LMFDB - Embedded newform 315.2.p.e.118.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(118,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("315.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.p (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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 $ x^16 - 4x^14 + 6x^12 - 12x^10 + 33x^8 - 48x^6 + 96x^4 - 256*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			118.5
Root			$-1.40927 + 0.118126i$ of defining polynomial
Character	$\chi$	$=$	315.118
Dual form			315.2.p.e.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167056 - 0.167056i) q^{2} +1.94418i q^{4} +(-2.23450 + 0.0836010i) q^{5} +(-2.64501 + 0.0627175i) q^{7} +(0.658899 + 0.658899i) q^{8} +O(q^{10})$	\(q+(0.167056 - 0.167056i) q^{2} +1.94418i q^{4} +(-2.23450 + 0.0836010i) q^{5} +(-2.64501 + 0.0627175i) q^{7} +(0.658899 + 0.658899i) q^{8} +(-0.359321 + 0.387253i) q^{10} -3.98602 q^{11} +(0.500437 - 0.500437i) q^{13} +(-0.431387 + 0.452341i) q^{14} -3.66822 q^{16} +(1.67840 + 1.67840i) q^{17} -7.21850 q^{19} +(-0.162536 - 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(5.16007 + 5.16007i) q^{23} +(4.98602 - 0.373614i) q^{25} -0.167202i q^{26} +(-0.121934 - 5.14238i) q^{28} -3.65191i q^{29} +4.93821i q^{31} +(-1.93060 + 1.93060i) q^{32} +0.560773 q^{34} +(5.90504 - 0.361268i) q^{35} +(0.292275 - 0.292275i) q^{37} +(-1.20589 + 1.20589i) q^{38} +(-1.52740 - 1.41723i) q^{40} +7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} -7.74956i q^{44} +1.72404 q^{46} +(0.305303 + 0.305303i) q^{47} +(6.99213 - 0.331777i) q^{49} +(0.770530 - 0.895358i) q^{50} +(0.972943 + 0.972943i) q^{52} +(-5.39653 - 5.39653i) q^{53} +(8.90678 - 0.333235i) q^{55} +(-1.78412 - 1.70147i) q^{56} +(-0.610073 - 0.610073i) q^{58} -6.10959 q^{59} +7.11047i q^{61} +(0.824957 + 0.824957i) q^{62} -6.69141i q^{64} +(-1.07639 + 1.16007i) q^{65} +(0.944185 - 0.944185i) q^{67} +(-3.26312 + 3.26312i) q^{68} +(0.926119 - 1.04682i) q^{70} -1.19297 q^{71} +(1.38298 - 1.38298i) q^{73} -0.0976524i q^{74} -14.0341i q^{76} +(10.5431 - 0.249993i) q^{77} -8.64027i q^{79} +(8.19666 - 0.306667i) q^{80} +(1.27494 + 1.27494i) q^{82} +(11.9895 - 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +1.22015 q^{86} +(-2.62639 - 2.62639i) q^{88} -7.82581 q^{89} +(-1.29227 + 1.35505i) q^{91} +(-10.0321 + 10.0321i) q^{92} +0.102005 q^{94} +(16.1298 - 0.603474i) q^{95} +(7.43671 + 7.43671i) q^{97} +(1.11265 - 1.22350i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) $ 16 * q - 8 * q^7 - 24 * q^8	$ 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.167056	−	0.167056i	0.118126	−	0.118126i	−0.645573	−	0.763699i	$-0.723381\pi$
$2$	0.167056	−	0.167056i	0.118126	−	0.118126i	0.763699	+	0.645573i	$0.223381\pi$
$3$		0			0
$3$		0			0
$4$			1.94418i			0.972092i
$5$	−2.23450	+	0.0836010i	−0.999301	+	0.0373875i
$5$	−2.23450	+	0.0836010i	−0.999301	+	0.0373875i
$6$		0			0
$7$	−2.64501	+	0.0627175i	−0.999719	+	0.0237050i
$7$	−2.64501	+	0.0627175i	−0.999719	+	0.0237050i
$8$	0.658899	+	0.658899i	0.232956	+	0.232956i
$9$		0			0
$10$	−0.359321	+	0.387253i	−0.113627	+	0.122460i
$11$	−3.98602			−1.20183			−0.600915	−	0.799313i	$-0.705197\pi$
$11$	−3.98602			−1.20183			−0.600915	+	0.799313i	$0.705197\pi$
$12$		0			0
$13$	0.500437	−	0.500437i	0.138796	−	0.138796i	−0.634295	−	0.773091i	$-0.718709\pi$
$13$	0.500437	−	0.500437i	0.138796	−	0.138796i	0.773091	+	0.634295i	$0.218709\pi$
$14$	−0.431387	+	0.452341i	−0.115293	+	0.120893i
$15$		0			0
$16$	−3.66822			−0.917056
$17$	1.67840	+	1.67840i	0.407071	+	0.407071i	0.880716	−	0.473645i	$-0.157062\pi$
$17$	1.67840	+	1.67840i	0.407071	+	0.407071i	−0.473645	+	0.880716i	$0.657062\pi$
$18$		0			0
$19$	−7.21850			−1.65604			−0.828019	−	0.560700i	$-0.810532\pi$
$19$	−7.21850			−1.65604			−0.828019	+	0.560700i	$0.810532\pi$
$20$	−0.162536	−	4.34429i	−0.0363441	−	0.971413i
$21$		0			0
$22$	−0.665888	+	0.665888i	−0.141968	+	0.141968i
$23$	5.16007	+	5.16007i	1.07595	+	1.07595i	0.996868	+	0.0790800i	$0.0251983\pi$
$23$	5.16007	+	5.16007i	1.07595	+	1.07595i	0.0790800	+	0.996868i	$0.474802\pi$
$24$		0			0
$25$	4.98602	−	0.373614i	0.997204	−	0.0747227i
$26$		−	0.167202i		−	0.0327910i
$27$		0			0
$28$	−0.121934	−	5.14238i	−0.0230434	−	0.971819i
$29$		−	3.65191i		−	0.678143i	−0.940761	−	0.339071i	$-0.889887\pi$
$29$		−	3.65191i		−	0.678143i	0.940761	−	0.339071i	$-0.110113\pi$
$30$		0			0
$31$			4.93821i			0.886929i	0.896292	+	0.443465i	$0.146251\pi$
$31$			4.93821i			0.886929i	−0.896292	+	0.443465i	$0.853749\pi$
$32$	−1.93060	+	1.93060i	−0.341284	+	0.341284i
$33$		0			0
$34$	0.560773			0.0961717
$35$	5.90504	−	0.361268i	0.998134	−	0.0610654i
$36$		0			0
$37$	0.292275	−	0.292275i	0.0480497	−	0.0480497i	−0.682674	−	0.730723i	$-0.739183\pi$
$37$	0.292275	−	0.292275i	0.0480497	−	0.0480497i	0.730723	+	0.682674i	$0.239183\pi$
$38$	−1.20589	+	1.20589i	−0.195622	+	0.195622i
$39$		0			0
$40$	−1.52740	−	1.41723i	−0.241503	−	0.224084i
$41$			7.63184i			1.19189i	0.803024	+	0.595947i	$0.203223\pi$
$41$			7.63184i			1.19189i	−0.803024	+	0.595947i	$0.796777\pi$
$42$		0			0
$43$	3.65191	+	3.65191i	0.556911	+	0.556911i	0.928427	−	0.371516i	$-0.121162\pi$
$43$	3.65191	+	3.65191i	0.556911	+	0.556911i	−0.371516	+	0.928427i	$0.621162\pi$
$44$		−	7.74956i		−	1.16829i
$45$		0			0
$46$	1.72404			0.254196
$47$	0.305303	+	0.305303i	0.0445331	+	0.0445331i	0.729023	−	0.684490i	$-0.239975\pi$
$47$	0.305303	+	0.305303i	0.0445331	+	0.0445331i	−0.684490	+	0.729023i	$0.739975\pi$
$48$		0			0
$49$	6.99213	−	0.331777i	0.998876	−	0.0473967i
$50$	0.770530	−	0.895358i	0.108969	−	0.126623i
$51$		0			0
$52$	0.972943	+	0.972943i	0.134923	+	0.134923i
$53$	−5.39653	−	5.39653i	−0.741270	−	0.741270i	0.231553	−	0.972822i	$-0.425619\pi$
$53$	−5.39653	−	5.39653i	−0.741270	−	0.741270i	−0.972822	+	0.231553i	$0.925619\pi$
$54$		0			0
$55$	8.90678	−	0.333235i	1.20099	−	0.0449335i
$56$	−1.78412	−	1.70147i	−0.238413	−	0.227368i
$57$		0			0
$58$	−0.610073	−	0.610073i	−0.0801065	−	0.0801065i
$59$	−6.10959			−0.795401			−0.397701	−	0.917515i	$-0.630192\pi$
$59$	−6.10959			−0.795401			−0.397701	+	0.917515i	$0.630192\pi$
$60$		0			0
$61$			7.11047i			0.910402i	0.890389	+	0.455201i	$0.150433\pi$
$61$			7.11047i			0.910402i	−0.890389	+	0.455201i	$0.849567\pi$
$62$	0.824957	+	0.824957i	0.104770	+	0.104770i
$63$		0			0
$64$		−	6.69141i		−	0.836426i
$65$	−1.07639	+	1.16007i	−0.133510	+	0.143889i
$66$		0			0
$67$	0.944185	−	0.944185i	0.115351	−	0.115351i	−0.647075	−	0.762426i	$-0.724008\pi$
$67$	0.944185	−	0.944185i	0.115351	−	0.115351i	0.762426	+	0.647075i	$0.224008\pi$
$68$	−3.26312	+	3.26312i	−0.395711	+	0.395711i
$69$		0			0
$70$	0.926119	−	1.04682i	0.110692	−	0.125119i
$71$	−1.19297			−0.141579			−0.0707897	−	0.997491i	$-0.522552\pi$
$71$	−1.19297			−0.141579			−0.0707897	+	0.997491i	$0.522552\pi$
$72$		0			0
$73$	1.38298	−	1.38298i	0.161865	−	0.161865i	−0.621527	−	0.783393i	$-0.713487\pi$
$73$	1.38298	−	1.38298i	0.161865	−	0.161865i	0.783393	+	0.621527i	$0.213487\pi$
$74$		−	0.0976524i		−	0.0113519i
$75$		0			0
$76$		−	14.0341i		−	1.60982i
$77$	10.5431	−	0.249993i	1.20149	−	0.0284894i
$78$		0			0
$79$		−	8.64027i		−	0.972106i	−0.873929	−	0.486053i	$-0.838436\pi$
$79$		−	8.64027i		−	0.972106i	0.873929	−	0.486053i	$-0.161564\pi$
$80$	8.19666	−	0.306667i	0.916415	−	0.0342864i
$81$		0			0
$82$	1.27494	+	1.27494i	0.140794	+	0.140794i
$83$	11.9895	−	11.9895i	1.31602	−	1.31602i	0.399122	−	0.916898i	$-0.369315\pi$
$83$	11.9895	−	11.9895i	1.31602	−	1.31602i	0.916898	−	0.399122i	$-0.130685\pi$
$84$		0			0
$85$	−3.89070	−	3.61007i	−0.422006	−	0.391567i
$86$	1.22015			0.131572
$87$		0			0
$88$	−2.62639	−	2.62639i	−0.279974	−	0.279974i
$89$	−7.82581			−0.829534			−0.414767	−	0.909928i	$-0.636137\pi$
$89$	−7.82581			−0.829534			−0.414767	+	0.909928i	$0.636137\pi$
$90$		0			0
$91$	−1.29227	+	1.35505i	−0.135467	+	0.142048i
$92$	−10.0321	+	10.0321i	−1.04592	+	1.04592i
$93$		0			0
$94$	0.102005			0.0105211
$95$	16.1298	−	0.603474i	1.65488	−	0.0619151i
$96$		0			0
$97$	7.43671	+	7.43671i	0.755083	+	0.755083i	0.975423	−	0.220340i	$-0.0707167\pi$
$97$	7.43671	+	7.43671i	0.755083	+	0.755083i	−0.220340	+	0.975423i	$0.570717\pi$
$98$	1.11265	−	1.22350i	0.112395	−	0.123592i
$99$		0			0
$100$	0.726374	+	9.69375i	0.0726374	+	0.969375i
$101$		−	6.31633i		−	0.628498i	−0.949341	−	0.314249i	$-0.898247\pi$
$101$		−	6.31633i		−	0.628498i	0.949341	−	0.314249i	$-0.101753\pi$
$102$		0			0
$103$	−12.5410	+	12.5410i	−1.23570	+	1.23570i	−0.273954	+	0.961743i	$0.588332\pi$
$103$	−12.5410	+	12.5410i	−1.23570	+	1.23570i	−0.961743	+	0.273954i	$0.911668\pi$
$104$	0.659476			0.0646669
$105$		0			0
$106$	−1.80304			−0.175127
$107$	−7.48020	+	7.48020i	−0.723138	+	0.723138i	−0.969243	−	0.246105i	$-0.920849\pi$
$107$	−7.48020	+	7.48020i	−0.723138	+	0.723138i	0.246105	+	0.969243i	$0.420849\pi$
$108$		0			0
$109$		−	0.668223i		−	0.0640042i	−0.999488	−	0.0320021i	$-0.989812\pi$
$109$		−	0.668223i		−	0.0640042i	0.999488	−	0.0320021i	$-0.0101883\pi$
$110$	1.43226	−	1.54360i	0.136561	−	0.147176i
$111$		0			0
$112$	9.70248	−	0.230062i	0.916798	−	0.0217388i
$113$	3.39653	+	3.39653i	0.319518	+	0.319518i	0.848582	−	0.529064i	$-0.177457\pi$
$113$	3.39653	+	3.39653i	0.319518	+	0.319518i	−0.529064	+	0.848582i	$0.677457\pi$
$114$		0			0
$115$	−11.9616	−	11.0988i	−1.11542	−	1.03497i
$116$	7.09999			0.659217
$117$		0			0
$118$	−1.02064	+	1.02064i	−0.0939578	+	0.0939578i
$119$	−4.54464	−	4.33411i	−0.416607	−	0.397307i
$120$		0			0
$121$	4.88837			0.444397
$122$	1.18785	+	1.18785i	0.107542	+	0.107542i
$123$		0			0
$124$	−9.60080			−0.862177
$125$	−11.1101	+	1.25168i	−0.993713	+	0.111953i
$126$		0			0
$127$	−5.88837	+	5.88837i	−0.522508	+	0.522508i	−0.918328	−	0.395820i	$-0.870460\pi$
$127$	−5.88837	+	5.88837i	−0.522508	+	0.522508i	0.395820	+	0.918328i	$0.370460\pi$
$128$	−4.97903	−	4.97903i	−0.440088	−	0.440088i
$129$		0			0
$130$	0.0139783	+	0.373614i	0.00122597	+	0.0327681i
$131$			18.8144i			1.64383i	0.569613	+	0.821913i	$0.307093\pi$
$131$			18.8144i			1.64383i	−0.569613	+	0.821913i	$0.692907\pi$
$132$		0			0
$133$	19.0930	−	0.452726i	1.65557	−	0.0392564i
$134$		−	0.315463i		−	0.0272519i
$135$		0			0
$136$			2.21179i			0.189659i
$137$	0.811977	−	0.811977i	0.0693719	−	0.0693719i	−0.671570	−	0.740941i	$-0.734380\pi$
$137$	0.811977	−	0.811977i	0.0693719	−	0.0693719i	0.740941	+	0.671570i	$0.234380\pi$
$138$		0			0
$139$	−0.442439			−0.0375272			−0.0187636	−	0.999824i	$-0.505973\pi$
$139$	−0.442439			−0.0375272			−0.0187636	+	0.999824i	$0.505973\pi$
$140$	0.702371	+	11.4805i	0.0593612	+	0.970278i
$141$		0			0
$142$	−0.199293	+	0.199293i	−0.0167243	+	0.0167243i
$143$	−1.99475	+	1.99475i	−0.166810	+	0.166810i
$144$		0			0
$145$	0.305303	+	8.16021i	0.0253541	+	0.677669i
$146$		−	0.462070i		−	0.0382411i
$147$		0			0
$148$	0.568236	+	0.568236i	0.0467087	+	0.0467087i
$149$		−	3.14114i		−	0.257332i	−0.991688	−	0.128666i	$-0.958930\pi$
$149$		−	3.14114i		−	0.257332i	0.991688	−	0.128666i	$-0.0410696\pi$
$150$		0			0
$151$	−14.7239			−1.19822			−0.599109	−	0.800668i	$-0.704478\pi$
$151$	−14.7239			−1.19822			−0.599109	+	0.800668i	$0.704478\pi$
$152$	−4.75626	−	4.75626i	−0.385784	−	0.385784i
$153$		0			0
$154$	1.71952	−	1.80304i	0.138563	−	0.145293i
$155$	−0.412839	−	11.0345i	−0.0331601	−	0.886309i
$156$		0			0
$157$	−7.96508	−	7.96508i	−0.635682	−	0.635682i	0.313805	−	0.949487i	$-0.398396\pi$
$157$	−7.96508	−	7.96508i	−0.635682	−	0.635682i	−0.949487	+	0.313805i	$0.898396\pi$
$158$	−1.44341	−	1.44341i	−0.114831	−	0.114831i
$159$		0			0
$160$	4.15253	−	4.47533i	0.328286	−	0.353806i
$161$	−13.9720	−	13.3248i	−1.10115	−	1.05014i
$162$		0			0
$163$	10.4450	+	10.4450i	0.818113	+	0.818113i	0.985834	−	0.167722i	$-0.0536410\pi$
$163$	10.4450	+	10.4450i	0.818113	+	0.818113i	−0.167722	+	0.985834i	$0.553641\pi$
$164$	−14.8377			−1.15863
$165$		0			0
$166$		−	4.00584i		−	0.310913i
$167$	−4.63621	−	4.63621i	−0.358761	−	0.358761i	0.504595	−	0.863356i	$-0.331642\pi$
$167$	−4.63621	−	4.63621i	−0.358761	−	0.358761i	−0.863356	+	0.504595i	$0.831642\pi$
$168$		0			0
$169$			12.4991i			0.961471i
$170$	−1.25305	+	0.0468811i	−0.0961045	+	0.00359562i
$171$		0			0
$172$	−7.09999	+	7.09999i	−0.541369	+	0.541369i
$173$	2.48531	−	2.48531i	0.188954	−	0.188954i	−0.606290	−	0.795244i	$-0.707343\pi$
$173$	2.48531	−	2.48531i	0.188954	−	0.188954i	0.795244	+	0.606290i	$0.207343\pi$
$174$		0			0
$175$	−13.1646	+	1.30092i	−0.995153	+	0.0983404i
$176$	14.6216			1.10215
$177$		0			0
$178$	−1.30735	+	1.30735i	−0.0979898	+	0.0979898i
$179$			22.1109i			1.65264i	0.563199	+	0.826321i	$0.309570\pi$
$179$			22.1109i			1.65264i	−0.563199	+	0.826321i	$0.690430\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	0.0104865	+	0.442251i	0.000777310	+	0.0327818i
$183$		0			0
$184$			6.79993i			0.501297i
$185$	−0.628655	+	0.677524i	−0.0462196	+	0.0498125i
$186$		0			0
$187$	−6.69013	−	6.69013i	−0.489231	−	0.489231i
$188$	−0.593566	+	0.593566i	−0.0432903	+	0.0432903i
$189$		0			0
$190$	2.59376	−	2.79539i	0.188171	−	0.202799i
$191$	−15.2898			−1.10633			−0.553167	−	0.833070i	$-0.686581\pi$
$191$	−15.2898			−1.10633			−0.553167	+	0.833070i	$0.686581\pi$
$192$		0			0
$193$	−8.92787	−	8.92787i	−0.642642	−	0.642642i	0.308562	−	0.951204i	$-0.400152\pi$
$193$	−8.92787	−	8.92787i	−0.642642	−	0.642642i	−0.951204	+	0.308562i	$0.900152\pi$
$194$	2.48469			0.178390
$195$		0			0
$196$	0.645035	+	13.5940i	0.0460739	+	0.971000i
$197$	2.68715	−	2.68715i	0.191451	−	0.191451i	−0.604872	−	0.796323i	$-0.706776\pi$
$197$	2.68715	−	2.68715i	0.191451	−	0.191451i	0.796323	+	0.604872i	$0.206776\pi$
$198$		0			0
$199$	0.616637			0.0437122			0.0218561	−	0.999761i	$-0.493042\pi$
$199$	0.616637			0.0437122			0.0218561	+	0.999761i	$0.493042\pi$
$200$	3.53146	+	3.03911i	0.249712	+	0.214898i
$201$		0			0
$202$	−1.05518	−	1.05518i	−0.0742422	−	0.0742422i
$203$	0.229039	+	9.65933i	0.0160754	+	0.677952i
$204$		0			0
$205$	−0.638029	−	17.0534i	−0.0445619	−	1.19106i
$206$			4.19008i			0.291937i
$207$		0			0
$208$	−1.83572	+	1.83572i	−0.127284	+	0.127284i
$209$	28.7731			1.99028
$210$		0			0
$211$	9.30849			0.640823			0.320411	−	0.947278i	$-0.396179\pi$
$211$	9.30849			0.640823			0.320411	+	0.947278i	$0.396179\pi$
$212$	10.4918	−	10.4918i	0.720583	−	0.720583i
$213$		0			0
$214$			2.49922i			0.170843i
$215$	−8.46551	−	7.85491i	−0.577343	−	0.535700i
$216$		0			0
$217$	−0.309712	−	13.0616i	−0.0210246	−	0.886680i
$218$	−0.111631	−	0.111631i	−0.00756058	−	0.00756058i
$219$		0			0
$220$	0.647871	+	17.3164i	0.0436795	+	1.16747i
$221$	1.67987			0.113000
$222$		0			0
$223$	−1.35505	+	1.35505i	−0.0907407	+	0.0907407i	−0.751020	−	0.660279i	$-0.770438\pi$
$223$	−1.35505	+	1.35505i	−0.0907407	+	0.0907407i	0.660279	+	0.751020i	$0.270438\pi$
$224$	4.98536	−	5.22753i	0.333098	−	0.349279i
$225$		0			0
$226$	1.13482			0.0754870
$227$	−4.15437	−	4.15437i	−0.275735	−	0.275735i	0.555668	−	0.831404i	$-0.312462\pi$
$227$	−4.15437	−	4.15437i	−0.275735	−	0.275735i	−0.831404	+	0.555668i	$0.812462\pi$
$228$		0			0
$229$	12.9900			0.858403			0.429202	−	0.903209i	$-0.358795\pi$
$229$	12.9900			0.858403			0.429202	+	0.903209i	$0.358795\pi$
$230$	−3.85237	+	0.144131i	−0.254018	+	0.00950374i
$231$		0			0
$232$	2.40624	−	2.40624i	0.157977	−	0.157977i
$233$	16.4639	+	16.4639i	1.07859	+	1.07859i	0.996637	+	0.0819485i	$0.0261143\pi$
$233$	16.4639	+	16.4639i	1.07859	+	1.07859i	0.0819485	+	0.996637i	$0.473886\pi$
$234$		0			0
$235$	−0.707725	−	0.656678i	−0.0461669	−	0.0428370i
$236$		−	11.8782i		−	0.773203i
$237$		0			0
$238$	−1.48325	+	0.0351703i	−0.0961447	+	0.00227975i
$239$			5.48048i			0.354503i	0.984166	+	0.177251i	$0.0567205\pi$
$239$			5.48048i			0.354503i	−0.984166	+	0.177251i	$0.943279\pi$
$240$		0			0
$241$			14.6507i			0.943737i	0.881669	+	0.471868i	$0.156420\pi$
$241$			14.6507i			0.943737i	−0.881669	+	0.471868i	$0.843580\pi$
$242$	0.816631	−	0.816631i	0.0524950	−	0.0524950i
$243$		0			0
$244$	−13.8241			−0.884995
$245$	−15.5962	+	1.32591i	−0.996406	+	0.0847090i
$246$		0			0
$247$	−3.61241	+	3.61241i	−0.229852	+	0.229852i
$248$	−3.25378	+	3.25378i	−0.206615	+	0.206615i
$249$		0			0
$250$	−1.64690	+	2.06510i	−0.104159	+	0.130608i
$251$			21.1506i			1.33501i	0.744604	+	0.667507i	$0.232639\pi$
$251$			21.1506i			1.33501i	−0.744604	+	0.667507i	$0.767361\pi$
$252$		0			0
$253$	−20.5681	−	20.5681i	−1.29311	−	1.29311i
$254$			1.96737i			0.123444i
$255$		0			0
$256$	11.7193			0.732454
$257$	9.39248	+	9.39248i	0.585887	+	0.585887i	0.936515	−	0.350628i	$-0.114032\pi$
$257$	9.39248	+	9.39248i	0.585887	+	0.585887i	−0.350628	+	0.936515i	$0.614032\pi$
$258$		0			0
$259$	−0.754738	+	0.791399i	−0.0468971	+	0.0491752i
$260$	−2.25538	−	2.09271i	−0.139873	−	0.129784i
$261$		0			0
$262$	3.14306	+	3.14306i	0.194179	+	0.194179i
$263$	−15.3779	−	15.3779i	−0.948241	−	0.948241i	0.0504843	−	0.998725i	$-0.483924\pi$
$263$	−15.3779	−	15.3779i	−0.948241	−	0.948241i	−0.998725	+	0.0504843i	$0.983924\pi$
$264$		0			0
$265$	12.5097	+	11.6074i	0.768466	+	0.713037i
$266$	3.11397	−	3.26523i	0.190929	−	0.200204i
$267$		0			0
$268$	1.83567	+	1.83567i	0.112131	+	0.112131i
$269$	22.9851			1.40143			0.700714	−	0.713442i	$-0.252865\pi$
$269$	22.9851			1.40143			0.700714	+	0.713442i	$0.252865\pi$
$270$		0			0
$271$		−	15.7596i		−	0.957330i	−0.877998	−	0.478665i	$-0.841121\pi$
$271$		−	15.7596i		−	0.957330i	0.877998	−	0.478665i	$-0.158879\pi$
$272$	−6.15674	−	6.15674i	−0.373307	−	0.373307i
$273$		0			0
$274$		−	0.271291i		−	0.0163893i
$275$	−19.8744	+	1.48923i	−1.19847	+	0.0898041i
$276$		0			0
$277$	4.80771	−	4.80771i	0.288867	−	0.288867i	−0.547765	−	0.836632i	$-0.684521\pi$
$277$	4.80771	−	4.80771i	0.288867	−	0.288867i	0.836632	+	0.547765i	$0.184521\pi$
$278$	−0.0739121	+	0.0739121i	−0.00443295	+	0.00443295i
$279$		0			0
$280$	4.12886	+	3.65279i	0.246747	+	0.218296i
$281$	9.65658			0.576063			0.288032	−	0.957621i	$-0.406999\pi$
$281$	9.65658			0.576063			0.288032	+	0.957621i	$0.406999\pi$
$282$		0			0
$283$	14.9095	−	14.9095i	0.886278	−	0.886278i	−0.107885	−	0.994163i	$-0.534408\pi$
$283$	14.9095	−	14.9095i	0.886278	−	0.886278i	0.994163	+	0.107885i	$0.0344079\pi$
$284$		−	2.31935i		−	0.137628i
$285$		0			0
$286$			0.666471i			0.0394092i
$287$	−0.478650	−	20.1863i	−0.0282538	−	1.19156i
$288$		0			0
$289$		−	11.3660i		−	0.668586i
$290$	1.41421	+	1.31221i	0.0830455	+	0.0770555i
$291$		0			0
$292$	2.68877	+	2.68877i	0.157348	+	0.157348i
$293$	−4.79236	+	4.79236i	−0.279973	+	0.279973i	−0.833098	−	0.553125i	$-0.813435\pi$
$293$	−4.79236	+	4.79236i	−0.279973	+	0.279973i	0.553125	+	0.833098i	$0.313435\pi$
$294$		0			0
$295$	13.6519	−	0.510768i	0.794845	−	0.0297381i
$296$	0.385159			0.0223869
$297$		0			0
$298$	−0.524746	−	0.524746i	−0.0303977	−	0.0303977i
$299$	5.16458			0.298675
$300$		0			0
$301$	−9.88837	−	9.43029i	−0.569956	−	0.543553i
$302$	−2.45972	+	2.45972i	−0.141541	+	0.141541i
$303$		0			0
$304$	26.4791			1.51868
$305$	−0.594442	−	15.8884i	−0.0340377	−	0.909765i
$306$		0			0
$307$	9.85063	+	9.85063i	0.562205	+	0.562205i	0.929933	−	0.367728i	$-0.119864\pi$
$307$	9.85063	+	9.85063i	0.562205	+	0.562205i	−0.367728	+	0.929933i	$0.619864\pi$
$308$	0.486033	+	20.4977i	0.0276943	+	1.16796i
$309$		0			0
$310$	−1.91234	−	1.77440i	−0.108614	−	0.100779i
$311$		−	27.3063i		−	1.54840i	−0.632941	−	0.774200i	$-0.718152\pi$
$311$		−	27.3063i		−	1.54840i	0.632941	−	0.774200i	$-0.281848\pi$
$312$		0			0
$313$	18.5080	−	18.5080i	1.04613	−	1.04613i	0.0472492	−	0.998883i	$-0.484955\pi$
$313$	18.5080	−	18.5080i	1.04613	−	1.04613i	0.998883	−	0.0472492i	$-0.0150455\pi$
$314$	−2.66123			−0.150182
$315$		0			0
$316$	16.7983			0.944977
$317$	21.8793	−	21.8793i	1.22887	−	1.22887i	0.264473	−	0.964393i	$-0.414802\pi$
$317$	21.8793	−	21.8793i	1.22887	−	1.22887i	0.964393	−	0.264473i	$-0.0851980\pi$
$318$		0			0
$319$			14.5566i			0.815013i
$320$	0.559409	+	14.9520i	0.0312719	+	0.835842i
$321$		0			0
$322$	−4.56010	+	0.108127i	−0.254124	+	0.00602570i
$323$	−12.1155	−	12.1155i	−0.674126	−	0.674126i
$324$		0			0
$325$	2.30822	−	2.68216i	0.128037	−	0.148780i
$326$	3.48978			0.193281
$327$		0			0
$328$	−5.02861	+	5.02861i	−0.277659	+	0.277659i
$329$	−0.826678	−	0.788382i	−0.0455762	−	0.0434649i
$330$		0			0
$331$	−16.6913			−0.917438			−0.458719	−	0.888581i	$-0.651691\pi$
$331$	−16.6913			−0.917438			−0.458719	+	0.888581i	$0.651691\pi$
$332$	23.3098	+	23.3098i	1.27929	+	1.27929i
$333$		0			0
$334$	−1.54901			−0.0847582
$335$	−2.03085	+	2.18872i	−0.110957	+	0.119583i
$336$		0			0
$337$	2.54028	−	2.54028i	0.138378	−	0.138378i	−0.634525	−	0.772903i	$-0.718804\pi$
$337$	2.54028	−	2.54028i	0.138378	−	0.138378i	0.772903	+	0.634525i	$0.218804\pi$
$338$	2.08805	+	2.08805i	0.113575	+	0.113575i
$339$		0			0
$340$	7.01865	−	7.56425i	0.380640	−	0.410229i
$341$		−	19.6838i		−	1.06594i
$342$		0			0
$343$	−18.4734	+	1.31608i	−0.997472	+	0.0710617i
$344$			4.81248i			0.259472i
$345$		0			0
$346$		−	0.830370i		−	0.0446410i
$347$	−13.6980	+	13.6980i	−0.735348	+	0.735348i	−0.971674	−	0.236326i	$-0.924057\pi$
$347$	−13.6980	+	13.6980i	−0.735348	+	0.735348i	0.236326	+	0.971674i	$0.424057\pi$
$348$		0			0
$349$	0.508601			0.0272248			0.0136124	−	0.999907i	$-0.495667\pi$
$349$	0.508601			0.0272248			0.0136124	+	0.999907i	$0.495667\pi$
$350$	−1.98190	+	2.41656i	−0.105937	+	0.129170i
$351$		0			0
$352$	7.69540	−	7.69540i	0.410166	−	0.410166i
$353$	−10.9217	+	10.9217i	−0.581305	+	0.581305i	−0.935262	−	0.353957i	$-0.884836\pi$
$353$	−10.9217	+	10.9217i	−0.581305	+	0.581305i	0.353957	+	0.935262i	$0.384836\pi$
$354$		0			0
$355$	2.66570	−	0.0997335i	0.141480	−	0.00529330i
$356$		−	15.2148i		−	0.806383i
$357$		0			0
$358$	3.69375	+	3.69375i	0.195221	+	0.195221i
$359$		−	15.9860i		−	0.843710i	−0.906663	−	0.421855i	$-0.861379\pi$
$359$		−	15.9860i		−	0.843710i	0.906663	−	0.421855i	$-0.138621\pi$
$360$		0			0
$361$	33.1068			1.74246
$362$	−1.41752	−	1.41752i	−0.0745030	−	0.0745030i
$363$		0			0
$364$	−2.63446	−	2.51242i	−0.138083	−	0.131687i
$365$	−2.97465	+	3.20589i	−0.155701	+	0.167804i
$366$		0			0
$367$	0.410036	+	0.410036i	0.0214037	+	0.0214037i	0.717728	−	0.696324i	$-0.245182\pi$
$367$	0.410036	+	0.410036i	0.0214037	+	0.0214037i	−0.696324	+	0.717728i	$0.745182\pi$
$368$	−18.9283	−	18.9283i	−0.986705	−	0.986705i
$369$		0			0
$370$	0.00816384	+	0.218205i	0.000424418	+	0.0113439i
$371$	14.6123	+	13.9354i	0.758633	+	0.723490i
$372$		0			0
$373$	−3.44496	−	3.44496i	−0.178373	−	0.178373i	0.612273	−	0.790646i	$-0.290255\pi$
$373$	−3.44496	−	3.44496i	−0.178373	−	0.178373i	−0.790646	+	0.612273i	$0.790255\pi$
$374$	−2.23525			−0.115582
$375$		0			0
$376$			0.402328i			0.0207485i
$377$	−1.82755	−	1.82755i	−0.0941237	−	0.0941237i
$378$		0			0
$379$			12.9179i			0.663547i	0.943359	+	0.331773i	$0.107647\pi$
$379$			12.9179i			0.663547i	−0.943359	+	0.331773i	$0.892353\pi$
$380$	1.17326	+	31.3593i	0.0601872	+	1.60870i
$381$		0			0
$382$	−2.55426	+	2.55426i	−0.130687	+	0.130687i
$383$	10.0770	−	10.0770i	0.514910	−	0.514910i	−0.401117	−	0.916027i	$-0.631378\pi$
$383$	10.0770	−	10.0770i	0.514910	−	0.514910i	0.916027	+	0.401117i	$0.131378\pi$
$384$		0			0
$385$	−23.5376	+	1.44002i	−1.19959	+	0.0733903i
$386$	−2.98291			−0.151826
$387$		0			0
$388$	−14.4583	+	14.4583i	−0.734011	+	0.734011i
$389$			24.3300i			1.23358i	0.787127	+	0.616791i	$0.211567\pi$
$389$			24.3300i			1.23358i	−0.787127	+	0.616791i	$0.788433\pi$
$390$		0			0
$391$			17.3213i			0.875976i
$392$	4.82572	+	4.38850i	0.243736	+	0.221653i
$393$		0			0
$394$		−	0.897808i		−	0.0452309i
$395$	0.722335	+	19.3067i	0.0363446	+	0.971426i
$396$		0			0
$397$	6.80633	+	6.80633i	0.341600	+	0.341600i	0.856969	−	0.515369i	$-0.172345\pi$
$397$	6.80633	+	6.80633i	0.341600	+	0.341600i	−0.515369	+	0.856969i	$0.672345\pi$
$398$	0.103013	−	0.103013i	0.00516356	−	0.00516356i
$399$		0			0
$400$	−18.2898	+	1.37050i	−0.914492	+	0.0685249i
$401$	8.83090			0.440994			0.220497	−	0.975388i	$-0.429232\pi$
$401$	8.83090			0.440994			0.220497	+	0.975388i	$0.429232\pi$
$402$		0			0
$403$	2.47127	+	2.47127i	0.123103	+	0.123103i
$404$	12.2801			0.610958
$405$		0			0
$406$	1.65191	+	1.57539i	0.0819829	+	0.0781851i
$407$	−1.16501	+	1.16501i	−0.0577476	+	0.0577476i
$408$		0			0
$409$	−23.1985			−1.14709			−0.573546	−	0.819174i	$-0.694432\pi$
$409$	−23.1985			−1.14709			−0.573546	+	0.819174i	$0.694432\pi$
$410$	−2.95545	−	2.74228i	−0.145959	−	0.135432i
$411$		0			0
$412$	−24.3819	−	24.3819i	−1.20121	−	1.20121i
$413$	16.1599	−	0.383178i	0.795178	−	0.0188550i
$414$		0			0
$415$	−25.7883	+	27.7930i	−1.26590	+	1.36430i
$416$			1.93229i			0.0947381i
$417$		0			0
$418$	4.80672	−	4.80672i	0.235104	−	0.235104i
$419$	−13.0393			−0.637009			−0.318505	−	0.947921i	$-0.603181\pi$
$419$	−13.0393			−0.637009			−0.318505	+	0.947921i	$0.603181\pi$
$420$		0			0
$421$	−31.3549			−1.52814			−0.764071	−	0.645132i	$-0.776802\pi$
$421$	−31.3549			−1.52814			−0.764071	+	0.645132i	$0.776802\pi$
$422$	1.55504	−	1.55504i	0.0756981	−	0.0756981i
$423$		0			0
$424$		−	7.11153i		−	0.345367i
$425$	8.99560	+	7.74146i	0.436351	+	0.375516i
$426$		0			0
$427$	−0.445951	−	18.8072i	−0.0215811	−	0.910146i
$428$	−14.5429	−	14.5429i	−0.702957	−	0.702957i
$429$		0			0
$430$	−2.72642	+	0.102005i	−0.131480	+	0.00491914i
$431$	22.5558			1.08648			0.543238	−	0.839579i	$-0.317198\pi$
$431$	22.5558			1.08648			0.543238	+	0.839579i	$0.317198\pi$
$432$		0			0
$433$	−19.9639	+	19.9639i	−0.959405	+	0.959405i	−0.999208	−	0.0398028i	$-0.987327\pi$
$433$	−19.9639	+	19.9639i	−0.959405	+	0.959405i	0.0398028	+	0.999208i	$0.487327\pi$
$434$	−2.23376	−	2.13028i	−0.107224	−	0.102257i
$435$		0			0
$436$	1.29915			0.0622180
$437$	−37.2479	−	37.2479i	−1.78181	−	1.78181i
$438$		0			0
$439$	30.1943			1.44110			0.720548	−	0.693405i	$-0.243890\pi$
$439$	30.1943			1.44110			0.720548	+	0.693405i	$0.243890\pi$
$440$	6.08824	+	5.64910i	0.290246	+	0.269310i
$441$		0			0
$442$	0.280632	−	0.280632i	0.0133483	−	0.0133483i
$443$	12.7423	+	12.7423i	0.605404	+	0.605404i	0.941742	−	0.336337i	$-0.109188\pi$
$443$	12.7423	+	12.7423i	0.605404	+	0.605404i	−0.336337	+	0.941742i	$0.609188\pi$
$444$		0			0
$445$	17.4868	−	0.654245i	0.828954	−	0.0310142i
$446$			0.452737i			0.0214377i
$447$		0			0
$448$	0.419669	+	17.6988i	0.0198275	+	0.836191i
$449$			30.4170i			1.43547i	0.696318	+	0.717734i	$0.254820\pi$
$449$			30.4170i			1.43547i	−0.696318	+	0.717734i	$0.745180\pi$
$450$		0			0
$451$		−	30.4207i		−	1.43245i
$452$	−6.60347	+	6.60347i	−0.310601	+	0.310601i
$453$		0			0
$454$	−1.38802			−0.0651432
$455$	2.77431	−	3.13589i	0.130062	−	0.147013i
$456$		0			0
$457$	1.31546	−	1.31546i	0.0615348	−	0.0615348i	−0.675670	−	0.737204i	$-0.736145\pi$
$457$	1.31546	−	1.31546i	0.0615348	−	0.0615348i	0.737204	+	0.675670i	$0.236145\pi$
$458$	2.17005	−	2.17005i	0.101400	−	0.101400i
$459$		0			0
$460$	21.5781	−	23.2555i	1.00609	−	1.08429i
$461$		−	1.29957i		−	0.0605272i	−0.999542	−	0.0302636i	$-0.990365\pi$
$461$		−	1.29957i		−	0.0605272i	0.999542	−	0.0302636i	$-0.00963467\pi$
$462$		0			0
$463$	16.5240	+	16.5240i	0.767934	+	0.767934i	0.977742	−	0.209809i	$-0.0672841\pi$
$463$	16.5240	+	16.5240i	0.767934	+	0.767934i	−0.209809	+	0.977742i	$0.567284\pi$
$464$			13.3960i			0.621895i
$465$		0			0
$466$	5.50078			0.254819
$467$	−20.1009	−	20.1009i	−0.930157	−	0.930157i	0.0675588	−	0.997715i	$-0.478479\pi$
$467$	−20.1009	−	20.1009i	−0.930157	−	0.930157i	−0.997715	+	0.0675588i	$0.978479\pi$
$468$		0			0
$469$	−2.43816	+	2.55659i	−0.112584	+	0.118052i
$470$	−0.227932	+	0.00852775i	−0.0105137	+	0.000393356i
$471$		0			0
$472$	−4.02560	−	4.02560i	−0.185293	−	0.185293i
$473$	−14.5566	−	14.5566i	−0.669313	−	0.669313i
$474$		0			0
$475$	−35.9916	+	2.69693i	−1.65141	+	0.123744i
$476$	8.42631	−	8.83562i	0.386219	−	0.404980i
$477$		0			0
$478$	0.915546	+	0.915546i	0.0418761	+	0.0418761i
$479$	11.0836			0.506425			0.253212	−	0.967411i	$-0.418513\pi$
$479$	11.0836			0.506425			0.253212	+	0.967411i	$0.418513\pi$
$480$		0			0
$481$		−	0.292530i		−	0.0133382i
$482$	2.44749	+	2.44749i	0.111480	+	0.111480i
$483$		0			0
$484$			9.50389i			0.431995i
$485$	−17.2391	−	15.9956i	−0.782786	−	0.726325i
$486$		0			0
$487$	−13.6519	+	13.6519i	−0.618627	+	0.618627i	−0.945179	−	0.326552i	$-0.894113\pi$
$487$	−13.6519	+	13.6519i	−0.618627	+	0.618627i	0.326552	+	0.945179i	$0.394113\pi$
$488$	−4.68508	+	4.68508i	−0.212084	+	0.212084i
$489$		0			0
$490$	−2.38394	+	2.82694i	−0.107695	+	0.127708i
$491$	−32.1155			−1.44935			−0.724677	−	0.689089i	$-0.758011\pi$
$491$	−32.1155			−1.44935			−0.724677	+	0.689089i	$0.758011\pi$
$492$		0			0
$493$	6.12936	−	6.12936i	0.276052	−	0.276052i
$494$			1.20695i			0.0543032i
$495$		0			0
$496$		−	18.1145i		−	0.813364i
$497$	3.15541	−	0.0748201i	0.141540	−	0.00335614i
$498$		0			0
$499$		−	4.27431i		−	0.191344i	−0.995413	−	0.0956722i	$-0.969500\pi$
$499$		−	4.27431i		−	0.191344i	0.995413	−	0.0956722i	$-0.0305000\pi$
$500$	−2.43349	−	21.6000i	−0.108829	−	0.965981i
$501$		0			0
$502$	3.53333	+	3.53333i	0.157700	+	0.157700i
$503$	−17.5637	+	17.5637i	−0.783128	+	0.783128i	−0.980357	−	0.197229i	$-0.936806\pi$
$503$	−17.5637	+	17.5637i	−0.783128	+	0.783128i	0.197229	+	0.980357i	$0.436806\pi$
$504$		0			0
$505$	0.528051	+	14.1139i	0.0234980	+	0.628059i
$506$	−6.87206			−0.305500
$507$		0			0
$508$	−11.4481	−	11.4481i	−0.507926	−	0.507926i
$509$	27.9162			1.23736			0.618682	−	0.785641i	$-0.287667\pi$
$509$	27.9162			1.23736			0.618682	+	0.785641i	$0.287667\pi$
$510$		0			0
$511$	−3.57125	+	3.74473i	−0.157983	+	0.165657i
$512$	11.9158	−	11.9158i	0.526611	−	0.526611i
$513$		0			0
$514$	3.13814			0.138417
$515$	26.9744	−	29.0713i	1.18863	−	1.28103i
$516$		0			0
$517$	−1.21695	−	1.21695i	−0.0535212	−	0.0535212i
$518$	0.00612451	+	0.258291i	0.000269096	+	0.0113487i
$519$		0			0
$520$	−1.47360	+	0.0551328i	−0.0646217	+	0.00241773i
$521$			28.8647i			1.26458i	0.774730	+	0.632292i	$0.217886\pi$
$521$			28.8647i			1.26458i	−0.774730	+	0.632292i	$0.782114\pi$
$522$		0			0
$523$	−3.54707	+	3.54707i	−0.155103	+	0.155103i	−0.780392	−	0.625290i	$-0.784981\pi$
$523$	−3.54707	+	3.54707i	−0.155103	+	0.155103i	0.625290	+	0.780392i	$0.284981\pi$
$524$	−36.5788			−1.59795
$525$		0			0
$526$	−5.13793			−0.224024
$527$	−8.28829	+	8.28829i	−0.361043	+	0.361043i
$528$		0			0
$529$			30.2526i			1.31533i
$530$	4.02891	−	0.150736i	0.175005	−	0.00654756i
$531$		0			0
$532$	0.880184	+	37.1203i	0.0381608	+	1.60937i
$533$	3.81926	+	3.81926i	0.165430	+	0.165430i
$534$		0			0
$535$	16.0892	−	17.3399i	0.695596	−	0.749669i
$536$	1.24424			0.0537432
$537$		0			0
$538$	3.83980	−	3.83980i	0.165546	−	0.165546i
$539$	−27.8708	+	1.32247i	−1.20048	+	0.0569628i
$540$		0			0
$541$	−4.08698			−0.175713			−0.0878565	−	0.996133i	$-0.528002\pi$
$541$	−4.08698			−0.175713			−0.0878565	+	0.996133i	$0.528002\pi$
$542$	−2.63274	−	2.63274i	−0.113086	−	0.113086i
$543$		0			0
$544$	−6.48062			−0.277854
$545$	0.0558641	+	1.49315i	0.00239296	+	0.0639594i
$546$		0			0
$547$	28.2200	−	28.2200i	1.20660	−	1.20660i	0.234482	−	0.972121i	$-0.424661\pi$
$547$	28.2200	−	28.2200i	1.20660	−	1.20660i	0.972121	−	0.234482i	$-0.0753392\pi$
$548$	1.57863	+	1.57863i	0.0674359	+	0.0674359i
$549$		0			0
$550$	−3.07135	+	3.56892i	−0.130963	+	0.152179i
$551$			26.3613i			1.12303i
$552$		0			0
$553$	0.541896	+	22.8536i	0.0230438	+	0.971833i
$554$		−	1.60631i		−	0.0682457i
$555$		0			0
$556$		−	0.860184i		−	0.0364799i
$557$	−28.1616	+	28.1616i	−1.19325	+	1.19325i	−0.217096	+	0.976150i	$0.569658\pi$
$557$	−28.1616	+	28.1616i	−1.19325	+	1.19325i	−0.976150	+	0.217096i	$0.930342\pi$
$558$		0			0
$559$	3.65510			0.154594
$560$	−21.6610	+	1.32521i	−0.915344	+	0.0560004i
$561$		0			0
$562$	1.61319	−	1.61319i	0.0680482	−	0.0680482i
$563$	27.3645	−	27.3645i	1.15328	−	1.15328i	0.167386	−	0.985891i	$-0.446467\pi$
$563$	27.3645	−	27.3645i	1.15328	−	1.15328i	0.985891	−	0.167386i	$-0.0535326\pi$
$564$		0			0
$565$	−7.87351	−	7.30560i	−0.331241	−	0.307349i
$566$		−	4.98144i		−	0.209386i
$567$		0			0
$568$	−0.786047	−	0.786047i	−0.0329818	−	0.0329818i
$569$		−	17.7767i		−	0.745240i	−0.927984	−	0.372620i	$-0.878460\pi$
$569$		−	17.7767i		−	0.745240i	0.927984	−	0.372620i	$-0.121540\pi$
$570$		0			0
$571$	−16.8866			−0.706683			−0.353342	−	0.935494i	$-0.614955\pi$
$571$	−16.8866			−0.706683			−0.353342	+	0.935494i	$0.614955\pi$
$572$	−3.87817	−	3.87817i	−0.162154	−	0.162154i
$573$		0			0
$574$	−3.45220	−	3.29227i	−0.144092	−	0.137417i
$575$	27.6561	+	23.8003i	1.15334	+	0.992543i
$576$		0			0
$577$	3.89677	+	3.89677i	0.162225	+	0.162225i	0.783552	−	0.621327i	$-0.213406\pi$
$577$	3.89677	+	3.89677i	0.162225	+	0.162225i	−0.621327	+	0.783552i	$0.713406\pi$
$578$	−1.89875	−	1.89875i	−0.0789776	−	0.0789776i
$579$		0			0
$580$	−15.8650	+	0.593566i	−0.658756	+	0.0246465i
$581$	−30.9604	+	32.4643i	−1.28445	+	1.34685i
$582$		0			0
$583$	21.5107	+	21.5107i	0.890881	+	0.890881i
$584$	1.82249			0.0754151
$585$		0			0
$586$			1.60118i			0.0661443i
$587$	15.1058	+	15.1058i	0.623484	+	0.623484i	0.946420	−	0.322937i	$-0.104670\pi$
$587$	15.1058	+	15.1058i	0.623484	+	0.623484i	−0.322937	+	0.946420i	$0.604670\pi$
$588$		0			0
$589$		−	35.6465i		−	1.46879i
$590$	2.19530	−	2.36596i	0.0903793	−	0.0974050i
$591$		0			0
$592$	−1.07213	+	1.07213i	−0.0440642	+	0.0440642i
$593$	3.43032	−	3.43032i	0.140866	−	0.140866i	−0.633157	−	0.774023i	$-0.718241\pi$
$593$	3.43032	−	3.43032i	0.140866	−	0.140866i	0.774023	+	0.633157i	$0.218241\pi$
$594$		0			0
$595$	10.5174	+	9.30466i	0.431170	+	0.381454i
$596$	6.10696			0.250151
$597$		0			0
$598$	0.862773	−	0.862773i	0.0352814	−	0.0352814i
$599$			10.1010i			0.412714i	0.978477	+	0.206357i	$0.0661608\pi$
$599$			10.1010i			0.412714i	−0.978477	+	0.206357i	$0.933839\pi$
$600$		0			0
$601$			38.4063i			1.56663i	0.621628	+	0.783313i	$0.286472\pi$
$601$			38.4063i			1.56663i	−0.621628	+	0.783313i	$0.713528\pi$
$602$	−3.22730	+	0.0765245i	−0.131535	+	0.00311891i
$603$		0			0
$604$		−	28.6261i		−	1.16478i
$605$	−10.9231	+	0.408673i	−0.444087	+	0.0166149i
$606$		0			0
$607$	10.2931	+	10.2931i	0.417783	+	0.417783i	0.884439	−	0.466656i	$-0.154541\pi$
$607$	10.2931	+	10.2931i	0.417783	+	0.417783i	−0.466656	+	0.884439i	$0.654541\pi$
$608$	13.9360	−	13.9360i	0.565180	−	0.565180i
$609$		0			0
$610$	−2.75355	−	2.55494i	−0.111488	−	0.103447i
$611$	0.305570			0.0123621
$612$		0			0
$613$	−14.4155	−	14.4155i	−0.582235	−	0.582235i	0.353282	−	0.935517i	$-0.385066\pi$
$613$	−14.4155	−	14.4155i	−0.582235	−	0.582235i	−0.935517	+	0.353282i	$0.885066\pi$
$614$	3.29121			0.132822
$615$		0			0
$616$	7.11153	+	6.78209i	0.286532	+	0.273258i
$617$	25.4196	−	25.4196i	1.02336	−	1.02336i	0.0236346	−	0.999721i	$-0.492476\pi$
$617$	25.4196	−	25.4196i	1.02336	−	1.02336i	0.999721	−	0.0236346i	$-0.00752382\pi$
$618$		0			0
$619$	−11.1991			−0.450129			−0.225064	−	0.974344i	$-0.572259\pi$
$619$	−11.1991			−0.450129			−0.225064	+	0.974344i	$0.572259\pi$
$620$	21.4530	−	0.802636i	0.861574	−	0.0322346i
$621$		0			0
$622$	−4.56168	−	4.56168i	−0.182907	−	0.182907i
$623$	20.6993	−	0.490815i	0.829301	−	0.0196641i
$624$		0			0
$625$	24.7208	−	3.72569i	0.988833	−	0.149028i
$626$		−	6.18373i		−	0.247152i
$627$		0			0
$628$	15.4856	−	15.4856i	0.617942	−	0.617942i
$629$	0.981107			0.0391193
$630$		0			0
$631$	21.2015			0.844020			0.422010	−	0.906591i	$-0.361325\pi$
$631$	21.2015			0.844020			0.422010	+	0.906591i	$0.361325\pi$
$632$	5.69306	−	5.69306i	0.226458	−	0.226458i
$633$		0			0
$634$		−	7.31014i		−	0.290323i
$635$	12.6653	−	13.6499i	0.502608	−	0.541678i
$636$		0			0
$637$	3.33309	−	3.66516i	0.132062	−	0.145219i
$638$	2.43176	+	2.43176i	0.0962745	+	0.0962745i
$639$		0			0
$640$	11.5419	+	10.7094i	0.456235	+	0.423327i
$641$	29.8969			1.18086			0.590428	−	0.807090i	$-0.298959\pi$
$641$	29.8969			1.18086			0.590428	+	0.807090i	$0.298959\pi$
$642$		0			0
$643$	11.2813	−	11.2813i	0.444891	−	0.444891i	−0.448761	−	0.893652i	$-0.648134\pi$
$643$	11.2813	−	11.2813i	0.444891	−	0.444891i	0.893652	+	0.448761i	$0.148134\pi$
$644$	25.9059	−	27.1642i	1.02083	−	1.07042i
$645$		0			0
$646$	−4.04794			−0.159264
$647$	26.2395	+	26.2395i	1.03158	+	1.03158i	0.999485	+	0.0320982i	$0.0102189\pi$
$647$	26.2395	+	26.2395i	1.03158	+	1.03158i	0.0320982	+	0.999485i	$0.489781\pi$
$648$		0			0
$649$	24.3530			0.955937
$650$	−0.0624689	−	0.833673i	−0.00245023	−	0.0326993i
$651$		0			0
$652$	−20.3069	+	20.3069i	−0.795281	+	0.795281i
$653$	1.97641	+	1.97641i	0.0773427	+	0.0773427i	0.744720	−	0.667377i	$-0.232583\pi$
$653$	1.97641	+	1.97641i	0.0773427	+	0.0773427i	−0.667377	+	0.744720i	$0.732583\pi$
$654$		0			0
$655$	−1.57291	−	42.0410i	−0.0614585	−	1.64268i
$656$		−	27.9953i		−	1.09303i
$657$		0			0
$658$	−0.269805	+	0.00639752i	−0.0105181	+	0.000249401i
$659$		−	15.1044i		−	0.588385i	−0.955746	−	0.294193i	$-0.904949\pi$
$659$		−	15.1044i		−	0.588385i	0.955746	−	0.294193i	$-0.0950507\pi$
$660$		0			0
$661$			1.10054i			0.0428062i	0.999771	+	0.0214031i	$0.00681333\pi$
$661$			1.10054i			0.0428062i	−0.999771	+	0.0214031i	$0.993187\pi$
$662$	−2.78838	+	2.78838i	−0.108374	+	0.108374i
$663$		0			0
$664$	15.7998			0.613150
$665$	−42.6255	+	2.60781i	−1.65295	+	0.101127i
$666$		0			0
$667$	18.8441	−	18.8441i	0.729646	−	0.729646i
$668$	9.01365	−	9.01365i	0.348749	−	0.348749i
$669$		0			0
$670$	0.0263730	+	0.704904i	0.00101888	+	0.0272328i
$671$		−	28.3425i		−	1.09415i
$672$		0			0
$673$	−11.4381	−	11.4381i	−0.440906	−	0.440906i	0.451411	−	0.892316i	$-0.350921\pi$
$673$	−11.4381	−	11.4381i	−0.440906	−	0.440906i	−0.892316	+	0.451411i	$0.850921\pi$
$674$		−	0.848737i		−	0.0326921i
$675$		0			0
$676$	−24.3006			−0.934639
$677$	24.6007	+	24.6007i	0.945481	+	0.945481i	0.998589	−	0.0531077i	$-0.0169127\pi$
$677$	24.6007	+	24.6007i	0.945481	+	0.945481i	−0.0531077	+	0.998589i	$0.516913\pi$
$678$		0			0
$679$	−20.1366	−	19.2037i	−0.772770	−	0.736972i
$680$	−0.184908	−	4.94226i	−0.00709089	−	0.189527i
$681$		0			0
$682$	−3.28830	−	3.28830i	−0.125915	−	0.125915i
$683$	13.8654	+	13.8654i	0.530543	+	0.530543i	0.920734	−	0.390191i	$-0.127591\pi$
$683$	13.8654	+	13.8654i	0.530543	+	0.530543i	−0.390191	+	0.920734i	$0.627591\pi$
$684$		0			0
$685$	−1.74648	+	1.88225i	−0.0667297	+	0.0719170i
$686$	−2.86624	+	3.30596i	−0.109433	+	0.126222i
$687$		0			0
$688$	−13.3960	−	13.3960i	−0.510719	−	0.510719i
$689$	−5.40125			−0.205771
$690$		0			0
$691$			12.4060i			0.471947i	0.971759	+	0.235974i	$0.0758279\pi$
$691$			12.4060i			0.471947i	−0.971759	+	0.235974i	$0.924172\pi$
$692$	4.83190	+	4.83190i	0.183681	+	0.183681i
$693$		0			0
$694$			4.57667i			0.173728i
$695$	0.988633	−	0.0369884i	0.0375010	−	0.00140305i
$696$		0			0
$697$	−12.8093	+	12.8093i	−0.485186	+	0.485186i
$698$	0.0849648	−	0.0849648i	0.00321597	−	0.00321597i
$699$		0			0
$700$	−2.52923	−	25.5945i	−0.0955960	−	0.967380i
$701$	−1.45193			−0.0548388			−0.0274194	−	0.999624i	$-0.508729\pi$
$701$	−1.45193			−0.0548388			−0.0274194	+	0.999624i	$0.508729\pi$
$702$		0			0
$703$	−2.10979	+	2.10979i	−0.0795720	+	0.0795720i
$704$			26.6721i			1.00524i
$705$		0			0
$706$			3.64907i			0.137335i
$707$	0.396144	+	16.7067i	0.0148985	+	0.628322i
$708$		0			0
$709$			48.5284i			1.82252i	0.411827	+	0.911262i	$0.364891\pi$
$709$			48.5284i			1.82252i	−0.411827	+	0.911262i	$0.635109\pi$
$710$	0.428659	−	0.461981i	0.0160873	−	0.0173378i
$711$		0			0
$712$	−5.15642	−	5.15642i	−0.193245	−	0.193245i
$713$	−25.4815	+	25.4815i	−0.954290	+	0.954290i
$714$		0			0
$715$	4.29052	−	4.62405i	0.160457	−	0.172930i
$716$	−42.9876			−1.60652
$717$		0			0
$718$	−2.67056	−	2.67056i	−0.0996644	−	0.0996644i
$719$	−43.5872			−1.62553			−0.812764	−	0.582593i	$-0.802038\pi$
$719$	−43.5872			−1.62553			−0.812764	+	0.582593i	$0.802038\pi$
$720$		0			0
$721$	32.3844	−	33.9575i	1.20606	−	1.26464i
$722$	5.53068	−	5.53068i	0.205831	−	0.205831i
$723$		0			0
$724$	16.4970			0.613104
$725$	−1.36440	−	18.2085i	−0.0506727	−	0.676247i
$726$		0			0
$727$	10.4498	+	10.4498i	0.387563	+	0.387563i	0.873817	−	0.486254i	$-0.161637\pi$
$727$	10.4498	+	10.4498i	0.387563	+	0.387563i	−0.486254	+	0.873817i	$0.661637\pi$
$728$	−1.74432	+	0.0413607i	−0.0646487	+	0.00153293i
$729$		0			0
$730$	0.0386295	+	1.03250i	0.00142974	+	0.0382144i
$731$			12.2587i			0.453405i
$732$		0			0
$733$	18.8687	−	18.8687i	0.696933	−	0.696933i	−0.266815	−	0.963748i	$-0.585971\pi$
$733$	18.8687	−	18.8687i	0.696933	−	0.696933i	0.963748	+	0.266815i	$0.0859712\pi$
$734$	0.136998			0.00505669
$735$		0			0
$736$	−19.9240			−0.734409
$737$	−3.76354	+	3.76354i	−0.138632	+	0.138632i
$738$		0			0
$739$		−	20.9689i		−	0.771354i	−0.922634	−	0.385677i	$-0.873968\pi$
$739$		−	20.9689i		−	0.771354i	0.922634	−	0.385677i	$-0.126032\pi$
$740$	−1.31723	−	1.22222i	−0.0484224	−	0.0449297i
$741$		0			0
$742$	4.76906	−	0.113082i	0.175078	−	0.00415138i
$743$	−9.18724	−	9.18724i	−0.337047	−	0.337047i	0.518208	−	0.855255i	$-0.326599\pi$
$743$	−9.18724	−	9.18724i	−0.337047	−	0.337047i	−0.855255	+	0.518208i	$0.826599\pi$
$744$		0			0
$745$	0.262603	+	7.01890i	0.00962102	+	0.257152i
$746$	−1.15100			−0.0421412
$747$		0			0
$748$	13.0069	−	13.0069i	0.475578	−	0.475578i
$749$	19.3160	−	20.2543i	0.705793	−	0.740077i
$750$		0			0
$751$	11.1969			0.408579			0.204290	−	0.978910i	$-0.434512\pi$
$751$	11.1969			0.408579			0.204290	+	0.978910i	$0.434512\pi$
$752$	−1.11992	−	1.11992i	−0.0408393	−	0.0408393i
$753$		0			0
$754$	−0.610607			−0.0222370
$755$	32.9007	−	1.23094i	1.19738	−	0.0447984i
$756$		0			0
$757$	−13.9324	+	13.9324i	−0.506383	+	0.506383i	−0.913414	−	0.407031i	$-0.866564\pi$
$757$	−13.9324	+	13.9324i	−0.506383	+	0.506383i	0.407031	+	0.913414i	$0.366564\pi$
$758$	2.15801	+	2.15801i	0.0783824	+	0.0783824i
$759$		0			0
$760$	11.0255	+	10.2303i	0.399938	+	0.371091i
$761$		−	8.78825i		−	0.318574i	−0.987232	−	0.159287i	$-0.949081\pi$
$761$		−	8.78825i		−	0.318574i	0.987232	−	0.159287i	$-0.0509195\pi$
$762$		0			0
$763$	0.0419093	+	1.76746i	0.00151722	+	0.0639862i
$764$		−	29.7263i		−	1.07546i
$765$		0			0
$766$		−	3.36684i		−	0.121649i
$767$	−3.05747	+	3.05747i	−0.110399	+	0.110399i
$768$		0			0
$769$	−11.2183			−0.404543			−0.202271	−	0.979330i	$-0.564832\pi$
$769$	−11.2183			−0.404543			−0.202271	+	0.979330i	$0.564832\pi$
$770$	−3.69153	+	4.17266i	−0.133034	+	0.150372i
$771$		0			0
$772$	17.3574	−	17.3574i	0.624708	−	0.624708i
$773$	−21.5065	+	21.5065i	−0.773535	+	0.773535i	−0.978723	−	0.205188i	$-0.934219\pi$
$773$	−21.5065	+	21.5065i	−0.773535	+	0.773535i	0.205188	+	0.978723i	$0.434219\pi$
$774$		0			0
$775$	1.84498	+	24.6220i	0.0662738	+	0.884450i
$776$			9.80008i			0.351802i
$777$		0			0
$778$	4.06447	+	4.06447i	0.145718	+	0.145718i
$779$		−	55.0905i		−	1.97382i
$780$		0			0
$781$	4.75520			0.170155
$782$	2.89362	+	2.89362i	0.103476	+	0.103476i
$783$		0			0
$784$	−25.6487	+	1.21703i	−0.916025	+	0.0434654i
$785$	18.4639	+	17.1321i	0.659004	+	0.611471i
$786$		0			0
$787$	37.4673	+	37.4673i	1.33557	+	1.33557i	0.900304	+	0.435262i	$0.143344\pi$
$787$	37.4673	+	37.4673i	1.33557	+	1.33557i	0.435262	+	0.900304i	$0.356656\pi$
$788$	5.22431	+	5.22431i	0.186108	+	0.186108i
$789$		0			0
$790$	3.34597	+	3.10463i	0.119044	+	0.110458i
$791$	−9.19686	−	8.77082i	−0.327003	−	0.311854i
$792$		0			0
$793$	3.55834	+	3.55834i	0.126360	+	0.126360i
$794$	2.27408			0.0807039
$795$		0			0
$796$			1.19886i			0.0424923i
$797$	−6.96365	−	6.96365i	−0.246665	−	0.246665i	0.572935	−	0.819601i	$-0.305805\pi$
$797$	−6.96365	−	6.96365i	−0.246665	−	0.246665i	−0.819601	+	0.572935i	$0.805805\pi$
$798$		0			0
$799$			1.02484i			0.0362563i
$800$	−8.90470	+	10.3473i	−0.314829	+	0.365832i
$801$		0			0
$802$	1.47525	−	1.47525i	0.0520930	−	0.0520930i
$803$	−5.51258	+	5.51258i	−0.194535	+	0.194535i
$804$		0			0
$805$	32.3346	+	28.6062i	1.13964	+	1.00824i
$806$	0.825679			0.0290833
$807$		0			0
$808$	4.16182	−	4.16182i	0.146412	−	0.146412i
$809$		−	42.2409i		−	1.48511i	−0.669784	−	0.742556i	$-0.733613\pi$
$809$		−	42.2409i		−	1.48511i	0.669784	−	0.742556i	$-0.266387\pi$
$810$		0			0
$811$			34.9480i			1.22719i	0.789620	+	0.613596i	$0.210277\pi$
$811$			34.9480i			1.22719i	−0.789620	+	0.613596i	$0.789723\pi$
$812$	−18.7795	+	0.445293i	−0.659032	+	0.0156267i
$813$		0			0
$814$			0.389245i			0.0136430i
$815$	−24.2125	−	22.4661i	−0.848128	−	0.786953i
$816$		0			0
$817$	−26.3613	−	26.3613i	−0.922266	−	0.922266i
$818$	−3.87544	+	3.87544i	−0.135502	+	0.135502i
$819$		0			0
$820$	33.1549	−	1.24045i	1.15782	−	0.0433183i
$821$	4.13417			0.144284			0.0721418	−	0.997394i	$-0.477017\pi$
$821$	4.13417			0.144284			0.0721418	+	0.997394i	$0.477017\pi$
$822$		0			0
$823$	−5.72102	−	5.72102i	−0.199422	−	0.199422i	0.600330	−	0.799752i	$-0.295036\pi$
$823$	−5.72102	−	5.72102i	−0.199422	−	0.199422i	−0.799752	+	0.600330i	$0.795036\pi$
$824$	−16.5264			−0.575726
$825$		0			0
$826$	2.63560	−	2.76362i	0.0917041	−	0.0961587i
$827$	−17.0630	+	17.0630i	−0.593339	+	0.593339i	−0.938532	−	0.345193i	$-0.887813\pi$
$827$	−17.0630	+	17.0630i	−0.593339	+	0.593339i	0.345193	+	0.938532i	$0.387813\pi$
$828$		0			0
$829$	−37.7146			−1.30988			−0.654940	−	0.755680i	$-0.727306\pi$
$829$	−37.7146			−1.30988			−0.654940	+	0.755680i	$0.727306\pi$
$830$	0.334892	+	8.95106i	0.0116243	+	0.310696i
$831$		0			0
$832$	−3.34863	−	3.34863i	−0.116093	−	0.116093i
$833$	12.2924	+	11.1787i	0.425908	+	0.387320i
$834$		0			0
$835$	10.7472	+	9.97204i	0.371923	+	0.345097i
$836$			55.9402i			1.93473i
$837$		0			0
$838$	−2.17828	+	2.17828i	−0.0752476	+	0.0752476i
$839$	−22.3652			−0.772133			−0.386066	−	0.922471i	$-0.626166\pi$
$839$	−22.3652			−0.772133			−0.386066	+	0.922471i	$0.626166\pi$
$840$		0			0
$841$	15.6636			0.540123
$842$	−5.23801	+	5.23801i	−0.180514	+	0.180514i
$843$		0			0
$844$			18.0974i			0.622939i
$845$	−1.04494	−	27.9294i	−0.0359470	−	0.960799i
$846$		0			0
$847$	−12.9298	+	0.306586i	−0.444272	+	0.0105344i
$848$	19.7957	+	19.7957i	0.679786	+	0.679786i
$849$		0			0
$850$	2.79602	−	0.209512i	0.0959028	−	0.00718621i
$851$	3.01631			0.103398
$852$		0			0
$853$	24.1276	−	24.1276i	0.826114	−	0.826114i	−0.160863	−	0.986977i	$-0.551428\pi$
$853$	24.1276	−	24.1276i	0.826114	−	0.826114i	0.986977	+	0.160863i	$0.0514276\pi$
$854$	−3.21636	−	3.06736i	−0.110062	−	0.104963i
$855$		0			0
$856$	−9.85740			−0.336919
$857$	1.53096	+	1.53096i	0.0522968	+	0.0522968i	0.732772	−	0.680475i	$-0.238226\pi$
$857$	1.53096	+	1.53096i	0.0522968	+	0.0522968i	−0.680475	+	0.732772i	$0.738226\pi$
$858$		0			0
$859$	−41.8095			−1.42652			−0.713261	−	0.700899i	$-0.752782\pi$
$859$	−41.8095			−1.42652			−0.713261	+	0.700899i	$0.752782\pi$
$860$	15.2714	−	16.4585i	0.520750	−	0.561231i
$861$		0			0
$862$	3.76808	−	3.76808i	0.128341	−	0.128341i
$863$	14.0647	+	14.0647i	0.478770	+	0.478770i	0.904738	−	0.425968i	$-0.140067\pi$
$863$	14.0647	+	14.0647i	0.478770	+	0.478770i	−0.425968	+	0.904738i	$0.640067\pi$
$864$		0			0
$865$	−5.34566	+	5.76121i	−0.181758	+	0.195887i
$866$			6.67018i			0.226662i
$867$		0			0
$868$	25.3942	−	0.602138i	0.861935	−	0.0204379i
$869$			34.4403i			1.16831i
$870$		0			0
$871$		−	0.945011i		−	0.0320205i
$872$	0.440292	−	0.440292i	0.0149102	−	0.0149102i
$873$		0			0
$874$	−12.4450			−0.420958
$875$	29.3077	−	4.00749i	0.990780	−	0.135478i
$876$		0			0
$877$	−39.3844	+	39.3844i	−1.32992	+	1.32992i	−0.424477	+	0.905438i	$0.639542\pi$
$877$	−39.3844	+	39.3844i	−1.32992	+	1.32992i	−0.905438	+	0.424477i	$0.860458\pi$
$878$	5.04414	−	5.04414i	0.170231	−	0.170231i
$879$		0			0
$880$	−32.6721	+	1.22238i	−1.10138	+	0.0412065i
$881$		−	25.7205i		−	0.866546i	−0.901263	−	0.433273i	$-0.857359\pi$
$881$		−	25.7205i		−	0.866546i	0.901263	−	0.433273i	$-0.142641\pi$
$882$		0			0
$883$	−25.0968	−	25.0968i	−0.844574	−	0.844574i	0.144876	−	0.989450i	$-0.453722\pi$
$883$	−25.0968	−	25.0968i	−0.844574	−	0.844574i	−0.989450	+	0.144876i	$0.953722\pi$
$884$			3.26597i			0.109846i
$885$		0			0
$886$	4.25735			0.143028
$887$	37.8947	+	37.8947i	1.27238	+	1.27238i	0.944837	+	0.327541i	$0.106220\pi$
$887$	37.8947	+	37.8947i	1.27238	+	1.27238i	0.327541	+	0.944837i	$0.393780\pi$
$888$		0			0
$889$	15.2055	−	15.9441i	0.509975	−	0.534748i
$890$	2.81198	−	3.03057i	0.0942577	−	0.101585i
$891$		0			0
$892$	−2.63446	−	2.63446i	−0.0882083	−	0.0882083i
$893$	−2.20383	−	2.20383i	−0.0737484	−	0.0737484i
$894$		0			0
$895$	−1.84849	−	49.4068i	−0.0617882	−	1.65149i
$896$	13.4819	+	12.8573i	0.450397	+	0.429533i
$897$		0			0
$898$	5.08134	+	5.08134i	0.169566	+	0.169566i
$899$	18.0339			0.601464
$900$		0			0
$901$		−	18.1150i		−	0.603499i
$902$	−5.08195	−	5.08195i	−0.169211	−	0.169211i
$903$		0			0
$904$			4.47594i			0.148867i
$905$	0.709378	+	18.9604i	0.0235805	+	0.630265i
$906$		0			0
$907$	−30.5961	+	30.5961i	−1.01593	+	1.01593i	−0.0160555	+	0.999871i	$0.505111\pi$
$907$	−30.5961	+	30.5961i	−1.01593	+	1.01593i	−0.999871	+	0.0160555i	$0.994889\pi$
$908$	8.07687	−	8.07687i	0.268040	−	0.268040i
$909$		0			0
$910$	−0.0604047	−	0.987334i	−0.00200240	−	0.0327298i
$911$	−20.7843			−0.688614			−0.344307	−	0.938857i	$-0.611886\pi$
$911$	−20.7843			−0.688614			−0.344307	+	0.938857i	$0.611886\pi$
$912$		0			0
$913$	−47.7905	+	47.7905i	−1.58163	+	1.58163i
$914$		−	0.439512i		−	0.0145378i
$915$		0			0
$916$			25.2550i			0.834447i
$917$	−1.17999	−	49.7643i	−0.0389669	−	1.64336i
$918$		0			0
$919$		−	47.6045i		−	1.57033i	−0.619288	−	0.785164i	$-0.712579\pi$
$919$		−	47.6045i		−	1.57033i	0.619288	−	0.785164i	$-0.287421\pi$
$920$	−0.568481	−	15.1945i	−0.0187423	−	0.500947i
$921$		0			0
$922$	−0.217101	−	0.217101i	−0.00714985	−	0.00714985i
$923$	−0.597007	+	0.597007i	−0.0196507	+	0.0196507i
$924$		0			0
$925$	1.34809	−	1.56649i	0.0443249	−	0.0515057i
$926$	5.52085			0.181426
$927$		0			0
$928$	7.05036	+	7.05036i	0.231440	+	0.231440i
$929$	−40.6532			−1.33379			−0.666895	−	0.745152i	$-0.732377\pi$
$929$	−40.6532			−1.33379			−0.666895	+	0.745152i	$0.732377\pi$
$930$		0			0
$931$	−50.4727	+	2.39493i	−1.65418	+	0.0784906i
$932$	−32.0088	+	32.0088i	−1.04848	+	1.04848i
$933$		0			0
$934$	−6.71593			−0.219752
$935$	15.5084	+	14.3898i	0.507180	+	0.470598i
$936$		0			0
$937$	−8.25994	−	8.25994i	−0.269841	−	0.269841i	0.559195	−	0.829036i	$-0.311110\pi$
$937$	−8.25994	−	8.25994i	−0.269841	−	0.269841i	−0.829036	+	0.559195i	$0.811110\pi$
$938$	0.0197851	+	0.834403i	0.000646005	+	0.0272442i
$939$		0			0
$940$	1.27670	−	1.37595i	0.0416415	−	0.0448785i
$941$		−	28.7824i		−	0.938281i	−0.883124	−	0.469140i	$-0.844564\pi$
$941$		−	28.7824i		−	0.938281i	0.883124	−	0.469140i	$-0.155436\pi$
$942$		0			0
$943$	−39.3808	+	39.3808i	−1.28242	+	1.28242i
$944$	22.4113			0.729427
$945$		0			0
$946$	−4.86353			−0.158127
$947$	−4.26936	+	4.26936i	−0.138736	+	0.138736i	−0.773064	−	0.634328i	$-0.781277\pi$
$947$	−4.26936	+	4.26936i	−0.138736	+	0.138736i	0.634328	+	0.773064i	$0.281277\pi$
$948$		0			0
$949$		−	1.38419i		−	0.0449327i
$950$	−5.56207	+	6.46315i	−0.180457	+	0.209692i
$951$		0			0
$952$	−0.138718	−	5.85020i	−0.00449588	−	0.189606i
$953$	−31.8382	−	31.8382i	−1.03134	−	1.03134i	−0.999493	−	0.0318472i	$-0.989861\pi$
$953$	−31.8382	−	31.8382i	−1.03134	−	1.03134i	−0.0318472	−	0.999493i	$-0.510139\pi$
$954$		0			0
$955$	34.1652	−	1.27825i	1.10556	−	0.0413631i
$956$	−10.6551			−0.344609
$957$		0			0
$958$	1.85159	−	1.85159i	0.0598221	−	0.0598221i
$959$	−2.09676	+	2.19861i	−0.0677079	+	0.0709968i
$960$		0			0
$961$	6.61406			0.213357
$962$	−0.0488689	−	0.0488689i	−0.00157560	−	0.00157560i
$963$		0			0
$964$	−28.4837			−0.917399
$965$	20.6957	+	19.2030i	0.666220	+	0.618166i
$966$		0			0
$967$	−17.5518	+	17.5518i	−0.564429	+	0.564429i	−0.930562	−	0.366134i	$-0.880681\pi$
$967$	−17.5518	+	17.5518i	−0.564429	+	0.564429i	0.366134	+	0.930562i	$0.380681\pi$
$968$	3.22094	+	3.22094i	0.103525	+	0.103525i
$969$		0			0
$970$	−5.55205	+	0.207723i	−0.178266	+	0.00666957i
$971$			0.0930634i			0.00298655i	0.999999	+	0.00149327i	$0.000475324\pi$
$971$			0.0930634i			0.00298655i	−0.999999	+	0.00149327i	$0.999525\pi$
$972$		0			0
$973$	1.17026	−	0.0277487i	0.0375167	−	0.000889582i
$974$			4.56126i			0.146152i
$975$		0			0
$976$		−	26.0828i		−	0.834889i
$977$	−5.19792	+	5.19792i	−0.166296	+	0.166296i	−0.785349	−	0.619053i	$-0.787517\pi$
$977$	−5.19792	+	5.19792i	−0.166296	+	0.166296i	0.619053	+	0.785349i	$0.287517\pi$
$978$		0			0
$979$	31.1938			0.996959
$980$	−2.57781	−	30.3219i	−0.0823450	−	0.968598i
$981$		0			0
$982$	−5.36509	+	5.36509i	−0.171207	+	0.171207i
$983$	30.3939	−	30.3939i	0.969415	−	0.969415i	−0.0301305	−	0.999546i	$-0.509592\pi$
$983$	30.3939	−	30.3939i	0.969415	−	0.969415i	0.999546	+	0.0301305i	$0.00959230\pi$
$984$		0			0
$985$	−5.77980	+	6.22909i	−0.184160	+	0.198475i
$986$		−	2.04789i		−	0.0652181i
$987$		0			0
$988$	−7.02319	−	7.02319i	−0.223437	−	0.223437i
$989$			37.6882i			1.19842i
$990$		0			0
$991$	34.2648			1.08846			0.544228	−	0.838937i	$-0.316823\pi$
$991$	34.2648			1.08846			0.544228	+	0.838937i	$0.316823\pi$
$992$	−9.53370	−	9.53370i	−0.302695	−	0.302695i
$993$		0			0
$994$	0.514631	−	0.539630i	0.0163231	−	0.0171160i
$995$	−1.37788	+	0.0515514i	−0.0436817	+	0.00163429i
$996$		0			0
$997$	−21.1809	−	21.1809i	−0.670805	−	0.670805i	0.287097	−	0.957902i	$-0.407310\pi$
$997$	−21.1809	−	21.1809i	−0.670805	−	0.670805i	−0.957902	+	0.287097i	$0.907310\pi$
$998$	−0.714048	−	0.714048i	−0.0226028	−	0.0226028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.p.e.118.5		16
3.2	odd	2		105.2.m.a.13.4	yes	16
5.2	odd	4	inner	315.2.p.e.307.6		16
7.6	odd	2	inner	315.2.p.e.118.6		16
12.11	even	2		1680.2.cz.d.433.4		16
15.2	even	4		105.2.m.a.97.3	yes	16
15.8	even	4		525.2.m.b.307.6		16
15.14	odd	2		525.2.m.b.118.5		16
21.2	odd	6		735.2.v.a.178.6		32
21.5	even	6		735.2.v.a.178.5		32
21.11	odd	6		735.2.v.a.313.3		32
21.17	even	6		735.2.v.a.313.4		32
21.20	even	2		105.2.m.a.13.3	✓	16
35.27	even	4	inner	315.2.p.e.307.5		16
60.47	odd	4		1680.2.cz.d.97.5		16
84.83	odd	2		1680.2.cz.d.433.5		16
105.2	even	12		735.2.v.a.472.4		32
105.17	odd	12		735.2.v.a.607.6		32
105.32	even	12		735.2.v.a.607.5		32
105.47	odd	12		735.2.v.a.472.3		32
105.62	odd	4		105.2.m.a.97.4	yes	16
105.83	odd	4		525.2.m.b.307.5		16
105.104	even	2		525.2.m.b.118.6		16
420.167	even	4		1680.2.cz.d.97.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.3	✓	16	21.20	even	2
105.2.m.a.13.4	yes	16	3.2	odd	2
105.2.m.a.97.3	yes	16	15.2	even	4
105.2.m.a.97.4	yes	16	105.62	odd	4
315.2.p.e.118.5		16	1.1	even	1	trivial
315.2.p.e.118.6		16	7.6	odd	2	inner
315.2.p.e.307.5		16	35.27	even	4	inner
315.2.p.e.307.6		16	5.2	odd	4	inner
525.2.m.b.118.5		16	15.14	odd	2
525.2.m.b.118.6		16	105.104	even	2
525.2.m.b.307.5		16	105.83	odd	4
525.2.m.b.307.6		16	15.8	even	4
735.2.v.a.178.5		32	21.5	even	6
735.2.v.a.178.6		32	21.2	odd	6
735.2.v.a.313.3		32	21.11	odd	6
735.2.v.a.313.4		32	21.17	even	6
735.2.v.a.472.3		32	105.47	odd	12
735.2.v.a.472.4		32	105.2	even	12
735.2.v.a.607.5		32	105.32	even	12
735.2.v.a.607.6		32	105.17	odd	12
1680.2.cz.d.97.4		16	420.167	even	4
1680.2.cz.d.97.5		16	60.47	odd	4
1680.2.cz.d.433.4		16	12.11	even	2
1680.2.cz.d.433.5		16	84.83	odd	2

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.167056 - 0.167056i) q^{2} +1.94418i q^{4} +(-2.23450 + 0.0836010i) q^{5} +(-2.64501 + 0.0627175i) q^{7} +(0.658899 + 0.658899i) q^{8} +O(q^{10})\)	\(q+(0.167056 - 0.167056i) q^{2} +1.94418i q^{4} +(-2.23450 + 0.0836010i) q^{5} +(-2.64501 + 0.0627175i) q^{7} +(0.658899 + 0.658899i) q^{8} +(-0.359321 + 0.387253i) q^{10} -3.98602 q^{11} +(0.500437 - 0.500437i) q^{13} +(-0.431387 + 0.452341i) q^{14} -3.66822 q^{16} +(1.67840 + 1.67840i) q^{17} -7.21850 q^{19} +(-0.162536 - 4.34429i) q^{20} +(-0.665888 + 0.665888i) q^{22} +(5.16007 + 5.16007i) q^{23} +(4.98602 - 0.373614i) q^{25} -0.167202i q^{26} +(-0.121934 - 5.14238i) q^{28} -3.65191i q^{29} +4.93821i q^{31} +(-1.93060 + 1.93060i) q^{32} +0.560773 q^{34} +(5.90504 - 0.361268i) q^{35} +(0.292275 - 0.292275i) q^{37} +(-1.20589 + 1.20589i) q^{38} +(-1.52740 - 1.41723i) q^{40} +7.63184i q^{41} +(3.65191 + 3.65191i) q^{43} -7.74956i q^{44} +1.72404 q^{46} +(0.305303 + 0.305303i) q^{47} +(6.99213 - 0.331777i) q^{49} +(0.770530 - 0.895358i) q^{50} +(0.972943 + 0.972943i) q^{52} +(-5.39653 - 5.39653i) q^{53} +(8.90678 - 0.333235i) q^{55} +(-1.78412 - 1.70147i) q^{56} +(-0.610073 - 0.610073i) q^{58} -6.10959 q^{59} +7.11047i q^{61} +(0.824957 + 0.824957i) q^{62} -6.69141i q^{64} +(-1.07639 + 1.16007i) q^{65} +(0.944185 - 0.944185i) q^{67} +(-3.26312 + 3.26312i) q^{68} +(0.926119 - 1.04682i) q^{70} -1.19297 q^{71} +(1.38298 - 1.38298i) q^{73} -0.0976524i q^{74} -14.0341i q^{76} +(10.5431 - 0.249993i) q^{77} -8.64027i q^{79} +(8.19666 - 0.306667i) q^{80} +(1.27494 + 1.27494i) q^{82} +(11.9895 - 11.9895i) q^{83} +(-3.89070 - 3.61007i) q^{85} +1.22015 q^{86} +(-2.62639 - 2.62639i) q^{88} -7.82581 q^{89} +(-1.29227 + 1.35505i) q^{91} +(-10.0321 + 10.0321i) q^{92} +0.102005 q^{94} +(16.1298 - 0.603474i) q^{95} +(7.43671 + 7.43671i) q^{97} +(1.11265 - 1.22350i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q - 8 * q^7 - 24 * q^8	\( 16 q - 8 q^{7} - 24 q^{8} + 16 q^{11} - 48 q^{16} - 16 q^{22} + 40 q^{23} + 24 q^{28} - 48 q^{32} + 8 q^{35} + 32 q^{37} - 16 q^{43} + 64 q^{46} + 72 q^{50} - 24 q^{53} - 24 q^{56} + 32 q^{58} - 40 q^{65} - 32 q^{67} - 40 q^{70} - 64 q^{71} + 24 q^{77} + 48 q^{85} - 64 q^{86} - 64 q^{88} - 48 q^{91} + 40 q^{92} + 72 q^{95} + 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 - 24 * q^8 + 16 * q^11 - 48 * q^16 - 16 * q^22 + 40 * q^23 + 24 * q^28 - 48 * q^32 + 8 * q^35 + 32 * q^37 - 16 * q^43 + 64 * q^46 + 72 * q^50 - 24 * q^53 - 24 * q^56 + 32 * q^58 - 40 * q^65 - 32 * q^67 - 40 * q^70 - 64 * q^71 + 24 * q^77 + 48 * q^85 - 64 * q^86 - 64 * q^88 - 48 * q^91 + 40 * q^92 + 72 * q^95 + 96 * q^98

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