LMFDB - Embedded newform 425.2.e.d.251.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(251,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.251"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.e (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 24x^{10} + 188x^{8} + 572x^{6} + 776x^{4} + 464x^{2} + 100 $ x^12 + 24x^10 + 188x^8 + 572x^6 + 776x^4 + 464*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 85)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			251.6
Root			$3.38621i$ of defining polynomial
Character	$\chi$	$=$	425.251
Dual form			425.2.e.d.276.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.38621i q^{2} +(2.23065 + 2.23065i) q^{3} -3.69399 q^{4} +(-5.32280 + 5.32280i) q^{6} +(0.155559 - 0.155559i) q^{7} -4.04223i q^{8} +6.95160i q^{9} +(0.371196 - 0.371196i) q^{11} +(-8.24001 - 8.24001i) q^{12} +1.96713 q^{13} +(0.371196 + 0.371196i) q^{14} +2.25761 q^{16} +(2.23065 - 3.46759i) q^{17} -16.5880 q^{18} -4.00000i q^{19} +0.693995 q^{21} +(0.885751 + 0.885751i) q^{22} +(0.263516 - 0.263516i) q^{23} +(9.01679 - 9.01679i) q^{24} +4.69399i q^{26} +(-8.81464 + 8.81464i) q^{27} +(-0.574634 + 0.574634i) q^{28} +(-4.95160 - 4.95160i) q^{29} +(2.06519 + 2.06519i) q^{31} -2.69733i q^{32} +1.65602 q^{33} +(8.27440 + 5.32280i) q^{34} -25.6792i q^{36} +(4.04223 + 4.04223i) q^{37} +9.54484 q^{38} +(4.38799 + 4.38799i) q^{39} +(0.563613 - 0.563613i) q^{41} +1.65602i q^{42} +2.49417i q^{43} +(-1.37120 + 1.37120i) q^{44} +(0.628804 + 0.628804i) q^{46} +6.73955 q^{47} +(5.03593 + 5.03593i) q^{48} +6.95160i q^{49} +(12.7108 - 2.75919i) q^{51} -7.26658 q^{52} -5.92169i q^{53} +(-21.0336 - 21.0336i) q^{54} +(-0.628804 - 0.628804i) q^{56} +(8.92260 - 8.92260i) q^{57} +(11.8156 - 11.8156i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(-4.92798 + 4.92798i) q^{62} +(1.08138 + 1.08138i) q^{63} +10.9516 q^{64} +3.95160i q^{66} -11.5120 q^{67} +(-8.24001 + 12.8093i) q^{68} +1.17562 q^{69} +(-5.06519 - 5.06519i) q^{71} +28.1000 q^{72} +(-0.838149 - 0.838149i) q^{73} +(-9.64560 + 9.64560i) q^{74} +14.7760i q^{76} -0.115486i q^{77} +(-10.4707 + 10.4707i) q^{78} +(4.75919 - 4.75919i) q^{79} -18.4700 q^{81} +(1.34490 + 1.34490i) q^{82} -6.11732i q^{83} -2.56361 q^{84} -5.95160 q^{86} -22.0906i q^{87} +(-1.50046 - 1.50046i) q^{88} -15.9852 q^{89} +(0.306005 - 0.306005i) q^{91} +(-0.973426 + 0.973426i) q^{92} +9.21344i q^{93} +16.0820i q^{94} +(6.01679 - 6.01679i) q^{96} +(6.51611 + 6.51611i) q^{97} -16.5880 q^{98} +(2.58041 + 2.58041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{4} - 20 q^{6} + 16 q^{11} + 16 q^{14} + 4 q^{16} - 24 q^{21} + 32 q^{24} - 4 q^{29} + 4 q^{31} - 12 q^{39} + 16 q^{41} - 28 q^{44} - 4 q^{46} + 44 q^{51} - 100 q^{54} + 4 q^{56} - 48 q^{61}+ \cdots - 36 q^{99}+O(q^{100}) $ 12 * q - 12 * q^4 - 20 * q^6 + 16 * q^11 + 16 * q^14 + 4 * q^16 - 24 * q^21 + 32 * q^24 - 4 * q^29 + 4 * q^31 - 12 * q^39 + 16 * q^41 - 28 * q^44 - 4 * q^46 + 44 * q^51 - 100 * q^54 + 4 * q^56 - 48 * q^61 + 76 * q^64 + 88 * q^69 - 40 * q^71 - 28 * q^74 + 4 * q^79 - 60 * q^81 - 40 * q^84 - 16 * q^86 + 16 * q^89 + 36 * q^91 - 4 * q^96 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$			2.38621i			1.68730i	0.536890	+	0.843652i	$0.319599\pi$
$2$			2.38621i			1.68730i	−0.536890	+	0.843652i	$0.680401\pi$
$3$	2.23065	+	2.23065i	1.28787	+	1.28787i	0.936080	+	0.351786i	$0.114426\pi$
$3$	2.23065	+	2.23065i	1.28787	+	1.28787i	0.351786	+	0.936080i	$0.385574\pi$
$4$	−3.69399			−1.84700
$5$		0			0
$5$		0			0
$6$	−5.32280	+	5.32280i	−2.17302	+	2.17302i
$7$	0.155559	−	0.155559i	0.0587957	−	0.0587957i	−0.677098	−	0.735893i	$-0.736762\pi$
$7$	0.155559	−	0.155559i	0.0587957	−	0.0587957i	0.735893	+	0.677098i	$0.236762\pi$
$8$		−	4.04223i		−	1.42914i
$9$			6.95160i			2.31720i
$10$		0			0
$11$	0.371196	−	0.371196i	0.111920	−	0.111920i	−0.648929	−	0.760849i	$-0.724783\pi$
$11$	0.371196	−	0.371196i	0.111920	−	0.111920i	0.760849	+	0.648929i	$0.224783\pi$
$12$	−8.24001	−	8.24001i	−2.37869	−	2.37869i
$13$	1.96713			0.545585			0.272792	−	0.962073i	$-0.412053\pi$
$13$	1.96713			0.545585			0.272792	+	0.962073i	$0.412053\pi$
$14$	0.371196	+	0.371196i	0.0992063	+	0.0992063i
$15$		0			0
$16$	2.25761			0.564402
$17$	2.23065	−	3.46759i	0.541012	−	0.841015i
$17$	2.23065	−	3.46759i	0.541012	−	0.841015i
$18$	−16.5880			−3.90982
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$	0.693995			0.151442
$22$	0.885751	+	0.885751i	0.188843	+	0.188843i
$23$	0.263516	−	0.263516i	0.0549469	−	0.0549469i	−0.679099	−	0.734046i	$-0.737629\pi$
$23$	0.263516	−	0.263516i	0.0549469	−	0.0549469i	0.734046	+	0.679099i	$0.237629\pi$
$24$	9.01679	−	9.01679i	1.84055	−	1.84055i
$25$		0			0
$26$			4.69399i			0.920568i
$27$	−8.81464	+	8.81464i	−1.69638	+	1.69638i
$28$	−0.574634	+	0.574634i	−0.108596	+	0.108596i
$29$	−4.95160	−	4.95160i	−0.919490	−	0.919490i	0.0775026	−	0.996992i	$-0.475305\pi$
$29$	−4.95160	−	4.95160i	−0.919490	−	0.919490i	−0.996992	+	0.0775026i	$0.975305\pi$
$30$		0			0
$31$	2.06519	+	2.06519i	0.370919	+	0.370919i	0.867812	−	0.496893i	$-0.165526\pi$
$31$	2.06519	+	2.06519i	0.370919	+	0.370919i	−0.496893	+	0.867812i	$0.665526\pi$
$32$		−	2.69733i		−	0.476825i
$33$	1.65602			0.288276
$34$	8.27440	+	5.32280i	1.41905	+	0.912852i
$35$		0			0
$36$		−	25.6792i		−	4.27986i
$37$	4.04223	+	4.04223i	0.664538	+	0.664538i	0.956446	−	0.291908i	$-0.0942902\pi$
$37$	4.04223	+	4.04223i	0.664538	+	0.664538i	−0.291908	+	0.956446i	$0.594290\pi$
$38$	9.54484			1.54838
$39$	4.38799	+	4.38799i	0.702641	+	0.702641i
$40$		0			0
$41$	0.563613	−	0.563613i	0.0880216	−	0.0880216i	−0.661725	−	0.749747i	$-0.730175\pi$
$41$	0.563613	−	0.563613i	0.0880216	−	0.0880216i	0.749747	+	0.661725i	$0.230175\pi$
$42$			1.65602i			0.255529i
$43$			2.49417i			0.380357i	0.981750	+	0.190178i	$0.0609066\pi$
$43$			2.49417i			0.380357i	−0.981750	+	0.190178i	$0.939093\pi$
$44$	−1.37120	+	1.37120i	−0.206716	+	0.206716i
$45$		0			0
$46$	0.628804	+	0.628804i	0.0927121	+	0.0927121i
$47$	6.73955			0.983065			0.491532	−	0.870859i	$-0.336437\pi$
$47$	6.73955			0.983065			0.491532	+	0.870859i	$0.336437\pi$
$48$	5.03593	+	5.03593i	0.726875	+	0.726875i
$49$			6.95160i			0.993086i
$50$		0			0
$51$	12.7108	−	2.75919i	1.77987	−	0.386363i
$52$	−7.26658			−1.00769
$53$		−	5.92169i		−	0.813406i	−0.913560	−	0.406703i	$-0.866678\pi$
$53$		−	5.92169i		−	0.813406i	0.913560	−	0.406703i	$-0.133322\pi$
$54$	−21.0336	−	21.0336i	−2.86231	−	2.86231i
$55$		0			0
$56$	−0.628804	−	0.628804i	−0.0840275	−	0.0840275i
$57$	8.92260	−	8.92260i	1.18183	−	1.18183i
$58$	11.8156	−	11.8156i	1.55146	−	1.55146i
$59$			6.00000i			0.781133i	0.920575	+	0.390567i	$0.127721\pi$
$59$			6.00000i			0.781133i	−0.920575	+	0.390567i	$0.872279\pi$
$60$		0			0
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$	−4.92798	+	4.92798i	−0.625854	+	0.625854i
$63$	1.08138	+	1.08138i	0.136241	+	0.136241i
$64$	10.9516			1.36895
$65$		0			0
$66$			3.95160i			0.486409i
$67$	−11.5120			−1.40641			−0.703206	−	0.710987i	$-0.748249\pi$
$67$	−11.5120			−1.40641			−0.703206	+	0.710987i	$0.748249\pi$
$68$	−8.24001	+	12.8093i	−0.999248	+	1.55335i
$69$	1.17562			0.141528
$70$		0			0
$71$	−5.06519	−	5.06519i	−0.601128	−	0.601128i	0.339484	−	0.940612i	$-0.389747\pi$
$71$	−5.06519	−	5.06519i	−0.601128	−	0.601128i	−0.940612	+	0.339484i	$0.889747\pi$
$72$	28.1000			3.31161
$73$	−0.838149	−	0.838149i	−0.0980980	−	0.0980980i	0.656355	−	0.754453i	$-0.272098\pi$
$73$	−0.838149	−	0.838149i	−0.0980980	−	0.0980980i	−0.754453	+	0.656355i	$0.772098\pi$
$74$	−9.64560	+	9.64560i	−1.12128	+	1.12128i
$75$		0			0
$76$			14.7760i			1.69492i
$77$		−	0.115486i		−	0.0131608i
$78$	−10.4707	+	10.4707i	−1.18557	+	1.18557i
$79$	4.75919	−	4.75919i	0.535450	−	0.535450i	−0.386739	−	0.922189i	$-0.626399\pi$
$79$	4.75919	−	4.75919i	0.535450	−	0.535450i	0.922189	+	0.386739i	$0.126399\pi$
$80$		0			0
$81$	−18.4700			−2.05222
$82$	1.34490	+	1.34490i	0.148519	+	0.148519i
$83$		−	6.11732i		−	0.671463i	−0.941958	−	0.335731i	$-0.891017\pi$
$83$		−	6.11732i		−	0.671463i	0.941958	−	0.335731i	$-0.108983\pi$
$84$	−2.56361			−0.279713
$85$		0			0
$86$	−5.95160			−0.641778
$87$		−	22.0906i		−	2.36836i
$88$	−1.50046	−	1.50046i	−0.159949	−	0.159949i
$89$	−15.9852			−1.69443			−0.847213	−	0.531253i	$-0.821721\pi$
$89$	−15.9852			−1.69443			−0.847213	+	0.531253i	$0.821721\pi$
$90$		0			0
$91$	0.306005	−	0.306005i	0.0320781	−	0.0320781i
$92$	−0.973426	+	0.973426i	−0.101487	+	0.101487i
$93$			9.21344i			0.955389i
$94$			16.0820i			1.65873i
$95$		0			0
$96$	6.01679	−	6.01679i	0.614086	−	0.614086i
$97$	6.51611	+	6.51611i	0.661611	+	0.661611i	0.955760	−	0.294149i	$-0.0950361\pi$
$97$	6.51611	+	6.51611i	0.661611	+	0.661611i	−0.294149	+	0.955760i	$0.595036\pi$
$98$	−16.5880			−1.67564
$99$	2.58041	+	2.58041i	0.259341	+	0.259341i
$100$		0			0
$101$	−7.20921			−0.717343			−0.358672	−	0.933464i	$-0.616770\pi$
$101$	−7.20921			−0.717343			−0.358672	+	0.933464i	$0.616770\pi$
$102$	6.58399	+	30.3306i	0.651913	+	3.00318i
$103$	9.52456			0.938482			0.469241	−	0.883070i	$-0.344528\pi$
$103$	9.52456			0.938482			0.469241	+	0.883070i	$0.344528\pi$
$104$		−	7.95160i		−	0.779719i
$105$		0			0
$106$	14.1304			1.37246
$107$	7.62530	+	7.62530i	0.737166	+	0.737166i	0.972029	−	0.234863i	$-0.0754640\pi$
$107$	7.62530	+	7.62530i	0.737166	+	0.737166i	−0.234863	+	0.972029i	$0.575464\pi$
$108$	32.5613	−	32.5613i	3.13321	−	3.13321i
$109$	9.95160	−	9.95160i	0.953191	−	0.953191i	−0.0457617	−	0.998952i	$-0.514571\pi$
$109$	9.95160	−	9.95160i	0.953191	−	0.953191i	0.998952	+	0.0457617i	$0.0145715\pi$
$110$		0			0
$111$			18.0336i			1.71167i
$112$	0.351191	−	0.351191i	0.0331844	−	0.0331844i
$113$	−5.08354	+	5.08354i	−0.478219	+	0.478219i	−0.904562	−	0.426343i	$-0.859802\pi$
$113$	−5.08354	+	5.08354i	−0.478219	+	0.478219i	0.426343	+	0.904562i	$0.359802\pi$
$114$	21.2912	+	21.2912i	1.99410	+	1.99410i
$115$		0			0
$116$	18.2912	+	18.2912i	1.69829	+	1.69829i
$117$			13.6747i			1.26423i
$118$	−14.3173			−1.31801
$119$	−0.192417	−	0.886412i	−0.0176389	−	0.0812573i
$120$		0			0
$121$			10.7244i			0.974948i
$122$	−9.54484	−	9.54484i	−0.864149	−	0.864149i
$123$	2.51445			0.226720
$124$	−7.62880	−	7.62880i	−0.685087	−	0.685087i
$125$		0			0
$126$	−2.58041	+	2.58041i	−0.229881	+	0.229881i
$127$		−	9.74047i		−	0.864327i	−0.901795	−	0.432163i	$-0.857750\pi$
$127$		−	9.74047i		−	0.864327i	0.901795	−	0.432163i	$-0.142250\pi$
$128$			20.7382i			1.83301i
$129$	−5.56361	+	5.56361i	−0.489849	+	0.489849i
$130$		0			0
$131$	−13.9200	−	13.9200i	−1.21620	−	1.21620i	−0.968954	−	0.247242i	$-0.920476\pi$
$131$	−13.9200	−	13.9200i	−1.21620	−	1.21620i	−0.247242	−	0.968954i	$-0.579524\pi$
$132$	−6.11732			−0.532444
$133$	−0.622235	−	0.622235i	−0.0539547	−	0.0539547i
$134$		−	27.4700i		−	2.37304i
$135$		0			0
$136$	−14.0168	−	9.01679i	−1.20193	−	0.773184i
$137$	4.65693			0.397869			0.198934	−	0.980013i	$-0.436252\pi$
$137$	4.65693			0.397869			0.198934	+	0.980013i	$0.436252\pi$
$138$			2.80528i			0.238802i
$139$	3.71079	+	3.71079i	0.314745	+	0.314745i	0.846745	−	0.532000i	$-0.178559\pi$
$139$	3.71079	+	3.71079i	0.314745	+	0.314745i	−0.532000	+	0.846745i	$0.678559\pi$
$140$		0			0
$141$	15.0336	+	15.0336i	1.26606	+	1.26606i
$142$	12.0866	−	12.0866i	1.01429	−	1.01429i
$143$	0.730192	−	0.730192i	0.0610618	−	0.0610618i
$144$			15.6940i			1.30783i
$145$		0			0
$146$	2.00000	−	2.00000i	0.165521	−	0.165521i
$147$	−15.5066	+	15.5066i	−1.27896	+	1.27896i
$148$	−14.9320	−	14.9320i	−1.22740	−	1.22740i
$149$	−8.74239			−0.716205			−0.358102	−	0.933682i	$-0.616576\pi$
$149$	−8.74239			−0.716205			−0.358102	+	0.933682i	$0.616576\pi$
$150$		0			0
$151$		−	15.9032i		−	1.29418i	−0.762412	−	0.647092i	$-0.775985\pi$
$151$		−	15.9032i		−	1.29418i	0.762412	−	0.647092i	$-0.224015\pi$
$152$	−16.1689			−1.31147
$153$	24.1053	+	15.5066i	1.94880	+	1.25363i
$154$	0.275573			0.0222063
$155$		0			0
$156$	−16.2092	−	16.2092i	−1.29778	−	1.29778i
$157$	10.0719			0.803823			0.401911	−	0.915679i	$-0.368346\pi$
$157$	10.0719			0.803823			0.401911	+	0.915679i	$0.368346\pi$
$158$	11.3564	+	11.3564i	0.903468	+	0.903468i
$159$	13.2092	−	13.2092i	1.04756	−	1.04756i
$160$		0			0
$161$		−	0.0819845i		−	0.00646128i
$162$		−	44.0732i		−	3.46272i
$163$	6.77963	−	6.77963i	0.531021	−	0.531021i	−0.389855	−	0.920876i	$-0.627475\pi$
$163$	6.77963	−	6.77963i	0.531021	−	0.531021i	0.920876	+	0.389855i	$0.127475\pi$
$164$	−2.08198	+	2.08198i	−0.162576	+	0.162576i
$165$		0			0
$166$	14.5972			1.13296
$167$	−3.77871	−	3.77871i	−0.292405	−	0.292405i	0.545624	−	0.838030i	$-0.316293\pi$
$167$	−3.77871	−	3.77871i	−0.292405	−	0.292405i	−0.838030	+	0.545624i	$0.816293\pi$
$168$		−	2.80528i		−	0.216432i
$169$	−9.13038			−0.702337
$170$		0			0
$171$	27.8064			2.12641
$172$		−	9.21344i		−	0.702518i
$173$	12.3426	+	12.3426i	0.938390	+	0.938390i	0.998209	−	0.0598193i	$-0.0190524\pi$
$173$	12.3426	+	12.3426i	0.938390	+	0.938390i	−0.0598193	+	0.998209i	$0.519052\pi$
$174$	52.7128			3.99614
$175$		0			0
$176$	0.838015	−	0.838015i	0.0631678	−	0.0631678i
$177$	−13.3839	+	13.3839i	−1.00600	+	1.00600i
$178$		−	38.1440i		−	2.85901i
$179$		−	21.3248i		−	1.59389i	−0.604052	−	0.796945i	$-0.706448\pi$
$179$		−	21.3248i		−	1.59389i	0.604052	−	0.796945i	$-0.293552\pi$
$180$		0			0
$181$	10.2092	−	10.2092i	0.758845	−	0.758845i	−0.217267	−	0.976112i	$-0.569714\pi$
$181$	10.2092	−	10.2092i	0.758845	−	0.758845i	0.976112	+	0.217267i	$0.0697144\pi$
$182$	0.730192	+	0.730192i	0.0541255	+	0.0541255i
$183$	−17.8452			−1.31916
$184$	−1.06519	−	1.06519i	−0.0785269	−	0.0785269i
$185$		0			0
$186$	−21.9852			−1.61203
$187$	−0.459148	−	2.11516i	−0.0335762	−	0.154676i
$188$	−24.8959			−1.81572
$189$			2.74239i			0.199480i
$190$		0			0
$191$	−6.74239			−0.487862			−0.243931	−	0.969793i	$-0.578437\pi$
$191$	−6.74239			−0.487862			−0.243931	+	0.969793i	$0.578437\pi$
$192$	24.4292	+	24.4292i	1.76303	+	1.76303i
$193$	−10.3627	+	10.3627i	−0.745924	+	0.745924i	−0.973711	−	0.227787i	$-0.926851\pi$
$193$	−10.3627	+	10.3627i	−0.745924	+	0.745924i	0.227787	+	0.973711i	$0.426851\pi$
$194$	−15.5488	+	15.5488i	−1.11634	+	1.11634i
$195$		0			0
$196$		−	25.6792i		−	1.83423i
$197$	0.614707	−	0.614707i	0.0437960	−	0.0437960i	−0.684870	−	0.728666i	$-0.740141\pi$
$197$	0.614707	−	0.614707i	0.0437960	−	0.0437960i	0.728666	+	0.684870i	$0.240141\pi$
$198$	−6.15739	+	6.15739i	−0.437587	+	0.437587i
$199$	−9.40478	−	9.40478i	−0.666687	−	0.666687i	0.290260	−	0.956948i	$-0.406258\pi$
$199$	−9.40478	−	9.40478i	−0.666687	−	0.666687i	−0.956948	+	0.290260i	$0.906258\pi$
$200$		0			0
$201$	−25.6792	−	25.6792i	−1.81127	−	1.81127i
$202$		−	17.2027i		−	1.21038i
$203$	−1.54053			−0.108124
$204$	−46.9536	+	10.1924i	−3.28741	+	0.713612i
$205$		0			0
$206$			22.7276i			1.58351i
$207$	1.83186	+	1.83186i	0.127323	+	0.127323i
$208$	4.44102			0.307929
$209$	−1.48478	−	1.48478i	−0.102705	−	0.102705i
$210$		0			0
$211$	−12.5804	+	12.5804i	−0.866071	+	0.866071i	−0.992035	−	0.125964i	$-0.959798\pi$
$211$	−12.5804	+	12.5804i	−0.866071	+	0.866071i	0.125964	+	0.992035i	$0.459798\pi$
$212$			21.8747i			1.50236i
$213$		−	22.5973i		−	1.54834i
$214$	−18.1956	+	18.1956i	−1.24382	+	1.24382i
$215$		0			0
$216$	35.6308	+	35.6308i	2.42437	+	2.42437i
$217$	0.642517			0.0436169
$218$	23.7466	+	23.7466i	1.60832	+	1.60832i
$219$		−	3.73924i		−	0.252674i
$220$		0			0
$221$	4.38799	−	6.82122i	0.295168	−	0.458845i
$222$	−43.0319			−2.88811
$223$			1.96713i			0.131729i	0.997829	+	0.0658645i	$0.0209805\pi$
$223$			1.96713i			0.131729i	−0.997829	+	0.0658645i	$0.979019\pi$
$224$	−0.419593	−	0.419593i	−0.0280352	−	0.0280352i
$225$		0			0
$226$	−12.1304	−	12.1304i	−0.806901	−	0.806901i
$227$	−8.45593	+	8.45593i	−0.561239	+	0.561239i	−0.929659	−	0.368420i	$-0.879899\pi$
$227$	−8.45593	+	8.45593i	−0.561239	+	0.561239i	0.368420	+	0.929659i	$0.379899\pi$
$228$	−32.9600	+	32.9600i	−2.18283	+	2.18283i
$229$			9.30601i			0.614958i	0.951555	+	0.307479i	$0.0994854\pi$
$229$			9.30601i			0.614958i	−0.951555	+	0.307479i	$0.900515\pi$
$230$		0			0
$231$	0.257608	−	0.257608i	0.0169494	−	0.0169494i
$232$	−20.0155	+	20.0155i	−1.31408	+	1.31408i
$233$	−18.2440	−	18.2440i	−1.19520	−	1.19520i	−0.975586	−	0.219618i	$-0.929519\pi$
$233$	−18.2440	−	18.2440i	−1.19520	−	1.19520i	−0.219618	−	0.975586i	$-0.570481\pi$
$234$	−32.6308			−2.13314
$235$		0			0
$236$		−	22.1640i		−	1.44275i
$237$	21.2322			1.37918
$238$	2.11516	−	0.459148i	0.137106	−	0.0297621i
$239$	29.2912			1.89469			0.947345	−	0.320215i	$-0.103755\pi$
$239$	29.2912			1.89469			0.947345	+	0.320215i	$0.103755\pi$
$240$		0			0
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	0.873435	−	0.486941i	$-0.161887\pi$
$241$	6.00000	+	6.00000i	0.386494	+	0.386494i	−0.486941	+	0.873435i	$0.661887\pi$
$242$	−25.5907			−1.64503
$243$	−14.7561	−	14.7561i	−0.946606	−	0.946606i
$244$	14.7760	−	14.7760i	0.945935	−	0.945935i
$245$		0			0
$246$			6.00000i			0.382546i
$247$		−	7.86854i		−	0.500663i
$248$	8.34797	−	8.34797i	0.530097	−	0.530097i
$249$	13.6456	−	13.6456i	0.864755	−	0.864755i
$250$		0			0
$251$	−1.77282			−0.111900			−0.0559498	−	0.998434i	$-0.517819\pi$
$251$	−1.77282			−0.111900			−0.0559498	+	0.998434i	$0.517819\pi$
$252$	−3.99462	−	3.99462i	−0.251638	−	0.251638i
$253$		−	0.195632i		−	0.0122993i
$254$	23.2428			1.45838
$255$		0			0
$256$	−27.5824			−1.72390
$257$		−	7.40235i		−	0.461746i	−0.972984	−	0.230873i	$-0.925842\pi$
$257$		−	7.40235i		−	0.461746i	0.972984	−	0.230873i	$-0.0741582\pi$
$258$	−13.2759	−	13.2759i	−0.826524	−	0.826524i
$259$	1.25761			0.0781440
$260$		0			0
$261$	34.4216	−	34.4216i	2.13064	−	2.13064i
$262$	33.2160	−	33.2160i	2.05209	−	2.05209i
$263$		−	7.67291i		−	0.473132i	−0.971615	−	0.236566i	$-0.923978\pi$
$263$		−	7.67291i		−	0.473132i	0.971615	−	0.236566i	$-0.0760219\pi$
$264$		−	6.69399i		−	0.411987i
$265$		0			0
$266$	1.48478	−	1.48478i	0.0910379	−	0.0910379i
$267$	−35.6574	−	35.6574i	−2.18220	−	2.18220i
$268$	42.5252			2.59764
$269$	5.56677	+	5.56677i	0.339412	+	0.339412i	0.856146	−	0.516734i	$-0.172852\pi$
$269$	5.56677	+	5.56677i	0.339412	+	0.339412i	−0.516734	+	0.856146i	$0.672852\pi$
$270$		0			0
$271$	18.0672			1.09750			0.548751	−	0.835986i	$-0.315103\pi$
$271$	18.0672			1.09750			0.548751	+	0.835986i	$0.315103\pi$
$272$	5.03593	−	7.82847i	0.305348	−	0.474670i
$273$	1.36518			0.0826245
$274$			11.1124i			0.671326i
$275$		0			0
$276$	−4.34275			−0.261403
$277$	−18.7786	−	18.7786i	−1.12829	−	1.12829i	−0.990455	−	0.137840i	$-0.955984\pi$
$277$	−18.7786	−	18.7786i	−1.12829	−	1.12829i	−0.137840	−	0.990455i	$-0.544016\pi$
$278$	−8.85472	+	8.85472i	−0.531071	+	0.531071i
$279$	−14.3564	+	14.3564i	−0.859494	+	0.859494i
$280$		0			0
$281$			13.7728i			0.821618i	0.911721	+	0.410809i	$0.134754\pi$
$281$			13.7728i			0.821618i	−0.911721	+	0.410809i	$0.865246\pi$
$282$	−35.8733	+	35.8733i	−2.13622	+	2.13622i
$283$	−9.72068	+	9.72068i	−0.577834	+	0.577834i	−0.934306	−	0.356472i	$-0.883980\pi$
$283$	−9.72068	+	9.72068i	−0.577834	+	0.577834i	0.356472	+	0.934306i	$0.383980\pi$
$284$	18.7108	+	18.7108i	1.11028	+	1.11028i
$285$		0			0
$286$	1.74239	+	1.74239i	0.103030	+	0.103030i
$287$		−	0.175350i		−	0.0103506i
$288$	18.7507			1.10490
$289$	−7.04840	−	15.4700i	−0.414612	−	0.909998i
$290$		0			0
$291$			29.0703i			1.70413i
$292$	3.09612	+	3.09612i	0.181187	+	0.181187i
$293$	19.8873			1.16183			0.580913	−	0.813966i	$-0.302696\pi$
$293$	19.8873			1.16183			0.580913	+	0.813966i	$0.302696\pi$
$294$	−37.0020	−	37.0020i	−2.15800	−	2.15800i
$295$		0			0
$296$	16.3396	−	16.3396i	0.949720	−	0.949720i
$297$			6.54392i			0.379717i
$298$		−	20.8612i		−	1.20846i
$299$	0.518371	−	0.518371i	0.0299782	−	0.0299782i
$300$		0			0
$301$	0.387990	+	0.387990i	0.0223634	+	0.0223634i
$302$	37.9484			2.18368
$303$	−16.0812	−	16.0812i	−0.923843	−	0.923843i
$304$		−	9.03043i		−	0.517931i
$305$		0			0
$306$	−37.0020	+	57.5204i	−2.11526	+	3.28822i
$307$	14.9598			0.853799			0.426900	−	0.904299i	$-0.359606\pi$
$307$	14.9598			0.853799			0.426900	+	0.904299i	$0.359606\pi$
$308$			0.426603i			0.0243080i
$309$	21.2460	+	21.2460i	1.20864	+	1.20864i
$310$		0			0
$311$	−20.9684	−	20.9684i	−1.18901	−	1.18901i	−0.977342	−	0.211667i	$-0.932111\pi$
$311$	−20.9684	−	20.9684i	−1.18901	−	1.18901i	−0.211667	−	0.977342i	$-0.567889\pi$
$312$	17.7372	−	17.7372i	1.00417	−	1.00417i
$313$	10.1671	−	10.1671i	0.574677	−	0.574677i	−0.358755	−	0.933432i	$-0.616799\pi$
$313$	10.1671	−	10.1671i	0.574677	−	0.574677i	0.933432	+	0.358755i	$0.116799\pi$
$314$			24.0336i			1.35629i
$315$		0			0
$316$	−17.5804	+	17.5804i	−0.988975	+	0.988975i
$317$	9.74047	−	9.74047i	0.547079	−	0.547079i	−0.378516	−	0.925595i	$-0.623565\pi$
$317$	9.74047	−	9.74047i	0.547079	−	0.547079i	0.925595	+	0.378516i	$0.123565\pi$
$318$	31.5199	+	31.5199i	1.76755	+	1.76755i
$319$	−3.67603			−0.205818
$320$		0			0
$321$			34.0188i			1.89874i
$322$	0.195632			0.0109021
$323$	−13.8704	−	8.92260i	−0.771768	−	0.496467i
$324$	68.2280			3.79044
$325$		0			0
$326$	16.1776	+	16.1776i	0.895995	+	0.895995i
$327$	44.3971			2.45516
$328$	−2.27825	−	2.27825i	−0.125795	−	0.125795i
$329$	1.04840	−	1.04840i	0.0578000	−	0.0578000i
$330$		0			0
$331$		−	20.1640i		−	1.10831i	−0.832413	−	0.554156i	$-0.813041\pi$
$331$		−	20.1640i		−	1.10831i	0.832413	−	0.554156i	$-0.186959\pi$
$332$			22.5973i			1.24019i
$333$	−28.1000	+	28.1000i	−1.53987	+	1.53987i
$334$	9.01679	−	9.01679i	0.493377	−	0.493377i
$335$		0			0
$336$	1.56677			0.0854742
$337$	20.2111	+	20.2111i	1.10097	+	1.10097i	0.994294	+	0.106677i	$0.0340210\pi$
$337$	20.2111	+	20.2111i	1.10097	+	1.10097i	0.106677	+	0.994294i	$0.465979\pi$
$338$		−	21.7870i		−	1.18506i
$339$	−22.6792			−1.23176
$340$		0			0
$341$	1.53318			0.0830264
$342$			66.3519i			3.58790i
$343$	2.17030	+	2.17030i	0.117185	+	0.117185i
$344$	10.0820			0.543584
$345$		0			0
$346$	−29.4520	+	29.4520i	−1.58335	+	1.58335i
$347$	−7.73326	+	7.73326i	−0.415143	+	0.415143i	−0.883526	−	0.468383i	$-0.844837\pi$
$347$	−7.73326	+	7.73326i	−0.415143	+	0.415143i	0.468383	+	0.883526i	$0.344837\pi$
$348$			81.6025i			4.37435i
$349$			0.645598i			0.0345581i	0.999851	+	0.0172790i	$0.00550036\pi$
$349$			0.645598i			0.0345581i	−0.999851	+	0.0172790i	$0.994500\pi$
$350$		0			0
$351$	−17.3396	+	17.3396i	−0.925519	+	0.925519i
$352$	−1.00124	−	1.00124i	−0.0533661	−	0.0533661i
$353$	14.3022			0.761229			0.380615	−	0.924734i	$-0.375712\pi$
$353$	14.3022			0.761229			0.380615	+	0.924734i	$0.375712\pi$
$354$	−31.9368	−	31.9368i	−1.69742	−	1.69742i
$355$		0			0
$356$	59.0492			3.12960
$357$	1.54806	−	2.40649i	0.0819320	−	0.127365i
$358$	50.8854			2.68938
$359$			15.6760i			0.827349i	0.910425	+	0.413675i	$0.135755\pi$
$359$			15.6760i			0.827349i	−0.910425	+	0.413675i	$0.864245\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	24.3613	+	24.3613i	1.28040	+	1.28040i
$363$	−23.9224	+	23.9224i	−1.25560	+	1.25560i
$364$	−1.13038	+	1.13038i	−0.0592481	+	0.0592481i
$365$		0			0
$366$		−	42.5824i		−	2.22582i
$367$	−15.4863	+	15.4863i	−0.808379	+	0.808379i	−0.984388	−	0.176009i	$-0.943681\pi$
$367$	−15.4863	+	15.4863i	−0.808379	+	0.808379i	0.176009	+	0.984388i	$0.443681\pi$
$368$	0.594916	−	0.594916i	0.0310121	−	0.0310121i
$369$	3.91802	+	3.91802i	0.203964	+	0.203964i
$370$		0			0
$371$	−0.921171	−	0.921171i	−0.0478248	−	0.0478248i
$372$		−	34.0344i		−	1.76460i
$373$	−6.50858			−0.337002			−0.168501	−	0.985702i	$-0.553893\pi$
$373$	−6.50858			−0.337002			−0.168501	+	0.985702i	$0.553893\pi$
$374$	5.04723	−	1.09562i	0.260986	−	0.0566533i
$375$		0			0
$376$		−	27.2428i		−	1.40494i
$377$	−9.74047	−	9.74047i	−0.501660	−	0.501660i
$378$	−6.54392			−0.336583
$379$	5.32280	+	5.32280i	0.273414	+	0.273414i	0.830473	−	0.557059i	$-0.188070\pi$
$379$	5.32280	+	5.32280i	0.273414	+	0.273414i	−0.557059	+	0.830473i	$0.688070\pi$
$380$		0			0
$381$	21.7276	−	21.7276i	1.11314	−	1.11314i
$382$		−	16.0888i		−	0.823172i
$383$			24.7752i			1.26595i	0.774172	+	0.632976i	$0.218167\pi$
$383$			24.7752i			1.26595i	−0.774172	+	0.632976i	$0.781833\pi$
$384$	−46.2596	+	46.2596i	−2.36067	+	2.36067i
$385$		0			0
$386$	−24.7276	−	24.7276i	−1.25860	−	1.25860i
$387$	−17.3385			−0.881363
$388$	−24.0705	−	24.0705i	−1.22199	−	1.22199i
$389$		−	23.6971i		−	1.20149i	−0.799440	−	0.600747i	$-0.794870\pi$
$389$		−	23.6971i		−	1.20149i	0.799440	−	0.600747i	$-0.205130\pi$
$390$		0			0
$391$	−0.325954	−	1.50158i	−0.0164842	−	0.0759380i
$392$	28.1000			1.41926
$393$		−	62.1013i		−	3.13260i
$394$	1.46682	+	1.46682i	0.0738973	+	0.0738973i
$395$		0			0
$396$	−9.53201	−	9.53201i	−0.479002	−	0.479002i
$397$	−19.5964	+	19.5964i	−0.983516	+	0.983516i	−0.999866	−	0.0163500i	$-0.994795\pi$
$397$	−19.5964	+	19.5964i	−0.983516	+	0.983516i	0.0163500	+	0.999866i	$0.494795\pi$
$398$	22.4418	−	22.4418i	1.12490	−	1.12490i
$399$		−	2.77598i		−	0.138973i
$400$		0			0
$401$	−21.5972	+	21.5972i	−1.07851	+	1.07851i	−0.0818697	+	0.996643i	$0.526089\pi$
$401$	−21.5972	+	21.5972i	−1.07851	+	1.07851i	−0.996643	+	0.0818697i	$0.973911\pi$
$402$	61.2759	−	61.2759i	3.05616	−	3.05616i
$403$	4.06251	+	4.06251i	0.202368	+	0.202368i
$404$	26.6308			1.32493
$405$		0			0
$406$		−	3.67603i		−	0.182438i
$407$	3.00092			0.148750
$408$	−11.1533	−	51.3799i	−0.552168	−	2.54368i
$409$	−5.90321			−0.291895			−0.145947	−	0.989292i	$-0.546623\pi$
$409$	−5.90321			−0.291895			−0.145947	+	0.989292i	$0.546623\pi$
$410$		0			0
$411$	10.3880	+	10.3880i	0.512402	+	0.512402i
$412$	−35.1837			−1.73337
$413$	0.933353	+	0.933353i	0.0459273	+	0.0459273i
$414$	−4.37120	+	4.37120i	−0.214833	+	0.214833i
$415$		0			0
$416$		−	5.30601i		−	0.260148i
$417$			16.5549i			0.810699i
$418$	3.54301	−	3.54301i	0.173294	−	0.173294i
$419$	−22.9716	+	22.9716i	−1.12223	+	1.12223i	−0.130829	+	0.991405i	$0.541764\pi$
$419$	−22.9716	+	22.9716i	−1.12223	+	1.12223i	−0.991405	+	0.130829i	$0.958236\pi$
$420$		0			0
$421$	30.1156			1.46774			0.733872	−	0.679288i	$-0.237711\pi$
$421$	30.1156			1.46774			0.733872	+	0.679288i	$0.237711\pi$
$422$	−30.0195	−	30.0195i	−1.46133	−	1.46133i
$423$			46.8507i			2.27796i
$424$	−23.9368			−1.16247
$425$		0			0
$426$	53.9220			2.61253
$427$			1.24447i			0.0602242i
$428$	−28.1678	−	28.1678i	−1.36154	−	1.36154i
$429$	3.25761			0.157279
$430$		0			0
$431$	−5.88641	+	5.88641i	−0.283538	+	0.283538i	−0.834518	−	0.550980i	$-0.814254\pi$
$431$	−5.88641	+	5.88641i	−0.283538	+	0.283538i	0.550980	+	0.834518i	$0.314254\pi$
$432$	−19.9000	+	19.9000i	−0.957440	+	0.957440i
$433$			13.5795i			0.652591i	0.945268	+	0.326295i	$0.105800\pi$
$433$			13.5795i			0.652591i	−0.945268	+	0.326295i	$0.894200\pi$
$434$			1.53318i			0.0735950i
$435$		0			0
$436$	−36.7612	+	36.7612i	−1.76054	+	1.76054i
$437$	−1.05406	−	1.05406i	−0.0504227	−	0.0504227i
$438$	8.92260			0.426338
$439$	−14.4048	−	14.4048i	−0.687503	−	0.687503i	0.274177	−	0.961679i	$-0.411595\pi$
$439$	−14.4048	−	14.4048i	−0.687503	−	0.687503i	−0.961679	+	0.274177i	$0.911595\pi$
$440$		0			0
$441$	−48.3248			−2.30118
$442$	16.2769	+	10.4707i	0.774211	+	0.498039i
$443$	−2.45360			−0.116574			−0.0582871	−	0.998300i	$-0.518564\pi$
$443$	−2.45360			−0.116574			−0.0582871	+	0.998300i	$0.518564\pi$
$444$		−	66.6160i		−	3.16145i
$445$		0			0
$446$	−4.69399			−0.222267
$447$	−19.5012	−	19.5012i	−0.922376	−	0.922376i
$448$	1.70362	−	1.70362i	0.0804884	−	0.0804884i
$449$	−2.26076	+	2.26076i	−0.106692	+	0.106692i	−0.758438	−	0.651746i	$-0.774037\pi$
$449$	−2.26076	+	2.26076i	−0.106692	+	0.106692i	0.651746	+	0.758438i	$0.274037\pi$
$450$		0			0
$451$		−	0.418422i		−	0.0197027i
$452$	18.7786	−	18.7786i	0.883269	−	0.883269i
$453$	35.4745	−	35.4745i	1.66674	−	1.66674i
$454$	−20.1776	−	20.1776i	−0.946982	−	0.946982i
$455$		0			0
$456$	−36.0672	−	36.0672i	−1.68900	−	1.68900i
$457$			30.1803i			1.41177i	0.708325	+	0.705887i	$0.249451\pi$
$457$			30.1803i			1.41177i	−0.708325	+	0.705887i	$0.750549\pi$
$458$	−22.2061			−1.03762
$459$	10.9032	+	50.2280i	0.508918	+	2.34444i
$460$		0			0
$461$		−	5.41527i		−	0.252214i	−0.992017	−	0.126107i	$-0.959752\pi$
$461$		−	5.41527i		−	0.252214i	0.992017	−	0.126107i	$-0.0402483\pi$
$462$	0.614707	+	0.614707i	0.0285987	+	0.0285987i
$463$	−15.7574			−0.732307			−0.366153	−	0.930555i	$-0.619325\pi$
$463$	−15.7574			−0.732307			−0.366153	+	0.930555i	$0.619325\pi$
$464$	−11.1788	−	11.1788i	−0.518962	−	0.518962i
$465$		0			0
$466$	43.5340	−	43.5340i	2.01667	−	2.01667i
$467$		−	10.7690i		−	0.498331i	−0.968461	−	0.249166i	$-0.919844\pi$
$467$		−	10.7690i		−	0.498331i	0.968461	−	0.249166i	$-0.0801563\pi$
$468$		−	50.5144i		−	2.33503i
$469$	−1.79079	+	1.79079i	−0.0826910	+	0.0826910i
$470$		0			0
$471$	22.4668	+	22.4668i	1.03522	+	1.03522i
$472$	24.2534			1.11635
$473$	0.925824	+	0.925824i	0.0425695	+	0.0425695i
$474$			50.6644i			2.32709i
$475$		0			0
$476$	0.710788	+	3.27440i	0.0325789	+	0.150082i
$477$	41.1652			1.88483
$478$			69.8949i			3.19692i
$479$	−26.0988	−	26.0988i	−1.19248	−	1.19248i	−0.976368	−	0.216116i	$-0.930661\pi$
$479$	−26.0988	−	26.0988i	−1.19248	−	1.19248i	−0.216116	−	0.976368i	$-0.569339\pi$
$480$		0			0
$481$	7.95160	+	7.95160i	0.362562	+	0.362562i
$482$	−14.3173	+	14.3173i	−0.652133	+	0.652133i
$483$	0.182879	−	0.182879i	0.00832127	−	0.00832127i
$484$		−	39.6160i		−	1.80073i
$485$		0			0
$486$	35.2112	−	35.2112i	1.59721	−	1.59721i
$487$	−27.0987	+	27.0987i	−1.22796	+	1.22796i	−0.263226	+	0.964734i	$0.584786\pi$
$487$	−27.0987	+	27.0987i	−1.22796	+	1.22796i	−0.964734	+	0.263226i	$0.915214\pi$
$488$	16.1689	+	16.1689i	0.731932	+	0.731932i
$489$	30.2460			1.36777
$490$		0			0
$491$		−	38.0336i		−	1.71643i	−0.513289	−	0.858216i	$-0.671573\pi$
$491$		−	38.0336i		−	1.71643i	0.513289	−	0.858216i	$-0.328427\pi$
$492$	−9.28836			−0.418752
$493$	−28.2154	+	6.12485i	−1.27076	+	0.275849i
$494$	18.7760			0.844771
$495$		0			0
$496$	4.66239	+	4.66239i	0.209348	+	0.209348i
$497$	−1.57587			−0.0706875
$498$	32.5613	+	32.5613i	1.45910	+	1.45910i
$499$	−6.58041	+	6.58041i	−0.294579	+	0.294579i	−0.838886	−	0.544307i	$-0.816793\pi$
$499$	−6.58041	+	6.58041i	−0.294579	+	0.294579i	0.544307	+	0.838886i	$0.316793\pi$
$500$		0			0
$501$		−	16.8580i		−	0.753158i
$502$		−	4.23033i		−	0.188809i
$503$	−1.10919	+	1.10919i	−0.0494565	+	0.0494565i	−0.731403	−	0.681946i	$-0.761134\pi$
$503$	−1.10919	+	1.10919i	−0.0494565	+	0.0494565i	0.681946	+	0.731403i	$0.261134\pi$
$504$	4.37120	−	4.37120i	0.194709	−	0.194709i
$505$		0			0
$506$	0.466819			0.0207526
$507$	−20.3667	−	20.3667i	−0.904516	−	0.904516i
$508$			35.9812i			1.59641i
$509$	24.4247			1.08261			0.541304	−	0.840827i	$-0.317931\pi$
$509$	24.4247			1.08261			0.541304	+	0.840827i	$0.317931\pi$
$510$		0			0
$511$	−0.260763			−0.0115355
$512$		−	24.3410i		−	1.07573i
$513$	35.2586	+	35.2586i	1.55670	+	1.55670i
$514$	17.6636			0.779106
$515$		0			0
$516$	20.5520	−	20.5520i	0.904750	−	0.904750i
$517$	2.50169	−	2.50169i	0.110024	−	0.110024i
$518$			3.00092i			0.131853i
$519$			55.0640i			2.41704i
$520$		0			0
$521$	−5.30916	+	5.30916i	−0.232599	+	0.232599i	−0.813776	−	0.581178i	$-0.802592\pi$
$521$	−5.30916	+	5.30916i	−0.232599	+	0.232599i	0.581178	+	0.813776i	$0.302592\pi$
$522$	82.1371	+	82.1371i	3.59504	+	3.59504i
$523$	−8.98247			−0.392776			−0.196388	−	0.980526i	$-0.562921\pi$
$523$	−8.98247			−0.392776			−0.196388	+	0.980526i	$0.562921\pi$
$524$	51.4204	+	51.4204i	2.24631	+	2.24631i
$525$		0			0
$526$	18.3092			0.798317
$527$	11.7680	−	2.55452i	0.512620	−	0.111277i
$528$	3.73864			0.162703
$529$			22.8611i			0.993962i
$530$		0			0
$531$	−41.7096			−1.81004
$532$	2.29853	+	2.29853i	0.0996541	+	0.0996541i
$533$	1.10870	−	1.10870i	0.0480233	−	0.0480233i
$534$	85.0860	−	85.0860i	3.68203	−	3.68203i
$535$		0			0
$536$			46.5340i			2.00996i
$537$	47.5681	−	47.5681i	2.05272	−	2.05272i
$538$	−13.2835	+	13.2835i	−0.572691	+	0.572691i
$539$	2.58041	+	2.58041i	0.111146	+	0.111146i
$540$		0			0
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	0.486654	−	0.873595i	$-0.338217\pi$
$541$	−9.00000	−	9.00000i	−0.386940	−	0.386940i	−0.873595	+	0.486654i	$0.838217\pi$
$542$			43.1121i			1.85182i
$543$	45.5464			1.95458
$544$	−9.35323	−	6.01679i	−0.401016	−	0.257968i
$545$		0			0
$546$			3.25761i			0.139413i
$547$	1.81910	+	1.81910i	0.0777793	+	0.0777793i	0.744926	−	0.667147i	$-0.232485\pi$
$547$	1.81910	+	1.81910i	0.0777793	+	0.0777793i	−0.667147	+	0.744926i	$0.732485\pi$
$548$	−17.2027			−0.734862
$549$	−27.8064	−	27.8064i	−1.18675	−	1.18675i
$550$		0			0
$551$	−19.8064	+	19.8064i	−0.843782	+	0.843782i
$552$		−	4.75214i		−	0.202264i
$553$		−	1.48067i		−	0.0629644i
$554$	44.8096	−	44.8096i	1.90378	−	1.90378i
$555$		0			0
$556$	−13.7076	−	13.7076i	−0.581333	−	0.581333i
$557$	−21.0162			−0.890487			−0.445243	−	0.895410i	$-0.646883\pi$
$557$	−21.0162			−0.890487			−0.445243	+	0.895410i	$0.646883\pi$
$558$	−34.2573	−	34.2573i	−1.45023	−	1.45023i
$559$			4.90636i			0.207517i
$560$		0			0
$561$	3.69399	−	5.74239i	0.155961	−	0.242444i
$562$	−32.8648			−1.38632
$563$		−	40.5377i		−	1.70846i	−0.519893	−	0.854231i	$-0.674028\pi$
$563$		−	40.5377i		−	1.70846i	0.519893	−	0.854231i	$-0.325972\pi$
$564$	−55.5340	−	55.5340i	−2.33840	−	2.33840i
$565$		0			0
$566$	−23.1956	−	23.1956i	−0.974983	−	0.974983i
$567$	−2.87317	+	2.87317i	−0.120662	+	0.120662i
$568$	−20.4746	+	20.4746i	−0.859097	+	0.859097i
$569$		−	0.612010i		−	0.0256568i	−0.999918	−	0.0128284i	$-0.995916\pi$
$569$		−	0.612010i		−	0.0256568i	0.999918	−	0.0128284i	$-0.00408352\pi$
$570$		0			0
$571$	−10.5320	+	10.5320i	−0.440751	+	0.440751i	−0.892264	−	0.451513i	$-0.850884\pi$
$571$	−10.5320	+	10.5320i	−0.440751	+	0.440751i	0.451513	+	0.892264i	$0.350884\pi$
$572$	−2.69733	+	2.69733i	−0.112781	+	0.112781i
$573$	−15.0399	−	15.0399i	−0.628302	−	0.628302i
$574$	0.418422			0.0174646
$575$		0			0
$576$			76.1312i			3.17213i
$577$	−37.2107			−1.54910			−0.774550	−	0.632513i	$-0.782024\pi$
$577$	−37.2107			−1.54910			−0.774550	+	0.632513i	$0.782024\pi$
$578$	36.9146	−	16.8190i	1.53544	−	0.699576i
$579$	−46.2311			−1.92130
$580$		0			0
$581$	−0.951603	−	0.951603i	−0.0394791	−	0.0394791i
$582$	−69.3679			−2.87539
$583$	−2.19811	−	2.19811i	−0.0910362	−	0.0910362i
$584$	−3.38799	+	3.38799i	−0.140196	+	0.140196i
$585$		0			0
$586$			47.4552i			1.96035i
$587$		−	9.60470i		−	0.396428i	−0.980159	−	0.198214i	$-0.936486\pi$
$587$		−	9.60470i		−	0.396428i	0.980159	−	0.198214i	$-0.0635142\pi$
$588$	57.2813	−	57.2813i	2.36224	−	2.36224i
$589$	8.26076	−	8.26076i	0.340379	−	0.340379i
$590$		0			0
$591$	2.74239			0.112807
$592$	9.12576	+	9.12576i	0.375067	+	0.375067i
$593$			16.5206i			0.678419i	0.940711	+	0.339210i	$0.110160\pi$
$593$			16.5206i			0.678419i	−0.940711	+	0.339210i	$0.889840\pi$
$594$	−15.6152			−0.640698
$595$		0			0
$596$	32.2944			1.32283
$597$		−	41.9576i		−	1.71721i
$598$	1.23694	+	1.23694i	0.0505823	+	0.0505823i
$599$	−34.8096			−1.42228			−0.711140	−	0.703050i	$-0.751821\pi$
$599$	−34.8096			−1.42228			−0.711140	+	0.703050i	$0.751821\pi$
$600$		0			0
$601$	−8.26076	+	8.26076i	−0.336964	+	0.336964i	−0.855223	−	0.518260i	$-0.826580\pi$
$601$	−8.26076	+	8.26076i	−0.336964	+	0.336964i	0.518260	+	0.855223i	$0.326580\pi$
$602$	−0.925824	+	0.925824i	−0.0377338	+	0.0377338i
$603$		−	80.0267i		−	3.25894i
$604$			58.7464i			2.39036i
$605$		0			0
$606$	38.3732	−	38.3732i	1.55880	−	1.55880i
$607$	19.0421	+	19.0421i	0.772894	+	0.772894i	0.978611	−	0.205718i	$-0.0659528\pi$
$607$	19.0421	+	19.0421i	0.772894	+	0.772894i	−0.205718	+	0.978611i	$0.565953\pi$
$608$	−10.7893			−0.437564
$609$	−3.43639	−	3.43639i	−0.139249	−	0.139249i
$610$		0			0
$611$	13.2576			0.536345
$612$	−89.0450	−	57.2813i	−3.59943	−	2.31546i
$613$	5.43522			0.219526			0.109763	−	0.993958i	$-0.464991\pi$
$613$	5.43522			0.219526			0.109763	+	0.993958i	$0.464991\pi$
$614$			35.6971i			1.44062i
$615$		0			0
$616$	−0.466819			−0.0188087
$617$	2.47388	+	2.47388i	0.0995948	+	0.0995948i	0.755149	−	0.655554i	$-0.227565\pi$
$617$	2.47388	+	2.47388i	0.0995948	+	0.0995948i	−0.655554	+	0.755149i	$0.727565\pi$
$618$	−50.6973	+	50.6973i	−2.03934	+	2.03934i
$619$	−8.57725	+	8.57725i	−0.344749	+	0.344749i	−0.858149	−	0.513400i	$-0.828386\pi$
$619$	−8.57725	+	8.57725i	−0.344749	+	0.344749i	0.513400	+	0.858149i	$0.328386\pi$
$620$		0			0
$621$			4.64560i			0.186421i
$622$	50.0350	−	50.0350i	2.00622	−	2.00622i
$623$	−2.48664	+	2.48664i	−0.0996250	+	0.0996250i
$624$	9.90636	+	9.90636i	0.396572	+	0.396572i
$625$		0			0
$626$	24.2608	+	24.2608i	0.969655	+	0.969655i
$627$		−	6.62407i		−	0.264540i
$628$	−37.2054			−1.48466
$629$	23.0336	−	5.00000i	0.918409	−	0.199363i
$630$		0			0
$631$		−	12.6183i		−	0.502327i	−0.967945	−	0.251164i	$-0.919187\pi$
$631$		−	12.6183i		−	0.502327i	0.967945	−	0.251164i	$-0.0808132\pi$
$632$	−19.2377	−	19.2377i	−0.765235	−	0.765235i
$633$	−56.1250			−2.23077
$634$	23.2428	+	23.2428i	0.923089	+	0.923089i
$635$		0			0
$636$	−48.7948	+	48.7948i	−1.93484	+	1.93484i
$637$			13.6747i			0.541813i
$638$		−	8.77178i		−	0.347278i
$639$	35.2112	−	35.2112i	1.39293	−	1.39293i
$640$		0			0
$641$	21.3544	+	21.3544i	0.843448	+	0.843448i	0.989306	−	0.145857i	$-0.0465941\pi$
$641$	21.3544	+	21.3544i	0.843448	+	0.843448i	−0.145857	+	0.989306i	$0.546594\pi$
$642$	−81.1759			−3.20376
$643$	−13.9383	−	13.9383i	−0.549671	−	0.549671i	0.376675	−	0.926346i	$-0.377068\pi$
$643$	−13.9383	−	13.9383i	−0.549671	−	0.549671i	−0.926346	+	0.376675i	$0.877068\pi$
$644$			0.302850i			0.0119340i
$645$		0			0
$646$	21.2912	−	33.0976i	0.837691	−	1.30221i
$647$	−21.0418			−0.827237			−0.413618	−	0.910450i	$-0.635735\pi$
$647$	−21.0418			−0.827237			−0.413618	+	0.910450i	$0.635735\pi$
$648$			74.6598i			2.93291i
$649$	2.22718	+	2.22718i	0.0874243	+	0.0874243i
$650$		0			0
$651$	1.43323	+	1.43323i	0.0561728	+	0.0561728i
$652$	−25.0439	+	25.0439i	−0.980795	+	0.980795i
$653$	−27.3773	+	27.3773i	−1.07136	+	1.07136i	−0.0741056	+	0.997250i	$0.523610\pi$
$653$	−27.3773	+	27.3773i	−1.07136	+	1.07136i	−0.997250	+	0.0741056i	$0.976390\pi$
$654$			105.941i			4.14261i
$655$		0			0
$656$	1.27242	−	1.27242i	0.0496796	−	0.0496796i
$657$	5.82648	−	5.82648i	0.227313	−	0.227313i
$658$	2.50169	+	2.50169i	0.0975262	+	0.0975262i
$659$	24.1577			0.941049			0.470524	−	0.882387i	$-0.344065\pi$
$659$	24.1577			0.941049			0.470524	+	0.882387i	$0.344065\pi$
$660$		0			0
$661$			25.7432i			1.00129i	0.865651	+	0.500647i	$0.166905\pi$
$661$			25.7432i			1.00129i	−0.865651	+	0.500647i	$0.833095\pi$
$662$	48.1155			1.87006
$663$	25.0038	−	5.42769i	0.971068	−	0.210794i
$664$	−24.7276			−0.959616
$665$		0			0
$666$	−67.0524	−	67.0524i	−2.59823	−	2.59823i
$667$	−2.60965			−0.101046
$668$	13.9585	+	13.9585i	0.540072	+	0.540072i
$669$	−4.38799	+	4.38799i	−0.169649	+	0.169649i
$670$		0			0
$671$			2.96957i			0.114639i
$672$		−	1.87193i		−	0.0722113i
$673$	−7.42165	+	7.42165i	−0.286084	+	0.286084i	−0.835529	−	0.549446i	$-0.814839\pi$
$673$	−7.42165	+	7.42165i	−0.286084	+	0.286084i	0.549446	+	0.835529i	$0.314839\pi$
$674$	−48.2280	+	48.2280i	−1.85767	+	1.85767i
$675$		0			0
$676$	33.7276			1.29721
$677$	−6.00183	−	6.00183i	−0.230669	−	0.230669i	0.582303	−	0.812972i	$-0.302152\pi$
$677$	−6.00183	−	6.00183i	−0.230669	−	0.230669i	−0.812972	+	0.582303i	$0.802152\pi$
$678$		−	54.1173i		−	2.07836i
$679$	2.02728			0.0777998
$680$		0			0
$681$	−37.7244			−1.44560
$682$			3.65849i			0.140091i
$683$	−10.1044	−	10.1044i	−0.386635	−	0.386635i	0.486851	−	0.873485i	$-0.338146\pi$
$683$	−10.1044	−	10.1044i	−0.386635	−	0.386635i	−0.873485	+	0.486851i	$0.838146\pi$
$684$	−102.717			−3.92747
$685$		0			0
$686$	−5.17878	+	5.17878i	−0.197727	+	0.197727i
$687$	−20.7584	+	20.7584i	−0.791984	+	0.791984i
$688$			5.63085i			0.214674i
$689$		−	11.6488i		−	0.443782i
$690$		0			0
$691$	−6.24081	+	6.24081i	−0.237412	+	0.237412i	−0.815778	−	0.578366i	$-0.803691\pi$
$691$	−6.24081	+	6.24081i	−0.237412	+	0.237412i	0.578366	+	0.815778i	$0.303691\pi$
$692$	−45.5935	−	45.5935i	−1.73320	−	1.73320i
$693$	0.802810			0.0304962
$694$	−18.4532	−	18.4532i	−0.700473	−	0.700473i
$695$		0			0
$696$	−89.2952			−3.38472
$697$	−0.697157	−	3.21161i	−0.0264067	−	0.121648i
$698$	−1.54053			−0.0583100
$699$		−	81.3920i		−	3.07853i
$700$		0			0
$701$	18.5340			0.700019			0.350010	−	0.936746i	$-0.386178\pi$
$701$	18.5340			0.700019			0.350010	+	0.936746i	$0.386178\pi$
$702$	−41.3759	−	41.3759i	−1.56163	−	1.56163i
$703$	16.1689	−	16.1689i	0.609822	−	0.609822i
$704$	4.06519	−	4.06519i	0.153213	−	0.153213i
$705$		0			0
$706$			34.1280i			1.28443i
$707$	−1.12146	+	1.12146i	−0.0421767	+	0.0421767i
$708$	49.4401	−	49.4401i	1.85807	−	1.85807i
$709$	18.0304	+	18.0304i	0.677147	+	0.677147i	0.959354	−	0.282207i	$-0.0910664\pi$
$709$	18.0304	+	18.0304i	0.677147	+	0.677147i	−0.282207	+	0.959354i	$0.591066\pi$
$710$		0			0
$711$	33.0840	+	33.0840i	1.24075	+	1.24075i
$712$			64.6158i			2.42158i
$713$	1.08842			0.0407617
$714$	5.74239	+	3.69399i	0.214904	+	0.138244i
$715$		0			0
$716$			78.7736i			2.94391i
$717$	65.3384	+	65.3384i	2.44011	+	2.44011i
$718$	−37.4063			−1.39599
$719$	−3.36804	−	3.36804i	−0.125607	−	0.125607i	0.641509	−	0.767116i	$-0.278309\pi$
$719$	−3.36804	−	3.36804i	−0.125607	−	0.125607i	−0.767116	+	0.641509i	$0.778309\pi$
$720$		0			0
$721$	1.48163	−	1.48163i	0.0551787	−	0.0551787i
$722$			7.15863i			0.266417i
$723$			26.7678i			0.995505i
$724$	−37.7128	+	37.7128i	−1.40158	+	1.40158i
$725$		0			0
$726$	−57.0840	−	57.0840i	−2.11858	−	2.11858i
$727$	11.1858			0.414858			0.207429	−	0.978250i	$-0.433490\pi$
$727$	11.1858			0.414858			0.207429	+	0.978250i	$0.433490\pi$
$728$	−1.23694	−	1.23694i	−0.0458441	−	0.0458441i
$729$		−	10.4216i		−	0.385984i
$730$		0			0
$731$	8.64875	+	5.56361i	0.319886	+	0.205778i
$732$	65.9201			2.43648
$733$			26.2804i			0.970687i	0.874324	+	0.485344i	$0.161305\pi$
$733$			26.2804i			0.970687i	−0.874324	+	0.485344i	$0.838695\pi$
$734$	−36.9536	−	36.9536i	−1.36398	−	1.36398i
$735$		0			0
$736$	−0.710788	−	0.710788i	−0.0262000	−	0.0262000i
$737$	−4.27320	+	4.27320i	−0.157405	+	0.157405i
$738$	−9.34921	+	9.34921i	−0.344149	+	0.344149i
$739$			6.00000i			0.220714i	0.993892	+	0.110357i	$0.0351994\pi$
$739$			6.00000i			0.220714i	−0.993892	+	0.110357i	$0.964801\pi$
$740$		0			0
$741$	17.5520	−	17.5520i	0.644787	−	0.644787i
$742$	2.19811	−	2.19811i	0.0806950	−	0.0806950i
$743$	24.0700	+	24.0700i	0.883042	+	0.883042i	0.993843	−	0.110800i	$-0.0353415\pi$
$743$	24.0700	+	24.0700i	0.883042	+	0.883042i	−0.110800	+	0.993843i	$0.535341\pi$
$744$	37.2428			1.36539
$745$		0			0
$746$		−	15.5308i		−	0.568624i
$747$	42.5252			1.55591
$748$	1.69609	+	7.81341i	0.0620152	+	0.285686i
$749$	2.37237			0.0866844
$750$		0			0
$751$	−9.22285	−	9.22285i	−0.336547	−	0.336547i	0.518519	−	0.855066i	$-0.326483\pi$
$751$	−9.22285	−	9.22285i	−0.336547	−	0.336547i	−0.855066	+	0.518519i	$0.826483\pi$
$752$	15.2153			0.554844
$753$	−3.95455	−	3.95455i	−0.144112	−	0.144112i
$754$	23.2428	−	23.2428i	0.846453	−	0.846453i
$755$		0			0
$756$		−	10.1304i		−	0.368438i
$757$			31.8716i			1.15839i	0.815188	+	0.579197i	$0.196634\pi$
$757$			31.8716i			1.15839i	−0.815188	+	0.579197i	$0.803366\pi$
$758$	−12.7013	+	12.7013i	−0.461332	+	0.461332i
$759$	0.436387	−	0.436387i	0.0158398	−	0.0158398i
$760$		0			0
$761$	18.7549			0.679863			0.339932	−	0.940450i	$-0.389596\pi$
$761$	18.7549			0.679863			0.339932	+	0.940450i	$0.389596\pi$
$762$	51.8466	+	51.8466i	1.87820	+	1.87820i
$763$		−	3.09612i		−	0.112087i
$764$	24.9064			0.901081
$765$		0			0
$766$	−59.1187			−2.13605
$767$			11.8028i			0.426175i
$768$	−61.5267	−	61.5267i	−2.22015	−	2.22015i
$769$	47.7916			1.72341			0.861705	−	0.507410i	$-0.169397\pi$
$769$	47.7916			1.72341			0.861705	+	0.507410i	$0.169397\pi$
$770$		0			0
$771$	16.5121	−	16.5121i	0.594667	−	0.594667i
$772$	38.2798	−	38.2798i	1.37772	−	1.37772i
$773$			28.3286i			1.01891i	0.860497	+	0.509455i	$0.170153\pi$
$773$			28.3286i			1.01891i	−0.860497	+	0.509455i	$0.829847\pi$
$774$		−	41.3732i		−	1.48713i
$775$		0			0
$776$	26.3396	−	26.3396i	0.945536	−	0.945536i
$777$	2.80528	+	2.80528i	0.100639	+	0.100639i
$778$	56.5464			2.02729
$779$	−2.25445	−	2.25445i	−0.0807742	−	0.0807742i
$780$		0			0
$781$	−3.76036			−0.134556
$782$	3.58308	−	0.777794i	0.128131	−	0.0278139i
$783$	87.2932			3.11961
$784$			15.6940i			0.560500i
$785$		0			0
$786$	148.187			5.28565
$787$	−29.9191	−	29.9191i	−1.06650	−	1.06650i	−0.997625	−	0.0688738i	$-0.978059\pi$
$787$	−29.9191	−	29.9191i	−1.06650	−	1.06650i	−0.0688738	−	0.997625i	$-0.521941\pi$
$788$	−2.27072	+	2.27072i	−0.0808912	+	0.0808912i
$789$	17.1156	−	17.1156i	0.609330	−	0.609330i
$790$		0			0
$791$			1.58158i			0.0562344i
$792$	10.4306	−	10.4306i	0.370635	−	0.370635i
$793$	−7.86854	+	7.86854i	−0.279420	+	0.279420i
$794$	−46.7612	−	46.7612i	−1.65949	−	1.65949i
$795$		0			0
$796$	34.7412	+	34.7412i	1.23137	+	1.23137i
$797$		−	54.1578i		−	1.91837i	−0.282780	−	0.959185i	$-0.591257\pi$
$797$		−	54.1578i		−	1.91837i	0.282780	−	0.959185i	$-0.408743\pi$
$798$	6.62407			0.234489
$799$	15.0336	−	23.3700i	0.531850	−	0.826772i
$800$		0			0
$801$		−	111.123i		−	3.92633i
$802$	−51.5354	−	51.5354i	−1.81978	−	1.81978i
$803$	−0.622235			−0.0219582
$804$	94.8588	+	94.8588i	3.34541	+	3.34541i
$805$		0			0
$806$	−9.69399	+	9.69399i	−0.341456	+	0.341456i
$807$			24.8350i			0.874234i
$808$			29.1413i			1.02519i
$809$	−21.9064	+	21.9064i	−0.770187	+	0.770187i	−0.978139	−	0.207952i	$-0.933320\pi$
$809$	−21.9064	+	21.9064i	−0.770187	+	0.770187i	0.207952	+	0.978139i	$0.433320\pi$
$810$		0			0
$811$	−2.93481	−	2.93481i	−0.103055	−	0.103055i	0.653699	−	0.756754i	$-0.273216\pi$
$811$	−2.93481	−	2.93481i	−0.103055	−	0.103055i	−0.756754	+	0.653699i	$0.773216\pi$
$812$	5.69071			0.199705
$813$	40.3016	+	40.3016i	1.41344	+	1.41344i
$814$			7.16081i			0.250986i
$815$		0			0
$816$	28.6960	−	6.22916i	1.00456	−	0.218064i
$817$	9.97667			0.349039
$818$		−	14.0863i		−	0.492515i
$819$	2.12723	+	2.12723i	0.0743313	+	0.0743313i
$820$		0			0
$821$	−0.996845	−	0.996845i	−0.0347901	−	0.0347901i	0.689498	−	0.724288i	$-0.257831\pi$
$821$	−0.996845	−	0.996845i	−0.0347901	−	0.0347901i	−0.724288	+	0.689498i	$0.757831\pi$
$822$	−24.7879	+	24.7879i	−0.864578	+	0.864578i
$823$	14.2899	−	14.2899i	0.498116	−	0.498116i	−0.412735	−	0.910851i	$-0.635427\pi$
$823$	14.2899	−	14.2899i	0.498116	−	0.498116i	0.910851	+	0.412735i	$0.135427\pi$
$824$		−	38.5004i		−	1.34123i
$825$		0			0
$826$	−2.22718	+	2.22718i	−0.0774934	+	0.0774934i
$827$	8.03163	−	8.03163i	0.279287	−	0.279287i	−0.553537	−	0.832824i	$-0.686722\pi$
$827$	8.03163	−	8.03163i	0.279287	−	0.279287i	0.832824	+	0.553537i	$0.186722\pi$
$828$	−6.76687	−	6.76687i	−0.235165	−	0.235165i
$829$	10.9336			0.379741			0.189870	−	0.981809i	$-0.439193\pi$
$829$	10.9336			0.379741			0.189870	+	0.981809i	$0.439193\pi$
$830$		0			0
$831$		−	83.7768i		−	2.90618i
$832$	21.5433			0.746879
$833$	24.1053	+	15.5066i	0.835200	+	0.537272i
$834$	−39.5036			−1.36790
$835$		0			0
$836$	5.48478	+	5.48478i	0.189695	+	0.189695i
$837$	−36.4078			−1.25844
$838$	−54.8149	−	54.8149i	−1.89355	−	1.89355i
$839$	−27.4836	+	27.4836i	−0.948840	+	0.948840i	−0.998754	−	0.0499138i	$-0.984105\pi$
$839$	−27.4836	+	27.4836i	−0.948840	+	0.948840i	0.0499138	+	0.998754i	$0.484105\pi$
$840$		0			0
$841$			20.0367i			0.690922i
$842$			71.8621i			2.47653i
$843$	−30.7224	+	30.7224i	−1.05813	+	1.05813i
$844$	46.4720	−	46.4720i	1.59963	−	1.59963i
$845$		0			0
$846$	−111.796			−3.84361
$847$	1.66828	+	1.66828i	0.0573228	+	0.0573228i
$848$		−	13.3688i		−	0.459088i
$849$	−43.3669			−1.48835
$850$		0			0
$851$	2.13038			0.0730285
$852$			83.4745i			2.85979i
$853$	22.6454	+	22.6454i	0.775365	+	0.775365i	0.979039	−	0.203674i	$-0.0652882\pi$
$853$	22.6454	+	22.6454i	0.775365	+	0.775365i	−0.203674	+	0.979039i	$0.565288\pi$
$854$	−2.96957			−0.101617
$855$		0			0
$856$	30.8232	−	30.8232i	1.05352	−	1.05352i
$857$	18.1563	−	18.1563i	0.620208	−	0.620208i	−0.325376	−	0.945585i	$-0.605491\pi$
$857$	18.1563	−	18.1563i	0.620208	−	0.620208i	0.945585	+	0.325376i	$0.105491\pi$
$858$			7.77333i			0.265377i
$859$		−	38.7065i		−	1.32065i	−0.750981	−	0.660324i	$-0.770419\pi$
$859$		−	38.7065i		−	1.32065i	0.750981	−	0.660324i	$-0.229581\pi$
$860$		0			0
$861$	0.391145	−	0.391145i	0.0133302	−	0.0133302i
$862$	−14.0462	−	14.0462i	−0.478416	−	0.478416i
$863$	−29.5881			−1.00719			−0.503596	−	0.863939i	$-0.667990\pi$
$863$	−29.5881			−1.00719			−0.503596	+	0.863939i	$0.667990\pi$
$864$	23.7760	+	23.7760i	0.808875	+	0.808875i
$865$		0			0
$866$	−32.4036			−1.10112
$867$	18.7856	−	50.2306i	0.637992	−	1.70592i
$868$	−2.37346			−0.0805603
$869$		−	3.53318i		−	0.119855i
$870$		0			0
$871$	−22.6456			−0.767317
$872$	−40.2266	−	40.2266i	−1.36225	−	1.36225i
$873$	−45.2974	+	45.2974i	−1.53309	+	1.53309i
$874$	2.51522	−	2.51522i	0.0850785	−	0.0850785i
$875$		0			0
$876$			13.8127i			0.466689i
$877$	−18.7380	+	18.7380i	−0.632737	+	0.632737i	−0.948754	−	0.316017i	$-0.897654\pi$
$877$	−18.7380	+	18.7380i	−0.632737	+	0.632737i	0.316017	+	0.948754i	$0.397654\pi$
$878$	34.3728	−	34.3728i	1.16003	−	1.16003i
$879$	44.3615	+	44.3615i	1.49628	+	1.49628i
$880$		0			0
$881$	−7.77282	−	7.77282i	−0.261873	−	0.261873i	0.563942	−	0.825815i	$-0.309284\pi$
$881$	−7.77282	−	7.77282i	−0.261873	−	0.261873i	−0.825815	+	0.563942i	$0.809284\pi$
$882$		−	115.313i		−	3.88279i
$883$	56.2202			1.89196			0.945980	−	0.324225i	$-0.105104\pi$
$883$	56.2202			1.89196			0.945980	+	0.324225i	$0.105104\pi$
$884$	−16.2092	+	25.1976i	−0.545175	+	0.847486i
$885$		0			0
$886$		−	5.85481i		−	0.196696i
$887$	4.87988	+	4.87988i	0.163850	+	0.163850i	0.784270	−	0.620420i	$-0.213038\pi$
$887$	4.87988	+	4.87988i	0.163850	+	0.163850i	−0.620420	+	0.784270i	$0.713038\pi$
$888$	72.8958			2.44622
$889$	−1.51522	−	1.51522i	−0.0508187	−	0.0508187i
$890$		0			0
$891$	−6.85598	+	6.85598i	−0.229684	+	0.229684i
$892$		−	7.26658i		−	0.243303i
$893$		−	26.9582i		−	0.902122i
$894$	46.5340	−	46.5340i	1.55633	−	1.55633i
$895$		0			0
$896$	3.22600	+	3.22600i	0.107773	+	0.107773i
$897$	2.31261			0.0772158
$898$	−5.39465	−	5.39465i	−0.180022	−	0.180022i
$899$		−	20.4520i		−	0.682113i
$900$		0			0
$901$	−20.5340	−	13.2092i	−0.684087	−	0.440063i
$902$	0.998442			0.0332445
$903$			1.73094i			0.0576020i
$904$	20.5488	+	20.5488i	0.683443	+	0.683443i
$905$		0			0
$906$	84.6496	+	84.6496i	2.81229	+	2.81229i
$907$	22.0708	−	22.0708i	0.732849	−	0.732849i	−0.238334	−	0.971183i	$-0.576601\pi$
$907$	22.0708	−	22.0708i	0.732849	−	0.732849i	0.971183	+	0.238334i	$0.0766014\pi$
$908$	31.2361	−	31.2361i	1.03661	−	1.03661i
$909$		−	50.1156i		−	1.66223i
$910$		0			0
$911$	30.0472	−	30.0472i	0.995509	−	0.995509i	−0.00448095	−	0.999990i	$-0.501426\pi$
$911$	30.0472	−	30.0472i	0.995509	−	0.995509i	0.999990	+	0.00448095i	$0.00142634\pi$
$912$	20.1437	−	20.1437i	0.667026	−	0.667026i
$913$	−2.27072	−	2.27072i	−0.0751500	−	0.0751500i
$914$	−72.0164			−2.38209
$915$		0			0
$916$		−	34.3763i		−	1.13583i
$917$	−4.33076			−0.143014
$918$	−119.854	+	26.0173i	−3.95579	+	0.858700i
$919$	29.1312			0.960949			0.480475	−	0.877009i	$-0.340464\pi$
$919$	29.1312			0.960949			0.480475	+	0.877009i	$0.340464\pi$
$920$		0			0
$921$	33.3700	+	33.3700i	1.09958	+	1.09958i
$922$	12.9220			0.425562
$923$	−9.96391	−	9.96391i	−0.327966	−	0.327966i
$924$	−0.951603	+	0.951603i	−0.0313054	+	0.0313054i
$925$		0			0
$926$		−	37.6004i		−	1.23562i
$927$			66.2109i			2.17465i
$928$	−13.3561	+	13.3561i	−0.438435	+	0.438435i
$929$	−0.921171	+	0.921171i	−0.0302226	+	0.0302226i	−0.722057	−	0.691834i	$-0.756803\pi$
$929$	−0.921171	+	0.921171i	−0.0302226	+	0.0302226i	0.691834	+	0.722057i	$0.256803\pi$
$930$		0			0
$931$	27.8064			0.911318
$932$	67.3932	+	67.3932i	2.20754	+	2.20754i
$933$		−	93.5463i		−	3.06257i
$934$	25.6971			0.840836
$935$		0			0
$936$	55.2764			1.80677
$937$		−	9.43458i		−	0.308214i	−0.988054	−	0.154107i	$-0.950750\pi$
$937$		−	9.43458i		−	0.308214i	0.988054	−	0.154107i	$-0.0492501\pi$
$938$	−4.27320	−	4.27320i	−0.139525	−	0.139525i
$939$	45.3584			1.48021
$940$		0			0
$941$	−17.8033	+	17.8033i	−0.580370	+	0.580370i	−0.935005	−	0.354635i	$-0.884605\pi$
$941$	−17.8033	+	17.8033i	−0.580370	+	0.580370i	0.354635	+	0.935005i	$0.384605\pi$
$942$	−53.6105	+	53.6105i	−1.74673	+	1.74673i
$943$		−	0.297042i		−	0.00967302i
$944$			13.5456i			0.440873i
$945$		0			0
$946$	−2.20921	+	2.20921i	−0.0718276	+	0.0718276i
$947$	19.5564	+	19.5564i	0.635496	+	0.635496i	0.949441	−	0.313945i	$-0.101651\pi$
$947$	19.5564	+	19.5564i	0.635496	+	0.635496i	−0.313945	+	0.949441i	$0.601651\pi$
$948$	−78.4315			−2.54734
$949$	−1.64875	−	1.64875i	−0.0535208	−	0.0535208i
$950$		0			0
$951$	43.4552			1.40913
$952$	−3.58308	+	0.777794i	−0.116128	+	0.0252085i
$953$	16.0279			0.519195			0.259598	−	0.965717i	$-0.416410\pi$
$953$	16.0279			0.519195			0.259598	+	0.965717i	$0.416410\pi$
$954$			98.2288i			3.18027i
$955$		0			0
$956$	−108.202			−3.49949
$957$	−8.19994	−	8.19994i	−0.265066	−	0.265066i
$958$	62.2771	−	62.2771i	2.01208	−	2.01208i
$959$	0.724427	−	0.724427i	0.0233930	−	0.0233930i
$960$		0			0
$961$		−	22.4700i		−	0.724838i
$962$	−18.9742	+	18.9742i	−0.611752	+	0.611752i
$963$	−53.0081	+	53.0081i	−1.70816	+	1.70816i
$964$	−22.1640	−	22.1640i	−0.713853	−	0.713853i
$965$		0			0
$966$	0.436387	+	0.436387i	0.0140405	+	0.0140405i
$967$			10.9849i			0.353252i	0.984278	+	0.176626i	$0.0565183\pi$
$967$			10.9849i			0.353252i	−0.984278	+	0.176626i	$0.943482\pi$
$968$	43.3506			1.39334
$969$	−11.0367	−	50.8432i	−0.354551	−	1.63332i
$970$		0			0
$971$		−	32.2944i		−	1.03638i	−0.855267	−	0.518188i	$-0.826607\pi$
$971$		−	32.2944i		−	1.03638i	0.855267	−	0.518188i	$-0.173393\pi$
$972$	54.5090	+	54.5090i	1.74838	+	1.74838i
$973$	1.15449			0.0370113
$974$	−64.6632	−	64.6632i	−2.07194	−	2.07194i
$975$		0			0
$976$	−9.03043	+	9.03043i	−0.289057	+	0.289057i
$977$			2.59459i			0.0830084i	0.999138	+	0.0415042i	$0.0132150\pi$
$977$			2.59459i			0.0830084i	−0.999138	+	0.0415042i	$0.986785\pi$
$978$			72.1732i			2.30784i
$979$	−5.93364	+	5.93364i	−0.189640	+	0.189640i
$980$		0			0
$981$	69.1796	+	69.1796i	2.20873	+	2.20873i
$982$	90.7561			2.89614
$983$	6.79991	+	6.79991i	0.216883	+	0.216883i	0.807184	−	0.590300i	$-0.200991\pi$
$983$	6.79991	+	6.79991i	0.216883	+	0.216883i	−0.590300	+	0.807184i	$0.700991\pi$
$984$		−	10.1640i		−	0.324015i
$985$		0			0
$986$	−14.6152	−	67.3279i	−0.465442	−	2.14416i
$987$	4.67721			0.148877
$988$			29.0663i			0.924723i
$989$	0.657252	+	0.657252i	0.0208994	+	0.0208994i
$990$		0			0
$991$	19.9864	+	19.9864i	0.634888	+	0.634888i	0.949290	−	0.314402i	$-0.101804\pi$
$991$	19.9864	+	19.9864i	0.634888	+	0.634888i	−0.314402	+	0.949290i	$0.601804\pi$
$992$	5.57049	−	5.57049i	0.176863	−	0.176863i
$993$	44.9788	−	44.9788i	1.42736	−	1.42736i
$994$		−	3.76036i		−	0.119271i
$995$		0			0
$996$	−50.4068	+	50.4068i	−1.59720	+	1.59720i
$997$	2.36593	−	2.36593i	0.0749297	−	0.0749297i	−0.668649	−	0.743578i	$-0.733127\pi$
$997$	2.36593	−	2.36593i	0.0749297	−	0.0749297i	0.743578	+	0.668649i	$0.233127\pi$
$998$	−15.7022	−	15.7022i	−0.497045	−	0.497045i
$999$	−71.2616			−2.25462

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.e.d.251.6		12
5.2	odd	4		85.2.j.c.64.1	yes	12
5.3	odd	4		85.2.j.c.64.6	yes	12
5.4	even	2	inner	425.2.e.d.251.1		12
15.2	even	4		765.2.t.e.64.6		12
15.8	even	4		765.2.t.e.64.1		12
17.2	even	8		7225.2.a.bp.1.2		12
17.4	even	4	inner	425.2.e.d.276.1		12
17.15	even	8		7225.2.a.bp.1.1		12
85.2	odd	8		1445.2.b.f.579.1		12
85.4	even	4	inner	425.2.e.d.276.6		12
85.19	even	8		7225.2.a.bp.1.11		12
85.32	odd	8		1445.2.b.f.579.2		12
85.38	odd	4		85.2.j.c.4.1	✓	12
85.49	even	8		7225.2.a.bp.1.12		12
85.53	odd	8		1445.2.b.f.579.12		12
85.72	odd	4		85.2.j.c.4.6	yes	12
85.83	odd	8		1445.2.b.f.579.11		12
255.38	even	4		765.2.t.e.514.6		12
255.242	even	4		765.2.t.e.514.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.1	✓	12	85.38	odd	4
85.2.j.c.4.6	yes	12	85.72	odd	4
85.2.j.c.64.1	yes	12	5.2	odd	4
85.2.j.c.64.6	yes	12	5.3	odd	4
425.2.e.d.251.1		12	5.4	even	2	inner
425.2.e.d.251.6		12	1.1	even	1	trivial
425.2.e.d.276.1		12	17.4	even	4	inner
425.2.e.d.276.6		12	85.4	even	4	inner
765.2.t.e.64.1		12	15.8	even	4
765.2.t.e.64.6		12	15.2	even	4
765.2.t.e.514.1		12	255.242	even	4
765.2.t.e.514.6		12	255.38	even	4
1445.2.b.f.579.1		12	85.2	odd	8
1445.2.b.f.579.2		12	85.32	odd	8
1445.2.b.f.579.11		12	85.83	odd	8
1445.2.b.f.579.12		12	85.53	odd	8
7225.2.a.bp.1.1		12	17.15	even	8
7225.2.a.bp.1.2		12	17.2	even	8
7225.2.a.bp.1.11		12	85.19	even	8
7225.2.a.bp.1.12		12	85.49	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.38621i q^{2} +(2.23065 + 2.23065i) q^{3} -3.69399 q^{4} +(-5.32280 + 5.32280i) q^{6} +(0.155559 - 0.155559i) q^{7} -4.04223i q^{8} +6.95160i q^{9} +(0.371196 - 0.371196i) q^{11} +(-8.24001 - 8.24001i) q^{12} +1.96713 q^{13} +(0.371196 + 0.371196i) q^{14} +2.25761 q^{16} +(2.23065 - 3.46759i) q^{17} -16.5880 q^{18} -4.00000i q^{19} +0.693995 q^{21} +(0.885751 + 0.885751i) q^{22} +(0.263516 - 0.263516i) q^{23} +(9.01679 - 9.01679i) q^{24} +4.69399i q^{26} +(-8.81464 + 8.81464i) q^{27} +(-0.574634 + 0.574634i) q^{28} +(-4.95160 - 4.95160i) q^{29} +(2.06519 + 2.06519i) q^{31} -2.69733i q^{32} +1.65602 q^{33} +(8.27440 + 5.32280i) q^{34} -25.6792i q^{36} +(4.04223 + 4.04223i) q^{37} +9.54484 q^{38} +(4.38799 + 4.38799i) q^{39} +(0.563613 - 0.563613i) q^{41} +1.65602i q^{42} +2.49417i q^{43} +(-1.37120 + 1.37120i) q^{44} +(0.628804 + 0.628804i) q^{46} +6.73955 q^{47} +(5.03593 + 5.03593i) q^{48} +6.95160i q^{49} +(12.7108 - 2.75919i) q^{51} -7.26658 q^{52} -5.92169i q^{53} +(-21.0336 - 21.0336i) q^{54} +(-0.628804 - 0.628804i) q^{56} +(8.92260 - 8.92260i) q^{57} +(11.8156 - 11.8156i) q^{58} +6.00000i q^{59} +(-4.00000 + 4.00000i) q^{61} +(-4.92798 + 4.92798i) q^{62} +(1.08138 + 1.08138i) q^{63} +10.9516 q^{64} +3.95160i q^{66} -11.5120 q^{67} +(-8.24001 + 12.8093i) q^{68} +1.17562 q^{69} +(-5.06519 - 5.06519i) q^{71} +28.1000 q^{72} +(-0.838149 - 0.838149i) q^{73} +(-9.64560 + 9.64560i) q^{74} +14.7760i q^{76} -0.115486i q^{77} +(-10.4707 + 10.4707i) q^{78} +(4.75919 - 4.75919i) q^{79} -18.4700 q^{81} +(1.34490 + 1.34490i) q^{82} -6.11732i q^{83} -2.56361 q^{84} -5.95160 q^{86} -22.0906i q^{87} +(-1.50046 - 1.50046i) q^{88} -15.9852 q^{89} +(0.306005 - 0.306005i) q^{91} +(-0.973426 + 0.973426i) q^{92} +9.21344i q^{93} +16.0820i q^{94} +(6.01679 - 6.01679i) q^{96} +(6.51611 + 6.51611i) q^{97} -16.5880 q^{98} +(2.58041 + 2.58041i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{4} - 20 q^{6} + 16 q^{11} + 16 q^{14} + 4 q^{16} - 24 q^{21} + 32 q^{24} - 4 q^{29} + 4 q^{31} - 12 q^{39} + 16 q^{41} - 28 q^{44} - 4 q^{46} + 44 q^{51} - 100 q^{54} + 4 q^{56} - 48 q^{61}+ \cdots - 36 q^{99}+O(q^{100}) \) 12 * q - 12 * q^4 - 20 * q^6 + 16 * q^11 + 16 * q^14 + 4 * q^16 - 24 * q^21 + 32 * q^24 - 4 * q^29 + 4 * q^31 - 12 * q^39 + 16 * q^41 - 28 * q^44 - 4 * q^46 + 44 * q^51 - 100 * q^54 + 4 * q^56 - 48 * q^61 + 76 * q^64 + 88 * q^69 - 40 * q^71 - 28 * q^74 + 4 * q^79 - 60 * q^81 - 40 * q^84 - 16 * q^86 + 16 * q^89 + 36 * q^91 - 4 * q^96 - 36 * q^99

Introduction

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