LMFDB - Embedded newform 525.2.m.b.307.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(118,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.118");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.m (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:	$4.19214610612$
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	$\chi$	$=$	525.307
Dual form			525.2.m.b.118.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.167056 + 0.167056i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.94418i q^{4} +0.236253i q^{6} +(0.0627175 + 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(0.167056 + 0.167056i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.94418i q^{4} +0.236253i q^{6} +(0.0627175 + 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +1.00000i q^{9} +3.98602 q^{11} +(1.37475 - 1.37475i) q^{12} +(0.500437 + 0.500437i) q^{13} +(-0.431387 + 0.452341i) q^{14} -3.66822 q^{16} +(-1.67840 + 1.67840i) q^{17} +(-0.167056 + 0.167056i) q^{18} +7.21850 q^{19} +(-1.82596 + 1.91465i) q^{21} +(0.665888 + 0.665888i) q^{22} +(5.16007 - 5.16007i) q^{23} +0.931824 q^{24} +0.167202i q^{26} +(-0.707107 + 0.707107i) q^{27} +(5.14238 - 0.121934i) q^{28} -3.65191i q^{29} +4.93821i q^{31} +(-1.93060 - 1.93060i) q^{32} +(2.81854 + 2.81854i) q^{33} -0.560773 q^{34} +1.94418 q^{36} +(-0.292275 - 0.292275i) q^{37} +(1.20589 + 1.20589i) q^{38} +0.707725i q^{39} -7.63184i q^{41} +(-0.624890 + 0.0148172i) q^{42} +(-3.65191 + 3.65191i) q^{43} -7.74956i q^{44} +1.72404 q^{46} +(-0.305303 + 0.305303i) q^{47} +(-2.59383 - 2.59383i) q^{48} +(-6.99213 + 0.331777i) q^{49} -2.37361 q^{51} +(0.972943 - 0.972943i) q^{52} +(-5.39653 + 5.39653i) q^{53} -0.236253 q^{54} +(1.78412 + 1.70147i) q^{56} +(5.10425 + 5.10425i) q^{57} +(0.610073 - 0.610073i) q^{58} -6.10959 q^{59} +7.11047i q^{61} +(-0.824957 + 0.824957i) q^{62} +(-2.64501 + 0.0627175i) q^{63} +6.69141i q^{64} +0.941708i q^{66} +(-0.944185 - 0.944185i) q^{67} +(3.26312 + 3.26312i) q^{68} +7.29744 q^{69} +1.19297 q^{71} +(0.658899 + 0.658899i) q^{72} +(1.38298 + 1.38298i) q^{73} -0.0976524i q^{74} -14.0341i q^{76} +(0.249993 + 10.5431i) q^{77} +(-0.118230 + 0.118230i) q^{78} +8.64027i q^{79} -1.00000 q^{81} +(1.27494 - 1.27494i) q^{82} +(-11.9895 - 11.9895i) q^{83} +(3.72244 + 3.54999i) q^{84} -1.22015 q^{86} +(2.58229 - 2.58229i) q^{87} +(2.62639 - 2.62639i) q^{88} -7.82581 q^{89} +(-1.29227 + 1.35505i) q^{91} +(-10.0321 - 10.0321i) q^{92} +(-3.49184 + 3.49184i) q^{93} -0.102005 q^{94} -2.73028i q^{96} +(7.43671 - 7.43671i) q^{97} +(-1.22350 - 1.11265i) q^{98} +3.98602i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) $ 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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	$0.723381\pi$
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.94418i		−	0.972092i
$5$		0			0
$5$		0			0
$6$			0.236253i			0.0964497i
$7$	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
$9$			1.00000i			0.333333i
$10$		0			0
$11$	3.98602			1.20183			0.600915	−	0.799313i	$-0.294803\pi$
$11$	3.98602			1.20183			0.600915	+	0.799313i	$0.294803\pi$
$12$	1.37475	−	1.37475i	0.396855	−	0.396855i
$13$	0.500437	+	0.500437i	0.138796	+	0.138796i	0.773091	−	0.634295i	$-0.218709\pi$
$13$	0.500437	+	0.500437i	0.138796	+	0.138796i	−0.634295	+	0.773091i	$0.718709\pi$
$14$	−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	$0.342938\pi$
$18$	−0.167056	+	0.167056i	−0.0393754	+	0.0393754i
$19$	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			0
$21$	−1.82596	+	1.91465i	−0.398456	+	0.417811i
$22$	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	$-0.0251983\pi$
$24$	0.931824			0.190208
$25$		0			0
$26$			0.167202i			0.0327910i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	5.14238	−	0.121934i	0.971819	−	0.0230434i
$29$		−	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
$33$	2.81854	+	2.81854i	0.490645	+	0.490645i
$34$	−0.560773			−0.0961717
$35$		0			0
$36$	1.94418			0.324031
$37$	−0.292275	−	0.292275i	−0.0480497	−	0.0480497i	0.682674	−	0.730723i	$-0.260817\pi$
$37$	−0.292275	−	0.292275i	−0.0480497	−	0.0480497i	−0.730723	+	0.682674i	$0.760817\pi$
$38$	1.20589	+	1.20589i	0.195622	+	0.195622i
$39$			0.707725i			0.113327i
$40$		0			0
$41$		−	7.63184i		−	1.19189i	−0.803024	−	0.595947i	$-0.796777\pi$
$41$		−	7.63184i		−	1.19189i	0.803024	−	0.595947i	$-0.203223\pi$
$42$	−0.624890	+	0.0148172i	−0.0964226	+	0.00228634i
$43$	−3.65191	+	3.65191i	−0.556911	+	0.556911i	−0.928427	−	0.371516i	$-0.878838\pi$
$43$	−3.65191	+	3.65191i	−0.556911	+	0.556911i	0.371516	+	0.928427i	$0.378838\pi$
$44$		−	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	$0.260025\pi$
$48$	−2.59383	−	2.59383i	−0.374386	−	0.374386i
$49$	−6.99213	+	0.331777i	−0.998876	+	0.0473967i
$50$		0			0
$51$	−2.37361			−0.332372
$52$	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	$0.425619\pi$
$54$	−0.236253			−0.0321499
$55$		0			0
$56$	1.78412	+	1.70147i	0.238413	+	0.227368i
$57$	5.10425	+	5.10425i	0.676075	+	0.676075i
$58$	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
$63$	−2.64501	+	0.0627175i	−0.333240	+	0.00790166i
$64$			6.69141i			0.836426i
$65$		0			0
$66$			0.941708i			0.115916i
$67$	−0.944185	−	0.944185i	−0.115351	−	0.115351i	0.647075	−	0.762426i	$-0.275992\pi$
$67$	−0.944185	−	0.944185i	−0.115351	−	0.115351i	−0.762426	+	0.647075i	$0.775992\pi$
$68$	3.26312	+	3.26312i	0.395711	+	0.395711i
$69$	7.29744			0.878508
$70$		0			0
$71$	1.19297			0.141579			0.0707897	−	0.997491i	$-0.477448\pi$
$71$	1.19297			0.141579			0.0707897	+	0.997491i	$0.477448\pi$
$72$	0.658899	+	0.658899i	0.0776520	+	0.0776520i
$73$	1.38298	+	1.38298i	0.161865	+	0.161865i	0.783393	−	0.621527i	$-0.213487\pi$
$73$	1.38298	+	1.38298i	0.161865	+	0.161865i	−0.621527	+	0.783393i	$0.713487\pi$
$74$		−	0.0976524i		−	0.0113519i
$75$		0			0
$76$		−	14.0341i		−	1.60982i
$77$	0.249993	+	10.5431i	0.0284894	+	1.20149i
$78$	−0.118230	+	0.118230i	−0.0133869	+	0.0133869i
$79$			8.64027i			0.972106i	0.873929	+	0.486053i	$0.161564\pi$
$79$			8.64027i			0.972106i	−0.873929	+	0.486053i	$0.838436\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$	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	$-0.630685\pi$
$84$	3.72244	+	3.54999i	0.406151	+	0.387336i
$85$		0			0
$86$	−1.22015			−0.131572
$87$	2.58229	−	2.58229i	0.276851	−	0.276851i
$88$	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
$93$	−3.49184	+	3.49184i	−0.362087	+	0.362087i
$94$	−0.102005			−0.0105211
$95$		0			0
$96$		−	2.73028i		−	0.278658i
$97$	7.43671	−	7.43671i	0.755083	−	0.755083i	−0.220340	−	0.975423i	$-0.570717\pi$
$97$	7.43671	−	7.43671i	0.755083	−	0.755083i	0.975423	+	0.220340i	$0.0707167\pi$
$98$	−1.22350	−	1.11265i	−0.123592	−	0.112395i
$99$			3.98602i			0.400610i
$100$		0			0
$101$			6.31633i			0.628498i	0.949341	+	0.314249i	$0.101753\pi$
$101$			6.31633i			0.628498i	−0.949341	+	0.314249i	$0.898247\pi$
$102$	−0.396526	−	0.396526i	−0.0392619	−	0.0392619i
$103$	−12.5410	−	12.5410i	−1.23570	−	1.23570i	−0.961743	−	0.273954i	$-0.911668\pi$
$103$	−12.5410	−	12.5410i	−1.23570	−	1.23570i	−0.273954	−	0.961743i	$-0.588332\pi$
$104$	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	$0.920849\pi$
$108$	1.37475	+	1.37475i	0.132285	+	0.132285i
$109$			0.668223i			0.0640042i	0.999488	+	0.0320021i	$0.0101883\pi$
$109$			0.668223i			0.0640042i	−0.999488	+	0.0320021i	$0.989812\pi$
$110$		0			0
$111$		−	0.413339i		−	0.0392324i
$112$	−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	$0.177457\pi$
$114$			1.70539i			0.159724i
$115$		0			0
$116$	−7.09999			−0.659217
$117$	−0.500437	+	0.500437i	−0.0462655	+	0.0462655i
$118$	−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
$123$	5.39653	−	5.39653i	0.486588	−	0.486588i
$124$	9.60080			0.862177
$125$		0			0
$126$	−0.452341	−	0.431387i	−0.0402978	−	0.0384310i
$127$	5.88837	+	5.88837i	0.522508	+	0.522508i	0.918328	−	0.395820i	$-0.129540\pi$
$127$	5.88837	+	5.88837i	0.522508	+	0.522508i	−0.395820	+	0.918328i	$0.629540\pi$
$128$	−4.97903	+	4.97903i	−0.440088	+	0.440088i
$129$	−5.16458			−0.454716
$130$		0			0
$131$		−	18.8144i		−	1.64383i	−0.569613	−	0.821913i	$-0.692907\pi$
$131$		−	18.8144i		−	1.64383i	0.569613	−	0.821913i	$-0.307093\pi$
$132$	5.47977	−	5.47977i	0.476953	−	0.476953i
$133$	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	$0.734380\pi$
$138$	1.21908	+	1.21908i	0.103775	+	0.103775i
$139$	0.442439			0.0375272			0.0187636	−	0.999824i	$-0.494027\pi$
$139$	0.442439			0.0375272			0.0187636	+	0.999824i	$0.494027\pi$
$140$		0			0
$141$	−0.431764			−0.0363611
$142$	0.199293	+	0.199293i	0.0167243	+	0.0167243i
$143$	1.99475	+	1.99475i	0.166810	+	0.166810i
$144$		−	3.66822i		−	0.305685i
$145$		0			0
$146$			0.462070i			0.0382411i
$147$	−5.17879	−	4.70958i	−0.427139	−	0.388440i
$148$	−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
$153$	−1.67840	−	1.67840i	−0.135690	−	0.135690i
$154$	−1.71952	+	1.80304i	−0.138563	+	0.145293i
$155$		0			0
$156$	1.37595			0.110164
$157$	−7.96508	+	7.96508i	−0.635682	+	0.635682i	−0.949487	−	0.313805i	$-0.898396\pi$
$157$	−7.96508	+	7.96508i	−0.635682	+	0.635682i	0.313805	+	0.949487i	$0.398396\pi$
$158$	−1.44341	+	1.44341i	−0.114831	+	0.114831i
$159$	−7.63184			−0.605244
$160$		0			0
$161$	13.9720	+	13.3248i	1.10115	+	1.05014i
$162$	−0.167056	−	0.167056i	−0.0131251	−	0.0131251i
$163$	−10.4450	+	10.4450i	−0.818113	+	0.818113i	−0.985834	−	0.167722i	$-0.946359\pi$
$163$	−10.4450	+	10.4450i	−0.818113	+	0.818113i	0.167722	+	0.985834i	$0.446359\pi$
$164$	−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	$0.168358\pi$
$168$	0.0584417	+	2.46468i	0.00450887	+	0.190154i
$169$		−	12.4991i		−	0.961471i
$170$		0			0
$171$			7.21850i			0.552013i
$172$	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	$0.792657\pi$
$174$	0.862773			0.0654067
$175$		0			0
$176$	−14.6216			−1.10215
$177$	−4.32013	−	4.32013i	−0.324721	−	0.324721i
$178$	−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	$-0.102123\pi$
$182$	−0.442251	+	0.0104865i	−0.0327818	+	0.000777310i
$183$	−5.02786	+	5.02786i	−0.371670	+	0.371670i
$184$		−	6.79993i		−	0.501297i
$185$		0			0
$186$	−1.16667			−0.0855441
$187$	−6.69013	+	6.69013i	−0.489231	+	0.489231i
$188$	0.593566	+	0.593566i	0.0432903	+	0.0432903i
$189$	−1.91465	−	1.82596i	−0.139270	−	0.132819i
$190$		0			0
$191$	15.2898			1.10633			0.553167	−	0.833070i	$-0.313419\pi$
$191$	15.2898			1.10633			0.553167	+	0.833070i	$0.313419\pi$
$192$	−4.73154	+	4.73154i	−0.341470	+	0.341470i
$193$	8.92787	−	8.92787i	0.642642	−	0.642642i	−0.308562	−	0.951204i	$-0.599848\pi$
$193$	8.92787	−	8.92787i	0.642642	−	0.642642i	0.951204	+	0.308562i	$0.0998477\pi$
$194$	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	$0.706776\pi$
$198$	−0.665888	+	0.665888i	−0.0473226	+	0.0473226i
$199$	−0.616637			−0.0437122			−0.0218561	−	0.999761i	$-0.506958\pi$
$199$	−0.616637			−0.0437122			−0.0218561	+	0.999761i	$0.506958\pi$
$200$		0			0
$201$		−	1.33528i		−	0.0941833i
$202$	−1.05518	+	1.05518i	−0.0742422	+	0.0742422i
$203$	9.65933	−	0.229039i	0.677952	−	0.0160754i
$204$			4.61474i			0.323097i
$205$		0			0
$206$		−	4.19008i		−	0.291937i
$207$	5.16007	+	5.16007i	0.358649	+	0.358649i
$208$	−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
$213$	0.843557	+	0.843557i	0.0577996	+	0.0577996i
$214$		−	2.49922i		−	0.170843i
$215$		0			0
$216$			0.931824i			0.0634026i
$217$	−13.0616	+	0.309712i	−0.886680	+	0.0210246i
$218$	−0.111631	+	0.111631i	−0.00756058	+	0.00756058i
$219$			1.95583i			0.132163i
$220$		0			0
$221$	−1.67987			−0.113000
$222$	0.0690507	−	0.0690507i	0.00463438	−	0.00463438i
$223$	−1.35505	−	1.35505i	−0.0907407	−	0.0907407i	0.660279	−	0.751020i	$-0.270438\pi$
$223$	−1.35505	−	1.35505i	−0.0907407	−	0.0907407i	−0.751020	+	0.660279i	$0.770438\pi$
$224$	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	$0.187538\pi$
$228$	9.92361	−	9.92361i	0.657207	−	0.657207i
$229$	−12.9900			−0.858403			−0.429202	−	0.903209i	$-0.641205\pi$
$229$	−12.9900			−0.858403			−0.429202	+	0.903209i	$0.641205\pi$
$230$		0			0
$231$	−7.27830	+	7.63184i	−0.478877	+	0.502138i
$232$	−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	$-0.0261143\pi$
$234$	−0.167202			−0.0109303
$235$		0			0
$236$			11.8782i			0.773203i
$237$	−6.10959	+	6.10959i	−0.396861	+	0.396861i
$238$	−0.0351703	−	1.48325i	−0.00227975	−	0.0961447i
$239$			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
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	13.8241			0.884995
$245$		0			0
$246$	1.80304			0.114958
$247$	3.61241	+	3.61241i	0.229852	+	0.229852i
$248$	3.25378	+	3.25378i	0.206615	+	0.206615i
$249$		−	16.9557i		−	1.07453i
$250$		0			0
$251$		−	21.1506i		−	1.33501i	−0.744604	−	0.667507i	$-0.767361\pi$
$251$		−	21.1506i		−	1.33501i	0.744604	−	0.667507i	$-0.232639\pi$
$252$	0.121934	+	5.14238i	0.00768115	+	0.323940i
$253$	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	$0.385968\pi$
$258$	−0.862773	−	0.862773i	−0.0537139	−	0.0537139i
$259$	0.754738	−	0.791399i	0.0468971	−	0.0491752i
$260$		0			0
$261$	3.65191			0.226048
$262$	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	$0.483924\pi$
$264$	3.71427			0.228598
$265$		0			0
$266$	−3.11397	+	3.26523i	−0.190929	+	0.200204i
$267$	−5.53368	−	5.53368i	−0.338656	−	0.338656i
$268$	−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
$273$	−1.87194	+	0.0443868i	−0.113295	+	0.00268641i
$274$			0.271291i			0.0163893i
$275$		0			0
$276$		−	14.1876i		−	0.853991i
$277$	−4.80771	−	4.80771i	−0.288867	−	0.288867i	0.547765	−	0.836632i	$-0.315479\pi$
$277$	−4.80771	−	4.80771i	−0.288867	−	0.288867i	−0.836632	+	0.547765i	$0.815479\pi$
$278$	0.0739121	+	0.0739121i	0.00443295	+	0.00443295i
$279$	−4.93821			−0.295643
$280$		0			0
$281$	−9.65658			−0.576063			−0.288032	−	0.957621i	$-0.593001\pi$
$281$	−9.65658			−0.576063			−0.288032	+	0.957621i	$0.593001\pi$
$282$	−0.0721287	−	0.0721287i	−0.00429520	−	0.00429520i
$283$	14.9095	+	14.9095i	0.886278	+	0.886278i	0.994163	−	0.107885i	$-0.0344079\pi$
$283$	14.9095	+	14.9095i	0.886278	+	0.886278i	−0.107885	+	0.994163i	$0.534408\pi$
$284$		−	2.31935i		−	0.137628i
$285$		0			0
$286$			0.666471i			0.0394092i
$287$	20.1863	−	0.478650i	1.19156	−	0.0282538i
$288$	1.93060	−	1.93060i	0.113761	−	0.113761i
$289$			11.3660i			0.668586i
$290$		0			0
$291$	10.5171			0.616523
$292$	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	$0.686565\pi$
$294$	−0.0783831	−	1.65191i	−0.00457140	−	0.0963413i
$295$		0			0
$296$	−0.385159			−0.0223869
$297$	−2.81854	+	2.81854i	−0.163548	+	0.163548i
$298$	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
$303$	−4.46632	+	4.46632i	−0.256583	+	0.256583i
$304$	−26.4791			−1.51868
$305$		0			0
$306$		−	0.560773i		−	0.0320572i
$307$	9.85063	−	9.85063i	0.562205	−	0.562205i	−0.367728	−	0.929933i	$-0.619864\pi$
$307$	9.85063	−	9.85063i	0.562205	−	0.562205i	0.929933	+	0.367728i	$0.119864\pi$
$308$	20.4977	−	0.486033i	1.16796	−	0.0276943i
$309$		−	17.7356i		−	1.00894i
$310$		0			0
$311$			27.3063i			1.54840i	0.632941	+	0.774200i	$0.281848\pi$
$311$			27.3063i			1.54840i	−0.632941	+	0.774200i	$0.718152\pi$
$312$	0.466320	+	0.466320i	0.0264002	+	0.0264002i
$313$	18.5080	+	18.5080i	1.04613	+	1.04613i	0.998883	+	0.0472492i	$0.0150455\pi$
$313$	18.5080	+	18.5080i	1.04613	+	1.04613i	0.0472492	+	0.998883i	$0.484955\pi$
$314$	−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	$0.414802\pi$
$318$	−1.27494	−	1.27494i	−0.0714953	−	0.0714953i
$319$		−	14.5566i		−	0.815013i
$320$		0			0
$321$		−	10.5786i		−	0.590440i
$322$	0.108127	+	4.56010i	0.00602570	+	0.254124i
$323$	−12.1155	+	12.1155i	−0.674126	+	0.674126i
$324$			1.94418i			0.108010i
$325$		0			0
$326$	−3.48978			−0.193281
$327$	−0.472505	+	0.472505i	−0.0261296	+	0.0261296i
$328$	−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
$333$	0.292275	−	0.292275i	0.0160166	−	0.0160166i
$334$	1.54901			0.0847582
$335$		0			0
$336$	6.69801	−	7.02337i	0.365406	−	0.383156i
$337$	−2.54028	−	2.54028i	−0.138378	−	0.138378i	0.634525	−	0.772903i	$-0.281196\pi$
$337$	−2.54028	−	2.54028i	−0.138378	−	0.138378i	−0.772903	+	0.634525i	$0.781196\pi$
$338$	2.08805	−	2.08805i	0.113575	−	0.113575i
$339$	4.80341			0.260886
$340$		0			0
$341$			19.6838i			1.06594i
$342$	−1.20589	+	1.20589i	−0.0652072	+	0.0652072i
$343$	−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	$0.924057\pi$
$348$	−5.02045	−	5.02045i	−0.269124	−	0.269124i
$349$	−0.508601			−0.0272248			−0.0136124	−	0.999907i	$-0.504333\pi$
$349$	−0.508601			−0.0272248			−0.0136124	+	0.999907i	$0.504333\pi$
$350$		0			0
$351$	−0.707725			−0.0377756
$352$	−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	$0.615164\pi$
$354$		−	1.44341i		−	0.0767162i
$355$		0			0
$356$			15.2148i			0.806383i
$357$	−0.148867	−	6.27823i	−0.00787888	−	0.332279i
$358$	−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
$363$	3.45660	+	3.45660i	0.181424	+	0.181424i
$364$	2.63446	+	2.51242i	0.138083	+	0.131687i
$365$		0			0
$366$	−1.67987			−0.0878080
$367$	0.410036	−	0.410036i	0.0214037	−	0.0214037i	−0.696324	−	0.717728i	$-0.745182\pi$
$367$	0.410036	−	0.410036i	0.0214037	−	0.0214037i	0.717728	+	0.696324i	$0.245182\pi$
$368$	−18.9283	+	18.9283i	−0.986705	+	0.986705i
$369$	7.63184			0.397298
$370$		0			0
$371$	−14.6123	−	13.9354i	−0.758633	−	0.723490i
$372$	6.78879	+	6.78879i	0.351982	+	0.351982i
$373$	3.44496	−	3.44496i	0.178373	−	0.178373i	−0.612273	−	0.790646i	$-0.709745\pi$
$373$	3.44496	−	3.44496i	0.178373	−	0.178373i	0.790646	+	0.612273i	$0.209745\pi$
$374$	−2.23525			−0.115582
$375$		0			0
$376$			0.402328i			0.0207485i
$377$	1.82755	−	1.82755i	0.0941237	−	0.0941237i
$378$	−0.0148172	−	0.624890i	−0.000762113	−	0.0321409i
$379$		−	12.9179i		−	0.663547i	−0.943359	−	0.331773i	$-0.892353\pi$
$379$		−	12.9179i		−	0.663547i	0.943359	−	0.331773i	$-0.107647\pi$
$380$		0			0
$381$			8.32741i			0.426626i
$382$	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	$0.868622\pi$
$384$	−7.04142			−0.359331
$385$		0			0
$386$	2.98291			0.151826
$387$	−3.65191	−	3.65191i	−0.185637	−	0.185637i
$388$	−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
$392$	−4.38850	+	4.82572i	−0.221653	+	0.243736i
$393$	13.3038	−	13.3038i	0.671089	−	0.671089i
$394$			0.897808i			0.0452309i
$395$		0			0
$396$	7.74956			0.389430
$397$	6.80633	−	6.80633i	0.341600	−	0.341600i	−0.515369	−	0.856969i	$-0.672345\pi$
$397$	6.80633	−	6.80633i	0.341600	−	0.341600i	0.856969	+	0.515369i	$0.172345\pi$
$398$	−0.103013	−	0.103013i	−0.00516356	−	0.00516356i
$399$	−13.1807	+	13.8209i	−0.659858	+	0.691911i
$400$		0			0
$401$	−8.83090			−0.440994			−0.220497	−	0.975388i	$-0.570768\pi$
$401$	−8.83090			−0.440994			−0.220497	+	0.975388i	$0.570768\pi$
$402$	0.223066	−	0.223066i	0.0111255	−	0.0111255i
$403$	−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
$408$	−1.56397	+	1.56397i	−0.0774282	+	0.0774282i
$409$	23.1985			1.14709			0.573546	−	0.819174i	$-0.305568\pi$
$409$	23.1985			1.14709			0.573546	+	0.819174i	$0.305568\pi$
$410$		0			0
$411$			1.14831i			0.0566419i
$412$	−24.3819	+	24.3819i	−1.20121	+	1.20121i
$413$	−0.383178	−	16.1599i	−0.0188550	−	0.795178i
$414$			1.72404i			0.0847319i
$415$		0			0
$416$		−	1.93229i		−	0.0947381i
$417$	0.312852	+	0.312852i	0.0153204	+	0.0153204i
$418$	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
$423$	−0.305303	−	0.305303i	−0.0148444	−	0.0148444i
$424$			7.11153i			0.345367i
$425$		0			0
$426$			0.281842i			0.0136553i
$427$	−18.8072	+	0.445951i	−0.910146	+	0.0215811i
$428$	−14.5429	+	14.5429i	−0.702957	+	0.702957i
$429$			2.82101i			0.136200i
$430$		0			0
$431$	−22.5558			−1.08648			−0.543238	−	0.839579i	$-0.682802\pi$
$431$	−22.5558			−1.08648			−0.543238	+	0.839579i	$0.682802\pi$
$432$	2.59383	−	2.59383i	0.124795	−	0.124795i
$433$	−19.9639	−	19.9639i	−0.959405	−	0.959405i	0.0398028	−	0.999208i	$-0.487327\pi$
$433$	−19.9639	−	19.9639i	−0.959405	−	0.959405i	−0.999208	+	0.0398028i	$0.987327\pi$
$434$	−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
$438$	−0.326732	+	0.326732i	−0.0156119	+	0.0156119i
$439$	−30.1943			−1.44110			−0.720548	−	0.693405i	$-0.756110\pi$
$439$	−30.1943			−1.44110			−0.720548	+	0.693405i	$0.756110\pi$
$440$		0			0
$441$	−0.331777	−	6.99213i	−0.0157989	−	0.332959i
$442$	−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	$0.109188\pi$
$444$	−0.803607			−0.0381375
$445$		0			0
$446$		−	0.452737i		−	0.0214377i
$447$	2.22112	−	2.22112i	0.105056	−	0.105056i
$448$	−17.6988	+	0.419669i	−0.836191	+	0.0198275i
$449$			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
$453$	−10.4114	−	10.4114i	−0.489170	−	0.489170i
$454$	1.38802			0.0651432
$455$		0			0
$456$	6.72637			0.314991
$457$	−1.31546	−	1.31546i	−0.0615348	−	0.0615348i	0.675670	−	0.737204i	$-0.263855\pi$
$457$	−1.31546	−	1.31546i	−0.0615348	−	0.0615348i	−0.737204	+	0.675670i	$0.763855\pi$
$458$	−2.17005	−	2.17005i	−0.101400	−	0.101400i
$459$		−	2.37361i		−	0.110791i
$460$		0			0
$461$			1.29957i			0.0605272i	0.999542	+	0.0302636i	$0.00963467\pi$
$461$			1.29957i			0.0605272i	−0.999542	+	0.0302636i	$0.990365\pi$
$462$	−2.49083	+	0.0590616i	−0.115884	+	0.00274779i
$463$	−16.5240	+	16.5240i	−0.767934	+	0.767934i	−0.977742	−	0.209809i	$-0.932716\pi$
$463$	−16.5240	+	16.5240i	−0.767934	+	0.767934i	0.209809	+	0.977742i	$0.432716\pi$
$464$			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	$0.0215210\pi$
$468$	0.972943	+	0.972943i	0.0449743	+	0.0449743i
$469$	2.43816	−	2.55659i	0.112584	−	0.118052i
$470$		0			0
$471$	−11.2643			−0.519032
$472$	−4.02560	+	4.02560i	−0.185293	+	0.185293i
$473$	−14.5566	+	14.5566i	−0.669313	+	0.669313i
$474$	−2.04129			−0.0937594
$475$		0			0
$476$	−8.42631	+	8.83562i	−0.386219	+	0.404980i
$477$	−5.39653	−	5.39653i	−0.247090	−	0.247090i
$478$	−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
$483$	0.457677	+	19.3018i	0.0208250	+	0.878261i
$484$		−	9.50389i		−	0.431995i
$485$		0			0
$486$		−	0.236253i		−	0.0107166i
$487$	13.6519	+	13.6519i	0.618627	+	0.618627i	0.945179	−	0.326552i	$-0.105887\pi$
$487$	13.6519	+	13.6519i	0.618627	+	0.618627i	−0.326552	+	0.945179i	$0.605887\pi$
$488$	4.68508	+	4.68508i	0.212084	+	0.212084i
$489$	−14.7714			−0.667986
$490$		0			0
$491$	32.1155			1.44935			0.724677	−	0.689089i	$-0.241989\pi$
$491$	32.1155			1.44935			0.724677	+	0.689089i	$0.241989\pi$
$492$	−10.4918	−	10.4918i	−0.473009	−	0.473009i
$493$	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
$498$	2.83255	−	2.83255i	0.126930	−	0.126930i
$499$			4.27431i			0.191344i	0.995413	+	0.0956722i	$0.0305000\pi$
$499$			4.27431i			0.191344i	−0.995413	+	0.0956722i	$0.969500\pi$
$500$		0			0
$501$	6.55659			0.292927
$502$	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	$0.563194\pi$
$504$	−1.70147	+	1.78412i	−0.0757894	+	0.0794709i
$505$		0			0
$506$	6.87206			0.305500
$507$	8.83822	−	8.83822i	0.392519	−	0.392519i
$508$	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
$513$	−5.10425	+	5.10425i	−0.225358	+	0.225358i
$514$	−3.13814			−0.138417
$515$		0			0
$516$			10.0409i			0.442026i
$517$	−1.21695	+	1.21695i	−0.0535212	+	0.0535212i
$518$	0.258291	−	0.00612451i	0.0113487	−	0.000269096i
$519$		−	3.51476i		−	0.154281i
$520$		0			0
$521$		−	28.8647i		−	1.26458i	−0.774730	−	0.632292i	$-0.782114\pi$
$521$		−	28.8647i		−	1.26458i	0.774730	−	0.632292i	$-0.217886\pi$
$522$	0.610073	+	0.610073i	0.0267022	+	0.0267022i
$523$	−3.54707	−	3.54707i	−0.155103	−	0.155103i	0.625290	−	0.780392i	$-0.284981\pi$
$523$	−3.54707	−	3.54707i	−0.155103	−	0.155103i	−0.780392	+	0.625290i	$0.784981\pi$
$524$	−36.5788			−1.59795
$525$		0			0
$526$	−5.13793			−0.224024
$527$	−8.28829	−	8.28829i	−0.361043	−	0.361043i
$528$	−10.3390	−	10.3390i	−0.449949	−	0.449949i
$529$		−	30.2526i		−	1.31533i
$530$		0			0
$531$		−	6.10959i		−	0.265134i
$532$	37.1203	−	0.880184i	1.60937	−	0.0381608i
$533$	3.81926	−	3.81926i	0.165430	−	0.165430i
$534$		−	1.84887i		−	0.0800083i
$535$		0			0
$536$	−1.24424			−0.0537432
$537$	−15.6347	+	15.6347i	−0.674688	+	0.674688i
$538$	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
$543$	6.00000	−	6.00000i	0.257485	−	0.257485i
$544$	6.48062			0.277854
$545$		0			0
$546$	−0.320133	−	0.305303i	−0.0137004	−	0.0130658i
$547$	−28.2200	−	28.2200i	−1.20660	−	1.20660i	−0.972121	−	0.234482i	$-0.924661\pi$
$547$	−28.2200	−	28.2200i	−1.20660	−	1.20660i	−0.234482	−	0.972121i	$-0.575339\pi$
$548$	1.57863	−	1.57863i	0.0674359	−	0.0674359i
$549$	−7.11047			−0.303467
$550$		0			0
$551$		−	26.3613i		−	1.12303i
$552$	4.80827	−	4.80827i	0.204654	−	0.204654i
$553$	−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	$-0.569658\pi$
$558$	−0.824957	−	0.824957i	−0.0349232	−	0.0349232i
$559$	−3.65510			−0.154594
$560$		0			0
$561$	−9.46128			−0.399455
$562$	−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	$-0.553533\pi$
$564$			0.839429i			0.0353463i
$565$		0			0
$566$			4.98144i			0.209386i
$567$	−0.0627175	−	2.64501i	−0.00263389	−	0.111080i
$568$	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
$573$	10.8116	+	10.8116i	0.451659	+	0.451659i
$574$	3.45220	+	3.29227i	0.144092	+	0.137417i
$575$		0			0
$576$	−6.69141			−0.278809
$577$	3.89677	−	3.89677i	0.162225	−	0.162225i	−0.621327	−	0.783552i	$-0.713406\pi$
$577$	3.89677	−	3.89677i	0.162225	−	0.162225i	0.783552	+	0.621327i	$0.213406\pi$
$578$	−1.89875	+	1.89875i	−0.0789776	+	0.0789776i
$579$	12.6259			0.524715
$580$		0			0
$581$	30.9604	−	32.4643i	1.28445	−	1.34685i
$582$	1.75694	+	1.75694i	0.0728276	+	0.0728276i
$583$	−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	$0.395330\pi$
$588$	−9.15630	+	10.0685i	−0.377599	+	0.415219i
$589$			35.6465i			1.46879i
$590$		0			0
$591$			3.80020i			0.156319i
$592$	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	$0.781759\pi$
$594$	−0.941708			−0.0386388
$595$		0			0
$596$	−6.10696			−0.250151
$597$	−0.436028	−	0.436028i	−0.0178454	−	0.0178454i
$598$	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	$0.713528\pi$
$602$	−0.0765245	−	3.22730i	−0.00311891	−	0.131535i
$603$	0.944185	−	0.944185i	0.0384502	−	0.0384502i
$604$			28.6261i			1.16478i
$605$		0			0
$606$	−1.49225			−0.0606185
$607$	10.2931	−	10.2931i	0.417783	−	0.417783i	−0.466656	−	0.884439i	$-0.654541\pi$
$607$	10.2931	−	10.2931i	0.417783	−	0.417783i	0.884439	+	0.466656i	$0.154541\pi$
$608$	−13.9360	−	13.9360i	−0.565180	−	0.565180i
$609$	6.99213	+	6.66822i	0.283336	+	0.270210i
$610$		0			0
$611$	−0.305570			−0.0123621
$612$	−3.26312	+	3.26312i	−0.131904	+	0.131904i
$613$	14.4155	−	14.4155i	0.582235	−	0.582235i	−0.353282	−	0.935517i	$-0.614934\pi$
$613$	14.4155	−	14.4155i	0.582235	−	0.582235i	0.935517	+	0.353282i	$0.114934\pi$
$614$	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	$0.492476\pi$
$618$	2.96283	−	2.96283i	0.119183	−	0.119183i
$619$	11.1991			0.450129			0.225064	−	0.974344i	$-0.427741\pi$
$619$	11.1991			0.450129			0.225064	+	0.974344i	$0.427741\pi$
$620$		0			0
$621$			7.29744i			0.292836i
$622$	−4.56168	+	4.56168i	−0.182907	+	0.182907i
$623$	−0.490815	−	20.6993i	−0.0196641	−	0.829301i
$624$		−	2.59609i		−	0.103927i
$625$		0			0
$626$			6.18373i			0.247152i
$627$	20.3457	+	20.3457i	0.812527	+	0.812527i
$628$	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
$633$	6.58210	+	6.58210i	0.261615	+	0.261615i
$634$			7.31014i			0.290323i
$635$		0			0
$636$			14.8377i			0.588353i
$637$	−3.66516	−	3.33309i	−0.145219	−	0.132062i
$638$	2.43176	−	2.43176i	0.0962745	−	0.0962745i
$639$			1.19297i			0.0471931i
$640$		0			0
$641$	−29.8969			−1.18086			−0.590428	−	0.807090i	$-0.701041\pi$
$641$	−29.8969			−1.18086			−0.590428	+	0.807090i	$0.701041\pi$
$642$	1.76722	−	1.76722i	0.0697465	−	0.0697465i
$643$	11.2813	+	11.2813i	0.444891	+	0.444891i	0.893652	−	0.448761i	$-0.148134\pi$
$643$	11.2813	+	11.2813i	0.444891	+	0.444891i	−0.448761	+	0.893652i	$0.648134\pi$
$644$	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	$0.989781\pi$
$648$	−0.658899	+	0.658899i	−0.0258840	+	0.0258840i
$649$	−24.3530			−0.955937
$650$		0			0
$651$	−9.45495	−	9.01695i	−0.370569	−	0.353402i
$652$	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	$0.232583\pi$
$654$	−0.157870			−0.00617319
$655$		0			0
$656$			27.9953i			1.09303i
$657$	−1.38298	+	1.38298i	−0.0539552	+	0.0539552i
$658$	−0.00639752	−	0.269805i	−0.000249401	−	0.0105181i
$659$		−	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
$663$	−1.18785	−	1.18785i	−0.0461321	−	0.0461321i
$664$	−15.7998			−0.613150
$665$		0			0
$666$	0.0976524			0.00378395
$667$	−18.8441	−	18.8441i	−0.729646	−	0.729646i
$668$	−9.01365	−	9.01365i	−0.348749	−	0.348749i
$669$		−	1.91633i		−	0.0740894i
$670$		0			0
$671$			28.3425i			1.09415i
$672$	7.22160	−	0.171236i	0.278579	−	0.00660558i
$673$	11.4381	−	11.4381i	0.440906	−	0.440906i	−0.451411	−	0.892316i	$-0.649079\pi$
$673$	11.4381	−	11.4381i	0.440906	−	0.440906i	0.892316	+	0.451411i	$0.149079\pi$
$674$		−	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	$0.483087\pi$
$678$	0.802438	+	0.802438i	0.0308175	+	0.0308175i
$679$	20.1366	+	19.2037i	0.772770	+	0.736972i
$680$		0			0
$681$	5.87517			0.225137
$682$	−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	$0.127591\pi$
$684$	14.0341			0.536607
$685$		0			0
$686$	2.86624	−	3.30596i	0.109433	−	0.126222i
$687$	−9.18531	−	9.18531i	−0.350442	−	0.350442i
$688$	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
$693$	−10.5431	+	0.249993i	−0.400498	+	0.00949646i
$694$		−	4.57667i		−	0.173728i
$695$		0			0
$696$		−	3.40294i		−	0.128988i
$697$	12.8093	+	12.8093i	0.485186	+	0.485186i
$698$	−0.0849648	−	0.0849648i	−0.00321597	−	0.00321597i
$699$	23.2835			0.880661
$700$		0			0
$701$	1.45193			0.0548388			0.0274194	−	0.999624i	$-0.491271\pi$
$701$	1.45193			0.0548388			0.0274194	+	0.999624i	$0.491271\pi$
$702$	−0.118230	−	0.118230i	−0.00446229	−	0.00446229i
$703$	−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
$708$	−8.39914	+	8.39914i	−0.315659	+	0.315659i
$709$		−	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			0
$711$	−8.64027			−0.324035
$712$	−5.15642	+	5.15642i	−0.193245	+	0.193245i
$713$	25.4815	+	25.4815i	0.954290	+	0.954290i
$714$	1.02395	−	1.07368i	0.0383202	−	0.0401816i
$715$		0			0
$716$	42.9876			1.60652
$717$	−3.87528	+	3.87528i	−0.144725	+	0.144725i
$718$	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
$723$	−10.3596	+	10.3596i	−0.385279	+	0.385279i
$724$	−16.4970			−0.613104
$725$		0			0
$726$			1.15489i			0.0428620i
$727$	10.4498	−	10.4498i	0.387563	−	0.387563i	−0.486254	−	0.873817i	$-0.661637\pi$
$727$	10.4498	−	10.4498i	0.387563	−	0.387563i	0.873817	+	0.486254i	$0.161637\pi$
$728$	0.0413607	+	1.74432i	0.00153293	+	0.0646487i
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$		−	12.2587i		−	0.453405i
$732$	9.77509	+	9.77509i	0.361298	+	0.361298i
$733$	18.8687	+	18.8687i	0.696933	+	0.696933i	0.963748	−	0.266815i	$-0.0859712\pi$
$733$	18.8687	+	18.8687i	0.696933	+	0.696933i	−0.266815	+	0.963748i	$0.585971\pi$
$734$	0.136998			0.00505669
$735$		0			0
$736$	−19.9240			−0.734409
$737$	−3.76354	−	3.76354i	−0.138632	−	0.138632i
$738$	1.27494	+	1.27494i	0.0469313	+	0.0469313i
$739$			20.9689i			0.771354i	0.922634	+	0.385677i	$0.126032\pi$
$739$			20.9689i			0.771354i	−0.922634	+	0.385677i	$0.873968\pi$
$740$		0			0
$741$			5.10872i			0.187673i
$742$	−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	$0.326599\pi$
$744$			4.60155i			0.168701i
$745$		0			0
$746$	1.15100			0.0421412
$747$	11.9895	−	11.9895i	0.438673	−	0.438673i
$748$	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
$753$	14.9557	−	14.9557i	0.545017	−	0.545017i
$754$	0.610607			0.0222370
$755$		0			0
$756$	−3.54999	+	3.72244i	−0.129112	+	0.135384i
$757$	13.9324	+	13.9324i	0.506383	+	0.506383i	0.913414	−	0.407031i	$-0.133436\pi$
$757$	13.9324	+	13.9324i	0.506383	+	0.506383i	−0.407031	+	0.913414i	$0.633436\pi$
$758$	2.15801	−	2.15801i	0.0783824	−	0.0783824i
$759$	29.0877			1.05582
$760$		0			0
$761$			8.78825i			0.318574i	0.987232	+	0.159287i	$0.0509195\pi$
$761$			8.78825i			0.318574i	−0.987232	+	0.159287i	$0.949081\pi$
$762$	−1.39114	+	1.39114i	−0.0503958	+	0.0503958i
$763$	−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
$768$	8.28678	+	8.28678i	0.299023	+	0.299023i
$769$	11.2183			0.404543			0.202271	−	0.979330i	$-0.435168\pi$
$769$	11.2183			0.404543			0.202271	+	0.979330i	$0.435168\pi$
$770$		0			0
$771$	−13.2830			−0.478374
$772$	−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	$0.565781\pi$
$774$		−	1.22015i		−	0.0438572i
$775$		0			0
$776$		−	9.80008i		−	0.351802i
$777$	1.09328	−	0.0259236i	0.0392214	−	0.000930003i
$778$	−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
$783$	2.58229	+	2.58229i	0.0922835	+	0.0922835i
$784$	25.6487	−	1.21703i	0.916025	−	0.0434654i
$785$		0			0
$786$	4.44496			0.158547
$787$	37.4673	−	37.4673i	1.33557	−	1.33557i	0.435262	−	0.900304i	$-0.356656\pi$
$787$	37.4673	−	37.4673i	1.33557	−	1.33557i	0.900304	−	0.435262i	$-0.143344\pi$
$788$	5.22431	−	5.22431i	0.186108	−	0.186108i
$789$	−21.7476			−0.774235
$790$		0			0
$791$	9.19686	+	8.77082i	0.327003	+	0.311854i
$792$	2.62639	+	2.62639i	0.0933246	+	0.0933246i
$793$	−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	$0.194195\pi$
$798$	−4.51077	+	0.106958i	−0.159680	+	0.00378627i
$799$		−	1.02484i		−	0.0362563i
$800$		0			0
$801$		−	7.82581i		−	0.276511i
$802$	−1.47525	−	1.47525i	−0.0520930	−	0.0520930i
$803$	5.51258	+	5.51258i	0.194535	+	0.194535i
$804$	−2.59603			−0.0915549
$805$		0			0
$806$	−0.825679			−0.0290833
$807$	16.2530	+	16.2530i	0.572131	+	0.572131i
$808$	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	$0.789723\pi$
$812$	−0.445293	−	18.7795i	−0.0156267	−	0.659032i
$813$	11.1438	−	11.1438i	0.390828	−	0.390828i
$814$		−	0.389245i		−	0.0136430i
$815$		0			0
$816$	8.70695			0.304804
$817$	−26.3613	+	26.3613i	−0.922266	+	0.922266i
$818$	3.87544	+	3.87544i	0.135502	+	0.135502i
$819$	−1.35505	−	1.29227i	−0.0473492	−	0.0451557i
$820$		0			0
$821$	−4.13417			−0.144284			−0.0721418	−	0.997394i	$-0.522983\pi$
$821$	−4.13417			−0.144284			−0.0721418	+	0.997394i	$0.522983\pi$
$822$	−0.191832	+	0.191832i	−0.00669090	+	0.00669090i
$823$	5.72102	−	5.72102i	0.199422	−	0.199422i	−0.600330	−	0.799752i	$-0.704964\pi$
$823$	5.72102	−	5.72102i	0.199422	−	0.199422i	0.799752	+	0.600330i	$0.204964\pi$
$824$	−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	$0.887813\pi$
$828$	10.0321	−	10.0321i	0.348640	−	0.348640i
$829$	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			0
$831$		−	6.79913i		−	0.235859i
$832$	−3.34863	+	3.34863i	−0.116093	+	0.116093i
$833$	11.1787	−	12.2924i	0.387320	−	0.425908i
$834$			0.104527i			0.00361949i
$835$		0			0
$836$		−	55.9402i		−	1.93473i
$837$	−3.49184	−	3.49184i	−0.120696	−	0.120696i
$838$	−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
$843$	−6.82823	−	6.82823i	−0.235177	−	0.235177i
$844$		−	18.0974i		−	0.622939i
$845$		0			0
$846$		−	0.102005i		−	0.00350702i
$847$	0.306586	+	12.9298i	0.0105344	+	0.444272i
$848$	19.7957	−	19.7957i	0.679786	−	0.679786i
$849$			21.0852i			0.723643i
$850$		0			0
$851$	−3.01631			−0.103398
$852$	1.64003	−	1.64003i	0.0561865	−	0.0561865i
$853$	24.1276	+	24.1276i	0.826114	+	0.826114i	0.986977	−	0.160863i	$-0.0514276\pi$
$853$	24.1276	+	24.1276i	0.826114	+	0.826114i	−0.160863	+	0.986977i	$0.551428\pi$
$854$	−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	$0.261774\pi$
$858$	−0.471266	+	0.471266i	−0.0160888	+	0.0160888i
$859$	41.8095			1.42652			0.713261	−	0.700899i	$-0.247218\pi$
$859$	41.8095			1.42652			0.713261	+	0.700899i	$0.247218\pi$
$860$		0			0
$861$	14.6123	+	13.9354i	0.497986	+	0.474917i
$862$	−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	$0.140067\pi$
$864$	2.73028			0.0928859
$865$		0			0
$866$		−	6.67018i		−	0.226662i
$867$	−8.03695	+	8.03695i	−0.272949	+	0.272949i
$868$	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
$873$	7.43671	+	7.43671i	0.251694	+	0.251694i
$874$	12.4450			0.420958
$875$		0			0
$876$	3.80249			0.128474
$877$	39.3844	+	39.3844i	1.32992	+	1.32992i	0.905438	+	0.424477i	$0.139542\pi$
$877$	39.3844	+	39.3844i	1.32992	+	1.32992i	0.424477	+	0.905438i	$0.360458\pi$
$878$	−5.04414	−	5.04414i	−0.170231	−	0.170231i
$879$			6.77742i			0.228597i
$880$		0			0
$881$			25.7205i			0.866546i	0.901263	+	0.433273i	$0.142641\pi$
$881$			25.7205i			0.866546i	−0.901263	+	0.433273i	$0.857359\pi$
$882$	1.11265	−	1.22350i	0.0374649	−	0.0411975i
$883$	25.0968	−	25.0968i	0.844574	−	0.844574i	−0.144876	−	0.989450i	$-0.546278\pi$
$883$	25.0968	−	25.0968i	0.844574	−	0.844574i	0.989450	+	0.144876i	$0.0462784\pi$
$884$			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	$0.893780\pi$
$888$	−0.272349	−	0.272349i	−0.00913942	−	0.00913942i
$889$	−15.2055	+	15.9441i	−0.509975	+	0.534748i
$890$		0			0
$891$	−3.98602			−0.133537
$892$	−2.63446	+	2.63446i	−0.0882083	+	0.0882083i
$893$	−2.20383	+	2.20383i	−0.0737484	+	0.0737484i
$894$	0.742103			0.0248196
$895$		0			0
$896$	−13.4819	−	12.8573i	−0.450397	−	0.429533i
$897$	3.65191	+	3.65191i	0.121934	+	0.121934i
$898$	−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
$903$	−0.323910	−	13.6604i	−0.0107790	−	0.454588i
$904$		−	4.47594i		−	0.148867i
$905$		0			0
$906$		−	3.47857i		−	0.115568i
$907$	30.5961	+	30.5961i	1.01593	+	1.01593i	0.999871	+	0.0160555i	$0.00511086\pi$
$907$	30.5961	+	30.5961i	1.01593	+	1.01593i	0.0160555	+	0.999871i	$0.494889\pi$
$908$	−8.07687	−	8.07687i	−0.268040	−	0.268040i
$909$	−6.31633			−0.209499
$910$		0			0
$911$	20.7843			0.688614			0.344307	−	0.938857i	$-0.388114\pi$
$911$	20.7843			0.688614			0.344307	+	0.938857i	$0.388114\pi$
$912$	−18.7235	−	18.7235i	−0.619998	−	0.619998i
$913$	−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
$918$	0.396526	−	0.396526i	0.0130873	−	0.0130873i
$919$			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			0
$921$	13.9309			0.459038
$922$	−0.217101	+	0.217101i	−0.00714985	+	0.00714985i
$923$	0.597007	+	0.597007i	0.0196507	+	0.0196507i
$924$	14.8377	+	14.1504i	0.488125	+	0.465512i
$925$		0			0
$926$	−5.52085			−0.181426
$927$	12.5410	−	12.5410i	0.411899	−	0.411899i
$928$	−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
$933$	−19.3085	+	19.3085i	−0.632132	+	0.632132i
$934$	6.71593			0.219752
$935$		0			0
$936$			0.659476i			0.0215556i
$937$	−8.25994	+	8.25994i	−0.269841	+	0.269841i	−0.829036	−	0.559195i	$-0.811110\pi$
$937$	−8.25994	+	8.25994i	−0.269841	+	0.269841i	0.559195	+	0.829036i	$0.311110\pi$
$938$	0.834403	−	0.0197851i	0.0272442	−	0.000646005i
$939$			26.1742i			0.854163i
$940$		0			0
$941$			28.7824i			0.938281i	0.883124	+	0.469140i	$0.155436\pi$
$941$			28.7824i			0.938281i	−0.883124	+	0.469140i	$0.844564\pi$
$942$	−1.88177	−	1.88177i	−0.0613114	−	0.0613114i
$943$	−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	$0.781277\pi$
$948$	11.8782	+	11.8782i	0.385785	+	0.385785i
$949$			1.38419i			0.0449327i
$950$		0			0
$951$			30.9421i			1.00336i
$952$	−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	$0.989861\pi$
$954$		−	1.80304i		−	0.0583757i
$955$		0			0
$956$	10.6551			0.344609
$957$	10.2931	−	10.2931i	0.332728	−	0.332728i
$958$	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
$963$	7.48020	−	7.48020i	0.241046	−	0.241046i
$964$	28.4837			0.917399
$965$		0			0
$966$	−3.14802	+	3.30093i	−0.101286	+	0.106206i
$967$	17.5518	+	17.5518i	0.564429	+	0.564429i	0.930562	−	0.366134i	$-0.119319\pi$
$967$	17.5518	+	17.5518i	0.564429	+	0.564429i	−0.366134	+	0.930562i	$0.619319\pi$
$968$	3.22094	−	3.22094i	0.103525	−	0.103525i
$969$	−17.1339			−0.550421
$970$		0			0
$971$		−	0.0930634i		−	0.00298655i	−0.999999	−	0.00149327i	$-0.999525\pi$
$971$		−	0.0930634i		−	0.00298655i	0.999999	−	0.00149327i	$-0.000475324\pi$
$972$	−1.37475	+	1.37475i	−0.0440950	+	0.0440950i
$973$	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	$0.787517\pi$
$978$	−2.46765	−	2.46765i	−0.0789067	−	0.0789067i
$979$	−31.1938			−0.996959
$980$		0			0
$981$	−0.668223			−0.0213347
$982$	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	$0.990408\pi$
$984$		−	7.11153i		−	0.226707i
$985$		0			0
$986$			2.04789i			0.0652181i
$987$	−0.0270792	−	1.14202i	−0.000861939	−	0.0363509i
$988$	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
$993$	−11.8025	−	11.8025i	−0.374542	−	0.374542i
$994$	−0.514631	+	0.539630i	−0.0163231	+	0.0171160i
$995$		0			0
$996$	−32.9651			−1.04454
$997$	−21.1809	+	21.1809i	−0.670805	+	0.670805i	−0.957902	−	0.287097i	$-0.907310\pi$
$997$	−21.1809	+	21.1809i	−0.670805	+	0.670805i	0.287097	+	0.957902i	$0.407310\pi$
$998$	−0.714048	+	0.714048i	−0.0226028	+	0.0226028i
$999$	0.413339			0.0130775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.m.b.307.6		16
5.2	odd	4		105.2.m.a.13.4	yes	16
5.3	odd	4	inner	525.2.m.b.118.5		16
5.4	even	2		105.2.m.a.97.3	yes	16
7.6	odd	2	inner	525.2.m.b.307.5		16
15.2	even	4		315.2.p.e.118.5		16
15.14	odd	2		315.2.p.e.307.6		16
20.7	even	4		1680.2.cz.d.433.4		16
20.19	odd	2		1680.2.cz.d.97.5		16
35.2	odd	12		735.2.v.a.178.6		32
35.4	even	6		735.2.v.a.607.5		32
35.9	even	6		735.2.v.a.472.4		32
35.12	even	12		735.2.v.a.178.5		32
35.13	even	4	inner	525.2.m.b.118.6		16
35.17	even	12		735.2.v.a.313.4		32
35.19	odd	6		735.2.v.a.472.3		32
35.24	odd	6		735.2.v.a.607.6		32
35.27	even	4		105.2.m.a.13.3	✓	16
35.32	odd	12		735.2.v.a.313.3		32
35.34	odd	2		105.2.m.a.97.4	yes	16
105.62	odd	4		315.2.p.e.118.6		16
105.104	even	2		315.2.p.e.307.5		16
140.27	odd	4		1680.2.cz.d.433.5		16
140.139	even	2		1680.2.cz.d.97.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.m.a.13.3	✓	16	35.27	even	4
105.2.m.a.13.4	yes	16	5.2	odd	4
105.2.m.a.97.3	yes	16	5.4	even	2
105.2.m.a.97.4	yes	16	35.34	odd	2
315.2.p.e.118.5		16	15.2	even	4
315.2.p.e.118.6		16	105.62	odd	4
315.2.p.e.307.5		16	105.104	even	2
315.2.p.e.307.6		16	15.14	odd	2
525.2.m.b.118.5		16	5.3	odd	4	inner
525.2.m.b.118.6		16	35.13	even	4	inner
525.2.m.b.307.5		16	7.6	odd	2	inner
525.2.m.b.307.6		16	1.1	even	1	trivial
735.2.v.a.178.5		32	35.12	even	12
735.2.v.a.178.6		32	35.2	odd	12
735.2.v.a.313.3		32	35.32	odd	12
735.2.v.a.313.4		32	35.17	even	12
735.2.v.a.472.3		32	35.19	odd	6
735.2.v.a.472.4		32	35.9	even	6
735.2.v.a.607.5		32	35.4	even	6
735.2.v.a.607.6		32	35.24	odd	6
1680.2.cz.d.97.4		16	140.139	even	2
1680.2.cz.d.97.5		16	20.19	odd	2
1680.2.cz.d.433.4		16	20.7	even	4
1680.2.cz.d.433.5		16	140.27	odd	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.167056 + 0.167056i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.94418i q^{4} +0.236253i q^{6} +(0.0627175 + 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.167056 + 0.167056i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.94418i q^{4} +0.236253i q^{6} +(0.0627175 + 2.64501i) q^{7} +(0.658899 - 0.658899i) q^{8} +1.00000i q^{9} +3.98602 q^{11} +(1.37475 - 1.37475i) q^{12} +(0.500437 + 0.500437i) q^{13} +(-0.431387 + 0.452341i) q^{14} -3.66822 q^{16} +(-1.67840 + 1.67840i) q^{17} +(-0.167056 + 0.167056i) q^{18} +7.21850 q^{19} +(-1.82596 + 1.91465i) q^{21} +(0.665888 + 0.665888i) q^{22} +(5.16007 - 5.16007i) q^{23} +0.931824 q^{24} +0.167202i q^{26} +(-0.707107 + 0.707107i) q^{27} +(5.14238 - 0.121934i) q^{28} -3.65191i q^{29} +4.93821i q^{31} +(-1.93060 - 1.93060i) q^{32} +(2.81854 + 2.81854i) q^{33} -0.560773 q^{34} +1.94418 q^{36} +(-0.292275 - 0.292275i) q^{37} +(1.20589 + 1.20589i) q^{38} +0.707725i q^{39} -7.63184i q^{41} +(-0.624890 + 0.0148172i) q^{42} +(-3.65191 + 3.65191i) q^{43} -7.74956i q^{44} +1.72404 q^{46} +(-0.305303 + 0.305303i) q^{47} +(-2.59383 - 2.59383i) q^{48} +(-6.99213 + 0.331777i) q^{49} -2.37361 q^{51} +(0.972943 - 0.972943i) q^{52} +(-5.39653 + 5.39653i) q^{53} -0.236253 q^{54} +(1.78412 + 1.70147i) q^{56} +(5.10425 + 5.10425i) q^{57} +(0.610073 - 0.610073i) q^{58} -6.10959 q^{59} +7.11047i q^{61} +(-0.824957 + 0.824957i) q^{62} +(-2.64501 + 0.0627175i) q^{63} +6.69141i q^{64} +0.941708i q^{66} +(-0.944185 - 0.944185i) q^{67} +(3.26312 + 3.26312i) q^{68} +7.29744 q^{69} +1.19297 q^{71} +(0.658899 + 0.658899i) q^{72} +(1.38298 + 1.38298i) q^{73} -0.0976524i q^{74} -14.0341i q^{76} +(0.249993 + 10.5431i) q^{77} +(-0.118230 + 0.118230i) q^{78} +8.64027i q^{79} -1.00000 q^{81} +(1.27494 - 1.27494i) q^{82} +(-11.9895 - 11.9895i) q^{83} +(3.72244 + 3.54999i) q^{84} -1.22015 q^{86} +(2.58229 - 2.58229i) q^{87} +(2.62639 - 2.62639i) q^{88} -7.82581 q^{89} +(-1.29227 + 1.35505i) q^{91} +(-10.0321 - 10.0321i) q^{92} +(-3.49184 + 3.49184i) q^{93} -0.102005 q^{94} -2.73028i q^{96} +(7.43671 - 7.43671i) q^{97} +(-1.22350 - 1.11265i) q^{98} +3.98602i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{7} - 24 q^{8}+O(q^{10}) \) 16 * q + 8 * q^7 - 24 * q^8	\( 16 q + 8 q^{7} - 24 q^{8} - 16 q^{11} - 48 q^{16} + 8 q^{21} + 16 q^{22} + 40 q^{23} - 24 q^{28} - 48 q^{32} - 16 q^{36} - 32 q^{37} + 16 q^{42} + 16 q^{43} + 64 q^{46} - 16 q^{51} - 24 q^{53} + 24 q^{56} - 8 q^{57} - 32 q^{58} - 8 q^{63} + 32 q^{67} + 64 q^{71} - 24 q^{72} + 24 q^{77} + 8 q^{78} - 16 q^{81} + 64 q^{86} + 64 q^{88} - 48 q^{91} + 40 q^{92} - 24 q^{93} + 96 q^{98}+O(q^{100}) \) 16 * q + 8 * q^7 - 24 * q^8 - 16 * q^11 - 48 * q^16 + 8 * q^21 + 16 * q^22 + 40 * q^23 - 24 * q^28 - 48 * q^32 - 16 * q^36 - 32 * q^37 + 16 * q^42 + 16 * q^43 + 64 * q^46 - 16 * q^51 - 24 * q^53 + 24 * q^56 - 8 * q^57 - 32 * q^58 - 8 * q^63 + 32 * q^67 + 64 * q^71 - 24 * q^72 + 24 * q^77 + 8 * q^78 - 16 * q^81 + 64 * q^86 + 64 * q^88 - 48 * q^91 + 40 * q^92 - 24 * q^93 + 96 * q^98

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