +(-4.41935 + 2.33865i) q^{25} +(-0.538510 + 0.932727i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(0.267050 + 3.05240i) q^{28} +(-4.28911 - 3.59899i) q^{29} +(-1.24857 - 1.85502i) q^{30} +(-1.15090 - 0.664472i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(2.36766 + 1.65785i) q^{33} +(0.515298 - 2.92240i) q^{34} +(5.99568 - 3.31574i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-2.45087 - 2.45087i) q^{37} +(-3.46296 + 2.64724i) q^{38} +1.07702i q^{39} +(-0.0412275 + 2.23569i) q^{40} +(3.72962 - 10.2470i) q^{41} +(1.75747 + 2.50993i) q^{42} +(6.89364 - 9.84514i) q^{43} +(-0.988567 - 2.71606i) q^{44} +(-2.00880 - 0.982207i) q^{45} +(-4.82609 + 2.78634i) q^{46} +(8.29119 - 0.725385i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(-2.06846 + 1.19423i) q^{49} +(4.60637 - 1.94458i) q^{50} +(-1.01494 - 2.78852i) q^{51} +(0.617753 - 0.882243i) q^{52} +(-1.14239 - 1.63150i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-4.65357 + 4.48505i) q^{55} -3.06406i q^{56} +(-1.67539 + 4.02406i) q^{57} +(3.95912 + 3.95912i) q^{58} +(4.79584 - 4.02419i) q^{59} +(1.08214 + 1.95678i) q^{60} +(1.11889 - 6.34556i) q^{61} +(1.08861 + 0.762251i) q^{62} +(2.77698 + 1.29493i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-2.36359 - 0.461852i) q^{65} +(-2.21416 - 1.85790i) q^{66} +(0.242677 + 2.77381i) q^{67} +(-0.768041 + 2.86637i) q^{68} +(-2.78634 + 4.82609i) q^{69} +(-6.26185 + 2.78057i) q^{70} +(10.1390 - 1.78778i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(3.00396 + 6.44202i) q^{73} +(2.22794 + 2.65516i) q^{74} +(3.01694 - 3.98724i) q^{75} +(3.68051 - 2.33535i) q^{76} +(6.26234 - 6.26234i) q^{77} +(0.0938685 - 1.07292i) q^{78} +(-1.53318 - 0.558033i) q^{79} +(0.235924 - 2.22359i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-4.60851 + 9.88299i) q^{82} +(-8.46000 + 2.26685i) q^{83} +(-1.53203 - 2.65355i) q^{84} +(6.55482 - 1.03156i) q^{85} +(-7.72547 + 9.20686i) q^{86} +(5.40825 + 1.44914i) q^{87} +(0.748084 + 2.79189i) q^{88} +(-12.6365 + 4.59931i) q^{89} +(1.91555 + 1.15355i) q^{90} +(3.24992 + 0.573048i) q^{91} +(5.05057 - 2.35512i) q^{92} +(1.32389 + 0.115825i) q^{93} -8.32286 q^{94} +(-8.11261 - 5.40237i) q^{95} +1.00000 q^{96} +(0.244230 + 0.0213673i) q^{97} +(2.16468 - 1.00941i) q^{98} +(-2.84646 - 0.501908i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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