LMFDB - Embedded newform 525.2.j.a.407.7

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			407.7
Root			$-0.0537601 - 1.73122i$ of defining polynomial
Character	$\chi$	$=$	525.407
Dual form			525.2.j.a.218.7

$q$-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	$-0.398958\pi$
$2$	1.78498	−	1.78498i	1.26217	−	1.26217i	0.950040	−	0.312129i	$-0.101042\pi$
$3$	−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	−0.294342	−	0.955700i	$-0.595100\pi$
$13$	2.38456	−	2.38456i	0.661359	−	0.661359i	0.955700	+	0.294342i	$0.0951003\pi$
$14$	2.52434			0.674658
$15$		0			0
$16$	−6.37228			−1.59307
$17$	3.00972	−	3.00972i	0.729965	−	0.729965i	−0.240648	−	0.970612i	$-0.577360\pi$
$17$	3.00972	−	3.00972i	0.729965	−	0.729965i	0.970612	+	0.240648i	$0.0773599\pi$
$18$	−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	0.914757	−	0.404004i	$-0.132382\pi$
$23$	2.44949	+	2.44949i	0.510754	+	0.510754i	−0.404004	+	0.914757i	$0.632382\pi$
$24$	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	0.980510	−	0.196470i	$-0.0629479\pi$
$37$	4.76913	+	4.76913i	0.784039	+	0.784039i	−0.196470	+	0.980510i	$0.562948\pi$
$38$	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	−0.991647	−	0.128984i	$-0.958828\pi$
$43$	−5.65685	+	5.65685i	−0.862662	+	0.862662i	0.128984	+	0.991647i	$0.458828\pi$
$44$	−25.5383			−3.85005
$45$		0			0
$46$	8.74456			1.28932
$47$	−5.45921	+	5.45921i	−0.796308	+	0.796308i	−0.982511	−	0.186203i	$-0.940382\pi$
$47$	−5.45921	+	5.45921i	−0.796308	+	0.796308i	0.186203	+	0.982511i	$0.440382\pi$
$48$	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	0.917275	−	0.398255i	$-0.130384\pi$
$53$	3.77852	+	3.77852i	0.519019	+	0.519019i	−0.398255	+	0.917275i	$0.630384\pi$
$54$	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	0.650798	−	0.759251i	$-0.274435\pi$
$67$	−0.887728	−	0.887728i	−0.108453	−	0.108453i	−0.759251	+	0.650798i	$0.774435\pi$
$68$	−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	−0.757146	−	0.653245i	$-0.773407\pi$
$73$	−0.887728	+	0.887728i	−0.103901	+	0.103901i	0.653245	+	0.757146i	$0.273407\pi$
$74$	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	0.976469	−	0.215656i	$-0.0691889\pi$
$83$	6.93134	+	6.93134i	0.760814	+	0.760814i	−0.215656	+	0.976469i	$0.569189\pi$
$84$	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	0.575609	−	0.817725i	$-0.304765\pi$
$97$	−2.38456	−	2.38456i	−0.242116	−	0.242116i	−0.817725	+	0.575609i	$0.804765\pi$
$98$	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	−0.965453	−	0.260579i	$-0.916087\pi$
$103$	−7.15369	+	7.15369i	−0.704874	+	0.704874i	0.260579	+	0.965453i	$0.416087\pi$
$104$	−20.1947			−1.98025
$105$		0			0
$106$	13.4891			1.31018
$107$	8.46893	−	8.46893i	0.818723	−	0.818723i	−0.167200	−	0.985923i	$-0.553473\pi$
$107$	8.46893	−	8.46893i	0.818723	−	0.818723i	0.985923	+	0.167200i	$0.0534727\pi$
$108$	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	0.757842	−	0.652438i	$-0.226254\pi$
$113$	1.12046	+	1.12046i	0.105404	+	0.105404i	−0.652438	+	0.757842i	$0.726254\pi$
$114$	−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	0.997388	−	0.0722317i	$-0.0230121\pi$
$127$	10.4260	+	10.4260i	0.925156	+	0.925156i	−0.0722317	+	0.997388i	$0.523012\pi$
$128$	−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	−0.584384	−	0.811477i	$-0.698664\pi$
$137$	2.65805	−	2.65805i	0.227093	−	0.227093i	0.811477	+	0.584384i	$0.198664\pi$
$138$	−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	0.741643	−	0.670795i	$-0.234047\pi$
$157$	0.887728	+	0.887728i	0.0708484	+	0.0708484i	−0.670795	+	0.741643i	$0.734047\pi$
$158$	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	−0.741018	−	0.671485i	$-0.765657\pi$
$163$	−0.887728	+	0.887728i	−0.0695322	+	0.0695322i	0.671485	+	0.741018i	$0.265657\pi$
$164$	23.3639			1.82441
$165$		0			0
$166$	24.7446			1.92055
$167$	−8.82060	+	8.82060i	−0.682559	+	0.682559i	−0.960576	−	0.278017i	$-0.910323\pi$
$167$	−8.82060	+	8.82060i	−0.682559	+	0.682559i	0.278017	+	0.960576i	$0.410323\pi$
$168$	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	0.693612	−	0.720349i	$-0.256018\pi$
$173$	−0.351668	−	0.351668i	−0.0267368	−	0.0267368i	−0.720349	+	0.693612i	$0.756018\pi$
$174$	−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	−0.640314	−	0.768114i	$-0.721196\pi$
$193$	1.77546	−	1.77546i	0.127800	−	0.127800i	0.768114	+	0.640314i	$0.221196\pi$
$194$	−8.51278			−0.611182
$195$		0			0
$196$	4.37228			0.312306
$197$	−1.53759	+	1.53759i	−0.109549	+	0.109549i	−0.759756	−	0.650208i	$-0.774682\pi$
$197$	−1.53759	+	1.53759i	−0.109549	+	0.109549i	0.650208	+	0.759756i	$0.274682\pi$
$198$	−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	−0.832540	−	0.553965i	$-0.813114\pi$
$223$	−4.16002	+	4.16002i	−0.278576	+	0.278576i	0.553965	+	0.832540i	$0.313114\pi$
$224$	−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	$0.529066\pi$
$227$	−16.3776	+	16.3776i	−1.08702	+	1.08702i	−0.995834	+	0.0911880i	$0.970934\pi$
$228$	−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	$-0.901789\pi$
$233$	−19.1788	−	19.1788i	−1.25644	−	1.25644i	−0.303666	−	0.952779i	$-0.598211\pi$
$234$	−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	−0.537606	−	0.843196i	$-0.680671\pi$
$257$	4.89898	−	4.89898i	0.305590	−	0.305590i	0.843196	+	0.537606i	$0.180671\pi$
$258$	−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	0.295076	−	0.955474i	$-0.404655\pi$
$263$	−10.7099	−	10.7099i	−0.660398	−	0.660398i	−0.955474	+	0.295076i	$0.904655\pi$
$264$	−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	0.875836	−	0.482610i	$-0.160311\pi$
$277$	6.54458	+	6.54458i	0.393226	+	0.393226i	−0.482610	+	0.875836i	$0.660311\pi$
$278$	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	−0.966270	−	0.257532i	$-0.917091\pi$
$283$	−11.9228	+	11.9228i	−0.708738	+	0.708738i	0.257532	+	0.966270i	$0.417091\pi$
$284$	−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	0.717304	−	0.696760i	$-0.245376\pi$
$293$	0.351668	+	0.351668i	0.0205447	+	0.0205447i	−0.696760	+	0.717304i	$0.745376\pi$
$294$	−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	0.980135	−	0.198333i	$-0.0635528\pi$
$307$	13.6983	+	13.6983i	0.781802	+	0.781802i	−0.198333	+	0.980135i	$0.563553\pi$
$308$	−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	−0.958617	−	0.284699i	$-0.908106\pi$
$313$	−11.9228	+	11.9228i	−0.673917	+	0.673917i	0.284699	+	0.958617i	$0.408106\pi$
$314$	3.16915			0.178845
$315$		0			0
$316$	9.25544			0.520659
$317$	−14.2798	+	14.2798i	−0.802034	+	0.802034i	−0.983413	−	0.181379i	$-0.941944\pi$
$317$	−14.2798	+	14.2798i	−0.802034	+	0.802034i	0.181379	+	0.983413i	$0.441944\pi$
$318$	−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	0.565178	−	0.824969i	$-0.308807\pi$
$337$	−4.76913	−	4.76913i	−0.259791	−	0.259791i	−0.824969	+	0.565178i	$0.808807\pi$
$338$	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	−0.569911	−	0.821706i	$-0.693022\pi$
$347$	4.69042	−	4.69042i	0.251795	−	0.251795i	0.821706	+	0.569911i	$0.193022\pi$
$348$	−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	0.727270	−	0.686351i	$-0.240789\pi$
$353$	0.768795	+	0.768795i	0.0409188	+	0.0409188i	−0.686351	+	0.727270i	$0.740789\pi$
$354$	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	0.495302	−	0.868721i	$-0.335058\pi$
$367$	−7.15369	−	7.15369i	−0.373420	−	0.373420i	−0.868721	+	0.495302i	$0.835058\pi$
$368$	−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	−0.350690	−	0.936492i	$-0.614053\pi$
$373$	11.3137	−	11.3137i	0.585802	−	0.585802i	0.936492	+	0.350690i	$0.114053\pi$
$374$	−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	0.432806	−	0.901487i	$-0.357523\pi$
$383$	−9.17227	−	9.17227i	−0.468681	−	0.468681i	−0.901487	+	0.432806i	$0.857523\pi$
$384$	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	$0.0976579\pi$
$397$	25.0120	+	25.0120i	1.25532	+	1.25532i	0.302011	+	0.953305i	$0.402342\pi$
$398$	−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	−0.911761	−	0.410721i	$-0.865277\pi$
$433$	−10.4260	+	10.4260i	−0.501041	+	0.501041i	0.410721	+	0.911761i	$0.365277\pi$
$434$	−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	0.786809	−	0.617196i	$-0.211731\pi$
$443$	3.56995	+	3.56995i	0.169614	+	0.169614i	−0.617196	+	0.786809i	$0.711731\pi$
$444$	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	$0.0718754\pi$
$457$	25.6211	+	25.6211i	1.19850	+	1.19850i	0.223889	+	0.974615i	$0.428125\pi$
$458$	−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	−0.946466	−	0.322802i	$-0.895375\pi$
$463$	−13.4196	+	13.4196i	−0.623664	+	0.623664i	0.322802	+	0.946466i	$0.395375\pi$
$464$	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	$-0.458763\pi$
$467$	24.2209	−	24.2209i	1.12081	−	1.12081i	0.991620	−	0.129188i	$-0.0412372\pi$
$468$	−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	$-0.855749\pi$
$487$	−29.5025	−	29.5025i	−1.33689	−	1.33689i	−0.437825	−	0.899060i	$-0.644251\pi$
$488$	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	$0.0331559\pi$
$503$	24.6380	+	24.6380i	1.09855	+	1.09855i	0.103974	+	0.994580i	$0.466844\pi$
$504$	−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	$-0.498763\pi$
$523$	22.9579	−	22.9579i	1.00388	−	1.00388i	0.999992	−	0.00388650i	$-0.00123711\pi$
$524$	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	0.530132	−	0.847915i	$-0.322142\pi$
$547$	−7.43231	−	7.43231i	−0.317783	−	0.317783i	−0.847915	+	0.530132i	$0.822142\pi$
$548$	−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	−0.848844	−	0.528643i	$-0.822701\pi$
$557$	−7.55703	+	7.55703i	−0.320202	+	0.320202i	0.528643	+	0.848844i	$0.322701\pi$
$558$	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	0.424445	−	0.905454i	$-0.360469\pi$
$563$	−11.4132	−	11.4132i	−0.481009	−	0.481009i	−0.905454	+	0.424445i	$0.860469\pi$
$564$	−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	$-0.884122\pi$
$577$	−30.9993	−	30.9993i	−1.29052	−	1.29052i	−0.356053	−	0.934466i	$-0.615878\pi$
$578$	−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	−0.182925	−	0.983127i	$-0.558557\pi$
$587$	19.3874	−	19.3874i	0.800202	−	0.800202i	0.983127	+	0.182925i	$0.0585566\pi$
$588$	−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	0.279138	−	0.960251i	$-0.409951\pi$
$593$	−16.5862	−	16.5862i	−0.681113	−	0.681113i	−0.960251	+	0.279138i	$0.909951\pi$
$594$	−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	0.224830	−	0.974398i	$-0.427817\pi$
$607$	−18.4674	−	18.4674i	−0.749569	−	0.749569i	−0.974398	+	0.224830i	$0.927817\pi$
$608$	−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	−0.996577	−	0.0826647i	$-0.973657\pi$
$613$	−22.6274	+	22.6274i	−0.913913	+	0.913913i	0.0826647	+	0.996577i	$0.473657\pi$
$614$	48.9022			1.97353
$615$		0			0
$616$	−34.9783			−1.40931
$617$	10.9184	−	10.9184i	0.439559	−	0.439559i	−0.452304	−	0.891864i	$-0.649398\pi$
$617$	10.9184	−	10.9184i	0.439559	−	0.439559i	0.891864	+	0.452304i	$0.149398\pi$
$618$	−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	−0.508771	−	0.860902i	$-0.669900\pi$
$643$	8.92915	−	8.92915i	0.352131	−	0.352131i	0.860902	+	0.508771i	$0.169900\pi$
$644$	15.1460			0.596837
$645$		0			0
$646$	42.9783			1.69096
$647$	12.6646	−	12.6646i	0.497896	−	0.497896i	−0.412887	−	0.910782i	$-0.635479\pi$
$647$	12.6646	−	12.6646i	0.497896	−	0.497896i	0.910782	+	0.412887i	$0.135479\pi$
$648$	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	0.952147	−	0.305641i	$-0.0988706\pi$
$653$	16.5207	+	16.5207i	0.646506	+	0.646506i	−0.305641	+	0.952147i	$0.598871\pi$
$654$	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	−0.236328	−	0.971673i	$-0.575944\pi$
$673$	19.0765	−	19.0765i	0.735345	−	0.735345i	0.971673	+	0.236328i	$0.0759440\pi$
$674$	−17.0256			−0.655800
$675$		0			0
$676$	7.11684			0.273725
$677$	−3.42685	+	3.42685i	−0.131704	+	0.131704i	−0.769886	−	0.638181i	$-0.779687\pi$
$677$	−3.42685	+	3.42685i	−0.131704	+	0.131704i	0.638181	+	0.769886i	$0.279687\pi$
$678$	−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	$0.0190125\pi$
$683$	27.6477	+	27.6477i	1.05791	+	1.05791i	0.0596940	+	0.998217i	$0.480988\pi$
$684$	−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	0.268131	−	0.963382i	$-0.413594\pi$
$727$	−18.7460	−	18.7460i	−0.695251	−	0.695251i	−0.963382	+	0.268131i	$0.913594\pi$
$728$	−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	−0.981930	−	0.189247i	$-0.939395\pi$
$733$	−21.4611	+	21.4611i	−0.792683	+	0.792683i	0.189247	+	0.981930i	$0.439395\pi$
$734$	−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	0.131008	−	0.991381i	$-0.458179\pi$
$743$	−23.4521	−	23.4521i	−0.860373	−	0.860373i	−0.991381	+	0.131008i	$0.958179\pi$
$744$	−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	0.986453	−	0.164045i	$-0.0524543\pi$
$757$	22.6274	+	22.6274i	0.822407	+	0.822407i	−0.164045	+	0.986453i	$0.552454\pi$
$758$	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	$-0.901825\pi$
$773$	−34.9307	−	34.9307i	−1.25637	−	1.25637i	−0.303558	−	0.952813i	$-0.598175\pi$
$774$	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	0.796436	−	0.604723i	$-0.206716\pi$
$787$	5.37823	+	5.37823i	0.191713	+	0.191713i	−0.604723	+	0.796436i	$0.706716\pi$
$788$	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	−0.320161	−	0.947363i	$-0.603737\pi$
$797$	17.7067	−	17.7067i	0.627202	−	0.627202i	0.947363	+	0.320161i	$0.103737\pi$
$798$	−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	−0.540077	−	0.841615i	$-0.681605\pi$
$823$	8.65052	−	8.65052i	0.301538	−	0.301538i	0.841615	+	0.540077i	$0.181605\pi$
$824$	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	$0.500117\pi$
$827$	−28.7682	+	28.7682i	−1.00037	+	1.00037i	−1.00000		0.000367902i	$0.999883\pi$
$828$	−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	−0.229060	−	0.973412i	$-0.573565\pi$
$853$	21.7397	−	21.7397i	0.744353	−	0.744353i	0.973412	+	0.229060i	$0.0735651\pi$
$854$	−11.9769			−0.409840
$855$		0			0
$856$	−71.7228			−2.45144
$857$	−14.6969	+	14.6969i	−0.502038	+	0.502038i	−0.912071	−	0.410033i	$-0.865517\pi$
$857$	−14.6969	+	14.6969i	−0.502038	+	0.502038i	0.410033	+	0.912071i	$0.365517\pi$
$858$	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	0.284518	−	0.958671i	$-0.408166\pi$
$863$	−19.8045	−	19.8045i	−0.674152	−	0.674152i	−0.958671	+	0.284518i	$0.908166\pi$
$864$	−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	0.999449	−	0.0331972i	$-0.0105689\pi$
$877$	28.6148	+	28.6148i	0.966252	+	0.966252i	−0.0331972	+	0.999449i	$0.510569\pi$
$878$	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	−0.987837	−	0.155493i	$-0.950303\pi$
$883$	−24.7334	+	24.7334i	−0.832344	+	0.832344i	0.155493	+	0.987837i	$0.450303\pi$
$884$	−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	$0.544816\pi$
$887$	−33.6672	+	33.6672i	−1.13043	+	1.13043i	−0.990105	+	0.140328i	$0.955184\pi$
$888$	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	0.512499	−	0.858688i	$-0.328720\pi$
$907$	−10.4260	−	10.4260i	−0.346189	−	0.346189i	−0.858688	+	0.512499i	$0.828720\pi$
$908$	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	0.814236	−	0.580535i	$-0.197156\pi$
$937$	7.15369	+	7.15369i	0.233701	+	0.233701i	−0.580535	+	0.814236i	$0.697156\pi$
$938$	−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	−0.989942	−	0.141476i	$-0.954815\pi$
$947$	−26.1101	+	26.1101i	−0.848465	+	0.848465i	0.141476	+	0.989942i	$0.454815\pi$
$948$	−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	0.999283	−	0.0378511i	$-0.0120513\pi$
$953$	29.6801	+	29.6801i	0.961432	+	0.961432i	−0.0378511	+	0.999283i	$0.512051\pi$
$954$	−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	0.972244	−	0.233968i	$-0.0751711\pi$
$967$	22.9579	+	22.9579i	0.738276	+	0.738276i	−0.233968	+	0.972244i	$0.575171\pi$
$968$	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	−0.599008	−	0.800743i	$-0.704438\pi$
$977$	6.30565	−	6.30565i	0.201736	−	0.201736i	0.800743	+	0.599008i	$0.204438\pi$
$978$	−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	0.187337	−	0.982296i	$-0.440014\pi$
$983$	−24.9242	−	24.9242i	−0.794959	−	0.794959i	−0.982296	+	0.187337i	$0.940014\pi$
$984$	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	0.811254	−	0.584694i	$-0.198785\pi$
$997$	7.15369	+	7.15369i	0.226560	+	0.226560i	−0.584694	+	0.811254i	$0.698785\pi$
$998$	−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.407.7	yes	16
3.2	odd	2	inner	525.2.j.a.407.1	yes	16
5.2	odd	4	inner	525.2.j.a.218.8	yes	16
5.3	odd	4	inner	525.2.j.a.218.1	✓	16
5.4	even	2	inner	525.2.j.a.407.2	yes	16
15.2	even	4	inner	525.2.j.a.218.2	yes	16
15.8	even	4	inner	525.2.j.a.218.7	yes	16
15.14	odd	2	inner	525.2.j.a.407.8	yes	16

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more