LMFDB - Embedded newform 980.2.c.e.979.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [980,2,Mod(979,980)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(980, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1]))

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

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

chi := DirichletCharacter("980.979");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	980.c (of order $2$, degree $1$, 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:	$7.82533939809$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			979.31
Character	$\chi$	$=$	980.979
Dual form			980.2.c.e.979.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 + 1.48845i) q^{4} +(-0.639901 - 2.14255i) q^{5} +(3.23064 - 1.44151i) q^{6} +(-2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +O(q^{10})$	\(q+(0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 + 1.48845i) q^{4} +(-0.639901 - 2.14255i) q^{5} +(3.23064 - 1.44151i) q^{6} +(-2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +(2.39832 - 2.06108i) q^{10} -2.25026i q^{11} +(3.72336 + 3.34164i) q^{12} +5.96620 q^{13} +(-5.35959 + 1.60071i) q^{15} +(-0.430987 - 3.97671i) q^{16} -2.00749 q^{17} +(-1.87716 - 4.20700i) q^{18} -7.81989 q^{19} +(4.04390 + 1.90967i) q^{20} +(2.90618 - 1.29673i) q^{22} -2.99226 q^{23} +(-2.17005 + 6.73430i) q^{24} +(-4.18105 + 2.74204i) q^{25} +(3.43807 + 7.70524i) q^{26} +0.644123i q^{27} -4.87936 q^{29} +(-5.15579 - 5.99939i) q^{30} +1.49990 q^{31} +(4.88750 - 2.84822i) q^{32} -5.62903 q^{33} +(-1.15683 - 2.59263i) q^{34} +(4.35154 - 4.84863i) q^{36} +4.78601i q^{37} +(-4.50627 - 10.0992i) q^{38} -14.9244i q^{39} +(-0.135982 + 6.32309i) q^{40} -8.82927i q^{41} +1.12695 q^{43} +(3.34941 + 3.00602i) q^{44} +(2.08447 + 6.97935i) q^{45} +(-1.72431 - 3.86446i) q^{46} -9.56972i q^{47} +(-9.94774 + 1.07811i) q^{48} +(-5.95066 - 3.81964i) q^{50} +5.02172i q^{51} +(-7.96997 + 8.88040i) q^{52} +7.06264i q^{53} +(-0.831874 + 0.371181i) q^{54} +(-4.82131 + 1.43994i) q^{55} +19.5614i q^{57} +(-2.81177 - 6.30161i) q^{58} -11.4057 q^{59} +(4.77705 - 10.1158i) q^{60} +1.21986i q^{61} +(0.864331 + 1.93710i) q^{62} +(6.49489 + 4.67081i) q^{64} +(-3.81777 - 12.7829i) q^{65} +(-3.24377 - 7.26979i) q^{66} +1.11485 q^{67} +(2.68171 - 2.98805i) q^{68} +7.48514i q^{69} -8.40090i q^{71} +(8.76953 + 2.82588i) q^{72} +5.88062 q^{73} +(-6.18105 + 2.75798i) q^{74} +(6.85921 + 10.4589i) q^{75} +(10.4462 - 11.6395i) q^{76} +(19.2746 - 8.60032i) q^{78} -12.1357i q^{79} +(-8.24453 + 3.46811i) q^{80} -8.16121 q^{81} +(11.4028 - 5.08793i) q^{82} +11.1319i q^{83} +(1.28459 + 4.30114i) q^{85} +(0.649414 + 1.45544i) q^{86} +12.2057i q^{87} +(-1.95210 + 6.05795i) q^{88} -4.57883i q^{89} +(-7.81252 + 6.71396i) q^{90} +(3.99723 - 4.45385i) q^{92} -3.75201i q^{93} +(12.3591 - 5.51462i) q^{94} +(5.00395 + 16.7545i) q^{95} +(-7.12483 - 12.2261i) q^{96} +4.62008 q^{97} +7.33022i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) $ 48 * q + 16 * q^4 - 64 * q^9	$ 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) $ 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$-1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.576258	+	1.29148i	0.407476	+	0.913216i
$2$	0.576258	+	1.29148i	0.407476	+	0.913216i
$3$		−	2.50150i		−	1.44424i	−0.691767	−	0.722120i	$-0.743168\pi$
$3$		−	2.50150i		−	1.44424i	0.691767	−	0.722120i	$-0.256832\pi$
$4$	−1.33585	+	1.48845i	−0.667927	+	0.744227i
$5$	−0.639901	−	2.14255i	−0.286172	−	0.958178i
$5$	−0.639901	−	2.14255i	−0.286172	−	0.958178i
$6$	3.23064	−	1.44151i	1.31890	−	0.588493i
$7$		0			0
$7$		0			0
$8$	−2.69211	−	0.867500i	−0.951804	−	0.306708i
$9$	−3.25749			−1.08583
$10$	2.39832	−	2.06108i	0.758415	−	0.651771i
$11$		−	2.25026i		−	0.678480i	−0.940700	−	0.339240i	$-0.889830\pi$
$11$		−	2.25026i		−	0.678480i	0.940700	−	0.339240i	$-0.110170\pi$
$12$	3.72336	+	3.34164i	1.07484	+	0.964648i
$13$	5.96620			1.65472			0.827362	−	0.561668i	$-0.189840\pi$
$13$	5.96620			1.65472			0.827362	+	0.561668i	$0.189840\pi$
$14$		0			0
$15$	−5.35959	+	1.60071i	−1.38384	+	0.413302i
$16$	−0.430987	−	3.97671i	−0.107747	−	0.994178i
$17$	−2.00749			−0.486887			−0.243443	−	0.969915i	$-0.578277\pi$
$17$	−2.00749			−0.486887			−0.243443	+	0.969915i	$0.578277\pi$
$18$	−1.87716	−	4.20700i	−0.442450	−	0.991599i
$19$	−7.81989			−1.79400			−0.897002	−	0.442026i	$-0.854260\pi$
$19$	−7.81989			−1.79400			−0.897002	+	0.442026i	$0.854260\pi$
$20$	4.04390	+	1.90967i	0.904244	+	0.427016i
$21$		0			0
$22$	2.90618	−	1.29673i	0.619599	−	0.276464i
$23$	−2.99226			−0.623930			−0.311965	−	0.950094i	$-0.600987\pi$
$23$	−2.99226			−0.623930			−0.311965	+	0.950094i	$0.600987\pi$
$24$	−2.17005	+	6.73430i	−0.442960	+	1.37463i
$25$	−4.18105	+	2.74204i	−0.836211	+	0.548408i
$26$	3.43807	+	7.70524i	0.674260	+	1.51112i
$27$			0.644123i			0.123962i
$28$		0			0
$29$	−4.87936			−0.906074			−0.453037	−	0.891492i	$-0.649659\pi$
$29$	−4.87936			−0.906074			−0.453037	+	0.891492i	$0.649659\pi$
$30$	−5.15579	−	5.99939i	−0.941315	−	1.09533i
$31$	1.49990			0.269391			0.134695	−	0.990887i	$-0.456994\pi$
$31$	1.49990			0.269391			0.134695	+	0.990887i	$0.456994\pi$
$32$	4.88750	−	2.84822i	0.863996	−	0.503500i
$33$	−5.62903			−0.979888
$34$	−1.15683	−	2.59263i	−0.198395	−	0.444633i
$35$		0			0
$36$	4.35154	−	4.84863i	0.725256	−	0.808105i
$37$			4.78601i			0.786816i	0.919364	+	0.393408i	$0.128704\pi$
$37$			4.78601i			0.786816i	−0.919364	+	0.393408i	$0.871296\pi$
$38$	−4.50627	−	10.0992i	−0.731013	−	1.63831i
$39$		−	14.9244i		−	2.38982i
$40$	−0.135982	+	6.32309i	−0.0215006	+	0.999769i
$41$		−	8.82927i		−	1.37890i	−0.724333	−	0.689450i	$-0.757852\pi$
$41$		−	8.82927i		−	1.37890i	0.724333	−	0.689450i	$-0.242148\pi$
$42$		0			0
$43$	1.12695			0.171858			0.0859292	−	0.996301i	$-0.472614\pi$
$43$	1.12695			0.171858			0.0859292	+	0.996301i	$0.472614\pi$
$44$	3.34941	+	3.00602i	0.504943	+	0.453175i
$45$	2.08447	+	6.97935i	0.310735	+	1.04042i
$46$	−1.72431	−	3.86446i	−0.254236	−	0.569783i
$47$		−	9.56972i		−	1.39589i	−0.716153	−	0.697943i	$-0.754099\pi$
$47$		−	9.56972i		−	1.39589i	0.716153	−	0.697943i	$-0.245901\pi$
$48$	−9.94774	+	1.07811i	−1.43583	+	0.155612i
$49$		0			0
$50$	−5.95066	−	3.81964i	−0.841551	−	0.540178i
$51$			5.02172i			0.703182i
$52$	−7.96997	+	8.88040i	−1.10524	+	1.23149i
$53$			7.06264i			0.970129i	0.874478	+	0.485064i	$0.161204\pi$
$53$			7.06264i			0.970129i	−0.874478	+	0.485064i	$0.838796\pi$
$54$	−0.831874	+	0.371181i	−0.113204	+	0.0505113i
$55$	−4.82131	+	1.43994i	−0.650105	+	0.194162i
$56$		0			0
$57$			19.5614i			2.59098i
$58$	−2.81177	−	6.30161i	−0.369203	−	0.827441i
$59$	−11.4057			−1.48490			−0.742450	−	0.669901i	$-0.766337\pi$
$59$	−11.4057			−1.48490			−0.742450	+	0.669901i	$0.766337\pi$
$60$	4.77705	−	10.1158i	0.616714	−	1.30595i
$61$			1.21986i			0.156187i	0.996946	+	0.0780935i	$0.0248833\pi$
$61$			1.21986i			0.156187i	−0.996946	+	0.0780935i	$0.975117\pi$
$62$	0.864331	+	1.93710i	0.109770	+	0.246012i
$63$		0			0
$64$	6.49489	+	4.67081i	0.811861	+	0.583851i
$65$	−3.81777	−	12.7829i	−0.473536	−	1.58552i
$66$	−3.24377	−	7.26979i	−0.399281	−	0.894850i
$67$	1.11485			0.136200			0.0681000	−	0.997678i	$-0.478306\pi$
$67$	1.11485			0.136200			0.0681000	+	0.997678i	$0.478306\pi$
$68$	2.68171	−	2.98805i	0.325205	−	0.362354i
$69$			7.48514i			0.901105i
$70$		0			0
$71$		−	8.40090i		−	0.997003i	−0.866889	−	0.498501i	$-0.833884\pi$
$71$		−	8.40090i		−	0.997003i	0.866889	−	0.498501i	$-0.166116\pi$
$72$	8.76953	+	2.82588i	1.03350	+	0.333033i
$73$	5.88062			0.688274			0.344137	−	0.938919i	$-0.388172\pi$
$73$	5.88062			0.688274			0.344137	+	0.938919i	$0.388172\pi$
$74$	−6.18105	+	2.75798i	−0.718533	+	0.320608i
$75$	6.85921	+	10.4589i	0.792033	+	1.20769i
$76$	10.4462	−	11.6395i	1.19826	−	1.33515i
$77$		0			0
$78$	19.2746	−	8.60032i	2.18242	−	0.973794i
$79$		−	12.1357i		−	1.36537i	−0.730711	−	0.682687i	$-0.760811\pi$
$79$		−	12.1357i		−	1.36537i	0.730711	−	0.682687i	$-0.239189\pi$
$80$	−8.24453	+	3.46811i	−0.921766	+	0.387747i
$81$	−8.16121			−0.906801
$82$	11.4028	−	5.08793i	1.25923	−	0.561868i
$83$			11.1319i			1.22188i	0.791677	+	0.610940i	$0.209208\pi$
$83$			11.1319i			1.22188i	−0.791677	+	0.610940i	$0.790792\pi$
$84$		0			0
$85$	1.28459	+	4.30114i	0.139334	+	0.466524i
$86$	0.649414	+	1.45544i	0.0700281	+	0.156944i
$87$			12.2057i			1.30859i
$88$	−1.95210	+	6.05795i	−0.208095	+	0.645780i
$89$		−	4.57883i		−	0.485355i	−0.970107	−	0.242677i	$-0.921974\pi$
$89$		−	4.57883i		−	0.485355i	0.970107	−	0.242677i	$-0.0780256\pi$
$90$	−7.81252	+	6.71396i	−0.823512	+	0.707714i
$91$		0			0
$92$	3.99723	−	4.45385i	0.416740	−	0.464345i
$93$		−	3.75201i		−	0.389065i
$94$	12.3591	−	5.51462i	1.27475	−	0.568790i
$95$	5.00395	+	16.7545i	0.513394	+	1.71898i
$96$	−7.12483	−	12.2261i	−0.727175	−	1.24782i
$97$	4.62008			0.469098			0.234549	−	0.972104i	$-0.424639\pi$
$97$	4.62008			0.469098			0.234549	+	0.972104i	$0.424639\pi$
$98$		0			0
$99$			7.33022i			0.736715i
$100$	1.50388	−	9.88627i	0.150388	−	0.988627i
$101$			0.111126i			0.0110574i	0.999985	+	0.00552872i	$0.00175986\pi$
$101$			0.111126i			0.0110574i	−0.999985	+	0.00552872i	$0.998240\pi$
$102$	−6.48547	+	2.89381i	−0.642157	+	0.286530i
$103$		−	12.9119i		−	1.27224i	−0.771588	−	0.636122i	$-0.780537\pi$
$103$		−	12.9119i		−	1.27224i	0.771588	−	0.636122i	$-0.219463\pi$
$104$	−16.0616	−	5.17567i	−1.57497	−	0.507517i
$105$		0			0
$106$	−9.12128	+	4.06990i	−0.885937	+	0.395304i
$107$	14.6070			1.41211			0.706056	−	0.708156i	$-0.250473\pi$
$107$	14.6070			1.41211			0.706056	+	0.708156i	$0.250473\pi$
$108$	−0.958748	−	0.860455i	−0.0922555	−	0.0827973i
$109$	4.45913			0.427107			0.213553	−	0.976931i	$-0.431496\pi$
$109$	4.45913			0.427107			0.213553	+	0.976931i	$0.431496\pi$
$110$	−4.63798	−	5.39685i	−0.442214	−	0.514570i
$111$	11.9722			1.13635
$112$		0			0
$113$			2.30454i			0.216793i	0.994108	+	0.108397i	$0.0345717\pi$
$113$			2.30454i			0.216793i	−0.994108	+	0.108397i	$0.965428\pi$
$114$	−25.2632	+	11.2724i	−2.36612	+	1.05576i
$115$	1.91475	+	6.41108i	0.178551	+	0.597836i
$116$	6.51811	−	7.26270i	0.605191	−	0.674324i
$117$	−19.4349			−1.79675
$118$	−6.57265	−	14.7303i	−0.605061	−	1.35604i
$119$		0			0
$120$	15.8172	+	0.340159i	1.44391	+	0.0310521i
$121$	5.93632			0.539665
$122$	−1.57543	+	0.702953i	−0.142632	+	0.0636424i
$123$	−22.0864			−1.99146
$124$	−2.00365	+	2.23254i	−0.179933	+	0.200488i
$125$	8.55042	+	7.20349i	0.764773	+	0.644300i
$126$		0			0
$127$	−6.18242			−0.548601			−0.274300	−	0.961644i	$-0.588446\pi$
$127$	−6.18242			−0.548601			−0.274300	+	0.961644i	$0.588446\pi$
$128$	−2.28954	+	11.0796i	−0.202368	+	0.979309i
$129$		−	2.81907i		−	0.248205i
$130$	14.3088	−	12.2968i	1.25497	−	1.07850i
$131$	8.16897			0.713726			0.356863	−	0.934157i	$-0.383846\pi$
$131$	8.16897			0.713726			0.356863	+	0.934157i	$0.383846\pi$
$132$	7.51956	−	8.37855i	0.654494	−	0.729259i
$133$		0			0
$134$	0.642438	+	1.43980i	0.0554982	+	0.124380i
$135$	1.38007	−	0.412175i	0.118777	−	0.0354744i
$136$	5.40437	+	1.74149i	0.463421	+	0.149332i
$137$		−	7.07703i		−	0.604631i	−0.953208	−	0.302316i	$-0.902240\pi$
$137$		−	7.07703i		−	0.604631i	0.953208	−	0.302316i	$-0.0977597\pi$
$138$	−9.66693	+	4.31337i	−0.822904	+	0.367179i
$139$	14.4633			1.22676			0.613382	−	0.789787i	$-0.289809\pi$
$139$	14.4633			1.22676			0.613382	+	0.789787i	$0.289809\pi$
$140$		0			0
$141$	−23.9386			−2.01600
$142$	10.8496	−	4.84108i	0.910479	−	0.406254i
$143$		−	13.4255i		−	1.12270i
$144$	1.40394	+	12.9541i	0.116995	+	1.07951i
$145$	3.12230	+	10.4543i	0.259293	+	0.868180i
$146$	3.38875	+	7.59471i	0.280455	+	0.628543i
$147$		0			0
$148$	−7.12376	−	6.39342i	−0.585569	−	0.525536i
$149$	19.6566			1.61033			0.805164	−	0.593053i	$-0.202077\pi$
$149$	19.6566			1.61033			0.805164	+	0.593053i	$0.202077\pi$
$150$	−9.55482	+	14.8856i	−0.780148	+	1.21540i
$151$			17.4157i			1.41727i	0.705574	+	0.708636i	$0.250689\pi$
$151$			17.4157i			1.41727i	−0.705574	+	0.708636i	$0.749311\pi$
$152$	21.0520	+	6.78375i	1.70754	+	0.550235i
$153$	6.53938			0.528677
$154$		0			0
$155$	−0.959789	−	3.21362i	−0.0770921	−	0.258124i
$156$	22.2143	+	19.9369i	1.77857	+	1.59623i
$157$	6.86058			0.547534			0.273767	−	0.961796i	$-0.411730\pi$
$157$	6.86058			0.547534			0.273767	+	0.961796i	$0.411730\pi$
$158$	15.6731	−	6.99330i	1.24688	−	0.556357i
$159$	17.6672			1.40110
$160$	−9.22998	−	8.64913i	−0.729694	−	0.683774i
$161$		0			0
$162$	−4.70296	−	10.5401i	−0.369499	−	0.828105i
$163$	2.86934			0.224744			0.112372	−	0.993666i	$-0.464155\pi$
$163$	2.86934			0.224744			0.112372	+	0.993666i	$0.464155\pi$
$164$	13.1420	+	11.7946i	1.02621	+	0.921005i
$165$	3.60202	+	12.0605i	0.280417	+	0.938908i
$166$	−14.3766	+	6.41482i	−1.11584	+	0.497886i
$167$		−	15.9389i		−	1.23339i	−0.787204	−	0.616693i	$-0.788472\pi$
$167$		−	15.9389i		−	1.23339i	0.787204	−	0.616693i	$-0.211528\pi$
$168$		0			0
$169$	22.5955			1.73811
$170$	−4.81460	+	4.13759i	−0.369263	+	0.317339i
$171$	25.4732			1.94799
$172$	−1.50544	+	1.67741i	−0.114789	+	0.127902i
$173$	1.02406			0.0778580			0.0389290	−	0.999242i	$-0.487605\pi$
$173$	1.02406			0.0778580			0.0389290	+	0.999242i	$0.487605\pi$
$174$	−15.7635	+	7.03363i	−1.19502	+	0.533218i
$175$		0			0
$176$	−8.94865	+	0.969834i	−0.674530	+	0.0731040i
$177$			28.5314i			2.14455i
$178$	5.91348	−	2.63858i	0.443234	−	0.197770i
$179$		−	4.19778i		−	0.313757i	−0.987618	−	0.156878i	$-0.949857\pi$
$179$		−	4.19778i		−	0.313757i	0.987618	−	0.156878i	$-0.0501431\pi$
$180$	−13.1730	−	6.22076i	−0.981857	−	0.463668i
$181$			5.33135i			0.396276i	0.980174	+	0.198138i	$0.0634894\pi$
$181$			5.33135i			0.396276i	−0.980174	+	0.198138i	$0.936511\pi$
$182$		0			0
$183$	3.05148			0.225572
$184$	8.05550	+	2.59579i	0.593859	+	0.191364i
$185$	10.2543	−	3.06257i	0.753910	−	0.225165i
$186$	4.84565	−	2.16212i	0.355300	−	0.158535i
$187$			4.51737i			0.330343i
$188$	14.2441	+	12.7837i	1.03886	+	0.932350i
$189$		0			0
$190$	−18.7546	+	16.1174i	−1.36060	+	1.16928i
$191$			16.7444i			1.21158i	0.795624	+	0.605791i	$0.207143\pi$
$191$			16.7444i			1.21158i	−0.795624	+	0.605791i	$0.792857\pi$
$192$	11.6840	−	16.2470i	0.843221	−	1.17252i
$193$			15.5425i			1.11877i	0.828907	+	0.559386i	$0.188963\pi$
$193$			15.5425i			1.11877i	−0.828907	+	0.559386i	$0.811037\pi$
$194$	2.66235	+	5.96675i	0.191146	+	0.428387i
$195$	−31.9764	+	9.55015i	−2.28987	+	0.683900i
$196$		0			0
$197$		−	10.4069i		−	0.741463i	−0.928740	−	0.370731i	$-0.879107\pi$
$197$		−	10.4069i		−	0.741463i	0.928740	−	0.370731i	$-0.120893\pi$
$198$	−9.46685	+	4.22410i	−0.672780	+	0.300193i
$199$	−15.4520			−1.09536			−0.547681	−	0.836687i	$-0.684489\pi$
$199$	−15.4520			−1.09536			−0.547681	+	0.836687i	$0.684489\pi$
$200$	13.6346	−	3.75480i	0.964110	−	0.265505i
$201$		−	2.78879i		−	0.196706i
$202$	−0.143517	+	0.0640372i	−0.0100978	+	0.00450564i
$203$		0			0
$204$	−7.47460	−	6.70829i	−0.523327	−	0.469674i
$205$	−18.9172	+	5.64985i	−1.32123	+	0.394603i
$206$	16.6755	−	7.44056i	1.16183	−	0.518409i
$207$	9.74728			0.677483
$208$	−2.57135	−	23.7258i	−0.178291	−	1.64509i
$209$			17.5968i			1.21720i
$210$		0			0
$211$		−	10.3988i		−	0.715879i	−0.933745	−	0.357940i	$-0.883479\pi$
$211$		−	10.3988i		−	0.715879i	0.933745	−	0.357940i	$-0.116521\pi$
$212$	−10.5124	−	9.43466i	−0.721996	−	0.647975i
$213$	−21.0148			−1.43991
$214$	8.41740	+	18.8647i	0.575402	+	1.28956i
$215$	−0.721137	−	2.41455i	−0.0491811	−	0.164671i
$216$	0.558777	−	1.73405i	0.0380200	−	0.117987i
$217$		0			0
$218$	2.56960	+	5.75888i	0.174036	+	0.390041i
$219$		−	14.7104i		−	0.994034i
$220$	4.29727	−	9.09984i	0.289722	−	0.613511i
$221$	−11.9771			−0.805664
$222$	6.89908	+	15.4619i	0.463036	+	1.03773i
$223$		−	11.3655i		−	0.761093i	−0.924762	−	0.380547i	$-0.875736\pi$
$223$		−	11.3655i		−	0.761093i	0.924762	−	0.380547i	$-0.124264\pi$
$224$		0			0
$225$	13.6198	−	8.93218i	0.907984	−	0.595479i
$226$	−2.97628	+	1.32801i	−0.197979	+	0.0883380i
$227$		−	6.17093i		−	0.409579i	−0.978806	−	0.204790i	$-0.934349\pi$
$227$		−	6.17093i		−	0.409579i	0.978806	−	0.204790i	$-0.0656510\pi$
$228$	−29.1163	−	26.1312i	−1.92827	−	1.73058i
$229$		−	8.28601i		−	0.547555i	−0.961793	−	0.273778i	$-0.911727\pi$
$229$		−	8.28601i		−	0.547555i	0.961793	−	0.273778i	$-0.0882732\pi$
$230$	−7.17641	+	6.16730i	−0.473198	+	0.406660i
$231$		0			0
$232$	13.1358	+	4.23284i	0.862405	+	0.277900i
$233$		−	14.0909i		−	0.923124i	−0.887108	−	0.461562i	$-0.847289\pi$
$233$		−	14.0909i		−	0.923124i	0.887108	−	0.461562i	$-0.152711\pi$
$234$	−11.1995	−	25.0998i	−0.732133	−	1.64082i
$235$	−20.5036	+	6.12367i	−1.33751	+	0.399464i
$236$	15.2364	−	16.9769i	0.991806	−	1.10510i
$237$	−30.3575			−1.97193
$238$		0			0
$239$		−	8.30653i		−	0.537305i	−0.963237	−	0.268652i	$-0.913422\pi$
$239$		−	8.30653i		−	0.537305i	0.963237	−	0.268652i	$-0.0865783\pi$
$240$	8.67548	+	20.6237i	0.560000	+	1.33125i
$241$		−	25.7383i		−	1.65795i	−0.559285	−	0.828975i	$-0.688924\pi$
$241$		−	25.7383i		−	1.65795i	0.559285	−	0.828975i	$-0.311076\pi$
$242$	3.42085	+	7.66665i	0.219900	+	0.492831i
$243$			22.3476i			1.43360i
$244$	−1.81570	−	1.62955i	−0.116239	−	0.104322i
$245$		0			0
$246$	−12.7275	−	28.5242i	−0.811473	−	1.81864i
$247$	−46.6550			−2.96858
$248$	−4.03790	−	1.30117i	−0.256407	−	0.0826241i
$249$	27.8463			1.76469
$250$	−4.37594	+	15.1938i	−0.276759	+	0.960939i
$251$	−4.80612			−0.303360			−0.151680	−	0.988430i	$-0.548468\pi$
$251$	−4.80612			−0.303360			−0.151680	+	0.988430i	$0.548468\pi$
$252$		0			0
$253$			6.73338i			0.423324i
$254$	−3.56267	−	7.98448i	−0.223541	−	0.500991i
$255$	10.7593	−	3.21340i	0.673774	−	0.201231i
$256$	−15.6285	+	3.42782i	−0.976781	+	0.214239i
$257$	−21.4125			−1.33567			−0.667837	−	0.744307i	$-0.732780\pi$
$257$	−21.4125			−1.33567			−0.667837	+	0.744307i	$0.732780\pi$
$258$	3.64078	−	1.62451i	0.226665	−	0.101138i
$259$		0			0
$260$	24.1267	+	11.3935i	1.49627	+	0.706594i
$261$	15.8945			0.983844
$262$	4.70743	+	10.5501i	0.290826	+	0.651786i
$263$	15.7285			0.969863			0.484931	−	0.874552i	$-0.338845\pi$
$263$	15.7285			0.969863			0.484931	+	0.874552i	$0.338845\pi$
$264$	15.1540	+	4.88318i	0.932662	+	0.300539i
$265$	15.1321	−	4.51939i	0.929556	−	0.277624i
$266$		0			0
$267$	−11.4539			−0.700969
$268$	−1.48927	+	1.65940i	−0.0909717	+	0.101364i
$269$		−	1.39293i		−	0.0849284i	−0.999098	−	0.0424642i	$-0.986479\pi$
$269$		−	1.39293i		−	0.0849284i	0.999098	−	0.0424642i	$-0.0135208\pi$
$270$	1.32759	+	1.54481i	0.0807946	+	0.0940144i
$271$	−14.2313			−0.864492			−0.432246	−	0.901756i	$-0.642279\pi$
$271$	−14.2313			−0.864492			−0.432246	+	0.901756i	$0.642279\pi$
$272$	0.865200	+	7.98320i	0.0524604	+	0.484052i
$273$		0			0
$274$	9.13986	−	4.07819i	0.552159	−	0.246373i
$275$	6.17031	+	9.40847i	0.372084	+	0.567352i
$276$	−11.1413	−	9.99906i	−0.670627	−	0.601873i
$277$		−	21.0130i		−	1.26255i	−0.775560	−	0.631273i	$-0.782533\pi$
$277$		−	21.0130i		−	1.26255i	0.775560	−	0.631273i	$-0.217467\pi$
$278$	8.33460	+	18.6791i	0.499876	+	1.12030i
$279$	−4.88593			−0.292513
$280$		0			0
$281$	3.92163			0.233945			0.116972	−	0.993135i	$-0.462681\pi$
$281$	3.92163			0.233945			0.116972	+	0.993135i	$0.462681\pi$
$282$	−13.7948	−	30.9163i	−0.821469	−	1.84104i
$283$			1.20399i			0.0715696i	0.999360	+	0.0357848i	$0.0113931\pi$
$283$			1.20399i			0.0715696i	−0.999360	+	0.0357848i	$0.988607\pi$
$284$	12.5043	+	11.2224i	0.741996	+	0.665925i
$285$	41.9114	−	12.5174i	2.48262	−	0.741465i
$286$	17.3388	−	7.73655i	1.02527	−	0.457472i
$287$		0			0
$288$	−15.9210	+	9.27807i	−0.938154	+	0.546716i
$289$	−12.9700			−0.762941
$290$	−11.7023	+	10.0568i	−0.687181	+	0.590553i
$291$		−	11.5571i		−	0.677490i
$292$	−7.85565	+	8.75302i	−0.459717	+	0.512232i
$293$	−14.4715			−0.845433			−0.422716	−	0.906262i	$-0.638923\pi$
$293$	−14.4715			−0.845433			−0.422716	+	0.906262i	$0.638923\pi$
$294$		0			0
$295$	7.29854	+	24.4374i	0.424937	+	1.42280i
$296$	4.15187	−	12.8845i	0.241322	−	0.748894i
$297$	1.44945			0.0841054
$298$	11.3272	+	25.3861i	0.656169	+	1.47058i
$299$	−17.8524			−1.03243
$300$	−24.7305	−	3.76196i	−1.42782	−	0.217197i
$301$		0			0
$302$	−22.4921	+	10.0359i	−1.29428	+	0.577504i
$303$	0.277982			0.0159696
$304$	3.37027	+	31.0974i	0.193298	+	1.78356i
$305$	2.61361	−	0.780589i	0.149655	−	0.0446964i
$306$	3.76837	+	8.44549i	0.215423	+	0.482797i
$307$			24.7976i			1.41527i	0.706576	+	0.707637i	$0.250239\pi$
$307$			24.7976i			1.41527i	−0.706576	+	0.707637i	$0.749761\pi$
$308$		0			0
$309$	−32.2990			−1.83743
$310$	3.59725	−	3.09142i	0.204310	−	0.175581i
$311$	7.05694			0.400162			0.200081	−	0.979779i	$-0.435879\pi$
$311$	7.05694			0.400162			0.200081	+	0.979779i	$0.435879\pi$
$312$	−12.9469	+	40.1782i	−0.732976	+	2.27464i
$313$	32.5746			1.84123			0.920613	−	0.390477i	$-0.127690\pi$
$313$	32.5746			1.84123			0.920613	+	0.390477i	$0.127690\pi$
$314$	3.95346	+	8.86032i	0.223107	+	0.500017i
$315$		0			0
$316$	18.0634	+	16.2115i	1.01615	+	0.911971i
$317$		−	22.3583i		−	1.25577i	−0.778307	−	0.627884i	$-0.783921\pi$
$317$		−	22.3583i		−	1.25577i	0.778307	−	0.627884i	$-0.216079\pi$
$318$	10.1809	+	22.8169i	0.570914	+	1.27951i
$319$			10.9798i			0.614753i
$320$	5.85136	−	16.9045i	0.327101	−	0.944989i
$321$		−	36.5394i		−	2.03943i
$322$		0			0
$323$	15.6983			0.873478
$324$	10.9022	−	12.1476i	0.605677	−	0.674866i
$325$	−24.9450	+	16.3595i	−1.38370	+	0.907464i
$326$	1.65348	+	3.70570i	0.0915777	+	0.205240i
$327$		−	11.1545i		−	0.616845i
$328$	−7.65939	+	23.7693i	−0.422919	+	1.31244i
$329$		0			0
$330$	−13.5002	+	11.6019i	−0.743163	+	0.638663i
$331$			24.2144i			1.33094i	0.746424	+	0.665471i	$0.231769\pi$
$331$			24.2144i			1.33094i	−0.746424	+	0.665471i	$0.768231\pi$
$332$	−16.5692	−	14.8705i	−0.909356	−	0.816127i
$333$		−	15.5904i		−	0.854350i
$334$	20.5848	−	9.18489i	1.12635	−	0.502575i
$335$	−0.713390	−	2.38861i	−0.0389767	−	0.130504i
$336$		0			0
$337$		−	7.95685i		−	0.433437i	−0.976234	−	0.216719i	$-0.930465\pi$
$337$		−	7.95685i		−	0.433437i	0.976234	−	0.216719i	$-0.0695354\pi$
$338$	13.0208	+	29.1817i	0.708239	+	1.58727i
$339$	5.76482			0.313102
$340$	−8.11808	−	3.83365i	−0.440265	−	0.207909i
$341$		−	3.37518i		−	0.182776i
$342$	14.6791	+	32.8982i	0.793757	+	1.77893i
$343$		0			0
$344$	−3.03387	−	0.977630i	−0.163576	−	0.0527103i
$345$	16.0373	−	4.78975i	0.863420	−	0.257871i
$346$	0.590124	+	1.32256i	0.0317252	+	0.0711012i
$347$	19.8756			1.06698			0.533489	−	0.845807i	$-0.320881\pi$
$347$	19.8756			1.06698			0.533489	+	0.845807i	$0.320881\pi$
$348$	−18.1676	−	16.3050i	−0.973887	−	0.874042i
$349$		−	12.8850i		−	0.689719i	−0.938654	−	0.344859i	$-0.887927\pi$
$349$		−	12.8850i		−	0.689719i	0.938654	−	0.344859i	$-0.112073\pi$
$350$		0			0
$351$			3.84297i			0.205122i
$352$	−6.40925	−	10.9982i	−0.341614	−	0.586204i
$353$	8.34671			0.444250			0.222125	−	0.975018i	$-0.428701\pi$
$353$	8.34671			0.444250			0.222125	+	0.975018i	$0.428701\pi$
$354$	−36.8479	+	16.4415i	−1.95844	+	0.873854i
$355$	−17.9994	+	5.37574i	−0.955306	+	0.285315i
$356$	6.81537	+	6.11665i	0.361214	+	0.324182i
$357$		0			0
$358$	5.42136	−	2.41900i	0.286528	−	0.127848i
$359$			1.81996i			0.0960538i	0.998846	+	0.0480269i	$0.0152933\pi$
$359$			1.81996i			0.0960538i	−0.998846	+	0.0480269i	$0.984707\pi$
$360$	0.442961	−	20.5974i	0.0233461	−	1.08558i
$361$	42.1506			2.21845
$362$	−6.88534	+	3.07223i	−0.361886	+	0.161473i
$363$		−	14.8497i		−	0.779406i
$364$		0			0
$365$	−3.76301	−	12.5995i	−0.196965	−	0.659489i
$366$	1.75844	+	3.94093i	0.0919149	+	0.205996i
$367$		−	1.06984i		−	0.0558451i	−0.999610	−	0.0279226i	$-0.991111\pi$
$367$		−	1.06984i		−	0.0558451i	0.999610	−	0.0279226i	$-0.00888918\pi$
$368$	1.28963	+	11.8994i	0.0672264	+	0.620298i
$369$			28.7613i			1.49725i
$370$	9.86437	+	11.4784i	0.512824	+	0.596733i
$371$		0			0
$372$	5.58469	+	5.01213i	0.289553	+	0.259867i
$373$			13.1871i			0.682803i	0.939918	+	0.341401i	$0.110902\pi$
$373$			13.1871i			0.682803i	−0.939918	+	0.341401i	$0.889098\pi$
$374$	−5.83411	+	2.60317i	−0.301675	+	0.134607i
$375$	18.0195	−	21.3889i	0.930524	−	1.10452i
$376$	−8.30173	+	25.7627i	−0.428129	+	1.32861i
$377$	−29.1112			−1.49930
$378$		0			0
$379$			16.9854i			0.872483i	0.899830	+	0.436241i	$0.143691\pi$
$379$			16.9854i			0.872483i	−0.899830	+	0.436241i	$0.856309\pi$
$380$	−31.6229	−	14.9334i	−1.62222	−	0.766069i
$381$			15.4653i			0.792312i
$382$	−21.6251	+	9.64908i	−1.10644	+	0.493690i
$383$		−	4.67572i		−	0.238918i	−0.992839	−	0.119459i	$-0.961884\pi$
$383$		−	4.67572i		−	0.238918i	0.992839	−	0.119459i	$-0.0381160\pi$
$384$	27.7157	+	5.72727i	1.41436	+	0.292269i
$385$		0			0
$386$	−20.0728	+	8.95648i	−1.02168	+	0.455873i
$387$	−3.67104			−0.186609
$388$	−6.17175	+	6.87677i	−0.313323	+	0.349115i
$389$	−25.7985			−1.30803			−0.654017	−	0.756480i	$-0.726918\pi$
$389$	−25.7985			−1.30803			−0.654017	+	0.756480i	$0.726918\pi$
$390$	−30.7605	−	35.7936i	−1.55762	−	1.81248i
$391$	6.00693			0.303783
$392$		0			0
$393$		−	20.4347i		−	1.03079i
$394$	13.4404	−	5.99707i	0.677116	−	0.302128i
$395$	−26.0014	+	7.76565i	−1.30827	+	0.390732i
$396$	−10.9107	−	9.79211i	−0.548283	−	0.492072i
$397$	−26.6167			−1.33586			−0.667928	−	0.744226i	$-0.732818\pi$
$397$	−26.6167			−1.33586			−0.667928	+	0.744226i	$0.732818\pi$
$398$	−8.90433	−	19.9560i	−0.446334	−	1.00030i
$399$		0			0
$400$	12.7063	+	15.4451i	0.635314	+	0.772254i
$401$	−9.02978			−0.450926			−0.225463	−	0.974252i	$-0.572389\pi$
$401$	−9.02978			−0.450926			−0.225463	+	0.974252i	$0.572389\pi$
$402$	3.60167	−	1.60706i	0.179635	−	0.0801528i
$403$	8.94872			0.445767
$404$	−0.165406	−	0.148448i	−0.00822925	−	0.00738557i
$405$	5.22236	+	17.4858i	0.259501	+	0.868877i
$406$		0			0
$407$	10.7698			0.533839
$408$	4.35634	−	13.5190i	0.215671	−	0.669291i
$409$			3.41447i			0.168834i	0.996430	+	0.0844172i	$0.0269029\pi$
$409$			3.41447i			0.168834i	−0.996430	+	0.0844172i	$0.973097\pi$
$410$	−18.1979	−	21.1754i	−0.898728	−	1.04578i
$411$	−17.7032			−0.873233
$412$	19.2187	+	17.2484i	0.946838	+	0.849766i
$413$		0			0
$414$	5.61695	+	12.5884i	0.276058	+	0.618688i
$415$	23.8506	−	7.12328i	1.17078	−	0.349668i
$416$	29.1598	−	16.9931i	1.42967	−	0.833153i
$417$		−	36.1800i		−	1.77174i
$418$	−22.7260	+	10.1403i	−1.11156	+	0.495978i
$419$	−15.7994			−0.771850			−0.385925	−	0.922530i	$-0.626118\pi$
$419$	−15.7994			−0.771850			−0.385925	+	0.922530i	$0.626118\pi$
$420$		0			0
$421$	20.8340			1.01538			0.507692	−	0.861538i	$-0.330499\pi$
$421$	20.8340			1.01538			0.507692	+	0.861538i	$0.330499\pi$
$422$	13.4298	−	5.99236i	0.653753	−	0.291703i
$423$			31.1733i			1.51570i
$424$	6.12684	−	19.0134i	0.297546	−	0.923372i
$425$	8.39341	−	5.50461i	0.407140	−	0.267013i
$426$	−12.1100	−	27.1403i	−0.586729	−	1.31495i
$427$		0			0
$428$	−19.5128	+	21.7418i	−0.943188	+	1.05093i
$429$	−33.5839			−1.62145
$430$	2.70279	−	2.32274i	0.130340	−	0.112012i
$431$		−	27.5487i		−	1.32697i	−0.748188	−	0.663487i	$-0.769076\pi$
$431$		−	27.5487i		−	1.32697i	0.748188	−	0.663487i	$-0.230924\pi$
$432$	2.56149	−	0.277609i	0.123240	−	0.0133565i
$433$	−2.28113			−0.109624			−0.0548121	−	0.998497i	$-0.517456\pi$
$433$	−2.28113			−0.109624			−0.0548121	+	0.998497i	$0.517456\pi$
$434$		0			0
$435$	26.1514	−	7.81044i	1.25386	−	0.374482i
$436$	−5.95674	+	6.63720i	−0.285276	+	0.317864i
$437$	23.3992			1.11933
$438$	18.9982	−	8.47695i	0.907768	−	0.405045i
$439$	−9.26625			−0.442254			−0.221127	−	0.975245i	$-0.570973\pi$
$439$	−9.26625			−0.442254			−0.221127	+	0.975245i	$0.570973\pi$
$440$	14.2286	+	0.305995i	0.678323	+	0.0145877i
$441$		0			0
$442$	−6.90187	−	15.4682i	−0.328288	−	0.735745i
$443$	27.3290			1.29844			0.649221	−	0.760600i	$-0.275095\pi$
$443$	27.3290			1.29844			0.649221	+	0.760600i	$0.275095\pi$
$444$	−15.9931	+	17.8201i	−0.759000	+	0.845703i
$445$	−9.81037	+	2.92999i	−0.465056	+	0.138895i
$446$	14.6784	−	6.54948i	0.695042	−	0.310127i
$447$		−	49.1708i		−	2.32570i
$448$		0			0
$449$	31.5958			1.49110			0.745549	−	0.666451i	$-0.232187\pi$
$449$	31.5958			1.49110			0.745549	+	0.666451i	$0.232187\pi$
$450$	19.3842	+	12.4425i	0.913782	+	0.586543i
$451$	−19.8682			−0.935556
$452$	−3.43021	−	3.07854i	−0.161343	−	0.144802i
$453$	43.5654			2.04688
$454$	7.96965	−	3.55605i	0.374034	−	0.166893i
$455$		0			0
$456$	16.9695	−	52.6615i	0.794672	−	2.46610i
$457$			20.1137i			0.940879i	0.882432	+	0.470439i	$0.155905\pi$
$457$			20.1137i			0.940879i	−0.882432	+	0.470439i	$0.844095\pi$
$458$	10.7012	−	4.77488i	0.500036	−	0.223115i
$459$		−	1.29307i		−	0.0603553i
$460$	−12.1004	−	5.71425i	−0.564185	−	0.266428i
$461$		−	1.57753i		−	0.0734730i	−0.999325	−	0.0367365i	$-0.988304\pi$
$461$		−	1.57753i		−	0.0734730i	0.999325	−	0.0367365i	$-0.0116962\pi$
$462$		0			0
$463$	−27.7330			−1.28886			−0.644431	−	0.764663i	$-0.722906\pi$
$463$	−27.7330			−1.28886			−0.644431	+	0.764663i	$0.722906\pi$
$464$	2.10294	+	19.4038i	0.0976265	+	0.900799i
$465$	−8.03887	+	2.40091i	−0.372794	+	0.111340i
$466$	18.1981	−	8.11998i	0.843012	−	0.376151i
$467$		−	9.24121i		−	0.427632i	−0.976874	−	0.213816i	$-0.931411\pi$
$467$		−	9.24121i		−	0.427632i	0.976874	−	0.213816i	$-0.0685893\pi$
$468$	25.9621	−	28.9279i	1.20010	−	1.33719i
$469$		0			0
$470$	−19.7240	−	22.9512i	−0.909799	−	1.05866i
$471$		−	17.1617i		−	0.790771i
$472$	30.7055	+	9.89448i	1.41333	+	0.455430i
$473$		−	2.53594i		−	0.116603i
$474$	−17.4937	−	39.2061i	−0.803513	−	1.80080i
$475$	32.6954	−	21.4424i	1.50017	−	0.983847i
$476$		0			0
$477$		−	23.0065i		−	1.05340i
$478$	10.7277	−	4.78670i	0.490675	−	0.218939i
$479$	10.5454			0.481833			0.240916	−	0.970546i	$-0.422552\pi$
$479$	10.5454			0.481833			0.240916	+	0.970546i	$0.422552\pi$
$480$	−21.6358	+	23.0888i	−0.987534	+	1.05385i
$481$			28.5543i			1.30196i
$482$	33.2406	−	14.8319i	1.51407	−	0.675575i
$483$		0			0
$484$	−7.93005	+	8.83593i	−0.360457	+	0.401633i
$485$	−2.95639	−	9.89875i	−0.134243	−	0.449479i
$486$	−28.8616	+	12.8780i	−1.30919	+	0.584158i
$487$	−18.0001			−0.815661			−0.407830	−	0.913058i	$-0.633715\pi$
$487$	−18.0001			−0.815661			−0.407830	+	0.913058i	$0.633715\pi$
$488$	1.05823	−	3.28399i	0.0479037	−	0.148659i
$489$		−	7.17765i		−	0.324584i
$490$		0			0
$491$		−	0.704833i		−	0.0318086i	−0.999874	−	0.0159043i	$-0.994937\pi$
$491$		−	0.704833i		−	0.0318086i	0.999874	−	0.0159043i	$-0.00506272\pi$
$492$	29.5042	−	32.8746i	1.33015	−	1.48210i
$493$	9.79524			0.441156
$494$	−26.8853	−	60.2541i	−1.20963	−	2.71096i
$495$	15.7054	−	4.69061i	0.705904	−	0.210827i
$496$	−0.646439	−	5.96469i	−0.0290259	−	0.267822i
$497$		0			0
$498$	16.0467	+	35.9630i	0.719068	+	1.61154i
$499$			6.53324i			0.292468i	0.989250	+	0.146234i	$0.0467153\pi$
$499$			6.53324i			0.292468i	−0.989250	+	0.146234i	$0.953285\pi$
$500$	−22.1442	+	3.10409i	−0.990318	+	0.138819i
$501$	−39.8710			−1.78131
$502$	−2.76956	−	6.20702i	−0.123612	−	0.277033i
$503$			29.3454i			1.30845i	0.756301	+	0.654224i	$0.227005\pi$
$503$			29.3454i			1.30845i	−0.756301	+	0.654224i	$0.772995\pi$
$504$		0			0
$505$	0.238093	−	0.0711096i	0.0105950	−	0.00316433i
$506$	−8.69604	+	3.88016i	−0.386586	+	0.172494i
$507$		−	56.5226i		−	2.51026i
$508$	8.25881	−	9.20224i	0.366425	−	0.408283i
$509$		−	20.6256i		−	0.914213i	−0.889412	−	0.457107i	$-0.848886\pi$
$509$		−	20.6256i		−	0.914213i	0.889412	−	0.457107i	$-0.151114\pi$
$510$	10.3502	+	12.0437i	0.458314	+	0.533304i
$511$		0			0
$512$	−13.4330	−	18.2086i	−0.593661	−	0.804715i
$513$		−	5.03697i		−	0.222388i
$514$	−12.3391	−	27.6539i	−0.544255	−	1.21976i
$515$	−27.6643	+	8.26231i	−1.21904	+	0.364081i
$516$	4.19605	+	3.76586i	0.184721	+	0.165783i
$517$	−21.5344			−0.947081
$518$		0			0
$519$		−	2.56169i		−	0.112446i
$520$	−0.811295	+	37.7248i	−0.0355776	+	1.65434i
$521$			5.87937i			0.257580i	0.991672	+	0.128790i	$0.0411093\pi$
$521$			5.87937i			0.257580i	−0.991672	+	0.128790i	$0.958891\pi$
$522$	9.15932	+	20.5274i	0.400892	+	0.898462i
$523$			23.1425i			1.01195i	0.862548	+	0.505975i	$0.168867\pi$
$523$			23.1425i			1.01195i	−0.862548	+	0.505975i	$0.831133\pi$
$524$	−10.9125	+	12.1591i	−0.476717	+	0.531174i
$525$		0			0
$526$	9.06369	+	20.3131i	0.395196	+	0.885694i
$527$	−3.01104			−0.131163
$528$	2.42604	+	22.3850i	0.105580	+	0.974184i
$529$	−14.0464			−0.610711
$530$	14.5567	+	16.9385i	0.632302	+	0.735761i
$531$	37.1541			1.61235
$532$		0			0
$533$		−	52.6771i		−	2.28170i
$534$	−6.60042	−	14.7926i	−0.285628	−	0.640136i
$535$	−9.34703	−	31.2963i	−0.404107	−	1.35306i
$536$	−3.00129	−	0.967129i	−0.129636	−	0.0417736i
$537$	−10.5007			−0.453141
$538$	1.79894	−	0.802686i	0.0775580	−	0.0346062i
$539$		0			0
$540$	−1.23007	+	2.60477i	−0.0529336	+	0.112092i
$541$	1.76517			0.0758907			0.0379453	−	0.999280i	$-0.487919\pi$
$541$	1.76517			0.0758907			0.0379453	+	0.999280i	$0.487919\pi$
$542$	−8.20092	−	18.3795i	−0.352260	−	0.789468i
$543$	13.3364			0.572318
$544$	−9.81158	+	5.71777i	−0.420668	+	0.245147i
$545$	−2.85340	−	9.55391i	−0.122226	−	0.409244i
$546$		0			0
$547$	28.3140			1.21062			0.605310	−	0.795990i	$-0.293049\pi$
$547$	28.3140			1.21062			0.605310	+	0.795990i	$0.293049\pi$
$548$	10.5338	+	9.45388i	0.449983	+	0.403850i
$549$		−	3.97369i		−	0.169593i
$550$	−8.59519	+	13.3906i	−0.366500	+	0.570975i
$551$	38.1560			1.62550
$552$	6.49336	−	20.1508i	0.276376	−	0.857676i
$553$		0			0
$554$	27.1379	−	12.1089i	1.15298	−	0.514457i
$555$	−7.66102	−	25.6511i	−0.325192	−	1.08883i
$556$	−19.3209	+	21.5280i	−0.819388	+	0.912990i
$557$		−	27.7580i		−	1.17614i	−0.808808	−	0.588072i	$-0.799887\pi$
$557$		−	27.7580i		−	1.17614i	0.808808	−	0.588072i	$-0.200113\pi$
$558$	−2.81555	−	6.31009i	−0.119192	−	0.267127i
$559$	6.72361			0.284378
$560$		0			0
$561$	11.3002			0.477095
$562$	2.25987	+	5.06472i	0.0953269	+	0.213642i
$563$			35.5787i			1.49947i	0.661741	+	0.749733i	$0.269818\pi$
$563$			35.5787i			1.49947i	−0.661741	+	0.749733i	$0.730182\pi$
$564$	31.9785	−	35.6315i	1.34654	−	1.50036i
$565$	4.93761	−	1.47468i	0.207727	−	0.0620402i
$566$	−1.55493	+	0.693807i	−0.0653585	+	0.0291629i
$567$		0			0
$568$	−7.28778	+	22.6161i	−0.305788	+	0.948951i
$569$	11.2535			0.471770			0.235885	−	0.971781i	$-0.424201\pi$
$569$	11.2535			0.471770			0.235885	+	0.971781i	$0.424201\pi$
$570$	40.3177	+	46.9146i	1.68872	+	1.96504i
$571$		−	0.667681i		−	0.0279416i	−0.999902	−	0.0139708i	$-0.995553\pi$
$571$		−	0.667681i		−	0.0279416i	0.999902	−	0.0139708i	$-0.00444718\pi$
$572$	19.9832	+	17.9345i	0.835541	+	0.749880i
$573$	41.8861			1.74982
$574$		0			0
$575$	12.5108	−	8.20491i	0.521737	−	0.342168i
$576$	−21.1571	−	15.2151i	−0.881544	−	0.633964i
$577$	−32.2214			−1.34139			−0.670696	−	0.741732i	$-0.734005\pi$
$577$	−32.2214			−1.34139			−0.670696	+	0.741732i	$0.734005\pi$
$578$	−7.47406	−	16.7505i	−0.310880	−	0.696730i
$579$	38.8795			1.61578
$580$	−19.7316	−	9.31799i	−0.819312	−	0.386908i
$581$		0			0
$582$	14.9258	−	6.65987i	0.618695	−	0.276061i
$583$	15.8928			0.658213
$584$	−15.8313	−	5.10143i	−0.655102	−	0.211099i
$585$	12.4364	+	41.6402i	0.514181	+	1.72161i
$586$	−8.33930	−	18.6897i	−0.344493	−	0.772063i
$587$		−	5.94377i		−	0.245326i	−0.992448	−	0.122663i	$-0.960857\pi$
$587$		−	5.94377i		−	0.245326i	0.992448	−	0.122663i	$-0.0391434\pi$
$588$		0			0
$589$	−11.7291			−0.483288
$590$	−27.3546	+	23.5082i	−1.12617	+	0.967816i
$591$	−26.0329			−1.07085
$592$	19.0326	−	2.06271i	0.782235	−	0.0847768i
$593$	−32.3521			−1.32854			−0.664270	−	0.747493i	$-0.731257\pi$
$593$	−32.3521			−1.32854			−0.664270	+	0.747493i	$0.731257\pi$
$594$	0.835255	+	1.87194i	0.0342709	+	0.0768064i
$595$		0			0
$596$	−26.2583	+	29.2579i	−1.07558	+	1.19845i
$597$			38.6531i			1.58197i
$598$	−10.2876	−	23.0561i	−0.420691	−	0.942834i
$599$			16.4047i			0.670277i	0.942169	+	0.335139i	$0.108783\pi$
$599$			16.4047i			0.670277i	−0.942169	+	0.335139i	$0.891217\pi$
$600$	−9.39263	−	34.1069i	−0.383453	−	1.39241i
$601$		−	17.5151i		−	0.714458i	−0.934017	−	0.357229i	$-0.883722\pi$
$601$		−	17.5151i		−	0.714458i	0.934017	−	0.357229i	$-0.116278\pi$
$602$		0			0
$603$	−3.63160			−0.147890
$604$	−25.9225	−	23.2649i	−1.05477	−	0.946634i
$605$	−3.79865	−	12.7189i	−0.154437	−	0.517095i
$606$	0.160189	+	0.359008i	0.00650723	+	0.0145837i
$607$		−	2.77165i		−	0.112498i	−0.998417	−	0.0562489i	$-0.982086\pi$
$607$		−	2.77165i		−	0.112498i	0.998417	−	0.0562489i	$-0.0179140\pi$
$608$	−38.2197	+	22.2728i	−1.55001	+	0.903281i
$609$		0			0
$610$	2.51423	+	2.92561i	0.101798	+	0.118455i
$611$		−	57.0948i		−	2.30981i
$612$	−8.73565	+	9.73356i	−0.353118	+	0.393456i
$613$		−	21.7127i		−	0.876966i	−0.898739	−	0.438483i	$-0.855516\pi$
$613$		−	21.7127i		−	0.876966i	0.898739	−	0.438483i	$-0.144484\pi$
$614$	−32.0257	+	14.2898i	−1.29245	+	0.576690i
$615$	14.1331	+	47.3213i	0.569902	+	1.90818i
$616$		0			0
$617$			4.75106i			0.191271i	0.995416	+	0.0956353i	$0.0304883\pi$
$617$			4.75106i			0.191271i	−0.995416	+	0.0956353i	$0.969512\pi$
$618$	−18.6126	−	41.7136i	−0.748707	−	1.67797i
$619$	31.5652			1.26871			0.634357	−	0.773040i	$-0.281265\pi$
$619$	31.5652			1.26871			0.634357	+	0.773040i	$0.281265\pi$
$620$	6.06546	+	2.86433i	0.243595	+	0.115034i
$621$		−	1.92739i		−	0.0773434i
$622$	4.06662	+	9.11391i	0.163056	+	0.365435i
$623$		0			0
$624$	−59.3502	+	6.43223i	−2.37591	+	0.257495i
$625$	9.96243	−	22.9292i	0.398497	−	0.917169i
$626$	18.7714	+	42.0695i	0.750255	+	1.68144i
$627$	44.0184			1.75792
$628$	−9.16474	+	10.2117i	−0.365713	+	0.407490i
$629$		−	9.60786i		−	0.383090i
$630$		0			0
$631$		−	13.2126i		−	0.525986i	−0.964798	−	0.262993i	$-0.915290\pi$
$631$		−	13.2126i		−	0.525986i	0.964798	−	0.262993i	$-0.0847096\pi$
$632$	−10.5277	+	32.6706i	−0.418771	+	1.29957i
$633$	−26.0125			−1.03390
$634$	28.8754	−	12.8841i	1.14679	−	0.511695i
$635$	3.95613	+	13.2461i	0.156994	+	0.525657i
$636$	−23.6008	+	26.2968i	−0.935832	+	1.04274i
$637$		0			0
$638$	−14.1803	+	6.32722i	−0.561402	+	0.250497i
$639$			27.3659i			1.08258i
$640$	25.2037	−	2.18441i	0.996265	−	0.0863463i
$641$	14.2989			0.564773			0.282386	−	0.959301i	$-0.408874\pi$
$641$	14.2989			0.564773			0.282386	+	0.959301i	$0.408874\pi$
$642$	47.1900	−	21.0561i	1.86244	−	0.831018i
$643$			8.53718i			0.336673i	0.985730	+	0.168337i	$0.0538396\pi$
$643$			8.53718i			0.336673i	−0.985730	+	0.168337i	$0.946160\pi$
$644$		0			0
$645$	−6.04000	+	1.80392i	−0.237825	+	0.0710294i
$646$	9.04627	+	20.2741i	0.355921	+	0.797674i
$647$			23.8661i			0.938275i	0.883125	+	0.469137i	$0.155435\pi$
$647$			23.8661i			0.938275i	−0.883125	+	0.469137i	$0.844565\pi$
$648$	21.9709	+	7.07985i	0.863097	+	0.278123i
$649$			25.6659i			1.00748i
$650$	−35.5028	−	22.7887i	−1.39253	−	0.893846i
$651$		0			0
$652$	−3.83302	+	4.27088i	−0.150113	+	0.167260i
$653$		−	18.0725i		−	0.707230i	−0.935391	−	0.353615i	$-0.884952\pi$
$653$		−	18.0725i		−	0.707230i	0.935391	−	0.353615i	$-0.115048\pi$
$654$	14.4058	−	6.42786i	0.563313	−	0.251349i
$655$	−5.22733	−	17.5024i	−0.204249	−	0.683877i
$656$	−35.1115	+	3.80530i	−1.37087	+	0.148572i
$657$	−19.1561			−0.747350
$658$		0			0
$659$		−	13.3401i		−	0.519657i	−0.965655	−	0.259828i	$-0.916334\pi$
$659$		−	13.3401i		−	0.519657i	0.965655	−	0.259828i	$-0.0836660\pi$
$660$	−22.7632	−	10.7496i	−0.886058	−	0.418428i
$661$		−	18.4115i		−	0.716123i	−0.933698	−	0.358062i	$-0.883438\pi$
$661$		−	18.4115i		−	0.716123i	0.933698	−	0.358062i	$-0.116562\pi$
$662$	−31.2724	+	13.9537i	−1.21544	+	0.542327i
$663$			29.9606i			1.16357i
$664$	9.65688	−	29.9682i	0.374760	−	1.16299i
$665$		0			0
$666$	20.1348	−	8.98410i	0.780206	−	0.348127i
$667$	14.6003			0.565327
$668$	23.7243	+	21.2920i	0.917919	+	0.823812i
$669$	−28.4309			−1.09920
$670$	2.67376	−	2.29779i	0.103296	−	0.0887713i
$671$	2.74500			0.105970
$672$		0			0
$673$			43.5683i			1.67944i	0.543023	+	0.839718i	$0.317280\pi$
$673$			43.5683i			1.67944i	−0.543023	+	0.839718i	$0.682720\pi$
$674$	10.2761	−	4.58520i	0.395822	−	0.176615i
$675$	−1.76621	−	2.69311i	−0.0679815	−	0.103658i
$676$	−30.1843	+	33.6323i	−1.16093	+	1.29355i
$677$	−12.8331			−0.493218			−0.246609	−	0.969115i	$-0.579316\pi$
$677$	−12.8331			−0.493218			−0.246609	+	0.969115i	$0.579316\pi$
$678$	3.32202	+	7.44516i	0.127581	+	0.285930i
$679$		0			0
$680$	0.272982	−	12.6935i	0.0104684	−	0.486774i
$681$	−15.4366			−0.591531
$682$	4.35898	−	1.94497i	0.166914	−	0.0744768i
$683$	−0.937655			−0.0358784			−0.0179392	−	0.999839i	$-0.505711\pi$
$683$	−0.937655			−0.0358784			−0.0179392	+	0.999839i	$0.505711\pi$
$684$	−34.0285	+	37.9157i	−1.30111	+	1.44974i
$685$	−15.1629	+	4.52860i	−0.579345	+	0.173029i
$686$		0			0
$687$	−20.7274			−0.790801
$688$	−0.485701	−	4.48156i	−0.0185172	−	0.170858i
$689$			42.1371i			1.60530i
$690$	15.4275	+	17.9518i	0.587315	+	0.683412i
$691$	8.12642			0.309144			0.154572	−	0.987982i	$-0.450600\pi$
$691$	8.12642			0.309144			0.154572	+	0.987982i	$0.450600\pi$
$692$	−1.36800	+	1.52427i	−0.0520035	+	0.0579440i
$693$		0			0
$694$	11.4535	+	25.6690i	0.434767	+	0.974381i
$695$	−9.25509	−	30.9884i	−0.351066	−	1.17546i
$696$	10.5884	−	32.8591i	0.401354	−	1.24552i
$697$			17.7246i			0.671369i
$698$	16.6408	−	7.42508i	0.629862	−	0.281044i
$699$	−35.2483			−1.33321
$700$		0			0
$701$	−27.4244			−1.03580			−0.517902	−	0.855440i	$-0.673287\pi$
$701$	−27.4244			−1.03580			−0.517902	+	0.855440i	$0.673287\pi$
$702$	−4.96312	+	2.21454i	−0.187321	+	0.0835824i
$703$		−	37.4261i		−	1.41155i
$704$	10.5105	−	14.6152i	0.396131	−	0.550831i
$705$	15.3183	+	51.2898i	0.576922	+	1.93168i
$706$	4.80985	+	10.7796i	0.181021	+	0.405697i
$707$		0			0
$708$	−42.4677	−	38.1139i	−1.59603	−	1.43241i
$709$	21.4972			0.807346			0.403673	−	0.914903i	$-0.367733\pi$
$709$	21.4972			0.807346			0.403673	+	0.914903i	$0.367733\pi$
$710$	−17.3149	−	20.1480i	−0.649818	−	0.756142i
$711$			39.5320i			1.48257i
$712$	−3.97213	+	12.3267i	−0.148862	+	0.461963i
$713$	−4.48811			−0.168081
$714$		0			0
$715$	−28.7648	+	8.59099i	−1.07574	+	0.321285i
$716$	6.24820	+	5.60762i	0.233506	+	0.209567i
$717$	−20.7788			−0.775998
$718$	−2.35045	+	1.04877i	−0.0877178	+	0.0391396i
$719$	−26.9012			−1.00325			−0.501623	−	0.865087i	$-0.667263\pi$
$719$	−26.9012			−1.00325			−0.501623	+	0.865087i	$0.667263\pi$
$720$	26.8565	−	11.2974i	1.00088	−	0.421028i
$721$		0			0
$722$	24.2896	+	54.4368i	0.903966	+	2.02593i
$723$	−64.3844			−2.39448
$724$	−7.93547	−	7.12191i	−0.294919	−	0.264684i
$725$	20.4009	−	13.3794i	0.757669	−	0.496898i
$726$	19.1781	−	8.55724i	0.711766	−	0.317589i
$727$			14.8535i			0.550886i	0.961317	+	0.275443i	$0.0888245\pi$
$727$			14.8535i			0.550886i	−0.961317	+	0.275443i	$0.911175\pi$
$728$		0			0
$729$	31.4189			1.16366
$730$	14.1036	−	12.1204i	0.521998	−	0.448597i
$731$	−2.26234			−0.0836756
$732$	−4.07633	+	4.54198i	−0.150665	+	0.167876i
$733$	16.4626			0.608059			0.304030	−	0.952663i	$-0.401668\pi$
$733$	16.4626			0.608059			0.304030	+	0.952663i	$0.401668\pi$
$734$	1.38168	−	0.616503i	0.0509987	−	0.0227555i
$735$		0			0
$736$	−14.6247	+	8.52264i	−0.539073	+	0.314149i
$737$		−	2.50870i		−	0.0924090i
$738$	−37.1447	+	16.5739i	−1.36732	+	0.610094i
$739$			44.4004i			1.63329i	0.577137	+	0.816647i	$0.304170\pi$
$739$			44.4004i			1.63329i	−0.577137	+	0.816647i	$0.695830\pi$
$740$	−9.13973	+	19.3542i	−0.335983	+	0.711474i
$741$			116.707i			4.28735i
$742$		0			0
$743$	34.9014			1.28041			0.640204	−	0.768205i	$-0.278850\pi$
$743$	34.9014			1.28041			0.640204	+	0.768205i	$0.278850\pi$
$744$	−3.25487	+	10.1008i	−0.119329	+	0.370314i
$745$	−12.5782	−	42.1152i	−0.460831	−	1.54298i
$746$	−17.0309	+	7.59917i	−0.623546	+	0.278226i
$747$		−	36.2620i		−	1.32676i
$748$	−6.72390	−	6.03455i	−0.245850	−	0.220645i
$749$		0			0
$750$	38.0072	+	10.9464i	1.38783	+	0.399706i
$751$		−	18.8248i		−	0.686927i	−0.939166	−	0.343463i	$-0.888400\pi$
$751$		−	18.8248i		−	0.686927i	0.939166	−	0.343463i	$-0.111600\pi$
$752$	−38.0560	+	4.12442i	−1.38776	+	0.150402i
$753$			12.0225i			0.438124i
$754$	−16.7756	−	37.5966i	−0.610930	−	1.36919i
$755$	37.3141	−	11.1443i	1.35800	−	0.405584i
$756$		0			0
$757$			54.4433i			1.97878i	0.145301	+	0.989388i	$0.453585\pi$
$757$			54.4433i			1.97878i	−0.145301	+	0.989388i	$0.546415\pi$
$758$	−21.9364	+	9.78798i	−0.796765	+	0.355516i
$759$	16.8435			0.611382
$760$	1.06336	−	49.4459i	0.0385722	−	1.79359i
$761$		−	25.8142i		−	0.935765i	−0.883791	−	0.467883i	$-0.845017\pi$
$761$		−	25.8142i		−	0.935765i	0.883791	−	0.467883i	$-0.154983\pi$
$762$	−19.9732	+	8.91200i	−0.723552	+	0.322848i
$763$		0			0
$764$	−24.9232	−	22.3681i	−0.901691	−	0.809248i
$765$	−4.18455	−	14.0110i	−0.151293	−	0.506567i
$766$	6.03861	−	2.69442i	0.218184	−	0.0973533i
$767$	−68.0489			−2.45710
$768$	8.57469	+	39.0947i	0.309412	+	1.41071i
$769$		−	40.1288i		−	1.44708i	−0.690281	−	0.723542i	$-0.742513\pi$
$769$		−	40.1288i		−	1.44708i	0.690281	−	0.723542i	$-0.257487\pi$
$770$		0			0
$771$			53.5633i			1.92904i
$772$	−23.1343	−	20.7625i	−0.832620	−	0.747259i
$773$	49.0224			1.76321			0.881607	−	0.471983i	$-0.156462\pi$
$773$	49.0224			1.76321			0.881607	+	0.471983i	$0.156462\pi$
$774$	−2.11546	−	4.74108i	−0.0760388	−	0.170415i
$775$	−6.27118	+	4.11280i	−0.225267	+	0.147736i
$776$	−12.4377	−	4.00792i	−0.446489	−	0.143876i
$777$		0			0
$778$	−14.8666	−	33.3183i	−0.532992	−	1.19452i
$779$			69.0439i			2.47375i
$780$	28.5008	−	60.3529i	1.02049	−	2.16098i
$781$	−18.9042			−0.676446
$782$	3.46154	+	7.75784i	0.123784	+	0.277420i
$783$		−	3.14291i		−	0.112318i
$784$		0			0
$785$	−4.39009	−	14.6992i	−0.156689	−	0.524635i
$786$	26.3910	−	11.7756i	0.941336	−	0.420023i
$787$			40.9623i			1.46015i	0.683368	+	0.730074i	$0.260515\pi$
$787$			40.9623i			1.46015i	−0.683368	+	0.730074i	$0.739485\pi$
$788$	15.4902	+	13.9021i	0.551816	+	0.495243i
$789$		−	39.3449i		−	1.40072i
$790$	−25.0127	−	29.1053i	−0.889912	−	1.03552i
$791$		0			0
$792$	6.35897	−	19.7337i	0.225956	−	0.701208i
$793$			7.27792i			0.258446i
$794$	−15.3381	−	34.3750i	−0.544329	−	1.21992i
$795$	−11.3052	−	37.8529i	−0.400956	−	1.34250i
$796$	20.6416	−	22.9996i	0.731623	−	0.815198i
$797$	15.6633			0.554824			0.277412	−	0.960751i	$-0.410523\pi$
$797$	15.6633			0.554824			0.277412	+	0.960751i	$0.410523\pi$
$798$		0			0
$799$			19.2111i			0.679639i
$800$	−12.6249	+	25.3103i	−0.446359	+	0.894854i
$801$			14.9155i			0.527014i
$802$	−5.20348	−	11.6618i	−0.183741	−	0.411793i
$803$		−	13.2329i		−	0.466980i
$804$	4.15098	+	3.72541i	0.146394	+	0.131385i
$805$		0			0
$806$	5.15677	+	11.5571i	0.181639	+	0.407082i
$807$	−3.48441			−0.122657
$808$	0.0964018	−	0.299163i	0.00339140	−	0.0105245i
$809$	10.0562			0.353558			0.176779	−	0.984251i	$-0.443432\pi$
$809$	10.0562			0.353558			0.176779	+	0.984251i	$0.443432\pi$
$810$	−19.5732	+	16.8209i	−0.687732	+	0.591027i
$811$	−35.5294			−1.24760			−0.623802	−	0.781582i	$-0.714413\pi$
$811$	−35.5294			−1.24760			−0.623802	+	0.781582i	$0.714413\pi$
$812$		0			0
$813$			35.5997i			1.24854i
$814$	6.20618	+	13.9090i	0.217526	+	0.487510i
$815$	−1.83609	−	6.14771i	−0.0643155	−	0.215345i
$816$	19.9700	−	2.16430i	0.699088	−	0.0757655i
$817$	−8.81263			−0.308315
$818$	−4.40972	+	1.96761i	−0.154182	+	0.0687959i
$819$		0			0
$820$	16.8610	−	35.7047i	0.588813	−	1.24686i
$821$	14.8302			0.517578			0.258789	−	0.965934i	$-0.416677\pi$
$821$	14.8302			0.517578			0.258789	+	0.965934i	$0.416677\pi$
$822$	−10.2016	−	22.8633i	−0.355821	−	0.797451i
$823$	17.0603			0.594685			0.297342	−	0.954771i	$-0.403900\pi$
$823$	17.0603			0.594685			0.297342	+	0.954771i	$0.403900\pi$
$824$	−11.2010	+	34.7601i	−0.390207	+	1.21093i
$825$	23.5353	−	15.4350i	0.819393	−	0.537379i
$826$		0			0
$827$	−33.2481			−1.15615			−0.578074	−	0.815984i	$-0.696196\pi$
$827$	−33.2481			−1.15615			−0.578074	+	0.815984i	$0.696196\pi$
$828$	−13.0210	+	14.5084i	−0.452509	+	0.504201i
$829$			10.1159i			0.351339i	0.984449	+	0.175669i	$0.0562090\pi$
$829$			10.1159i			0.351339i	−0.984449	+	0.175669i	$0.943791\pi$
$830$	22.9437	+	26.6978i	0.796386	+	0.926693i
$831$	−52.5639			−1.82342
$832$	38.7498	+	27.8669i	1.34341	+	0.966112i
$833$		0			0
$834$	46.7258	−	20.8490i	1.61798	−	0.721942i
$835$	−34.1498	+	10.1993i	−1.18180	+	0.352961i
$836$	−26.1920	−	23.5068i	−0.905870	−	0.812998i
$837$			0.966123i			0.0333941i
$838$	−9.10452	−	20.4046i	−0.314510	−	0.704866i
$839$	−31.0058			−1.07044			−0.535220	−	0.844713i	$-0.679771\pi$
$839$	−31.0058			−1.07044			−0.535220	+	0.844713i	$0.679771\pi$
$840$		0			0
$841$	−5.19187			−0.179030
$842$	12.0057	+	26.9067i	0.413745	+	0.927266i
$843$		−	9.80995i		−	0.337873i
$844$	15.4781	+	13.8912i	0.532777	+	0.478155i
$845$	−14.4589	−	48.4120i	−0.497400	−	1.66542i
$846$	−40.2598	+	17.9639i	−1.38416	+	0.617610i
$847$		0			0
$848$	28.0861	−	3.04391i	0.964481	−	0.104528i
$849$	3.01177			0.103364
$850$	11.9459	+	7.66787i	0.409740	+	0.263006i
$851$		−	14.3210i		−	0.490918i
$852$	28.0727	−	31.2796i	0.961757	−	1.07162i
$853$	−36.3392			−1.24423			−0.622116	−	0.782925i	$-0.713727\pi$
$853$	−36.3392			−1.24423			−0.622116	+	0.782925i	$0.713727\pi$
$854$		0			0
$855$	−16.3003	−	54.5777i	−0.557460	−	1.86652i
$856$	−39.3236	−	12.6716i	−1.34405	−	0.433106i
$857$	30.8736			1.05462			0.527311	−	0.849673i	$-0.323200\pi$
$857$	30.8736			1.05462			0.527311	+	0.849673i	$0.323200\pi$
$858$	−19.3530	−	43.3730i	−0.660700	−	1.48073i
$859$	15.7409			0.537071			0.268536	−	0.963270i	$-0.413460\pi$
$859$	15.7409			0.537071			0.268536	+	0.963270i	$0.413460\pi$
$860$	4.55728	+	2.15211i	0.155402	+	0.0733864i
$861$		0			0
$862$	35.5786	−	15.8751i	1.21181	−	0.540709i
$863$	19.3611			0.659058			0.329529	−	0.944145i	$-0.393110\pi$
$863$	19.3611			0.659058			0.329529	+	0.944145i	$0.393110\pi$
$864$	1.83461	+	3.14815i	0.0624146	+	0.107102i
$865$	−0.655298	−	2.19411i	−0.0222808	−	0.0746018i
$866$	−1.31452	−	2.94604i	−0.0446692	−	0.100111i
$867$			32.4444i			1.10187i
$868$		0			0
$869$	−27.3086			−0.926379
$870$	25.1570	+	29.2732i	0.852901	+	0.992454i
$871$	6.65139			0.225374
$872$	−12.0044	−	3.86829i	−0.406522	−	0.130997i
$873$	−15.0499			−0.509361
$874$	13.4839	+	30.2196i	0.456101	+	1.02219i
$875$		0			0
$876$	21.8957	+	19.6509i	0.739786	+	0.663942i
$877$			51.4669i			1.73791i	0.494887	+	0.868957i	$0.335209\pi$
$877$			51.4669i			1.73791i	−0.494887	+	0.868957i	$0.664791\pi$
$878$	−5.33975	−	11.9672i	−0.180208	−	0.403873i
$879$			36.2004i			1.22101i
$880$	7.80417	+	18.5524i	0.263078	+	0.625400i
$881$		−	9.28126i		−	0.312694i	−0.987702	−	0.156347i	$-0.950028\pi$
$881$		−	9.28126i		−	0.312694i	0.987702	−	0.156347i	$-0.0499718\pi$
$882$		0			0
$883$	−52.8990			−1.78019			−0.890096	−	0.455774i	$-0.849363\pi$
$883$	−52.8990			−1.78019			−0.890096	+	0.455774i	$0.849363\pi$
$884$	15.9996	−	17.8273i	0.538125	−	0.599597i
$885$	61.1301	−	18.2573i	2.05487	−	0.613712i
$886$	15.7486	+	35.2950i	0.529083	+	1.18576i
$887$			17.6748i			0.593461i	0.954961	+	0.296730i	$0.0958963\pi$
$887$			17.6748i			0.593461i	−0.954961	+	0.296730i	$0.904104\pi$
$888$	−32.2305	−	10.3859i	−1.08158	−	0.348528i
$889$		0			0
$890$	−9.43734	−	10.9815i	−0.316340	−	0.368101i
$891$			18.3649i			0.615246i
$892$	16.9171	+	15.1827i	0.566426	+	0.508355i
$893$			74.8341i			2.50423i
$894$	63.5033	−	28.3351i	2.12387	−	0.947666i
$895$	−8.99396	+	2.68616i	−0.300635	+	0.0897885i
$896$		0			0
$897$			44.6578i			1.49108i
$898$	18.2073	+	40.8054i	0.607586	+	1.36169i
$899$	−7.31857			−0.244088
$900$	−4.89889	+	32.2045i	−0.163296	+	1.07348i
$901$		−	14.1782i		−	0.472343i
$902$	−11.4492	−	25.6594i	−0.381216	−	0.854365i
$903$		0			0
$904$	1.99919	−	6.20408i	0.0664921	−	0.206345i
$905$	11.4227	−	3.41153i	0.379703	−	0.113403i
$906$	25.1049	+	56.2640i	0.834055	+	1.86925i
$907$	57.6529			1.91433			0.957166	−	0.289539i	$-0.0935021\pi$
$907$	57.6529			1.91433			0.957166	+	0.289539i	$0.0935021\pi$
$908$	9.18514	+	8.24346i	0.304820	+	0.273569i
$909$		−	0.361992i		−	0.0120065i
$910$		0			0
$911$		−	4.76210i		−	0.157776i	−0.996884	−	0.0788878i	$-0.974863\pi$
$911$		−	4.76210i		−	0.157776i	0.996884	−	0.0788878i	$-0.0251369\pi$
$912$	77.7902	−	8.43072i	2.57589	−	0.279169i
$913$	25.0496			0.829021
$914$	−25.9765	+	11.5907i	−0.859225	+	0.383385i
$915$	−1.95264	−	6.53795i	−0.0645523	−	0.216138i
$916$	12.3333	+	11.0689i	0.407505	+	0.365727i
$917$		0			0
$918$	1.66998	−	0.745141i	0.0551174	−	0.0245933i
$919$			7.04133i			0.232272i	0.993233	+	0.116136i	$0.0370509\pi$
$919$			7.04133i			0.232272i	−0.993233	+	0.116136i	$0.962949\pi$
$920$	0.406894	−	18.9204i	0.0134149	−	0.623786i
$921$	62.0312			2.04400
$922$	2.03735	−	0.909065i	0.0670967	−	0.0299385i
$923$		−	50.1214i		−	1.64977i
$924$		0			0
$925$	−13.1234	−	20.0106i	−0.431496	−	0.657944i
$926$	−15.9814	−	35.8167i	−0.525180	−	1.17701i
$927$			42.0603i			1.38144i
$928$	−23.8478	+	13.8975i	−0.782844	+	0.456208i
$929$			51.2738i			1.68224i	0.540849	+	0.841120i	$0.318103\pi$
$929$			51.2738i			1.68224i	−0.540849	+	0.841120i	$0.681897\pi$
$930$	−7.73319	−	8.99851i	−0.253581	−	0.295073i
$931$		0			0
$932$	20.9736	+	18.8234i	0.687014	+	0.616580i
$933$		−	17.6529i		−	0.577931i
$934$	11.9349	−	5.32532i	0.390521	−	0.174250i
$935$	9.67870	−	2.89067i	0.316527	−	0.0945350i
$936$	52.3207	+	16.8597i	1.71016	+	0.551078i
$937$	57.1992			1.86862			0.934308	−	0.356467i	$-0.116019\pi$
$937$	57.1992			1.86862			0.934308	+	0.356467i	$0.116019\pi$
$938$		0			0
$939$		−	81.4853i		−	2.65917i
$940$	18.2750	−	38.6990i	0.596066	−	1.26222i
$941$			14.7089i			0.479497i	0.970835	+	0.239748i	$0.0770649\pi$
$941$			14.7089i			0.479497i	−0.970835	+	0.239748i	$0.922935\pi$
$942$	22.1641	−	9.88958i	0.722145	−	0.322220i
$943$			26.4195i			0.860337i
$944$	4.91572	+	45.3574i	0.159993	+	1.47626i
$945$		0			0
$946$	3.27512	−	1.46135i	0.106483	−	0.0475127i
$947$	18.7265			0.608528			0.304264	−	0.952588i	$-0.401589\pi$
$947$	18.7265			0.608528			0.304264	+	0.952588i	$0.401589\pi$
$948$	40.5532	−	45.1857i	1.31711	−	1.46756i
$949$	35.0849			1.13890
$950$	46.5335	+	29.8691i	1.50975	+	0.969083i
$951$	−55.9293			−1.81363
$952$		0			0
$953$		−	20.9501i		−	0.678639i	−0.940671	−	0.339320i	$-0.889803\pi$
$953$		−	20.9501i		−	0.678639i	0.940671	−	0.339320i	$-0.110197\pi$
$954$	29.7125	−	13.2577i	0.961979	−	0.429233i
$955$	35.8757	−	10.7147i	1.16091	−	0.346721i
$956$	12.3639	+	11.0963i	0.399877	+	0.358880i
$957$	27.4661			0.887851
$958$	6.07688	+	13.6192i	0.196335	+	0.440018i
$959$		0			0
$960$	−42.2865	−	14.6372i	−1.36479	−	0.472413i
$961$	−28.7503			−0.927429
$962$	−36.8774	+	16.4546i	−1.18897	+	0.530519i
$963$	−47.5822			−1.53332
$964$	38.3103	+	34.3826i	1.23389	+	1.10739i
$965$	33.3006	−	9.94564i	1.07198	−	0.320162i
$966$		0			0
$967$	37.8488			1.21714			0.608568	−	0.793501i	$-0.291744\pi$
$967$	37.8488			1.21714			0.608568	+	0.793501i	$0.291744\pi$
$968$	−15.9812	−	5.14975i	−0.513655	−	0.165519i
$969$		−	39.2693i		−	1.26151i
$970$	11.0804	−	9.52236i	0.355771	−	0.305744i
$971$	28.5491			0.916185			0.458093	−	0.888904i	$-0.348533\pi$
$971$	28.5491			0.916185			0.458093	+	0.888904i	$0.348533\pi$
$972$	−33.2634	−	29.8532i	−1.06692	−	0.957541i
$973$		0			0
$974$	−10.3727	−	23.2468i	−0.332362	−	0.744875i
$975$	40.9234	+	62.3998i	1.31060	+	1.99839i
$976$	4.85103	−	0.525743i	0.155278	−	0.0168286i
$977$			19.5942i			0.626874i	0.949609	+	0.313437i	$0.101480\pi$
$977$			19.5942i			0.626874i	−0.949609	+	0.313437i	$0.898520\pi$
$978$	9.26981	−	4.13617i	0.296416	−	0.132260i
$979$	−10.3036			−0.329303
$980$		0			0
$981$	−14.5256			−0.463766
$982$	0.910279	−	0.406165i	0.0290482	−	0.0129613i
$983$		−	1.58532i		−	0.0505638i	−0.999680	−	0.0252819i	$-0.991952\pi$
$983$		−	1.58532i		−	0.0505638i	0.999680	−	0.0252819i	$-0.00804833\pi$
$984$	59.4590	+	19.1600i	1.89548	+	0.610797i
$985$	−22.2974	+	6.65940i	−0.710453	+	0.212186i
$986$	5.64458	+	12.6504i	0.179760	+	0.402870i
$987$		0			0
$988$	62.3242	−	69.4437i	1.98280	−	2.20930i
$989$	−3.37214			−0.107228
$990$	15.1082	+	17.5802i	0.480170	+	0.558736i
$991$		−	59.2749i		−	1.88293i	−0.337112	−	0.941465i	$-0.609450\pi$
$991$		−	59.2749i		−	1.88293i	0.337112	−	0.941465i	$-0.390550\pi$
$992$	7.33077	−	4.27206i	0.232752	−	0.135638i
$993$	60.5722			1.92220
$994$		0			0
$995$	9.88774	+	33.1067i	0.313462	+	1.04955i
$996$	−37.1986	+	41.4480i	−1.17868	+	1.31333i
$997$	−33.9972			−1.07670			−0.538351	−	0.842721i	$-0.680953\pi$
$997$	−33.9972			−1.07670			−0.538351	+	0.842721i	$0.680953\pi$
$998$	−8.43757	+	3.76483i	−0.267087	+	0.119174i
$999$	−3.08278			−0.0975350

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.2.c.e.979.31	yes	48
4.3	odd	2	inner	980.2.c.e.979.20	yes	48
5.4	even	2	inner	980.2.c.e.979.18	yes	48
7.2	even	3		980.2.s.g.619.34		96
7.3	odd	6		980.2.s.g.19.2		96
7.4	even	3		980.2.s.g.19.1		96
7.5	odd	6		980.2.s.g.619.33		96
7.6	odd	2	inner	980.2.c.e.979.32	yes	48
20.19	odd	2	inner	980.2.c.e.979.29	yes	48
28.3	even	6		980.2.s.g.19.15		96
28.11	odd	6		980.2.s.g.19.16		96
28.19	even	6		980.2.s.g.619.48		96
28.23	odd	6		980.2.s.g.619.47		96
28.27	even	2	inner	980.2.c.e.979.19	yes	48
35.4	even	6		980.2.s.g.19.48		96
35.9	even	6		980.2.s.g.619.15		96
35.19	odd	6		980.2.s.g.619.16		96
35.24	odd	6		980.2.s.g.19.47		96
35.34	odd	2	inner	980.2.c.e.979.17	✓	48
140.19	even	6		980.2.s.g.619.1		96
140.39	odd	6		980.2.s.g.19.33		96
140.59	even	6		980.2.s.g.19.34		96
140.79	odd	6		980.2.s.g.619.2		96
140.139	even	2	inner	980.2.c.e.979.30	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
980.2.c.e.979.17	✓	48	35.34	odd	2	inner
980.2.c.e.979.18	yes	48	5.4	even	2	inner
980.2.c.e.979.19	yes	48	28.27	even	2	inner
980.2.c.e.979.20	yes	48	4.3	odd	2	inner
980.2.c.e.979.29	yes	48	20.19	odd	2	inner
980.2.c.e.979.30	yes	48	140.139	even	2	inner
980.2.c.e.979.31	yes	48	1.1	even	1	trivial
980.2.c.e.979.32	yes	48	7.6	odd	2	inner
980.2.s.g.19.1		96	7.4	even	3
980.2.s.g.19.2		96	7.3	odd	6
980.2.s.g.19.15		96	28.3	even	6
980.2.s.g.19.16		96	28.11	odd	6
980.2.s.g.19.33		96	140.39	odd	6
980.2.s.g.19.34		96	140.59	even	6
980.2.s.g.19.47		96	35.24	odd	6
980.2.s.g.19.48		96	35.4	even	6
980.2.s.g.619.1		96	140.19	even	6
980.2.s.g.619.2		96	140.79	odd	6
980.2.s.g.619.15		96	35.9	even	6
980.2.s.g.619.16		96	35.19	odd	6
980.2.s.g.619.33		96	7.5	odd	6
980.2.s.g.619.34		96	7.2	even	3
980.2.s.g.619.47		96	28.23	odd	6
980.2.s.g.619.48		96	28.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	980.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 + 1.48845i) q^{4} +(-0.639901 - 2.14255i) q^{5} +(3.23064 - 1.44151i) q^{6} +(-2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +O(q^{10})\)	\(q+(0.576258 + 1.29148i) q^{2} -2.50150i q^{3} +(-1.33585 + 1.48845i) q^{4} +(-0.639901 - 2.14255i) q^{5} +(3.23064 - 1.44151i) q^{6} +(-2.69211 - 0.867500i) q^{8} -3.25749 q^{9} +(2.39832 - 2.06108i) q^{10} -2.25026i q^{11} +(3.72336 + 3.34164i) q^{12} +5.96620 q^{13} +(-5.35959 + 1.60071i) q^{15} +(-0.430987 - 3.97671i) q^{16} -2.00749 q^{17} +(-1.87716 - 4.20700i) q^{18} -7.81989 q^{19} +(4.04390 + 1.90967i) q^{20} +(2.90618 - 1.29673i) q^{22} -2.99226 q^{23} +(-2.17005 + 6.73430i) q^{24} +(-4.18105 + 2.74204i) q^{25} +(3.43807 + 7.70524i) q^{26} +0.644123i q^{27} -4.87936 q^{29} +(-5.15579 - 5.99939i) q^{30} +1.49990 q^{31} +(4.88750 - 2.84822i) q^{32} -5.62903 q^{33} +(-1.15683 - 2.59263i) q^{34} +(4.35154 - 4.84863i) q^{36} +4.78601i q^{37} +(-4.50627 - 10.0992i) q^{38} -14.9244i q^{39} +(-0.135982 + 6.32309i) q^{40} -8.82927i q^{41} +1.12695 q^{43} +(3.34941 + 3.00602i) q^{44} +(2.08447 + 6.97935i) q^{45} +(-1.72431 - 3.86446i) q^{46} -9.56972i q^{47} +(-9.94774 + 1.07811i) q^{48} +(-5.95066 - 3.81964i) q^{50} +5.02172i q^{51} +(-7.96997 + 8.88040i) q^{52} +7.06264i q^{53} +(-0.831874 + 0.371181i) q^{54} +(-4.82131 + 1.43994i) q^{55} +19.5614i q^{57} +(-2.81177 - 6.30161i) q^{58} -11.4057 q^{59} +(4.77705 - 10.1158i) q^{60} +1.21986i q^{61} +(0.864331 + 1.93710i) q^{62} +(6.49489 + 4.67081i) q^{64} +(-3.81777 - 12.7829i) q^{65} +(-3.24377 - 7.26979i) q^{66} +1.11485 q^{67} +(2.68171 - 2.98805i) q^{68} +7.48514i q^{69} -8.40090i q^{71} +(8.76953 + 2.82588i) q^{72} +5.88062 q^{73} +(-6.18105 + 2.75798i) q^{74} +(6.85921 + 10.4589i) q^{75} +(10.4462 - 11.6395i) q^{76} +(19.2746 - 8.60032i) q^{78} -12.1357i q^{79} +(-8.24453 + 3.46811i) q^{80} -8.16121 q^{81} +(11.4028 - 5.08793i) q^{82} +11.1319i q^{83} +(1.28459 + 4.30114i) q^{85} +(0.649414 + 1.45544i) q^{86} +12.2057i q^{87} +(-1.95210 + 6.05795i) q^{88} -4.57883i q^{89} +(-7.81252 + 6.71396i) q^{90} +(3.99723 - 4.45385i) q^{92} -3.75201i q^{93} +(12.3591 - 5.51462i) q^{94} +(5.00395 + 16.7545i) q^{95} +(-7.12483 - 12.2261i) q^{96} +4.62008 q^{97} +7.33022i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 16 q^{4} - 64 q^{9}+O(q^{10}) \) 48 * q + 16 * q^4 - 64 * q^9	\( 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) \) 48 * q + 16 * q^4 - 64 * q^9 + 16 * q^16 - 16 * q^25 - 48 * q^29 - 8 * q^30 + 176 * q^36 - 48 * q^44 - 32 * q^46 + 32 * q^50 + 24 * q^60 - 80 * q^64 - 16 * q^65 - 112 * q^74 - 48 * q^81 - 64 * q^85 - 112 * q^86

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