LMFDB - Embedded newform 504.2.t.c.193.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, degree $2$, 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:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.6
Character	$\chi$	$=$	504.193
Dual form			504.2.t.c.457.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.341725 - 1.69801i) q^{3} +0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} +(-2.76645 + 1.16050i) q^{9} +O(q^{10})$	\(q+(-0.341725 - 1.69801i) q^{3} +0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} +(-2.76645 + 1.16050i) q^{9} +4.61052 q^{11} +(0.244554 - 0.423580i) q^{13} +(-0.179749 - 0.893158i) q^{15} +(2.75579 - 4.77318i) q^{17} +(1.83782 + 3.18319i) q^{19} +(0.904788 - 4.49237i) q^{21} -0.0539537 q^{23} -4.72332 q^{25} +(2.91591 + 4.30087i) q^{27} +(-3.28471 - 5.68929i) q^{29} +(-3.03820 - 5.26231i) q^{31} +(-1.57553 - 7.82869i) q^{33} +(1.28325 + 0.538539i) q^{35} +(0.223731 + 0.387513i) q^{37} +(-0.802811 - 0.270506i) q^{39} +(2.52284 - 4.36968i) q^{41} +(2.84893 + 4.93449i) q^{43} +(-1.45516 + 0.610430i) q^{45} +(4.59810 - 7.96415i) q^{47} +(4.90354 + 4.99552i) q^{49} +(-9.04661 - 3.04824i) q^{51} +(-4.37138 + 7.57145i) q^{53} +2.42515 q^{55} +(4.77705 - 4.20840i) q^{57} +(3.31538 + 5.74241i) q^{59} +(0.232812 - 0.403243i) q^{61} +(-7.93725 - 0.00117907i) q^{63} +(0.128636 - 0.222805i) q^{65} +(-2.59679 - 4.49777i) q^{67} +(0.0184374 + 0.0916137i) q^{69} +1.76328 q^{71} +(-5.23776 + 9.07207i) q^{73} +(1.61408 + 8.02022i) q^{75} +(11.2479 + 4.72039i) q^{77} +(-8.18509 + 14.1770i) q^{79} +(6.30646 - 6.42094i) q^{81} +(4.49251 + 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(-8.53797 + 7.52163i) q^{87} +(-7.05145 - 12.2135i) q^{89} +(1.03029 - 0.782994i) q^{91} +(-7.89721 + 6.95714i) q^{93} +(0.966699 + 1.67437i) q^{95} +(5.22413 + 9.04847i) q^{97} +(-12.7548 + 5.35052i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7	$ 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) $ 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−0.341725	−	1.69801i	−0.197295	−	0.980344i
$3$	−0.341725	−	1.69801i	−0.197295	−	0.980344i
$4$		0			0
$5$	0.526004			0.235236			0.117618	−	0.993059i	$-0.462474\pi$
$5$	0.526004			0.235236			0.117618	+	0.993059i	$0.462474\pi$
$6$		0			0
$7$	2.43963	+	1.02383i	0.922092	+	0.386971i
$7$	2.43963	+	1.02383i	0.922092	+	0.386971i
$8$		0			0
$9$	−2.76645	+	1.16050i	−0.922149	+	0.386834i
$10$		0			0
$11$	4.61052			1.39012			0.695062	−	0.718950i	$-0.255377\pi$
$11$	4.61052			1.39012			0.695062	+	0.718950i	$0.255377\pi$
$12$		0			0
$13$	0.244554	−	0.423580i	0.0678270	−	0.117480i	−0.830118	−	0.557588i	$-0.811727\pi$
$13$	0.244554	−	0.423580i	0.0678270	−	0.117480i	0.897945	+	0.440109i	$0.145060\pi$
$14$		0			0
$15$	−0.179749	−	0.893158i	−0.0464110	−	0.230613i
$16$		0			0
$17$	2.75579	−	4.77318i	0.668378	−	1.15767i	−0.309979	−	0.950743i	$-0.600322\pi$
$17$	2.75579	−	4.77318i	0.668378	−	1.15767i	0.978357	−	0.206922i	$-0.0663446\pi$
$18$		0			0
$19$	1.83782	+	3.18319i	0.421624	+	0.730274i	0.996099	−	0.0882484i	$-0.0281269\pi$
$19$	1.83782	+	3.18319i	0.421624	+	0.730274i	−0.574475	+	0.818522i	$0.694794\pi$
$20$		0			0
$21$	0.904788	−	4.49237i	0.197441	−	0.980315i
$22$		0			0
$23$	−0.0539537			−0.0112501			−0.00562506	−	0.999984i	$-0.501791\pi$
$23$	−0.0539537			−0.0112501			−0.00562506	+	0.999984i	$0.501791\pi$
$24$		0			0
$25$	−4.72332			−0.944664
$26$		0			0
$27$	2.91591	+	4.30087i	0.561167	+	0.827703i
$28$		0			0
$29$	−3.28471	−	5.68929i	−0.609956	−	1.05647i	−0.991247	−	0.132019i	$-0.957854\pi$
$29$	−3.28471	−	5.68929i	−0.609956	−	1.05647i	0.381292	−	0.924455i	$-0.375479\pi$
$30$		0			0
$31$	−3.03820	−	5.26231i	−0.545676	−	0.945139i	−0.998564	−	0.0535717i	$-0.982939\pi$
$31$	−3.03820	−	5.26231i	−0.545676	−	0.945139i	0.452888	−	0.891568i	$-0.350394\pi$
$32$		0			0
$33$	−1.57553	−	7.82869i	−0.274265	−	1.36280i
$34$		0			0
$35$	1.28325	+	0.538539i	0.216909	+	0.0910297i
$36$		0			0
$37$	0.223731	+	0.387513i	0.0367811	+	0.0637068i	0.883830	−	0.467808i	$-0.154956\pi$
$37$	0.223731	+	0.387513i	0.0367811	+	0.0637068i	−0.847049	+	0.531515i	$0.821623\pi$
$38$		0			0
$39$	−0.802811	−	0.270506i	−0.128553	−	0.0433156i
$40$		0			0
$41$	2.52284	−	4.36968i	0.394001	−	0.682430i	−0.598972	−	0.800770i	$-0.704424\pi$
$41$	2.52284	−	4.36968i	0.394001	−	0.682430i	0.992973	+	0.118340i	$0.0377574\pi$
$42$		0			0
$43$	2.84893	+	4.93449i	0.434458	+	0.752503i	0.997251	−	0.0740947i	$-0.0236067\pi$
$43$	2.84893	+	4.93449i	0.434458	+	0.752503i	−0.562794	+	0.826598i	$0.690273\pi$
$44$		0			0
$45$	−1.45516	+	0.610430i	−0.216923	+	0.0909975i
$46$		0			0
$47$	4.59810	−	7.96415i	0.670702	−	1.16169i	−0.307003	−	0.951709i	$-0.599326\pi$
$47$	4.59810	−	7.96415i	0.670702	−	1.16169i	0.977705	−	0.209982i	$-0.0673406\pi$
$48$		0			0
$49$	4.90354	+	4.99552i	0.700506	+	0.713646i
$50$		0			0
$51$	−9.04661	−	3.04824i	−1.26678	−	0.426839i
$52$		0			0
$53$	−4.37138	+	7.57145i	−0.600455	+	1.04002i	0.392297	+	0.919839i	$0.371680\pi$
$53$	−4.37138	+	7.57145i	−0.600455	+	1.04002i	−0.992752	+	0.120180i	$0.961653\pi$
$54$		0			0
$55$	2.42515			0.327008
$56$		0			0
$57$	4.77705	−	4.20840i	0.632735	−	0.557416i
$58$		0			0
$59$	3.31538	+	5.74241i	0.431626	+	0.747598i	0.997014	−	0.0772273i	$-0.0246067\pi$
$59$	3.31538	+	5.74241i	0.431626	+	0.747598i	−0.565388	+	0.824825i	$0.691273\pi$
$60$		0			0
$61$	0.232812	−	0.403243i	0.0298086	−	0.0516299i	−0.850736	−	0.525593i	$-0.823844\pi$
$61$	0.232812	−	0.403243i	0.0298086	−	0.0516299i	0.880545	+	0.473963i	$0.157177\pi$
$62$		0			0
$63$	−7.93725	−	0.00117907i	−1.00000	−	0.000148549i
$64$		0			0
$65$	0.128636	−	0.222805i	0.0159554	−	0.0276355i
$66$		0			0
$67$	−2.59679	−	4.49777i	−0.317248	−	0.549490i	0.662665	−	0.748916i	$-0.269425\pi$
$67$	−2.59679	−	4.49777i	−0.317248	−	0.549490i	−0.979913	+	0.199426i	$0.936092\pi$
$68$		0			0
$69$	0.0184374	+	0.0916137i	0.00221960	+	0.0110290i
$70$		0			0
$71$	1.76328			0.209263			0.104632	−	0.994511i	$-0.466634\pi$
$71$	1.76328			0.209263			0.104632	+	0.994511i	$0.466634\pi$
$72$		0			0
$73$	−5.23776	+	9.07207i	−0.613034	+	1.06181i	0.377692	+	0.925931i	$0.376718\pi$
$73$	−5.23776	+	9.07207i	−0.613034	+	1.06181i	−0.990726	+	0.135875i	$0.956616\pi$
$74$		0			0
$75$	1.61408	+	8.02022i	0.186378	+	0.926096i
$76$		0			0
$77$	11.2479	+	4.72039i	1.28182	+	0.537938i
$78$		0			0
$79$	−8.18509	+	14.1770i	−0.920895	+	1.59504i	−0.122860	+	0.992424i	$0.539207\pi$
$79$	−8.18509	+	14.1770i	−0.920895	+	1.59504i	−0.798034	+	0.602612i	$0.794127\pi$
$80$		0			0
$81$	6.30646	−	6.42094i	0.700718	−	0.713438i
$82$		0			0
$83$	4.49251	+	7.78126i	0.493117	+	0.854104i	0.999969	−	0.00792925i	$-0.00252399\pi$
$83$	4.49251	+	7.78126i	0.493117	+	0.854104i	−0.506851	+	0.862034i	$0.669191\pi$
$84$		0			0
$85$	1.44956	−	2.51071i	0.157227	−	0.272325i
$86$		0			0
$87$	−8.53797	+	7.52163i	−0.915367	+	0.806404i
$88$		0			0
$89$	−7.05145	−	12.2135i	−0.747452	−	1.29463i	−0.949040	−	0.315155i	$-0.897944\pi$
$89$	−7.05145	−	12.2135i	−0.747452	−	1.29463i	0.201588	−	0.979470i	$-0.435390\pi$
$90$		0			0
$91$	1.03029	−	0.782994i	0.108004	−	0.0820801i
$92$		0			0
$93$	−7.89721	+	6.95714i	−0.818902	+	0.721422i
$94$		0			0
$95$	0.966699	+	1.67437i	0.0991813	+	0.171787i
$96$		0			0
$97$	5.22413	+	9.04847i	0.530430	+	0.918732i	0.999370	+	0.0355020i	$0.0113030\pi$
$97$	5.22413	+	9.04847i	0.530430	+	0.918732i	−0.468939	+	0.883230i	$0.655364\pi$
$98$		0			0
$99$	−12.7548	+	5.35052i	−1.28190	+	0.537748i
$100$		0			0
$101$	−9.96508			−0.991562			−0.495781	−	0.868448i	$-0.665118\pi$
$101$	−9.96508			−0.991562			−0.495781	+	0.868448i	$0.665118\pi$
$102$		0			0
$103$	11.6511			1.14801			0.574006	−	0.818851i	$-0.305389\pi$
$103$	11.6511			1.14801			0.574006	+	0.818851i	$0.305389\pi$
$104$		0			0
$105$	0.475922	−	2.36300i	0.0464453	−	0.230606i
$106$		0			0
$107$	2.45556	+	4.25316i	0.237388	+	0.411168i	0.959964	−	0.280123i	$-0.0903754\pi$
$107$	2.45556	+	4.25316i	0.237388	+	0.411168i	−0.722576	+	0.691292i	$0.757042\pi$
$108$		0			0
$109$	−9.76353	+	16.9109i	−0.935177	+	1.61977i	−0.160858	+	0.986978i	$0.551426\pi$
$109$	−9.76353	+	16.9109i	−0.935177	+	1.61977i	−0.774319	+	0.632796i	$0.781907\pi$
$110$		0			0
$111$	0.581545	−	0.512319i	0.0551978	−	0.0486272i
$112$		0			0
$113$	5.48658	−	9.50304i	0.516134	−	0.893971i	−0.483690	−	0.875239i	$-0.660704\pi$
$113$	5.48658	−	9.50304i	0.516134	−	0.893971i	0.999825	−	0.0187317i	$-0.00596282\pi$
$114$		0			0
$115$	−0.0283799			−0.00264644
$116$		0			0
$117$	−0.184980	+	1.45562i	−0.0171014	+	0.134572i
$118$		0			0
$119$	11.6100	−	8.82330i	1.06429	−	0.808830i
$120$		0			0
$121$	10.2569			0.932444
$122$		0			0
$123$	−8.28186	−	2.79056i	−0.746750	−	0.251616i
$124$		0			0
$125$	−5.11451			−0.457456
$126$		0			0
$127$	−16.6107			−1.47396			−0.736979	−	0.675915i	$-0.763748\pi$
$127$	−16.6107			−1.47396			−0.736979	+	0.675915i	$0.763748\pi$
$128$		0			0
$129$	7.40524	−	6.52374i	0.651995	−	0.574383i
$130$		0			0
$131$	5.81696			0.508230			0.254115	−	0.967174i	$-0.418216\pi$
$131$	5.81696			0.508230			0.254115	+	0.967174i	$0.418216\pi$
$132$		0			0
$133$	1.22454	+	9.64740i	0.106181	+	0.836536i
$134$		0			0
$135$	1.53378	+	2.26228i	0.132007	+	0.194706i
$136$		0			0
$137$	−9.22626			−0.788253			−0.394126	−	0.919056i	$-0.628953\pi$
$137$	−9.22626			−0.788253			−0.394126	+	0.919056i	$0.628953\pi$
$138$		0			0
$139$	6.88477	−	11.9248i	0.583959	−	1.01145i	−0.411046	−	0.911615i	$-0.634836\pi$
$139$	6.88477	−	11.9248i	0.583959	−	1.01145i	0.995004	−	0.0998314i	$-0.0318303\pi$
$140$		0			0
$141$	−15.0945	−	5.08606i	−1.27118	−	0.428323i
$142$		0			0
$143$	1.12752	−	1.95292i	0.0942880	−	0.163312i
$144$		0			0
$145$	−1.72777	−	2.99259i	−0.143484	−	0.248521i
$146$		0			0
$147$	6.80676	−	10.0333i	0.561412	−	0.827536i
$148$		0			0
$149$	−8.30086			−0.680033			−0.340016	−	0.940420i	$-0.610433\pi$
$149$	−8.30086			−0.680033			−0.340016	+	0.940420i	$0.610433\pi$
$150$		0			0
$151$	−14.4979			−1.17982			−0.589911	−	0.807468i	$-0.700837\pi$
$151$	−14.4979			−1.17982			−0.589911	+	0.807468i	$0.700837\pi$
$152$		0			0
$153$	−2.08447	+	16.4028i	−0.168520	+	1.32609i
$154$		0			0
$155$	−1.59811	−	2.76800i	−0.128363	−	0.222331i
$156$		0			0
$157$	6.24434	+	10.8155i	0.498352	+	0.863172i	0.999998	−	0.00190155i	$-0.000605282\pi$
$157$	6.24434	+	10.8155i	0.498352	+	0.863172i	−0.501646	+	0.865073i	$0.667272\pi$
$158$		0			0
$159$	14.3502	+	4.83527i	1.13804	+	0.383462i
$160$		0			0
$161$	−0.131627	−	0.0552394i	−0.0103736	−	0.00435348i
$162$		0			0
$163$	−2.48448	−	4.30325i	−0.194600	−	0.337057i	0.752169	−	0.658970i	$-0.229007\pi$
$163$	−2.48448	−	4.30325i	−0.194600	−	0.337057i	−0.946769	+	0.321913i	$0.895674\pi$
$164$		0			0
$165$	−0.828736	−	4.11792i	−0.0645170	−	0.320580i
$166$		0			0
$167$	−10.0088	+	17.3357i	−0.774504	+	1.34148i	0.160569	+	0.987025i	$0.448667\pi$
$167$	−10.0088	+	17.3357i	−0.774504	+	1.34148i	−0.935073	+	0.354456i	$0.884666\pi$
$168$		0			0
$169$	6.38039	+	11.0512i	0.490799	+	0.850089i
$170$		0			0
$171$	−8.77833	−	6.67334i	−0.671295	−	0.510323i
$172$		0			0
$173$	−4.52742	+	7.84173i	−0.344214	+	0.596196i	−0.985211	−	0.171348i	$-0.945188\pi$
$173$	−4.52742	+	7.84173i	−0.344214	+	0.596196i	0.640997	+	0.767543i	$0.278521\pi$
$174$		0			0
$175$	−11.5231	−	4.83588i	−0.871067	−	0.365558i
$176$		0			0
$177$	8.61770	−	7.59187i	0.647746	−	0.570640i
$178$		0			0
$179$	−7.69175	+	13.3225i	−0.574908	+	0.995770i	0.421143	+	0.906994i	$0.361629\pi$
$179$	−7.69175	+	13.3225i	−0.574908	+	0.995770i	−0.996052	+	0.0887763i	$0.971704\pi$
$180$		0			0
$181$	−9.54973			−0.709826			−0.354913	−	0.934899i	$-0.615489\pi$
$181$	−9.54973			−0.709826			−0.354913	+	0.934899i	$0.615489\pi$
$182$		0			0
$183$	−0.764266	−	0.257518i	−0.0564962	−	0.0190363i
$184$		0			0
$185$	0.117683	+	0.203834i	0.00865225	+	0.0149861i
$186$		0			0
$187$	12.7056	−	22.0068i	0.929129	−	1.60930i
$188$		0			0
$189$	2.71036	+	13.4779i	0.197150	+	0.980373i
$190$		0			0
$191$	5.52163	−	9.56375i	0.399531	−	0.692009i	−0.594137	−	0.804364i	$-0.702506\pi$
$191$	5.52163	−	9.56375i	0.399531	−	0.692009i	0.993668	+	0.112355i	$0.0358395\pi$
$192$		0			0
$193$	−13.3496	−	23.1221i	−0.960923	−	1.66437i	−0.720192	−	0.693775i	$-0.755946\pi$
$193$	−13.3496	−	23.1221i	−0.960923	−	1.66437i	−0.240731	−	0.970592i	$-0.577387\pi$
$194$		0			0
$195$	−0.422282	−	0.142287i	−0.0302403	−	0.0101894i
$196$		0			0
$197$	12.8386			0.914715			0.457357	−	0.889283i	$-0.348796\pi$
$197$	12.8386			0.914715			0.457357	+	0.889283i	$0.348796\pi$
$198$		0			0
$199$	10.1408	−	17.5644i	0.718864	−	1.24511i	−0.242586	−	0.970130i	$-0.577996\pi$
$199$	10.1408	−	17.5644i	0.718864	−	1.24511i	0.961450	−	0.274979i	$-0.0886710\pi$
$200$		0			0
$201$	−6.74985	+	5.94636i	−0.476098	+	0.419424i
$202$		0			0
$203$	−2.18860	−	17.2427i	−0.153610	−	1.21020i
$204$		0			0
$205$	1.32702	−	2.29847i	0.0926833	−	0.160532i
$206$		0			0
$207$	0.149260	−	0.0626135i	0.0103743	−	0.00435194i
$208$		0			0
$209$	8.47329	+	14.6762i	0.586109	+	1.01517i
$210$		0			0
$211$	4.77903	−	8.27752i	0.329002	−	0.569848i	−0.653312	−	0.757088i	$-0.726621\pi$
$211$	4.77903	−	8.27752i	0.329002	−	0.569848i	0.982314	+	0.187241i	$0.0599545\pi$
$212$		0			0
$213$	−0.602559	−	2.99407i	−0.0412867	−	0.205150i
$214$		0			0
$215$	1.49855	+	2.59556i	0.102200	+	0.177016i
$216$		0			0
$217$	−2.02435	−	15.9487i	−0.137422	−	1.08267i
$218$		0			0
$219$	17.1943	+	5.79360i	1.16188	+	0.391495i
$220$		0			0
$221$	−1.34788	−	2.33460i	−0.0906683	−	0.157042i
$222$		0			0
$223$	11.9155	+	20.6383i	0.797921	+	1.38204i	0.920968	+	0.389639i	$0.127400\pi$
$223$	11.9155	+	20.6383i	0.797921	+	1.38204i	−0.123046	+	0.992401i	$0.539266\pi$
$224$		0			0
$225$	13.0668	−	5.48143i	0.871121	−	0.365429i
$226$		0			0
$227$	−2.67134			−0.177303			−0.0886514	−	0.996063i	$-0.528256\pi$
$227$	−2.67134			−0.177303			−0.0886514	+	0.996063i	$0.528256\pi$
$228$		0			0
$229$	6.32516			0.417978			0.208989	−	0.977918i	$-0.432983\pi$
$229$	6.32516			0.417978			0.208989	+	0.977918i	$0.432983\pi$
$230$		0			0
$231$	4.17154	−	20.7121i	0.274467	−	1.36276i
$232$		0			0
$233$	4.63381	+	8.02600i	0.303571	+	0.525801i	0.976942	−	0.213504i	$-0.0684877\pi$
$233$	4.63381	+	8.02600i	0.303571	+	0.525801i	−0.673371	+	0.739305i	$0.735154\pi$
$234$		0			0
$235$	2.41862	−	4.18918i	0.157774	−	0.273272i
$236$		0			0
$237$	26.8697	+	9.05369i	1.74537	+	0.588100i
$238$		0			0
$239$	1.69219	−	2.93096i	0.109459	−	0.189588i	−0.806092	−	0.591790i	$-0.798422\pi$
$239$	1.69219	−	2.93096i	0.109459	−	0.189588i	0.915551	+	0.402202i	$0.131755\pi$
$240$		0			0
$241$	13.1596			0.847687			0.423844	−	0.905735i	$-0.360681\pi$
$241$	13.1596			0.847687			0.423844	+	0.905735i	$0.360681\pi$
$242$		0			0
$243$	−13.0579	−	8.51421i	−0.837663	−	0.546187i
$244$		0			0
$245$	2.57929	+	2.62767i	0.164784	+	0.167876i
$246$		0			0
$247$	1.79778			0.114390
$248$		0			0
$249$	11.6774	−	10.2874i	0.740026	−	0.651935i
$250$		0			0
$251$	−2.30235			−0.145323			−0.0726614	−	0.997357i	$-0.523149\pi$
$251$	−2.30235			−0.145323			−0.0726614	+	0.997357i	$0.523149\pi$
$252$		0			0
$253$	−0.248755			−0.0156391
$254$		0			0
$255$	−4.75855	−	1.60339i	−0.297992	−	0.100408i
$256$		0			0
$257$	−29.1323			−1.81722			−0.908610	−	0.417646i	$-0.862855\pi$
$257$	−29.1323			−1.81722			−0.908610	+	0.417646i	$0.862855\pi$
$258$		0			0
$259$	0.149072	+	1.17445i	0.00926286	+	0.0729767i
$260$		0			0
$261$	15.6894	+	11.9272i	0.971151	+	0.738275i
$262$		0			0
$263$	−2.71837			−0.167622			−0.0838110	−	0.996482i	$-0.526709\pi$
$263$	−2.71837			−0.167622			−0.0838110	+	0.996482i	$0.526709\pi$
$264$		0			0
$265$	−2.29936	+	3.98261i	−0.141249	+	0.244650i
$266$		0			0
$267$	−18.3289	+	16.1471i	−1.12171	+	0.988184i
$268$		0			0
$269$	2.80840	−	4.86428i	0.171231	−	0.296581i	−0.767620	−	0.640906i	$-0.778559\pi$
$269$	2.80840	−	4.86428i	0.171231	−	0.296581i	0.938850	+	0.344325i	$0.111892\pi$
$270$		0			0
$271$	−7.25164	−	12.5602i	−0.440506	−	0.762978i	0.557221	−	0.830364i	$-0.311867\pi$
$271$	−7.25164	−	12.5602i	−0.440506	−	0.762978i	−0.997727	+	0.0673860i	$0.978534\pi$
$272$		0			0
$273$	−1.68161	−	1.48188i	−0.101775	−	0.0896872i
$274$		0			0
$275$	−21.7770			−1.31320
$276$		0			0
$277$	−1.74791			−0.105022			−0.0525108	−	0.998620i	$-0.516722\pi$
$277$	−1.74791			−0.105022			−0.0525108	+	0.998620i	$0.516722\pi$
$278$		0			0
$279$	14.5119	+	11.0321i	0.868808	+	0.660473i
$280$		0			0
$281$	5.35657	+	9.27786i	0.319546	+	0.553471i	0.980393	−	0.197050i	$-0.0631361\pi$
$281$	5.35657	+	9.27786i	0.319546	+	0.553471i	−0.660847	+	0.750521i	$0.729803\pi$
$282$		0			0
$283$	6.29833	+	10.9090i	0.374397	+	0.648474i	0.990237	−	0.139397i	$-0.0445165\pi$
$283$	6.29833	+	10.9090i	0.374397	+	0.648474i	−0.615840	+	0.787871i	$0.711183\pi$
$284$		0			0
$285$	2.51275	−	2.21364i	0.148842	−	0.131125i
$286$		0			0
$287$	10.6286	−	8.07743i	0.627386	−	0.476796i
$288$		0			0
$289$	−6.68881	−	11.5854i	−0.393459	−	0.681491i
$290$		0			0
$291$	13.5791	−	11.9627i	0.796023	−	0.701266i
$292$		0			0
$293$	−1.57575	+	2.72928i	−0.0920562	+	0.159446i	−0.908376	−	0.418154i	$-0.862677\pi$
$293$	−1.57575	+	2.72928i	−0.0920562	+	0.159446i	0.816320	+	0.577600i	$0.196011\pi$
$294$		0			0
$295$	1.74391	+	3.02053i	0.101534	+	0.175862i
$296$		0			0
$297$	13.4438	+	19.8292i	0.780091	+	1.15061i
$298$		0			0
$299$	−0.0131946	+	0.0228537i	−0.000763063	+	0.00132166i
$300$		0			0
$301$	1.89824	+	14.9551i	0.109413	+	0.861999i
$302$		0			0
$303$	3.40532	+	16.9208i	0.195631	+	0.972072i
$304$		0			0
$305$	0.122460	−	0.212107i	0.00701206	−	0.0121452i
$306$		0			0
$307$	−20.3884			−1.16363			−0.581813	−	0.813322i	$-0.697657\pi$
$307$	−20.3884			−1.16363			−0.581813	+	0.813322i	$0.697657\pi$
$308$		0			0
$309$	−3.98146	−	19.7836i	−0.226497	−	1.12545i
$310$		0			0
$311$	−11.3507	−	19.6600i	−0.643640	−	1.11482i	−0.984614	−	0.174744i	$-0.944090\pi$
$311$	−11.3507	−	19.6600i	−0.643640	−	1.11482i	0.340974	−	0.940073i	$-0.389243\pi$
$312$		0			0
$313$	8.35389	−	14.4694i	0.472190	−	0.817857i	−0.527304	−	0.849677i	$-0.676797\pi$
$313$	8.35389	−	14.4694i	0.472190	−	0.817857i	0.999494	+	0.0318201i	$0.0101304\pi$
$314$		0			0
$315$	−4.17503		0.000620197i	−0.235236		3.49441e-5i
$316$		0			0
$317$	−5.16401	+	8.94433i	−0.290040	+	0.502364i	−0.973819	−	0.227325i	$-0.927002\pi$
$317$	−5.16401	+	8.94433i	−0.290040	+	0.502364i	0.683779	+	0.729689i	$0.260335\pi$
$318$		0			0
$319$	−15.1442	−	26.2306i	−0.847914	−	1.46863i
$320$		0			0
$321$	6.38276	−	5.62297i	0.356251	−	0.313844i
$322$		0			0
$323$	20.2586			1.12722
$324$		0			0
$325$	−1.15511	+	2.00070i	−0.0640738	+	0.110979i
$326$		0			0
$327$	32.0513	+	10.7996i	1.77244	+	0.597221i
$328$		0			0
$329$	19.3716	−	14.7219i	1.06799	−	0.811643i
$330$		0			0
$331$	11.3158	−	19.5995i	0.621970	−	1.07728i	−0.367148	−	0.930162i	$-0.619666\pi$
$331$	11.3158	−	19.5995i	0.621970	−	1.07728i	0.989118	−	0.147122i	$-0.0470008\pi$
$332$		0			0
$333$	−1.06865	−	0.812394i	−0.0585617	−	0.0445189i
$334$		0			0
$335$	−1.36592	−	2.36585i	−0.0746283	−	0.129260i
$336$		0			0
$337$	6.78253	−	11.7477i	0.369468	−	0.639938i	−0.620014	−	0.784590i	$-0.712873\pi$
$337$	6.78253	−	11.7477i	0.369468	−	0.639938i	0.989482	+	0.144653i	$0.0462066\pi$
$338$		0			0
$339$	−18.0111	−	6.06882i	−0.978230	−	0.329613i
$340$		0			0
$341$	−14.0077	−	24.2620i	−0.758558	−	1.31386i
$342$		0			0
$343$	6.84824	+	17.2076i	0.369770	+	0.929123i
$344$		0			0
$345$	0.00969813	+	0.0481892i	0.000522130	+	0.00259442i
$346$		0			0
$347$	16.5131	+	28.6015i	0.886470	+	1.53541i	0.844019	+	0.536313i	$0.180183\pi$
$347$	16.5131	+	28.6015i	0.886470	+	1.53541i	0.0424511	+	0.999099i	$0.486483\pi$
$348$		0			0
$349$	−10.1773	−	17.6276i	−0.544778	−	0.943584i	−0.998621	−	0.0525019i	$-0.983280\pi$
$349$	−10.1773	−	17.6276i	−0.544778	−	0.943584i	0.453842	−	0.891082i	$-0.350053\pi$
$350$		0			0
$351$	2.53486	−	0.183325i	0.135301	−	0.00978514i
$352$		0			0
$353$	−5.50763			−0.293141			−0.146571	−	0.989200i	$-0.546824\pi$
$353$	−5.50763			−0.293141			−0.146571	+	0.989200i	$0.546824\pi$
$354$		0			0
$355$	0.927495			0.0492263
$356$		0			0
$357$	−18.9494	−	16.6988i	−1.00291	−	0.883792i
$358$		0			0
$359$	−10.4656	−	18.1270i	−0.552354	−	0.956704i	−0.998104	−	0.0615472i	$-0.980397\pi$
$359$	−10.4656	−	18.1270i	−0.552354	−	0.956704i	0.445751	−	0.895157i	$-0.352937\pi$
$360$		0			0
$361$	2.74486	−	4.75424i	0.144467	−	0.250223i
$362$		0			0
$363$	−3.50504	−	17.4163i	−0.183967	−	0.914116i
$364$		0			0
$365$	−2.75509	+	4.77195i	−0.144208	+	0.249775i
$366$		0			0
$367$	4.28637			0.223747			0.111873	−	0.993722i	$-0.464315\pi$
$367$	4.28637			0.223747			0.111873	+	0.993722i	$0.464315\pi$
$368$		0			0
$369$	−1.90826	+	15.0163i	−0.0993403	+	0.781715i
$370$		0			0
$371$	−18.4164	+	13.9959i	−0.956132	+	0.726633i
$372$		0			0
$373$	−11.2892			−0.584534			−0.292267	−	0.956337i	$-0.594410\pi$
$373$	−11.2892			−0.584534			−0.292267	+	0.956337i	$0.594410\pi$
$374$		0			0
$375$	1.74776	+	8.68446i	0.0902538	+	0.448464i
$376$		0			0
$377$	−3.21316			−0.165486
$378$		0			0
$379$	−20.5828			−1.05727			−0.528634	−	0.848850i	$-0.677295\pi$
$379$	−20.5828			−1.05727			−0.528634	+	0.848850i	$0.677295\pi$
$380$		0			0
$381$	5.67629	+	28.2050i	0.290805	+	1.44499i
$382$		0			0
$383$	−21.6215			−1.10481			−0.552405	−	0.833576i	$-0.686290\pi$
$383$	−21.6215			−1.10481			−0.552405	+	0.833576i	$0.686290\pi$
$384$		0			0
$385$	5.91646	+	2.48295i	0.301531	+	0.126543i
$386$		0			0
$387$	−13.6079	−	10.3448i	−0.691729	−	0.525857i
$388$		0			0
$389$	−14.6848			−0.744550			−0.372275	−	0.928123i	$-0.621422\pi$
$389$	−14.6848			−0.744550			−0.372275	+	0.928123i	$0.621422\pi$
$390$		0			0
$391$	−0.148685	+	0.257531i	−0.00751934	+	0.0130239i
$392$		0			0
$393$	−1.98780	−	9.87723i	−0.100271	−	0.498240i
$394$		0			0
$395$	−4.30539	+	7.45716i	−0.216628	+	0.375210i
$396$		0			0
$397$	−3.13424	−	5.42866i	−0.157303	−	0.272457i	0.776592	−	0.630003i	$-0.216947\pi$
$397$	−3.13424	−	5.42866i	−0.157303	−	0.272457i	−0.933895	+	0.357547i	$0.883613\pi$
$398$		0			0
$399$	15.9629	−	5.37603i	0.799144	−	0.269138i
$400$		0			0
$401$	29.3901			1.46767			0.733836	−	0.679327i	$-0.237728\pi$
$401$	29.3901			1.46767			0.733836	+	0.679327i	$0.237728\pi$
$402$		0			0
$403$	−2.97201			−0.148046
$404$		0			0
$405$	3.31723	−	3.37744i	0.164834	−	0.167827i
$406$		0			0
$407$	1.03152	+	1.78664i	0.0511303	+	0.0885603i
$408$		0			0
$409$	0.816425	+	1.41409i	0.0403696	+	0.0699222i	0.885504	−	0.464631i	$-0.153813\pi$
$409$	0.816425	+	1.41409i	0.0403696	+	0.0699222i	−0.845135	+	0.534554i	$0.820480\pi$
$410$		0			0
$411$	3.15285	+	15.6662i	0.155518	+	0.772759i
$412$		0			0
$413$	2.20904	+	17.4037i	0.108700	+	0.856381i
$414$		0			0
$415$	2.36308	+	4.09298i	0.115999	+	0.200916i
$416$		0			0
$417$	−22.6010	−	7.61538i	−1.10678	−	0.372927i
$418$		0			0
$419$	−9.01823	+	15.6200i	−0.440569	+	0.763088i	−0.997732	−	0.0673151i	$-0.978557\pi$
$419$	−9.01823	+	15.6200i	−0.440569	+	0.763088i	0.557162	+	0.830404i	$0.311890\pi$
$420$		0			0
$421$	16.8278	+	29.1465i	0.820135	+	1.42052i	0.905581	+	0.424172i	$0.139435\pi$
$421$	16.8278	+	29.1465i	0.820135	+	1.42052i	−0.0854466	+	0.996343i	$0.527232\pi$
$422$		0			0
$423$	−3.47799	+	27.3685i	−0.169106	+	1.33070i
$424$		0			0
$425$	−13.0165	+	22.5452i	−0.631393	+	1.09360i
$426$		0			0
$427$	0.980827	−	0.745401i	0.0474655	−	0.0360725i
$428$		0			0
$429$	−3.70138	−	1.24717i	−0.178704	−	0.0602141i
$430$		0			0
$431$	−11.1545	+	19.3202i	−0.537295	+	0.930622i	0.461754	+	0.887008i	$0.347220\pi$
$431$	−11.1545	+	19.3202i	−0.537295	+	0.930622i	−0.999048	+	0.0436135i	$0.986113\pi$
$432$		0			0
$433$	7.32414			0.351976			0.175988	−	0.984392i	$-0.443688\pi$
$433$	7.32414			0.351976			0.175988	+	0.984392i	$0.443688\pi$
$434$		0			0
$435$	−4.49101	+	3.95641i	−0.215327	+	0.189695i
$436$		0			0
$437$	−0.0991570	−	0.171745i	−0.00474332	−	0.00821567i
$438$		0			0
$439$	12.3364	−	21.3673i	0.588785	−	1.01981i	−0.405607	−	0.914048i	$-0.632940\pi$
$439$	12.3364	−	21.3673i	0.588785	−	1.01981i	0.994392	−	0.105758i	$-0.0337270\pi$
$440$		0			0
$441$	−19.3627	−	8.12928i	−0.922034	−	0.387108i
$442$		0			0
$443$	−15.2682	+	26.4452i	−0.725412	+	1.25645i	0.233393	+	0.972383i	$0.425017\pi$
$443$	−15.2682	+	26.4452i	−0.725412	+	1.25645i	−0.958804	+	0.284067i	$0.908316\pi$
$444$		0			0
$445$	−3.70909	−	6.42434i	−0.175828	−	0.304543i
$446$		0			0
$447$	2.83661	+	14.0949i	0.134167	+	0.666666i
$448$		0			0
$449$	−41.4782			−1.95748			−0.978738	−	0.205116i	$-0.934243\pi$
$449$	−41.4782			−1.95748			−0.978738	+	0.205116i	$0.934243\pi$
$450$		0			0
$451$	11.6316	−	20.1465i	0.547710	−	0.948662i
$452$		0			0
$453$	4.95430	+	24.6175i	0.232773	+	1.15663i
$454$		0			0
$455$	0.541939	−	0.411858i	0.0254065	−	0.0193082i
$456$		0			0
$457$	5.81446	−	10.0709i	0.271989	−	0.471099i	−0.697382	−	0.716700i	$-0.745652\pi$
$457$	5.81446	−	10.0709i	0.271989	−	0.471099i	0.969371	+	0.245601i	$0.0789852\pi$
$458$		0			0
$459$	28.5645	−	2.06582i	1.33327	−	0.0964243i
$460$		0			0
$461$	−5.60886	−	9.71483i	−0.261231	−	0.452465i	0.705339	−	0.708871i	$-0.250795\pi$
$461$	−5.60886	−	9.71483i	−0.261231	−	0.452465i	−0.966569	+	0.256406i	$0.917462\pi$
$462$		0			0
$463$	−19.9362	+	34.5305i	−0.926514	+	1.60477i	−0.137405	+	0.990515i	$0.543876\pi$
$463$	−19.9362	+	34.5305i	−0.926514	+	1.60477i	−0.789108	+	0.614254i	$0.789457\pi$
$464$		0			0
$465$	−4.15397	+	3.65949i	−0.192636	+	0.169705i
$466$		0			0
$467$	11.7818	+	20.4067i	0.545198	+	0.944311i	0.998594	+	0.0530016i	$0.0168788\pi$
$467$	11.7818	+	20.4067i	0.545198	+	0.944311i	−0.453397	+	0.891309i	$0.649788\pi$
$468$		0			0
$469$	−1.73024	−	13.6315i	−0.0798950	−	0.629446i
$470$		0			0
$471$	16.2309	−	14.2989i	0.747883	−	0.658856i
$472$		0			0
$473$	13.1350	+	22.7506i	0.603950	+	1.04607i
$474$		0			0
$475$	−8.68059	−	15.0352i	−0.398293	−	0.689864i
$476$		0			0
$477$	3.30650	−	26.0190i	0.151394	−	1.19133i
$478$		0			0
$479$	14.2297			0.650172			0.325086	−	0.945685i	$-0.394607\pi$
$479$	14.2297			0.650172			0.325086	+	0.945685i	$0.394607\pi$
$480$		0			0
$481$	0.218857			0.00997902
$482$		0			0
$483$	−0.0488167	+	0.242380i	−0.00222123	+	0.0110287i
$484$		0			0
$485$	2.74792	+	4.75953i	0.124776	+	0.216119i
$486$		0			0
$487$	−13.9818	+	24.2171i	−0.633574	+	1.09738i	0.353242	+	0.935532i	$0.385079\pi$
$487$	−13.9818	+	24.2171i	−0.633574	+	1.09738i	−0.986815	+	0.161850i	$0.948254\pi$
$488$		0			0
$489$	−6.45794	+	5.68920i	−0.292038	+	0.257275i
$490$		0			0
$491$	17.2543	−	29.8853i	0.778676	−	1.34871i	−0.154030	−	0.988066i	$-0.549225\pi$
$491$	17.2543	−	29.8853i	0.778676	−	1.34871i	0.932705	−	0.360639i	$-0.117442\pi$
$492$		0			0
$493$	−36.2080			−1.63072
$494$		0			0
$495$	−6.70906	+	2.81440i	−0.301550	+	0.126498i
$496$		0			0
$497$	4.30175	+	1.80530i	0.192960	+	0.0809789i
$498$		0			0
$499$	26.2873			1.17678			0.588390	−	0.808577i	$-0.299762\pi$
$499$	26.2873			1.17678			0.588390	+	0.808577i	$0.299762\pi$
$500$		0			0
$501$	32.8565	+	11.0709i	1.46792	+	0.494613i
$502$		0			0
$503$	6.09068			0.271570			0.135785	−	0.990738i	$-0.456644\pi$
$503$	6.09068			0.271570			0.135785	+	0.990738i	$0.456644\pi$
$504$		0			0
$505$	−5.24167			−0.233251
$506$		0			0
$507$	16.5846	−	14.6104i	0.736547	−	0.648870i
$508$		0			0
$509$	−8.17231			−0.362231			−0.181116	−	0.983462i	$-0.557971\pi$
$509$	−8.17231			−0.362231			−0.181116	+	0.983462i	$0.557971\pi$
$510$		0			0
$511$	−22.0664	+	16.7699i	−0.976162	+	0.741856i
$512$		0			0
$513$	−8.33159	+	17.1861i	−0.367849	+	0.758785i
$514$		0			0
$515$	6.12850			0.270054
$516$		0			0
$517$	21.1996	−	36.7189i	0.932360	−	1.61489i
$518$		0			0
$519$	14.8624	+	5.00788i	0.652389	+	0.219821i
$520$		0			0
$521$	13.0485	−	22.6007i	0.571666	−	0.990155i	−0.424729	−	0.905321i	$-0.639630\pi$
$521$	13.0485	−	22.6007i	0.571666	−	0.990155i	0.996395	−	0.0848346i	$-0.0270362\pi$
$522$		0			0
$523$	13.6655	+	23.6694i	0.597553	+	1.03499i	0.993181	+	0.116581i	$0.0371935\pi$
$523$	13.6655	+	23.6694i	0.597553	+	1.03499i	−0.395628	+	0.918411i	$0.629473\pi$
$524$		0			0
$525$	−4.27360	+	21.2189i	−0.186515	+	0.926068i
$526$		0			0
$527$	−33.4906			−1.45887
$528$		0			0
$529$	−22.9971			−0.999873
$530$		0			0
$531$	−15.8359	−	12.0386i	−0.687220	−	0.522429i
$532$		0			0
$533$	−1.23394	−	2.13725i	−0.0534478	−	0.0925744i
$534$		0			0
$535$	1.29164	+	2.23718i	0.0558423	+	0.0967217i
$536$		0			0
$537$	25.2501	+	8.50800i	1.08962	+	0.367147i
$538$		0			0
$539$	22.6079	+	23.0320i	0.973790	+	0.992057i
$540$		0			0
$541$	−5.79086	−	10.0301i	−0.248969	−	0.431226i	0.714271	−	0.699869i	$-0.246758\pi$
$541$	−5.79086	−	10.0301i	−0.248969	−	0.431226i	−0.963240	+	0.268643i	$0.913425\pi$
$542$		0			0
$543$	3.26339	+	16.2155i	0.140045	+	0.695874i
$544$		0			0
$545$	−5.13566	+	8.89522i	−0.219987	+	0.381029i
$546$		0			0
$547$	20.3651	+	35.2734i	0.870750	+	1.50818i	0.861222	+	0.508228i	$0.169699\pi$
$547$	20.3651	+	35.2734i	0.870750	+	1.50818i	0.00952755	+	0.999955i	$0.496967\pi$
$548$		0			0
$549$	−0.176098	+	1.38573i	−0.00751570	+	0.0591415i
$550$		0			0
$551$	12.0734	−	20.9117i	0.514344	−	0.890869i
$552$		0			0
$553$	−34.4834	+	26.2064i	−1.46638	+	1.11441i
$554$		0			0
$555$	0.305895	−	0.269482i	0.0129845	−	0.0114389i
$556$		0			0
$557$	10.0085	−	17.3353i	0.424075	−	0.734520i	−0.572258	−	0.820074i	$-0.693932\pi$
$557$	10.0085	−	17.3353i	0.424075	−	0.734520i	0.996334	+	0.0855533i	$0.0272658\pi$
$558$		0			0
$559$	2.78687			0.117872
$560$		0			0
$561$	−41.7095	−	14.0540i	−1.76098	−	0.593359i
$562$		0			0
$563$	−12.4664	−	21.5924i	−0.525396	−	0.910013i	−0.999562	−	0.0295776i	$-0.990584\pi$
$563$	−12.4664	−	21.5924i	−0.525396	−	0.910013i	0.474166	−	0.880435i	$-0.342750\pi$
$564$		0			0
$565$	2.88597	−	4.99864i	0.121414	−	0.210294i
$566$		0			0
$567$	21.9594	−	9.20795i	0.922207	−	0.386697i
$568$		0			0
$569$	4.90013	−	8.48727i	0.205424	−	0.355805i	−0.744844	−	0.667239i	$-0.767476\pi$
$569$	4.90013	−	8.48727i	0.205424	−	0.355805i	0.950268	+	0.311434i	$0.100809\pi$
$570$		0			0
$571$	20.3948	+	35.3247i	0.853494	+	1.47829i	0.878035	+	0.478596i	$0.158854\pi$
$571$	20.3948	+	35.3247i	0.853494	+	1.47829i	−0.0245416	+	0.999699i	$0.507813\pi$
$572$		0			0
$573$	−18.1262	−	6.10759i	−0.757232	−	0.255148i
$574$		0			0
$575$	0.254841			0.0106276
$576$		0			0
$577$	−10.2505	+	17.7544i	−0.426734	+	0.739125i	−0.996581	−	0.0826259i	$-0.973669\pi$
$577$	−10.2505	+	17.7544i	−0.426734	+	0.739125i	0.569846	+	0.821751i	$0.307003\pi$
$578$		0			0
$579$	−34.6996	+	30.5691i	−1.44207	+	1.27041i
$580$		0			0
$581$	2.99336	+	23.5829i	0.124185	+	0.978385i
$582$		0			0
$583$	−20.1543	+	34.9083i	−0.834707	+	1.44575i
$584$		0			0
$585$	−0.0973001	+	0.765661i	−0.00402287	+	0.0316562i
$586$		0			0
$587$	−19.2916	−	33.4141i	−0.796251	−	1.37915i	−0.922042	−	0.387090i	$-0.873480\pi$
$587$	−19.2916	−	33.4141i	−0.796251	−	1.37915i	0.125791	−	0.992057i	$-0.459853\pi$
$588$		0			0
$589$	11.1673	−	19.3423i	0.460141	−	0.796987i
$590$		0			0
$591$	−4.38729	−	21.8001i	−0.180469	−	0.896735i
$592$		0			0
$593$	−1.26539	−	2.19172i	−0.0519634	−	0.0900032i	0.838874	−	0.544326i	$-0.183215\pi$
$593$	−1.26539	−	2.19172i	−0.0519634	−	0.0900032i	−0.890837	+	0.454323i	$0.849881\pi$
$594$		0			0
$595$	6.10693	−	4.64109i	0.250360	−	0.190266i
$596$		0			0
$597$	−33.2899	−	11.2170i	−1.36246	−	0.459080i
$598$		0			0
$599$	8.01092	+	13.8753i	0.327317	+	0.566930i	0.981979	−	0.188992i	$-0.0605221\pi$
$599$	8.01092	+	13.8753i	0.327317	+	0.566930i	−0.654661	+	0.755922i	$0.727189\pi$
$600$		0			0
$601$	−22.1601	−	38.3824i	−0.903929	−	1.56565i	−0.822349	−	0.568983i	$-0.807337\pi$
$601$	−22.1601	−	38.3824i	−0.903929	−	1.56565i	−0.0815796	−	0.996667i	$-0.525996\pi$
$602$		0			0
$603$	12.4036	+	9.42926i	0.505112	+	0.383989i
$604$		0			0
$605$	5.39517			0.219345
$606$		0			0
$607$	−9.59214			−0.389333			−0.194666	−	0.980870i	$-0.562362\pi$
$607$	−9.59214			−0.389333			−0.194666	+	0.980870i	$0.562362\pi$
$608$		0			0
$609$	−28.5303	+	9.60853i	−1.15611	+	0.389357i
$610$		0			0
$611$	−2.24897	−	3.89533i	−0.0909835	−	0.157588i
$612$		0			0
$613$	11.2371	−	19.4632i	0.453861	−	0.786110i	−0.544761	−	0.838591i	$-0.683380\pi$
$613$	11.2371	−	19.4632i	0.453861	−	0.786110i	0.998622	+	0.0524815i	$0.0167131\pi$
$614$		0			0
$615$	−4.35630	−	1.46785i	−0.175663	−	0.0591893i
$616$		0			0
$617$	11.7056	−	20.2746i	0.471248	−	0.816226i	−0.528211	−	0.849113i	$-0.677137\pi$
$617$	11.7056	−	20.2746i	0.471248	−	0.816226i	0.999459	+	0.0328875i	$0.0104703\pi$
$618$		0			0
$619$	15.9769			0.642164			0.321082	−	0.947051i	$-0.395953\pi$
$619$	15.9769			0.642164			0.321082	+	0.947051i	$0.395953\pi$
$620$		0			0
$621$	−0.157324	−	0.232048i	−0.00631319	−	0.00931176i
$622$		0			0
$623$	−4.69838	−	37.0158i	−0.188236	−	1.48301i
$624$		0			0
$625$	20.9263			0.837054
$626$		0			0
$627$	22.0247	−	19.4029i	0.879581	−	0.774877i
$628$		0			0
$629$	2.46622			0.0983348
$630$		0			0
$631$	−0.882517			−0.0351324			−0.0175662	−	0.999846i	$-0.505592\pi$
$631$	−0.882517			−0.0351324			−0.0175662	+	0.999846i	$0.505592\pi$
$632$		0			0
$633$	−15.6884	−	5.28618i	−0.623557	−	0.210107i
$634$		0			0
$635$	−8.73728			−0.346729
$636$		0			0
$637$	3.31518	−	0.855367i	0.131352	−	0.0338909i
$638$		0			0
$639$	−4.87803	+	2.04630i	−0.192972	+	0.0809503i
$640$		0			0
$641$	40.4282			1.59682			0.798408	−	0.602116i	$-0.205676\pi$
$641$	40.4282			1.59682			0.798408	+	0.602116i	$0.205676\pi$
$642$		0			0
$643$	2.99047	−	5.17964i	0.117932	−	0.204265i	−0.801016	−	0.598643i	$-0.795707\pi$
$643$	2.99047	−	5.17964i	0.117932	−	0.204265i	0.918948	+	0.394378i	$0.129040\pi$
$644$		0			0
$645$	3.89519	−	3.43152i	0.153373	−	0.135116i
$646$		0			0
$647$	−16.4743	+	28.5343i	−0.647672	+	1.12180i	0.336005	+	0.941860i	$0.390924\pi$
$647$	−16.4743	+	28.5343i	−0.647672	+	1.12180i	−0.983677	+	0.179941i	$0.942409\pi$
$648$		0			0
$649$	15.2856	+	26.4755i	0.600014	+	1.03925i
$650$		0			0
$651$	−26.3892	+	8.88742i	−1.03427	+	0.348326i
$652$		0			0
$653$	26.0333			1.01876			0.509380	−	0.860542i	$-0.329875\pi$
$653$	26.0333			1.01876			0.509380	+	0.860542i	$0.329875\pi$
$654$		0			0
$655$	3.05974			0.119554
$656$		0			0
$657$	3.96183	−	31.1759i	0.154566	−	1.21629i
$658$		0			0
$659$	4.91651	+	8.51565i	0.191520	+	0.331722i	0.945754	−	0.324883i	$-0.105325\pi$
$659$	4.91651	+	8.51565i	0.191520	+	0.331722i	−0.754234	+	0.656606i	$0.771992\pi$
$660$		0			0
$661$	2.75760	+	4.77630i	0.107258	+	0.185777i	0.914659	−	0.404227i	$-0.132460\pi$
$661$	2.75760	+	4.77630i	0.107258	+	0.185777i	−0.807400	+	0.590004i	$0.799126\pi$
$662$		0			0
$663$	−3.50356	+	3.08650i	−0.136067	+	0.119870i
$664$		0			0
$665$	0.644111	+	5.07458i	0.0249776	+	0.196784i
$666$		0			0
$667$	0.177222	+	0.306958i	0.00686208	+	0.0118855i
$668$		0			0
$669$	30.9721	−	27.2852i	1.19745	−	1.05491i
$670$		0			0
$671$	1.07339	−	1.85916i	0.0414376	−	0.0717720i
$672$		0			0
$673$	19.6176	+	33.9788i	0.756205	+	1.30978i	0.944773	+	0.327725i	$0.106282\pi$
$673$	19.6176	+	33.9788i	0.756205	+	1.30978i	−0.188569	+	0.982060i	$0.560385\pi$
$674$		0			0
$675$	−13.7728	−	20.3144i	−0.530114	−	0.781901i
$676$		0			0
$677$	18.5816	−	32.1843i	0.714149	−	1.23694i	−0.249138	−	0.968468i	$-0.580147\pi$
$677$	18.5816	−	32.1843i	0.714149	−	1.23694i	0.963287	−	0.268474i	$-0.0865193\pi$
$678$		0			0
$679$	3.48084	+	27.4235i	0.133582	+	1.05242i
$680$		0			0
$681$	0.912864	+	4.53595i	0.0349810	+	0.173818i
$682$		0			0
$683$	−5.10586	+	8.84360i	−0.195370	+	0.338391i	−0.947022	−	0.321169i	$-0.895924\pi$
$683$	−5.10586	+	8.84360i	−0.195370	+	0.338391i	0.751652	+	0.659560i	$0.229257\pi$
$684$		0			0
$685$	−4.85305			−0.185426
$686$		0			0
$687$	−2.16147	−	10.7402i	−0.0824651	−	0.409763i
$688$		0			0
$689$	2.13807	+	3.70325i	0.0814542	+	0.141083i
$690$		0			0
$691$	17.5381	−	30.3768i	0.667179	−	1.15559i	−0.311510	−	0.950243i	$-0.600835\pi$
$691$	17.5381	−	30.3768i	0.667179	−	1.15559i	0.978690	−	0.205346i	$-0.0658318\pi$
$692$		0			0
$693$	−36.5949	−	0.00543613i	−1.39012	−	0.000206502i
$694$		0			0
$695$	3.62142	−	6.27248i	0.137368	−	0.237929i
$696$		0			0
$697$	−13.9048	−	24.0839i	−0.526683	−	0.912242i
$698$		0			0
$699$	12.0447	−	10.6109i	0.455572	−	0.401342i
$700$		0			0
$701$	17.2500			0.651522			0.325761	−	0.945452i	$-0.394379\pi$
$701$	17.2500			0.651522			0.325761	+	0.945452i	$0.394379\pi$
$702$		0			0
$703$	−0.822352	+	1.42436i	−0.0310156	+	0.0537206i
$704$		0			0
$705$	−7.93975	−	2.67529i	−0.299028	−	0.100757i
$706$		0			0
$707$	−24.3111	−	10.2025i	−0.914311	−	0.383706i
$708$		0			0
$709$	7.25734	−	12.5701i	0.272555	−	0.472079i	−0.696960	−	0.717110i	$-0.745465\pi$
$709$	7.25734	−	12.5701i	0.272555	−	0.472079i	0.969515	+	0.245030i	$0.0787980\pi$
$710$		0			0
$711$	6.19117	−	48.7187i	0.232187	−	1.82709i
$712$		0			0
$713$	0.163922	+	0.283921i	0.00613893	+	0.0106329i
$714$		0			0
$715$	0.593081	−	1.02725i	0.0221800	−	0.0384168i
$716$		0			0
$717$	−5.55504	−	1.87176i	−0.207457	−	0.0699023i
$718$		0			0
$719$	−22.4295	−	38.8491i	−0.836480	−	1.44883i	−0.892820	−	0.450414i	$-0.851277\pi$
$719$	−22.4295	−	38.8491i	−0.836480	−	1.44883i	0.0563403	−	0.998412i	$-0.482057\pi$
$720$		0			0
$721$	28.4242	+	11.9287i	1.05857	+	0.444248i
$722$		0			0
$723$	−4.49699	−	22.3452i	−0.167245	−	0.831025i
$724$		0			0
$725$	15.5147	+	26.8723i	0.576203	+	0.998013i
$726$		0			0
$727$	−2.22039	−	3.84582i	−0.0823496	−	0.142634i	0.821909	−	0.569619i	$-0.192909\pi$
$727$	−2.22039	−	3.84582i	−0.0823496	−	0.142634i	−0.904259	+	0.426985i	$0.859576\pi$
$728$		0			0
$729$	−9.99497	+	25.0819i	−0.370184	+	0.928958i
$730$		0			0
$731$	31.4043			1.16153
$732$		0			0
$733$	−38.2720			−1.41361			−0.706803	−	0.707410i	$-0.749863\pi$
$733$	−38.2720			−1.41361			−0.706803	+	0.707410i	$0.749863\pi$
$734$		0			0
$735$	3.58039	−	5.27758i	0.132065	−	0.194667i
$736$		0			0
$737$	−11.9725	−	20.7370i	−0.441014	−	0.763859i
$738$		0			0
$739$	−2.59381	+	4.49261i	−0.0954148	+	0.165263i	−0.909782	−	0.415087i	$-0.863751\pi$
$739$	−2.59381	+	4.49261i	−0.0954148	+	0.165263i	0.814367	+	0.580350i	$0.197084\pi$
$740$		0			0
$741$	−0.614347	−	3.05264i	−0.0225686	−	0.112142i
$742$		0			0
$743$	16.3351	−	28.2932i	0.599276	−	1.03798i	−0.393653	−	0.919259i	$-0.628789\pi$
$743$	16.3351	−	28.2932i	0.599276	−	1.03798i	0.992928	−	0.118716i	$-0.0378779\pi$
$744$		0			0
$745$	−4.36629			−0.159968
$746$		0			0
$747$	−21.4585	−	16.3129i	−0.785125	−	0.596857i
$748$		0			0
$749$	1.63614	+	12.8902i	0.0597832	+	0.470997i
$750$		0			0
$751$	−16.1221			−0.588304			−0.294152	−	0.955759i	$-0.595037\pi$
$751$	−16.1221			−0.588304			−0.294152	+	0.955759i	$0.595037\pi$
$752$		0			0
$753$	0.786771	+	3.90940i	0.0286715	+	0.142466i
$754$		0			0
$755$	−7.62595			−0.277537
$756$		0			0
$757$	45.6421			1.65889			0.829444	−	0.558589i	$-0.188657\pi$
$757$	45.6421			1.65889			0.829444	+	0.558589i	$0.188657\pi$
$758$		0			0
$759$	0.0850058	+	0.422387i	0.00308551	+	0.0153317i
$760$		0			0
$761$	12.2300			0.443338			0.221669	−	0.975122i	$-0.428850\pi$
$761$	12.2300			0.443338			0.221669	+	0.975122i	$0.428850\pi$
$762$		0			0
$763$	−41.1333	+	31.2601i	−1.48912	+	1.13169i
$764$		0			0
$765$	−1.09644	+	8.62797i	−0.0396419	+	0.311945i
$766$		0			0
$767$	3.24316			0.117104
$768$		0			0
$769$	3.17344	−	5.49656i	0.114437	−	0.198211i	−0.803117	−	0.595821i	$-0.796827\pi$
$769$	3.17344	−	5.49656i	0.114437	−	0.198211i	0.917555	+	0.397610i	$0.130160\pi$
$770$		0			0
$771$	9.95523	+	49.4667i	0.358529	+	1.78150i
$772$		0			0
$773$	24.4515	−	42.3512i	0.879459	−	1.52327i	0.0275225	−	0.999621i	$-0.491238\pi$
$773$	24.4515	−	42.3512i	0.879459	−	1.52327i	0.851936	−	0.523646i	$-0.175428\pi$
$774$		0			0
$775$	14.3504	+	24.8556i	0.515481	+	0.892839i
$776$		0			0
$777$	1.94328	−	0.654464i	0.0697148	−	0.0234788i
$778$		0			0
$779$	18.5460			0.664481
$780$		0			0
$781$	8.12965			0.290902
$782$		0			0
$783$	14.8910	−	30.7165i	0.532160	−	1.09772i
$784$		0			0
$785$	3.28455	+	5.68900i	0.117231	+	0.203049i
$786$		0			0
$787$	11.5749	+	20.0483i	0.412600	+	0.714645i	0.995173	−	0.0981337i	$-0.0312873\pi$
$787$	11.5749	+	20.0483i	0.412600	+	0.714645i	−0.582573	+	0.812778i	$0.697954\pi$
$788$		0			0
$789$	0.928937	+	4.61581i	0.0330710	+	0.164327i
$790$		0			0
$791$	23.1147	−	17.5665i	0.821864	−	0.624594i
$792$		0			0
$793$	−0.113870	−	0.197229i	−0.00404365	−	0.00700381i
$794$		0			0
$795$	7.54825	+	2.54337i	0.267709	+	0.0902041i
$796$		0			0
$797$	24.2284	−	41.9648i	0.858214	−	1.48647i	−0.0154170	−	0.999881i	$-0.504908\pi$
$797$	24.2284	−	41.9648i	0.858214	−	1.48647i	0.873631	−	0.486589i	$-0.161759\pi$
$798$		0			0
$799$	−25.3429	−	43.8951i	−0.896566	−	1.55290i
$800$		0			0
$801$	33.6812	+	25.6047i	1.19007	+	0.904697i
$802$		0			0
$803$	−24.1488	+	41.8270i	−0.852193	+	1.47604i
$804$		0			0
$805$	−0.0692363	−	0.0290562i	−0.00244026	−	0.00102410i
$806$		0			0
$807$	−9.21928	−	3.10642i	−0.324534	−	0.109351i
$808$		0			0
$809$	−10.2647	+	17.7791i	−0.360889	+	0.625078i	−0.988107	−	0.153765i	$-0.950860\pi$
$809$	−10.2647	+	17.7791i	−0.360889	+	0.625078i	0.627218	+	0.778844i	$0.284193\pi$
$810$		0			0
$811$	27.7882			0.975776			0.487888	−	0.872906i	$-0.337767\pi$
$811$	27.7882			0.975776			0.487888	+	0.872906i	$0.337767\pi$
$812$		0			0
$813$	−18.8492	+	16.6055i	−0.661071	+	0.582379i
$814$		0			0
$815$	−1.30685	−	2.26353i	−0.0457769	−	0.0792880i
$816$		0			0
$817$	−10.4716	+	18.1374i	−0.366356	+	0.634546i
$818$		0			0
$819$	−1.94159	+	3.36177i	−0.0678445	+	0.117470i
$820$		0			0
$821$	8.27932	−	14.3402i	0.288950	−	0.500477i	−0.684609	−	0.728910i	$-0.740027\pi$
$821$	8.27932	−	14.3402i	0.288950	−	0.500477i	0.973559	+	0.228434i	$0.0733604\pi$
$822$		0			0
$823$	−12.7352	−	22.0580i	−0.443922	−	0.768895i	0.554055	−	0.832480i	$-0.313080\pi$
$823$	−12.7352	−	22.0580i	−0.443922	−	0.768895i	−0.997976	+	0.0635853i	$0.979746\pi$
$824$		0			0
$825$	7.44174	+	36.9774i	0.259088	+	1.28739i
$826$		0			0
$827$	36.0798			1.25462			0.627309	−	0.778771i	$-0.284156\pi$
$827$	36.0798			1.25462			0.627309	+	0.778771i	$0.284156\pi$
$828$		0			0
$829$	22.3539	−	38.7180i	0.776381	−	1.34473i	−0.157633	−	0.987498i	$-0.550386\pi$
$829$	22.3539	−	38.7180i	0.776381	−	1.34473i	0.934015	−	0.357234i	$-0.116280\pi$
$830$		0			0
$831$	0.597304	+	2.96796i	0.0207203	+	0.102957i
$832$		0			0
$833$	37.3577	−	9.63884i	1.29437	−	0.333966i
$834$		0			0
$835$	−5.26467	+	9.11868i	−0.182191	+	0.315565i
$836$		0			0
$837$	13.7734	−	28.4113i	0.476079	−	0.982039i
$838$		0			0
$839$	−7.86805	−	13.6279i	−0.271635	−	0.470486i	0.697645	−	0.716443i	$-0.254231\pi$
$839$	−7.86805	−	13.6279i	−0.271635	−	0.470486i	−0.969281	+	0.245957i	$0.920898\pi$
$840$		0			0
$841$	−7.07866	+	12.2606i	−0.244092	+	0.422779i
$842$		0			0
$843$	13.9234	−	12.2660i	0.479547	−	0.422463i
$844$		0			0
$845$	3.35611	+	5.81296i	0.115454	+	0.199972i
$846$		0			0
$847$	25.0230	+	10.5013i	0.859799	+	0.360829i
$848$		0			0
$849$	16.3713	−	14.4225i	0.561861	−	0.494978i
$850$		0			0
$851$	−0.0120711	−	0.0209078i	−0.000413792	−	0.000716709i
$852$		0			0
$853$	14.2010	+	24.5968i	0.486231	+	0.842177i	0.999875	−	0.0158264i	$-0.00503792\pi$
$853$	14.2010	+	24.5968i	0.486231	+	0.842177i	−0.513643	+	0.858004i	$0.671705\pi$
$854$		0			0
$855$	−4.61744	−	3.51021i	−0.157913	−	0.120046i
$856$		0			0
$857$	−8.97734			−0.306660			−0.153330	−	0.988175i	$-0.549000\pi$
$857$	−8.97734			−0.306660			−0.153330	+	0.988175i	$0.549000\pi$
$858$		0			0
$859$	−0.942900			−0.0321713			−0.0160857	−	0.999871i	$-0.505120\pi$
$859$	−0.942900			−0.0321713			−0.0160857	+	0.999871i	$0.505120\pi$
$860$		0			0
$861$	−17.3476	−	15.2871i	−0.591204	−	0.520984i
$862$		0			0
$863$	−13.0488	−	22.6011i	−0.444185	−	0.769351i	0.553810	−	0.832643i	$-0.313173\pi$
$863$	−13.0488	−	22.6011i	−0.444185	−	0.769351i	−0.997995	+	0.0632920i	$0.979840\pi$
$864$		0			0
$865$	−2.38145	+	4.12478i	−0.0809716	+	0.140247i
$866$		0			0
$867$	−17.3863	+	15.3166i	−0.590468	+	0.520180i
$868$		0			0
$869$	−37.7375	+	65.3633i	−1.28016	+	2.21730i
$870$		0			0
$871$	−2.54022			−0.0860720
$872$		0			0
$873$	−24.9531	−	18.9695i	−0.844533	−	0.642020i
$874$		0			0
$875$	−12.4775	−	5.23639i	−0.421816	−	0.177022i
$876$		0			0
$877$	−26.3589			−0.890077			−0.445038	−	0.895512i	$-0.646810\pi$
$877$	−26.3589			−0.890077			−0.445038	+	0.895512i	$0.646810\pi$
$878$		0			0
$879$	5.17280	+	1.74297i	0.174474	+	0.0587888i
$880$		0			0
$881$	−45.6077			−1.53656			−0.768281	−	0.640113i	$-0.778888\pi$
$881$	−45.6077			−1.53656			−0.768281	+	0.640113i	$0.778888\pi$
$882$		0			0
$883$	−26.1575			−0.880271			−0.440136	−	0.897931i	$-0.645070\pi$
$883$	−26.1575			−0.880271			−0.440136	+	0.897931i	$0.645070\pi$
$884$		0			0
$885$	4.53295	−	3.99335i	0.152373	−	0.134235i
$886$		0			0
$887$	37.1925			1.24880			0.624401	−	0.781104i	$-0.285343\pi$
$887$	37.1925			1.24880			0.624401	+	0.781104i	$0.285343\pi$
$888$		0			0
$889$	−40.5238	−	17.0065i	−1.35912	−	0.570380i
$890$		0			0
$891$	29.0761	−	29.6039i	0.974085	−	0.991767i
$892$		0			0
$893$	33.8019			1.13114
$894$		0			0
$895$	−4.04589	+	7.00769i	−0.135239	+	0.234241i
$896$		0			0
$897$	0.0433146	+	0.0145948i	0.00144623	+	0.000487306i
$898$		0			0
$899$	−19.9592	+	34.5704i	−0.665677	+	1.15299i
$900$		0			0
$901$	24.0932	+	41.7307i	0.802662	+	1.39025i
$902$		0			0
$903$	24.7452	−	8.33377i	0.823469	−	0.277330i
$904$		0			0
$905$	−5.02320			−0.166977
$906$		0			0
$907$	25.8461			0.858206			0.429103	−	0.903255i	$-0.358830\pi$
$907$	25.8461			0.858206			0.429103	+	0.903255i	$0.358830\pi$
$908$		0			0
$909$	27.5679	−	11.5645i	0.914368	−	0.383570i
$910$		0			0
$911$	−2.41211	−	4.17790i	−0.0799169	−	0.138420i	0.823297	−	0.567611i	$-0.192132\pi$
$911$	−2.41211	−	4.17790i	−0.0799169	−	0.138420i	−0.903214	+	0.429191i	$0.858799\pi$
$912$		0			0
$913$	20.7128	+	35.8756i	0.685494	+	1.18731i
$914$		0			0
$915$	−0.402007	−	0.135456i	−0.0132900	−	0.00447803i
$916$		0			0
$917$	14.1912	+	5.95558i	0.468635	+	0.196670i
$918$		0			0
$919$	9.58183	+	16.5962i	0.316075	+	0.547459i	0.979666	−	0.200638i	$-0.0643014\pi$
$919$	9.58183	+	16.5962i	0.316075	+	0.547459i	−0.663590	+	0.748096i	$0.730968\pi$
$920$		0			0
$921$	6.96723	+	34.6196i	0.229578	+	1.14075i
$922$		0			0
$923$	0.431218	−	0.746891i	0.0141937	−	0.0245842i
$924$		0			0
$925$	−1.05675	−	1.83035i	−0.0347458	−	0.0601815i
$926$		0			0
$927$	−32.2320	+	13.5211i	−1.05864	+	0.444091i
$928$		0			0
$929$	−27.0457	+	46.8445i	−0.887340	+	1.53692i	−0.0443327	+	0.999017i	$0.514116\pi$
$929$	−27.0457	+	46.8445i	−0.887340	+	1.53692i	−0.843008	+	0.537902i	$0.819217\pi$
$930$		0			0
$931$	−6.88990	+	24.7898i	−0.225807	+	0.812452i
$932$		0			0
$933$	−29.5040	+	25.9919i	−0.965917	+	0.850937i
$934$		0			0
$935$	6.68322	−	11.5757i	0.218565	−	0.378565i
$936$		0			0
$937$	−16.6345			−0.543426			−0.271713	−	0.962378i	$-0.587590\pi$
$937$	−16.6345			−0.543426			−0.271713	+	0.962378i	$0.587590\pi$
$938$		0			0
$939$	−27.4238	−	9.24041i	−0.894942	−	0.301549i
$940$		0			0
$941$	1.44956	+	2.51071i	0.0472543	+	0.0818468i	0.888685	−	0.458518i	$-0.151620\pi$
$941$	1.44956	+	2.51071i	0.0472543	+	0.0818468i	−0.841431	+	0.540365i	$0.818286\pi$
$942$		0			0
$943$	−0.136116	+	0.235760i	−0.00443256	+	0.00767742i
$944$		0			0
$945$	1.42566	+	7.08944i	0.0463767	+	0.230619i
$946$		0			0
$947$	28.8655	−	49.9966i	0.938004	−	1.62467i	0.168816	−	0.985648i	$-0.446006\pi$
$947$	28.8655	−	49.9966i	0.938004	−	1.62467i	0.769188	−	0.639023i	$-0.220661\pi$
$948$		0			0
$949$	2.56183	+	4.43722i	0.0831605	+	0.144038i
$950$		0			0
$951$	16.9522	+	5.71202i	0.549713	+	0.185225i
$952$		0			0
$953$	20.4070			0.661046			0.330523	−	0.943798i	$-0.392775\pi$
$953$	20.4070			0.661046			0.330523	+	0.943798i	$0.392775\pi$
$954$		0			0
$955$	2.90440	−	5.03057i	0.0939843	−	0.162786i
$956$		0			0
$957$	−39.3645	+	34.6786i	−1.27247	+	1.12100i
$958$		0			0
$959$	−22.5086	−	9.44612i	−0.726841	−	0.305031i
$960$		0			0
$961$	−2.96129	+	5.12911i	−0.0955256	+	0.165455i
$962$		0			0
$963$	−11.7290	−	8.91645i	−0.377961	−	0.287329i
$964$		0			0
$965$	−7.02193	−	12.1623i	−0.226044	−	0.391519i
$966$		0			0
$967$	4.26365	−	7.38486i	0.137110	−	0.237481i	−0.789292	−	0.614019i	$-0.789552\pi$
$967$	4.26365	−	7.38486i	0.137110	−	0.237481i	0.926401	+	0.376537i	$0.122885\pi$
$968$		0			0
$969$	−6.92287	−	34.3992i	−0.222395	−	1.10506i
$970$		0			0
$971$	9.42651	+	16.3272i	0.302511	+	0.523965i	0.976704	−	0.214590i	$-0.0688417\pi$
$971$	9.42651	+	16.3272i	0.302511	+	0.523965i	−0.674193	+	0.738555i	$0.735508\pi$
$972$		0			0
$973$	29.0052	−	22.0431i	0.929864	−	0.706671i
$974$		0			0
$975$	3.79193	+	1.27769i	0.121439	+	0.0409187i
$976$		0			0
$977$	−0.305649	−	0.529400i	−0.00977859	−	0.0169370i	0.861095	−	0.508445i	$-0.169779\pi$
$977$	−0.305649	−	0.529400i	−0.00977859	−	0.0169370i	−0.870873	+	0.491508i	$0.836446\pi$
$978$		0			0
$979$	−32.5108	−	56.3104i	−1.03905	−	1.79969i
$980$		0			0
$981$	7.38510	−	58.1138i	0.235788	−	1.85543i
$982$		0			0
$983$	−7.25167			−0.231292			−0.115646	−	0.993290i	$-0.536894\pi$
$983$	−7.25167			−0.231292			−0.115646	+	0.993290i	$0.536894\pi$
$984$		0			0
$985$	6.75318			0.215174
$986$		0			0
$987$	−31.6176	−	27.8622i	−1.00640	−	0.886865i
$988$		0			0
$989$	−0.153710	−	0.266234i	−0.00488770	−	0.00846575i
$990$		0			0
$991$	−2.49266	+	4.31741i	−0.0791819	+	0.137147i	−0.902897	−	0.429857i	$-0.858564\pi$
$991$	−2.49266	+	4.31741i	−0.0791819	+	0.137147i	0.823715	+	0.567004i	$0.191897\pi$
$992$		0			0
$993$	−37.1469	−	12.5166i	−1.17882	−	0.397202i
$994$		0			0
$995$	5.33412	−	9.23896i	0.169103	−	0.292895i
$996$		0			0
$997$	−3.18344			−0.100821			−0.0504104	−	0.998729i	$-0.516053\pi$
$997$	−3.18344			−0.100821			−0.0504104	+	0.998729i	$0.516053\pi$
$998$		0			0
$999$	−1.01427	+	2.09219i	−0.0320899	+	0.0661939i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.c.193.6	yes	22
3.2	odd	2		1512.2.t.c.361.5		22
4.3	odd	2		1008.2.t.l.193.6		22
7.2	even	3		504.2.q.c.121.10	yes	22
9.2	odd	6		1512.2.q.d.1369.7		22
9.7	even	3		504.2.q.c.25.10	✓	22
12.11	even	2		3024.2.t.k.1873.5		22
21.2	odd	6		1512.2.q.d.793.7		22
28.23	odd	6		1008.2.q.l.625.2		22
36.7	odd	6		1008.2.q.l.529.2		22
36.11	even	6		3024.2.q.l.2881.7		22
63.2	odd	6		1512.2.t.c.289.5		22
63.16	even	3	inner	504.2.t.c.457.6	yes	22
84.23	even	6		3024.2.q.l.2305.7		22
252.79	odd	6		1008.2.t.l.961.6		22
252.191	even	6		3024.2.t.k.289.5		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.c.25.10	✓	22	9.7	even	3
504.2.q.c.121.10	yes	22	7.2	even	3
504.2.t.c.193.6	yes	22	1.1	even	1	trivial
504.2.t.c.457.6	yes	22	63.16	even	3	inner
1008.2.q.l.529.2		22	36.7	odd	6
1008.2.q.l.625.2		22	28.23	odd	6
1008.2.t.l.193.6		22	4.3	odd	2
1008.2.t.l.961.6		22	252.79	odd	6
1512.2.q.d.793.7		22	21.2	odd	6
1512.2.q.d.1369.7		22	9.2	odd	6
1512.2.t.c.289.5		22	63.2	odd	6
1512.2.t.c.361.5		22	3.2	odd	2
3024.2.q.l.2305.7		22	84.23	even	6
3024.2.q.l.2881.7		22	36.11	even	6
3024.2.t.k.289.5		22	252.191	even	6
3024.2.t.k.1873.5		22	12.11	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.341725 - 1.69801i) q^{3} +0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} +(-2.76645 + 1.16050i) q^{9} +O(q^{10})\)	\(q+(-0.341725 - 1.69801i) q^{3} +0.526004 q^{5} +(2.43963 + 1.02383i) q^{7} +(-2.76645 + 1.16050i) q^{9} +4.61052 q^{11} +(0.244554 - 0.423580i) q^{13} +(-0.179749 - 0.893158i) q^{15} +(2.75579 - 4.77318i) q^{17} +(1.83782 + 3.18319i) q^{19} +(0.904788 - 4.49237i) q^{21} -0.0539537 q^{23} -4.72332 q^{25} +(2.91591 + 4.30087i) q^{27} +(-3.28471 - 5.68929i) q^{29} +(-3.03820 - 5.26231i) q^{31} +(-1.57553 - 7.82869i) q^{33} +(1.28325 + 0.538539i) q^{35} +(0.223731 + 0.387513i) q^{37} +(-0.802811 - 0.270506i) q^{39} +(2.52284 - 4.36968i) q^{41} +(2.84893 + 4.93449i) q^{43} +(-1.45516 + 0.610430i) q^{45} +(4.59810 - 7.96415i) q^{47} +(4.90354 + 4.99552i) q^{49} +(-9.04661 - 3.04824i) q^{51} +(-4.37138 + 7.57145i) q^{53} +2.42515 q^{55} +(4.77705 - 4.20840i) q^{57} +(3.31538 + 5.74241i) q^{59} +(0.232812 - 0.403243i) q^{61} +(-7.93725 - 0.00117907i) q^{63} +(0.128636 - 0.222805i) q^{65} +(-2.59679 - 4.49777i) q^{67} +(0.0184374 + 0.0916137i) q^{69} +1.76328 q^{71} +(-5.23776 + 9.07207i) q^{73} +(1.61408 + 8.02022i) q^{75} +(11.2479 + 4.72039i) q^{77} +(-8.18509 + 14.1770i) q^{79} +(6.30646 - 6.42094i) q^{81} +(4.49251 + 7.78126i) q^{83} +(1.44956 - 2.51071i) q^{85} +(-8.53797 + 7.52163i) q^{87} +(-7.05145 - 12.2135i) q^{89} +(1.03029 - 0.782994i) q^{91} +(-7.89721 + 6.95714i) q^{93} +(0.966699 + 1.67437i) q^{95} +(5.22413 + 9.04847i) q^{97} +(-12.7548 + 5.35052i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7}+O(q^{10}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7	\( 22 q - 2 q^{3} - 2 q^{5} - q^{7} - 6 q^{11} + 7 q^{13} - q^{15} - q^{17} + 13 q^{19} + 33 q^{21} + 44 q^{25} - 2 q^{27} - 7 q^{29} + 6 q^{31} + 9 q^{33} + 2 q^{35} + 6 q^{37} - 4 q^{39} + 4 q^{41} + 2 q^{43} + 17 q^{47} + 29 q^{49} - 25 q^{51} + q^{53} + 2 q^{55} - 21 q^{57} - 21 q^{59} + 31 q^{61} - 7 q^{63} - 3 q^{65} - 26 q^{67} - 40 q^{69} - 32 q^{71} + 17 q^{73} - 16 q^{75} - 4 q^{77} - 16 q^{79} - 36 q^{83} + 28 q^{85} + 7 q^{87} - 2 q^{89} + 15 q^{91} - 56 q^{93} - 24 q^{95} + 19 q^{97} + 24 q^{99}+O(q^{100}) \) 22 * q - 2 * q^3 - 2 * q^5 - q^7 - 6 * q^11 + 7 * q^13 - q^15 - q^17 + 13 * q^19 + 33 * q^21 + 44 * q^25 - 2 * q^27 - 7 * q^29 + 6 * q^31 + 9 * q^33 + 2 * q^35 + 6 * q^37 - 4 * q^39 + 4 * q^41 + 2 * q^43 + 17 * q^47 + 29 * q^49 - 25 * q^51 + q^53 + 2 * q^55 - 21 * q^57 - 21 * q^59 + 31 * q^61 - 7 * q^63 - 3 * q^65 - 26 * q^67 - 40 * q^69 - 32 * q^71 + 17 * q^73 - 16 * q^75 - 4 * q^77 - 16 * q^79 - 36 * q^83 + 28 * q^85 + 7 * q^87 - 2 * q^89 + 15 * q^91 - 56 * q^93 - 24 * q^95 + 19 * q^97 + 24 * q^99

Introduction

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