LMFDB - Embedded newform 315.2.p.e.307.6

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			307.6
Root			$1.40927 + 0.118126i$ of defining polynomial
Character	$\chi$	$=$	315.307
Dual form			315.2.p.e.118.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167056 + 0.167056i) q^{2} -1.94418i q^{4} +(2.23450 + 0.0836010i) q^{5} +(-0.0627175 - 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +O(q^{10})$	\(q+(0.167056 + 0.167056i) q^{2} -1.94418i q^{4} +(2.23450 + 0.0836010i) q^{5} +(-0.0627175 - 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +(0.359321 + 0.387253i) q^{10} -3.98602 q^{11} +(-0.500437 - 0.500437i) q^{13} +(0.431387 - 0.452341i) q^{14} -3.66822 q^{16} +(-1.67840 + 1.67840i) q^{17} +7.21850 q^{19} +(0.162536 - 4.34429i) q^{20} +(-0.665888 - 0.665888i) q^{22} +(5.16007 - 5.16007i) q^{23} +(4.98602 + 0.373614i) q^{25} -0.167202i q^{26} +(-5.14238 + 0.121934i) q^{28} +3.65191i q^{29} +4.93821i q^{31} +(-1.93060 - 1.93060i) q^{32} -0.560773 q^{34} +(0.0809828 - 5.91553i) q^{35} +(0.292275 + 0.292275i) q^{37} +(1.20589 + 1.20589i) q^{38} +(1.52740 - 1.41723i) q^{40} +7.63184i q^{41} +(3.65191 - 3.65191i) q^{43} +7.74956i q^{44} +1.72404 q^{46} +(-0.305303 + 0.305303i) q^{47} +(-6.99213 + 0.331777i) q^{49} +(0.770530 + 0.895358i) q^{50} +(-0.972943 + 0.972943i) q^{52} +(-5.39653 + 5.39653i) q^{53} +(-8.90678 - 0.333235i) q^{55} +(-1.78412 - 1.70147i) q^{56} +(-0.610073 + 0.610073i) q^{58} +6.10959 q^{59} +7.11047i q^{61} +(-0.824957 + 0.824957i) q^{62} +6.69141i q^{64} +(-1.07639 - 1.16007i) q^{65} +(0.944185 + 0.944185i) q^{67} +(3.26312 + 3.26312i) q^{68} +(1.00175 - 0.974695i) q^{70} -1.19297 q^{71} +(-1.38298 - 1.38298i) q^{73} +0.0976524i q^{74} -14.0341i q^{76} +(0.249993 + 10.5431i) q^{77} +8.64027i q^{79} +(-8.19666 - 0.306667i) q^{80} +(-1.27494 + 1.27494i) q^{82} +(-11.9895 - 11.9895i) q^{83} +(-3.89070 + 3.61007i) q^{85} +1.22015 q^{86} +(-2.62639 + 2.62639i) q^{88} +7.82581 q^{89} +(-1.29227 + 1.35505i) q^{91} +(-10.0321 - 10.0321i) q^{92} -0.102005 q^{94} +(16.1298 + 0.603474i) q^{95} +(-7.43671 + 7.43671i) q^{97} +(-1.22350 - 1.11265i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	0.167056	+	0.167056i	0.118126	+	0.118126i	0.763699	−	0.645573i	$-0.223381\pi$
$2$	0.167056	+	0.167056i	0.118126	+	0.118126i	−0.645573	+	0.763699i	$0.723381\pi$
$3$		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
$7$	−0.0627175	−	2.64501i	−0.0237050	−	0.999719i
$7$	−0.0627175	−	2.64501i	−0.0237050	−	0.999719i
$8$	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	$-0.281291\pi$
$13$	−0.500437	−	0.500437i	−0.138796	−	0.138796i	−0.773091	+	0.634295i	$0.781291\pi$
$14$	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	$-0.842938\pi$
$17$	−1.67840	+	1.67840i	−0.407071	+	0.407071i	0.473645	+	0.880716i	$0.342938\pi$
$18$		0			0
$19$	7.21850			1.65604			0.828019	−	0.560700i	$-0.189468\pi$
$19$	7.21850			1.65604			0.828019	+	0.560700i	$0.189468\pi$
$20$	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	0.0790800	−	0.996868i	$-0.474802\pi$
$23$	5.16007	−	5.16007i	1.07595	−	1.07595i	0.996868	−	0.0790800i	$-0.0251983\pi$
$24$		0			0
$25$	4.98602	+	0.373614i	0.997204	+	0.0747227i
$26$		−	0.167202i		−	0.0327910i
$27$		0			0
$28$	−5.14238	+	0.121934i	−0.971819	+	0.0230434i
$29$			3.65191i			0.678143i	0.940761	+	0.339071i	$0.110113\pi$
$29$			3.65191i			0.678143i	−0.940761	+	0.339071i	$0.889887\pi$
$30$		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
$35$	0.0809828	−	5.91553i	0.0136886	−	0.999906i
$36$		0			0
$37$	0.292275	+	0.292275i	0.0480497	+	0.0480497i	0.730723	−	0.682674i	$-0.239183\pi$
$37$	0.292275	+	0.292275i	0.0480497	+	0.0480497i	−0.682674	+	0.730723i	$0.739183\pi$
$38$	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	−0.371516	−	0.928427i	$-0.621162\pi$
$43$	3.65191	−	3.65191i	0.556911	−	0.556911i	0.928427	+	0.371516i	$0.121162\pi$
$44$			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	$-0.760025\pi$
$47$	−0.305303	+	0.305303i	−0.0445331	+	0.0445331i	0.684490	+	0.729023i	$0.260025\pi$
$48$		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	−0.972822	−	0.231553i	$-0.925619\pi$
$53$	−5.39653	+	5.39653i	−0.741270	+	0.741270i	0.231553	+	0.972822i	$0.425619\pi$
$54$		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	$-0.369808\pi$
$59$	6.10959			0.795401			0.397701	+	0.917515i	$0.369808\pi$
$60$		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	0.762426	−	0.647075i	$-0.224008\pi$
$67$	0.944185	+	0.944185i	0.115351	+	0.115351i	−0.647075	+	0.762426i	$0.724008\pi$
$68$	3.26312	+	3.26312i	0.395711	+	0.395711i
$69$		0			0
$70$	1.00175	−	0.974695i	0.119732	−	0.116498i
$71$	−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	$-0.286513\pi$
$73$	−1.38298	−	1.38298i	−0.161865	−	0.161865i	−0.783393	+	0.621527i	$0.786513\pi$
$74$			0.0976524i			0.0113519i
$75$		0			0
$76$		−	14.0341i		−	1.60982i
$77$	0.249993	+	10.5431i	0.0284894	+	1.20149i
$78$		0			0
$79$			8.64027i			0.972106i	0.873929	+	0.486053i	$0.161564\pi$
$79$			8.64027i			0.972106i	−0.873929	+	0.486053i	$0.838436\pi$
$80$	−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	−0.916898	−	0.399122i	$-0.869315\pi$
$83$	−11.9895	−	11.9895i	−1.31602	−	1.31602i	−0.399122	−	0.916898i	$-0.630685\pi$
$84$		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	$-0.363863\pi$
$89$	7.82581			0.829534			0.414767	+	0.909928i	$0.363863\pi$
$90$		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	$-0.929283\pi$
$97$	−7.43671	+	7.43671i	−0.755083	+	0.755083i	0.220340	+	0.975423i	$0.429283\pi$
$98$	−1.22350	−	1.11265i	−0.123592	−	0.112395i
$99$		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	0.961743	+	0.273954i	$0.0883316\pi$
$103$	12.5410	+	12.5410i	1.23570	+	1.23570i	0.273954	+	0.961743i	$0.411668\pi$
$104$	−0.659476			−0.0646669
$105$		0			0
$106$	−1.80304			−0.175127
$107$	−7.48020	−	7.48020i	−0.723138	−	0.723138i	0.246105	−	0.969243i	$-0.420849\pi$
$107$	−7.48020	−	7.48020i	−0.723138	−	0.723138i	−0.969243	+	0.246105i	$0.920849\pi$
$108$		0			0
$109$			0.668223i			0.0640042i	0.999488	+	0.0320021i	$0.0101883\pi$
$109$			0.668223i			0.0640042i	−0.999488	+	0.0320021i	$0.989812\pi$
$110$	−1.43226	−	1.54360i	−0.136561	−	0.147176i
$111$		0			0
$112$	0.230062	+	9.70248i	0.0217388	+	0.916798i
$113$	3.39653	−	3.39653i	0.319518	−	0.319518i	−0.529064	−	0.848582i	$-0.677457\pi$
$113$	3.39653	−	3.39653i	0.319518	−	0.319518i	0.848582	+	0.529064i	$0.177457\pi$
$114$		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	0.395820	−	0.918328i	$-0.370460\pi$
$127$	−5.88837	−	5.88837i	−0.522508	−	0.522508i	−0.918328	+	0.395820i	$0.870460\pi$
$128$	−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
$133$	−0.452726	−	19.0930i	−0.0392564	−	1.65557i
$134$			0.315463i			0.0272519i
$135$		0			0
$136$			2.21179i			0.189659i
$137$	0.811977	+	0.811977i	0.0693719	+	0.0693719i	0.740941	−	0.671570i	$-0.234380\pi$
$137$	0.811977	+	0.811977i	0.0693719	+	0.0693719i	−0.671570	+	0.740941i	$0.734380\pi$
$138$		0			0
$139$	0.442439			0.0375272			0.0187636	−	0.999824i	$-0.494027\pi$
$139$	0.442439			0.0375272			0.0187636	+	0.999824i	$0.494027\pi$
$140$	−11.5009	−	0.157445i	−0.972001	−	0.0133066i
$141$		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	$0.0410696\pi$
$149$			3.14114i			0.257332i	−0.991688	+	0.128666i	$0.958930\pi$
$150$		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	$-0.601604\pi$
$157$	7.96508	−	7.96508i	0.635682	−	0.635682i	0.949487	+	0.313805i	$0.101604\pi$
$158$	−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	−0.167722	−	0.985834i	$-0.553641\pi$
$163$	10.4450	−	10.4450i	0.818113	−	0.818113i	0.985834	+	0.167722i	$0.0536410\pi$
$164$	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	$-0.668358\pi$
$167$	4.63621	−	4.63621i	0.358761	−	0.358761i	0.863356	+	0.504595i	$0.168358\pi$
$168$		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	$-0.292657\pi$
$173$	−2.48531	−	2.48531i	−0.188954	−	0.188954i	−0.795244	+	0.606290i	$0.792657\pi$
$174$		0			0
$175$	0.675500	−	13.2115i	0.0510630	−	0.998695i
$176$	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	$-0.690430\pi$
$179$		−	22.1109i		−	1.65264i	0.563199	−	0.826321i	$-0.309570\pi$
$180$		0			0
$181$		−	8.48528i		−	0.630706i	−0.948974	−	0.315353i	$-0.897877\pi$
$181$		−	8.48528i		−	0.630706i	0.948974	−	0.315353i	$-0.102123\pi$
$182$	−0.442251	+	0.0104865i	−0.0327818	+	0.000777310i
$183$		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	−0.951204	−	0.308562i	$-0.900152\pi$
$193$	−8.92787	+	8.92787i	−0.642642	+	0.642642i	0.308562	+	0.951204i	$0.400152\pi$
$194$	−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	0.796323	−	0.604872i	$-0.206776\pi$
$197$	2.68715	+	2.68715i	0.191451	+	0.191451i	−0.604872	+	0.796323i	$0.706776\pi$
$198$		0			0
$199$	−0.616637			−0.0437122			−0.0218561	−	0.999761i	$-0.506958\pi$
$199$	−0.616637			−0.0437122			−0.0218561	+	0.999761i	$0.506958\pi$
$200$	3.53146	−	3.03911i	0.249712	−	0.214898i
$201$		0			0
$202$	1.05518	−	1.05518i	0.0742422	−	0.0742422i
$203$	9.65933	−	0.229039i	0.677952	−	0.0160754i
$204$		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
$217$	13.0616	−	0.309712i	0.886680	−	0.0210246i
$218$	−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	$-0.229562\pi$
$223$	1.35505	+	1.35505i	0.0907407	+	0.0907407i	−0.660279	+	0.751020i	$0.729562\pi$
$224$	−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	$-0.687538\pi$
$227$	4.15437	−	4.15437i	0.275735	−	0.275735i	0.831404	+	0.555668i	$0.187538\pi$
$228$		0			0
$229$	−12.9900			−0.858403			−0.429202	−	0.903209i	$-0.641205\pi$
$229$	−12.9900			−0.858403			−0.429202	+	0.903209i	$0.641205\pi$
$230$	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	0.0819485	−	0.996637i	$-0.473886\pi$
$233$	16.4639	−	16.4639i	1.07859	−	1.07859i	0.996637	−	0.0819485i	$-0.0261143\pi$
$234$		0			0
$235$	−0.707725	+	0.656678i	−0.0461669	+	0.0428370i
$236$		−	11.8782i		−	0.773203i
$237$		0			0
$238$	0.0351703	+	1.48325i	0.00227975	+	0.0961447i
$239$		−	5.48048i		−	0.354503i	−0.984166	−	0.177251i	$-0.943279\pi$
$239$		−	5.48048i		−	0.354503i	0.984166	−	0.177251i	$-0.0567205\pi$
$240$		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
$245$	−15.6517	+	0.156807i	−0.999950	+	0.0100180i
$246$		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	$-0.885968\pi$
$257$	−9.39248	+	9.39248i	−0.585887	+	0.585887i	0.350628	+	0.936515i	$0.385968\pi$
$258$		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	−0.998725	−	0.0504843i	$-0.983924\pi$
$263$	−15.3779	+	15.3779i	−0.948241	+	0.948241i	0.0504843	+	0.998725i	$0.483924\pi$
$264$		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	$-0.747135\pi$
$269$	−22.9851			−1.40143			−0.700714	+	0.713442i	$0.747135\pi$
$270$		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	0.836632	−	0.547765i	$-0.184521\pi$
$277$	4.80771	+	4.80771i	0.288867	+	0.288867i	−0.547765	+	0.836632i	$0.684521\pi$
$278$	0.0739121	+	0.0739121i	0.00443295	+	0.00443295i
$279$		0			0
$280$	−3.84438	−	3.95109i	−0.229745	−	0.236123i
$281$	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	$-0.465592\pi$
$283$	−14.9095	−	14.9095i	−0.886278	−	0.886278i	−0.994163	+	0.107885i	$0.965592\pi$
$284$			2.31935i			0.137628i
$285$		0			0
$286$			0.666471i			0.0394092i
$287$	20.1863	−	0.478650i	1.19156	−	0.0282538i
$288$		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	$-0.186565\pi$
$293$	4.79236	+	4.79236i	0.279973	+	0.279973i	−0.553125	+	0.833098i	$0.686565\pi$
$294$		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	$-0.880136\pi$
$307$	−9.85063	+	9.85063i	−0.562205	+	0.562205i	0.367728	+	0.929933i	$0.380136\pi$
$308$	20.4977	−	0.486033i	1.16796	−	0.0276943i
$309$		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	−0.998883	−	0.0472492i	$-0.984955\pi$
$313$	−18.5080	−	18.5080i	−1.04613	−	1.04613i	−0.0472492	−	0.998883i	$-0.515045\pi$
$314$	2.66123			0.150182
$315$		0			0
$316$	16.7983			0.944977
$317$	21.8793	+	21.8793i	1.22887	+	1.22887i	0.964393	+	0.264473i	$0.0851980\pi$
$317$	21.8793	+	21.8793i	1.22887	+	1.22887i	0.264473	+	0.964393i	$0.414802\pi$
$318$		0			0
$319$		−	14.5566i		−	0.815013i
$320$	−0.559409	+	14.9520i	−0.0312719	+	0.835842i
$321$		0			0
$322$	−0.108127	−	4.56010i	−0.00602570	−	0.254124i
$323$	−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	0.772903	−	0.634525i	$-0.218804\pi$
$337$	2.54028	+	2.54028i	0.138378	+	0.138378i	−0.634525	+	0.772903i	$0.718804\pi$
$338$	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
$343$	1.31608	+	18.4734i	0.0710617	+	0.997472i
$344$		−	4.81248i		−	0.259472i
$345$		0			0
$346$		−	0.830370i		−	0.0446410i
$347$	−13.6980	−	13.6980i	−0.735348	−	0.735348i	0.236326	−	0.971674i	$-0.424057\pi$
$347$	−13.6980	−	13.6980i	−0.735348	−	0.735348i	−0.971674	+	0.236326i	$0.924057\pi$
$348$		0			0
$349$	−0.508601			−0.0272248			−0.0136124	−	0.999907i	$-0.504333\pi$
$349$	−0.508601			−0.0272248			−0.0136124	+	0.999907i	$0.504333\pi$
$350$	2.31990	−	2.09421i	0.124004	−	0.111940i
$351$		0			0
$352$	7.69540	+	7.69540i	0.410166	+	0.410166i
$353$	10.9217	+	10.9217i	0.581305	+	0.581305i	0.935262	−	0.353957i	$-0.115164\pi$
$353$	10.9217	+	10.9217i	0.581305	+	0.581305i	−0.353957	+	0.935262i	$0.615164\pi$
$354$		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	$0.138621\pi$
$359$			15.9860i			0.843710i	−0.906663	+	0.421855i	$0.861379\pi$
$360$		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	$-0.754818\pi$
$367$	−0.410036	+	0.410036i	−0.0214037	+	0.0214037i	0.696324	+	0.717728i	$0.254818\pi$
$368$	−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	−0.790646	−	0.612273i	$-0.790255\pi$
$373$	−3.44496	+	3.44496i	−0.178373	+	0.178373i	0.612273	+	0.790646i	$0.290255\pi$
$374$	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	$-0.892353\pi$
$379$		−	12.9179i		−	0.663547i	0.943359	−	0.331773i	$-0.107647\pi$
$380$	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	$-0.368622\pi$
$383$	−10.0770	−	10.0770i	−0.514910	−	0.514910i	−0.916027	+	0.401117i	$0.868622\pi$
$384$		0			0
$385$	−0.322799	+	23.5794i	−0.0164514	+	1.20172i
$386$	−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	$-0.788433\pi$
$389$		−	24.3300i		−	1.23358i	0.787127	−	0.616791i	$-0.211567\pi$
$390$		0			0
$391$			17.3213i			0.875976i
$392$	−4.38850	+	4.82572i	−0.221653	+	0.243736i
$393$		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	$-0.827655\pi$
$397$	−6.80633	+	6.80633i	−0.341600	+	0.341600i	0.515369	+	0.856969i	$0.327655\pi$
$398$	−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	$-0.305568\pi$
$409$	23.1985			1.14709			0.573546	+	0.819174i	$0.305568\pi$
$410$	−2.95545	+	2.74228i	−0.145959	+	0.135432i
$411$		0			0
$412$	24.3819	−	24.3819i	1.20121	−	1.20121i
$413$	−0.383178	−	16.1599i	−0.0188550	−	0.795178i
$414$		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	$-0.396819\pi$
$419$	13.0393			0.637009			0.318505	+	0.947921i	$0.396819\pi$
$420$		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
$427$	18.8072	−	0.445951i	0.910146	−	0.0215811i
$428$	−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	$-0.0126730\pi$
$433$	19.9639	+	19.9639i	0.959405	+	0.959405i	−0.0398028	+	0.999208i	$0.512673\pi$
$434$	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	$-0.756110\pi$
$439$	−30.1943			−1.44110			−0.720548	+	0.693405i	$0.756110\pi$
$440$	−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	−0.336337	−	0.941742i	$-0.609188\pi$
$443$	12.7423	−	12.7423i	0.605404	−	0.605404i	0.941742	+	0.336337i	$0.109188\pi$
$444$		0			0
$445$	17.4868	+	0.654245i	0.828954	+	0.0310142i
$446$			0.452737i			0.0214377i
$447$		0			0
$448$	17.6988	−	0.419669i	0.836191	−	0.0198275i
$449$		−	30.4170i		−	1.43547i	−0.696318	−	0.717734i	$-0.745180\pi$
$449$		−	30.4170i		−	1.43547i	0.696318	−	0.717734i	$-0.254820\pi$
$450$		0			0
$451$		−	30.4207i		−	1.43245i
$452$	−6.60347	−	6.60347i	−0.310601	−	0.310601i
$453$		0			0
$454$	1.38802			0.0651432
$455$	−3.00088	+	2.91982i	−0.140683	+	0.136883i
$456$		0			0
$457$	1.31546	+	1.31546i	0.0615348	+	0.0615348i	0.737204	−	0.675670i	$-0.236145\pi$
$457$	1.31546	+	1.31546i	0.0615348	+	0.0615348i	−0.675670	+	0.737204i	$0.736145\pi$
$458$	−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	−0.209809	−	0.977742i	$-0.567284\pi$
$463$	16.5240	−	16.5240i	0.767934	−	0.767934i	0.977742	+	0.209809i	$0.0672841\pi$
$464$		−	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	$-0.521521\pi$
$467$	20.1009	−	20.1009i	0.930157	−	0.930157i	0.997715	+	0.0675588i	$0.0215210\pi$
$468$		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	$-0.581487\pi$
$479$	−11.0836			−0.506425			−0.253212	+	0.967411i	$0.581487\pi$
$480$		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	0.326552	−	0.945179i	$-0.394113\pi$
$487$	−13.6519	−	13.6519i	−0.618627	−	0.618627i	−0.945179	+	0.326552i	$0.894113\pi$
$488$	4.68508	+	4.68508i	0.212084	+	0.212084i
$489$		0			0
$490$	−2.64090	−	2.58851i	−0.119304	−	0.116937i
$491$	−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
$497$	0.0748201	+	3.15541i	0.00335614	+	0.141540i
$498$		0			0
$499$			4.27431i			0.191344i	0.995413	+	0.0956722i	$0.0305000\pi$
$499$			4.27431i			0.191344i	−0.995413	+	0.0956722i	$0.969500\pi$
$500$	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	$-0.0631943\pi$
$503$	17.5637	+	17.5637i	0.783128	+	0.783128i	−0.197229	+	0.980357i	$0.563194\pi$
$504$		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	$-0.712333\pi$
$509$	−27.9162			−1.23736			−0.618682	+	0.785641i	$0.712333\pi$
$510$		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
$518$	0.258291	−	0.00612451i	0.0113487	−	0.000269096i
$519$		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	$-0.215019\pi$
$523$	3.54707	+	3.54707i	0.155103	+	0.155103i	−0.625290	+	0.780392i	$0.715019\pi$
$524$	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
$532$	−37.1203	+	0.880184i	−1.60937	+	0.0381608i
$533$	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	0.972121	+	0.234482i	$0.0753392\pi$
$547$	28.2200	+	28.2200i	1.20660	+	1.20660i	0.234482	+	0.972121i	$0.424661\pi$
$548$	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
$553$	22.8536	−	0.541896i	0.971833	−	0.0230438i
$554$			1.60631i			0.0682457i
$555$		0			0
$556$		−	0.860184i		−	0.0364799i
$557$	−28.1616	−	28.1616i	−1.19325	−	1.19325i	−0.976150	−	0.217096i	$-0.930342\pi$
$557$	−28.1616	−	28.1616i	−1.19325	−	1.19325i	−0.217096	−	0.976150i	$-0.569658\pi$
$558$		0			0
$559$	−3.65510			−0.154594
$560$	−0.297063	+	21.6995i	−0.0125532	+	0.916970i
$561$		0			0
$562$	1.61319	+	1.61319i	0.0680482	+	0.0680482i
$563$	−27.3645	−	27.3645i	−1.15328	−	1.15328i	−0.985891	−	0.167386i	$-0.946467\pi$
$563$	−27.3645	−	27.3645i	−1.15328	−	1.15328i	−0.167386	−	0.985891i	$-0.553533\pi$
$564$		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	$0.121540\pi$
$569$			17.7767i			0.745240i	−0.927984	+	0.372620i	$0.878460\pi$
$570$		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	$-0.786594\pi$
$577$	−3.89677	+	3.89677i	−0.162225	+	0.162225i	0.621327	+	0.783552i	$0.286594\pi$
$578$	−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	$-0.895330\pi$
$587$	−15.1058	+	15.1058i	−0.623484	+	0.623484i	0.322937	+	0.946420i	$0.395330\pi$
$588$		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	$-0.281759\pi$
$593$	−3.43032	−	3.43032i	−0.140866	−	0.140866i	−0.774023	+	0.633157i	$0.781759\pi$
$594$		0			0
$595$	9.79269	+	10.0645i	0.401461	+	0.412605i
$596$	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	$-0.933839\pi$
$599$		−	10.1010i		−	0.412714i	0.978477	−	0.206357i	$-0.0661608\pi$
$600$		0			0
$601$			38.4063i			1.56663i	0.621628	+	0.783313i	$0.286472\pi$
$601$			38.4063i			1.56663i	−0.621628	+	0.783313i	$0.713528\pi$
$602$	−0.0765245	−	3.22730i	−0.00311891	−	0.131535i
$603$		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	$-0.845459\pi$
$607$	−10.2931	+	10.2931i	−0.417783	+	0.417783i	0.466656	+	0.884439i	$0.345459\pi$
$608$	−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	−0.935517	−	0.353282i	$-0.885066\pi$
$613$	−14.4155	+	14.4155i	−0.582235	+	0.582235i	0.353282	+	0.935517i	$0.385066\pi$
$614$	−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	0.999721	+	0.0236346i	$0.00752382\pi$
$617$	25.4196	+	25.4196i	1.02336	+	1.02336i	0.0236346	+	0.999721i	$0.492476\pi$
$618$		0			0
$619$	11.1991			0.450129			0.225064	−	0.974344i	$-0.427741\pi$
$619$	11.1991			0.450129			0.225064	+	0.974344i	$0.427741\pi$
$620$	21.4530	+	0.802636i	0.861574	+	0.0322346i
$621$		0			0
$622$	4.56168	−	4.56168i	0.182907	−	0.182907i
$623$	−0.490815	−	20.6993i	−0.0196641	−	0.829301i
$624$		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
$637$	3.66516	+	3.33309i	0.145219	+	0.132062i
$638$	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	$-0.351866\pi$
$643$	−11.2813	−	11.2813i	−0.444891	−	0.444891i	−0.893652	+	0.448761i	$0.851866\pi$
$644$	−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	−0.0320982	+	0.999485i	$0.510219\pi$
$647$	−26.2395	+	26.2395i	−1.03158	+	1.03158i	−0.999485	+	0.0320982i	$0.989781\pi$
$648$		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	−0.667377	−	0.744720i	$-0.732583\pi$
$653$	1.97641	−	1.97641i	0.0773427	−	0.0773427i	0.744720	+	0.667377i	$0.232583\pi$
$654$		0			0
$655$	−1.57291	+	42.0410i	−0.0614585	+	1.64268i
$656$		−	27.9953i		−	1.09303i
$657$		0			0
$658$	0.00639752	+	0.269805i	0.000249401	+	0.0105181i
$659$			15.1044i			0.588385i	0.955746	+	0.294193i	$0.0950507\pi$
$659$			15.1044i			0.588385i	−0.955746	+	0.294193i	$0.904949\pi$
$660$		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
$665$	0.584574	−	42.7012i	0.0226688	−	1.65588i
$666$		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	−0.892316	−	0.451411i	$-0.850921\pi$
$673$	−11.4381	+	11.4381i	−0.440906	+	0.440906i	0.451411	+	0.892316i	$0.350921\pi$
$674$			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	$-0.983087\pi$
$677$	−24.6007	+	24.6007i	−0.945481	+	0.945481i	0.0531077	+	0.998589i	$0.483087\pi$
$678$		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	−0.390191	−	0.920734i	$-0.627591\pi$
$683$	13.8654	−	13.8654i	0.530543	−	0.530543i	0.920734	+	0.390191i	$0.127591\pi$
$684$		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
$700$	−25.6856	−	1.31330i	−0.970824	−	0.0496380i
$701$	−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
$707$	−16.7067	+	0.396144i	−0.628322	+	0.0148985i
$708$		0			0
$709$		−	48.5284i		−	1.82252i	−0.411827	−	0.911262i	$-0.635109\pi$
$709$		−	48.5284i		−	1.82252i	0.411827	−	0.911262i	$-0.364891\pi$
$710$	−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	$-0.197962\pi$
$719$	43.5872			1.62553			0.812764	+	0.582593i	$0.197962\pi$
$720$		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	$-0.838363\pi$
$727$	−10.4498	+	10.4498i	−0.387563	+	0.387563i	0.486254	+	0.873817i	$0.338363\pi$
$728$	0.0413607	+	1.74432i	0.00153293	+	0.0646487i
$729$		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	$-0.414029\pi$
$733$	−18.8687	−	18.8687i	−0.696933	−	0.696933i	−0.963748	+	0.266815i	$0.914029\pi$
$734$	−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	$0.126032\pi$
$739$			20.9689i			0.771354i	−0.922634	+	0.385677i	$0.873968\pi$
$740$	1.31723	−	1.22222i	0.0484224	−	0.0449297i
$741$		0			0
$742$	0.113082	+	4.76906i	0.00415138	+	0.175078i
$743$	−9.18724	+	9.18724i	−0.337047	+	0.337047i	−0.855255	−	0.518208i	$-0.826599\pi$
$743$	−9.18724	+	9.18724i	−0.337047	+	0.337047i	0.518208	+	0.855255i	$0.326599\pi$
$744$		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	0.407031	−	0.913414i	$-0.366564\pi$
$757$	−13.9324	−	13.9324i	−0.506383	−	0.506383i	−0.913414	+	0.407031i	$0.866564\pi$
$758$	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
$763$	1.76746	−	0.0419093i	0.0639862	−	0.00151722i
$764$			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	$-0.435168\pi$
$769$	11.2183			0.404543			0.202271	+	0.979330i	$0.435168\pi$
$770$	−3.99300	+	3.88515i	−0.143898	+	0.140011i
$771$		0			0
$772$	17.3574	+	17.3574i	0.624708	+	0.624708i
$773$	21.5065	+	21.5065i	0.773535	+	0.773535i	0.978723	−	0.205188i	$-0.0657806\pi$
$773$	21.5065	+	21.5065i	0.773535	+	0.773535i	−0.205188	+	0.978723i	$0.565781\pi$
$774$		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	−0.435262	+	0.900304i	$0.643344\pi$
$787$	−37.4673	+	37.4673i	−1.33557	+	1.33557i	−0.900304	+	0.435262i	$0.856656\pi$
$788$	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	$-0.694195\pi$
$797$	6.96365	−	6.96365i	0.246665	−	0.246665i	0.819601	+	0.572935i	$0.194195\pi$
$798$		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
$805$	−30.1066	−	30.9424i	−1.06112	−	1.09058i
$806$	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	$0.266387\pi$
$809$			42.2409i			1.48511i	−0.669784	+	0.742556i	$0.733613\pi$
$810$		0			0
$811$			34.9480i			1.22719i	0.789620	+	0.613596i	$0.210277\pi$
$811$			34.9480i			1.22719i	−0.789620	+	0.613596i	$0.789723\pi$
$812$	−0.445293	−	18.7795i	−0.0156267	−	0.659032i
$813$		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	−0.799752	−	0.600330i	$-0.795036\pi$
$823$	−5.72102	+	5.72102i	−0.199422	+	0.199422i	0.600330	+	0.799752i	$0.295036\pi$
$824$	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	0.345193	−	0.938532i	$-0.387813\pi$
$827$	−17.0630	−	17.0630i	−0.593339	−	0.593339i	−0.938532	+	0.345193i	$0.887813\pi$
$828$		0			0
$829$	37.7146			1.30988			0.654940	−	0.755680i	$-0.272694\pi$
$829$	37.7146			1.30988			0.654940	+	0.755680i	$0.272694\pi$
$830$	0.334892	−	8.95106i	0.0116243	−	0.310696i
$831$		0			0
$832$	3.34863	−	3.34863i	0.116093	−	0.116093i
$833$	11.1787	−	12.2924i	0.387320	−	0.425908i
$834$		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	$-0.373834\pi$
$839$	22.3652			0.772133			0.386066	+	0.922471i	$0.373834\pi$
$840$		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
$847$	−0.306586	−	12.9298i	−0.0105344	−	0.444272i
$848$	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	$-0.448572\pi$
$853$	−24.1276	−	24.1276i	−0.826114	−	0.826114i	−0.986977	+	0.160863i	$0.948572\pi$
$854$	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	$-0.761774\pi$
$857$	−1.53096	+	1.53096i	−0.0522968	+	0.0522968i	0.680475	+	0.732772i	$0.261774\pi$
$858$		0			0
$859$	41.8095			1.42652			0.713261	−	0.700899i	$-0.247218\pi$
$859$	41.8095			1.42652			0.713261	+	0.700899i	$0.247218\pi$
$860$	−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	−0.425968	−	0.904738i	$-0.640067\pi$
$863$	14.0647	−	14.0647i	0.478770	−	0.478770i	0.904738	+	0.425968i	$0.140067\pi$
$864$		0			0
$865$	−5.34566	−	5.76121i	−0.181758	−	0.195887i
$866$			6.67018i			0.226662i
$867$		0			0
$868$	−0.602138	−	25.3942i	−0.0204379	−	0.861935i
$869$		−	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
$875$	2.61390	−	29.4647i	0.0883660	−	0.996088i
$876$		0			0
$877$	−39.3844	−	39.3844i	−1.32992	−	1.32992i	−0.905438	−	0.424477i	$-0.860458\pi$
$877$	−39.3844	−	39.3844i	−1.32992	−	1.32992i	−0.424477	−	0.905438i	$-0.639542\pi$
$878$	−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	−0.989450	−	0.144876i	$-0.953722\pi$
$883$	−25.0968	+	25.0968i	−0.844574	+	0.844574i	0.144876	+	0.989450i	$0.453722\pi$
$884$		−	3.26597i		−	0.109846i
$885$		0			0
$886$	4.25735			0.143028
$887$	−37.8947	+	37.8947i	−1.27238	+	1.27238i	−0.327541	+	0.944837i	$0.606220\pi$
$887$	−37.8947	+	37.8947i	−1.27238	+	1.27238i	−0.944837	+	0.327541i	$0.893780\pi$
$888$		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	−0.999871	−	0.0160555i	$-0.994889\pi$
$907$	−30.5961	−	30.5961i	−1.01593	−	1.01593i	−0.0160555	−	0.999871i	$-0.505111\pi$
$908$	−8.07687	−	8.07687i	−0.268040	−	0.268040i
$909$		0			0
$910$	−0.989088	−	0.0135405i	−0.0327879	−	0.000448862i
$911$	−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
$917$	49.7643	−	1.17999i	1.64336	−	0.0389669i
$918$		0			0
$919$			47.6045i			1.57033i	0.619288	+	0.785164i	$0.287421\pi$
$919$			47.6045i			1.57033i	−0.619288	+	0.785164i	$0.712579\pi$
$920$	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	$-0.267623\pi$
$929$	40.6532			1.33379			0.666895	+	0.745152i	$0.267623\pi$
$930$		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	$-0.688890\pi$
$937$	8.25994	−	8.25994i	0.269841	−	0.269841i	0.829036	+	0.559195i	$0.188890\pi$
$938$	0.834403	−	0.0197851i	0.0272442	−	0.000646005i
$939$		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	0.634328	−	0.773064i	$-0.281277\pi$
$947$	−4.26936	−	4.26936i	−0.138736	−	0.138736i	−0.773064	+	0.634328i	$0.781277\pi$
$948$		0			0
$949$			1.38419i			0.0449327i
$950$	5.56207	+	6.46315i	0.180457	+	0.209692i
$951$		0			0
$952$	5.85020	−	0.138718i	0.189606	−	0.00449588i
$953$	−31.8382	+	31.8382i	−1.03134	+	1.03134i	−0.0318472	+	0.999493i	$0.510139\pi$
$953$	−31.8382	+	31.8382i	−1.03134	+	1.03134i	−0.999493	+	0.0318472i	$0.989861\pi$
$954$		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	0.366134	−	0.930562i	$-0.380681\pi$
$967$	−17.5518	−	17.5518i	−0.564429	−	0.564429i	−0.930562	+	0.366134i	$0.880681\pi$
$968$	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
$973$	−0.0277487	−	1.17026i	−0.000889582	−	0.0375167i
$974$		−	4.56126i		−	0.146152i
$975$		0			0
$976$		−	26.0828i		−	0.834889i
$977$	−5.19792	−	5.19792i	−0.166296	−	0.166296i	0.619053	−	0.785349i	$-0.287517\pi$
$977$	−5.19792	−	5.19792i	−0.166296	−	0.166296i	−0.785349	+	0.619053i	$0.787517\pi$
$978$		0			0
$979$	−31.1938			−0.996959
$980$	0.304862	+	30.4298i	0.00973845	+	0.972044i
$981$		0			0
$982$	−5.36509	−	5.36509i	−0.171207	−	0.171207i
$983$	−30.3939	−	30.3939i	−0.969415	−	0.969415i	0.0301305	−	0.999546i	$-0.490408\pi$
$983$	−30.3939	−	30.3939i	−0.969415	−	0.969415i	−0.999546	+	0.0301305i	$0.990408\pi$
$984$		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	$-0.592690\pi$
$997$	21.1809	−	21.1809i	0.670805	−	0.670805i	0.957902	+	0.287097i	$0.0926901\pi$
$998$	−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.307.6		16
3.2	odd	2		105.2.m.a.97.3	yes	16
5.3	odd	4	inner	315.2.p.e.118.5		16
7.6	odd	2	inner	315.2.p.e.307.5		16
12.11	even	2		1680.2.cz.d.97.5		16
15.2	even	4		525.2.m.b.118.5		16
15.8	even	4		105.2.m.a.13.4	yes	16
15.14	odd	2		525.2.m.b.307.6		16
21.2	odd	6		735.2.v.a.472.4		32
21.5	even	6		735.2.v.a.472.3		32
21.11	odd	6		735.2.v.a.607.5		32
21.17	even	6		735.2.v.a.607.6		32
21.20	even	2		105.2.m.a.97.4	yes	16
35.13	even	4	inner	315.2.p.e.118.6		16
60.23	odd	4		1680.2.cz.d.433.4		16
84.83	odd	2		1680.2.cz.d.97.4		16
105.23	even	12		735.2.v.a.178.6		32
105.38	odd	12		735.2.v.a.313.4		32
105.53	even	12		735.2.v.a.313.3		32
105.62	odd	4		525.2.m.b.118.6		16
105.68	odd	12		735.2.v.a.178.5		32
105.83	odd	4		105.2.m.a.13.3	✓	16
105.104	even	2		525.2.m.b.307.5		16
420.83	even	4		1680.2.cz.d.433.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.3	✓	16	105.83	odd	4
105.2.m.a.13.4	yes	16	15.8	even	4
105.2.m.a.97.3	yes	16	3.2	odd	2
105.2.m.a.97.4	yes	16	21.20	even	2
315.2.p.e.118.5		16	5.3	odd	4	inner
315.2.p.e.118.6		16	35.13	even	4	inner
315.2.p.e.307.5		16	7.6	odd	2	inner
315.2.p.e.307.6		16	1.1	even	1	trivial
525.2.m.b.118.5		16	15.2	even	4
525.2.m.b.118.6		16	105.62	odd	4
525.2.m.b.307.5		16	105.104	even	2
525.2.m.b.307.6		16	15.14	odd	2
735.2.v.a.178.5		32	105.68	odd	12
735.2.v.a.178.6		32	105.23	even	12
735.2.v.a.313.3		32	105.53	even	12
735.2.v.a.313.4		32	105.38	odd	12
735.2.v.a.472.3		32	21.5	even	6
735.2.v.a.472.4		32	21.2	odd	6
735.2.v.a.607.5		32	21.11	odd	6
735.2.v.a.607.6		32	21.17	even	6
1680.2.cz.d.97.4		16	84.83	odd	2
1680.2.cz.d.97.5		16	12.11	even	2
1680.2.cz.d.433.4		16	60.23	odd	4
1680.2.cz.d.433.5		16	420.83	even	4

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)

\(f(q)\)	\(=\)	\(q+(0.167056 + 0.167056i) q^{2} -1.94418i q^{4} +(2.23450 + 0.0836010i) q^{5} +(-0.0627175 - 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +O(q^{10})\)	\(q+(0.167056 + 0.167056i) q^{2} -1.94418i q^{4} +(2.23450 + 0.0836010i) q^{5} +(-0.0627175 - 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +(0.359321 + 0.387253i) q^{10} -3.98602 q^{11} +(-0.500437 - 0.500437i) q^{13} +(0.431387 - 0.452341i) q^{14} -3.66822 q^{16} +(-1.67840 + 1.67840i) q^{17} +7.21850 q^{19} +(0.162536 - 4.34429i) q^{20} +(-0.665888 - 0.665888i) q^{22} +(5.16007 - 5.16007i) q^{23} +(4.98602 + 0.373614i) q^{25} -0.167202i q^{26} +(-5.14238 + 0.121934i) q^{28} +3.65191i q^{29} +4.93821i q^{31} +(-1.93060 - 1.93060i) q^{32} -0.560773 q^{34} +(0.0809828 - 5.91553i) q^{35} +(0.292275 + 0.292275i) q^{37} +(1.20589 + 1.20589i) q^{38} +(1.52740 - 1.41723i) q^{40} +7.63184i q^{41} +(3.65191 - 3.65191i) q^{43} +7.74956i q^{44} +1.72404 q^{46} +(-0.305303 + 0.305303i) q^{47} +(-6.99213 + 0.331777i) q^{49} +(0.770530 + 0.895358i) q^{50} +(-0.972943 + 0.972943i) q^{52} +(-5.39653 + 5.39653i) q^{53} +(-8.90678 - 0.333235i) q^{55} +(-1.78412 - 1.70147i) q^{56} +(-0.610073 + 0.610073i) q^{58} +6.10959 q^{59} +7.11047i q^{61} +(-0.824957 + 0.824957i) q^{62} +6.69141i q^{64} +(-1.07639 - 1.16007i) q^{65} +(0.944185 + 0.944185i) q^{67} +(3.26312 + 3.26312i) q^{68} +(1.00175 - 0.974695i) q^{70} -1.19297 q^{71} +(-1.38298 - 1.38298i) q^{73} +0.0976524i q^{74} -14.0341i q^{76} +(0.249993 + 10.5431i) q^{77} +8.64027i q^{79} +(-8.19666 - 0.306667i) q^{80} +(-1.27494 + 1.27494i) q^{82} +(-11.9895 - 11.9895i) q^{83} +(-3.89070 + 3.61007i) q^{85} +1.22015 q^{86} +(-2.62639 + 2.62639i) q^{88} +7.82581 q^{89} +(-1.29227 + 1.35505i) q^{91} +(-10.0321 - 10.0321i) q^{92} -0.102005 q^{94} +(16.1298 + 0.603474i) q^{95} +(-7.43671 + 7.43671i) q^{97} +(-1.22350 - 1.11265i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{7} - 24 q^{8}+O(q^{10}) \) 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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