LMFDB - Embedded newform 525.2.j.a.407.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.6040479020157644046336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 7x^{12} - 32x^{8} - 567x^{4} + 6561 $ x^16 - 7x^12 - 32x^8 - 567*x^4 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			407.2
Root			$0.0537601 + 1.73122i$ of defining polynomial
Character	$\chi$	$=$	525.407
Dual form			525.2.j.a.218.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.78498 + 1.78498i) q^{2} +(0.912166 - 1.47240i) q^{3} -4.37228i q^{4} +(1.00000 + 4.25639i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(4.23447 + 4.23447i) q^{8} +(-1.33591 - 2.68614i) q^{9} +O(q^{10})$	\(q+(-1.78498 + 1.78498i) q^{2} +(0.912166 - 1.47240i) q^{3} -4.37228i q^{4} +(1.00000 + 4.25639i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(4.23447 + 4.23447i) q^{8} +(-1.33591 - 2.68614i) q^{9} -5.84096i q^{11} +(-6.43773 - 3.98825i) q^{12} +(-2.38456 + 2.38456i) q^{13} +2.52434 q^{14} -6.37228 q^{16} +(-3.00972 + 3.00972i) q^{17} +(7.17926 + 2.41013i) q^{18} +4.00000i q^{19} +(-1.68614 + 0.396143i) q^{21} +(10.4260 + 10.4260i) q^{22} +(-2.44949 - 2.44949i) q^{23} +(10.0974 - 2.37228i) q^{24} -8.51278i q^{26} +(-5.17364 - 0.483219i) q^{27} +(-3.09167 + 3.09167i) q^{28} -2.67181 q^{29} -6.74456 q^{31} +(2.90544 - 2.90544i) q^{32} +(-8.60022 - 5.32793i) q^{33} -10.7446i q^{34} +(-11.7446 + 5.84096i) q^{36} +(-4.76913 - 4.76913i) q^{37} +(-7.13991 - 7.13991i) q^{38} +(1.33591 + 5.68614i) q^{39} +5.34363i q^{41} +(2.30261 - 3.71683i) q^{42} +(5.65685 - 5.65685i) q^{43} -25.5383 q^{44} +8.74456 q^{46} +(5.45921 - 5.45921i) q^{47} +(-5.81258 + 9.38253i) q^{48} +1.00000i q^{49} +(1.68614 + 7.17687i) q^{51} +(10.4260 + 10.4260i) q^{52} +(-3.77852 - 3.77852i) q^{53} +(10.0974 - 8.37228i) q^{54} -5.98844i q^{56} +(5.88959 + 3.64866i) q^{57} +(4.76913 - 4.76913i) q^{58} +5.34363 q^{59} -4.74456 q^{61} +(12.0389 - 12.0389i) q^{62} +(-0.954759 + 2.84402i) q^{63} -2.37228i q^{64} +(24.8614 - 5.84096i) q^{66} +(0.887728 + 0.887728i) q^{67} +(13.1593 + 13.1593i) q^{68} +(-5.84096 + 1.37228i) q^{69} -8.51278i q^{71} +(5.71752 - 17.0312i) q^{72} +(0.887728 - 0.887728i) q^{73} +17.0256 q^{74} +17.4891 q^{76} +(-4.13018 + 4.13018i) q^{77} +(-12.5342 - 7.76506i) q^{78} +2.11684i q^{79} +(-5.43070 + 7.17687i) q^{81} +(-9.53825 - 9.53825i) q^{82} +(-6.93134 - 6.93134i) q^{83} +(1.73205 + 7.37228i) q^{84} +20.1947i q^{86} +(-2.43714 + 3.93397i) q^{87} +(24.7334 - 24.7334i) q^{88} +17.0256 q^{89} +3.37228 q^{91} +(-10.7099 + 10.7099i) q^{92} +(-6.15216 + 9.93068i) q^{93} +19.4891i q^{94} +(-1.62772 - 6.92820i) q^{96} +(2.38456 + 2.38456i) q^{97} +(-1.78498 - 1.78498i) q^{98} +(-15.6896 + 7.80298i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{6}+O(q^{10}) $ 16 * q + 16 * q^6	$ 16 q + 16 q^{6} - 56 q^{16} - 4 q^{21} - 16 q^{31} - 96 q^{36} + 48 q^{46} + 4 q^{51} + 16 q^{61} + 168 q^{66} + 96 q^{76} + 28 q^{81} + 8 q^{91} - 72 q^{96}+O(q^{100}) $ 16 * q + 16 * q^6 - 56 * q^16 - 4 * q^21 - 16 * q^31 - 96 * q^36 + 48 * q^46 + 4 * q^51 + 16 * q^61 + 168 * q^66 + 96 * q^76 + 28 * q^81 + 8 * q^91 - 72 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.78498	+	1.78498i	−1.26217	+	1.26217i	−0.312129	+	0.950040i	$0.601042\pi$
$2$	−1.78498	+	1.78498i	−1.26217	+	1.26217i	−0.950040	+	0.312129i	$0.898958\pi$
$3$	0.912166	−	1.47240i	0.526639	−	0.850089i
$3$	0.912166	−	1.47240i	0.526639	−	0.850089i
$4$		−	4.37228i		−	2.18614i
$5$		0			0
$5$		0			0
$6$	1.00000	+	4.25639i	0.408248	+	1.73766i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$	4.23447	+	4.23447i	1.49711	+	1.49711i
$9$	−1.33591	−	2.68614i	−0.445302	−	0.895380i
$10$		0			0
$11$		−	5.84096i		−	1.76112i	−0.473938	−	0.880558i	$-0.657168\pi$
$11$		−	5.84096i		−	1.76112i	0.473938	−	0.880558i	$-0.342832\pi$
$12$	−6.43773	−	3.98825i	−1.85841	−	1.15131i
$13$	−2.38456	+	2.38456i	−0.661359	+	0.661359i	−0.955700	−	0.294342i	$-0.904900\pi$
$13$	−2.38456	+	2.38456i	−0.661359	+	0.661359i	0.294342	+	0.955700i	$0.404900\pi$
$14$	2.52434			0.674658
$15$		0			0
$16$	−6.37228			−1.59307
$17$	−3.00972	+	3.00972i	−0.729965	+	0.729965i	−0.970612	−	0.240648i	$-0.922640\pi$
$17$	−3.00972	+	3.00972i	−0.729965	+	0.729965i	0.240648	+	0.970612i	$0.422640\pi$
$18$	7.17926	+	2.41013i	1.69217	+	0.568074i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$	−1.68614	+	0.396143i	−0.367946	+	0.0864456i
$22$	10.4260	+	10.4260i	2.22283	+	2.22283i
$23$	−2.44949	−	2.44949i	−0.510754	−	0.510754i	0.404004	−	0.914757i	$-0.367618\pi$
$23$	−2.44949	−	2.44949i	−0.510754	−	0.510754i	−0.914757	+	0.404004i	$0.867618\pi$
$24$	10.0974	−	2.37228i	2.06111	−	0.484240i
$25$		0			0
$26$		−	8.51278i		−	1.66949i
$27$	−5.17364	−	0.483219i	−0.995667	−	0.0929956i
$28$	−3.09167	+	3.09167i	−0.584271	+	0.584271i
$29$	−2.67181			−0.496144			−0.248072	−	0.968742i	$-0.579797\pi$
$29$	−2.67181			−0.496144			−0.248072	+	0.968742i	$0.579797\pi$
$30$		0			0
$31$	−6.74456			−1.21136			−0.605680	−	0.795709i	$-0.707099\pi$
$31$	−6.74456			−1.21136			−0.605680	+	0.795709i	$0.707099\pi$
$32$	2.90544	−	2.90544i	0.513614	−	0.513614i
$33$	−8.60022	−	5.32793i	−1.49711	−	0.927473i
$34$		−	10.7446i		−	1.84268i
$35$		0			0
$36$	−11.7446	+	5.84096i	−1.95743	+	0.973494i
$37$	−4.76913	−	4.76913i	−0.784039	−	0.784039i	0.196470	−	0.980510i	$-0.437052\pi$
$37$	−4.76913	−	4.76913i	−0.784039	−	0.784039i	−0.980510	+	0.196470i	$0.937052\pi$
$38$	−7.13991	−	7.13991i	−1.15825	−	1.15825i
$39$	1.33591	+	5.68614i	0.213916	+	0.910511i
$40$		0			0
$41$			5.34363i			0.834535i	0.908784	+	0.417267i	$0.137012\pi$
$41$			5.34363i			0.834535i	−0.908784	+	0.417267i	$0.862988\pi$
$42$	2.30261	−	3.71683i	0.355301	−	0.573519i
$43$	5.65685	−	5.65685i	0.862662	−	0.862662i	−0.128984	−	0.991647i	$-0.541172\pi$
$43$	5.65685	−	5.65685i	0.862662	−	0.862662i	0.991647	+	0.128984i	$0.0411717\pi$
$44$	−25.5383			−3.85005
$45$		0			0
$46$	8.74456			1.28932
$47$	5.45921	−	5.45921i	0.796308	−	0.796308i	−0.186203	−	0.982511i	$-0.559618\pi$
$47$	5.45921	−	5.45921i	0.796308	−	0.796308i	0.982511	+	0.186203i	$0.0596184\pi$
$48$	−5.81258	+	9.38253i	−0.838973	+	1.35425i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	1.68614	+	7.17687i	0.236107	+	1.00496i
$52$	10.4260	+	10.4260i	1.44582	+	1.44582i
$53$	−3.77852	−	3.77852i	−0.519019	−	0.519019i	0.398255	−	0.917275i	$-0.369616\pi$
$53$	−3.77852	−	3.77852i	−0.519019	−	0.519019i	−0.917275	+	0.398255i	$0.869616\pi$
$54$	10.0974	−	8.37228i	1.37408	−	1.13932i
$55$		0			0
$56$		−	5.98844i		−	0.800239i
$57$	5.88959	+	3.64866i	0.780095	+	0.483277i
$58$	4.76913	−	4.76913i	0.626217	−	0.626217i
$59$	5.34363			0.695681			0.347841	−	0.937554i	$-0.386915\pi$
$59$	5.34363			0.695681			0.347841	+	0.937554i	$0.386915\pi$
$60$		0			0
$61$	−4.74456			−0.607479			−0.303739	−	0.952755i	$-0.598235\pi$
$61$	−4.74456			−0.607479			−0.303739	+	0.952755i	$0.598235\pi$
$62$	12.0389	−	12.0389i	1.52894	−	1.52894i
$63$	−0.954759	+	2.84402i	−0.120288	+	0.358313i
$64$		−	2.37228i		−	0.296535i
$65$		0			0
$66$	24.8614	−	5.84096i	3.06023	−	0.718973i
$67$	0.887728	+	0.887728i	0.108453	+	0.108453i	0.759251	−	0.650798i	$-0.225565\pi$
$67$	0.887728	+	0.887728i	0.108453	+	0.108453i	−0.650798	+	0.759251i	$0.725565\pi$
$68$	13.1593	+	13.1593i	1.59581	+	1.59581i
$69$	−5.84096	+	1.37228i	−0.703169	+	0.165203i
$70$		0			0
$71$		−	8.51278i		−	1.01028i	−0.863037	−	0.505140i	$-0.831441\pi$
$71$		−	8.51278i		−	1.01028i	0.863037	−	0.505140i	$-0.168559\pi$
$72$	5.71752	−	17.0312i	0.673816	−	2.00715i
$73$	0.887728	−	0.887728i	0.103901	−	0.103901i	−0.653245	−	0.757146i	$-0.726593\pi$
$73$	0.887728	−	0.887728i	0.103901	−	0.103901i	0.757146	+	0.653245i	$0.226593\pi$
$74$	17.0256			1.97918
$75$		0			0
$76$	17.4891			2.00614
$77$	−4.13018	+	4.13018i	−0.470678	+	0.470678i
$78$	−12.5342	−	7.76506i	−1.41922	−	0.879220i
$79$			2.11684i			0.238164i	0.992884	+	0.119082i	$0.0379951\pi$
$79$			2.11684i			0.238164i	−0.992884	+	0.119082i	$0.962005\pi$
$80$		0			0
$81$	−5.43070	+	7.17687i	−0.603411	+	0.797430i
$82$	−9.53825	−	9.53825i	−1.05332	−	1.05332i
$83$	−6.93134	−	6.93134i	−0.760814	−	0.760814i	0.215656	−	0.976469i	$-0.430811\pi$
$83$	−6.93134	−	6.93134i	−0.760814	−	0.760814i	−0.976469	+	0.215656i	$0.930811\pi$
$84$	1.73205	+	7.37228i	0.188982	+	0.804382i
$85$		0			0
$86$			20.1947i			2.17765i
$87$	−2.43714	+	3.93397i	−0.261289	+	0.421766i
$88$	24.7334	−	24.7334i	2.63658	−	2.63658i
$89$	17.0256			1.80471			0.902353	−	0.430999i	$-0.141839\pi$
$89$	17.0256			1.80471			0.902353	+	0.430999i	$0.141839\pi$
$90$		0			0
$91$	3.37228			0.353511
$92$	−10.7099	+	10.7099i	−1.11658	+	1.11658i
$93$	−6.15216	+	9.93068i	−0.637949	+	1.02976i
$94$			19.4891i			2.01015i
$95$		0			0
$96$	−1.62772	−	6.92820i	−0.166128	−	0.707107i
$97$	2.38456	+	2.38456i	0.242116	+	0.242116i	0.817725	−	0.575609i	$-0.195235\pi$
$97$	2.38456	+	2.38456i	0.242116	+	0.242116i	−0.575609	+	0.817725i	$0.695235\pi$
$98$	−1.78498	−	1.78498i	−0.180310	−	0.180310i
$99$	−15.6896	+	7.80298i	−1.57687	+	0.784229i
$100$		0			0
$101$		−	17.0256i		−	1.69411i	−0.531508	−	0.847053i	$-0.678375\pi$
$101$		−	17.0256i		−	1.69411i	0.531508	−	0.847053i	$-0.321625\pi$
$102$	−15.8203	−	9.80082i	−1.56644	−	0.970426i
$103$	7.15369	−	7.15369i	0.704874	−	0.704874i	−0.260579	−	0.965453i	$-0.583913\pi$
$103$	7.15369	−	7.15369i	0.704874	−	0.704874i	0.965453	+	0.260579i	$0.0839133\pi$
$104$	−20.1947			−1.98025
$105$		0			0
$106$	13.4891			1.31018
$107$	−8.46893	+	8.46893i	−0.818723	+	0.818723i	−0.985923	−	0.167200i	$-0.946527\pi$
$107$	−8.46893	+	8.46893i	−0.818723	+	0.818723i	0.167200	+	0.985923i	$0.446527\pi$
$108$	−2.11277	+	22.6206i	−0.203301	+	2.17667i
$109$		−	2.62772i		−	0.251690i	−0.992050	−	0.125845i	$-0.959836\pi$
$109$		−	2.62772i		−	0.251690i	0.992050	−	0.125845i	$-0.0401642\pi$
$110$		0			0
$111$	−11.3723	+	2.67181i	−1.07941	+	0.253597i
$112$	4.50588	+	4.50588i	0.425766	+	0.425766i
$113$	−1.12046	−	1.12046i	−0.105404	−	0.105404i	0.652438	−	0.757842i	$-0.273746\pi$
$113$	−1.12046	−	1.12046i	−0.105404	−	0.105404i	−0.757842	+	0.652438i	$0.773746\pi$
$114$	−17.0256	+	4.00000i	−1.59459	+	0.374634i
$115$		0			0
$116$			11.6819i			1.08464i
$117$	9.59083	+	3.21972i	0.886672	+	0.297663i
$118$	−9.53825	+	9.53825i	−0.878067	+	0.878067i
$119$	4.25639			0.390183
$120$		0			0
$121$	−23.1168			−2.10153
$122$	8.46893	−	8.46893i	0.766741	−	0.766741i
$123$	7.86794	+	4.87428i	0.709429	+	0.439499i
$124$			29.4891i			2.64820i
$125$		0			0
$126$	−3.37228	−	6.78073i	−0.300427	−	0.604075i
$127$	−10.4260	−	10.4260i	−0.925156	−	0.925156i	0.0722317	−	0.997388i	$-0.476988\pi$
$127$	−10.4260	−	10.4260i	−0.925156	−	0.925156i	−0.997388	+	0.0722317i	$0.976988\pi$
$128$	10.0453	+	10.0453i	0.887891	+	0.887891i
$129$	−3.16915	−	13.4891i	−0.279028	−	1.18765i
$130$		0			0
$131$			11.6819i			1.02065i	0.859980	+	0.510327i	$0.170476\pi$
$131$			11.6819i			1.02065i	−0.859980	+	0.510327i	$0.829524\pi$
$132$	−23.2952	+	37.6026i	−2.02759	+	3.27288i
$133$	2.82843	−	2.82843i	0.245256	−	0.245256i
$134$	−3.16915			−0.273773
$135$		0			0
$136$	−25.4891			−2.18567
$137$	−2.65805	+	2.65805i	−0.227093	+	0.227093i	−0.811477	−	0.584384i	$-0.801336\pi$
$137$	−2.65805	+	2.65805i	−0.227093	+	0.227093i	0.584384	+	0.811477i	$0.301336\pi$
$138$	7.97649	−	12.8755i	0.679004	−	1.09603i
$139$			10.7446i			0.911342i	0.890148	+	0.455671i	$0.150601\pi$
$139$			10.7446i			0.911342i	−0.890148	+	0.455671i	$0.849399\pi$
$140$		0			0
$141$	−3.05842	−	13.0178i	−0.257566	−	1.09630i
$142$	15.1951	+	15.1951i	1.27514	+	1.27514i
$143$	13.9281	+	13.9281i	1.16473	+	1.16473i
$144$	8.51278	+	17.1168i	0.709398	+	1.42640i
$145$		0			0
$146$			3.16915i			0.262281i
$147$	1.47240	+	0.912166i	0.121441	+	0.0752342i
$148$	−20.8520	+	20.8520i	−1.71402	+	1.71402i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$	10.1168			0.823297			0.411649	−	0.911343i	$-0.364953\pi$
$151$	10.1168			0.823297			0.411649	+	0.911343i	$0.364953\pi$
$152$	−16.9379	+	16.9379i	−1.37384	+	1.37384i
$153$	12.1052	+	4.06383i	0.978651	+	0.328541i
$154$		−	14.7446i		−	1.18815i
$155$		0			0
$156$	24.8614	−	5.84096i	1.99051	−	0.467651i
$157$	−0.887728	−	0.887728i	−0.0708484	−	0.0708484i	0.670795	−	0.741643i	$-0.265953\pi$
$157$	−0.887728	−	0.887728i	−0.0708484	−	0.0708484i	−0.741643	+	0.670795i	$0.765953\pi$
$158$	−3.77852	−	3.77852i	−0.300603	−	0.300603i
$159$	−9.01011	+	2.11684i	−0.714548	+	0.167877i
$160$		0			0
$161$			3.46410i			0.273009i
$162$	−3.11687	−	22.5042i	−0.244884	−	1.76810i
$163$	0.887728	−	0.887728i	0.0695322	−	0.0695322i	−0.671485	−	0.741018i	$-0.734343\pi$
$163$	0.887728	−	0.887728i	0.0695322	−	0.0695322i	0.741018	+	0.671485i	$0.234343\pi$
$164$	23.3639			1.82441
$165$		0			0
$166$	24.7446			1.92055
$167$	8.82060	−	8.82060i	0.682559	−	0.682559i	−0.278017	−	0.960576i	$-0.589677\pi$
$167$	8.82060	−	8.82060i	0.682559	−	0.682559i	0.960576	+	0.278017i	$0.0896773\pi$
$168$	−8.81736	−	5.46245i	−0.680274	−	0.421437i
$169$			1.62772i			0.125209i
$170$		0			0
$171$	10.7446	−	5.34363i	0.821657	−	0.408638i
$172$	−24.7334	−	24.7334i	−1.88590	−	1.88590i
$173$	0.351668	+	0.351668i	0.0267368	+	0.0267368i	0.720349	−	0.693612i	$-0.243982\pi$
$173$	0.351668	+	0.351668i	0.0267368	+	0.0267368i	−0.693612	+	0.720349i	$0.743982\pi$
$174$	−2.67181	−	11.3723i	−0.202550	−	0.862130i
$175$		0			0
$176$			37.2203i			2.80558i
$177$	4.87428	−	7.86794i	0.366373	−	0.591391i
$178$	−30.3902	+	30.3902i	−2.27784	+	2.27784i
$179$	−8.51278			−0.636275			−0.318137	−	0.948045i	$-0.603057\pi$
$179$	−8.51278			−0.636275			−0.318137	+	0.948045i	$0.603057\pi$
$180$		0			0
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$	−6.01944	+	6.01944i	−0.446191	+	0.446191i
$183$	−4.32783	+	6.98588i	−0.319922	+	0.516411i
$184$		−	20.7446i		−	1.52931i
$185$		0			0
$186$	−6.74456	−	28.7075i	−0.494535	−	2.10493i
$187$	17.5797	+	17.5797i	1.28555	+	1.28555i
$188$	−23.8692	−	23.8692i	−1.74084	−	1.74084i
$189$	3.31662	+	4.00000i	0.241249	+	0.290957i
$190$		0			0
$191$		−	0.497333i		−	0.0359858i	−0.999838	−	0.0179929i	$-0.994272\pi$
$191$		−	0.497333i		−	0.0359858i	0.999838	−	0.0179929i	$-0.00572762\pi$
$192$	−3.49294	−	2.16391i	−0.252081	−	0.156167i
$193$	−1.77546	+	1.77546i	−0.127800	+	0.127800i	−0.768114	−	0.640314i	$-0.778804\pi$
$193$	−1.77546	+	1.77546i	−0.127800	+	0.127800i	0.640314	+	0.768114i	$0.278804\pi$
$194$	−8.51278			−0.611182
$195$		0			0
$196$	4.37228			0.312306
$197$	1.53759	−	1.53759i	0.109549	−	0.109549i	−0.650208	−	0.759756i	$-0.725318\pi$
$197$	1.53759	−	1.53759i	0.109549	−	0.109549i	0.759756	+	0.650208i	$0.225318\pi$
$198$	14.0775	−	41.9338i	1.00044	−	2.98010i
$199$		−	1.25544i		−	0.0889956i	−0.999009	−	0.0444978i	$-0.985831\pi$
$199$		−	1.25544i		−	0.0889956i	0.999009	−	0.0444978i	$-0.0141688\pi$
$200$		0			0
$201$	2.11684	−	0.497333i	0.149311	−	0.0350792i
$202$	30.3902	+	30.3902i	2.13825	+	2.13825i
$203$	1.88926	+	1.88926i	0.132600	+	0.132600i
$204$	31.3793	−	7.37228i	2.19699	−	0.516163i
$205$		0			0
$206$			25.5383i			1.77934i
$207$	−3.30738	+	9.85197i	−0.229879	+	0.684759i
$208$	15.1951	−	15.1951i	1.05359	−	1.05359i
$209$	23.3639			1.61611
$210$		0			0
$211$	15.3723			1.05827			0.529136	−	0.848537i	$-0.322516\pi$
$211$	15.3723			1.05827			0.529136	+	0.848537i	$0.322516\pi$
$212$	−16.5207	+	16.5207i	−1.13465	+	1.13465i
$213$	−12.5342	−	7.76506i	−0.858829	−	0.532053i
$214$		−	30.2337i		−	2.06673i
$215$		0			0
$216$	−19.8614	−	23.9538i	−1.35140	−	1.62985i
$217$	4.76913	+	4.76913i	0.323749	+	0.323749i
$218$	4.69042	+	4.69042i	0.317675	+	0.317675i
$219$	−0.497333	−	2.11684i	−0.0336067	−	0.143043i
$220$		0			0
$221$		−	14.3537i		−	0.965537i
$222$	15.5301	−	25.0684i	1.04231	−	1.68248i
$223$	4.16002	−	4.16002i	0.278576	−	0.278576i	−0.553965	−	0.832540i	$-0.686886\pi$
$223$	4.16002	−	4.16002i	0.278576	−	0.278576i	0.832540	+	0.553965i	$0.186886\pi$
$224$	−4.10891			−0.274538
$225$		0			0
$226$	4.00000			0.266076
$227$	16.3776	−	16.3776i	1.08702	−	1.08702i	0.0911880	−	0.995834i	$-0.470934\pi$
$227$	16.3776	−	16.3776i	1.08702	−	1.08702i	0.995834	−	0.0911880i	$-0.0290664\pi$
$228$	15.9530	−	25.7509i	1.05651	−	1.70540i
$229$		−	16.9783i		−	1.12195i	−0.827831	−	0.560977i	$-0.810426\pi$
$229$		−	16.9783i		−	1.12195i	0.827831	−	0.560977i	$-0.189574\pi$
$230$		0			0
$231$	2.31386	+	9.84868i	0.152241	+	0.647996i
$232$	−11.3137	−	11.3137i	−0.742781	−	0.742781i
$233$	19.1788	+	19.1788i	1.25644	+	1.25644i	0.952779	+	0.303666i	$0.0982106\pi$
$233$	19.1788	+	19.1788i	1.25644	+	1.25644i	0.303666	+	0.952779i	$0.401789\pi$
$234$	−22.8665	+	11.3723i	−1.49483	+	0.743429i
$235$		0			0
$236$		−	23.3639i		−	1.52086i
$237$	3.11684	+	1.93091i	0.202460	+	0.125426i
$238$	−7.59755	+	7.59755i	−0.492476	+	0.492476i
$239$	−11.1846			−0.723471			−0.361736	−	0.932281i	$-0.617816\pi$
$239$	−11.1846			−0.723471			−0.361736	+	0.932281i	$0.617816\pi$
$240$		0			0
$241$	−11.4891			−0.740080			−0.370040	−	0.929016i	$-0.620656\pi$
$241$	−11.4891			−0.740080			−0.370040	+	0.929016i	$0.620656\pi$
$242$	41.2630	−	41.2630i	2.65249	−	2.65249i
$243$	5.61350	+	14.5426i	0.360106	+	0.932911i
$244$			20.7446i			1.32803i
$245$		0			0
$246$	−22.7446	+	5.34363i	−1.45014	+	0.340697i
$247$	−9.53825	−	9.53825i	−0.606904	−	0.606904i
$248$	−28.5596	−	28.5596i	−1.81354	−	1.81354i
$249$	−16.5282	+	3.88316i	−1.04743	+	0.246085i
$250$		0			0
$251$			18.0202i			1.13743i	0.822536	+	0.568713i	$0.192559\pi$
$251$			18.0202i			1.13743i	−0.822536	+	0.568713i	$0.807441\pi$
$252$	12.4348	+	4.17448i	0.783322	+	0.262967i
$253$	−14.3074	+	14.3074i	−0.899497	+	0.899497i
$254$	37.2203			2.33541
$255$		0			0
$256$	−31.1168			−1.94480
$257$	−4.89898	+	4.89898i	−0.305590	+	0.305590i	−0.843196	−	0.537606i	$-0.819329\pi$
$257$	−4.89898	+	4.89898i	−0.305590	+	0.305590i	0.537606	+	0.843196i	$0.319329\pi$
$258$	29.7346	+	18.4209i	1.85120	+	1.14684i
$259$			6.74456i			0.419087i
$260$		0			0
$261$	3.56930	+	7.17687i	0.220934	+	0.444237i
$262$	−20.8520	−	20.8520i	−1.28824	−	1.28824i
$263$	10.7099	+	10.7099i	0.660398	+	0.660398i	0.955474	−	0.295076i	$-0.0953449\pi$
$263$	10.7099	+	10.7099i	0.660398	+	0.660398i	−0.295076	+	0.955474i	$0.595345\pi$
$264$	−13.8564	−	58.9783i	−0.852803	−	3.62986i
$265$		0			0
$266$			10.0974i			0.619108i
$267$	15.5301	−	25.0684i	0.950428	−	1.53416i
$268$	3.88140	−	3.88140i	0.237094	−	0.237094i
$269$	−5.34363			−0.325807			−0.162903	−	0.986642i	$-0.552086\pi$
$269$	−5.34363			−0.325807			−0.162903	+	0.986642i	$0.552086\pi$
$270$		0			0
$271$	−21.4891			−1.30537			−0.652686	−	0.757629i	$-0.726358\pi$
$271$	−21.4891			−1.30537			−0.652686	+	0.757629i	$0.726358\pi$
$272$	19.1788	−	19.1788i	1.16288	−	1.16288i
$273$	3.07608	−	4.96534i	0.186173	−	0.300516i
$274$		−	9.48913i		−	0.573259i
$275$		0			0
$276$	6.00000	+	25.5383i	0.361158	+	1.53723i
$277$	−6.54458	−	6.54458i	−0.393226	−	0.393226i	0.482610	−	0.875836i	$-0.339689\pi$
$277$	−6.54458	−	6.54458i	−0.393226	−	0.393226i	−0.875836	+	0.482610i	$0.839689\pi$
$278$	−19.1788	−	19.1788i	−1.15027	−	1.15027i
$279$	9.01011	+	18.1168i	0.539421	+	1.08463i
$280$		0			0
$281$		−	26.0357i		−	1.55316i	−0.630020	−	0.776579i	$-0.716953\pi$
$281$		−	26.0357i		−	1.55316i	0.630020	−	0.776579i	$-0.283047\pi$
$282$	28.6957	+	17.7773i	1.70881	+	1.05862i
$283$	11.9228	−	11.9228i	0.708738	−	0.708738i	−0.257532	−	0.966270i	$-0.582909\pi$
$283$	11.9228	−	11.9228i	0.708738	−	0.708738i	0.966270	+	0.257532i	$0.0829093\pi$
$284$	−37.2203			−2.20862
$285$		0			0
$286$	−49.7228			−2.94017
$287$	3.77852	−	3.77852i	0.223039	−	0.223039i
$288$	−11.6858	−	3.92302i	−0.688593	−	0.231166i
$289$		−	1.11684i		−	0.0656967i
$290$		0			0
$291$	5.68614	−	1.33591i	0.333327	−	0.0783123i
$292$	−3.88140	−	3.88140i	−0.227142	−	0.227142i
$293$	−0.351668	−	0.351668i	−0.0205447	−	0.0205447i	0.696760	−	0.717304i	$-0.254624\pi$
$293$	−0.351668	−	0.351668i	−0.0205447	−	0.0205447i	−0.717304	+	0.696760i	$0.754624\pi$
$294$	−4.25639	+	1.00000i	−0.248238	+	0.0583212i
$295$		0			0
$296$		−	40.3894i		−	2.34759i
$297$	−2.82247	+	30.2190i	−0.163776	+	1.75348i
$298$		0			0
$299$	11.6819			0.675583
$300$		0			0
$301$	−8.00000			−0.461112
$302$	−18.0583	+	18.0583i	−1.03914	+	1.03914i
$303$	−25.0684	−	15.5301i	−1.44014	−	0.892183i
$304$		−	25.4891i		−	1.46190i
$305$		0			0
$306$	−28.8614	+	14.3537i	−1.64990	+	0.820549i
$307$	−13.6983	−	13.6983i	−0.781802	−	0.781802i	0.198333	−	0.980135i	$-0.436447\pi$
$307$	−13.6983	−	13.6983i	−0.781802	−	0.781802i	−0.980135	+	0.198333i	$0.936447\pi$
$308$	18.0583	+	18.0583i	1.02897	+	1.02897i
$309$	−4.00772	−	17.0584i	−0.227991	−	0.970420i
$310$		0			0
$311$		−	17.0256i		−	0.965431i	−0.875777	−	0.482715i	$-0.839651\pi$
$311$		−	17.0256i		−	0.965431i	0.875777	−	0.482715i	$-0.160349\pi$
$312$	−18.4209	+	29.7346i	−1.04288	+	1.68339i
$313$	11.9228	−	11.9228i	0.673917	−	0.673917i	−0.284699	−	0.958617i	$-0.591894\pi$
$313$	11.9228	−	11.9228i	0.673917	−	0.673917i	0.958617	+	0.284699i	$0.0918938\pi$
$314$	3.16915			0.178845
$315$		0			0
$316$	9.25544			0.520659
$317$	14.2798	−	14.2798i	0.802034	−	0.802034i	−0.181379	−	0.983413i	$-0.558056\pi$
$317$	14.2798	−	14.2798i	0.802034	−	0.802034i	0.983413	+	0.181379i	$0.0580561\pi$
$318$	12.3043	−	19.8614i	0.689992	−	1.11377i
$319$			15.6060i			0.873767i
$320$		0			0
$321$	4.74456	+	20.1947i	0.264816	+	1.12716i
$322$	−6.18334	−	6.18334i	−0.344584	−	0.344584i
$323$	−12.0389	−	12.0389i	−0.669861	−	0.669861i
$324$	31.3793	+	23.7446i	1.74329	+	1.31914i
$325$		0			0
$326$			3.16915i			0.175523i
$327$	−3.86905	−	2.39691i	−0.213959	−	0.132550i
$328$	−22.6274	+	22.6274i	−1.24939	+	1.24939i
$329$	−7.72049			−0.425644
$330$		0			0
$331$	30.9783			1.70272			0.851359	−	0.524583i	$-0.175779\pi$
$331$	30.9783			1.70272			0.851359	+	0.524583i	$0.175779\pi$
$332$	−30.3058	+	30.3058i	−1.66325	+	1.66325i
$333$	−6.43943	+	19.1817i	−0.352879	+	1.05115i
$334$			31.4891i			1.72301i
$335$		0			0
$336$	10.7446	−	2.52434i	0.586164	−	0.137714i
$337$	4.76913	+	4.76913i	0.259791	+	0.259791i	0.824969	−	0.565178i	$-0.191193\pi$
$337$	4.76913	+	4.76913i	0.259791	+	0.259791i	−0.565178	+	0.824969i	$0.691193\pi$
$338$	−2.90544	−	2.90544i	−0.158035	−	0.158035i
$339$	−2.67181	+	0.627719i	−0.145113	+	0.0340930i
$340$		0			0
$341$			39.3947i			2.13334i
$342$	−9.64054	+	28.7170i	−0.521301	+	1.55284i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	47.9075			2.58300
$345$		0			0
$346$	−1.25544			−0.0674927
$347$	−4.69042	+	4.69042i	−0.251795	+	0.251795i	−0.821706	−	0.569911i	$-0.806978\pi$
$347$	−4.69042	+	4.69042i	−0.251795	+	0.251795i	0.569911	+	0.821706i	$0.306978\pi$
$348$	17.2004	+	10.6559i	0.922040	+	0.571214i
$349$		−	35.7228i		−	1.91220i	−0.293043	−	0.956099i	$-0.594668\pi$
$349$		−	35.7228i		−	1.91220i	0.293043	−	0.956099i	$-0.405332\pi$
$350$		0			0
$351$	13.4891	−	11.1846i	0.719996	−	0.596989i
$352$	−16.9706	−	16.9706i	−0.904534	−	0.904534i
$353$	−0.768795	−	0.768795i	−0.0409188	−	0.0409188i	0.686351	−	0.727270i	$-0.259211\pi$
$353$	−0.768795	−	0.768795i	−0.0409188	−	0.0409188i	−0.727270	+	0.686351i	$0.759211\pi$
$354$	5.34363	+	22.7446i	0.284011	+	1.20886i
$355$		0			0
$356$		−	74.4405i		−	3.94534i
$357$	3.88253	−	6.26709i	0.205485	−	0.331690i
$358$	15.1951	−	15.1951i	0.803086	−	0.803086i
$359$	36.2256			1.91191			0.955957	−	0.293508i	$-0.0948226\pi$
$359$	36.2256			1.91191			0.955957	+	0.293508i	$0.0948226\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−10.7099	+	10.7099i	−0.562898	+	0.562898i
$363$	−21.0864	+	34.0372i	−1.10675	+	1.78649i
$364$		−	14.7446i		−	0.772825i
$365$		0			0
$366$	−4.74456	−	20.1947i	−0.248002	−	1.05559i
$367$	7.15369	+	7.15369i	0.373420	+	0.373420i	0.868721	−	0.495302i	$-0.164942\pi$
$367$	7.15369	+	7.15369i	0.373420	+	0.373420i	−0.495302	+	0.868721i	$0.664942\pi$
$368$	15.6088	+	15.6088i	0.813667	+	0.813667i
$369$	14.3537	−	7.13859i	0.747226	−	0.371620i
$370$		0			0
$371$			5.34363i			0.277427i
$372$	43.4197	+	26.8990i	2.25121	+	1.39465i
$373$	−11.3137	+	11.3137i	−0.585802	+	0.585802i	−0.936492	−	0.350690i	$-0.885947\pi$
$373$	−11.3137	+	11.3137i	−0.585802	+	0.585802i	0.350690	+	0.936492i	$0.385947\pi$
$374$	−62.7586			−3.24517
$375$		0			0
$376$	46.2337			2.38432
$377$	6.37111	−	6.37111i	0.328129	−	0.328129i
$378$	−13.0600	−	1.21981i	−0.671734	−	0.0627402i
$379$			12.0000i			0.616399i	0.951322	+	0.308199i	$0.0997264\pi$
$379$			12.0000i			0.616399i	−0.951322	+	0.308199i	$0.900274\pi$
$380$		0			0
$381$	−24.8614	+	5.84096i	−1.27369	+	0.299242i
$382$	0.887728	+	0.887728i	0.0454201	+	0.0454201i
$383$	9.17227	+	9.17227i	0.468681	+	0.468681i	0.901487	−	0.432806i	$-0.142477\pi$
$383$	9.17227	+	9.17227i	0.468681	+	0.468681i	−0.432806	+	0.901487i	$0.642477\pi$
$384$	23.9538	−	5.62772i	1.22239	−	0.287188i
$385$		0			0
$386$		−	6.33830i		−	0.322611i
$387$	−22.7521	−	7.63807i	−1.15656	−	0.388265i
$388$	10.4260	−	10.4260i	0.529299	−	0.529299i
$389$	3.66648			0.185898			0.0929490	−	0.995671i	$-0.470371\pi$
$389$	3.66648			0.185898			0.0929490	+	0.995671i	$0.470371\pi$
$390$		0			0
$391$	14.7446			0.745665
$392$	−4.23447	+	4.23447i	−0.213873	+	0.213873i
$393$	17.2004	+	10.6559i	0.867647	+	0.537517i
$394$			5.48913i			0.276538i
$395$		0			0
$396$	34.1168	+	68.5996i	1.71444	+	3.44726i
$397$	−25.0120	−	25.0120i	−1.25532	−	1.25532i	−0.953305	−	0.302011i	$-0.902342\pi$
$397$	−25.0120	−	25.0120i	−1.25532	−	1.25532i	−0.302011	−	0.953305i	$-0.597658\pi$
$398$	2.24093	+	2.24093i	0.112327	+	0.112327i
$399$	−1.58457	−	6.74456i	−0.0793279	−	0.337650i
$400$		0			0
$401$			3.66648i			0.183095i	0.995801	+	0.0915477i	$0.0291814\pi$
$401$			3.66648i			0.183095i	−0.995801	+	0.0915477i	$0.970819\pi$
$402$	−2.89079	+	4.66624i	−0.144179	+	0.232731i
$403$	16.0828	−	16.0828i	0.801143	−	0.801143i
$404$	−74.4405			−3.70355
$405$		0			0
$406$	−6.74456			−0.334727
$407$	−27.8563	+	27.8563i	−1.38078	+	1.38078i
$408$	−23.2503	+	37.5301i	−1.15106	+	1.85802i
$409$		−	28.7446i		−	1.42133i	−0.703532	−	0.710664i	$-0.748395\pi$
$409$		−	28.7446i		−	1.42133i	0.703532	−	0.710664i	$-0.251605\pi$
$410$		0			0
$411$	1.48913	+	6.33830i	0.0734531	+	0.312645i
$412$	−31.2779	−	31.2779i	−1.54095	−	1.54095i
$413$	−3.77852	−	3.77852i	−0.185929	−	0.185929i
$414$	−11.6819	−	23.4891i	−0.574135	−	1.15443i
$415$		0			0
$416$			13.8564i			0.679366i
$417$	15.8203	+	9.80082i	0.774722	+	0.479948i
$418$	−41.7039	+	41.7039i	−2.03981	+	2.03981i
$419$	−18.0202			−0.880345			−0.440173	−	0.897913i	$-0.645083\pi$
$419$	−18.0202			−0.880345			−0.440173	+	0.897913i	$0.645083\pi$
$420$		0			0
$421$	5.37228			0.261829			0.130914	−	0.991394i	$-0.458209\pi$
$421$	5.37228			0.261829			0.130914	+	0.991394i	$0.458209\pi$
$422$	−27.4392	+	27.4392i	−1.33572	+	1.33572i
$423$	−21.9572	−	7.37121i	−1.06760	−	0.358400i
$424$		−	32.0000i		−	1.55406i
$425$		0			0
$426$	36.2337	−	8.51278i	1.75553	−	0.412445i
$427$	3.35491	+	3.35491i	0.162356	+	0.162356i
$428$	37.0286	+	37.0286i	1.78984	+	1.78984i
$429$	33.2125	−	7.80298i	1.60352	−	0.376732i
$430$		0			0
$431$			22.8665i			1.10144i	0.834690	+	0.550721i	$0.185647\pi$
$431$			22.8665i			1.10144i	−0.834690	+	0.550721i	$0.814353\pi$
$432$	32.9679	+	3.07921i	1.58617	+	0.148149i
$433$	10.4260	−	10.4260i	0.501041	−	0.501041i	−0.410721	−	0.911761i	$-0.634723\pi$
$433$	10.4260	−	10.4260i	0.501041	−	0.501041i	0.911761	+	0.410721i	$0.134723\pi$
$434$	−17.0256			−0.817253
$435$		0			0
$436$	−11.4891			−0.550229
$437$	9.79796	−	9.79796i	0.468700	−	0.468700i
$438$	4.66624	+	2.89079i	0.222962	+	0.138127i
$439$			30.7446i			1.46736i	0.679496	+	0.733679i	$0.262198\pi$
$439$			30.7446i			1.46736i	−0.679496	+	0.733679i	$0.737802\pi$
$440$		0			0
$441$	2.68614	−	1.33591i	0.127911	−	0.0636146i
$442$	25.6211	+	25.6211i	1.21867	+	1.21867i
$443$	−3.56995	−	3.56995i	−0.169614	−	0.169614i	0.617196	−	0.786809i	$-0.288269\pi$
$443$	−3.56995	−	3.56995i	−0.169614	−	0.169614i	−0.786809	+	0.617196i	$0.788269\pi$
$444$	11.6819	+	49.7228i	0.554400	+	2.35974i
$445$		0			0
$446$			14.8511i			0.703219i
$447$		0			0
$448$	−1.67746	+	1.67746i	−0.0792524	+	0.0792524i
$449$	−31.3793			−1.48088			−0.740440	−	0.672122i	$-0.765383\pi$
$449$	−31.3793			−1.48088			−0.740440	+	0.672122i	$0.765383\pi$
$450$		0			0
$451$	31.2119			1.46971
$452$	−4.89898	+	4.89898i	−0.230429	+	0.230429i
$453$	9.22824	−	14.8960i	0.433580	−	0.699876i
$454$			58.4674i			2.74401i
$455$		0			0
$456$	9.48913	+	40.3894i	0.444369	+	1.89141i
$457$	−25.6211	−	25.6211i	−1.19850	−	1.19850i	−0.974615	−	0.223889i	$-0.928125\pi$
$457$	−25.6211	−	25.6211i	−1.19850	−	1.19850i	−0.223889	−	0.974615i	$-0.571875\pi$
$458$	30.3058	+	30.3058i	1.41610	+	1.41610i
$459$	17.0256	−	14.1168i	0.794685	−	0.658918i
$460$		0			0
$461$		−	6.33830i		−	0.295204i	−0.989047	−	0.147602i	$-0.952845\pi$
$461$		−	6.33830i		−	0.295204i	0.989047	−	0.147602i	$-0.0471554\pi$
$462$	−21.7099	−	13.4495i	−1.01003	−	0.625727i
$463$	13.4196	−	13.4196i	0.623664	−	0.623664i	−0.322802	−	0.946466i	$-0.604625\pi$
$463$	13.4196	−	13.4196i	0.623664	−	0.623664i	0.946466	+	0.322802i	$0.104625\pi$
$464$	17.0256			0.790392
$465$		0			0
$466$	−68.4674			−3.17169
$467$	−24.2209	+	24.2209i	−1.12081	+	1.12081i	−0.129188	+	0.991620i	$0.541237\pi$
$467$	−24.2209	+	24.2209i	−1.12081	+	1.12081i	−0.991620	+	0.129188i	$0.958763\pi$
$468$	14.0775	−	41.9338i	0.650733	−	1.93839i
$469$		−	1.25544i		−	0.0579707i
$470$		0			0
$471$	−2.11684	+	0.497333i	−0.0975390	+	0.0229159i
$472$	22.6274	+	22.6274i	1.04151	+	1.04151i
$473$	−33.0415	−	33.0415i	−1.51925	−	1.51925i
$474$	−9.01011	+	2.11684i	−0.413848	+	0.0972299i
$475$		0			0
$476$		−	18.6101i		−	0.852994i
$477$	−5.10188	+	15.1974i	−0.233599	+	0.695840i
$478$	19.9642	−	19.9642i	0.913143	−	0.913143i
$479$	−35.0458			−1.60128			−0.800641	−	0.599144i	$-0.795508\pi$
$479$	−35.0458			−1.60128			−0.800641	+	0.599144i	$0.795508\pi$
$480$		0			0
$481$	22.7446			1.03706
$482$	20.5078	−	20.5078i	0.934105	−	0.934105i
$483$	5.10053	+	3.15983i	0.232082	+	0.143777i
$484$			101.073i			4.59424i
$485$		0			0
$486$	−35.9783	−	15.9383i	−1.63201	−	0.722977i
$487$	29.5025	+	29.5025i	1.33689	+	1.33689i	0.899060	+	0.437825i	$0.144251\pi$
$487$	29.5025	+	29.5025i	1.33689	+	1.33689i	0.437825	+	0.899060i	$0.355749\pi$
$488$	−20.0907	−	20.0907i	−0.909463	−	0.909463i
$489$	−0.497333	−	2.11684i	−0.0224902	−	0.0957270i
$490$		0			0
$491$		−	38.8974i		−	1.75542i	−0.479196	−	0.877708i	$-0.659072\pi$
$491$		−	38.8974i		−	1.75542i	0.479196	−	0.877708i	$-0.340928\pi$
$492$	21.3117	−	34.4009i	0.960806	−	1.55091i
$493$	8.04142	−	8.04142i	0.362167	−	0.362167i
$494$	34.0511			1.53203
$495$		0			0
$496$	42.9783			1.92978
$497$	−6.01944	+	6.01944i	−0.270009	+	0.270009i
$498$	22.5711	−	36.4338i	1.01144	−	1.63264i
$499$		−	7.37228i		−	0.330029i	−0.986291	−	0.165014i	$-0.947233\pi$
$499$		−	7.37228i		−	0.330029i	0.986291	−	0.165014i	$-0.0527670\pi$
$500$		0			0
$501$	−4.94158	−	21.0333i	−0.220773	−	0.939697i
$502$	−32.1657	−	32.1657i	−1.43562	−	1.43562i
$503$	−24.6380	−	24.6380i	−1.09855	−	1.09855i	−0.994580	−	0.103974i	$-0.966844\pi$
$503$	−24.6380	−	24.6380i	−1.09855	−	1.09855i	−0.103974	−	0.994580i	$-0.533156\pi$
$504$	−16.0858	+	8.00000i	−0.716518	+	0.356348i
$505$		0			0
$506$		−	51.0767i		−	2.27063i
$507$	2.39665	+	1.48475i	0.106439	+	0.0659400i
$508$	−45.5853	+	45.5853i	−2.02252	+	2.02252i
$509$	−11.6819			−0.517792			−0.258896	−	0.965905i	$-0.583359\pi$
$509$	−11.6819			−0.517792			−0.258896	+	0.965905i	$0.583359\pi$
$510$		0			0
$511$	−1.25544			−0.0555373
$512$	35.4521	−	35.4521i	1.56678	−	1.56678i
$513$	1.93288	−	20.6945i	0.0853386	−	0.913686i
$514$		−	17.4891i		−	0.771412i
$515$		0			0
$516$	−58.9783	+	13.8564i	−2.59637	+	0.609994i
$517$	−31.8870	−	31.8870i	−1.40239	−	1.40239i
$518$	−12.0389	−	12.0389i	−0.528958	−	0.528958i
$519$	0.838574	−	0.197015i	0.0368093	−	0.00864801i
$520$		0			0
$521$			6.33830i			0.277686i	0.990314	+	0.138843i	$0.0443383\pi$
$521$			6.33830i			0.277686i	−0.990314	+	0.138843i	$0.955662\pi$
$522$	−19.1817	−	6.43943i	−0.839558	−	0.281846i
$523$	−22.9579	+	22.9579i	−1.00388	+	1.00388i	−0.00388650	+	0.999992i	$0.501237\pi$
$523$	−22.9579	+	22.9579i	−1.00388	+	1.00388i	−0.999992	+	0.00388650i	$0.998763\pi$
$524$	51.0767			2.23129
$525$		0			0
$526$	−38.2337			−1.66707
$527$	20.2993	−	20.2993i	0.884249	−	0.884249i
$528$	54.8030	+	33.9510i	2.38499	+	1.47753i
$529$		−	11.0000i		−	0.478261i
$530$		0			0
$531$	−7.13859	−	14.3537i	−0.309789	−	0.622899i
$532$	−12.3667	−	12.3667i	−0.536164	−	0.536164i
$533$	−12.7422	−	12.7422i	−0.551927	−	0.551927i
$534$	17.0256	+	72.4674i	0.736768	+	3.13597i
$535$		0			0
$536$			7.51811i			0.324733i
$537$	−7.76506	+	12.5342i	−0.335087	+	0.540890i
$538$	9.53825	−	9.53825i	0.411223	−	0.411223i
$539$	5.84096			0.251588
$540$		0			0
$541$	−18.6277			−0.800868			−0.400434	−	0.916326i	$-0.631141\pi$
$541$	−18.6277			−0.800868			−0.400434	+	0.916326i	$0.631141\pi$
$542$	38.3576	−	38.3576i	1.64760	−	1.64760i
$543$	5.47299	−	8.83438i	0.234869	−	0.379120i
$544$			17.4891i			0.749840i
$545$		0			0
$546$	3.37228	+	14.3537i	0.144320	+	0.614283i
$547$	7.43231	+	7.43231i	0.317783	+	0.317783i	0.847915	−	0.530132i	$-0.177858\pi$
$547$	7.43231	+	7.43231i	0.317783	+	0.317783i	−0.530132	+	0.847915i	$0.677858\pi$
$548$	11.6218	+	11.6218i	0.496457	+	0.496457i
$549$	6.33830	+	12.7446i	0.270512	+	0.543925i
$550$		0			0
$551$		−	10.6873i		−	0.455293i
$552$	−30.5442	−	18.9225i	−1.30005	−	0.805394i
$553$	1.49683	−	1.49683i	0.0636519	−	0.0636519i
$554$	23.3639			0.992635
$555$		0			0
$556$	46.9783			1.99232
$557$	7.55703	−	7.55703i	0.320202	−	0.320202i	−0.528643	−	0.848844i	$-0.677299\pi$
$557$	7.55703	−	7.55703i	0.320202	−	0.320202i	0.848844	+	0.528643i	$0.177299\pi$
$558$	−48.4210	−	16.2553i	−2.04982	−	0.688142i
$559$			26.9783i			1.14106i
$560$		0			0
$561$	41.9198	−	9.84868i	1.76986	−	0.415812i
$562$	46.4730	+	46.4730i	1.96035	+	1.96035i
$563$	11.4132	+	11.4132i	0.481009	+	0.481009i	0.905454	−	0.424445i	$-0.139531\pi$
$563$	11.4132	+	11.4132i	0.481009	+	0.481009i	−0.424445	+	0.905454i	$0.639531\pi$
$564$	−56.9176	+	13.3723i	−2.39666	+	0.563075i
$565$		0			0
$566$			42.5639i			1.78909i
$567$	8.91490	−	1.23473i	0.374391	−	0.0518536i
$568$	36.0471	−	36.0471i	1.51250	−	1.51250i
$569$	−17.0256			−0.713748			−0.356874	−	0.934152i	$-0.616158\pi$
$569$	−17.0256			−0.713748			−0.356874	+	0.934152i	$0.616158\pi$
$570$		0			0
$571$	30.9783			1.29640			0.648200	−	0.761470i	$-0.275522\pi$
$571$	30.9783			1.29640			0.648200	+	0.761470i	$0.275522\pi$
$572$	60.8978	−	60.8978i	2.54626	−	2.54626i
$573$	−0.732272	−	0.453650i	−0.0305911	−	0.0189515i
$574$			13.4891i			0.563025i
$575$		0			0
$576$	−6.37228	+	3.16915i	−0.265512	+	0.132048i
$577$	30.9993	+	30.9993i	1.29052	+	1.29052i	0.934466	+	0.356053i	$0.115878\pi$
$577$	30.9993	+	30.9993i	1.29052	+	1.29052i	0.356053	+	0.934466i	$0.384122\pi$
$578$	1.99354	+	1.99354i	0.0829203	+	0.0829203i
$579$	0.994667	+	4.23369i	0.0413369	+	0.175946i
$580$		0			0
$581$			9.80240i			0.406672i
$582$	−7.76506	+	12.5342i	−0.321872	+	0.519559i
$583$	−22.0702	+	22.0702i	−0.914053	+	0.914053i
$584$	7.51811			0.311102
$585$		0			0
$586$	1.25544			0.0518616
$587$	−19.3874	+	19.3874i	−0.800202	+	0.800202i	−0.983127	−	0.182925i	$-0.941443\pi$
$587$	−19.3874	+	19.3874i	−0.800202	+	0.800202i	0.182925	+	0.983127i	$0.441443\pi$
$588$	3.98825	−	6.43773i	0.164472	−	0.265488i
$589$		−	26.9783i		−	1.11162i
$590$		0			0
$591$	−0.861407	−	3.66648i	−0.0354335	−	0.150819i
$592$	30.3902	+	30.3902i	1.24903	+	1.24903i
$593$	16.5862	+	16.5862i	0.681113	+	0.681113i	0.960251	−	0.279138i	$-0.0900486\pi$
$593$	16.5862	+	16.5862i	0.681113	+	0.681113i	−0.279138	+	0.960251i	$0.590049\pi$
$594$	−48.9022	−	58.9783i	−2.00648	−	2.41991i
$595$		0			0
$596$		0			0
$597$	−1.84850	−	1.14517i	−0.0756542	−	0.0468686i
$598$	−20.8520	+	20.8520i	−0.852700	+	0.852700i
$599$	−23.8612			−0.974942			−0.487471	−	0.873139i	$-0.662080\pi$
$599$	−23.8612			−0.974942			−0.487471	+	0.873139i	$0.662080\pi$
$600$		0			0
$601$	−10.2337			−0.417441			−0.208720	−	0.977975i	$-0.566930\pi$
$601$	−10.2337			−0.417441			−0.208720	+	0.977975i	$0.566930\pi$
$602$	14.2798	−	14.2798i	0.582002	−	0.582002i
$603$	1.19864	−	3.57049i	0.0488124	−	0.145401i
$604$		−	44.2337i		−	1.79984i
$605$		0			0
$606$	72.4674	−	17.0256i	2.94379	−	0.691616i
$607$	18.4674	+	18.4674i	0.749569	+	0.749569i	0.974398	−	0.224830i	$-0.0721825\pi$
$607$	18.4674	+	18.4674i	0.749569	+	0.749569i	−0.224830	+	0.974398i	$0.572183\pi$
$608$	11.6218	+	11.6218i	0.471325	+	0.471325i
$609$	4.50506	−	1.05842i	0.182554	−	0.0428894i
$610$		0			0
$611$			26.0357i			1.05329i
$612$	17.7682	−	52.9275i	0.718237	−	2.13947i
$613$	22.6274	−	22.6274i	0.913913	−	0.913913i	−0.0826647	−	0.996577i	$-0.526343\pi$
$613$	22.6274	−	22.6274i	0.913913	−	0.913913i	0.996577	+	0.0826647i	$0.0263430\pi$
$614$	48.9022			1.97353
$615$		0			0
$616$	−34.9783			−1.40931
$617$	−10.9184	+	10.9184i	−0.439559	+	0.439559i	−0.891864	−	0.452304i	$-0.850602\pi$
$617$	−10.9184	+	10.9184i	−0.439559	+	0.439559i	0.452304	+	0.891864i	$0.350602\pi$
$618$	37.6026	+	23.2952i	1.51260	+	0.937070i
$619$		−	26.7446i		−	1.07495i	−0.843278	−	0.537477i	$-0.819377\pi$
$619$		−	26.7446i		−	1.07495i	0.843278	−	0.537477i	$-0.180623\pi$
$620$		0			0
$621$	11.4891	+	13.8564i	0.461043	+	0.556038i
$622$	30.3902	+	30.3902i	1.21854	+	1.21854i
$623$	−12.0389	−	12.0389i	−0.482328	−	0.482328i
$624$	−8.51278	−	36.2337i	−0.340784	−	1.45051i
$625$		0			0
$626$			42.5639i			1.70120i
$627$	21.3117	−	34.4009i	0.851107	−	1.37384i
$628$	−3.88140	+	3.88140i	−0.154885	+	0.154885i
$629$	28.7075			1.14464
$630$		0			0
$631$	−45.0951			−1.79521			−0.897604	−	0.440803i	$-0.854694\pi$
$631$	−45.0951			−1.79521			−0.897604	+	0.440803i	$0.854694\pi$
$632$	−8.96370	+	8.96370i	−0.356557	+	0.356557i
$633$	14.0221	−	22.6341i	0.557327	−	0.899625i
$634$			50.9783i			2.02460i
$635$		0			0
$636$	9.25544	+	39.3947i	0.367002	+	1.56210i
$637$	−2.38456	−	2.38456i	−0.0944798	−	0.0944798i
$638$	−27.8563	−	27.8563i	−1.10284	−	1.10284i
$639$	−22.8665	+	11.3723i	−0.904585	+	0.449880i
$640$		0			0
$641$		−	17.0256i		−	0.672469i	−0.941778	−	0.336234i	$-0.890847\pi$
$641$		−	17.0256i		−	0.672469i	0.941778	−	0.336234i	$-0.109153\pi$
$642$	−44.5160	−	27.5781i	−1.75691	−	1.08842i
$643$	−8.92915	+	8.92915i	−0.352131	+	0.352131i	−0.860902	−	0.508771i	$-0.830100\pi$
$643$	−8.92915	+	8.92915i	−0.352131	+	0.352131i	0.508771	+	0.860902i	$0.330100\pi$
$644$	15.1460			0.596837
$645$		0			0
$646$	42.9783			1.69096
$647$	−12.6646	+	12.6646i	−0.497896	+	0.497896i	−0.910782	−	0.412887i	$-0.864521\pi$
$647$	−12.6646	+	12.6646i	−0.497896	+	0.497896i	0.412887	+	0.910782i	$0.364521\pi$
$648$	−53.3863	+	7.39408i	−2.09721	+	0.290467i
$649$		−	31.2119i		−	1.22518i
$650$		0			0
$651$	11.3723	−	2.67181i	0.445715	−	0.104717i
$652$	−3.88140	−	3.88140i	−0.152007	−	0.152007i
$653$	−16.5207	−	16.5207i	−0.646506	−	0.646506i	0.305641	−	0.952147i	$-0.401129\pi$
$653$	−16.5207	−	16.5207i	−0.646506	−	0.646506i	−0.952147	+	0.305641i	$0.901129\pi$
$654$	11.1846	−	2.62772i	0.437352	−	0.102752i
$655$		0			0
$656$		−	34.0511i		−	1.32947i
$657$	−3.57049	−	1.19864i	−0.139298	−	0.0467634i
$658$	13.7809	−	13.7809i	0.537235	−	0.537235i
$659$	−4.84630			−0.188785			−0.0943924	−	0.995535i	$-0.530091\pi$
$659$	−4.84630			−0.188785			−0.0943924	+	0.995535i	$0.530091\pi$
$660$		0			0
$661$	42.2337			1.64270			0.821350	−	0.570425i	$-0.193221\pi$
$661$	42.2337			1.64270			0.821350	+	0.570425i	$0.193221\pi$
$662$	−55.2954	+	55.2954i	−2.14912	+	2.14912i
$663$	−21.1344	−	13.0930i	−0.820792	−	0.508490i
$664$		−	58.7011i		−	2.27804i
$665$		0			0
$666$	−22.7446	−	45.7330i	−0.881334	−	1.77212i
$667$	6.54458	+	6.54458i	0.253407	+	0.253407i
$668$	−38.5661	−	38.5661i	−1.49217	−	1.49217i
$669$	−2.33057	−	9.91983i	−0.0901052	−	0.383523i
$670$		0			0
$671$			27.7128i			1.06984i
$672$	−3.74801	+	6.04995i	−0.144583	+	0.233382i
$673$	−19.0765	+	19.0765i	−0.735345	+	0.735345i	−0.971673	−	0.236328i	$-0.924056\pi$
$673$	−19.0765	+	19.0765i	−0.735345	+	0.735345i	0.236328	+	0.971673i	$0.424056\pi$
$674$	−17.0256			−0.655800
$675$		0			0
$676$	7.11684			0.273725
$677$	3.42685	−	3.42685i	0.131704	−	0.131704i	−0.638181	−	0.769886i	$-0.720313\pi$
$677$	3.42685	−	3.42685i	0.131704	−	0.131704i	0.769886	+	0.638181i	$0.220313\pi$
$678$	3.64866	−	5.88959i	0.140126	−	0.226188i
$679$		−	3.37228i		−	0.129416i
$680$		0			0
$681$	−9.17527	−	39.0535i	−0.351597	−	1.49653i
$682$	−70.3187	−	70.3187i	−2.69264	−	2.69264i
$683$	−27.6477	−	27.6477i	−1.05791	−	1.05791i	−0.998217	−	0.0596940i	$-0.980988\pi$
$683$	−27.6477	−	27.6477i	−1.05791	−	1.05791i	−0.0596940	−	0.998217i	$-0.519012\pi$
$684$	−23.3639	−	46.9783i	−0.893339	−	1.79626i
$685$		0			0
$686$			2.52434i			0.0963797i
$687$	−24.9987	−	15.4870i	−0.953761	−	0.590865i
$688$	−36.0471	+	36.0471i	−1.37428	+	1.37428i
$689$	18.0202			0.686516
$690$		0			0
$691$	−4.00000			−0.152167			−0.0760836	−	0.997101i	$-0.524242\pi$
$691$	−4.00000			−0.152167			−0.0760836	+	0.997101i	$0.524242\pi$
$692$	1.53759	−	1.53759i	0.0584504	−	0.0584504i
$693$	16.6118	+	5.57671i	0.631030	+	0.211842i
$694$		−	16.7446i		−	0.635615i
$695$		0			0
$696$	−26.9783	+	6.33830i	−1.02261	+	0.240252i
$697$	−16.0828	−	16.0828i	−0.609181	−	0.609181i
$698$	63.7644	+	63.7644i	2.41352	+	2.41352i
$699$	45.7330	−	10.7446i	1.72978	−	0.406397i
$700$		0			0
$701$			43.0612i			1.62640i	0.581984	+	0.813200i	$0.302276\pi$
$701$			43.0612i			1.62640i	−0.581984	+	0.813200i	$0.697724\pi$
$702$	−4.11354	+	44.0420i	−0.155255	+	1.66226i
$703$	19.0765	−	19.0765i	0.719484	−	0.719484i
$704$	−13.8564			−0.522233
$705$		0			0
$706$	2.74456			0.103293
$707$	−12.0389	+	12.0389i	−0.452769	+	0.452769i
$708$	−34.4009	−	21.3117i	−1.29286	−	0.800943i
$709$			32.3505i			1.21495i	0.794339	+	0.607475i	$0.207817\pi$
$709$			32.3505i			1.21495i	−0.794339	+	0.607475i	$0.792183\pi$
$710$		0			0
$711$	5.68614	−	2.82791i	0.213247	−	0.106055i
$712$	72.0941	+	72.0941i	2.70184	+	2.70184i
$713$	16.5207	+	16.5207i	0.618706	+	0.618706i
$714$	4.25639	+	18.1168i	0.159291	+	0.678006i
$715$		0			0
$716$			37.2203i			1.39099i
$717$	−10.2022	+	16.4682i	−0.381008	+	0.615015i
$718$	−64.6618	+	64.6618i	−2.41316	+	2.41316i
$719$	−5.34363			−0.199284			−0.0996419	−	0.995023i	$-0.531770\pi$
$719$	−5.34363			−0.199284			−0.0996419	+	0.995023i	$0.531770\pi$
$720$		0			0
$721$	−10.1168			−0.376771
$722$	−5.35493	+	5.35493i	−0.199290	+	0.199290i
$723$	−10.4800	+	16.9166i	−0.389755	+	0.629134i
$724$		−	26.2337i		−	0.974967i
$725$		0			0
$726$	−23.1168	−	98.3943i	−0.857947	−	3.65175i
$727$	18.7460	+	18.7460i	0.695251	+	0.695251i	0.963382	−	0.268131i	$-0.0864060\pi$
$727$	18.7460	+	18.7460i	0.695251	+	0.695251i	−0.268131	+	0.963382i	$0.586406\pi$
$728$	14.2798	+	14.2798i	0.529245	+	0.529245i
$729$	26.5330	+	5.00000i	0.982704	+	0.185185i
$730$		0			0
$731$			34.0511i			1.25943i
$732$	30.5442	+	18.9225i	1.12895	+	0.699395i
$733$	21.4611	−	21.4611i	0.792683	−	0.792683i	−0.189247	−	0.981930i	$-0.560605\pi$
$733$	21.4611	−	21.4611i	0.792683	−	0.792683i	0.981930	+	0.189247i	$0.0606047\pi$
$734$	−25.5383			−0.942637
$735$		0			0
$736$	−14.2337			−0.524661
$737$	5.18519	−	5.18519i	0.190999	−	0.190999i
$738$	−12.8789	+	38.3633i	−0.474078	+	1.41217i
$739$		−	15.3723i		−	0.565479i	−0.959197	−	0.282739i	$-0.908757\pi$
$739$		−	15.3723i		−	0.565479i	0.959197	−	0.282739i	$-0.0912431\pi$
$740$		0			0
$741$	−22.7446	+	5.34363i	−0.835542	+	0.196303i
$742$	−9.53825	−	9.53825i	−0.350160	−	0.350160i
$743$	23.4521	+	23.4521i	0.860373	+	0.860373i	0.991381	−	0.131008i	$-0.0418214\pi$
$743$	23.4521	+	23.4521i	0.860373	+	0.860373i	−0.131008	+	0.991381i	$0.541821\pi$
$744$	−68.1022	+	16.0000i	−2.49675	+	0.586588i
$745$		0			0
$746$		−	40.3894i		−	1.47876i
$747$	−9.35893	+	27.8782i	−0.342425	+	1.02001i
$748$	76.8633	−	76.8633i	2.81040	−	2.81040i
$749$	11.9769			0.437626
$750$		0			0
$751$	−19.3723			−0.706905			−0.353452	−	0.935453i	$-0.614992\pi$
$751$	−19.3723			−0.706905			−0.353452	+	0.935453i	$0.614992\pi$
$752$	−34.7876	+	34.7876i	−1.26857	+	1.26857i
$753$	26.5329	+	16.4374i	0.966914	+	0.599013i
$754$			22.7446i			0.828308i
$755$		0			0
$756$	17.4891	−	14.5012i	0.636073	−	0.527404i
$757$	−22.6274	−	22.6274i	−0.822407	−	0.822407i	0.164045	−	0.986453i	$-0.447546\pi$
$757$	−22.6274	−	22.6274i	−0.822407	−	0.822407i	−0.986453	+	0.164045i	$0.947546\pi$
$758$	−21.4197	−	21.4197i	−0.777999	−	0.777999i
$759$	8.01544	+	34.1168i	0.290942	+	1.23836i
$760$		0			0
$761$		−	0.994667i		−	0.0360566i	−0.999837	−	0.0180283i	$-0.994261\pi$
$761$		−	0.994667i		−	0.0360566i	0.999837	−	0.0180283i	$-0.00573890\pi$
$762$	33.9510	−	54.8030i	1.22992	−	1.98530i
$763$	−1.85808	+	1.85808i	−0.0672669	+	0.0672669i
$764$	−2.17448			−0.0786700
$765$		0			0
$766$	−32.7446			−1.18311
$767$	−12.7422	+	12.7422i	−0.460095	+	0.460095i
$768$	−28.3837	+	45.8164i	−1.02421	+	1.65326i
$769$			18.2337i			0.657524i	0.944413	+	0.328762i	$0.106631\pi$
$769$			18.2337i			0.657524i	−0.944413	+	0.328762i	$0.893369\pi$
$770$		0			0
$771$	2.74456	+	11.6819i	0.0988430	+	0.420714i
$772$	7.76280	+	7.76280i	0.279389	+	0.279389i
$773$	34.9307	+	34.9307i	1.25637	+	1.25637i	0.952813	+	0.303558i	$0.0981747\pi$
$773$	34.9307	+	34.9307i	1.25637	+	1.25637i	0.303558	+	0.952813i	$0.401825\pi$
$774$	54.2458	−	26.9783i	1.94983	−	0.969713i
$775$		0			0
$776$			20.1947i			0.724948i
$777$	9.93068	+	6.15216i	0.356261	+	0.220707i
$778$	−6.54458	+	6.54458i	−0.234635	+	0.234635i
$779$	−21.3745			−0.765822
$780$		0			0
$781$	−49.7228			−1.77922
$782$	−26.3187	+	26.3187i	−0.941155	+	0.941155i
$783$	13.8230	+	1.29107i	0.493993	+	0.0461392i
$784$		−	6.37228i		−	0.227581i
$785$		0			0
$786$	−49.7228	+	11.6819i	−1.77355	+	0.416680i
$787$	−5.37823	−	5.37823i	−0.191713	−	0.191713i	0.604723	−	0.796436i	$-0.293284\pi$
$787$	−5.37823	−	5.37823i	−0.191713	−	0.191713i	−0.796436	+	0.604723i	$0.793284\pi$
$788$	−6.72278	−	6.72278i	−0.239489	−	0.239489i
$789$	25.5383	−	6.00000i	0.909189	−	0.213606i
$790$		0			0
$791$			1.58457i			0.0563410i
$792$	−99.4788	−	33.3958i	−3.53482	−	1.18667i
$793$	11.3137	−	11.3137i	0.401762	−	0.401762i
$794$	89.2916			3.16884
$795$		0			0
$796$	−5.48913			−0.194557
$797$	−17.7067	+	17.7067i	−0.627202	+	0.627202i	−0.947363	−	0.320161i	$-0.896263\pi$
$797$	−17.7067	+	17.7067i	−0.627202	+	0.627202i	0.320161	+	0.947363i	$0.396263\pi$
$798$	14.8673	+	9.21046i	0.526297	+	0.326047i
$799$			32.8614i			1.16255i
$800$		0			0
$801$	−22.7446	−	45.7330i	−0.803640	−	1.61590i
$802$	−6.54458	−	6.54458i	−0.231097	−	0.231097i
$803$	−5.18519	−	5.18519i	−0.182981	−	0.182981i
$804$	−2.17448	−	9.25544i	−0.0766880	−	0.326414i
$805$		0			0
$806$			57.4150i			2.02236i
$807$	−4.87428	+	7.86794i	−0.171583	+	0.276965i
$808$	72.0941	−	72.0941i	2.53626	−	2.53626i
$809$	9.01011			0.316779			0.158389	−	0.987377i	$-0.449370\pi$
$809$	9.01011			0.316779			0.158389	+	0.987377i	$0.449370\pi$
$810$		0			0
$811$	21.2554			0.746379			0.373190	−	0.927755i	$-0.378264\pi$
$811$	21.2554			0.746379			0.373190	+	0.927755i	$0.378264\pi$
$812$	8.26037	−	8.26037i	0.289882	−	0.289882i
$813$	−19.6016	+	31.6405i	−0.687460	+	1.10968i
$814$		−	99.4456i		−	3.48557i
$815$		0			0
$816$	−10.7446	−	45.7330i	−0.376135	−	1.60098i
$817$	22.6274	+	22.6274i	0.791633	+	0.791633i
$818$	51.3084	+	51.3084i	1.79395	+	1.79395i
$819$	−4.50506	−	9.05842i	−0.157419	−	0.316527i
$820$		0			0
$821$			14.3537i			0.500949i	0.968123	+	0.250474i	$0.0805866\pi$
$821$			14.3537i			0.500949i	−0.968123	+	0.250474i	$0.919413\pi$
$822$	−13.9718	−	8.65566i	−0.487321	−	0.301901i
$823$	−8.65052	+	8.65052i	−0.301538	+	0.301538i	−0.841615	−	0.540077i	$-0.818395\pi$
$823$	−8.65052	+	8.65052i	−0.301538	+	0.301538i	0.540077	+	0.841615i	$0.318395\pi$
$824$	60.5841			2.11055
$825$		0			0
$826$	13.4891			0.469347
$827$	28.7682	−	28.7682i	1.00037	−	1.00037i	0.000367902	−	1.00000i	$-0.499883\pi$
$827$	28.7682	−	28.7682i	1.00037	−	1.00037i	1.00000		0.000367902i	$-0.000117107\pi$
$828$	43.0756	+	14.4608i	1.49698	+	0.502548i
$829$			46.0000i			1.59765i	0.601566	+	0.798823i	$0.294544\pi$
$829$			46.0000i			1.59765i	−0.601566	+	0.798823i	$0.705456\pi$
$830$		0			0
$831$	−15.6060	+	3.66648i	−0.541365	+	0.127189i
$832$	5.65685	+	5.65685i	0.196116	+	0.196116i
$833$	−3.00972	−	3.00972i	−0.104281	−	0.104281i
$834$	−45.7330	+	10.7446i	−1.58361	+	0.372054i
$835$		0			0
$836$		−	102.153i		−	3.53305i
$837$	34.8939	+	3.25910i	1.20611	+	0.112651i
$838$	32.1657	−	32.1657i	1.11114	−	1.11114i
$839$	−45.7330			−1.57888			−0.789440	−	0.613828i	$-0.789629\pi$
$839$	−45.7330			−1.57888			−0.789440	+	0.613828i	$0.789629\pi$
$840$		0			0
$841$	−21.8614			−0.753842
$842$	−9.58940	+	9.58940i	−0.330472	+	0.330472i
$843$	−38.3348	−	23.7488i	−1.32032	−	0.817954i
$844$		−	67.2119i		−	2.31353i
$845$		0			0
$846$	52.3505	−	26.0357i	1.79985	−	0.895125i
$847$	16.3461	+	16.3461i	0.561658	+	0.561658i
$848$	24.0778	+	24.0778i	0.826834	+	0.826834i
$849$	−6.67954	−	28.4307i	−0.229241	−	0.975739i
$850$		0			0
$851$			23.3639i			0.800902i
$852$	−33.9510	+	54.8030i	−1.16314	+	1.87752i
$853$	−21.7397	+	21.7397i	−0.744353	+	0.744353i	−0.973412	−	0.229060i	$-0.926435\pi$
$853$	−21.7397	+	21.7397i	−0.744353	+	0.744353i	0.229060	+	0.973412i	$0.426435\pi$
$854$	−11.9769			−0.409840
$855$		0			0
$856$	−71.7228			−2.45144
$857$	14.6969	−	14.6969i	0.502038	−	0.502038i	−0.410033	−	0.912071i	$-0.634483\pi$
$857$	14.6969	−	14.6969i	0.502038	−	0.502038i	0.912071	+	0.410033i	$0.134483\pi$
$858$	−45.3554	+	73.2117i	−1.54841	+	2.49941i
$859$			28.0000i			0.955348i	0.878537	+	0.477674i	$0.158520\pi$
$859$			28.0000i			0.955348i	−0.878537	+	0.477674i	$0.841480\pi$
$860$		0			0
$861$	−2.11684	−	9.01011i	−0.0721418	−	0.307064i
$862$	−40.8162	−	40.8162i	−1.39021	−	1.39021i
$863$	19.8045	+	19.8045i	0.674152	+	0.674152i	0.958671	−	0.284518i	$-0.0918336\pi$
$863$	19.8045	+	19.8045i	0.674152	+	0.674152i	−0.284518	+	0.958671i	$0.591834\pi$
$864$	−16.4356	+	13.6277i	−0.559152	+	0.463624i
$865$		0			0
$866$			37.2203i			1.26480i
$867$	−1.64444	−	1.01875i	−0.0558480	−	0.0345985i
$868$	20.8520	−	20.8520i	0.707762	−	0.707762i
$869$	12.3644			0.419434
$870$		0			0
$871$	−4.23369			−0.143453
$872$	11.1270	−	11.1270i	0.376807	−	0.376807i
$873$	3.21972	−	9.59083i	0.108971	−	0.324600i
$874$			34.9783i			1.18316i
$875$		0			0
$876$	−9.25544	+	2.17448i	−0.312712	+	0.0734689i
$877$	−28.6148	−	28.6148i	−0.966252	−	0.966252i	0.0331972	−	0.999449i	$-0.489431\pi$
$877$	−28.6148	−	28.6148i	−0.966252	−	0.966252i	−0.999449	+	0.0331972i	$0.989431\pi$
$878$	−54.8783	−	54.8783i	−1.85205	−	1.85205i
$879$	−0.838574	+	0.197015i	−0.0282844	+	0.00664516i
$880$		0			0
$881$		0			0		1.00000			$0$
$881$		0			0		−1.00000			$\pi$
$882$	−2.41013	+	7.17926i	−0.0811535	+	0.241738i
$883$	24.7334	−	24.7334i	0.832344	−	0.832344i	−0.155493	−	0.987837i	$-0.549697\pi$
$883$	24.7334	−	24.7334i	0.832344	−	0.832344i	0.987837	+	0.155493i	$0.0496967\pi$
$884$	−62.7586			−2.11080
$885$		0			0
$886$	12.7446			0.428162
$887$	33.6672	−	33.6672i	1.13043	−	1.13043i	0.140328	−	0.990105i	$-0.455184\pi$
$887$	33.6672	−	33.6672i	1.13043	−	1.13043i	0.990105	−	0.140328i	$-0.0448156\pi$
$888$	−59.4692	−	36.8418i	−1.99566	−	1.23633i
$889$			14.7446i			0.494517i
$890$		0			0
$891$	41.9198	+	31.7205i	1.40437	+	1.06268i
$892$	−18.1888	−	18.1888i	−0.609005	−	0.609005i
$893$	21.8368	+	21.8368i	0.730742	+	0.730742i
$894$		0			0
$895$		0			0
$896$		−	14.2063i		−	0.474598i
$897$	10.6559	−	17.2004i	0.355789	−	0.574306i
$898$	56.0113	−	56.0113i	1.86912	−	1.86912i
$899$	18.0202			0.601008
$900$		0			0
$901$	22.7446			0.757731
$902$	−55.7126	+	55.7126i	−1.85503	+	1.85503i
$903$	−7.29733	+	11.7792i	−0.242840	+	0.391986i
$904$		−	9.48913i		−	0.315604i
$905$		0			0
$906$	10.1168	+	43.0612i	0.336110	+	1.43061i
$907$	10.4260	+	10.4260i	0.346189	+	0.346189i	0.858688	−	0.512499i	$-0.171280\pi$
$907$	10.4260	+	10.4260i	0.346189	+	0.346189i	−0.512499	+	0.858688i	$0.671280\pi$
$908$	−71.6076	−	71.6076i	−2.37638	−	2.37638i
$909$	−45.7330	+	22.7446i	−1.51687	+	0.754390i
$910$		0			0
$911$		−	14.8511i		−	0.492038i	−0.969265	−	0.246019i	$-0.920877\pi$
$911$		−	14.8511i		−	0.492038i	0.969265	−	0.246019i	$-0.0791226\pi$
$912$	−37.5301	−	23.2503i	−1.24275	−	0.769895i
$913$	−40.4857	+	40.4857i	−1.33988	+	1.33988i
$914$	91.4661			3.02543
$915$		0			0
$916$	−74.2337			−2.45275
$917$	8.26037	−	8.26037i	0.272781	−	0.272781i
$918$	−5.19198	+	55.5884i	−0.171361	+	1.83469i
$919$		−	5.88316i		−	0.194067i	−0.995281	−	0.0970337i	$-0.969065\pi$
$919$		−	5.88316i		−	0.194067i	0.995281	−	0.0970337i	$-0.0309355\pi$
$920$		0			0
$921$	−32.6644	+	7.67420i	−1.07633	+	0.252874i
$922$	11.3137	+	11.3137i	0.372597	+	0.372597i
$923$	20.2993	+	20.2993i	0.668158	+	0.668158i
$924$	43.0612	−	10.1168i	1.41661	−	0.332820i
$925$		0			0
$926$			47.9075i			1.57434i
$927$	−28.7725	−	9.65915i	−0.945012	−	0.317248i
$928$	−7.76280	+	7.76280i	−0.254826	+	0.254826i
$929$	−41.3841			−1.35777			−0.678884	−	0.734246i	$-0.737536\pi$
$929$	−41.3841			−1.35777			−0.678884	+	0.734246i	$0.737536\pi$
$930$		0			0
$931$	−4.00000			−0.131095
$932$	83.8551	−	83.8551i	2.74676	−	2.74676i
$933$	−25.0684	−	15.5301i	−0.820702	−	0.508434i
$934$		−	86.4674i		−	2.82930i
$935$		0			0
$936$	26.9783	+	54.2458i	0.881812	+	1.77308i
$937$	−7.15369	−	7.15369i	−0.233701	−	0.233701i	0.580535	−	0.814236i	$-0.302844\pi$
$937$	−7.15369	−	7.15369i	−0.233701	−	0.233701i	−0.814236	+	0.580535i	$0.802844\pi$
$938$	2.24093	+	2.24093i	0.0731688	+	0.0731688i
$939$	−6.67954	−	28.4307i	−0.217978	−	0.927801i
$940$		0			0
$941$		−	29.7021i		−	0.968262i	−0.874995	−	0.484131i	$-0.839136\pi$
$941$		−	29.7021i		−	0.968262i	0.874995	−	0.484131i	$-0.160864\pi$
$942$	2.89079	−	4.66624i	0.0941870	−	0.152034i
$943$	13.0892	−	13.0892i	0.426242	−	0.426242i
$944$	−34.0511			−1.10827
$945$		0			0
$946$	117.957			3.83510
$947$	26.1101	−	26.1101i	0.848465	−	0.848465i	−0.141476	−	0.989942i	$-0.545185\pi$
$947$	26.1101	−	26.1101i	0.848465	−	0.848465i	0.989942	+	0.141476i	$0.0451849\pi$
$948$	8.44249	−	13.6277i	0.274199	−	0.442606i
$949$			4.23369i			0.137431i
$950$		0			0
$951$	−8.00000	−	34.0511i	−0.259418	−	1.10418i
$952$	18.0235	+	18.0235i	0.584146	+	0.584146i
$953$	−29.6801	−	29.6801i	−0.961432	−	0.961432i	0.0378511	−	0.999283i	$-0.487949\pi$
$953$	−29.6801	−	29.6801i	−0.961432	−	0.961432i	−0.999283	+	0.0378511i	$0.987949\pi$
$954$	−18.0202	−	36.2337i	−0.583426	−	1.17311i
$955$		0			0
$956$			48.9022i			1.58161i
$957$	22.9782	+	14.2352i	0.742779	+	0.460160i
$958$	62.5559	−	62.5559i	2.02109	−	2.02109i
$959$	3.75906			0.121386
$960$		0			0
$961$	14.4891			0.467391
$962$	−40.5985	+	40.5985i	−1.30895	+	1.30895i
$963$	34.0625	+	11.4350i	1.09765	+	0.368489i
$964$			50.2337i			1.61792i
$965$		0			0
$966$	−14.7446	+	3.46410i	−0.474399	+	0.111456i
$967$	−22.9579	−	22.9579i	−0.738276	−	0.738276i	0.233968	−	0.972244i	$-0.424829\pi$
$967$	−22.9579	−	22.9579i	−0.738276	−	0.738276i	−0.972244	+	0.233968i	$0.924829\pi$
$968$	−97.8875	−	97.8875i	−3.14622	−	3.14622i
$969$	−28.7075	+	6.74456i	−0.922217	+	0.216667i
$970$		0			0
$971$		−	56.4203i		−	1.81061i	−0.424759	−	0.905307i	$-0.639641\pi$
$971$		−	56.4203i		−	1.81061i	0.424759	−	0.905307i	$-0.360359\pi$
$972$	63.5845	−	24.5438i	2.03948	−	0.787243i
$973$	7.59755	−	7.59755i	0.243566	−	0.243566i
$974$	−105.322			−3.37475
$975$		0			0
$976$	30.2337			0.967757
$977$	−6.30565	+	6.30565i	−0.201736	+	0.201736i	−0.800743	−	0.599008i	$-0.795562\pi$
$977$	−6.30565	+	6.30565i	−0.201736	+	0.201736i	0.599008	+	0.800743i	$0.295562\pi$
$978$	4.66624	+	2.89079i	0.149210	+	0.0924372i
$979$		−	99.4456i		−	3.17830i
$980$		0			0
$981$	−7.05842	+	3.51039i	−0.225358	+	0.112078i
$982$	69.4309	+	69.4309i	2.21563	+	2.21563i
$983$	24.9242	+	24.9242i	0.794959	+	0.794959i	0.982296	−	0.187337i	$-0.0599856\pi$
$983$	24.9242	+	24.9242i	0.794959	+	0.794959i	−0.187337	+	0.982296i	$0.559986\pi$
$984$	12.6766	+	53.9565i	0.404115	+	1.72007i
$985$		0			0
$986$			28.7075i			0.914232i
$987$	−7.04237	+	11.3676i	−0.224161	+	0.361836i
$988$	−41.7039	+	41.7039i	−1.32678	+	1.32678i
$989$	−27.7128			−0.881216
$990$		0			0
$991$	5.02175			0.159521			0.0797606	−	0.996814i	$-0.474584\pi$
$991$	5.02175			0.159521			0.0797606	+	0.996814i	$0.474584\pi$
$992$	−19.5959	+	19.5959i	−0.622171	+	0.622171i
$993$	28.2573	−	45.6123i	0.896718	−	1.44746i
$994$		−	21.4891i		−	0.681594i
$995$		0			0
$996$	16.9783	+	72.2660i	0.537976	+	2.28984i
$997$	−7.15369	−	7.15369i	−0.226560	−	0.226560i	0.584694	−	0.811254i	$-0.301215\pi$
$997$	−7.15369	−	7.15369i	−0.226560	−	0.226560i	−0.811254	+	0.584694i	$0.801215\pi$
$998$	13.1593	+	13.1593i	0.416552	+	0.416552i
$999$	22.3692	+	26.9783i	0.707730	+	0.853554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.a.407.2	yes	16
3.2	odd	2	inner	525.2.j.a.407.8	yes	16
5.2	odd	4	inner	525.2.j.a.218.1	✓	16
5.3	odd	4	inner	525.2.j.a.218.8	yes	16
5.4	even	2	inner	525.2.j.a.407.7	yes	16
15.2	even	4	inner	525.2.j.a.218.7	yes	16
15.8	even	4	inner	525.2.j.a.218.2	yes	16
15.14	odd	2	inner	525.2.j.a.407.1	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.j.a.218.1	✓	16	5.2	odd	4	inner
525.2.j.a.218.2	yes	16	15.8	even	4	inner
525.2.j.a.218.7	yes	16	15.2	even	4	inner
525.2.j.a.218.8	yes	16	5.3	odd	4	inner
525.2.j.a.407.1	yes	16	15.14	odd	2	inner
525.2.j.a.407.2	yes	16	1.1	even	1	trivial
525.2.j.a.407.7	yes	16	5.4	even	2	inner
525.2.j.a.407.8	yes	16	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.78498 + 1.78498i) q^{2} +(0.912166 - 1.47240i) q^{3} -4.37228i q^{4} +(1.00000 + 4.25639i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(4.23447 + 4.23447i) q^{8} +(-1.33591 - 2.68614i) q^{9} +O(q^{10})\)	\(q+(-1.78498 + 1.78498i) q^{2} +(0.912166 - 1.47240i) q^{3} -4.37228i q^{4} +(1.00000 + 4.25639i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(4.23447 + 4.23447i) q^{8} +(-1.33591 - 2.68614i) q^{9} -5.84096i q^{11} +(-6.43773 - 3.98825i) q^{12} +(-2.38456 + 2.38456i) q^{13} +2.52434 q^{14} -6.37228 q^{16} +(-3.00972 + 3.00972i) q^{17} +(7.17926 + 2.41013i) q^{18} +4.00000i q^{19} +(-1.68614 + 0.396143i) q^{21} +(10.4260 + 10.4260i) q^{22} +(-2.44949 - 2.44949i) q^{23} +(10.0974 - 2.37228i) q^{24} -8.51278i q^{26} +(-5.17364 - 0.483219i) q^{27} +(-3.09167 + 3.09167i) q^{28} -2.67181 q^{29} -6.74456 q^{31} +(2.90544 - 2.90544i) q^{32} +(-8.60022 - 5.32793i) q^{33} -10.7446i q^{34} +(-11.7446 + 5.84096i) q^{36} +(-4.76913 - 4.76913i) q^{37} +(-7.13991 - 7.13991i) q^{38} +(1.33591 + 5.68614i) q^{39} +5.34363i q^{41} +(2.30261 - 3.71683i) q^{42} +(5.65685 - 5.65685i) q^{43} -25.5383 q^{44} +8.74456 q^{46} +(5.45921 - 5.45921i) q^{47} +(-5.81258 + 9.38253i) q^{48} +1.00000i q^{49} +(1.68614 + 7.17687i) q^{51} +(10.4260 + 10.4260i) q^{52} +(-3.77852 - 3.77852i) q^{53} +(10.0974 - 8.37228i) q^{54} -5.98844i q^{56} +(5.88959 + 3.64866i) q^{57} +(4.76913 - 4.76913i) q^{58} +5.34363 q^{59} -4.74456 q^{61} +(12.0389 - 12.0389i) q^{62} +(-0.954759 + 2.84402i) q^{63} -2.37228i q^{64} +(24.8614 - 5.84096i) q^{66} +(0.887728 + 0.887728i) q^{67} +(13.1593 + 13.1593i) q^{68} +(-5.84096 + 1.37228i) q^{69} -8.51278i q^{71} +(5.71752 - 17.0312i) q^{72} +(0.887728 - 0.887728i) q^{73} +17.0256 q^{74} +17.4891 q^{76} +(-4.13018 + 4.13018i) q^{77} +(-12.5342 - 7.76506i) q^{78} +2.11684i q^{79} +(-5.43070 + 7.17687i) q^{81} +(-9.53825 - 9.53825i) q^{82} +(-6.93134 - 6.93134i) q^{83} +(1.73205 + 7.37228i) q^{84} +20.1947i q^{86} +(-2.43714 + 3.93397i) q^{87} +(24.7334 - 24.7334i) q^{88} +17.0256 q^{89} +3.37228 q^{91} +(-10.7099 + 10.7099i) q^{92} +(-6.15216 + 9.93068i) q^{93} +19.4891i q^{94} +(-1.62772 - 6.92820i) q^{96} +(2.38456 + 2.38456i) q^{97} +(-1.78498 - 1.78498i) q^{98} +(-15.6896 + 7.80298i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{6}+O(q^{10}) \) 16 * q + 16 * q^6	\( 16 q + 16 q^{6} - 56 q^{16} - 4 q^{21} - 16 q^{31} - 96 q^{36} + 48 q^{46} + 4 q^{51} + 16 q^{61} + 168 q^{66} + 96 q^{76} + 28 q^{81} + 8 q^{91} - 72 q^{96}+O(q^{100}) \) 16 * q + 16 * q^6 - 56 * q^16 - 4 * q^21 - 16 * q^31 - 96 * q^36 + 48 * q^46 + 4 * q^51 + 16 * q^61 + 168 * q^66 + 96 * q^76 + 28 * q^81 + 8 * q^91 - 72 * q^96

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