LMFDB - Embedded newform 425.2.e.d.276.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(251,425)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			276.1
Root			$-3.38621i$ of defining polynomial
Character	$\chi$	$=$	425.276
Dual form			425.2.e.d.251.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.38621i q^{2} +(2.23065 - 2.23065i) q^{3} -3.69399 q^{4} +(-5.32280 - 5.32280i) q^{6} +(0.155559 + 0.155559i) q^{7} +4.04223i q^{8} -6.95160i q^{9} +(0.371196 + 0.371196i) q^{11} +(-8.24001 + 8.24001i) q^{12} +1.96713 q^{13} +(0.371196 - 0.371196i) q^{14} +2.25761 q^{16} +(2.23065 + 3.46759i) q^{17} -16.5880 q^{18} +4.00000i q^{19} +0.693995 q^{21} +(0.885751 - 0.885751i) q^{22} +(0.263516 + 0.263516i) q^{23} +(9.01679 + 9.01679i) q^{24} -4.69399i q^{26} +(-8.81464 - 8.81464i) q^{27} +(-0.574634 - 0.574634i) q^{28} +(-4.95160 + 4.95160i) q^{29} +(2.06519 - 2.06519i) q^{31} +2.69733i q^{32} +1.65602 q^{33} +(8.27440 - 5.32280i) q^{34} +25.6792i q^{36} +(4.04223 - 4.04223i) q^{37} +9.54484 q^{38} +(4.38799 - 4.38799i) q^{39} +(0.563613 + 0.563613i) q^{41} -1.65602i q^{42} -2.49417i q^{43} +(-1.37120 - 1.37120i) q^{44} +(0.628804 - 0.628804i) q^{46} +6.73955 q^{47} +(5.03593 - 5.03593i) q^{48} -6.95160i q^{49} +(12.7108 + 2.75919i) q^{51} -7.26658 q^{52} +5.92169i q^{53} +(-21.0336 + 21.0336i) q^{54} +(-0.628804 + 0.628804i) q^{56} +(8.92260 + 8.92260i) q^{57} +(11.8156 + 11.8156i) q^{58} -6.00000i q^{59} +(-4.00000 - 4.00000i) q^{61} +(-4.92798 - 4.92798i) q^{62} +(1.08138 - 1.08138i) q^{63} +10.9516 q^{64} -3.95160i q^{66} -11.5120 q^{67} +(-8.24001 - 12.8093i) q^{68} +1.17562 q^{69} +(-5.06519 + 5.06519i) q^{71} +28.1000 q^{72} +(-0.838149 + 0.838149i) q^{73} +(-9.64560 - 9.64560i) q^{74} -14.7760i q^{76} +0.115486i q^{77} +(-10.4707 - 10.4707i) q^{78} +(4.75919 + 4.75919i) q^{79} -18.4700 q^{81} +(1.34490 - 1.34490i) q^{82} +6.11732i q^{83} -2.56361 q^{84} -5.95160 q^{86} +22.0906i q^{87} +(-1.50046 + 1.50046i) q^{88} -15.9852 q^{89} +(0.306005 + 0.306005i) q^{91} +(-0.973426 - 0.973426i) q^{92} -9.21344i q^{93} -16.0820i q^{94} +(6.01679 + 6.01679i) q^{96} +(6.51611 - 6.51611i) q^{97} -16.5880 q^{98} +(2.58041 - 2.58041i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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	$-0.680401\pi$
$2$		−	2.38621i		−	1.68730i	0.536890	−	0.843652i	$-0.319599\pi$
$3$	2.23065	−	2.23065i	1.28787	−	1.28787i	0.351786	−	0.936080i	$-0.385574\pi$
$3$	2.23065	−	2.23065i	1.28787	−	1.28787i	0.936080	−	0.351786i	$-0.114426\pi$
$4$	−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	0.735893	−	0.677098i	$-0.236762\pi$
$7$	0.155559	+	0.155559i	0.0587957	+	0.0587957i	−0.677098	+	0.735893i	$0.736762\pi$
$8$			4.04223i			1.42914i
$9$		−	6.95160i		−	2.31720i
$10$		0			0
$11$	0.371196	+	0.371196i	0.111920	+	0.111920i	0.760849	−	0.648929i	$-0.224783\pi$
$11$	0.371196	+	0.371196i	0.111920	+	0.111920i	−0.648929	+	0.760849i	$0.724783\pi$
$12$	−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	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		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	0.734046	−	0.679099i	$-0.237629\pi$
$23$	0.263516	+	0.263516i	0.0549469	+	0.0549469i	−0.679099	+	0.734046i	$0.737629\pi$
$24$	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	−0.996992	−	0.0775026i	$-0.975305\pi$
$29$	−4.95160	+	4.95160i	−0.919490	+	0.919490i	0.0775026	+	0.996992i	$0.475305\pi$
$30$		0			0
$31$	2.06519	−	2.06519i	0.370919	−	0.370919i	−0.496893	−	0.867812i	$-0.665526\pi$
$31$	2.06519	−	2.06519i	0.370919	−	0.370919i	0.867812	+	0.496893i	$0.165526\pi$
$32$			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	−0.291908	−	0.956446i	$-0.594290\pi$
$37$	4.04223	−	4.04223i	0.664538	−	0.664538i	0.956446	+	0.291908i	$0.0942902\pi$
$38$	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	0.749747	−	0.661725i	$-0.230175\pi$
$41$	0.563613	+	0.563613i	0.0880216	+	0.0880216i	−0.661725	+	0.749747i	$0.730175\pi$
$42$		−	1.65602i		−	0.255529i
$43$		−	2.49417i		−	0.380357i	−0.981750	−	0.190178i	$-0.939093\pi$
$43$		−	2.49417i		−	0.380357i	0.981750	−	0.190178i	$-0.0609066\pi$
$44$	−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	$0.133322\pi$
$53$			5.92169i			0.813406i	−0.913560	+	0.406703i	$0.866678\pi$
$54$	−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	$-0.872279\pi$
$59$		−	6.00000i		−	0.781133i	0.920575	−	0.390567i	$-0.127721\pi$
$60$		0			0
$61$	−4.00000	−	4.00000i	−0.512148	−	0.512148i	0.403036	−	0.915184i	$-0.367955\pi$
$61$	−4.00000	−	4.00000i	−0.512148	−	0.512148i	−0.915184	+	0.403036i	$0.867955\pi$
$62$	−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	−0.940612	−	0.339484i	$-0.889747\pi$
$71$	−5.06519	+	5.06519i	−0.601128	+	0.601128i	0.339484	+	0.940612i	$0.389747\pi$
$72$	28.1000			3.31161
$73$	−0.838149	+	0.838149i	−0.0980980	+	0.0980980i	−0.754453	−	0.656355i	$-0.772098\pi$
$73$	−0.838149	+	0.838149i	−0.0980980	+	0.0980980i	0.656355	+	0.754453i	$0.272098\pi$
$74$	−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	0.922189	−	0.386739i	$-0.126399\pi$
$79$	4.75919	+	4.75919i	0.535450	+	0.535450i	−0.386739	+	0.922189i	$0.626399\pi$
$80$		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	$0.108983\pi$
$83$			6.11732i			0.671463i	−0.941958	+	0.335731i	$0.891017\pi$
$84$	−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	−0.294149	−	0.955760i	$-0.595036\pi$
$97$	6.51611	−	6.51611i	0.661611	−	0.661611i	0.955760	+	0.294149i	$0.0950361\pi$
$98$	−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	−0.234863	−	0.972029i	$-0.575464\pi$
$107$	7.62530	−	7.62530i	0.737166	−	0.737166i	0.972029	+	0.234863i	$0.0754640\pi$
$108$	32.5613	+	32.5613i	3.13321	+	3.13321i
$109$	9.95160	+	9.95160i	0.953191	+	0.953191i	0.998952	−	0.0457617i	$-0.0145715\pi$
$109$	9.95160	+	9.95160i	0.953191	+	0.953191i	−0.0457617	+	0.998952i	$0.514571\pi$
$110$		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	0.426343	−	0.904562i	$-0.359802\pi$
$113$	−5.08354	−	5.08354i	−0.478219	−	0.478219i	−0.904562	+	0.426343i	$0.859802\pi$
$114$	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	$0.142250\pi$
$127$			9.74047i			0.864327i	−0.901795	+	0.432163i	$0.857750\pi$
$128$		−	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	−0.247242	+	0.968954i	$0.579524\pi$
$131$	−13.9200	+	13.9200i	−1.21620	+	1.21620i	−0.968954	+	0.247242i	$0.920476\pi$
$132$	−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	−0.532000	−	0.846745i	$-0.678559\pi$
$139$	3.71079	−	3.71079i	0.314745	−	0.314745i	0.846745	+	0.532000i	$0.178559\pi$
$140$		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	$0.224015\pi$
$151$			15.9032i			1.29418i	−0.762412	+	0.647092i	$0.775985\pi$
$152$	−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	0.920876	−	0.389855i	$-0.127475\pi$
$163$	6.77963	+	6.77963i	0.531021	+	0.531021i	−0.389855	+	0.920876i	$0.627475\pi$
$164$	−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	−0.838030	−	0.545624i	$-0.816293\pi$
$167$	−3.77871	+	3.77871i	−0.292405	+	0.292405i	0.545624	+	0.838030i	$0.316293\pi$
$168$			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	−0.0598193	−	0.998209i	$-0.519052\pi$
$173$	12.3426	−	12.3426i	0.938390	−	0.938390i	0.998209	+	0.0598193i	$0.0190524\pi$
$174$	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	$0.293552\pi$
$179$			21.3248i			1.59389i	−0.604052	+	0.796945i	$0.706448\pi$
$180$		0			0
$181$	10.2092	+	10.2092i	0.758845	+	0.758845i	0.976112	−	0.217267i	$-0.0697144\pi$
$181$	10.2092	+	10.2092i	0.758845	+	0.758845i	−0.217267	+	0.976112i	$0.569714\pi$
$182$	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	0.227787	−	0.973711i	$-0.426851\pi$
$193$	−10.3627	−	10.3627i	−0.745924	−	0.745924i	−0.973711	+	0.227787i	$0.926851\pi$
$194$	−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	0.728666	−	0.684870i	$-0.240141\pi$
$197$	0.614707	+	0.614707i	0.0437960	+	0.0437960i	−0.684870	+	0.728666i	$0.740141\pi$
$198$	−6.15739	−	6.15739i	−0.437587	−	0.437587i
$199$	−9.40478	+	9.40478i	−0.666687	+	0.666687i	−0.956948	−	0.290260i	$-0.906258\pi$
$199$	−9.40478	+	9.40478i	−0.666687	+	0.666687i	0.290260	+	0.956948i	$0.406258\pi$
$200$		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	0.125964	−	0.992035i	$-0.459798\pi$
$211$	−12.5804	−	12.5804i	−0.866071	−	0.866071i	−0.992035	+	0.125964i	$0.959798\pi$
$212$		−	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	$-0.979019\pi$
$223$		−	1.96713i		−	0.131729i	0.997829	−	0.0658645i	$-0.0209805\pi$
$224$	−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	0.368420	−	0.929659i	$-0.379899\pi$
$227$	−8.45593	−	8.45593i	−0.561239	−	0.561239i	−0.929659	+	0.368420i	$0.879899\pi$
$228$	−32.9600	−	32.9600i	−2.18283	−	2.18283i
$229$		−	9.30601i		−	0.614958i	−0.951555	−	0.307479i	$-0.900515\pi$
$229$		−	9.30601i		−	0.614958i	0.951555	−	0.307479i	$-0.0994854\pi$
$230$		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	−0.219618	+	0.975586i	$0.570481\pi$
$233$	−18.2440	+	18.2440i	−1.19520	+	1.19520i	−0.975586	+	0.219618i	$0.929519\pi$
$234$	−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	−0.486941	−	0.873435i	$-0.661887\pi$
$241$	6.00000	−	6.00000i	0.386494	−	0.386494i	0.873435	+	0.486941i	$0.161887\pi$
$242$	−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	$0.0741582\pi$
$257$			7.40235i			0.461746i	−0.972984	+	0.230873i	$0.925842\pi$
$258$	−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	$0.0760219\pi$
$263$			7.67291i			0.473132i	−0.971615	+	0.236566i	$0.923978\pi$
$264$			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	−0.516734	−	0.856146i	$-0.672852\pi$
$269$	5.56677	−	5.56677i	0.339412	−	0.339412i	0.856146	+	0.516734i	$0.172852\pi$
$270$		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	−0.137840	+	0.990455i	$0.544016\pi$
$277$	−18.7786	+	18.7786i	−1.12829	+	1.12829i	−0.990455	+	0.137840i	$0.955984\pi$
$278$	−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	$-0.865246\pi$
$281$		−	13.7728i		−	0.821618i	0.911721	−	0.410809i	$-0.134754\pi$
$282$	−35.8733	−	35.8733i	−2.13622	−	2.13622i
$283$	−9.72068	−	9.72068i	−0.577834	−	0.577834i	0.356472	−	0.934306i	$-0.383980\pi$
$283$	−9.72068	−	9.72068i	−0.577834	−	0.577834i	−0.934306	+	0.356472i	$0.883980\pi$
$284$	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	−0.211667	+	0.977342i	$0.567889\pi$
$311$	−20.9684	+	20.9684i	−1.18901	+	1.18901i	−0.977342	+	0.211667i	$0.932111\pi$
$312$	17.7372	+	17.7372i	1.00417	+	1.00417i
$313$	10.1671	+	10.1671i	0.574677	+	0.574677i	0.933432	−	0.358755i	$-0.116799\pi$
$313$	10.1671	+	10.1671i	0.574677	+	0.574677i	−0.358755	+	0.933432i	$0.616799\pi$
$314$		−	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	0.925595	−	0.378516i	$-0.123565\pi$
$317$	9.74047	+	9.74047i	0.547079	+	0.547079i	−0.378516	+	0.925595i	$0.623565\pi$
$318$	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	$0.186959\pi$
$331$			20.1640i			1.10831i	−0.832413	+	0.554156i	$0.813041\pi$
$332$		−	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	0.106677	−	0.994294i	$-0.465979\pi$
$337$	20.2111	−	20.2111i	1.10097	−	1.10097i	0.994294	−	0.106677i	$-0.0340210\pi$
$338$			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	0.468383	−	0.883526i	$-0.344837\pi$
$347$	−7.73326	−	7.73326i	−0.415143	−	0.415143i	−0.883526	+	0.468383i	$0.844837\pi$
$348$		−	81.6025i		−	4.37435i
$349$		−	0.645598i		−	0.0345581i	−0.999851	−	0.0172790i	$-0.994500\pi$
$349$		−	0.645598i		−	0.0345581i	0.999851	−	0.0172790i	$-0.00550036\pi$
$350$		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	$-0.864245\pi$
$359$		−	15.6760i		−	0.827349i	0.910425	−	0.413675i	$-0.135755\pi$
$360$		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	0.176009	−	0.984388i	$-0.443681\pi$
$367$	−15.4863	−	15.4863i	−0.808379	−	0.808379i	−0.984388	+	0.176009i	$0.943681\pi$
$368$	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	−0.557059	−	0.830473i	$-0.688070\pi$
$379$	5.32280	−	5.32280i	0.273414	−	0.273414i	0.830473	+	0.557059i	$0.188070\pi$
$380$		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	$-0.781833\pi$
$383$		−	24.7752i		−	1.26595i	0.774172	−	0.632976i	$-0.218167\pi$
$384$	−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	$0.205130\pi$
$389$			23.6971i			1.20149i	−0.799440	+	0.600747i	$0.794870\pi$
$390$		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	0.0163500	−	0.999866i	$-0.494795\pi$
$397$	−19.5964	−	19.5964i	−0.983516	−	0.983516i	−0.999866	+	0.0163500i	$0.994795\pi$
$398$	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	−0.996643	−	0.0818697i	$-0.973911\pi$
$401$	−21.5972	−	21.5972i	−1.07851	−	1.07851i	−0.0818697	−	0.996643i	$-0.526089\pi$
$402$	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	−0.991405	−	0.130829i	$-0.958236\pi$
$419$	−22.9716	−	22.9716i	−1.12223	−	1.12223i	−0.130829	−	0.991405i	$-0.541764\pi$
$420$		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	0.550980	−	0.834518i	$-0.314254\pi$
$431$	−5.88641	−	5.88641i	−0.283538	−	0.283538i	−0.834518	+	0.550980i	$0.814254\pi$
$432$	−19.9000	−	19.9000i	−0.957440	−	0.957440i
$433$		−	13.5795i		−	0.652591i	−0.945268	−	0.326295i	$-0.894200\pi$
$433$		−	13.5795i		−	0.652591i	0.945268	−	0.326295i	$-0.105800\pi$
$434$		−	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	−0.961679	−	0.274177i	$-0.911595\pi$
$439$	−14.4048	+	14.4048i	−0.687503	+	0.687503i	0.274177	+	0.961679i	$0.411595\pi$
$440$		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	0.651746	−	0.758438i	$-0.274037\pi$
$449$	−2.26076	−	2.26076i	−0.106692	−	0.106692i	−0.758438	+	0.651746i	$0.774037\pi$
$450$		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	$-0.750549\pi$
$457$		−	30.1803i		−	1.41177i	0.708325	−	0.705887i	$-0.249451\pi$
$458$	−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	$0.0402483\pi$
$461$			5.41527i			0.252214i	−0.992017	+	0.126107i	$0.959752\pi$
$462$	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	$0.0801563\pi$
$467$			10.7690i			0.498331i	−0.968461	+	0.249166i	$0.919844\pi$
$468$			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	−0.216116	+	0.976368i	$0.569339\pi$
$479$	−26.0988	+	26.0988i	−1.19248	+	1.19248i	−0.976368	+	0.216116i	$0.930661\pi$
$480$		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	−0.964734	−	0.263226i	$-0.915214\pi$
$487$	−27.0987	−	27.0987i	−1.22796	−	1.22796i	−0.263226	−	0.964734i	$-0.584786\pi$
$488$	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	$0.328427\pi$
$491$			38.0336i			1.71643i	−0.513289	+	0.858216i	$0.671573\pi$
$492$	−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	0.544307	−	0.838886i	$-0.316793\pi$
$499$	−6.58041	−	6.58041i	−0.294579	−	0.294579i	−0.838886	+	0.544307i	$0.816793\pi$
$500$		0			0
$501$			16.8580i			0.753158i
$502$			4.23033i			0.188809i
$503$	−1.10919	−	1.10919i	−0.0494565	−	0.0494565i	0.681946	−	0.731403i	$-0.261134\pi$
$503$	−1.10919	−	1.10919i	−0.0494565	−	0.0494565i	−0.731403	+	0.681946i	$0.761134\pi$
$504$	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	0.581178	−	0.813776i	$-0.302592\pi$
$521$	−5.30916	−	5.30916i	−0.232599	−	0.232599i	−0.813776	+	0.581178i	$0.802592\pi$
$522$	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	−0.873595	−	0.486654i	$-0.838217\pi$
$541$	−9.00000	+	9.00000i	−0.386940	+	0.386940i	0.486654	+	0.873595i	$0.338217\pi$
$542$		−	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	−0.667147	−	0.744926i	$-0.732485\pi$
$547$	1.81910	−	1.81910i	0.0777793	−	0.0777793i	0.744926	+	0.667147i	$0.232485\pi$
$548$	−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	$0.325972\pi$
$563$			40.5377i			1.70846i	−0.519893	+	0.854231i	$0.674028\pi$
$564$	−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	$0.00408352\pi$
$569$			0.612010i			0.0256568i	−0.999918	+	0.0128284i	$0.995916\pi$
$570$		0			0
$571$	−10.5320	−	10.5320i	−0.440751	−	0.440751i	0.451513	−	0.892264i	$-0.350884\pi$
$571$	−10.5320	−	10.5320i	−0.440751	−	0.440751i	−0.892264	+	0.451513i	$0.850884\pi$
$572$	−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	$0.0635142\pi$
$587$			9.60470i			0.396428i	−0.980159	+	0.198214i	$0.936486\pi$
$588$	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	$-0.889840\pi$
$593$		−	16.5206i		−	0.678419i	0.940711	−	0.339210i	$-0.110160\pi$
$594$	−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	0.518260	−	0.855223i	$-0.326580\pi$
$601$	−8.26076	−	8.26076i	−0.336964	−	0.336964i	−0.855223	+	0.518260i	$0.826580\pi$
$602$	−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	−0.205718	−	0.978611i	$-0.565953\pi$
$607$	19.0421	−	19.0421i	0.772894	−	0.772894i	0.978611	+	0.205718i	$0.0659528\pi$
$608$	−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	−0.655554	−	0.755149i	$-0.727565\pi$
$617$	2.47388	−	2.47388i	0.0995948	−	0.0995948i	0.755149	+	0.655554i	$0.227565\pi$
$618$	−50.6973	−	50.6973i	−2.03934	−	2.03934i
$619$	−8.57725	−	8.57725i	−0.344749	−	0.344749i	0.513400	−	0.858149i	$-0.328386\pi$
$619$	−8.57725	−	8.57725i	−0.344749	−	0.344749i	−0.858149	+	0.513400i	$0.828386\pi$
$620$		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	$0.0808132\pi$
$631$			12.6183i			0.502327i	−0.967945	+	0.251164i	$0.919187\pi$
$632$	−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	−0.145857	−	0.989306i	$-0.546594\pi$
$641$	21.3544	−	21.3544i	0.843448	−	0.843448i	0.989306	+	0.145857i	$0.0465941\pi$
$642$	−81.1759			−3.20376
$643$	−13.9383	+	13.9383i	−0.549671	+	0.549671i	−0.926346	−	0.376675i	$-0.877068\pi$
$643$	−13.9383	+	13.9383i	−0.549671	+	0.549671i	0.376675	+	0.926346i	$0.377068\pi$
$644$		−	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	−0.997250	−	0.0741056i	$-0.976390\pi$
$653$	−27.3773	−	27.3773i	−1.07136	−	1.07136i	−0.0741056	−	0.997250i	$-0.523610\pi$
$654$		−	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	$-0.833095\pi$
$661$		−	25.7432i		−	1.00129i	0.865651	−	0.500647i	$-0.166905\pi$
$662$	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	0.549446	−	0.835529i	$-0.314839\pi$
$673$	−7.42165	−	7.42165i	−0.286084	−	0.286084i	−0.835529	+	0.549446i	$0.814839\pi$
$674$	−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	−0.812972	−	0.582303i	$-0.802152\pi$
$677$	−6.00183	+	6.00183i	−0.230669	+	0.230669i	0.582303	+	0.812972i	$0.302152\pi$
$678$			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	−0.873485	−	0.486851i	$-0.838146\pi$
$683$	−10.1044	+	10.1044i	−0.386635	+	0.386635i	0.486851	+	0.873485i	$0.338146\pi$
$684$	−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	0.578366	−	0.815778i	$-0.303691\pi$
$691$	−6.24081	−	6.24081i	−0.237412	−	0.237412i	−0.815778	+	0.578366i	$0.803691\pi$
$692$	−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	−0.282207	−	0.959354i	$-0.591066\pi$
$709$	18.0304	−	18.0304i	0.677147	−	0.677147i	0.959354	+	0.282207i	$0.0910664\pi$
$710$		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	−0.767116	−	0.641509i	$-0.778309\pi$
$719$	−3.36804	+	3.36804i	−0.125607	+	0.125607i	0.641509	+	0.767116i	$0.278309\pi$
$720$		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	$-0.838695\pi$
$733$		−	26.2804i		−	0.970687i	0.874324	−	0.485344i	$-0.161305\pi$
$734$	−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	$-0.964801\pi$
$739$		−	6.00000i		−	0.220714i	0.993892	−	0.110357i	$-0.0351994\pi$
$740$		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	−0.110800	−	0.993843i	$-0.535341\pi$
$743$	24.0700	−	24.0700i	0.883042	−	0.883042i	0.993843	+	0.110800i	$0.0353415\pi$
$744$	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	−0.855066	−	0.518519i	$-0.826483\pi$
$751$	−9.22285	+	9.22285i	−0.336547	+	0.336547i	0.518519	+	0.855066i	$0.326483\pi$
$752$	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	$-0.803366\pi$
$757$		−	31.8716i		−	1.15839i	0.815188	−	0.579197i	$-0.196634\pi$
$758$	−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	$-0.829847\pi$
$773$		−	28.3286i		−	1.01891i	0.860497	−	0.509455i	$-0.170153\pi$
$774$			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	−0.0688738	+	0.997625i	$0.521941\pi$
$787$	−29.9191	+	29.9191i	−1.06650	+	1.06650i	−0.997625	+	0.0688738i	$0.978059\pi$
$788$	−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	$0.408743\pi$
$797$			54.1578i			1.91837i	−0.282780	+	0.959185i	$0.591257\pi$
$798$	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	0.207952	−	0.978139i	$-0.433320\pi$
$809$	−21.9064	−	21.9064i	−0.770187	−	0.770187i	−0.978139	+	0.207952i	$0.933320\pi$
$810$		0			0
$811$	−2.93481	+	2.93481i	−0.103055	+	0.103055i	−0.756754	−	0.653699i	$-0.773216\pi$
$811$	−2.93481	+	2.93481i	−0.103055	+	0.103055i	0.653699	+	0.756754i	$0.273216\pi$
$812$	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	−0.724288	−	0.689498i	$-0.757831\pi$
$821$	−0.996845	+	0.996845i	−0.0347901	+	0.0347901i	0.689498	+	0.724288i	$0.257831\pi$
$822$	−24.7879	−	24.7879i	−0.864578	−	0.864578i
$823$	14.2899	+	14.2899i	0.498116	+	0.498116i	0.910851	−	0.412735i	$-0.135427\pi$
$823$	14.2899	+	14.2899i	0.498116	+	0.498116i	−0.412735	+	0.910851i	$0.635427\pi$
$824$			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	0.832824	−	0.553537i	$-0.186722\pi$
$827$	8.03163	+	8.03163i	0.279287	+	0.279287i	−0.553537	+	0.832824i	$0.686722\pi$
$828$	−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	0.0499138	−	0.998754i	$-0.484105\pi$
$839$	−27.4836	−	27.4836i	−0.948840	−	0.948840i	−0.998754	+	0.0499138i	$0.984105\pi$
$840$		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	−0.203674	−	0.979039i	$-0.565288\pi$
$853$	22.6454	−	22.6454i	0.775365	−	0.775365i	0.979039	+	0.203674i	$0.0652882\pi$
$854$	−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	0.945585	−	0.325376i	$-0.105491\pi$
$857$	18.1563	+	18.1563i	0.620208	+	0.620208i	−0.325376	+	0.945585i	$0.605491\pi$
$858$		−	7.77333i		−	0.265377i
$859$			38.7065i			1.32065i	0.750981	+	0.660324i	$0.229581\pi$
$859$			38.7065i			1.32065i	−0.750981	+	0.660324i	$0.770419\pi$
$860$		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	0.316017	−	0.948754i	$-0.397654\pi$
$877$	−18.7380	−	18.7380i	−0.632737	−	0.632737i	−0.948754	+	0.316017i	$0.897654\pi$
$878$	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	−0.825815	−	0.563942i	$-0.809284\pi$
$881$	−7.77282	+	7.77282i	−0.261873	+	0.261873i	0.563942	+	0.825815i	$0.309284\pi$
$882$			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	−0.620420	−	0.784270i	$-0.713038\pi$
$887$	4.87988	−	4.87988i	0.163850	−	0.163850i	0.784270	+	0.620420i	$0.213038\pi$
$888$	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	0.971183	−	0.238334i	$-0.0766014\pi$
$907$	22.0708	+	22.0708i	0.732849	+	0.732849i	−0.238334	+	0.971183i	$0.576601\pi$
$908$	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	0.999990	−	0.00448095i	$-0.00142634\pi$
$911$	30.0472	+	30.0472i	0.995509	+	0.995509i	−0.00448095	+	0.999990i	$0.501426\pi$
$912$	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	0.691834	−	0.722057i	$-0.256803\pi$
$929$	−0.921171	−	0.921171i	−0.0302226	−	0.0302226i	−0.722057	+	0.691834i	$0.756803\pi$
$930$		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	$0.0492501\pi$
$937$			9.43458i			0.308214i	−0.988054	+	0.154107i	$0.950750\pi$
$938$	−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	0.354635	−	0.935005i	$-0.384605\pi$
$941$	−17.8033	−	17.8033i	−0.580370	−	0.580370i	−0.935005	+	0.354635i	$0.884605\pi$
$942$	−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	−0.313945	−	0.949441i	$-0.601651\pi$
$947$	19.5564	−	19.5564i	0.635496	−	0.635496i	0.949441	+	0.313945i	$0.101651\pi$
$948$	−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	$-0.943482\pi$
$967$		−	10.9849i		−	0.353252i	0.984278	−	0.176626i	$-0.0565183\pi$
$968$	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	$0.173393\pi$
$971$			32.2944i			1.03638i	−0.855267	+	0.518188i	$0.826607\pi$
$972$	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	$-0.986785\pi$
$977$		−	2.59459i		−	0.0830084i	0.999138	−	0.0415042i	$-0.0132150\pi$
$978$		−	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	−0.590300	−	0.807184i	$-0.700991\pi$
$983$	6.79991	−	6.79991i	0.216883	−	0.216883i	0.807184	+	0.590300i	$0.200991\pi$
$984$			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	−0.314402	−	0.949290i	$-0.601804\pi$
$991$	19.9864	−	19.9864i	0.634888	−	0.634888i	0.949290	+	0.314402i	$0.101804\pi$
$992$	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	0.743578	−	0.668649i	$-0.233127\pi$
$997$	2.36593	+	2.36593i	0.0749297	+	0.0749297i	−0.668649	+	0.743578i	$0.733127\pi$
$998$	−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.276.1		12
5.2	odd	4		85.2.j.c.4.6	yes	12
5.3	odd	4		85.2.j.c.4.1	✓	12
5.4	even	2	inner	425.2.e.d.276.6		12
15.2	even	4		765.2.t.e.514.1		12
15.8	even	4		765.2.t.e.514.6		12
17.8	even	8		7225.2.a.bp.1.1		12
17.9	even	8		7225.2.a.bp.1.2		12
17.13	even	4	inner	425.2.e.d.251.6		12
85.8	odd	8		1445.2.b.f.579.11		12
85.9	even	8		7225.2.a.bp.1.11		12
85.13	odd	4		85.2.j.c.64.6	yes	12
85.42	odd	8		1445.2.b.f.579.2		12
85.43	odd	8		1445.2.b.f.579.12		12
85.47	odd	4		85.2.j.c.64.1	yes	12
85.59	even	8		7225.2.a.bp.1.12		12
85.64	even	4	inner	425.2.e.d.251.1		12
85.77	odd	8		1445.2.b.f.579.1		12
255.47	even	4		765.2.t.e.64.6		12
255.98	even	4		765.2.t.e.64.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.j.c.4.1	✓	12	5.3	odd	4
85.2.j.c.4.6	yes	12	5.2	odd	4
85.2.j.c.64.1	yes	12	85.47	odd	4
85.2.j.c.64.6	yes	12	85.13	odd	4
425.2.e.d.251.1		12	85.64	even	4	inner
425.2.e.d.251.6		12	17.13	even	4	inner
425.2.e.d.276.1		12	1.1	even	1	trivial
425.2.e.d.276.6		12	5.4	even	2	inner
765.2.t.e.64.1		12	255.98	even	4
765.2.t.e.64.6		12	255.47	even	4
765.2.t.e.514.1		12	15.2	even	4
765.2.t.e.514.6		12	15.8	even	4
1445.2.b.f.579.1		12	85.77	odd	8
1445.2.b.f.579.2		12	85.42	odd	8
1445.2.b.f.579.11		12	85.8	odd	8
1445.2.b.f.579.12		12	85.43	odd	8
7225.2.a.bp.1.1		12	17.8	even	8
7225.2.a.bp.1.2		12	17.9	even	8
7225.2.a.bp.1.11		12	85.9	even	8
7225.2.a.bp.1.12		12	85.59	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 $\F_{q}$

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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