LMFDB - Embedded newform 425.2.e.f.276.6

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} + 18x^{10} + 83x^{8} + 152x^{6} + 111x^{4} + 22x^{2} + 1 $ x^12 + 18x^10 + 83x^8 + 152x^6 + 111x^4 + 22*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			276.6
Root			$1.19804i$ of defining polynomial
Character	$\chi$	$=$	425.276
Dual form			425.2.e.f.251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.24891i q^{2} +(-0.140032 + 0.140032i) q^{3} -3.05761 q^{4} +(-0.314920 - 0.314920i) q^{6} +(1.33807 + 1.33807i) q^{7} -2.37848i q^{8} +2.96078i q^{9} +(2.49536 + 2.49536i) q^{11} +(0.428164 - 0.428164i) q^{12} -1.27324 q^{13} +(-3.00920 + 3.00920i) q^{14} -0.766231 q^{16} +(-3.68381 - 1.85190i) q^{17} -6.65854 q^{18} -4.69149i q^{19} -0.374744 q^{21} +(-5.61186 + 5.61186i) q^{22} +(0.406537 + 0.406537i) q^{23} +(0.333063 + 0.333063i) q^{24} -2.86340i q^{26} +(-0.834700 - 0.834700i) q^{27} +(-4.09129 - 4.09129i) q^{28} +(-3.81711 + 3.81711i) q^{29} +(-4.39574 + 4.39574i) q^{31} -6.48015i q^{32} -0.698861 q^{33} +(4.16476 - 8.28457i) q^{34} -9.05292i q^{36} +(6.00080 - 6.00080i) q^{37} +10.5508 q^{38} +(0.178294 - 0.178294i) q^{39} +(4.28894 + 4.28894i) q^{41} -0.842768i q^{42} +9.16040i q^{43} +(-7.62986 - 7.62986i) q^{44} +(-0.914266 + 0.914266i) q^{46} +10.7932 q^{47} +(0.107297 - 0.107297i) q^{48} -3.41915i q^{49} +(0.775177 - 0.256526i) q^{51} +3.89307 q^{52} +9.90174i q^{53} +(1.87717 - 1.87717i) q^{54} +(3.18256 - 3.18256i) q^{56} +(0.656958 + 0.656958i) q^{57} +(-8.58435 - 8.58435i) q^{58} +3.15903i q^{59} +(3.63666 + 3.63666i) q^{61} +(-9.88565 - 9.88565i) q^{62} +(-3.96173 + 3.96173i) q^{63} +13.0408 q^{64} -1.57168i q^{66} -0.281859 q^{67} +(11.2637 + 5.66239i) q^{68} -0.113856 q^{69} +(8.30385 - 8.30385i) q^{71} +7.04216 q^{72} +(6.95405 - 6.95405i) q^{73} +(13.4953 + 13.4953i) q^{74} +14.3448i q^{76} +6.67793i q^{77} +(0.400968 + 0.400968i) q^{78} +(-11.9789 - 11.9789i) q^{79} -8.64858 q^{81} +(-9.64544 + 9.64544i) q^{82} -8.51139i q^{83} +1.14582 q^{84} -20.6010 q^{86} -1.06903i q^{87} +(5.93517 - 5.93517i) q^{88} +16.7227 q^{89} +(-1.70368 - 1.70368i) q^{91} +(-1.24303 - 1.24303i) q^{92} -1.23109i q^{93} +24.2729i q^{94} +(0.907427 + 0.907427i) q^{96} +(-4.18100 + 4.18100i) q^{97} +7.68938 q^{98} +(-7.38823 + 7.38823i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{3} - 12 q^{4} - 4 q^{11} + 8 q^{12} - 4 q^{14} + 4 q^{16} - 12 q^{17} - 28 q^{18} - 16 q^{21} - 20 q^{22} - 12 q^{23} + 4 q^{24} + 4 q^{27} - 4 q^{28} - 12 q^{29} + 16 q^{33} - 12 q^{34} - 12 q^{37}+ \cdots - 44 q^{98}+O(q^{100}) $ 12 * q + 4 * q^3 - 12 * q^4 - 4 * q^11 + 8 * q^12 - 4 * q^14 + 4 * q^16 - 12 * q^17 - 28 * q^18 - 16 * q^21 - 20 * q^22 - 12 * q^23 + 4 * q^24 + 4 * q^27 - 4 * q^28 - 12 * q^29 + 16 * q^33 - 12 * q^34 - 12 * q^37 - 24 * q^38 - 20 * q^39 - 24 * q^41 + 8 * q^44 - 24 * q^46 + 48 * q^47 + 20 * q^48 + 32 * q^51 + 56 * q^52 + 28 * q^54 + 40 * q^56 - 36 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^63 + 28 * q^64 + 8 * q^67 + 40 * q^68 + 28 * q^71 - 20 * q^72 + 48 * q^73 + 28 * q^74 + 92 * q^78 - 8 * q^79 + 28 * q^81 - 40 * q^82 - 96 * q^86 + 72 * q^88 + 24 * q^89 - 36 * q^91 + 16 * q^92 - 32 * q^96 - 4 * q^97 - 44 * q^98

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 $

$2$			2.24891i			1.59022i	0.606464	+	0.795111i	$0.292587\pi$
$2$			2.24891i			1.59022i	−0.606464	+	0.795111i	$0.707413\pi$
$3$	−0.140032	+	0.140032i	−0.0808475	+	0.0808475i	−0.746374	−	0.665527i	$-0.768207\pi$
$3$	−0.140032	+	0.140032i	−0.0808475	+	0.0808475i	0.665527	+	0.746374i	$0.268207\pi$
$4$	−3.05761			−1.52881
$5$		0			0
$5$		0			0
$6$	−0.314920	−	0.314920i	−0.128565	−	0.128565i
$7$	1.33807	+	1.33807i	0.505742	+	0.505742i	0.913217	−	0.407475i	$-0.133591\pi$
$7$	1.33807	+	1.33807i	0.505742	+	0.505742i	−0.407475	+	0.913217i	$0.633591\pi$
$8$		−	2.37848i		−	0.840919i
$9$			2.96078i			0.986927i
$10$		0			0
$11$	2.49536	+	2.49536i	0.752381	+	0.752381i	0.974923	−	0.222542i	$-0.0714356\pi$
$11$	2.49536	+	2.49536i	0.752381	+	0.752381i	−0.222542	+	0.974923i	$0.571436\pi$
$12$	0.428164	−	0.428164i	0.123600	−	0.123600i
$13$	−1.27324			−0.353133			−0.176566	−	0.984289i	$-0.556499\pi$
$13$	−1.27324			−0.353133			−0.176566	+	0.984289i	$0.556499\pi$
$14$	−3.00920	+	3.00920i	−0.804242	+	0.804242i
$15$		0			0
$16$	−0.766231			−0.191558
$17$	−3.68381	−	1.85190i	−0.893455	−	0.449152i
$17$	−3.68381	−	1.85190i	−0.893455	−	0.449152i
$18$	−6.65854			−1.56943
$19$		−	4.69149i		−	1.07630i	−0.842849	−	0.538151i	$-0.819123\pi$
$19$		−	4.69149i		−	1.07630i	0.842849	−	0.538151i	$-0.180877\pi$
$20$		0			0
$21$	−0.374744			−0.0817759
$22$	−5.61186	+	5.61186i	−1.19645	+	1.19645i
$23$	0.406537	+	0.406537i	0.0847687	+	0.0847687i	0.748220	−	0.663451i	$-0.230909\pi$
$23$	0.406537	+	0.406537i	0.0847687	+	0.0847687i	−0.663451	+	0.748220i	$0.730909\pi$
$24$	0.333063	+	0.333063i	0.0679862	+	0.0679862i
$25$		0			0
$26$		−	2.86340i		−	0.561560i
$27$	−0.834700	−	0.834700i	−0.160638	−	0.160638i
$28$	−4.09129	−	4.09129i	−0.773181	−	0.773181i
$29$	−3.81711	+	3.81711i	−0.708819	+	0.708819i	−0.966287	−	0.257468i	$-0.917112\pi$
$29$	−3.81711	+	3.81711i	−0.708819	+	0.708819i	0.257468	+	0.966287i	$0.417112\pi$
$30$		0			0
$31$	−4.39574	+	4.39574i	−0.789499	+	0.789499i	−0.981412	−	0.191913i	$-0.938531\pi$
$31$	−4.39574	+	4.39574i	−0.789499	+	0.789499i	0.191913	+	0.981412i	$0.438531\pi$
$32$		−	6.48015i		−	1.14554i
$33$	−0.698861			−0.121656
$34$	4.16476	−	8.28457i	0.714251	−	1.42079i
$35$		0			0
$36$		−	9.05292i		−	1.50882i
$37$	6.00080	−	6.00080i	0.986526	−	0.986526i	−0.0133844	−	0.999910i	$-0.504261\pi$
$37$	6.00080	−	6.00080i	0.986526	−	0.986526i	0.999910	+	0.0133844i	$0.00426051\pi$
$38$	10.5508			1.71156
$39$	0.178294	−	0.178294i	0.0285499	−	0.0285499i
$40$		0			0
$41$	4.28894	+	4.28894i	0.669819	+	0.669819i	0.957674	−	0.287855i	$-0.0929421\pi$
$41$	4.28894	+	4.28894i	0.669819	+	0.669819i	−0.287855	+	0.957674i	$0.592942\pi$
$42$		−	0.842768i		−	0.130042i
$43$			9.16040i			1.39695i	0.715635	+	0.698474i	$0.246137\pi$
$43$			9.16040i			1.39695i	−0.715635	+	0.698474i	$0.753863\pi$
$44$	−7.62986	−	7.62986i	−1.15024	−	1.15024i
$45$		0			0
$46$	−0.914266	+	0.914266i	−0.134801	+	0.134801i
$47$	10.7932			1.57434			0.787172	−	0.616734i	$-0.211545\pi$
$47$	10.7932			1.57434			0.787172	+	0.616734i	$0.211545\pi$
$48$	0.107297	−	0.107297i	0.0154870	−	0.0154870i
$49$		−	3.41915i		−	0.488450i
$50$		0			0
$51$	0.775177	−	0.256526i	0.108546	−	0.0359208i
$52$	3.89307			0.539872
$53$			9.90174i			1.36011i	0.733162	+	0.680054i	$0.238044\pi$
$53$			9.90174i			1.36011i	−0.733162	+	0.680054i	$0.761956\pi$
$54$	1.87717	−	1.87717i	0.255450	−	0.255450i
$55$		0			0
$56$	3.18256	−	3.18256i	0.425288	−	0.425288i
$57$	0.656958	+	0.656958i	0.0870163	+	0.0870163i
$58$	−8.58435	−	8.58435i	−1.12718	−	1.12718i
$59$			3.15903i			0.411270i	0.978629	+	0.205635i	$0.0659260\pi$
$59$			3.15903i			0.411270i	−0.978629	+	0.205635i	$0.934074\pi$
$60$		0			0
$61$	3.63666	+	3.63666i	0.465627	+	0.465627i	0.900495	−	0.434867i	$-0.143205\pi$
$61$	3.63666	+	3.63666i	0.465627	+	0.465627i	−0.434867	+	0.900495i	$0.643205\pi$
$62$	−9.88565	−	9.88565i	−1.25548	−	1.25548i
$63$	−3.96173	+	3.96173i	−0.499130	+	0.499130i
$64$	13.0408			1.63010
$65$		0			0
$66$		−	1.57168i		−	0.193460i
$67$	−0.281859			−0.0344345			−0.0172173	−	0.999852i	$-0.505481\pi$
$67$	−0.281859			−0.0344345			−0.0172173	+	0.999852i	$0.505481\pi$
$68$	11.2637	+	5.66239i	1.36592	+	0.686666i
$69$	−0.113856			−0.0137067
$70$		0			0
$71$	8.30385	−	8.30385i	0.985486	−	0.985486i	−0.0144101	−	0.999896i	$-0.504587\pi$
$71$	8.30385	−	8.30385i	0.985486	−	0.985486i	0.999896	+	0.0144101i	$0.00458704\pi$
$72$	7.04216			0.829926
$73$	6.95405	−	6.95405i	0.813910	−	0.813910i	−0.171308	−	0.985218i	$-0.554799\pi$
$73$	6.95405	−	6.95405i	0.813910	−	0.813910i	0.985218	+	0.171308i	$0.0547993\pi$
$74$	13.4953	+	13.4953i	1.56880	+	1.56880i
$75$		0			0
$76$			14.3448i			1.64546i
$77$			6.67793i			0.761021i
$78$	0.400968	+	0.400968i	0.0454007	+	0.0454007i
$79$	−11.9789	−	11.9789i	−1.34773	−	1.34773i	−0.888126	−	0.459600i	$-0.847993\pi$
$79$	−11.9789	−	11.9789i	−1.34773	−	1.34773i	−0.459600	−	0.888126i	$-0.652007\pi$
$80$		0			0
$81$	−8.64858			−0.960953
$82$	−9.64544	+	9.64544i	−1.06516	+	1.06516i
$83$		−	8.51139i		−	0.934246i	−0.884192	−	0.467123i	$-0.845291\pi$
$83$		−	8.51139i		−	0.934246i	0.884192	−	0.467123i	$-0.154709\pi$
$84$	1.14582			0.125020
$85$		0			0
$86$	−20.6010			−2.22146
$87$		−	1.06903i		−	0.114613i
$88$	5.93517	−	5.93517i	0.632691	−	0.632691i
$89$	16.7227			1.77260			0.886300	−	0.463112i	$-0.153267\pi$
$89$	16.7227			1.77260			0.886300	+	0.463112i	$0.153267\pi$
$90$		0			0
$91$	−1.70368	−	1.70368i	−0.178594	−	0.178594i
$92$	−1.24303	−	1.24303i	−0.129595	−	0.129595i
$93$		−	1.23109i		−	0.127658i
$94$			24.2729i			2.50356i
$95$		0			0
$96$	0.907427	+	0.907427i	0.0926139	+	0.0926139i
$97$	−4.18100	+	4.18100i	−0.424516	+	0.424516i	−0.886755	−	0.462239i	$-0.847046\pi$
$97$	−4.18100	+	4.18100i	−0.424516	+	0.424516i	0.462239	+	0.886755i	$0.347046\pi$
$98$	7.68938			0.776745
$99$	−7.38823	+	7.38823i	−0.742545	+	0.742545i
$100$		0			0
$101$	10.0971			1.00470			0.502348	−	0.864666i	$-0.332470\pi$
$101$	10.0971			1.00470			0.502348	+	0.864666i	$0.332470\pi$
$102$	0.576905	+	1.74331i	0.0571221	+	0.172613i
$103$	1.07322			0.105747			0.0528736	−	0.998601i	$-0.483162\pi$
$103$	1.07322			0.105747			0.0528736	+	0.998601i	$0.483162\pi$
$104$			3.02837i			0.296956i
$105$		0			0
$106$	−22.2681			−2.16287
$107$	−4.48903	+	4.48903i	−0.433971	+	0.433971i	−0.889977	−	0.456006i	$-0.849280\pi$
$107$	−4.48903	+	4.48903i	−0.433971	+	0.433971i	0.456006	+	0.889977i	$0.349280\pi$
$108$	2.55219	+	2.55219i	0.245585	+	0.245585i
$109$	7.13161	+	7.13161i	0.683085	+	0.683085i	0.960694	−	0.277609i	$-0.0895421\pi$
$109$	7.13161	+	7.13161i	0.683085	+	0.683085i	−0.277609	+	0.960694i	$0.589542\pi$
$110$		0			0
$111$			1.68061i			0.159516i
$112$	−1.02527	−	1.02527i	−0.0968787	−	0.0968787i
$113$	2.64734	+	2.64734i	0.249041	+	0.249041i	0.820577	−	0.571536i	$-0.193652\pi$
$113$	2.64734	+	2.64734i	0.249041	+	0.249041i	−0.571536	+	0.820577i	$0.693652\pi$
$114$	−1.47744	+	1.47744i	−0.138375	+	0.138375i
$115$		0			0
$116$	11.6712	−	11.6712i	1.08365	−	1.08365i
$117$		−	3.76978i		−	0.348516i
$118$	−7.10438			−0.654011
$119$	−2.45122	−	7.40715i	−0.224703	−	0.679013i
$120$		0			0
$121$			1.45368i			0.132153i
$122$	−8.17855	+	8.17855i	−0.740451	+	0.740451i
$123$	−1.20118			−0.108306
$124$	13.4405	−	13.4405i	1.20699	−	1.20699i
$125$		0			0
$126$	−8.90958	−	8.90958i	−0.793728	−	0.793728i
$127$			12.8352i			1.13894i	0.822012	+	0.569470i	$0.192852\pi$
$127$			12.8352i			1.13894i	−0.822012	+	0.569470i	$0.807148\pi$
$128$			16.3674i			1.44669i
$129$	−1.28275	−	1.28275i	−0.112940	−	0.112940i
$130$		0			0
$131$	4.96719	−	4.96719i	0.433985	−	0.433985i	−0.455996	−	0.889982i	$-0.650717\pi$
$131$	4.96719	−	4.96719i	0.433985	−	0.433985i	0.889982	+	0.455996i	$0.150717\pi$
$132$	2.13685			0.185989
$133$	6.27753	−	6.27753i	0.544331	−	0.544331i
$134$		−	0.633876i		−	0.0547585i
$135$		0			0
$136$	−4.40471	+	8.76187i	−0.377700	+	0.751324i
$137$	15.1475			1.29414			0.647071	−	0.762430i	$-0.275994\pi$
$137$	15.1475			1.29414			0.647071	+	0.762430i	$0.275994\pi$
$138$		−	0.256053i		−	0.0217967i
$139$	−8.79167	+	8.79167i	−0.745700	+	0.745700i	−0.973668	−	0.227969i	$-0.926792\pi$
$139$	−8.79167	+	8.79167i	−0.745700	+	0.745700i	0.227969	+	0.973668i	$0.426792\pi$
$140$		0			0
$141$	−1.51139	+	1.51139i	−0.127282	+	0.127282i
$142$	18.6746	+	18.6746i	1.56714	+	1.56714i
$143$	−3.17719	−	3.17719i	−0.265690	−	0.265690i
$144$		−	2.26864i		−	0.189053i
$145$		0			0
$146$	15.6391	+	15.6391i	1.29430	+	1.29430i
$147$	0.478791	+	0.478791i	0.0394900	+	0.0394900i
$148$	−18.3481	+	18.3481i	−1.50821	+	1.50821i
$149$	11.6094			0.951076			0.475538	−	0.879695i	$-0.342253\pi$
$149$	11.6094			0.951076			0.475538	+	0.879695i	$0.342253\pi$
$150$		0			0
$151$		−	1.31768i		−	0.107231i	−0.998562	−	0.0536156i	$-0.982925\pi$
$151$		−	1.31768i		−	0.107231i	0.998562	−	0.0536156i	$-0.0170746\pi$
$152$	−11.1586			−0.905083
$153$	5.48307	−	10.9070i	0.443280	−	0.881776i
$154$	−15.0181			−1.21019
$155$		0			0
$156$	−0.545154	+	0.545154i	−0.0436473	+	0.0436473i
$157$	0.183886			0.0146757			0.00733783	−	0.999973i	$-0.497664\pi$
$157$	0.183886			0.0146757			0.00733783	+	0.999973i	$0.497664\pi$
$158$	26.9394	−	26.9394i	2.14318	−	2.14318i
$159$	−1.38656	−	1.38656i	−0.109961	−	0.109961i
$160$		0			0
$161$			1.08795i			0.0857422i
$162$		−	19.4499i		−	1.52813i
$163$	−12.7635	−	12.7635i	−0.999718	−	0.999718i	0.000282311	−	1.00000i	$-0.499910\pi$
$163$	−12.7635	−	12.7635i	−0.999718	−	0.999718i	−1.00000		0.000282311i	$0.999910\pi$
$164$	−13.1139	−	13.1139i	−1.02402	−	1.02402i
$165$		0			0
$166$	19.1414			1.48566
$167$	5.35646	−	5.35646i	0.414495	−	0.414495i	−0.468806	−	0.883301i	$-0.655316\pi$
$167$	5.35646	−	5.35646i	0.414495	−	0.414495i	0.883301	+	0.468806i	$0.155316\pi$
$168$			0.891322i			0.0687670i
$169$	−11.3789			−0.875297
$170$		0			0
$171$	13.8905			1.06223
$172$		−	28.0090i		−	2.13566i
$173$	4.89485	−	4.89485i	0.372149	−	0.372149i	−0.496111	−	0.868259i	$-0.665239\pi$
$173$	4.89485	−	4.89485i	0.372149	−	0.372149i	0.868259	+	0.496111i	$0.165239\pi$
$174$	2.40417			0.182259
$175$		0			0
$176$	−1.91202	−	1.91202i	−0.144124	−	0.144124i
$177$	−0.442365	−	0.442365i	−0.0332502	−	0.0332502i
$178$			37.6078i			2.81883i
$179$			10.2788i			0.768274i	0.923276	+	0.384137i	$0.125501\pi$
$179$			10.2788i			0.768274i	−0.923276	+	0.384137i	$0.874499\pi$
$180$		0			0
$181$	−14.1846	−	14.1846i	−1.05434	−	1.05434i	−0.998436	−	0.0558986i	$-0.982198\pi$
$181$	−14.1846	−	14.1846i	−1.05434	−	1.05434i	−0.0558986	−	0.998436i	$-0.517802\pi$
$182$	3.83143	−	3.83143i	0.284004	−	0.284004i
$183$	−1.01850			−0.0752896
$184$	0.966939	−	0.966939i	0.0712837	−	0.0712837i
$185$		0			0
$186$	2.76861			0.203005
$187$	−4.57128	−	13.8136i	−0.334285	−	1.01015i
$188$	−33.0013			−2.40687
$189$		−	2.23377i		−	0.162483i
$190$		0			0
$191$	4.11140			0.297491			0.148745	−	0.988876i	$-0.452477\pi$
$191$	4.11140			0.297491			0.148745	+	0.988876i	$0.452477\pi$
$192$	−1.82613	+	1.82613i	−0.131790	+	0.131790i
$193$	10.1106	+	10.1106i	0.727779	+	0.727779i	0.970177	−	0.242398i	$-0.0779340\pi$
$193$	10.1106	+	10.1106i	0.727779	+	0.727779i	−0.242398	+	0.970177i	$0.577934\pi$
$194$	−9.40270	−	9.40270i	−0.675075	−	0.675075i
$195$		0			0
$196$			10.4544i			0.746746i
$197$	−3.78391	−	3.78391i	−0.269593	−	0.269593i	0.559343	−	0.828936i	$-0.311053\pi$
$197$	−3.78391	−	3.78391i	−0.269593	−	0.269593i	−0.828936	+	0.559343i	$0.811053\pi$
$198$	−16.6155	−	16.6155i	−1.18081	−	1.18081i
$199$	2.38613	−	2.38613i	0.169148	−	0.169148i	−0.617457	−	0.786605i	$-0.711837\pi$
$199$	2.38613	−	2.38613i	0.169148	−	0.169148i	0.786605	+	0.617457i	$0.211837\pi$
$200$		0			0
$201$	0.0394692	−	0.0394692i	0.00278394	−	0.00278394i
$202$			22.7074i			1.59769i
$203$	−10.2151			−0.716959
$204$	−2.37019	+	0.784357i	−0.165946	+	0.0549160i
$205$		0			0
$206$			2.41357i			0.168162i
$207$	−1.20367	+	1.20367i	−0.0836606	+	0.0836606i
$208$	0.975594			0.0676453
$209$	11.7070	−	11.7070i	0.809788	−	0.809788i
$210$		0			0
$211$	−1.66415	−	1.66415i	−0.114565	−	0.114565i	0.647500	−	0.762065i	$-0.275814\pi$
$211$	−1.66415	−	1.66415i	−0.114565	−	0.114565i	−0.762065	+	0.647500i	$0.775814\pi$
$212$		−	30.2757i		−	2.07934i
$213$			2.32561i			0.159348i
$214$	−10.0954	−	10.0954i	−0.690110	−	0.690110i
$215$		0			0
$216$	−1.98532	+	1.98532i	−0.135084	+	0.135084i
$217$	−11.7636			−0.798565
$218$	−16.0384	+	16.0384i	−1.08626	+	1.08626i
$219$			1.94758i			0.131605i
$220$		0			0
$221$	4.69037	+	2.35791i	0.315508	+	0.158610i
$222$	−3.77954			−0.253666
$223$		−	3.45702i		−	0.231499i	−0.993278	−	0.115750i	$-0.963073\pi$
$223$		−	3.45702i		−	0.231499i	0.993278	−	0.115750i	$-0.0369270\pi$
$224$	8.67087	−	8.67087i	0.579347	−	0.579347i
$225$		0			0
$226$	−5.95365	+	5.95365i	−0.396031	+	0.396031i
$227$	−15.3558	−	15.3558i	−1.01920	−	1.01920i	−0.999812	−	0.0193889i	$-0.993828\pi$
$227$	−15.3558	−	15.3558i	−1.01920	−	1.01920i	−0.0193889	−	0.999812i	$-0.506172\pi$
$228$	−2.00872	−	2.00872i	−0.133031	−	0.133031i
$229$		−	8.59173i		−	0.567757i	−0.958860	−	0.283879i	$-0.908379\pi$
$229$		−	8.59173i		−	0.567757i	0.958860	−	0.283879i	$-0.0916213\pi$
$230$		0			0
$231$	−0.935124	−	0.935124i	−0.0615266	−	0.0615266i
$232$	9.07891	+	9.07891i	0.596060	+	0.596060i
$233$	−6.29903	+	6.29903i	−0.412663	+	0.412663i	−0.882665	−	0.470002i	$-0.844253\pi$
$233$	−6.29903	+	6.29903i	−0.412663	+	0.412663i	0.470002	+	0.882665i	$0.344253\pi$
$234$	8.47791			0.554219
$235$		0			0
$236$		−	9.65908i		−	0.628753i
$237$	3.35484			0.217921
$238$	16.6580	−	5.51258i	1.07978	−	0.357328i
$239$	−12.3246			−0.797212			−0.398606	−	0.917122i	$-0.630506\pi$
$239$	−12.3246			−0.797212			−0.398606	+	0.917122i	$0.630506\pi$
$240$		0			0
$241$	1.88979	−	1.88979i	0.121732	−	0.121732i	−0.643616	−	0.765348i	$-0.722567\pi$
$241$	1.88979	−	1.88979i	0.121732	−	0.121732i	0.765348	+	0.643616i	$0.222567\pi$
$242$	−3.26921			−0.210153
$243$	3.71518	−	3.71518i	0.238329	−	0.238329i
$244$	−11.1195	−	11.1195i	−0.711854	−	0.711854i
$245$		0			0
$246$		−	2.70134i		−	0.172231i
$247$			5.97338i			0.380077i
$248$	10.4552	+	10.4552i	0.663905	+	0.663905i
$249$	1.19187	+	1.19187i	0.0755315	+	0.0755315i
$250$		0			0
$251$	−27.4415			−1.73209			−0.866046	−	0.499964i	$-0.833347\pi$
$251$	−27.4415			−1.73209			−0.866046	+	0.499964i	$0.833347\pi$
$252$	12.1134	−	12.1134i	0.763074	−	0.763074i
$253$			2.02891i			0.127557i
$254$	−28.8653			−1.81117
$255$		0			0
$256$	−10.7272			−0.670451
$257$			22.8819i			1.42734i	0.700484	+	0.713668i	$0.252968\pi$
$257$			22.8819i			1.42734i	−0.700484	+	0.713668i	$0.747032\pi$
$258$	2.88479	−	2.88479i	0.179599	−	0.179599i
$259$	16.0590			0.997855
$260$		0			0
$261$	−11.3016	−	11.3016i	−0.699553	−	0.699553i
$262$	11.1708	+	11.1708i	0.690133	+	0.690133i
$263$		−	9.48703i		−	0.584995i	−0.956266	−	0.292498i	$-0.905514\pi$
$263$		−	9.48703i		−	0.584995i	0.956266	−	0.292498i	$-0.0944864\pi$
$264$			1.66223i			0.102303i
$265$		0			0
$266$	14.1176	+	14.1176i	0.865606	+	0.865606i
$267$	−2.34171	+	2.34171i	−0.143310	+	0.143310i
$268$	0.861814			0.0526437
$269$	4.30494	−	4.30494i	0.262477	−	0.262477i	−0.563583	−	0.826060i	$-0.690577\pi$
$269$	4.30494	−	4.30494i	0.262477	−	0.262477i	0.826060	+	0.563583i	$0.190577\pi$
$270$		0			0
$271$	23.6580			1.43712			0.718562	−	0.695463i	$-0.244801\pi$
$271$	23.6580			1.43712			0.718562	+	0.695463i	$0.244801\pi$
$272$	2.82265	+	1.41898i	0.171148	+	0.0860385i
$273$	0.477139			0.0288778
$274$			34.0655i			2.05797i
$275$		0			0
$276$	0.348128			0.0209549
$277$	5.82477	−	5.82477i	0.349976	−	0.349976i	−0.510124	−	0.860101i	$-0.670401\pi$
$277$	5.82477	−	5.82477i	0.349976	−	0.349976i	0.860101	+	0.510124i	$0.170401\pi$
$278$	−19.7717	−	19.7717i	−1.18583	−	1.18583i
$279$	−13.0148	−	13.0148i	−0.779178	−	0.779178i
$280$		0			0
$281$		−	15.0835i		−	0.899808i	−0.893077	−	0.449904i	$-0.851458\pi$
$281$		−	15.0835i		−	0.899808i	0.893077	−	0.449904i	$-0.148542\pi$
$282$	−3.39898	−	3.39898i	−0.202406	−	0.202406i
$283$	−12.5516	−	12.5516i	−0.746115	−	0.746115i	0.227632	−	0.973747i	$-0.426902\pi$
$283$	−12.5516	−	12.5516i	−0.746115	−	0.746115i	−0.973747	+	0.227632i	$0.926902\pi$
$284$	−25.3900	+	25.3900i	−1.50662	+	1.50662i
$285$		0			0
$286$	7.14523	−	7.14523i	0.422507	−	0.422507i
$287$			11.4778i			0.677511i
$288$	19.1863			1.13056
$289$	10.1409	+	13.6441i	0.596525	+	0.802594i
$290$		0			0
$291$		−	1.17095i		−	0.0686421i
$292$	−21.2628	+	21.2628i	−1.24431	+	1.24431i
$293$	−10.9192			−0.637907			−0.318953	−	0.947770i	$-0.603331\pi$
$293$	−10.9192			−0.637907			−0.318953	+	0.947770i	$0.603331\pi$
$294$	−1.07676	+	1.07676i	−0.0627979	+	0.0627979i
$295$		0			0
$296$	−14.2728	−	14.2728i	−0.829589	−	0.829589i
$297$		−	4.16576i		−	0.241722i
$298$			26.1084i			1.51242i
$299$	−0.517618	−	0.517618i	−0.0299346	−	0.0299346i
$300$		0			0
$301$	−12.2572	+	12.2572i	−0.706495	+	0.706495i
$302$	2.96335			0.170522
$303$	−1.41391	+	1.41391i	−0.0812272	+	0.0812272i
$304$			3.59476i			0.206174i
$305$		0			0
$306$	24.5288	+	12.3310i	1.40222	+	0.704914i
$307$	−6.82894			−0.389748			−0.194874	−	0.980828i	$-0.562430\pi$
$307$	−6.82894			−0.389748			−0.194874	+	0.980828i	$0.562430\pi$
$308$		−	20.4185i		−	1.16345i
$309$	−0.150285	+	0.150285i	−0.00854940	+	0.00854940i
$310$		0			0
$311$	0.467408	−	0.467408i	0.0265043	−	0.0265043i	−0.693730	−	0.720235i	$-0.744034\pi$
$311$	0.467408	−	0.467408i	0.0265043	−	0.0265043i	0.720235	+	0.693730i	$0.244034\pi$
$312$	−0.424069	−	0.424069i	−0.0240082	−	0.0240082i
$313$	2.96511	+	2.96511i	0.167598	+	0.167598i	0.785923	−	0.618325i	$-0.212188\pi$
$313$	2.96511	+	2.96511i	0.167598	+	0.167598i	−0.618325	+	0.785923i	$0.712188\pi$
$314$			0.413543i			0.0233376i
$315$		0			0
$316$	36.6267	+	36.6267i	2.06041	+	2.06041i
$317$	15.0370	+	15.0370i	0.844564	+	0.844564i	0.989449	−	0.144884i	$-0.0462810\pi$
$317$	15.0370	+	15.0370i	0.844564	+	0.844564i	−0.144884	+	0.989449i	$0.546281\pi$
$318$	3.11825	−	3.11825i	0.174863	−	0.174863i
$319$	−19.0502			−1.06660
$320$		0			0
$321$		−	1.25721i		−	0.0701709i
$322$	−2.44670			−0.136349
$323$	−8.68817	+	17.2826i	−0.483423	+	0.961627i
$324$	26.4440			1.46911
$325$		0			0
$326$	28.7041	−	28.7041i	1.58977	−	1.58977i
$327$	−1.99731			−0.110451
$328$	10.2011	−	10.2011i	0.563264	−	0.563264i
$329$	14.4420	+	14.4420i	0.796211	+	0.796211i
$330$		0			0
$331$			27.7582i			1.52573i	0.646559	+	0.762864i	$0.276207\pi$
$331$			27.7582i			1.52573i	−0.646559	+	0.762864i	$0.723793\pi$
$332$			26.0245i			1.42828i
$333$	17.7671	+	17.7671i	0.973630	+	0.973630i
$334$	12.0462	+	12.0462i	0.659140	+	0.659140i
$335$		0			0
$336$	0.287141			0.0156648
$337$	−6.20814	+	6.20814i	−0.338179	+	0.338179i	−0.855682	−	0.517503i	$-0.826862\pi$
$337$	−6.20814	+	6.20814i	−0.338179	+	0.338179i	0.517503	+	0.855682i	$0.326862\pi$
$338$		−	25.5901i		−	1.39192i
$339$	−0.741426			−0.0402687
$340$		0			0
$341$	−21.9380			−1.18801
$342$			31.2385i			1.68918i
$343$	13.9415	−	13.9415i	0.752772	−	0.752772i
$344$	21.7878			1.17472
$345$		0			0
$346$	11.0081	+	11.0081i	0.591799	+	0.591799i
$347$	−3.72663	−	3.72663i	−0.200056	−	0.200056i	0.599968	−	0.800024i	$-0.295180\pi$
$347$	−3.72663	−	3.72663i	−0.200056	−	0.200056i	−0.800024	+	0.599968i	$0.795180\pi$
$348$			3.26869i			0.175220i
$349$		−	10.8634i		−	0.581504i	−0.956799	−	0.290752i	$-0.906095\pi$
$349$		−	10.8634i		−	0.581504i	0.956799	−	0.290752i	$-0.0939054\pi$
$350$		0			0
$351$	1.06277	+	1.06277i	0.0567266	+	0.0567266i
$352$	16.1703	−	16.1703i	0.861881	−	0.861881i
$353$	27.2304			1.44933			0.724664	−	0.689102i	$-0.241995\pi$
$353$	27.2304			1.44933			0.724664	+	0.689102i	$0.241995\pi$
$354$	0.994840	−	0.994840i	0.0528752	−	0.0528752i
$355$		0			0
$356$	−51.1314			−2.70996
$357$	1.38049	+	0.693989i	0.0730631	+	0.0367298i
$358$	−23.1161			−1.22173
$359$			13.0217i			0.687258i	0.939105	+	0.343629i	$0.111656\pi$
$359$			13.0217i			0.687258i	−0.939105	+	0.343629i	$0.888344\pi$
$360$		0			0
$361$	−3.01006			−0.158424
$362$	31.9000	−	31.9000i	1.67663	−	1.67663i
$363$	−0.203562	−	0.203562i	−0.0106842	−	0.0106842i
$364$	5.20919	+	5.20919i	0.273036	+	0.273036i
$365$		0			0
$366$		−	2.29052i		−	0.119727i
$367$	−11.8536	−	11.8536i	−0.618755	−	0.618755i	0.326457	−	0.945212i	$-0.394145\pi$
$367$	−11.8536	−	11.8536i	−0.618755	−	0.618755i	−0.945212	+	0.326457i	$0.894145\pi$
$368$	−0.311501	−	0.311501i	−0.0162381	−	0.0162381i
$369$	−12.6986	+	12.6986i	−0.661063	+	0.661063i
$370$		0			0
$371$	−13.2492	+	13.2492i	−0.687864	+	0.687864i
$372$			3.76419i			0.195164i
$373$	−1.14057			−0.0590567			−0.0295283	−	0.999564i	$-0.509401\pi$
$373$	−1.14057			−0.0590567			−0.0295283	+	0.999564i	$0.509401\pi$
$374$	31.0656	−	10.2804i	1.60637	−	0.531588i
$375$		0			0
$376$		−	25.6713i		−	1.32390i
$377$	4.86009	−	4.86009i	0.250307	−	0.250307i
$378$	5.02355			0.258384
$379$	6.20062	−	6.20062i	0.318504	−	0.318504i	−0.529688	−	0.848192i	$-0.677691\pi$
$379$	6.20062	−	6.20062i	0.318504	−	0.318504i	0.848192	+	0.529688i	$0.177691\pi$
$380$		0			0
$381$	−1.79734	−	1.79734i	−0.0920805	−	0.0920805i
$382$			9.24619i			0.473076i
$383$			11.9977i			0.613053i	0.951862	+	0.306526i	$0.0991668\pi$
$383$			11.9977i			0.613053i	−0.951862	+	0.306526i	$0.900833\pi$
$384$	−2.29196	−	2.29196i	−0.116961	−	0.116961i
$385$		0			0
$386$	−22.7379	+	22.7379i	−1.15733	+	1.15733i
$387$	−27.1220			−1.37869
$388$	12.7839	−	12.7839i	0.649003	−	0.649003i
$389$		−	0.165600i		−	0.00839627i	−0.999991	−	0.00419813i	$-0.998664\pi$
$389$		−	0.165600i		−	0.00839627i	0.999991	−	0.00419813i	$-0.00133631\pi$
$390$		0			0
$391$	−0.744739	−	2.25047i	−0.0376631	−	0.113811i
$392$	−8.13238			−0.410747
$393$			1.39113i			0.0701733i
$394$	8.50969	−	8.50969i	0.428712	−	0.428712i
$395$		0			0
$396$	22.5903	−	22.5903i	1.13521	−	1.13521i
$397$	−21.5282	−	21.5282i	−1.08047	−	1.08047i	−0.996465	−	0.0840060i	$-0.973228\pi$
$397$	−21.5282	−	21.5282i	−1.08047	−	1.08047i	−0.0840060	−	0.996465i	$-0.526772\pi$
$398$	5.36620	+	5.36620i	0.268983	+	0.268983i
$399$			1.75811i			0.0880155i
$400$		0			0
$401$	−26.0214	−	26.0214i	−1.29945	−	1.29945i	−0.928757	−	0.370690i	$-0.879121\pi$
$401$	−26.0214	−	26.0214i	−1.29945	−	1.29945i	−0.370690	−	0.928757i	$-0.620879\pi$
$402$	0.0887629	+	0.0887629i	0.00442709	+	0.00442709i
$403$	5.59683	−	5.59683i	0.278798	−	0.278798i
$404$	−30.8729			−1.53599
$405$		0			0
$406$		−	22.9729i		−	1.14012i
$407$	29.9484			1.48449
$408$	−0.610142	−	1.84374i	−0.0302065	−	0.0912788i
$409$	7.05575			0.348885			0.174442	−	0.984667i	$-0.444188\pi$
$409$	7.05575			0.348885			0.174442	+	0.984667i	$0.444188\pi$
$410$		0			0
$411$	−2.12114	+	2.12114i	−0.104628	+	0.104628i
$412$	−3.28148			−0.161667
$413$	−4.22699	+	4.22699i	−0.207997	+	0.207997i
$414$	−2.70694	−	2.70694i	−0.133039	−	0.133039i
$415$		0			0
$416$			8.25077i			0.404527i
$417$		−	2.46223i		−	0.120576i
$418$	26.3280	+	26.3280i	1.28774	+	1.28774i
$419$	9.53560	+	9.53560i	0.465844	+	0.465844i	0.900565	−	0.434721i	$-0.143153\pi$
$419$	9.53560	+	9.53560i	0.465844	+	0.465844i	−0.434721	+	0.900565i	$0.643153\pi$
$420$		0			0
$421$	11.9003			0.579984			0.289992	−	0.957029i	$-0.406347\pi$
$421$	11.9003			0.579984			0.289992	+	0.957029i	$0.406347\pi$
$422$	3.74252	−	3.74252i	0.182183	−	0.182183i
$423$			31.9562i			1.55376i
$424$	23.5511			1.14374
$425$		0			0
$426$	−5.23010			−0.253399
$427$			9.73220i			0.470974i
$428$	13.7257	−	13.7257i	0.663457	−	0.663457i
$429$	0.889817			0.0429608
$430$		0			0
$431$	−8.47563	−	8.47563i	−0.408257	−	0.408257i	0.472874	−	0.881130i	$-0.343217\pi$
$431$	−8.47563	−	8.47563i	−0.408257	−	0.408257i	−0.881130	+	0.472874i	$0.843217\pi$
$432$	0.639573	+	0.639573i	0.0307715	+	0.0307715i
$433$			7.39430i			0.355347i	0.984089	+	0.177674i	$0.0568572\pi$
$433$			7.39430i			0.355347i	−0.984089	+	0.177674i	$0.943143\pi$
$434$		−	26.4553i		−	1.26990i
$435$		0			0
$436$	−21.8057	−	21.8057i	−1.04430	−	1.04430i
$437$	1.90726	−	1.90726i	0.0912367	−	0.0912367i
$438$	−4.37994			−0.209281
$439$	22.3750	−	22.3750i	1.06790	−	1.06790i	0.0703785	−	0.997520i	$-0.477579\pi$
$439$	22.3750	−	22.3750i	1.06790	−	1.06790i	0.997520	−	0.0703785i	$-0.0224207\pi$
$440$		0			0
$441$	10.1234			0.482065
$442$	−5.30274	+	10.5482i	−0.252226	+	0.501729i
$443$	−35.6597			−1.69424			−0.847121	−	0.531401i	$-0.821666\pi$
$443$	−35.6597			−1.69424			−0.847121	+	0.531401i	$0.821666\pi$
$444$		−	5.13865i		−	0.243870i
$445$		0			0
$446$	7.77454			0.368135
$447$	−1.62568	+	1.62568i	−0.0768921	+	0.0768921i
$448$	17.4495	+	17.4495i	0.824411	+	0.824411i
$449$	−0.824876	−	0.824876i	−0.0389283	−	0.0389283i	0.687375	−	0.726303i	$-0.258763\pi$
$449$	−0.824876	−	0.824876i	−0.0389283	−	0.0389283i	−0.726303	+	0.687375i	$0.758763\pi$
$450$		0			0
$451$			21.4049i			1.00792i
$452$	−8.09455	−	8.09455i	−0.380736	−	0.380736i
$453$	0.184517	+	0.184517i	0.00866938	+	0.00866938i
$454$	34.5339	−	34.5339i	1.62076	−	1.62076i
$455$		0			0
$456$	1.56256	−	1.56256i	0.0731737	−	0.0731737i
$457$		−	37.6351i		−	1.76050i	−0.474514	−	0.880248i	$-0.657376\pi$
$457$		−	37.6351i		−	1.76050i	0.474514	−	0.880248i	$-0.342624\pi$
$458$	19.3221			0.902860
$459$	1.52910	+	4.62066i	0.0713721	+	0.215674i
$460$		0			0
$461$			22.0741i			1.02809i	0.857763	+	0.514046i	$0.171854\pi$
$461$			22.0741i			1.02809i	−0.857763	+	0.514046i	$0.828146\pi$
$462$	2.10301	−	2.10301i	0.0978410	−	0.0978410i
$463$	−11.0361			−0.512893			−0.256447	−	0.966558i	$-0.582552\pi$
$463$	−11.0361			−0.512893			−0.256447	+	0.966558i	$0.582552\pi$
$464$	2.92479	−	2.92479i	0.135780	−	0.135780i
$465$		0			0
$466$	−14.1660	−	14.1660i	−0.656226	−	0.656226i
$467$		−	22.0407i		−	1.01992i	−0.860198	−	0.509960i	$-0.829660\pi$
$467$		−	22.0407i		−	1.01992i	0.860198	−	0.509960i	$-0.170340\pi$
$468$			11.5265i			0.532814i
$469$	−0.377146	−	0.377146i	−0.0174150	−	0.0174150i
$470$		0			0
$471$	−0.0257499	+	0.0257499i	−0.00118649	+	0.00118649i
$472$	7.51368			0.345845
$473$	−22.8585	+	22.8585i	−1.05104	+	1.05104i
$474$			7.54475i			0.346542i
$475$		0			0
$476$	7.49488	+	22.6482i	0.343527	+	1.03808i
$477$	−29.3169			−1.34233
$478$		−	27.7170i		−	1.26774i
$479$	−22.1659	+	22.1659i	−1.01279	+	1.01279i	−0.0128704	+	0.999917i	$0.504097\pi$
$479$	−22.1659	+	22.1659i	−1.01279	+	1.01279i	−0.999917	+	0.0128704i	$0.995903\pi$
$480$		0			0
$481$	−7.64045	+	7.64045i	−0.348375	+	0.348375i
$482$	4.24998	+	4.24998i	0.193581	+	0.193581i
$483$	−0.152347	−	0.152347i	−0.00693204	−	0.00693204i
$484$		−	4.44480i		−	0.202036i
$485$		0			0
$486$	8.35511	+	8.35511i	0.378996	+	0.378996i
$487$	1.89382	+	1.89382i	0.0858170	+	0.0858170i	0.748712	−	0.662895i	$-0.230673\pi$
$487$	1.89382	+	1.89382i	0.0858170	+	0.0858170i	−0.662895	+	0.748712i	$0.730673\pi$
$488$	8.64973	−	8.64973i	0.391555	−	0.391555i
$489$	3.57461			0.161649
$490$		0			0
$491$		−	19.7985i		−	0.893496i	−0.894660	−	0.446748i	$-0.852582\pi$
$491$		−	19.7985i		−	0.893496i	0.894660	−	0.446748i	$-0.147418\pi$
$492$	3.67273			0.165580
$493$	21.1304	−	6.99260i	0.951666	−	0.314931i
$494$	−13.4336			−0.604407
$495$		0			0
$496$	3.36815	−	3.36815i	0.151235	−	0.151235i
$497$	22.2222			0.996803
$498$	−2.68040	+	2.68040i	−0.120112	+	0.120112i
$499$	−19.5941	−	19.5941i	−0.877152	−	0.877152i	0.116087	−	0.993239i	$-0.462965\pi$
$499$	−19.5941	−	19.5941i	−0.877152	−	0.877152i	−0.993239	+	0.116087i	$0.962965\pi$
$500$		0			0
$501$			1.50015i			0.0670218i
$502$		−	61.7136i		−	2.75441i
$503$	−2.90654	−	2.90654i	−0.129596	−	0.129596i	0.639333	−	0.768930i	$-0.279210\pi$
$503$	−2.90654	−	2.90654i	−0.129596	−	0.129596i	−0.768930	+	0.639333i	$0.779210\pi$
$504$	9.42288	+	9.42288i	0.419728	+	0.419728i
$505$		0			0
$506$	−4.56285			−0.202843
$507$	1.59340	−	1.59340i	0.0707656	−	0.0707656i
$508$		−	39.2451i		−	1.74122i
$509$	41.9347			1.85872			0.929362	−	0.369169i	$-0.120358\pi$
$509$	41.9347			1.85872			0.929362	+	0.369169i	$0.120358\pi$
$510$		0			0
$511$	18.6100			0.823256
$512$			8.61021i			0.380521i
$513$	−3.91599	+	3.91599i	−0.172895	+	0.172895i
$514$	−51.4595			−2.26978
$515$		0			0
$516$	3.92215	+	3.92215i	0.172663	+	0.172663i
$517$	26.9328	+	26.9328i	1.18451	+	1.18451i
$518$			36.1152i			1.58681i
$519$			1.37087i			0.0601746i
$520$		0			0
$521$	25.0405	+	25.0405i	1.09705	+	1.09705i	0.994754	+	0.102292i	$0.0326176\pi$
$521$	25.0405	+	25.0405i	1.09705	+	1.09705i	0.102292	+	0.994754i	$0.467382\pi$
$522$	25.4164	−	25.4164i	1.11244	−	1.11244i
$523$	−6.37043			−0.278560			−0.139280	−	0.990253i	$-0.544479\pi$
$523$	−6.37043			−0.278560			−0.139280	+	0.990253i	$0.544479\pi$
$524$	−15.1877	+	15.1877i	−0.663480	+	0.663480i
$525$		0			0
$526$	21.3355			0.930273
$527$	24.3336	−	8.05261i	1.05999	−	0.350777i
$528$	0.535489			0.0233042
$529$		−	22.6695i		−	0.985629i
$530$		0			0
$531$	−9.35319			−0.405894
$532$	−19.1942	+	19.1942i	−0.832176	+	0.832176i
$533$	−5.46084	−	5.46084i	−0.236535	−	0.236535i
$534$	−5.26630	−	5.26630i	−0.227895	−	0.227895i
$535$		0			0
$536$			0.670395i			0.0289566i
$537$	−1.43936	−	1.43936i	−0.0621130	−	0.0621130i
$538$	9.68144	+	9.68144i	0.417397	+	0.417397i
$539$	8.53203	−	8.53203i	0.367501	−	0.367501i
$540$		0			0
$541$	−11.5578	+	11.5578i	−0.496908	+	0.496908i	−0.910474	−	0.413566i	$-0.864283\pi$
$541$	−11.5578	+	11.5578i	−0.496908	+	0.496908i	0.413566	+	0.910474i	$0.364283\pi$
$542$			53.2049i			2.28535i
$543$	3.97260			0.170481
$544$	−12.0006	+	23.8716i	−0.514521	+	1.02349i
$545$		0			0
$546$			1.07304i			0.0459221i
$547$	0.909839	−	0.909839i	0.0389019	−	0.0389019i	−0.687388	−	0.726290i	$-0.741243\pi$
$547$	0.909839	−	0.909839i	0.0389019	−	0.0389019i	0.726290	+	0.687388i	$0.241243\pi$
$548$	−46.3153			−1.97849
$549$	−10.7674	+	10.7674i	−0.459540	+	0.459540i
$550$		0			0
$551$	17.9079	+	17.9079i	0.762903	+	0.762903i
$552$			0.270805i			0.0115262i
$553$		−	32.0570i		−	1.36320i
$554$	13.0994	+	13.0994i	0.556540	+	0.556540i
$555$		0			0
$556$	26.8815	−	26.8815i	1.14003	−	1.14003i
$557$	−35.2859			−1.49511			−0.747555	−	0.664200i	$-0.768773\pi$
$557$	−35.2859			−1.49511			−0.747555	+	0.664200i	$0.768773\pi$
$558$	29.2693	−	29.2693i	1.23907	−	1.23907i
$559$		−	11.6634i		−	0.493308i
$560$		0			0
$561$	2.57447	+	1.29422i	0.108694	+	0.0546421i
$562$	33.9216			1.43089
$563$		−	0.931153i		−	0.0392434i	−0.999807	−	0.0196217i	$-0.993754\pi$
$563$		−	0.931153i		−	0.0392434i	0.999807	−	0.0196217i	$-0.00624618\pi$
$564$	4.62123	−	4.62123i	0.194589	−	0.194589i
$565$		0			0
$566$	28.2275	−	28.2275i	1.18649	−	1.18649i
$567$	−11.5724	−	11.5724i	−0.485994	−	0.485994i
$568$	−19.7505	−	19.7505i	−0.828714	−	0.828714i
$569$			17.5921i			0.737498i	0.929529	+	0.368749i	$0.120214\pi$
$569$			17.5921i			0.737498i	−0.929529	+	0.368749i	$0.879786\pi$
$570$		0			0
$571$	−12.2000	−	12.2000i	−0.510554	−	0.510554i	0.404142	−	0.914696i	$-0.367570\pi$
$571$	−12.2000	−	12.2000i	−0.510554	−	0.510554i	−0.914696	+	0.404142i	$0.867570\pi$
$572$	9.71463	+	9.71463i	0.406189	+	0.406189i
$573$	−0.575728	+	0.575728i	−0.0240514	+	0.0240514i
$574$	−25.8125			−1.07739
$575$		0			0
$576$			38.6110i			1.60879i
$577$	−8.50534			−0.354082			−0.177041	−	0.984203i	$-0.556653\pi$
$577$	−8.50534			−0.354082			−0.177041	+	0.984203i	$0.556653\pi$
$578$	−30.6844	+	22.8061i	−1.27630	+	0.948608i
$579$	−2.83162			−0.117678
$580$		0			0
$581$	11.3888	−	11.3888i	0.472487	−	0.472487i
$582$	2.63336			0.109156
$583$	−24.7084	+	24.7084i	−1.02332	+	1.02332i
$584$	−16.5401	−	16.5401i	−0.684433	−	0.684433i
$585$		0			0
$586$		−	24.5563i		−	1.01441i
$587$			1.55649i			0.0642433i	0.999484	+	0.0321217i	$0.0102264\pi$
$587$			1.55649i			0.0642433i	−0.999484	+	0.0321217i	$0.989774\pi$
$588$	−1.46396	−	1.46396i	−0.0603726	−	0.0603726i
$589$	20.6226	+	20.6226i	0.849739	+	0.849739i
$590$		0			0
$591$	1.05974			0.0435918
$592$	−4.59800	+	4.59800i	−0.188977	+	0.188977i
$593$		−	19.6862i		−	0.808415i	−0.914667	−	0.404207i	$-0.867547\pi$
$593$		−	19.6862i		−	0.808415i	0.914667	−	0.404207i	$-0.132453\pi$
$594$	9.36844			0.384392
$595$		0			0
$596$	−35.4969			−1.45401
$597$			0.668269i			0.0273504i
$598$	1.16408	−	1.16408i	0.0476027	−	0.0476027i
$599$	−24.7552			−1.01147			−0.505735	−	0.862689i	$-0.668779\pi$
$599$	−24.7552			−1.01147			−0.505735	+	0.862689i	$0.668779\pi$
$600$		0			0
$601$	−20.0336	−	20.0336i	−0.817186	−	0.817186i	0.168513	−	0.985699i	$-0.446103\pi$
$601$	−20.0336	−	20.0336i	−0.817186	−	0.817186i	−0.985699	+	0.168513i	$0.946103\pi$
$602$	−27.5655	−	27.5655i	−1.12348	−	1.12348i
$603$		−	0.834522i		−	0.0339844i
$604$			4.02895i			0.163936i
$605$		0			0
$606$	−3.17977	−	3.17977i	−0.129169	−	0.129169i
$607$	−32.9490	+	32.9490i	−1.33736	+	1.33736i	−0.438750	+	0.898609i	$0.644579\pi$
$607$	−32.9490	+	32.9490i	−1.33736	+	1.33736i	−0.898609	+	0.438750i	$0.855421\pi$
$608$	−30.4015			−1.23294
$609$	1.43044	−	1.43044i	0.0579644	−	0.0579644i
$610$		0			0
$611$	−13.7423			−0.555952
$612$	−16.7651	+	33.3493i	−0.677690	+	1.34806i
$613$	42.0358			1.69781			0.848905	−	0.528546i	$-0.177263\pi$
$613$	42.0358			1.69781			0.848905	+	0.528546i	$0.177263\pi$
$614$		−	15.3577i		−	0.619786i
$615$		0			0
$616$	15.8833			0.639957
$617$	−12.8737	+	12.8737i	−0.518275	+	0.518275i	−0.917049	−	0.398774i	$-0.869436\pi$
$617$	−12.8737	+	12.8737i	−0.518275	+	0.518275i	0.398774	+	0.917049i	$0.369436\pi$
$618$	−0.337978	−	0.337978i	−0.0135955	−	0.0135955i
$619$	−9.74184	−	9.74184i	−0.391558	−	0.391558i	0.483685	−	0.875242i	$-0.339298\pi$
$619$	−9.74184	−	9.74184i	−0.391558	−	0.391558i	−0.875242	+	0.483685i	$0.839298\pi$
$620$		0			0
$621$		−	0.678672i		−	0.0272342i
$622$	1.05116	+	1.05116i	0.0421477	+	0.0421477i
$623$	22.3761	+	22.3761i	0.896478	+	0.896478i
$624$	−0.136614	+	0.136614i	−0.00546895	+	0.00546895i
$625$		0			0
$626$	−6.66827	+	6.66827i	−0.266518	+	0.266518i
$627$			3.27870i			0.130939i
$628$	−0.562251			−0.0224362
$629$	−33.2187	+	10.9929i	−1.32452	+	0.438317i
$630$		0			0
$631$			20.2307i			0.805372i	0.915338	+	0.402686i	$0.131923\pi$
$631$			20.2307i			0.805372i	−0.915338	+	0.402686i	$0.868077\pi$
$632$	−28.4914	+	28.4914i	−1.13333	+	1.13333i
$633$	0.466068			0.0185245
$634$	−33.8170	+	33.8170i	−1.34304	+	1.34304i
$635$		0			0
$636$	4.23956	+	4.23956i	0.168110	+	0.168110i
$637$			4.35340i			0.172488i
$638$		−	42.8421i		−	1.69614i
$639$	24.5859	+	24.5859i	0.972603	+	0.972603i
$640$		0			0
$641$	−3.37688	+	3.37688i	−0.133379	+	0.133379i	−0.770644	−	0.637266i	$-0.780065\pi$
$641$	−3.37688	+	3.37688i	−0.133379	+	0.133379i	0.637266	+	0.770644i	$0.280065\pi$
$642$	2.82737			0.111587
$643$	6.97016	−	6.97016i	0.274876	−	0.274876i	−0.556183	−	0.831060i	$-0.687735\pi$
$643$	6.97016	−	6.97016i	0.274876	−	0.274876i	0.831060	+	0.556183i	$0.187735\pi$
$644$		−	3.32652i		−	0.131083i
$645$		0			0
$646$	−38.8670	−	19.5389i	−1.52920	−	0.768749i
$647$	36.4555			1.43321			0.716607	−	0.697477i	$-0.245694\pi$
$647$	36.4555			1.43321			0.716607	+	0.697477i	$0.245694\pi$
$648$			20.5705i			0.808084i
$649$	−7.88292	+	7.88292i	−0.309432	+	0.309432i
$650$		0			0
$651$	1.64728	−	1.64728i	0.0645620	−	0.0645620i
$652$	39.0260	+	39.0260i	1.52837	+	1.52837i
$653$	−12.7332	−	12.7332i	−0.498288	−	0.498288i	0.412617	−	0.910905i	$-0.364615\pi$
$653$	−12.7332	−	12.7332i	−0.498288	−	0.498288i	−0.910905	+	0.412617i	$0.864615\pi$
$654$		−	4.49177i		−	0.175642i
$655$		0			0
$656$	−3.28631	−	3.28631i	−0.128309	−	0.128309i
$657$	20.5894	+	20.5894i	0.803270	+	0.803270i
$658$	−32.4787	+	32.4787i	−1.26615	+	1.26615i
$659$	−0.175710			−0.00684470			−0.00342235	−	0.999994i	$-0.501089\pi$
$659$	−0.175710			−0.00684470			−0.00342235	+	0.999994i	$0.501089\pi$
$660$		0			0
$661$			4.14751i			0.161319i	0.996742	+	0.0806597i	$0.0257027\pi$
$661$			4.14751i			0.161319i	−0.996742	+	0.0806597i	$0.974297\pi$
$662$	−62.4258			−2.42625
$663$	−0.986985	+	0.326619i	−0.0383313	+	0.0126848i
$664$	−20.2442			−0.785626
$665$		0			0
$666$	−39.9566	+	39.9566i	−1.54829	+	1.54829i
$667$	−3.10359			−0.120171
$668$	−16.3780	+	16.3780i	−0.633683	+	0.633683i
$669$	0.484093	+	0.484093i	0.0187161	+	0.0187161i
$670$		0			0
$671$			18.1496i			0.700658i
$672$			2.42840i			0.0936775i
$673$	6.18030	+	6.18030i	0.238233	+	0.238233i	0.816118	−	0.577885i	$-0.196122\pi$
$673$	6.18030	+	6.18030i	0.238233	+	0.238233i	−0.577885	+	0.816118i	$0.696122\pi$
$674$	−13.9616	−	13.9616i	−0.537780	−	0.537780i
$675$		0			0
$676$	34.7922			1.33816
$677$	−6.62704	+	6.62704i	−0.254698	+	0.254698i	−0.822893	−	0.568196i	$-0.807642\pi$
$677$	−6.62704	+	6.62704i	−0.254698	+	0.254698i	0.568196	+	0.822893i	$0.307642\pi$
$678$		−	1.66740i		−	0.0640362i
$679$	−11.1889			−0.429391
$680$		0			0
$681$	4.30061			0.164800
$682$		−	49.3366i		−	1.88920i
$683$	26.4889	−	26.4889i	1.01357	−	1.01357i	0.0136635	−	0.999907i	$-0.495651\pi$
$683$	26.4889	−	26.4889i	1.01357	−	1.01357i	0.999907	−	0.0136635i	$-0.00434937\pi$
$684$	−42.4717			−1.62395
$685$		0			0
$686$	31.3533	+	31.3533i	1.19707	+	1.19707i
$687$	1.20312	+	1.20312i	0.0459018	+	0.0459018i
$688$		−	7.01898i		−	0.267596i
$689$		−	12.6073i		−	0.480299i
$690$		0			0
$691$	−31.5901	−	31.5901i	−1.20175	−	1.20175i	−0.973635	−	0.228110i	$-0.926745\pi$
$691$	−31.5901	−	31.5901i	−1.20175	−	1.20175i	−0.228110	−	0.973635i	$-0.573255\pi$
$692$	−14.9666	+	14.9666i	−0.568943	+	0.568943i
$693$	−19.7719			−0.751072
$694$	8.38088	−	8.38088i	0.318134	−	0.318134i
$695$		0			0
$696$	−2.54268			−0.0963799
$697$	−7.85695	−	23.7423i	−0.297603	−	0.899304i
$698$	24.4308			0.924720
$699$		−	1.76413i		−	0.0667256i
$700$		0			0
$701$	−18.7355			−0.707630			−0.353815	−	0.935315i	$-0.615116\pi$
$701$	−18.7355			−0.707630			−0.353815	+	0.935315i	$0.615116\pi$
$702$	−2.39008	+	2.39008i	−0.0902079	+	0.0902079i
$703$	−28.1527	−	28.1527i	−1.06180	−	1.06180i
$704$	32.5416	+	32.5416i	1.22646	+	1.22646i
$705$		0			0
$706$			61.2388i			2.30475i
$707$	13.5106	+	13.5106i	0.508117	+	0.508117i
$708$	1.35258	+	1.35258i	0.0508331	+	0.0508331i
$709$	4.05125	−	4.05125i	0.152148	−	0.152148i	−0.626929	−	0.779077i	$-0.715688\pi$
$709$	4.05125	−	4.05125i	0.152148	−	0.152148i	0.779077	+	0.626929i	$0.215688\pi$
$710$		0			0
$711$	35.4668	−	35.4668i	1.33011	−	1.33011i
$712$		−	39.7745i		−	1.49061i
$713$	−3.57406			−0.133850
$714$	−1.56072	+	3.10460i	−0.0584085	+	0.116187i
$715$		0			0
$716$		−	31.4286i		−	1.17454i
$717$	1.72584	−	1.72584i	0.0644526	−	0.0644526i
$718$	−29.2846			−1.09289
$719$	−20.7647	+	20.7647i	−0.774393	+	0.774393i	−0.978871	−	0.204478i	$-0.934450\pi$
$719$	−20.7647	+	20.7647i	−0.774393	+	0.774393i	0.204478	+	0.978871i	$0.434450\pi$
$720$		0			0
$721$	1.43604	+	1.43604i	0.0534808	+	0.0534808i
$722$		−	6.76937i		−	0.251930i
$723$			0.529263i			0.0196835i
$724$	43.3711	+	43.3711i	1.61187	+	1.61187i
$725$		0			0
$726$	0.457794	−	0.457794i	0.0169903	−	0.0169903i
$727$	48.1662			1.78639			0.893193	−	0.449674i	$-0.148460\pi$
$727$	48.1662			1.78639			0.893193	+	0.449674i	$0.148460\pi$
$728$	−4.05216	+	4.05216i	−0.150183	+	0.150183i
$729$		−	24.9052i		−	0.922416i
$730$		0			0
$731$	16.9642	−	33.7452i	0.627442	−	1.24811i
$732$	3.11417			0.115103
$733$		−	14.3419i		−	0.529731i	−0.964285	−	0.264866i	$-0.914672\pi$
$733$		−	14.3419i		−	0.529731i	0.964285	−	0.264866i	$-0.0853276\pi$
$734$	26.6578	−	26.6578i	0.983958	−	0.983958i
$735$		0			0
$736$	2.63442	−	2.63442i	0.0971059	−	0.0971059i
$737$	−0.703340	−	0.703340i	−0.0259079	−	0.0259079i
$738$	−28.5581	−	28.5581i	−1.05124	−	1.05124i
$739$		−	9.73758i		−	0.358203i	−0.983831	−	0.179101i	$-0.942681\pi$
$739$		−	9.73758i		−	0.358203i	0.983831	−	0.179101i	$-0.0573190\pi$
$740$		0			0
$741$	−0.836465	−	0.836465i	−0.0307283	−	0.0307283i
$742$	−29.7963	−	29.7963i	−1.09386	−	1.09386i
$743$	16.9727	−	16.9727i	0.622667	−	0.622667i	−0.323545	−	0.946213i	$-0.604875\pi$
$743$	16.9727	−	16.9727i	0.622667	−	0.622667i	0.946213	+	0.323545i	$0.104875\pi$
$744$	−2.92812			−0.107350
$745$		0			0
$746$		−	2.56505i		−	0.0939133i
$747$	25.2004			0.922033
$748$	13.9772	+	42.2367i	0.511058	+	1.54433i
$749$	−12.0132			−0.438954
$750$		0			0
$751$	33.9092	−	33.9092i	1.23736	−	1.23736i	0.276289	−	0.961075i	$-0.410895\pi$
$751$	33.9092	−	33.9092i	1.23736	−	1.23736i	0.961075	−	0.276289i	$-0.0891047\pi$
$752$	−8.27004			−0.301578
$753$	3.84269	−	3.84269i	0.140035	−	0.140035i
$754$	10.9299	+	10.9299i	0.398044	+	0.398044i
$755$		0			0
$756$			6.83000i			0.248405i
$757$			18.5200i			0.673119i	0.941662	+	0.336560i	$0.109263\pi$
$757$			18.5200i			0.673119i	−0.941662	+	0.336560i	$0.890737\pi$
$758$	13.9447	+	13.9447i	0.506493	+	0.506493i
$759$	−0.284113	−	0.284113i	−0.0103126	−	0.0103126i
$760$		0			0
$761$	35.9145			1.30190			0.650950	−	0.759120i	$-0.274371\pi$
$761$	35.9145			1.30190			0.650950	+	0.759120i	$0.274371\pi$
$762$	4.04206	−	4.04206i	0.146428	−	0.146428i
$763$			19.0851i			0.690929i
$764$	−12.5711			−0.454806
$765$		0			0
$766$	−26.9818			−0.974890
$767$		−	4.02220i		−	0.145233i
$768$	1.50215	−	1.50215i	0.0542043	−	0.0542043i
$769$	17.7831			0.641276			0.320638	−	0.947202i	$-0.396103\pi$
$769$	17.7831			0.641276			0.320638	+	0.947202i	$0.396103\pi$
$770$		0			0
$771$	−3.20420	−	3.20420i	−0.115397	−	0.115397i
$772$	−30.9144	−	30.9144i	−1.11263	−	1.11263i
$773$			7.33018i			0.263648i	0.991273	+	0.131824i	$0.0420834\pi$
$773$			7.33018i			0.263648i	−0.991273	+	0.131824i	$0.957917\pi$
$774$		−	60.9949i		−	2.19242i
$775$		0			0
$776$	9.94441	+	9.94441i	0.356984	+	0.356984i
$777$	−2.24877	+	2.24877i	−0.0806741	+	0.0806741i
$778$	0.372421			0.0133519
$779$	20.1215	−	20.1215i	0.720927	−	0.720927i
$780$		0			0
$781$	41.4423			1.48292
$782$	5.06111	−	1.67485i	0.180985	−	0.0598926i
$783$	6.37228			0.227727
$784$			2.61986i			0.0935664i
$785$		0			0
$786$	−3.12853			−0.111591
$787$	−27.4321	+	27.4321i	−0.977850	+	0.977850i	−0.999760	−	0.0219095i	$-0.993025\pi$
$787$	−27.4321	+	27.4321i	−0.977850	+	0.977850i	0.0219095	+	0.999760i	$0.493025\pi$
$788$	11.5697	+	11.5697i	0.412155	+	0.412155i
$789$	1.32849	+	1.32849i	0.0472954	+	0.0472954i
$790$		0			0
$791$			7.08465i			0.251901i
$792$	17.5727	+	17.5727i	0.624420	+	0.624420i
$793$	−4.63034	−	4.63034i	−0.164428	−	0.164428i
$794$	48.4151	−	48.4151i	1.71819	−	1.71819i
$795$		0			0
$796$	−7.29586	+	7.29586i	−0.258595	+	0.258595i
$797$		−	36.6386i		−	1.29780i	−0.760872	−	0.648902i	$-0.775228\pi$
$797$		−	36.6386i		−	1.29780i	0.760872	−	0.648902i	$-0.224772\pi$
$798$	−3.95383			−0.139964
$799$	−39.7599	−	19.9878i	−1.40661	−	0.707119i
$800$		0			0
$801$			49.5122i			1.74943i
$802$	58.5199	−	58.5199i	2.06641	−	2.06641i
$803$	34.7058			1.22474
$804$	−0.120682	+	0.120682i	−0.00425611	+	0.00425611i
$805$		0			0
$806$	12.5868	+	12.5868i	0.443351	+	0.443351i
$807$			1.20566i			0.0424412i
$808$		−	24.0157i		−	0.844868i
$809$	−11.0838	−	11.0838i	−0.389685	−	0.389685i	0.484890	−	0.874575i	$-0.338860\pi$
$809$	−11.0838	−	11.0838i	−0.389685	−	0.389685i	−0.874575	+	0.484890i	$0.838860\pi$
$810$		0			0
$811$	5.58363	−	5.58363i	0.196068	−	0.196068i	−0.602244	−	0.798312i	$-0.705727\pi$
$811$	5.58363	−	5.58363i	0.196068	−	0.196068i	0.798312	+	0.602244i	$0.205727\pi$
$812$	31.2338			1.09609
$813$	−3.31288	+	3.31288i	−0.116188	+	0.116188i
$814$			67.3513i			2.36066i
$815$		0			0
$816$	−0.593964	+	0.196558i	−0.0207929	+	0.00688091i
$817$	42.9759			1.50354
$818$			15.8678i			0.554804i
$819$	5.04422	−	5.04422i	0.176259	−	0.176259i
$820$		0			0
$821$	16.6878	−	16.6878i	0.582408	−	0.582408i	−0.353157	−	0.935564i	$-0.614892\pi$
$821$	16.6878	−	16.6878i	0.582408	−	0.582408i	0.935564	+	0.353157i	$0.114892\pi$
$822$	−4.77026	−	4.77026i	−0.166382	−	0.166382i
$823$	10.0348	+	10.0348i	0.349792	+	0.349792i	0.860032	−	0.510240i	$-0.170444\pi$
$823$	10.0348	+	10.0348i	0.349792	+	0.349792i	−0.510240	+	0.860032i	$0.670444\pi$
$824$		−	2.55263i		−	0.0889250i
$825$		0			0
$826$	−9.50614	−	9.50614i	−0.330761	−	0.330761i
$827$	−26.8417	−	26.8417i	−0.933377	−	0.933377i	0.0645378	−	0.997915i	$-0.479443\pi$
$827$	−26.8417	−	26.8417i	−0.933377	−	0.933377i	−0.997915	+	0.0645378i	$0.979443\pi$
$828$	3.68034	−	3.68034i	0.127901	−	0.127901i
$829$	4.91163			0.170588			0.0852939	−	0.996356i	$-0.472817\pi$
$829$	4.91163			0.170588			0.0852939	+	0.996356i	$0.472817\pi$
$830$		0			0
$831$			1.63131i			0.0565894i
$832$	−16.6041			−0.575643
$833$	−6.33193	+	12.5955i	−0.219388	+	0.436409i
$834$	5.53734			0.191743
$835$		0			0
$836$	−35.7954	+	35.7954i	−1.23801	+	1.23801i
$837$	7.33826			0.253647
$838$	−21.4447	+	21.4447i	−0.740796	+	0.740796i
$839$	7.80546	+	7.80546i	0.269474	+	0.269474i	0.828888	−	0.559414i	$-0.188974\pi$
$839$	7.80546	+	7.80546i	0.269474	+	0.269474i	−0.559414	+	0.828888i	$0.688974\pi$
$840$		0			0
$841$		−	0.140644i		−	0.00484980i
$842$			26.7627i			0.922303i
$843$	2.11218	+	2.11218i	0.0727472	+	0.0727472i
$844$	5.08832	+	5.08832i	0.175147	+	0.175147i
$845$		0			0
$846$	−71.8667			−2.47083
$847$	−1.94513	+	1.94513i	−0.0668353	+	0.0668353i
$848$		−	7.58701i		−	0.260539i
$849$	3.51525			0.120643
$850$		0			0
$851$	4.87909			0.167253
$852$		−	7.11081i		−	0.243612i
$853$	−28.8483	+	28.8483i	−0.987746	+	0.987746i	−0.999926	−	0.0121803i	$-0.996123\pi$
$853$	−28.8483	+	28.8483i	−0.987746	+	0.987746i	0.0121803	+	0.999926i	$0.496123\pi$
$854$	−21.8869			−0.748954
$855$		0			0
$856$	10.6771	+	10.6771i	0.364934	+	0.364934i
$857$	2.91939	+	2.91939i	0.0997244	+	0.0997244i	0.755209	−	0.655484i	$-0.227535\pi$
$857$	2.91939	+	2.91939i	0.0997244	+	0.0997244i	−0.655484	+	0.755209i	$0.727535\pi$
$858$			2.00112i			0.0683172i
$859$			8.53800i			0.291313i	0.989335	+	0.145656i	$0.0465294\pi$
$859$			8.53800i			0.291313i	−0.989335	+	0.145656i	$0.953471\pi$
$860$		0			0
$861$	−1.60725	−	1.60725i	−0.0547751	−	0.0547751i
$862$	19.0610	−	19.0610i	0.649219	−	0.649219i
$863$	−3.08921			−0.105158			−0.0525790	−	0.998617i	$-0.516744\pi$
$863$	−3.08921			−0.105158			−0.0525790	+	0.998617i	$0.516744\pi$
$864$	−5.40898	+	5.40898i	−0.184017	+	0.184017i
$865$		0			0
$866$	−16.6291			−0.565081
$867$	−3.33067	−	0.490556i	−0.113115	−	0.0166602i
$868$	35.9685			1.22085
$869$		−	59.7832i		−	2.02801i
$870$		0			0
$871$	0.358873			0.0121600
$872$	16.9624	−	16.9624i	0.574419	−	0.574419i
$873$	−12.3790	−	12.3790i	−0.418966	−	0.418966i
$874$	4.28927	+	4.28927i	0.145087	+	0.145087i
$875$		0			0
$876$		−	5.95494i		−	0.201199i
$877$	21.7154	+	21.7154i	0.733278	+	0.733278i	0.971268	−	0.237990i	$-0.0764884\pi$
$877$	21.7154	+	21.7154i	0.733278	+	0.733278i	−0.237990	+	0.971268i	$0.576488\pi$
$878$	50.3194	+	50.3194i	1.69820	+	1.69820i
$879$	1.52904	−	1.52904i	0.0515731	−	0.0515731i
$880$		0			0
$881$	−6.18749	+	6.18749i	−0.208462	+	0.208462i	−0.803613	−	0.595152i	$-0.797092\pi$
$881$	−6.18749	+	6.18749i	−0.208462	+	0.208462i	0.595152	+	0.803613i	$0.297092\pi$
$882$			22.7666i			0.766591i
$883$	29.5875			0.995698			0.497849	−	0.867264i	$-0.334123\pi$
$883$	29.5875			0.995698			0.497849	+	0.867264i	$0.334123\pi$
$884$	−14.3413	−	7.20958i	−0.482351	−	0.242484i
$885$		0			0
$886$		−	80.1955i		−	2.69422i
$887$	−5.92290	+	5.92290i	−0.198872	+	0.198872i	−0.799516	−	0.600645i	$-0.794911\pi$
$887$	−5.92290	+	5.92290i	−0.198872	+	0.198872i	0.600645	+	0.799516i	$0.294911\pi$
$888$	3.99729			0.134140
$889$	−17.1744	+	17.1744i	−0.576010	+	0.576010i
$890$		0			0
$891$	−21.5813	−	21.5813i	−0.723002	−	0.723002i
$892$			10.5702i			0.353917i
$893$		−	50.6360i		−	1.69447i
$894$	−3.65602	−	3.65602i	−0.122276	−	0.122276i
$895$		0			0
$896$	−21.9007	+	21.9007i	−0.731650	+	0.731650i
$897$	0.144966			0.00484028
$898$	1.85507	−	1.85507i	0.0619046	−	0.0619046i
$899$		−	33.5581i		−	1.11922i
$900$		0			0
$901$	18.3370	−	36.4761i	0.610895	−	1.21520i
$902$	−48.1378			−1.60281
$903$		−	3.43281i		−	0.114237i
$904$	6.29665	−	6.29665i	0.209424	−	0.209424i
$905$		0			0
$906$	−0.414963	+	0.414963i	−0.0137862	+	0.0137862i
$907$	−14.2310	−	14.2310i	−0.472534	−	0.472534i	0.430200	−	0.902734i	$-0.358443\pi$
$907$	−14.2310	−	14.2310i	−0.472534	−	0.472534i	−0.902734	+	0.430200i	$0.858443\pi$
$908$	46.9521	+	46.9521i	1.55816	+	1.55816i
$909$			29.8952i			0.991562i
$910$		0			0
$911$	5.67260	+	5.67260i	0.187942	+	0.187942i	0.794806	−	0.606864i	$-0.207573\pi$
$911$	5.67260	+	5.67260i	0.187942	+	0.187942i	−0.606864	+	0.794806i	$0.707573\pi$
$912$	−0.503382	−	0.503382i	−0.0166686	−	0.0166686i
$913$	21.2390	−	21.2390i	0.702909	−	0.702909i
$914$	84.6381			2.79958
$915$		0			0
$916$			26.2702i			0.867991i
$917$	13.2929			0.438969
$918$	−10.3915	+	3.43880i	−0.342969	+	0.113497i
$919$	30.7678			1.01494			0.507468	−	0.861671i	$-0.330582\pi$
$919$	30.7678			1.01494			0.507468	+	0.861671i	$0.330582\pi$
$920$		0			0
$921$	0.956270	−	0.956270i	0.0315102	−	0.0315102i
$922$	−49.6427			−1.63489
$923$	−10.5728	+	10.5728i	−0.348008	+	0.348008i
$924$	2.85925	+	2.85925i	0.0940623	+	0.0940623i
$925$		0			0
$926$		−	24.8193i		−	0.815614i
$927$			3.17756i			0.104365i
$928$	24.7354	+	24.7354i	0.811980	+	0.811980i
$929$	25.5343	+	25.5343i	0.837755	+	0.837755i	0.988563	−	0.150808i	$-0.0481876\pi$
$929$	25.5343	+	25.5343i	0.837755	+	0.837755i	−0.150808	+	0.988563i	$0.548188\pi$
$930$		0			0
$931$	−16.0409			−0.525720
$932$	19.2600	−	19.2600i	0.630882	−	0.630882i
$933$			0.130904i			0.00428561i
$934$	49.5675			1.62190
$935$		0			0
$936$	−8.96635			−0.293074
$937$		−	36.7492i		−	1.20054i	−0.799796	−	0.600272i	$-0.795059\pi$
$937$		−	36.7492i		−	1.20054i	0.799796	−	0.600272i	$-0.204941\pi$
$938$	0.848168	−	0.848168i	0.0276937	−	0.0276937i
$939$	−0.830420			−0.0270997
$940$		0			0
$941$	−8.24873	−	8.24873i	−0.268901	−	0.268901i	0.559756	−	0.828657i	$-0.310895\pi$
$941$	−8.24873	−	8.24873i	−0.268901	−	0.268901i	−0.828657	+	0.559756i	$0.810895\pi$
$942$	−0.0579092	−	0.0579092i	−0.00188678	−	0.00188678i
$943$			3.48722i			0.113559i
$944$		−	2.42054i		−	0.0787820i
$945$		0			0
$946$	−51.4069	−	51.4069i	−1.67138	−	1.67138i
$947$	−32.9727	+	32.9727i	−1.07147	+	1.07147i	−0.0742285	+	0.997241i	$0.523649\pi$
$947$	−32.9727	+	32.9727i	−1.07147	+	1.07147i	−0.997241	+	0.0742285i	$0.976351\pi$
$948$	−10.2578			−0.333158
$949$	−8.85416	+	8.85416i	−0.287418	+	0.287418i
$950$		0			0
$951$	−4.21133			−0.136562
$952$	−17.6178	+	5.83017i	−0.570995	+	0.188957i
$953$	−15.8298			−0.512778			−0.256389	−	0.966574i	$-0.582533\pi$
$953$	−15.8298			−0.512778			−0.256389	+	0.966574i	$0.582533\pi$
$954$		−	65.9311i		−	2.13460i
$955$		0			0
$956$	37.6839			1.21878
$957$	2.66763	−	2.66763i	0.0862322	−	0.0862322i
$958$	−49.8493	−	49.8493i	−1.61056	−	1.61056i
$959$	20.2684	+	20.2684i	0.654502	+	0.654502i
$960$		0			0
$961$		−	7.64513i		−	0.246617i
$962$	−17.1827	−	17.1827i	−0.553993	−	0.553993i
$963$	−13.2910	−	13.2910i	−0.428297	−	0.428297i
$964$	−5.77825	+	5.77825i	−0.186105	+	0.186105i
$965$		0			0
$966$	0.342616	−	0.342616i	0.0110235	−	0.0110235i
$967$		−	18.4139i		−	0.592152i	−0.955164	−	0.296076i	$-0.904322\pi$
$967$		−	18.4139i		−	0.592152i	0.955164	−	0.296076i	$-0.0956781\pi$
$968$	3.45755			0.111130
$969$	−1.20349	−	3.63673i	−0.0386616	−	0.116829i
$970$		0			0
$971$			16.3118i			0.523470i	0.965140	+	0.261735i	$0.0842947\pi$
$971$			16.3118i			0.523470i	−0.965140	+	0.261735i	$0.915705\pi$
$972$	−11.3596	+	11.3596i	−0.364358	+	0.364358i
$973$	−23.5277			−0.754263
$974$	−4.25903	+	4.25903i	−0.136468	+	0.136468i
$975$		0			0
$976$	−2.78652	−	2.78652i	−0.0891945	−	0.0891945i
$977$			52.7849i			1.68874i	0.535762	+	0.844369i	$0.320024\pi$
$977$			52.7849i			1.68874i	−0.535762	+	0.844369i	$0.679976\pi$
$978$			8.03898i			0.257058i
$979$	41.7291	+	41.7291i	1.33367	+	1.33367i
$980$		0			0
$981$	−21.1151	+	21.1151i	−0.674155	+	0.674155i
$982$	44.5252			1.42086
$983$	23.5672	−	23.5672i	0.751677	−	0.751677i	−0.223115	−	0.974792i	$-0.571622\pi$
$983$	23.5672	−	23.5672i	0.751677	−	0.751677i	0.974792	+	0.223115i	$0.0716225\pi$
$984$			2.85697i			0.0910770i
$985$		0			0
$986$	15.7258	+	47.5205i	0.500810	+	1.51336i
$987$	−4.04467			−0.128743
$988$		−	18.2643i		−	0.581065i
$989$	−3.72404	+	3.72404i	−0.118418	+	0.118418i
$990$		0			0
$991$	−27.9267	+	27.9267i	−0.887122	+	0.887122i	−0.994246	−	0.107124i	$-0.965836\pi$
$991$	−27.9267	+	27.9267i	−0.887122	+	0.887122i	0.107124	+	0.994246i	$0.465836\pi$
$992$	28.4851	+	28.4851i	0.904402	+	0.904402i
$993$	−3.88703	−	3.88703i	−0.123351	−	0.123351i
$994$			49.9759i			1.58514i
$995$		0			0
$996$	−3.64427	−	3.64427i	−0.115473	−	0.115473i
$997$	−18.8643	−	18.8643i	−0.597437	−	0.597437i	0.342193	−	0.939630i	$-0.388830\pi$
$997$	−18.8643	−	18.8643i	−0.597437	−	0.597437i	−0.939630	+	0.342193i	$0.888830\pi$
$998$	44.0654	−	44.0654i	1.39487	−	1.39487i
$999$	−10.0177			−0.316947

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.e.f.276.6		12
5.2	odd	4		425.2.j.c.174.1		12
5.3	odd	4		425.2.j.b.174.6		12
5.4	even	2		85.2.e.a.21.1	✓	12
15.14	odd	2		765.2.k.b.361.6		12
17.8	even	8		7225.2.a.z.1.6		6
17.9	even	8		7225.2.a.bb.1.6		6
17.13	even	4	inner	425.2.e.f.251.1		12
20.19	odd	2		1360.2.bt.d.1041.3		12
85.9	even	8		1445.2.a.n.1.1		6
85.13	odd	4		425.2.j.c.149.1		12
85.19	even	8		1445.2.d.g.866.11		12
85.47	odd	4		425.2.j.b.149.6		12
85.49	even	8		1445.2.d.g.866.12		12
85.59	even	8		1445.2.a.o.1.1		6
85.64	even	4		85.2.e.a.81.6	yes	12
255.149	odd	4		765.2.k.b.676.1		12
340.319	odd	4		1360.2.bt.d.81.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.2.e.a.21.1	✓	12	5.4	even	2
85.2.e.a.81.6	yes	12	85.64	even	4
425.2.e.f.251.1		12	17.13	even	4	inner
425.2.e.f.276.6		12	1.1	even	1	trivial
425.2.j.b.149.6		12	85.47	odd	4
425.2.j.b.174.6		12	5.3	odd	4
425.2.j.c.149.1		12	85.13	odd	4
425.2.j.c.174.1		12	5.2	odd	4
765.2.k.b.361.6		12	15.14	odd	2
765.2.k.b.676.1		12	255.149	odd	4
1360.2.bt.d.81.3		12	340.319	odd	4
1360.2.bt.d.1041.3		12	20.19	odd	2
1445.2.a.n.1.1		6	85.9	even	8
1445.2.a.o.1.1		6	85.59	even	8
1445.2.d.g.866.11		12	85.19	even	8
1445.2.d.g.866.12		12	85.49	even	8
7225.2.a.z.1.6		6	17.8	even	8
7225.2.a.bb.1.6		6	17.9	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)

\(f(q)\)	\(=\)	\(q+2.24891i q^{2} +(-0.140032 + 0.140032i) q^{3} -3.05761 q^{4} +(-0.314920 - 0.314920i) q^{6} +(1.33807 + 1.33807i) q^{7} -2.37848i q^{8} +2.96078i q^{9} +(2.49536 + 2.49536i) q^{11} +(0.428164 - 0.428164i) q^{12} -1.27324 q^{13} +(-3.00920 + 3.00920i) q^{14} -0.766231 q^{16} +(-3.68381 - 1.85190i) q^{17} -6.65854 q^{18} -4.69149i q^{19} -0.374744 q^{21} +(-5.61186 + 5.61186i) q^{22} +(0.406537 + 0.406537i) q^{23} +(0.333063 + 0.333063i) q^{24} -2.86340i q^{26} +(-0.834700 - 0.834700i) q^{27} +(-4.09129 - 4.09129i) q^{28} +(-3.81711 + 3.81711i) q^{29} +(-4.39574 + 4.39574i) q^{31} -6.48015i q^{32} -0.698861 q^{33} +(4.16476 - 8.28457i) q^{34} -9.05292i q^{36} +(6.00080 - 6.00080i) q^{37} +10.5508 q^{38} +(0.178294 - 0.178294i) q^{39} +(4.28894 + 4.28894i) q^{41} -0.842768i q^{42} +9.16040i q^{43} +(-7.62986 - 7.62986i) q^{44} +(-0.914266 + 0.914266i) q^{46} +10.7932 q^{47} +(0.107297 - 0.107297i) q^{48} -3.41915i q^{49} +(0.775177 - 0.256526i) q^{51} +3.89307 q^{52} +9.90174i q^{53} +(1.87717 - 1.87717i) q^{54} +(3.18256 - 3.18256i) q^{56} +(0.656958 + 0.656958i) q^{57} +(-8.58435 - 8.58435i) q^{58} +3.15903i q^{59} +(3.63666 + 3.63666i) q^{61} +(-9.88565 - 9.88565i) q^{62} +(-3.96173 + 3.96173i) q^{63} +13.0408 q^{64} -1.57168i q^{66} -0.281859 q^{67} +(11.2637 + 5.66239i) q^{68} -0.113856 q^{69} +(8.30385 - 8.30385i) q^{71} +7.04216 q^{72} +(6.95405 - 6.95405i) q^{73} +(13.4953 + 13.4953i) q^{74} +14.3448i q^{76} +6.67793i q^{77} +(0.400968 + 0.400968i) q^{78} +(-11.9789 - 11.9789i) q^{79} -8.64858 q^{81} +(-9.64544 + 9.64544i) q^{82} -8.51139i q^{83} +1.14582 q^{84} -20.6010 q^{86} -1.06903i q^{87} +(5.93517 - 5.93517i) q^{88} +16.7227 q^{89} +(-1.70368 - 1.70368i) q^{91} +(-1.24303 - 1.24303i) q^{92} -1.23109i q^{93} +24.2729i q^{94} +(0.907427 + 0.907427i) q^{96} +(-4.18100 + 4.18100i) q^{97} +7.68938 q^{98} +(-7.38823 + 7.38823i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{3} - 12 q^{4} - 4 q^{11} + 8 q^{12} - 4 q^{14} + 4 q^{16} - 12 q^{17} - 28 q^{18} - 16 q^{21} - 20 q^{22} - 12 q^{23} + 4 q^{24} + 4 q^{27} - 4 q^{28} - 12 q^{29} + 16 q^{33} - 12 q^{34} - 12 q^{37}+ \cdots - 44 q^{98}+O(q^{100}) \) 12 * q + 4 * q^3 - 12 * q^4 - 4 * q^11 + 8 * q^12 - 4 * q^14 + 4 * q^16 - 12 * q^17 - 28 * q^18 - 16 * q^21 - 20 * q^22 - 12 * q^23 + 4 * q^24 + 4 * q^27 - 4 * q^28 - 12 * q^29 + 16 * q^33 - 12 * q^34 - 12 * q^37 - 24 * q^38 - 20 * q^39 - 24 * q^41 + 8 * q^44 - 24 * q^46 + 48 * q^47 + 20 * q^48 + 32 * q^51 + 56 * q^52 + 28 * q^54 + 40 * q^56 - 36 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^63 + 28 * q^64 + 8 * q^67 + 40 * q^68 + 28 * q^71 - 20 * q^72 + 48 * q^73 + 28 * q^74 + 92 * q^78 - 8 * q^79 + 28 * q^81 - 40 * q^82 - 96 * q^86 + 72 * q^88 + 24 * q^89 - 36 * q^91 + 16 * q^92 - 32 * q^96 - 4 * q^97 - 44 * q^98

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