LMFDB - Embedded newform 105.2.m.a.97.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,2,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, 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("105.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	105.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:	$0.838429221223$
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^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			97.3
Root			$1.40927 - 0.118126i$ of defining polynomial
Character	$\chi$	$=$	105.97
Dual form			105.2.m.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.167056 - 0.167056i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-0.0627175 - 2.64501i) q^{7} +(-0.658899 + 0.658899i) q^{8} +1.00000i q^{9} +O(q^{10})$	\(q+(-0.167056 - 0.167056i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-0.0627175 - 2.64501i) q^{7} +(-0.658899 + 0.658899i) q^{8} +1.00000i q^{9} +(0.359321 + 0.387253i) q^{10} +3.98602 q^{11} +(-1.37475 + 1.37475i) q^{12} +(-0.500437 - 0.500437i) q^{13} +(-0.431387 + 0.452341i) q^{14} +(1.52092 + 1.63915i) q^{15} -3.66822 q^{16} +(1.67840 - 1.67840i) q^{17} +(0.167056 - 0.167056i) q^{18} +7.21850 q^{19} +(-0.162536 + 4.34429i) q^{20} +(-1.82596 + 1.91465i) q^{21} +(-0.665888 - 0.665888i) q^{22} +(-5.16007 + 5.16007i) q^{23} +0.931824 q^{24} +(4.98602 + 0.373614i) q^{25} +0.167202i q^{26} +(0.707107 - 0.707107i) q^{27} +(-5.14238 + 0.121934i) q^{28} -3.65191i q^{29} +(0.0197510 - 0.527908i) q^{30} +4.93821i q^{31} +(1.93060 + 1.93060i) q^{32} +(-2.81854 - 2.81854i) q^{33} -0.560773 q^{34} +(-0.0809828 + 5.91553i) q^{35} +1.94418 q^{36} +(0.292275 + 0.292275i) q^{37} +(-1.20589 - 1.20589i) q^{38} +0.707725i q^{39} +(1.52740 - 1.41723i) q^{40} -7.63184i q^{41} +(0.624890 - 0.0148172i) q^{42} +(3.65191 - 3.65191i) q^{43} -7.74956i q^{44} +(0.0836010 - 2.23450i) q^{45} +1.72404 q^{46} +(0.305303 - 0.305303i) q^{47} +(2.59383 + 2.59383i) q^{48} +(-6.99213 + 0.331777i) q^{49} +(-0.770530 - 0.895358i) q^{50} -2.37361 q^{51} +(-0.972943 + 0.972943i) q^{52} +(5.39653 - 5.39653i) q^{53} -0.236253 q^{54} +(-8.90678 - 0.333235i) q^{55} +(1.78412 + 1.70147i) q^{56} +(-5.10425 - 5.10425i) q^{57} +(-0.610073 + 0.610073i) q^{58} -6.10959 q^{59} +(3.18681 - 2.95695i) q^{60} +7.11047i q^{61} +(0.824957 - 0.824957i) q^{62} +(2.64501 - 0.0627175i) q^{63} +6.69141i q^{64} +(1.07639 + 1.16007i) q^{65} +0.941708i q^{66} +(0.944185 + 0.944185i) q^{67} +(-3.26312 - 3.26312i) q^{68} +7.29744 q^{69} +(1.00175 - 0.974695i) q^{70} +1.19297 q^{71} +(-0.658899 - 0.658899i) q^{72} +(-1.38298 - 1.38298i) q^{73} -0.0976524i q^{74} +(-3.26147 - 3.78983i) q^{75} -14.0341i q^{76} +(-0.249993 - 10.5431i) q^{77} +(0.118230 - 0.118230i) q^{78} +8.64027i q^{79} +(8.19666 + 0.306667i) q^{80} -1.00000 q^{81} +(-1.27494 + 1.27494i) q^{82} +(11.9895 + 11.9895i) q^{83} +(3.72244 + 3.54999i) q^{84} +(-3.89070 + 3.61007i) q^{85} -1.22015 q^{86} +(-2.58229 + 2.58229i) q^{87} +(-2.62639 + 2.62639i) q^{88} -7.82581 q^{89} +(-0.387253 + 0.359321i) q^{90} +(-1.29227 + 1.35505i) q^{91} +(10.0321 + 10.0321i) q^{92} +(3.49184 - 3.49184i) q^{93} -0.102005 q^{94} +(-16.1298 - 0.603474i) q^{95} -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} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) $ 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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	0.645573	−	0.763699i	$-0.276619\pi$
$2$	−0.167056	−	0.167056i	−0.118126	−	0.118126i	−0.763699	+	0.645573i	$0.776619\pi$
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$		−	1.94418i		−	0.972092i
$5$	−2.23450	−	0.0836010i	−0.999301	−	0.0373875i
$5$	−2.23450	−	0.0836010i	−0.999301	−	0.0373875i
$6$			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
$10$	0.359321	+	0.387253i	0.113627	+	0.122460i
$11$	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	0.634295	−	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
$15$	1.52092	+	1.63915i	0.392699	+	0.423226i
$16$	−3.66822			−0.917056
$17$	1.67840	−	1.67840i	0.407071	−	0.407071i	−0.473645	−	0.880716i	$-0.657062\pi$
$17$	1.67840	−	1.67840i	0.407071	−	0.407071i	0.880716	+	0.473645i	$0.157062\pi$
$18$	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	$0.189468\pi$
$20$	−0.162536	+	4.34429i	−0.0363441	+	0.971413i
$21$	−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	$0.525198\pi$
$23$	−5.16007	+	5.16007i	−1.07595	+	1.07595i	−0.996868	+	0.0790800i	$0.974802\pi$
$24$	0.931824			0.190208
$25$	4.98602	+	0.373614i	0.997204	+	0.0747227i
$26$			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	$-0.110113\pi$
$30$	0.0197510	−	0.527908i	0.00360602	−	0.0963823i
$31$			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
$35$	−0.0809828	+	5.91553i	−0.0136886	+	0.999906i
$36$	1.94418			0.324031
$37$	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
$39$			0.707725i			0.113327i
$40$	1.52740	−	1.41723i	0.241503	−	0.224084i
$41$		−	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	−0.371516	−	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
$45$	0.0836010	−	2.23450i	0.0124625	−	0.333100i
$46$	1.72404			0.254196
$47$	0.305303	−	0.305303i	0.0445331	−	0.0445331i	−0.684490	−	0.729023i	$-0.739975\pi$
$47$	0.305303	−	0.305303i	0.0445331	−	0.0445331i	0.729023	+	0.684490i	$0.239975\pi$
$48$	2.59383	+	2.59383i	0.374386	+	0.374386i
$49$	−6.99213	+	0.331777i	−0.998876	+	0.0473967i
$50$	−0.770530	−	0.895358i	−0.108969	−	0.126623i
$51$	−2.37361			−0.332372
$52$	−0.972943	+	0.972943i	−0.134923	+	0.134923i
$53$	5.39653	−	5.39653i	0.741270	−	0.741270i	−0.231553	−	0.972822i	$-0.574381\pi$
$53$	5.39653	−	5.39653i	0.741270	−	0.741270i	0.972822	+	0.231553i	$0.0743805\pi$
$54$	−0.236253			−0.0321499
$55$	−8.90678	−	0.333235i	−1.20099	−	0.0449335i
$56$	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	$0.630192\pi$
$60$	3.18681	−	2.95695i	0.411415	−	0.381740i
$61$			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
$65$	1.07639	+	1.16007i	0.133510	+	0.143889i
$66$			0.941708i			0.115916i
$67$	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
$69$	7.29744			0.878508
$70$	1.00175	−	0.974695i	0.119732	−	0.116498i
$71$	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	0.621527	−	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
$75$	−3.26147	−	3.78983i	−0.376602	−	0.437612i
$76$		−	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	$0.838436\pi$
$80$	8.19666	+	0.306667i	0.916415	+	0.0342864i
$81$	−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	$0.130685\pi$
$83$	11.9895	+	11.9895i	1.31602	+	1.31602i	0.399122	+	0.916898i	$0.369315\pi$
$84$	3.72244	+	3.54999i	0.406151	+	0.387336i
$85$	−3.89070	+	3.61007i	−0.422006	+	0.391567i
$86$	−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	$0.636137\pi$
$90$	−0.387253	+	0.359321i	−0.0408201	+	0.0378758i
$91$	−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
$95$	−16.1298	−	0.603474i	−1.65488	−	0.0619151i
$96$		−	2.73028i		−	0.278658i
$97$	−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
$99$			3.98602i			0.400610i
$100$	0.726374	−	9.69375i	0.0726374	−	0.969375i
$101$			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	$0.0883316\pi$
$103$	12.5410	+	12.5410i	1.23570	+	1.23570i	0.273954	+	0.961743i	$0.411668\pi$
$104$	0.659476			0.0646669
$105$	4.24017	−	4.12564i	0.413798	−	0.402622i
$106$	−1.80304			−0.175127
$107$	7.48020	+	7.48020i	0.723138	+	0.723138i	0.969243	−	0.246105i	$-0.0791508\pi$
$107$	7.48020	+	7.48020i	0.723138	+	0.723138i	−0.246105	+	0.969243i	$0.579151\pi$
$108$	−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	$0.989812\pi$
$110$	1.43226	+	1.54360i	0.136561	+	0.147176i
$111$		−	0.413339i		−	0.0392324i
$112$	0.230062	+	9.70248i	0.0217388	+	0.916798i
$113$	−3.39653	+	3.39653i	−0.319518	+	0.319518i	−0.848582	−	0.529064i	$-0.822543\pi$
$113$	−3.39653	+	3.39653i	−0.319518	+	0.319518i	0.529064	+	0.848582i	$0.322543\pi$
$114$			1.70539i			0.159724i
$115$	11.9616	−	11.0988i	1.11542	−	1.03497i
$116$	−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
$120$	−2.08217	−	0.0779014i	−0.190075	−	0.00711139i
$121$	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
$125$	−11.1101	−	1.25168i	−0.993713	−	0.111953i
$126$	−0.452341	−	0.431387i	−0.0402978	−	0.0384310i
$127$	−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
$129$	−5.16458			−0.454716
$130$	0.0139783	−	0.373614i	0.00122597	−	0.0327681i
$131$		−	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
$135$	−1.63915	+	1.52092i	−0.141075	+	0.130900i
$136$			2.21179i			0.189659i
$137$	−0.811977	−	0.811977i	−0.0693719	−	0.0693719i	0.671570	−	0.740941i	$-0.265620\pi$
$137$	−0.811977	−	0.811977i	−0.0693719	−	0.0693719i	−0.740941	+	0.671570i	$0.765620\pi$
$138$	−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	$0.494027\pi$
$140$	11.5009	+	0.157445i	0.972001	+	0.0133066i
$141$	−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
$145$	−0.305303	+	8.16021i	−0.0253541	+	0.677669i
$146$			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	$-0.0410696\pi$
$150$	−0.0882672	+	1.17796i	−0.00720699	+	0.0961801i
$151$	−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
$155$	0.412839	−	11.0345i	0.0331601	−	0.886309i
$156$	1.37595			0.110164
$157$	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
$159$	−7.63184			−0.605244
$160$	−4.15253	−	4.47533i	−0.328286	−	0.353806i
$161$	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	−0.167722	−	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
$165$	6.06241	+	6.53368i	0.471958	+	0.508646i
$166$		−	4.00584i		−	0.310913i
$167$	−4.63621	+	4.63621i	−0.358761	+	0.358761i	−0.863356	−	0.504595i	$-0.831642\pi$
$167$	−4.63621	+	4.63621i	−0.358761	+	0.358761i	0.504595	+	0.863356i	$0.331642\pi$
$168$	−0.0584417	−	2.46468i	−0.00450887	−	0.190154i
$169$		−	12.4991i		−	0.961471i
$170$	1.25305	+	0.0468811i	0.0961045	+	0.00359562i
$171$			7.21850i			0.552013i
$172$	−7.09999	−	7.09999i	−0.541369	−	0.541369i
$173$	2.48531	+	2.48531i	0.188954	+	0.188954i	0.795244	−	0.606290i	$-0.207343\pi$
$173$	2.48531	+	2.48531i	0.188954	+	0.188954i	−0.606290	+	0.795244i	$0.707343\pi$
$174$	0.862773			0.0654067
$175$	0.675500	−	13.2115i	0.0510630	−	0.998695i
$176$	−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	$0.690430\pi$
$180$	−4.34429	−	0.162536i	−0.323804	−	0.0121147i
$181$		−	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
$185$	−0.628655	−	0.677524i	−0.0462196	−	0.0498125i
$186$	−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
$190$	2.59376	+	2.79539i	0.188171	+	0.202799i
$191$	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	−0.951204	−	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
$195$	0.0591665	−	1.58142i	0.00423700	−	0.113248i
$196$	0.645035	+	13.5940i	0.0460739	+	0.971000i
$197$	−2.68715	−	2.68715i	−0.191451	−	0.191451i	0.604872	−	0.796323i	$-0.293224\pi$
$197$	−2.68715	−	2.68715i	−0.191451	−	0.191451i	−0.796323	+	0.604872i	$0.793224\pi$
$198$	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	$0.506958\pi$
$200$	−3.53146	+	3.03911i	−0.249712	+	0.214898i
$201$		−	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
$205$	−0.638029	+	17.0534i	−0.0445619	+	1.19106i
$206$		−	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
$210$	−1.39756	−	0.0191324i	−0.0964407	−	0.00132026i
$211$	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
$215$	−8.46551	+	7.85491i	−0.577343	+	0.535700i
$216$			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
$220$	−0.647871	+	17.3164i	−0.0436795	+	1.16747i
$221$	−1.67987			−0.113000
$222$	−0.0690507	+	0.0690507i	−0.00463438	+	0.00463438i
$223$	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
$225$	−0.373614	+	4.98602i	−0.0249076	+	0.332401i
$226$	1.13482			0.0754870
$227$	−4.15437	+	4.15437i	−0.275735	+	0.275735i	−0.831404	−	0.555668i	$-0.812462\pi$
$227$	−4.15437	+	4.15437i	−0.275735	+	0.275735i	0.555668	+	0.831404i	$0.312462\pi$
$228$	−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	$0.641205\pi$
$230$	−3.85237	−	0.144131i	−0.254018	−	0.00950374i
$231$	−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	$0.526114\pi$
$233$	−16.4639	+	16.4639i	−1.07859	+	1.07859i	−0.996637	+	0.0819485i	$0.973886\pi$
$234$	−0.167202			−0.0109303
$235$	−0.707725	+	0.656678i	−0.0461669	+	0.0428370i
$236$			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	$0.943279\pi$
$240$	−5.57907	−	6.01276i	−0.360127	−	0.388122i
$241$			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
$245$	15.6517	−	0.156807i	0.999950	−	0.0100180i
$246$	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
$250$	1.64690	+	2.06510i	0.104159	+	0.130608i
$251$		−	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
$255$	5.30385	+	0.198436i	0.332140	+	0.0124266i
$256$	11.7193			0.732454
$257$	9.39248	−	9.39248i	0.585887	−	0.585887i	−0.350628	−	0.936515i	$-0.614032\pi$
$257$	9.39248	−	9.39248i	0.585887	−	0.585887i	0.936515	+	0.350628i	$0.114032\pi$
$258$	0.862773	+	0.862773i	0.0537139	+	0.0537139i
$259$	0.754738	−	0.791399i	0.0468971	−	0.0491752i
$260$	2.25538	−	2.09271i	0.139873	−	0.129784i
$261$	3.65191			0.226048
$262$	−3.14306	+	3.14306i	−0.194179	+	0.194179i
$263$	15.3779	−	15.3779i	0.948241	−	0.948241i	−0.0504843	−	0.998725i	$-0.516076\pi$
$263$	15.3779	−	15.3779i	0.948241	−	0.948241i	0.998725	+	0.0504843i	$0.0160765\pi$
$264$	3.71427			0.228598
$265$	−12.5097	+	11.6074i	−0.768466	+	0.713037i
$266$	−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	$0.252865\pi$
$270$	0.527908	+	0.0197510i	0.0321274	+	0.00120201i
$271$		−	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
$275$	19.8744	+	1.48923i	1.19847	+	0.0898041i
$276$		−	14.1876i		−	0.853991i
$277$	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
$279$	−4.93821			−0.295643
$280$	−3.84438	−	3.95109i	−0.229745	−	0.236123i
$281$	−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	0.107885	−	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
$285$	10.9788	+	11.8322i	0.650325	+	0.700879i
$286$			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
$290$	1.41421	−	1.31221i	0.0830455	−	0.0770555i
$291$	10.5171			0.616523
$292$	−2.68877	+	2.68877i	−0.157348	+	0.157348i
$293$	−4.79236	−	4.79236i	−0.279973	−	0.279973i	0.553125	−	0.833098i	$-0.313435\pi$
$293$	−4.79236	−	4.79236i	−0.279973	−	0.279973i	−0.833098	+	0.553125i	$0.813435\pi$
$294$	−0.0783831	−	1.65191i	−0.00457140	−	0.0963413i
$295$	13.6519	+	0.510768i	0.794845	+	0.0297381i
$296$	−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
$300$	−7.36814	+	6.34089i	−0.425400	+	0.366091i
$301$	−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
$305$	0.594442	−	15.8884i	0.0340377	−	0.909765i
$306$		−	0.560773i		−	0.0320572i
$307$	−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
$309$		−	17.7356i		−	1.00894i
$310$	−1.91234	+	1.77440i	−0.108614	+	0.100779i
$311$			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	$-0.984955\pi$
$313$	−18.5080	−	18.5080i	−1.04613	−	1.04613i	−0.0472492	−	0.998883i	$-0.515045\pi$
$314$	−2.66123			−0.150182
$315$	−5.91553	−	0.0809828i	−0.333302	−	0.00456286i
$316$	16.7983			0.944977
$317$	−21.8793	−	21.8793i	−1.22887	−	1.22887i	−0.964393	−	0.264473i	$-0.914802\pi$
$317$	−21.8793	−	21.8793i	−1.22887	−	1.22887i	−0.264473	−	0.964393i	$-0.585198\pi$
$318$	1.27494	+	1.27494i	0.0714953	+	0.0714953i
$319$		−	14.5566i		−	0.815013i
$320$	0.559409	−	14.9520i	0.0312719	−	0.835842i
$321$		−	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
$325$	−2.30822	−	2.68216i	−0.128037	−	0.148780i
$326$	−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
$330$	0.0787277	−	2.10425i	0.00433382	−	0.115835i
$331$	−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
$335$	−2.03085	−	2.18872i	−0.110957	−	0.119583i
$336$	6.69801	−	7.02337i	0.365406	−	0.383156i
$337$	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
$339$	4.80341			0.260886
$340$	7.01865	+	7.56425i	0.380640	+	0.410229i
$341$			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
$345$	−16.3062	−	0.610073i	−0.877894	−	0.0328452i
$346$		−	0.830370i		−	0.0446410i
$347$	13.6980	+	13.6980i	0.735348	+	0.735348i	0.971674	−	0.236326i	$-0.0759433\pi$
$347$	13.6980	+	13.6980i	0.735348	+	0.735348i	−0.236326	+	0.971674i	$0.575943\pi$
$348$	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	$0.504333\pi$
$350$	−2.31990	+	2.09421i	−0.124004	+	0.111940i
$351$	−0.707725			−0.0377756
$352$	7.69540	+	7.69540i	0.410166	+	0.410166i
$353$	−10.9217	−	10.9217i	−0.581305	−	0.581305i	0.353957	−	0.935262i	$-0.384836\pi$
$353$	−10.9217	−	10.9217i	−0.581305	−	0.581305i	−0.935262	+	0.353957i	$0.884836\pi$
$354$		−	1.44341i		−	0.0767162i
$355$	−2.66570	−	0.0997335i	−0.141480	−	0.00529330i
$356$			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	$-0.138621\pi$
$360$	1.41723	+	1.52740i	0.0746945	+	0.0805009i
$361$	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
$365$	2.97465	+	3.20589i	0.155701	+	0.167804i
$366$	−1.67987			−0.0878080
$367$	−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
$369$	7.63184			0.397298
$370$	−0.00816384	+	0.218205i	−0.000424418	+	0.0113439i
$371$	−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	−0.790646	−	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
$375$	6.97092	+	8.74106i	0.359977	+	0.451387i
$376$			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	$-0.107647\pi$
$380$	−1.17326	+	31.3593i	−0.0601872	+	1.60870i
$381$			8.32741i			0.426626i
$382$	−2.55426	−	2.55426i	−0.130687	−	0.130687i
$383$	10.0770	+	10.0770i	0.514910	+	0.514910i	0.916027	−	0.401117i	$-0.131378\pi$
$383$	10.0770	+	10.0770i	0.514910	+	0.514910i	−0.401117	+	0.916027i	$0.631378\pi$
$384$	−7.04142			−0.359331
$385$	−0.322799	+	23.5794i	−0.0164514	+	1.20172i
$386$	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	$0.788433\pi$
$390$	−0.274069	+	0.254301i	−0.0138780	+	0.0128770i
$391$			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
$395$	0.722335	−	19.3067i	0.0363446	−	0.971426i
$396$	7.74956			0.389430
$397$	−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
$399$	−13.1807	+	13.8209i	−0.659858	+	0.691911i
$400$	−18.2898	−	1.37050i	−0.914492	−	0.0685249i
$401$	−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
$405$	2.23450	+	0.0836010i	0.111033	+	0.00415417i
$406$	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	$0.305568\pi$
$410$	2.95545	−	2.74228i	0.145959	−	0.135432i
$411$			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
$415$	−25.7883	−	27.7930i	−1.26590	−	1.36430i
$416$		−	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	$0.603181\pi$
$420$	−8.02102	−	8.24368i	−0.391385	−	0.402250i
$421$	−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
$425$	8.99560	−	7.74146i	0.436351	−	0.375516i
$426$			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
$430$	2.72642	+	0.102005i	0.131480	+	0.00491914i
$431$	−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	0.999208	−	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
$435$	5.98602	−	5.55426i	0.287008	−	0.266306i
$436$	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	$0.756110\pi$
$440$	6.08824	−	5.64910i	0.290246	−	0.269310i
$441$	−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	−0.941742	−	0.336337i	$-0.890812\pi$
$443$	−12.7423	+	12.7423i	−0.605404	+	0.605404i	0.336337	+	0.941742i	$0.390812\pi$
$444$	−0.803607			−0.0381375
$445$	17.4868	+	0.654245i	0.828954	+	0.0310142i
$446$		−	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	$0.745180\pi$
$450$	0.895358	−	0.770530i	0.0422076	−	0.0363231i
$451$		−	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
$455$	3.00088	−	2.91982i	0.140683	−	0.136883i
$456$	6.72637			0.314991
$457$	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
$459$		−	2.37361i		−	0.110791i
$460$	−21.5781	−	23.2555i	−1.00609	−	1.08429i
$461$			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	−0.209809	−	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
$465$	−8.09446	+	7.51062i	−0.375372	+	0.348297i
$466$	5.50078			0.254819
$467$	−20.1009	+	20.1009i	−0.930157	+	0.930157i	−0.997715	−	0.0675588i	$-0.978479\pi$
$467$	−20.1009	+	20.1009i	−0.930157	+	0.930157i	0.0675588	+	0.997715i	$0.478479\pi$
$468$	−0.972943	−	0.972943i	−0.0449743	−	0.0449743i
$469$	2.43816	−	2.55659i	0.112584	−	0.118052i
$470$	0.227932	+	0.00852775i	0.0105137	+	0.000393356i
$471$	−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
$475$	35.9916	+	2.69693i	1.65141	+	0.123744i
$476$	−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	$0.418513\pi$
$480$	−0.228254	+	6.10081i	−0.0104183	+	0.278463i
$481$		−	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
$485$	17.2391	−	15.9956i	0.782786	−	0.726325i
$486$		−	0.236253i		−	0.0107166i
$487$	−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
$489$	−14.7714			−0.667986
$490$	−2.64090	−	2.58851i	−0.119304	−	0.116937i
$491$	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
$495$	0.333235	−	8.90678i	0.0149778	−	0.400330i
$496$		−	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	$0.969500\pi$
$500$	−2.43349	+	21.6000i	−0.108829	+	0.965981i
$501$	6.55659			0.292927
$502$	−3.53333	+	3.53333i	−0.157700	+	0.157700i
$503$	−17.5637	−	17.5637i	−0.783128	−	0.783128i	0.197229	−	0.980357i	$-0.436806\pi$
$503$	−17.5637	−	17.5637i	−0.783128	−	0.783128i	−0.980357	+	0.197229i	$0.936806\pi$
$504$	−1.70147	+	1.78412i	−0.0757894	+	0.0794709i
$505$	0.528051	−	14.1139i	0.0234980	−	0.628059i
$506$	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	$0.287667\pi$
$510$	−0.852889	−	0.919189i	−0.0377666	−	0.0407024i
$511$	−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
$515$	−26.9744	−	29.0713i	−1.18863	−	1.28103i
$516$			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
$520$	−1.47360	−	0.0551328i	−0.0646217	−	0.00241773i
$521$		−	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	0.780392	−	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
$525$	−9.81959	+	8.86429i	−0.428562	+	0.386869i
$526$	−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
$530$	4.02891	+	0.150736i	0.175005	+	0.00654756i
$531$		−	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
$535$	−16.0892	−	17.3399i	−0.695596	−	0.749669i
$536$	−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
$540$	2.95695	+	3.18681i	0.127247	+	0.137138i
$541$	−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
$545$	0.0558641	−	1.49315i	0.00239296	−	0.0639594i
$546$	−0.320133	−	0.305303i	−0.0137004	−	0.0130658i
$547$	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
$549$	−7.11047			−0.303467
$550$	−3.07135	−	3.56892i	−0.130963	−	0.152179i
$551$		−	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
$555$	−0.0345555	+	0.923607i	−0.00146680	+	0.0392050i
$556$		−	0.860184i		−	0.0364799i
$557$	28.1616	+	28.1616i	1.19325	+	1.19325i	0.976150	+	0.217096i	$0.0696584\pi$
$557$	28.1616	+	28.1616i	1.19325	+	1.19325i	0.217096	+	0.976150i	$0.430342\pi$
$558$	0.824957	+	0.824957i	0.0349232	+	0.0349232i
$559$	−3.65510			−0.154594
$560$	0.297063	−	21.6995i	0.0125532	−	0.916970i
$561$	−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	$0.0535326\pi$
$563$	27.3645	+	27.3645i	1.15328	+	1.15328i	0.167386	+	0.985891i	$0.446467\pi$
$564$			0.839429i			0.0353463i
$565$	7.87351	−	7.30560i	0.331241	−	0.307349i
$566$			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	$-0.121540\pi$
$570$	0.142572	−	3.81070i	0.00597170	−	0.159613i
$571$	−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
$575$	−27.6561	+	23.8003i	−1.15334	+	0.992543i
$576$	−6.69141			−0.278809
$577$	−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
$579$	12.6259			0.524715
$580$	15.8650	+	0.593566i	0.658756	+	0.0246465i
$581$	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
$585$	−1.16007	+	1.07639i	−0.0479629	+	0.0445034i
$586$			1.60118i			0.0661443i
$587$	15.1058	−	15.1058i	0.623484	−	0.623484i	−0.322937	−	0.946420i	$-0.604670\pi$
$587$	15.1058	−	15.1058i	0.623484	−	0.623484i	0.946420	+	0.322937i	$0.104670\pi$
$588$	9.15630	−	10.0685i	0.377599	−	0.415219i
$589$			35.6465i			1.46879i
$590$	−2.19530	−	2.36596i	−0.0903793	−	0.0974050i
$591$			3.80020i			0.156319i
$592$	−1.07213	−	1.07213i	−0.0440642	−	0.0440642i
$593$	3.43032	+	3.43032i	0.140866	+	0.140866i	0.774023	−	0.633157i	$-0.218241\pi$
$593$	3.43032	+	3.43032i	0.140866	+	0.140866i	−0.633157	+	0.774023i	$0.718241\pi$
$594$	−0.941708			−0.0386388
$595$	9.79269	+	10.0645i	0.401461	+	0.412605i
$596$	−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	$0.933839\pi$
$600$	4.64610	+	0.348142i	0.189676	+	0.0142128i
$601$			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
$605$	−10.9231	−	0.408673i	−0.444087	−	0.0166149i
$606$	−1.49225			−0.0606185
$607$	−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
$609$	6.99213	+	6.66822i	0.283336	+	0.270210i
$610$	−2.75355	+	2.55494i	−0.111488	+	0.103447i
$611$	−0.305570			−0.0123621
$612$	3.26312	−	3.26312i	0.131904	−	0.131904i
$613$	−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
$615$	12.5097	−	11.6074i	0.504440	−	0.468056i
$616$	7.11153	+	6.78209i	0.286532	+	0.273258i
$617$	−25.4196	−	25.4196i	−1.02336	−	1.02336i	−0.999721	−	0.0236346i	$-0.992476\pi$
$617$	−25.4196	−	25.4196i	−1.02336	−	1.02336i	−0.0236346	−	0.999721i	$-0.507524\pi$
$618$	−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	$0.427741\pi$
$620$	−21.4530	−	0.802636i	−0.861574	−	0.0322346i
$621$			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
$625$	24.7208	+	3.72569i	0.988833	+	0.149028i
$626$			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
$630$	0.974695	+	1.00175i	0.0388328	+	0.0399107i
$631$	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
$635$	12.6653	+	13.6499i	0.502608	+	0.541678i
$636$			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
$640$	−11.5419	+	10.7094i	−0.456235	+	0.423327i
$641$	−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	0.448761	−	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
$645$	11.5403	+	0.431764i	0.454398	+	0.0170007i
$646$	−4.04794			−0.159264
$647$	26.2395	−	26.2395i	1.03158	−	1.03158i	0.0320982	−	0.999485i	$-0.489781\pi$
$647$	26.2395	−	26.2395i	1.03158	−	1.03158i	0.999485	−	0.0320982i	$-0.0102189\pi$
$648$	0.658899	−	0.658899i	0.0258840	−	0.0258840i
$649$	−24.3530			−0.955937
$650$	−0.0624689	+	0.833673i	−0.00245023	+	0.0326993i
$651$	−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	−0.744720	−	0.667377i	$-0.767417\pi$
$653$	−1.97641	+	1.97641i	−0.0773427	+	0.0773427i	0.667377	+	0.744720i	$0.267417\pi$
$654$	−0.157870			−0.00617319
$655$	−1.57291	+	42.0410i	−0.0614585	+	1.64268i
$656$			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	$-0.0950507\pi$
$660$	12.7027	−	11.7865i	0.494451	−	0.458787i
$661$			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
$665$	−0.584574	+	42.7012i	−0.0226688	+	1.65588i
$666$	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
$670$	−0.0263730	+	0.704904i	−0.00101888	+	0.0272328i
$671$			28.3425i			1.09415i
$672$	−7.22160	+	0.171236i	−0.278579	+	0.00660558i
$673$	−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
$675$	3.78983	−	3.26147i	0.145871	−	0.125534i
$676$	−24.3006			−0.934639
$677$	24.6007	−	24.6007i	0.945481	−	0.945481i	−0.0531077	−	0.998589i	$-0.516913\pi$
$677$	24.6007	−	24.6007i	0.945481	−	0.945481i	0.998589	+	0.0531077i	$0.0169127\pi$
$678$	−0.802438	−	0.802438i	−0.0308175	−	0.0308175i
$679$	20.1366	+	19.2037i	0.772770	+	0.736972i
$680$	0.184908	−	4.94226i	0.00709089	−	0.189527i
$681$	5.87517			0.225137
$682$	3.28830	−	3.28830i	0.125915	−	0.125915i
$683$	−13.8654	+	13.8654i	−0.530543	+	0.530543i	−0.920734	−	0.390191i	$-0.872409\pi$
$683$	−13.8654	+	13.8654i	−0.530543	+	0.530543i	0.390191	+	0.920734i	$0.372409\pi$
$684$	14.0341			0.536607
$685$	1.74648	+	1.88225i	0.0667297	+	0.0719170i
$686$	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
$690$	2.62212	+	2.82596i	0.0998225	+	0.107582i
$691$			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
$695$	−0.988633	−	0.0369884i	−0.0375010	−	0.00140305i
$696$		−	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
$700$	−25.6856	−	1.31330i	−0.970824	−	0.0496380i
$701$	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
$705$	0.964779	+	0.0360959i	0.0363357	+	0.00135945i
$706$			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	$-0.364891\pi$
$710$	0.428659	+	0.461981i	0.0160873	+	0.0173378i
$711$	−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
$715$	4.29052	+	4.62405i	0.160457	+	0.172930i
$716$	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	$0.802038\pi$
$720$	−0.306667	+	8.19666i	−0.0114288	+	0.305472i
$721$	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
$725$	1.36440	−	18.2085i	0.0506727	−	0.676247i
$726$			1.15489i			0.0428620i
$727$	−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
$729$		−	1.00000i		−	0.0370370i
$730$	0.0386295	−	1.03250i	0.00142974	−	0.0382144i
$731$		−	12.2587i		−	0.453405i
$732$	−9.77509	−	9.77509i	−0.361298	−	0.361298i
$733$	−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
$735$	−11.1783	−	10.9565i	−0.412318	−	0.404138i
$736$	−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	$0.873968\pi$
$740$	−1.31723	+	1.22222i	−0.0484224	+	0.0449297i
$741$			5.10872i			0.187673i
$742$	0.113082	+	4.76906i	0.00415138	+	0.175078i
$743$	9.18724	−	9.18724i	0.337047	−	0.337047i	−0.518208	−	0.855255i	$-0.673401\pi$
$743$	9.18724	−	9.18724i	0.337047	−	0.337047i	0.855255	+	0.518208i	$0.173401\pi$
$744$			4.60155i			0.168701i
$745$	−0.262603	+	7.01890i	−0.00962102	+	0.257152i
$746$	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
$750$	0.295712	−	2.62478i	0.0107979	−	0.0958434i
$751$	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
$755$	32.9007	+	1.23094i	1.19738	+	0.0447984i
$756$	−3.54999	+	3.72244i	−0.129112	+	0.135384i
$757$	−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
$759$	29.0877			1.05582
$760$	11.0255	−	10.2303i	0.399938	−	0.371091i
$761$			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
$765$	−3.61007	−	3.89070i	−0.130522	−	0.140669i
$766$		−	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	$0.435168\pi$
$770$	3.99300	−	3.88515i	0.143898	−	0.140011i
$771$	−13.2830			−0.478374
$772$	17.3574	+	17.3574i	0.624708	+	0.624708i
$773$	−21.5065	−	21.5065i	−0.773535	−	0.773535i	0.205188	−	0.978723i	$-0.434219\pi$
$773$	−21.5065	−	21.5065i	−0.773535	−	0.773535i	−0.978723	+	0.205188i	$0.934219\pi$
$774$		−	1.22015i		−	0.0438572i
$775$	−1.84498	+	24.6220i	−0.0662738	+	0.884450i
$776$		−	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
$780$	−3.07456	−	0.115031i	−0.110087	−	0.00411876i
$781$	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
$785$	−18.4639	+	17.1321i	−0.659004	+	0.611471i
$786$	4.44496			0.158547
$787$	−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
$789$	−21.7476			−0.774235
$790$	−3.34597	+	3.10463i	−0.119044	+	0.110458i
$791$	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
$795$	17.0534	+	0.638029i	0.604821	+	0.0226286i
$796$			1.19886i			0.0424923i
$797$	−6.96365	+	6.96365i	−0.246665	+	0.246665i	−0.819601	−	0.572935i	$-0.805805\pi$
$797$	−6.96365	+	6.96365i	−0.246665	+	0.246665i	0.572935	+	0.819601i	$0.305805\pi$
$798$	4.51077	−	0.106958i	0.159680	−	0.00378627i
$799$		−	1.02484i		−	0.0362563i
$800$	8.90470	+	10.3473i	0.314829	+	0.365832i
$801$		−	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
$805$	−30.1066	−	30.9424i	−1.06112	−	1.09058i
$806$	−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	$-0.266387\pi$
$810$	−0.359321	−	0.387253i	−0.0126253	−	0.0136067i
$811$			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
$815$	−24.2125	+	22.4661i	−0.848128	+	0.786953i
$816$	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
$820$	33.1549	+	1.24045i	1.15782	+	0.0433183i
$821$	−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	−0.799752	−	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
$825$	−13.0003	−	15.1064i	−0.452611	−	0.525936i
$826$	2.63560	−	2.76362i	0.0917041	−	0.0961587i
$827$	17.0630	+	17.0630i	0.593339	+	0.593339i	0.938532	−	0.345193i	$-0.112187\pi$
$827$	17.0630	+	17.0630i	0.593339	+	0.593339i	−0.345193	+	0.938532i	$0.612187\pi$
$828$	−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	$0.272694\pi$
$830$	−0.334892	+	8.95106i	−0.0116243	+	0.310696i
$831$		−	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
$835$	10.7472	−	9.97204i	0.371923	−	0.345097i
$836$		−	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	$0.626166\pi$
$840$	−0.0754617	+	5.51223i	−0.00260368	+	0.190190i
$841$	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
$845$	−1.04494	+	27.9294i	−0.0359470	+	0.960799i
$846$		−	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
$850$	−2.79602	−	0.209512i	−0.0959028	−	0.00718621i
$851$	−3.01631			−0.103398
$852$	−1.64003	+	1.64003i	−0.0561865	+	0.0561865i
$853$	−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
$855$	0.603474	−	16.1298i	0.0206384	−	0.551627i
$856$	−9.85740			−0.336919
$857$	1.53096	−	1.53096i	0.0522968	−	0.0522968i	−0.680475	−	0.732772i	$-0.738226\pi$
$857$	1.53096	−	1.53096i	0.0522968	−	0.0522968i	0.732772	+	0.680475i	$0.238226\pi$
$858$	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	$0.247218\pi$
$860$	15.2714	+	16.4585i	0.520750	+	0.561231i
$861$	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	−0.904738	−	0.425968i	$-0.859933\pi$
$863$	−14.0647	+	14.0647i	−0.478770	+	0.478770i	0.425968	+	0.904738i	$0.359933\pi$
$864$	2.73028			0.0928859
$865$	−5.34566	−	5.76121i	−0.181758	−	0.195887i
$866$		−	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
$870$	−1.92787	−	0.0721287i	−0.0653610	−	0.00244539i
$871$		−	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
$875$	−2.61390	+	29.4647i	−0.0883660	+	0.996088i
$876$	3.80249			0.128474
$877$	−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
$879$			6.77742i			0.228597i
$880$	32.6721	+	1.22238i	1.10138	+	0.0412065i
$881$			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	−0.989450	−	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
$885$	−9.29219	−	10.0145i	−0.312354	−	0.336635i
$886$	4.25735			0.143028
$887$	37.8947	−	37.8947i	1.27238	−	1.27238i	0.327541	−	0.944837i	$-0.393780\pi$
$887$	37.8947	−	37.8947i	1.27238	−	1.27238i	0.944837	−	0.327541i	$-0.106220\pi$
$888$	0.272349	+	0.272349i	0.00913942	+	0.00913942i
$889$	−15.2055	+	15.9441i	−0.509975	+	0.534748i
$890$	−2.81198	−	3.03057i	−0.0942577	−	0.101585i
$891$	−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
$895$	1.84849	−	49.4068i	0.0617882	−	1.65149i
$896$	−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
$900$	9.69375	+	0.726374i	0.323125	+	0.0242125i
$901$		−	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
$905$	−0.709378	+	18.9604i	−0.0235805	+	0.630265i
$906$		−	3.47857i		−	0.115568i
$907$	−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
$909$	−6.31633			−0.209499
$910$	−0.989088	−	0.0135405i	−0.0327879	−	0.000448862i
$911$	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
$915$	−11.6551	+	10.8144i	−0.385306	+	0.357514i
$916$			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	$0.712579\pi$
$920$	−0.568481	+	15.1945i	−0.0187423	+	0.500947i
$921$	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
$925$	1.34809	+	1.56649i	0.0443249	+	0.0515057i
$926$	−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	$0.732377\pi$
$930$	2.60692	+	0.0975344i	0.0854843	+	0.00319828i
$931$	−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
$935$	−15.5084	+	14.3898i	−0.507180	+	0.470598i
$936$			0.659476i			0.0215556i
$937$	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
$939$			26.1742i			0.854163i
$940$	1.27670	+	1.37595i	0.0416415	+	0.0448785i
$941$			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
$945$	4.12564	+	4.24017i	0.134207	+	0.137933i
$946$	−4.86353			−0.158127
$947$	4.26936	+	4.26936i	0.138736	+	0.138736i	0.773064	−	0.634328i	$-0.218723\pi$
$947$	4.26936	+	4.26936i	0.138736	+	0.138736i	−0.634328	+	0.773064i	$0.718723\pi$
$948$	−11.8782	−	11.8782i	−0.385785	−	0.385785i
$949$			1.38419i			0.0449327i
$950$	−5.56207	−	6.46315i	−0.180457	−	0.209692i
$951$			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	$-0.489861\pi$
$953$	31.8382	−	31.8382i	1.03134	−	1.03134i	0.999493	−	0.0318472i	$-0.0101390\pi$
$954$		−	1.80304i		−	0.0583757i
$955$	−34.1652	−	1.27825i	−1.10556	−	0.0413631i
$956$	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
$960$	−10.9682	+	10.1771i	−0.353998	+	0.328464i
$961$	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
$965$	20.6957	−	19.2030i	0.666220	−	0.618166i
$966$	−3.14802	+	3.30093i	−0.101286	+	0.106206i
$967$	−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
$969$	−17.1339			−0.550421
$970$	−5.55205	−	0.207723i	−0.178266	−	0.00666957i
$971$		−	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
$975$	−0.264416	+	3.52873i	−0.00846808	+	0.113010i
$976$		−	26.0828i		−	0.834889i
$977$	5.19792	+	5.19792i	0.166296	+	0.166296i	0.785349	−	0.619053i	$-0.212483\pi$
$977$	5.19792	+	5.19792i	0.166296	+	0.166296i	−0.619053	+	0.785349i	$0.712483\pi$
$978$	2.46765	+	2.46765i	0.0789067	+	0.0789067i
$979$	−31.1938			−0.996959
$980$	−0.304862	−	30.4298i	−0.00973845	−	0.972044i
$981$	−0.668223			−0.0213347
$982$	−5.36509	−	5.36509i	−0.171207	−	0.171207i
$983$	30.3939	+	30.3939i	0.969415	+	0.969415i	0.999546	−	0.0301305i	$-0.00959230\pi$
$983$	30.3939	+	30.3939i	0.969415	+	0.969415i	−0.0301305	+	0.999546i	$0.509592\pi$
$984$		−	7.11153i		−	0.226707i
$985$	5.77980	+	6.22909i	0.184160	+	0.198475i
$986$			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
$990$	−1.54360	+	1.43226i	−0.0490588	+	0.0455203i
$991$	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
$995$	1.37788	+	0.0515514i	0.0436817	+	0.00163429i
$996$	−32.9651			−1.04454
$997$	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
$999$	0.413339			0.0130775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.2.m.a.97.3	yes	16
3.2	odd	2		315.2.p.e.307.6		16
4.3	odd	2		1680.2.cz.d.97.5		16
5.2	odd	4		525.2.m.b.118.5		16
5.3	odd	4	inner	105.2.m.a.13.4	yes	16
5.4	even	2		525.2.m.b.307.6		16
7.2	even	3		735.2.v.a.472.4		32
7.3	odd	6		735.2.v.a.607.6		32
7.4	even	3		735.2.v.a.607.5		32
7.5	odd	6		735.2.v.a.472.3		32
7.6	odd	2	inner	105.2.m.a.97.4	yes	16
15.8	even	4		315.2.p.e.118.5		16
20.3	even	4		1680.2.cz.d.433.4		16
21.20	even	2		315.2.p.e.307.5		16
28.27	even	2		1680.2.cz.d.97.4		16
35.3	even	12		735.2.v.a.313.4		32
35.13	even	4	inner	105.2.m.a.13.3	✓	16
35.18	odd	12		735.2.v.a.313.3		32
35.23	odd	12		735.2.v.a.178.6		32
35.27	even	4		525.2.m.b.118.6		16
35.33	even	12		735.2.v.a.178.5		32
35.34	odd	2		525.2.m.b.307.5		16
105.83	odd	4		315.2.p.e.118.6		16
140.83	odd	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	35.13	even	4	inner
105.2.m.a.13.4	yes	16	5.3	odd	4	inner
105.2.m.a.97.3	yes	16	1.1	even	1	trivial
105.2.m.a.97.4	yes	16	7.6	odd	2	inner
315.2.p.e.118.5		16	15.8	even	4
315.2.p.e.118.6		16	105.83	odd	4
315.2.p.e.307.5		16	21.20	even	2
315.2.p.e.307.6		16	3.2	odd	2
525.2.m.b.118.5		16	5.2	odd	4
525.2.m.b.118.6		16	35.27	even	4
525.2.m.b.307.5		16	35.34	odd	2
525.2.m.b.307.6		16	5.4	even	2
735.2.v.a.178.5		32	35.33	even	12
735.2.v.a.178.6		32	35.23	odd	12
735.2.v.a.313.3		32	35.18	odd	12
735.2.v.a.313.4		32	35.3	even	12
735.2.v.a.472.3		32	7.5	odd	6
735.2.v.a.472.4		32	7.2	even	3
735.2.v.a.607.5		32	7.4	even	3
735.2.v.a.607.6		32	7.3	odd	6
1680.2.cz.d.97.4		16	28.27	even	2
1680.2.cz.d.97.5		16	4.3	odd	2
1680.2.cz.d.433.4		16	20.3	even	4
1680.2.cz.d.433.5		16	140.83	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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.167056 - 0.167056i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-0.0627175 - 2.64501i) q^{7} +(-0.658899 + 0.658899i) q^{8} +1.00000i q^{9} +O(q^{10})\)	\(q+(-0.167056 - 0.167056i) q^{2} +(-0.707107 - 0.707107i) q^{3} -1.94418i q^{4} +(-2.23450 - 0.0836010i) q^{5} +0.236253i q^{6} +(-0.0627175 - 2.64501i) q^{7} +(-0.658899 + 0.658899i) q^{8} +1.00000i q^{9} +(0.359321 + 0.387253i) q^{10} +3.98602 q^{11} +(-1.37475 + 1.37475i) q^{12} +(-0.500437 - 0.500437i) q^{13} +(-0.431387 + 0.452341i) q^{14} +(1.52092 + 1.63915i) q^{15} -3.66822 q^{16} +(1.67840 - 1.67840i) q^{17} +(0.167056 - 0.167056i) q^{18} +7.21850 q^{19} +(-0.162536 + 4.34429i) q^{20} +(-1.82596 + 1.91465i) q^{21} +(-0.665888 - 0.665888i) q^{22} +(-5.16007 + 5.16007i) q^{23} +0.931824 q^{24} +(4.98602 + 0.373614i) q^{25} +0.167202i q^{26} +(0.707107 - 0.707107i) q^{27} +(-5.14238 + 0.121934i) q^{28} -3.65191i q^{29} +(0.0197510 - 0.527908i) q^{30} +4.93821i q^{31} +(1.93060 + 1.93060i) q^{32} +(-2.81854 - 2.81854i) q^{33} -0.560773 q^{34} +(-0.0809828 + 5.91553i) q^{35} +1.94418 q^{36} +(0.292275 + 0.292275i) q^{37} +(-1.20589 - 1.20589i) q^{38} +0.707725i q^{39} +(1.52740 - 1.41723i) q^{40} -7.63184i q^{41} +(0.624890 - 0.0148172i) q^{42} +(3.65191 - 3.65191i) q^{43} -7.74956i q^{44} +(0.0836010 - 2.23450i) q^{45} +1.72404 q^{46} +(0.305303 - 0.305303i) q^{47} +(2.59383 + 2.59383i) q^{48} +(-6.99213 + 0.331777i) q^{49} +(-0.770530 - 0.895358i) q^{50} -2.37361 q^{51} +(-0.972943 + 0.972943i) q^{52} +(5.39653 - 5.39653i) q^{53} -0.236253 q^{54} +(-8.90678 - 0.333235i) q^{55} +(1.78412 + 1.70147i) q^{56} +(-5.10425 - 5.10425i) q^{57} +(-0.610073 + 0.610073i) q^{58} -6.10959 q^{59} +(3.18681 - 2.95695i) q^{60} +7.11047i q^{61} +(0.824957 - 0.824957i) q^{62} +(2.64501 - 0.0627175i) q^{63} +6.69141i q^{64} +(1.07639 + 1.16007i) q^{65} +0.941708i q^{66} +(0.944185 + 0.944185i) q^{67} +(-3.26312 - 3.26312i) q^{68} +7.29744 q^{69} +(1.00175 - 0.974695i) q^{70} +1.19297 q^{71} +(-0.658899 - 0.658899i) q^{72} +(-1.38298 - 1.38298i) q^{73} -0.0976524i q^{74} +(-3.26147 - 3.78983i) q^{75} -14.0341i q^{76} +(-0.249993 - 10.5431i) q^{77} +(0.118230 - 0.118230i) q^{78} +8.64027i q^{79} +(8.19666 + 0.306667i) q^{80} -1.00000 q^{81} +(-1.27494 + 1.27494i) q^{82} +(11.9895 + 11.9895i) q^{83} +(3.72244 + 3.54999i) q^{84} +(-3.89070 + 3.61007i) q^{85} -1.22015 q^{86} +(-2.58229 + 2.58229i) q^{87} +(-2.62639 + 2.62639i) q^{88} -7.82581 q^{89} +(-0.387253 + 0.359321i) q^{90} +(-1.29227 + 1.35505i) q^{91} +(10.0321 + 10.0321i) q^{92} +(3.49184 - 3.49184i) q^{93} -0.102005 q^{94} +(-16.1298 - 0.603474i) q^{95} -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	\( 16 q - 8 q^{7} + 24 q^{8} - 16 q^{11} + 8 q^{15} - 48 q^{16} + 8 q^{21} - 16 q^{22} - 40 q^{23} + 24 q^{28} - 8 q^{30} + 48 q^{32} - 8 q^{35} - 16 q^{36} + 32 q^{37} - 16 q^{42} - 16 q^{43} + 64 q^{46} - 72 q^{50} - 16 q^{51} + 24 q^{53} + 24 q^{56} + 8 q^{57} + 32 q^{58} + 40 q^{60} + 8 q^{63} + 40 q^{65} - 32 q^{67} - 40 q^{70} + 64 q^{71} + 24 q^{72} - 24 q^{77} - 8 q^{78} - 16 q^{81} + 48 q^{85} + 64 q^{86} - 64 q^{88} - 48 q^{91} - 40 q^{92} + 24 q^{93} - 72 q^{95} - 96 q^{98}+O(q^{100}) \) 16 * q - 8 * q^7 + 24 * q^8 - 16 * q^11 + 8 * q^15 - 48 * q^16 + 8 * q^21 - 16 * q^22 - 40 * q^23 + 24 * q^28 - 8 * q^30 + 48 * q^32 - 8 * q^35 - 16 * q^36 + 32 * q^37 - 16 * q^42 - 16 * q^43 + 64 * q^46 - 72 * q^50 - 16 * q^51 + 24 * q^53 + 24 * q^56 + 8 * q^57 + 32 * q^58 + 40 * q^60 + 8 * q^63 + 40 * q^65 - 32 * q^67 - 40 * q^70 + 64 * q^71 + 24 * q^72 - 24 * q^77 - 8 * q^78 - 16 * q^81 + 48 * q^85 + 64 * q^86 - 64 * q^88 - 48 * q^91 - 40 * q^92 + 24 * q^93 - 72 * q^95 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more