LMFDB - Embedded newform 414.2.i.a.397.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [414,2,Mod(55,414)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(414, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("414.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 414 = 2 \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	414.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.30580664368$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 138)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.1
Root			$0.959493 - 0.281733i$ of defining polynomial
Character	$\chi$	$=$	414.397
Dual form			414.2.i.a.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.47672 + 1.59169i) q^{5} +(-0.151894 + 1.05645i) q^{7} +(-0.959493 + 0.281733i) q^{8} +O(q^{10})$	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.47672 + 1.59169i) q^{5} +(-0.151894 + 1.05645i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.418986 + 2.91411i) q^{10} +(1.74302 + 3.81667i) q^{11} +(0.834716 + 5.80558i) q^{13} +(0.897877 + 0.577031i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(3.51479 - 4.05628i) q^{17} +(-1.59283 - 1.83823i) q^{19} +(2.82482 + 0.829443i) q^{20} +4.19584 q^{22} +(2.13467 + 4.29455i) q^{23} +(1.52357 - 3.33616i) q^{25} +(5.62769 + 1.65244i) q^{26} +(0.897877 - 0.577031i) q^{28} +(-5.90509 + 6.81484i) q^{29} +(-4.40357 + 1.29301i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-2.22963 - 4.88220i) q^{34} +(-1.30533 - 2.85828i) q^{35} +(-7.22349 - 4.64226i) q^{37} +(-2.33380 + 0.685265i) q^{38} +(1.92796 - 2.22499i) q^{40} +(3.67379 - 2.36100i) q^{41} +(0.521162 + 0.153027i) q^{43} +(1.74302 - 3.81667i) q^{44} +(4.79324 - 0.157744i) q^{46} +1.61130 q^{47} +(5.62345 + 1.65119i) q^{49} +(-2.40176 - 2.77178i) q^{50} +(3.84094 - 4.43268i) q^{52} +(0.409819 - 2.85036i) q^{53} +(-10.3919 - 6.67848i) q^{55} +(-0.151894 - 1.05645i) q^{56} +(3.74593 + 8.20244i) q^{58} +(0.0614238 + 0.427212i) q^{59} +(1.04061 - 0.305550i) q^{61} +(-0.653151 + 4.54276i) q^{62} +(0.841254 - 0.540641i) q^{64} +(-11.3080 - 13.0502i) q^{65} +(-1.19561 + 2.61803i) q^{67} -5.36723 q^{68} -3.14224 q^{70} +(2.66906 - 5.84442i) q^{71} +(8.77594 + 10.1280i) q^{73} +(-7.22349 + 4.64226i) q^{74} +(-0.346156 + 2.40757i) q^{76} +(-4.29686 + 1.26167i) q^{77} +(0.186826 + 1.29941i) q^{79} +(-1.22301 - 2.67803i) q^{80} +(-0.621496 - 4.32260i) q^{82} +(-10.9598 - 7.04340i) q^{83} +(-2.24879 + 15.6407i) q^{85} +(0.355697 - 0.410496i) q^{86} +(-2.74769 - 3.17101i) q^{88} +(6.91251 + 2.02970i) q^{89} -6.26006 q^{91} +(1.84769 - 4.42561i) q^{92} +(0.669357 - 1.46569i) q^{94} +(6.87088 + 2.01747i) q^{95} +(9.65194 - 6.20292i) q^{97} +(3.83804 - 4.42934i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8	$ 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) $ 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/414\mathbb{Z}\right)^\times$.

$n$	$47$	$235$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$

Coefficient data

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

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

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

$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$2$	0.415415	−	0.909632i	0.293743	−	0.643207i
$3$		0			0
$3$		0			0
$4$	−0.654861	−	0.755750i	−0.327430	−	0.377875i
$5$	−2.47672	+	1.59169i	−1.10762	+	0.711825i	−0.960773	−	0.277334i	$-0.910549\pi$
$5$	−2.47672	+	1.59169i	−1.10762	+	0.711825i	−0.146848	+	0.989159i	$0.546913\pi$
$6$		0			0
$7$	−0.151894	+	1.05645i	−0.0574105	+	0.399299i	0.940772	+	0.339039i	$0.110102\pi$
$7$	−0.151894	+	1.05645i	−0.0574105	+	0.399299i	−0.998183	+	0.0602596i	$0.980807\pi$
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$		0			0
$10$	0.418986	+	2.91411i	0.132495	+	0.921523i
$11$	1.74302	+	3.81667i	0.525539	+	1.15077i	0.967299	+	0.253637i	$0.0816270\pi$
$11$	1.74302	+	3.81667i	0.525539	+	1.15077i	−0.441760	+	0.897133i	$0.645646\pi$
$12$		0			0
$13$	0.834716	+	5.80558i	0.231508	+	1.61018i	0.691583	+	0.722297i	$0.256914\pi$
$13$	0.834716	+	5.80558i	0.231508	+	1.61018i	−0.460075	+	0.887880i	$0.652177\pi$
$14$	0.897877	+	0.577031i	0.239968	+	0.154218i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	3.51479	−	4.05628i	0.852461	−	0.983792i	−0.147525	−	0.989058i	$-0.547131\pi$
$17$	3.51479	−	4.05628i	0.852461	−	0.983792i	0.999986	+	0.00526614i	$0.00167627\pi$
$18$		0			0
$19$	−1.59283	−	1.83823i	−0.365421	−	0.421718i	0.543028	−	0.839715i	$-0.317278\pi$
$19$	−1.59283	−	1.83823i	−0.365421	−	0.421718i	−0.908449	+	0.417997i	$0.862732\pi$
$20$	2.82482	+	0.829443i	0.631649	+	0.185469i
$21$		0			0
$22$	4.19584			0.894557
$23$	2.13467	+	4.29455i	0.445110	+	0.895476i
$23$	2.13467	+	4.29455i	0.445110	+	0.895476i
$24$		0			0
$25$	1.52357	−	3.33616i	0.304715	−	0.667232i
$26$	5.62769	+	1.65244i	1.10368	+	0.324070i
$27$		0			0
$28$	0.897877	−	0.577031i	0.169683	−	0.109049i
$29$	−5.90509	+	6.81484i	−1.09655	+	1.26548i	−0.135000	+	0.990846i	$0.543103\pi$
$29$	−5.90509	+	6.81484i	−1.09655	+	1.26548i	−0.961548	+	0.274638i	$0.911442\pi$
$30$		0			0
$31$	−4.40357	+	1.29301i	−0.790905	+	0.232231i	−0.652144	−	0.758095i	$-0.726130\pi$
$31$	−4.40357	+	1.29301i	−0.790905	+	0.232231i	−0.138761	+	0.990326i	$0.544312\pi$
$32$	0.841254	+	0.540641i	0.148714	+	0.0955727i
$33$		0			0
$34$	−2.22963	−	4.88220i	−0.382378	−	0.837290i
$35$	−1.30533	−	2.85828i	−0.220642	−	0.483138i
$36$		0			0
$37$	−7.22349	−	4.64226i	−1.18753	−	0.763182i	−0.210778	−	0.977534i	$-0.567600\pi$
$37$	−7.22349	−	4.64226i	−1.18753	−	0.763182i	−0.976757	+	0.214352i	$0.931236\pi$
$38$	−2.33380	+	0.685265i	−0.378592	+	0.111165i
$39$		0			0
$40$	1.92796	−	2.22499i	0.304837	−	0.351801i
$41$	3.67379	−	2.36100i	0.573750	−	0.368727i	−0.221360	−	0.975192i	$-0.571049\pi$
$41$	3.67379	−	2.36100i	0.573750	−	0.368727i	0.795110	+	0.606465i	$0.207413\pi$
$42$		0			0
$43$	0.521162	+	0.153027i	0.0794764	+	0.0233364i	0.321229	−	0.947002i	$-0.395904\pi$
$43$	0.521162	+	0.153027i	0.0794764	+	0.0233364i	−0.241753	+	0.970338i	$0.577722\pi$
$44$	1.74302	−	3.81667i	0.262770	−	0.575385i
$45$		0			0
$46$	4.79324	−	0.157744i	0.706724	−	0.0232580i
$47$	1.61130			0.235032			0.117516	−	0.993071i	$-0.462507\pi$
$47$	1.61130			0.235032			0.117516	+	0.993071i	$0.462507\pi$
$48$		0			0
$49$	5.62345	+	1.65119i	0.803349	+	0.235885i
$50$	−2.40176	−	2.77178i	−0.339661	−	0.391989i
$51$		0			0
$52$	3.84094	−	4.43268i	0.532642	−	0.614702i
$53$	0.409819	−	2.85036i	0.0562930	−	0.391526i	−0.942123	−	0.335267i	$-0.891174\pi$
$53$	0.409819	−	2.85036i	0.0562930	−	0.391526i	0.998416	−	0.0562595i	$-0.0179174\pi$
$54$		0			0
$55$	−10.3919	−	6.67848i	−1.40125	−	0.900526i
$56$	−0.151894	−	1.05645i	−0.0202977	−	0.141173i
$57$		0			0
$58$	3.74593	+	8.20244i	0.491865	+	1.07703i
$59$	0.0614238	+	0.427212i	0.00799670	+	0.0556182i	0.993429	−	0.114450i	$-0.0365104\pi$
$59$	0.0614238	+	0.427212i	0.00799670	+	0.0556182i	−0.985432	+	0.170068i	$0.945601\pi$
$60$		0			0
$61$	1.04061	−	0.305550i	0.133236	−	0.0391217i	−0.214434	−	0.976738i	$-0.568791\pi$
$61$	1.04061	−	0.305550i	0.133236	−	0.0391217i	0.347671	+	0.937617i	$0.386973\pi$
$62$	−0.653151	+	4.54276i	−0.0829502	+	0.576931i
$63$		0			0
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−11.3080	−	13.0502i	−1.40259	−	1.61867i
$66$		0			0
$67$	−1.19561	+	2.61803i	−0.146067	+	0.319843i	−0.968498	−	0.249023i	$-0.919890\pi$
$67$	−1.19561	+	2.61803i	−0.146067	+	0.319843i	0.822430	+	0.568866i	$0.192618\pi$
$68$	−5.36723			−0.650872
$69$		0			0
$70$	−3.14224			−0.375570
$71$	2.66906	−	5.84442i	0.316759	−	0.693605i	−0.682548	−	0.730841i	$-0.739128\pi$
$71$	2.66906	−	5.84442i	0.316759	−	0.693605i	0.999307	+	0.0372358i	$0.0118553\pi$
$72$		0			0
$73$	8.77594	+	10.1280i	1.02715	+	1.18539i	0.982476	+	0.186389i	$0.0596783\pi$
$73$	8.77594	+	10.1280i	1.02715	+	1.18539i	0.0446704	+	0.999002i	$0.485776\pi$
$74$	−7.22349	+	4.64226i	−0.839714	+	0.539651i
$75$		0			0
$76$	−0.346156	+	2.40757i	−0.0397068	+	0.276167i
$77$	−4.29686	+	1.26167i	−0.489673	+	0.143781i
$78$		0			0
$79$	0.186826	+	1.29941i	0.0210196	+	0.146195i	0.997628	−	0.0688290i	$-0.0219263\pi$
$79$	0.186826	+	1.29941i	0.0210196	+	0.146195i	−0.976609	+	0.215024i	$0.931017\pi$
$80$	−1.22301	−	2.67803i	−0.136737	−	0.299413i
$81$		0			0
$82$	−0.621496	−	4.32260i	−0.0686327	−	0.477351i
$83$	−10.9598	−	7.04340i	−1.20299	−	0.773114i	−0.223518	−	0.974700i	$-0.571754\pi$
$83$	−10.9598	−	7.04340i	−1.20299	−	0.773114i	−0.979471	+	0.201586i	$0.935391\pi$
$84$		0			0
$85$	−2.24879	+	15.6407i	−0.243916	+	1.69647i
$86$	0.355697	−	0.410496i	0.0383558	−	0.0442649i
$87$		0			0
$88$	−2.74769	−	3.17101i	−0.292905	−	0.338031i
$89$	6.91251	+	2.02970i	0.732724	+	0.215147i	0.626749	−	0.779221i	$-0.284385\pi$
$89$	6.91251	+	2.02970i	0.732724	+	0.215147i	0.105976	+	0.994369i	$0.466203\pi$
$90$		0			0
$91$	−6.26006			−0.656233
$92$	1.84769	−	4.42561i	0.192635	−	0.461402i
$93$		0			0
$94$	0.669357	−	1.46569i	0.0690389	−	0.151174i
$95$	6.87088	+	2.01747i	0.704937	+	0.206988i
$96$		0			0
$97$	9.65194	−	6.20292i	0.980006	−	0.629812i	0.0505409	−	0.998722i	$-0.483905\pi$
$97$	9.65194	−	6.20292i	0.980006	−	0.629812i	0.929465	+	0.368910i	$0.120269\pi$
$98$	3.83804	−	4.42934i	0.387701	−	0.447431i
$99$		0			0
$100$	−3.51903	+	1.03328i	−0.351903	+	0.103328i
$101$	13.0578	+	8.39172i	1.29930	+	0.835008i	0.993135	−	0.116972i	$-0.0373188\pi$
$101$	13.0578	+	8.39172i	1.29930	+	0.835008i	0.306162	+	0.951979i	$0.400955\pi$
$102$		0			0
$103$	−7.30113	−	15.9873i	−0.719402	−	1.57527i	−0.814740	−	0.579826i	$-0.803121\pi$
$103$	−7.30113	−	15.9873i	−0.719402	−	1.57527i	0.0953384	−	0.995445i	$-0.469607\pi$
$104$	−2.43652	−	5.33524i	−0.238921	−	0.523164i
$105$		0			0
$106$	−2.42253	−	1.55686i	−0.235297	−	0.151216i
$107$	−9.30959	+	2.73354i	−0.899992	+	0.264262i	−0.698823	−	0.715295i	$-0.746292\pi$
$107$	−9.30959	+	2.73354i	−0.899992	+	0.264262i	−0.201170	+	0.979556i	$0.564474\pi$
$108$		0			0
$109$	6.46567	−	7.46178i	0.619299	−	0.714709i	−0.356275	−	0.934381i	$-0.615953\pi$
$109$	6.46567	−	7.46178i	0.619299	−	0.714709i	0.975574	+	0.219672i	$0.0704988\pi$
$110$	−10.3919	+	6.67848i	−0.990830	+	0.636768i
$111$		0			0
$112$	−1.02408	−	0.300696i	−0.0967660	−	0.0284131i
$113$	−3.76094	+	8.23531i	−0.353800	+	0.774713i	0.646134	+	0.763224i	$0.276385\pi$
$113$	−3.76094	+	8.23531i	−0.353800	+	0.774713i	−0.999934	+	0.0114894i	$0.996343\pi$
$114$		0			0
$115$	−12.1226	−	7.23865i	−1.13043	−	0.675008i
$116$	9.01732			0.837237
$117$		0			0
$118$	0.414122	+	0.121597i	0.0381230	+	0.0111939i
$119$	3.75136	+	4.32930i	0.343887	+	0.396867i
$120$		0			0
$121$	−4.32543	+	4.99181i	−0.393221	+	0.453801i
$122$	0.154346	−	1.07350i	0.0139739	−	0.0971903i
$123$		0			0
$124$	3.86091	+	2.48126i	0.346720	+	0.222824i
$125$	−0.558260	−	3.88278i	−0.0499322	−	0.347286i
$126$		0			0
$127$	5.10228	+	11.1724i	0.452754	+	0.991393i	0.989080	+	0.147382i	$0.0470847\pi$
$127$	5.10228	+	11.1724i	0.452754	+	0.991393i	−0.536326	+	0.844011i	$0.680188\pi$
$128$	−0.142315	−	0.989821i	−0.0125790	−	0.0874887i
$129$		0			0
$130$	−16.5684	+	4.86491i	−1.45314	+	0.426681i
$131$	3.19189	−	22.2001i	0.278877	−	1.93963i	−0.0585665	−	0.998284i	$-0.518653\pi$
$131$	3.19189	−	22.2001i	0.278877	−	1.93963i	0.337443	−	0.941346i	$-0.390438\pi$
$132$		0			0
$133$	2.18393	−	1.40353i	0.189371	−	0.121701i
$134$	1.88477	+	2.17514i	0.162819	+	0.187903i
$135$		0			0
$136$	−2.22963	+	4.88220i	−0.191189	+	0.418645i
$137$	−4.22885			−0.361295			−0.180647	−	0.983548i	$-0.557819\pi$
$137$	−4.22885			−0.361295			−0.180647	+	0.983548i	$0.557819\pi$
$138$		0			0
$139$	6.61895			0.561412			0.280706	−	0.959794i	$-0.409431\pi$
$139$	6.61895			0.561412			0.280706	+	0.959794i	$0.409431\pi$
$140$	−1.30533	+	2.85828i	−0.110321	+	0.241569i
$141$		0			0
$142$	−4.20751	−	4.85572i	−0.353086	−	0.407483i
$143$	−20.7031	+	13.3051i	−1.73128	+	1.11262i
$144$		0			0
$145$	3.77813	−	26.2775i	0.313757	−	2.18223i
$146$	12.8584	−	3.77556i	1.06417	−	0.312468i
$147$		0			0
$148$	1.22200	+	8.49918i	0.100448	+	0.698628i
$149$	1.46152	+	3.20028i	0.119732	+	0.262177i	0.960003	−	0.279990i	$-0.0903312\pi$
$149$	1.46152	+	3.20028i	0.119732	+	0.262177i	−0.840271	+	0.542167i	$0.817604\pi$
$150$		0			0
$151$	−2.72272	−	18.9370i	−0.221572	−	1.54107i	−0.732094	−	0.681204i	$-0.761457\pi$
$151$	−2.72272	−	18.9370i	−0.221572	−	1.54107i	0.510522	−	0.859865i	$-0.329452\pi$
$152$	2.04620	+	1.31501i	0.165969	+	0.106662i
$153$		0			0
$154$	−0.637323	+	4.43268i	−0.0513570	+	0.357196i
$155$	8.84833	−	10.2115i	0.710715	−	0.820209i
$156$		0			0
$157$	15.0902	+	17.4150i	1.20433	+	1.38987i	0.899186	+	0.437566i	$0.144159\pi$
$157$	15.0902	+	17.4150i	1.20433	+	1.38987i	0.305144	+	0.952306i	$0.401295\pi$
$158$	1.25959	+	0.369849i	0.100208	+	0.0294236i
$159$		0			0
$160$	−2.94408			−0.232750
$161$	−4.86120	+	1.60285i	−0.383116	+	0.126322i
$162$		0			0
$163$	−3.72694	+	8.16087i	−0.291917	+	0.639209i	−0.997594	−	0.0693247i	$-0.977916\pi$
$163$	−3.72694	+	8.16087i	−0.291917	+	0.639209i	0.705677	+	0.708533i	$0.250643\pi$
$164$	−4.19015	−	1.23034i	−0.327196	−	0.0960734i
$165$		0			0
$166$	−10.9598	+	7.04340i	−0.850642	+	0.546674i
$167$	3.26093	−	3.76332i	0.252339	−	0.291214i	−0.615421	−	0.788199i	$-0.711014\pi$
$167$	3.26093	−	3.76332i	0.252339	−	0.291214i	0.867759	+	0.496984i	$0.165559\pi$
$168$		0			0
$169$	−20.5345	+	6.02949i	−1.57958	+	0.463807i
$170$	13.2931	+	8.54295i	1.01953	+	0.655215i
$171$		0			0
$172$	−0.225638	−	0.494079i	−0.0172048	−	0.0376732i
$173$	5.06771	+	11.0967i	0.385291	+	0.843670i	0.998552	+	0.0537896i	$0.0171300\pi$
$173$	5.06771	+	11.0967i	0.385291	+	0.843670i	−0.613261	+	0.789880i	$0.710143\pi$
$174$		0			0
$175$	3.29305	+	2.11631i	0.248931	+	0.159978i
$176$	−4.02588	+	1.18211i	−0.303462	+	0.0891046i
$177$		0			0
$178$	4.71784	−	5.44467i	0.353617	−	0.408095i
$179$	−8.90515	+	5.72299i	−0.665602	+	0.427757i	−0.829338	−	0.558748i	$-0.811282\pi$
$179$	−8.90515	+	5.72299i	−0.665602	+	0.427757i	0.163735	+	0.986504i	$0.447646\pi$
$180$		0			0
$181$	21.5175	+	6.31810i	1.59938	+	0.469620i	0.955374	−	0.295400i	$-0.0954528\pi$
$181$	21.5175	+	6.31810i	1.59938	+	0.469620i	0.644006	+	0.765020i	$0.277271\pi$
$182$	−2.60052	+	5.69435i	−0.192764	+	0.422093i
$183$		0			0
$184$	−3.25812	−	3.51919i	−0.240192	−	0.259438i
$185$	25.2796			1.85859
$186$		0			0
$187$	21.6078	+	6.34463i	1.58012	+	0.463965i
$188$	−1.05518	−	1.21774i	−0.0769566	−	0.0888126i
$189$		0			0
$190$	4.68942	−	5.41188i	0.340207	−	0.392619i
$191$	−0.807404	+	5.61562i	−0.0584217	+	0.406332i	0.939536	+	0.342451i	$0.111257\pi$
$191$	−0.807404	+	5.61562i	−0.0584217	+	0.406332i	−0.997958	+	0.0638812i	$0.979652\pi$
$192$		0			0
$193$	1.61317	+	1.03672i	0.116119	+	0.0746250i	0.597411	−	0.801935i	$-0.296196\pi$
$193$	1.61317	+	1.03672i	0.116119	+	0.0746250i	−0.481292	+	0.876560i	$0.659832\pi$
$194$	−1.63282	−	11.3565i	−0.117230	−	0.815349i
$195$		0			0
$196$	−2.43469	−	5.33122i	−0.173906	−	0.380801i
$197$	1.14154	+	7.93960i	0.0813315	+	0.565673i	0.989217	+	0.146455i	$0.0467865\pi$
$197$	1.14154	+	7.93960i	0.0813315	+	0.565673i	−0.907886	+	0.419218i	$0.862304\pi$
$198$		0			0
$199$	14.4780	−	4.25114i	1.02632	−	0.301355i	0.275107	−	0.961414i	$-0.411287\pi$
$199$	14.4780	−	4.25114i	1.02632	−	0.301355i	0.751214	+	0.660059i	$0.229469\pi$
$200$	−0.521953	+	3.63026i	−0.0369077	+	0.256698i
$201$		0			0
$202$	13.0578	−	8.39172i	0.918742	−	0.590439i
$203$	−6.30255	−	7.27354i	−0.442353	−	0.510502i
$204$		0			0
$205$	−5.34096	+	11.6951i	−0.373029	+	0.816819i
$206$	−17.5755			−1.22454
$207$		0			0
$208$	−5.86528			−0.406684
$209$	4.23958	−	9.28338i	0.293258	−	0.642145i
$210$		0			0
$211$	14.4100	+	16.6300i	0.992024	+	1.14486i	0.989452	+	0.144860i	$0.0462730\pi$
$211$	14.4100	+	16.6300i	0.992024	+	1.14486i	0.00257137	+	0.999997i	$0.499182\pi$
$212$	−2.42253	+	1.55686i	−0.166380	+	0.106926i
$213$		0			0
$214$	−1.38083	+	9.60386i	−0.0943914	+	0.656506i
$215$	−1.53434	+	0.450523i	−0.104641	+	0.0307254i
$216$		0			0
$217$	−0.697114	−	4.84853i	−0.0473231	−	0.329140i
$218$	−4.10154	−	8.98111i	−0.277791	−	0.608278i
$219$		0			0
$220$	1.75800	+	12.2272i	0.118524	+	0.824355i
$221$	26.4829	+	17.0195i	1.78143	+	1.14486i
$222$		0			0
$223$	3.16488	−	22.0122i	0.211936	−	1.47405i	−0.554746	−	0.832020i	$-0.687184\pi$
$223$	3.16488	−	22.0122i	0.211936	−	1.47405i	0.766682	−	0.642027i	$-0.221906\pi$
$224$	−0.698939	+	0.806618i	−0.0466998	+	0.0538944i
$225$		0			0
$226$	5.92875	+	6.84214i	0.394375	+	0.455133i
$227$	13.5344	+	3.97405i	0.898307	+	0.263767i	0.698111	−	0.715989i	$-0.254024\pi$
$227$	13.5344	+	3.97405i	0.898307	+	0.263767i	0.200196	+	0.979756i	$0.435842\pi$
$228$		0			0
$229$	−8.87229			−0.586297			−0.293149	−	0.956067i	$-0.594703\pi$
$229$	−8.87229			−0.586297			−0.293149	+	0.956067i	$0.594703\pi$
$230$	−11.6204	+	8.02003i	−0.766227	+	0.528825i
$231$		0			0
$232$	3.74593	−	8.20244i	0.245932	−	0.538517i
$233$	6.87234	+	2.01790i	0.450222	+	0.132197i	0.498980	−	0.866614i	$-0.333708\pi$
$233$	6.87234	+	2.01790i	0.450222	+	0.132197i	−0.0487581	+	0.998811i	$0.515526\pi$
$234$		0			0
$235$	−3.99073	+	2.56468i	−0.260326	+	0.167302i
$236$	0.282641	−	0.326185i	0.0183984	−	0.0212329i
$237$		0			0
$238$	5.49644	−	1.61390i	0.356282	−	0.104614i
$239$	−17.9431	−	11.5313i	−1.16064	−	0.745900i	−0.188913	−	0.981994i	$-0.560497\pi$
$239$	−17.9431	−	11.5313i	−1.16064	−	0.745900i	−0.971730	+	0.236093i	$0.924133\pi$
$240$		0			0
$241$	−7.03867	−	15.4125i	−0.453401	−	0.992809i	−0.988942	−	0.148300i	$-0.952620\pi$
$241$	−7.03867	−	15.4125i	−0.453401	−	0.992809i	0.535542	−	0.844509i	$-0.320107\pi$
$242$	2.74386	+	6.00822i	0.176382	+	0.386223i
$243$		0			0
$244$	−0.912374	−	0.586347i	−0.0584087	−	0.0375370i
$245$	−16.5559	+	4.86124i	−1.05772	+	0.310573i
$246$		0			0
$247$	9.34240	−	10.7817i	0.594443	−	0.686024i
$248$	3.86091	−	2.48126i	0.245168	−	0.157560i
$249$		0			0
$250$	−3.76381	−	1.10515i	−0.238044	−	0.0698961i
$251$	12.3350	−	27.0099i	0.778579	−	1.70485i	0.0717955	−	0.997419i	$-0.477127\pi$
$251$	12.3350	−	27.0099i	0.778579	−	1.70485i	0.706783	−	0.707430i	$-0.250146\pi$
$252$		0			0
$253$	−12.6701	+	15.6328i	−0.796565	+	0.982827i
$254$	12.2824			0.770664
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	3.09138	+	3.56764i	0.192835	+	0.222543i	0.843931	−	0.536452i	$-0.180236\pi$
$257$	3.09138	+	3.56764i	0.192835	+	0.222543i	−0.651096	+	0.758996i	$0.725690\pi$
$258$		0			0
$259$	6.00149	−	6.92609i	0.372915	−	0.430366i
$260$	−2.45747	+	17.0921i	−0.152406	+	1.06000i
$261$		0			0
$262$	−18.8679	−	12.1257i	−1.16567	−	0.749127i
$263$	2.76109	+	19.2038i	0.170256	+	1.18416i	0.878342	+	0.478033i	$0.158650\pi$
$263$	2.76109	+	19.2038i	0.170256	+	1.18416i	−0.708086	+	0.706126i	$0.750441\pi$
$264$		0			0
$265$	3.52187	+	7.71182i	0.216347	+	0.473734i
$266$	−0.369455	−	2.56962i	−0.0226527	−	0.157553i
$267$		0			0
$268$	2.76153	−	0.810859i	0.168687	−	0.0495311i
$269$	0.313108	−	2.17772i	0.0190905	−	0.132778i	−0.978047	−	0.208383i	$-0.933180\pi$
$269$	0.313108	−	2.17772i	0.0190905	−	0.132778i	0.997138	+	0.0756055i	$0.0240890\pi$
$270$		0			0
$271$	−24.4453	+	15.7101i	−1.48495	+	0.954319i	−0.488287	+	0.872683i	$0.662378\pi$
$271$	−24.4453	+	15.7101i	−1.48495	+	0.954319i	−0.996662	+	0.0816353i	$0.973986\pi$
$272$	3.51479	+	4.05628i	0.213115	+	0.245948i
$273$		0			0
$274$	−1.75673	+	3.84669i	−0.106128	+	0.232387i
$275$	15.3887			0.927971
$276$		0			0
$277$	5.48016			0.329271			0.164636	−	0.986354i	$-0.447355\pi$
$277$	5.48016			0.329271			0.164636	+	0.986354i	$0.447355\pi$
$278$	2.74961	−	6.02081i	0.164911	−	0.361104i
$279$		0			0
$280$	2.05773	+	2.37475i	0.122973	+	0.141918i
$281$	16.1491	−	10.3784i	0.963377	−	0.619125i	0.0384466	−	0.999261i	$-0.487759\pi$
$281$	16.1491	−	10.3784i	0.963377	−	0.619125i	0.924931	+	0.380136i	$0.124123\pi$
$282$		0			0
$283$	−1.95699	+	13.6111i	−0.116331	+	0.809098i	0.845210	+	0.534435i	$0.179475\pi$
$283$	−1.95699	+	13.6111i	−0.116331	+	0.809098i	−0.961540	+	0.274663i	$0.911434\pi$
$284$	−6.16478	+	1.81014i	−0.365813	+	0.107412i
$285$		0			0
$286$	3.50234	+	24.3593i	0.207098	+	1.44040i
$287$	1.93624	+	4.23978i	0.114293	+	0.250267i
$288$		0			0
$289$	−1.68033	−	11.6869i	−0.0988428	−	0.687467i
$290$	−22.3333	−	14.3528i	−1.31146	−	0.842823i
$291$		0			0
$292$	1.90719	−	13.2648i	0.111610	−	0.776266i
$293$	−0.556992	+	0.642804i	−0.0325398	+	0.0375530i	−0.771786	−	0.635882i	$-0.780636\pi$
$293$	−0.556992	+	0.642804i	−0.0325398	+	0.0375530i	0.739246	+	0.673435i	$0.235182\pi$
$294$		0			0
$295$	−0.832117	−	0.960315i	−0.0484478	−	0.0559117i
$296$	8.23876	+	2.41912i	0.478868	+	0.140608i
$297$		0			0
$298$	3.51821			0.203805
$299$	−23.1505	+	15.9777i	−1.33883	+	0.924016i
$300$		0			0
$301$	−0.240826	+	0.527335i	−0.0138810	+	0.0303951i
$302$	−18.3567	−	5.39002i	−1.05631	−	0.310161i
$303$		0			0
$304$	2.04620	−	1.31501i	0.117358	−	0.0754212i
$305$	−2.09095	+	2.41309i	−0.119728	+	0.138173i
$306$		0			0
$307$	−6.52363	+	1.91551i	−0.372323	+	0.109324i	−0.462540	−	0.886598i	$-0.653062\pi$
$307$	−6.52363	+	1.91551i	−0.372323	+	0.109324i	0.0902174	+	0.995922i	$0.471244\pi$
$308$	3.76735	+	2.42113i	0.214665	+	0.137957i
$309$		0			0
$310$	−5.61299	−	12.2907i	−0.318797	−	0.698067i
$311$	5.96225	+	13.0555i	0.338088	+	0.740310i	0.999957	−	0.00931005i	$-0.00296352\pi$
$311$	5.96225	+	13.0555i	0.338088	+	0.740310i	−0.661868	+	0.749620i	$0.730236\pi$
$312$		0			0
$313$	2.78966	+	1.79280i	0.157681	+	0.101335i	0.617102	−	0.786883i	$-0.288307\pi$
$313$	2.78966	+	1.79280i	0.157681	+	0.101335i	−0.459421	+	0.888219i	$0.651943\pi$
$314$	22.1100	−	6.49208i	1.24774	−	0.366369i
$315$		0			0
$316$	0.859680	−	0.992123i	0.0483608	−	0.0558113i
$317$	16.4694	−	10.5842i	0.925012	−	0.594469i	0.0109042	−	0.999941i	$-0.496529\pi$
$317$	16.4694	−	10.5842i	0.925012	−	0.594469i	0.914108	+	0.405472i	$0.132893\pi$
$318$		0			0
$319$	−36.3027	−	10.6594i	−2.03256	−	0.596813i
$320$	−1.22301	+	2.67803i	−0.0683686	+	0.149706i
$321$		0			0
$322$	−0.561416	+	5.08775i	−0.0312865	+	0.283529i
$323$	−13.0548			−0.726390
$324$		0			0
$325$	20.6401	+	6.06048i	1.14491	+	0.336175i
$326$	5.87516	+	6.78030i	0.325395	+	0.375526i
$327$		0			0
$328$	−2.85981	+	3.30039i	−0.157906	+	0.182234i
$329$	−0.244746	+	1.70225i	−0.0134933	+	0.0938479i
$330$		0			0
$331$	3.01005	+	1.93444i	0.165447	+	0.106327i	0.620744	−	0.784013i	$-0.286831\pi$
$331$	3.01005	+	1.93444i	0.165447	+	0.106327i	−0.455297	+	0.890340i	$0.650467\pi$
$332$	1.85406	+	12.8953i	0.101755	+	0.707720i
$333$		0			0
$334$	−2.06859	−	4.52959i	−0.113188	−	0.247848i
$335$	−1.20589	−	8.38715i	−0.0658848	−	0.458239i
$336$		0			0
$337$	−26.1806	+	7.68732i	−1.42615	+	0.418755i	−0.901580	−	0.432613i	$-0.857591\pi$
$337$	−26.1806	+	7.68732i	−1.42615	+	0.418755i	−0.524568	+	0.851368i	$0.675773\pi$
$338$	−3.04575	+	21.1836i	−0.165667	+	1.15224i
$339$		0			0
$340$	13.2931	−	8.54295i	0.720919	−	0.463307i
$341$	−12.6105	−	14.5533i	−0.682896	−	0.788103i
$342$		0			0
$343$	−5.70219	+	12.4861i	−0.307890	+	0.674184i
$344$	−0.543164			−0.0292854
$345$		0			0
$346$	12.1992			0.655831
$347$	−10.8471	+	23.7519i	−0.582304	+	1.27507i	0.357679	+	0.933845i	$0.383568\pi$
$347$	−10.8471	+	23.7519i	−0.582304	+	1.27507i	−0.939982	+	0.341223i	$0.889159\pi$
$348$		0			0
$349$	−10.8357	−	12.5051i	−0.580022	−	0.669381i	0.387588	−	0.921833i	$-0.373308\pi$
$349$	−10.8357	−	12.5051i	−0.580022	−	0.669381i	−0.967609	+	0.252452i	$0.918763\pi$
$350$	3.29305	−	2.11631i	0.176021	−	0.113122i
$351$		0			0
$352$	−0.597131	+	4.15314i	−0.0318272	+	0.221363i
$353$	−7.19931	+	2.11391i	−0.383181	+	0.112512i	−0.467649	−	0.883914i	$-0.654899\pi$
$353$	−7.19931	+	2.11391i	−0.383181	+	0.112512i	0.0844685	+	0.996426i	$0.473081\pi$
$354$		0			0
$355$	2.69200	+	18.7233i	0.142877	+	0.993729i
$356$	−2.99279	−	6.55329i	−0.158617	−	0.347324i
$357$		0			0
$358$	1.50648	+	10.4778i	0.0796202	+	0.553771i
$359$	2.88413	+	1.85351i	0.152218	+	0.0978248i	0.614533	−	0.788891i	$-0.289345\pi$
$359$	2.88413	+	1.85351i	0.152218	+	0.0978248i	−0.462315	+	0.886716i	$0.652981\pi$
$360$		0			0
$361$	1.86202	−	12.9506i	0.0980010	−	0.681612i
$362$	14.6858	−	16.9483i	0.771870	−	0.890785i
$363$		0			0
$364$	4.09947	+	4.73104i	0.214871	+	0.247974i
$365$	−37.8561	−	11.1156i	−1.98148	−	0.581815i
$366$		0			0
$367$	−6.27368			−0.327483			−0.163742	−	0.986503i	$-0.552356\pi$
$367$	−6.27368			−0.327483			−0.163742	+	0.986503i	$0.552356\pi$
$368$	−4.55464	+	1.50176i	−0.237427	+	0.0782849i
$369$		0			0
$370$	10.5015	−	22.9951i	0.545947	−	1.19546i
$371$	2.94900	+	0.865903i	0.153104	+	0.0449554i
$372$		0			0
$373$	−8.62549	+	5.54327i	−0.446611	+	0.287019i	−0.744552	−	0.667565i	$-0.767337\pi$
$373$	−8.62549	+	5.54327i	−0.446611	+	0.287019i	0.297941	+	0.954584i	$0.403700\pi$
$374$	14.7475	−	17.0195i	0.762575	−	0.880058i
$375$		0			0
$376$	−1.54603	+	0.453955i	−0.0797303	+	0.0234109i
$377$	−44.4931	−	28.5940i	−2.29151	−	1.47267i
$378$		0			0
$379$	−8.22602	−	18.0125i	−0.422542	−	0.925238i	−0.994479	−	0.104940i	$-0.966535\pi$
$379$	−8.22602	−	18.0125i	−0.422542	−	0.925238i	0.571936	−	0.820298i	$-0.306192\pi$
$380$	−2.97477	−	6.51383i	−0.152602	−	0.334152i
$381$		0			0
$382$	4.77274	+	3.06725i	0.244195	+	0.156934i
$383$	−6.43842	+	1.89049i	−0.328988	+	0.0965996i	−0.442055	−	0.896988i	$-0.645751\pi$
$383$	−6.43842	+	1.89049i	−0.328988	+	0.0965996i	0.113068	+	0.993587i	$0.463932\pi$
$384$		0			0
$385$	8.63391	−	9.96407i	0.440025	−	0.507816i
$386$	1.61317	−	1.03672i	0.0821084	−	0.0527678i
$387$		0			0
$388$	−11.0085	−	3.23240i	−0.558874	−	0.164100i
$389$	4.92999	−	10.7952i	0.249960	−	0.547337i	−0.742508	−	0.669837i	$-0.766364\pi$
$389$	4.92999	−	10.7952i	0.249960	−	0.547337i	0.992468	+	0.122500i	$0.0390913\pi$
$390$		0			0
$391$	24.9228	+	6.43561i	1.26040	+	0.325463i
$392$	−5.86085			−0.296018
$393$		0			0
$394$	7.69633	+	2.25985i	0.387735	+	0.113849i
$395$	−2.53096	−	2.92089i	−0.127347	−	0.146966i
$396$		0			0
$397$	−3.14471	+	3.62919i	−0.157828	+	0.182144i	−0.829156	−	0.559017i	$-0.811179\pi$
$397$	−3.14471	+	3.62919i	−0.157828	+	0.182144i	0.671328	+	0.741160i	$0.265724\pi$
$398$	2.14743	−	14.9357i	0.107641	−	0.748658i
$399$		0			0
$400$	3.08538	+	1.98285i	0.154269	+	0.0991425i
$401$	2.30938	+	16.0621i	0.115325	+	0.802102i	0.962596	+	0.270941i	$0.0873350\pi$
$401$	2.30938	+	16.0621i	0.115325	+	0.802102i	−0.847271	+	0.531161i	$0.821756\pi$
$402$		0			0
$403$	−11.1824	−	24.4860i	−0.557033	−	1.21973i
$404$	−2.20898	−	15.3638i	−0.109901	−	0.764378i
$405$		0			0
$406$	−9.23442	+	2.71147i	−0.458296	+	0.134568i
$407$	5.12731	−	35.6612i	0.254151	−	1.76766i
$408$		0			0
$409$	21.6257	−	13.8980i	1.06932	−	0.687212i	0.117255	−	0.993102i	$-0.462590\pi$
$409$	21.6257	−	13.8980i	1.06932	−	0.687212i	0.952067	+	0.305890i	$0.0989540\pi$
$410$	8.41950	+	9.71662i	0.415809	+	0.479869i
$411$		0			0
$412$	−7.30113	+	15.9873i	−0.359701	+	0.787635i
$413$	−0.460656			−0.0226674
$414$		0			0
$415$	38.3551			1.88278
$416$	−2.43652	+	5.33524i	−0.119460	+	0.261582i
$417$		0			0
$418$	−6.68328	−	7.71291i	−0.326890	−	0.377251i
$419$	1.28477	−	0.825669i	0.0627649	−	0.0403366i	−0.508882	−	0.860836i	$-0.669941\pi$
$419$	1.28477	−	0.825669i	0.0627649	−	0.0403366i	0.571647	+	0.820500i	$0.306305\pi$
$420$		0			0
$421$	2.17221	−	15.1080i	0.105867	−	0.736320i	−0.865873	−	0.500264i	$-0.833236\pi$
$421$	2.17221	−	15.1080i	0.105867	−	0.736320i	0.971740	−	0.236056i	$-0.0758547\pi$
$422$	21.1133	−	6.19942i	1.02778	−	0.301783i
$423$		0			0
$424$	0.409819	+	2.85036i	0.0199026	+	0.138425i
$425$	−8.17736	−	17.9059i	−0.396660	−	0.868565i
$426$		0			0
$427$	0.164735	+	1.14576i	0.00797209	+	0.0554471i
$428$	8.16236	+	5.24563i	0.394543	+	0.253557i
$429$		0			0
$430$	−0.227578	+	1.58284i	−0.0109748	+	0.0763313i
$431$	1.10430	−	1.27443i	0.0531924	−	0.0613873i	−0.728530	−	0.685014i	$-0.759796\pi$
$431$	1.10430	−	1.27443i	0.0531924	−	0.0613873i	0.781722	+	0.623627i	$0.214341\pi$
$432$		0			0
$433$	−9.91925	−	11.4474i	−0.476689	−	0.550128i	0.465571	−	0.885010i	$-0.345849\pi$
$433$	−9.91925	−	11.4474i	−0.476689	−	0.550128i	−0.942260	+	0.334882i	$0.891303\pi$
$434$	−4.69997	−	1.38004i	−0.225606	−	0.0662438i
$435$		0			0
$436$	−9.87335			−0.472848
$437$	4.49419	−	10.7645i	0.214986	−	0.514937i
$438$		0			0
$439$	−7.06459	+	15.4693i	−0.337175	+	0.738309i	−0.999945	−	0.0105135i	$-0.996653\pi$
$439$	−7.06459	+	15.4693i	−0.337175	+	0.738309i	0.662770	+	0.748823i	$0.269381\pi$
$440$	11.8525	+	3.48021i	0.565046	+	0.165913i
$441$		0			0
$442$	26.4829	−	17.0195i	1.25966	−	0.809536i
$443$	−9.98045	+	11.5180i	−0.474185	+	0.547239i	−0.941571	−	0.336814i	$-0.890650\pi$
$443$	−9.98045	+	11.5180i	−0.474185	+	0.547239i	0.467386	+	0.884054i	$0.345196\pi$
$444$		0			0
$445$	−20.3510	+	5.97558i	−0.964728	+	0.283270i
$446$	−18.7083	−	12.0231i	−0.885863	−	0.569310i
$447$		0			0
$448$	0.443376	+	0.970858i	0.0209476	+	0.0458687i
$449$	0.207060	+	0.453399i	0.00977177	+	0.0213972i	0.914455	−	0.404688i	$-0.132620\pi$
$449$	0.207060	+	0.453399i	0.00977177	+	0.0213972i	−0.904683	+	0.426085i	$0.859892\pi$
$450$		0			0
$451$	15.4147	+	9.90640i	0.725848	+	0.466474i
$452$	8.68673	−	2.55065i	0.408589	−	0.119973i
$453$		0			0
$454$	9.23730	−	10.6604i	0.433528	−	0.500318i
$455$	15.5044	−	9.96407i	0.726857	−	0.467123i
$456$		0			0
$457$	7.30868	+	2.14602i	0.341886	+	0.100387i	0.448168	−	0.893949i	$-0.352077\pi$
$457$	7.30868	+	2.14602i	0.341886	+	0.100387i	−0.106282	+	0.994336i	$0.533895\pi$
$458$	−3.68568	+	8.07052i	−0.172221	+	0.377111i
$459$		0			0
$460$	2.46798	+	13.9019i	0.115070	+	0.648181i
$461$	−14.5940			−0.679709			−0.339855	−	0.940478i	$-0.610378\pi$
$461$	−14.5940			−0.679709			−0.339855	+	0.940478i	$0.610378\pi$
$462$		0			0
$463$	−33.4669	−	9.82675i	−1.55534	−	0.456688i	−0.612646	−	0.790357i	$-0.709895\pi$
$463$	−33.4669	−	9.82675i	−1.55534	−	0.456688i	−0.942690	+	0.333669i	$0.891713\pi$
$464$	−5.90509	−	6.81484i	−0.274137	−	0.316371i
$465$		0			0
$466$	4.69042	−	5.41303i	0.217279	−	0.250754i
$467$	1.81080	−	12.5944i	0.0837939	−	0.582799i	−0.904059	−	0.427407i	$-0.859427\pi$
$467$	1.81080	−	12.5944i	0.0837939	−	0.582799i	0.987853	−	0.155392i	$-0.0496639\pi$
$468$		0			0
$469$	−2.58420	−	1.66076i	−0.119327	−	0.0766869i
$470$	0.675111	+	4.69550i	0.0311405	+	0.216587i
$471$		0			0
$472$	−0.179295	−	0.392602i	−0.00825273	−	0.0180710i
$473$	0.324340	+	2.25583i	0.0149132	+	0.103723i
$474$		0			0
$475$	−8.55942	+	2.51327i	−0.392733	+	0.115317i
$476$	0.815249	−	5.67018i	0.0373669	−	0.259892i
$477$		0			0
$478$	−17.9431	+	11.5313i	−0.820699	+	0.527431i
$479$	4.39108	+	5.06758i	0.200634	+	0.231544i	0.847146	−	0.531360i	$-0.178319\pi$
$479$	4.39108	+	5.06758i	0.200634	+	0.231544i	−0.646513	+	0.762903i	$0.723773\pi$
$480$		0			0
$481$	20.9214	−	45.8115i	0.953934	−	2.08882i
$482$	−16.9437			−0.771765
$483$		0			0
$484$	6.60511			0.300232
$485$	−14.0320	+	30.7258i	−0.637160	+	1.39518i
$486$		0			0
$487$	19.5530	+	22.5653i	0.886030	+	1.02253i	0.999579	+	0.0290004i	$0.00923241\pi$
$487$	19.5530	+	22.5653i	0.886030	+	1.02253i	−0.113550	+	0.993532i	$0.536222\pi$
$488$	−0.912374	+	0.586347i	−0.0413012	+	0.0265427i
$489$		0			0
$490$	−2.45561	+	17.0792i	−0.110933	+	0.771558i
$491$	4.98861	−	1.46479i	0.225133	−	0.0661049i	−0.167221	−	0.985919i	$-0.553479\pi$
$491$	4.98861	−	1.46479i	0.225133	−	0.0661049i	0.392353	+	0.919815i	$0.371661\pi$
$492$		0			0
$493$	6.88775	+	47.9054i	0.310209	+	2.15755i
$494$	−5.92641	−	12.9770i	−0.266642	−	0.583864i
$495$		0			0
$496$	−0.653151	−	4.54276i	−0.0293273	−	0.203976i
$497$	5.76890	+	3.70745i	0.258771	+	0.166302i
$498$		0			0
$499$	2.00133	−	13.9195i	0.0895916	−	0.623124i	−0.894712	−	0.446643i	$-0.852620\pi$
$499$	2.00133	−	13.9195i	0.0895916	−	0.623124i	0.984304	−	0.176481i	$-0.0564714\pi$
$500$	−2.56883	+	2.96458i	−0.114881	+	0.132580i
$501$		0			0
$502$	−19.4449	−	22.4406i	−0.867869	−	1.00157i
$503$	−23.7212	−	6.96518i	−1.05768	−	0.310562i	−0.293762	−	0.955879i	$-0.594907\pi$
$503$	−23.7212	−	6.96518i	−1.05768	−	0.310562i	−0.763915	+	0.645317i	$0.776725\pi$
$504$		0			0
$505$	−45.6974			−2.03351
$506$	8.95675	+	18.0193i	0.398176	+	0.801054i
$507$		0			0
$508$	5.10228	−	11.1724i	0.226377	−	0.495697i
$509$	17.5533	+	5.15410i	0.778035	+	0.228452i	0.646555	−	0.762867i	$-0.276209\pi$
$509$	17.5533	+	5.15410i	0.778035	+	0.228452i	0.131480	+	0.991319i	$0.458027\pi$
$510$		0			0
$511$	−12.0327	+	7.73293i	−0.532294	+	0.342085i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$		0			0
$514$	4.52944	−	1.32997i	0.199785	−	0.0586622i
$515$	43.5296	+	27.9747i	1.91814	+	1.23271i
$516$		0			0
$517$	2.80852	+	6.14980i	0.123518	+	0.270468i
$518$	−3.80708	−	8.33635i	−0.167274	−	0.366278i
$519$		0			0
$520$	14.5266	+	9.33569i	0.637034	+	0.409397i
$521$	−15.8178	+	4.64451i	−0.692988	+	0.203480i	−0.609215	−	0.793005i	$-0.708515\pi$
$521$	−15.8178	+	4.64451i	−0.692988	+	0.203480i	−0.0837733	+	0.996485i	$0.526697\pi$
$522$		0			0
$523$	10.6183	−	12.2542i	0.464306	−	0.535837i	−0.474513	−	0.880248i	$-0.657376\pi$
$523$	10.6183	−	12.2542i	0.464306	−	0.535837i	0.938819	+	0.344411i	$0.111921\pi$
$524$	−18.8679	+	12.1257i	−0.824250	+	0.529713i
$525$		0			0
$526$	18.6154	+	5.46598i	0.811671	+	0.238328i
$527$	−10.2328	+	22.4067i	−0.445749	+	0.976053i
$528$		0			0
$529$	−13.8864	+	18.3349i	−0.603755	+	0.797170i
$530$	8.47796			0.368259
$531$		0			0
$532$	−2.49088	−	0.731389i	−0.107993	−	0.0317097i
$533$	16.7736	+	19.3577i	0.726544	+	0.838476i
$534$		0			0
$535$	18.7063	−	21.5882i	0.808742	−	0.933339i
$536$	0.409599	−	2.84882i	0.0176920	−	0.123050i
$537$		0			0
$538$	−1.85085	−	1.18947i	−0.0797958	−	0.0512817i
$539$	3.49970	+	24.3409i	0.150743	+	1.04844i
$540$		0			0
$541$	−2.89899	−	6.34790i	−0.124637	−	0.272917i	0.837020	−	0.547173i	$-0.184296\pi$
$541$	−2.89899	−	6.34790i	−0.124637	−	0.272917i	−0.961657	+	0.274255i	$0.911569\pi$
$542$	4.13542	+	28.7625i	0.177631	+	1.23545i
$543$		0			0
$544$	5.14982	−	1.51212i	0.220797	−	0.0648317i
$545$	−4.13679	+	28.7720i	−0.177201	+	1.23246i
$546$		0			0
$547$	−36.0522	+	23.1693i	−1.54148	+	0.990649i	−0.554070	+	0.832470i	$0.686926\pi$
$547$	−36.0522	+	23.1693i	−1.54148	+	0.990649i	−0.987410	+	0.158179i	$0.949438\pi$
$548$	2.76931	+	3.19595i	0.118299	+	0.136524i
$549$		0			0
$550$	6.39268	−	13.9980i	0.272585	−	0.596877i
$551$	21.9330			0.934379
$552$		0			0
$553$	−1.40113			−0.0595820
$554$	2.27654	−	4.98493i	0.0967210	−	0.211789i
$555$		0			0
$556$	−4.33449	−	5.00227i	−0.183823	−	0.212144i
$557$	19.4597	−	12.5060i	0.824536	−	0.529897i	−0.0590015	−	0.998258i	$-0.518792\pi$
$557$	19.4597	−	12.5060i	0.824536	−	0.529897i	0.883537	+	0.468361i	$0.155155\pi$
$558$		0			0
$559$	−0.453387	+	3.15338i	−0.0191762	+	0.133374i
$560$	3.01496	−	0.885271i	0.127405	−	0.0374095i
$561$		0			0
$562$	−2.73195	−	19.0011i	−0.115240	−	0.801515i
$563$	−12.9279	−	28.3081i	−0.544845	−	1.19304i	−0.959148	−	0.282905i	$-0.908702\pi$
$563$	−12.9279	−	28.3081i	−0.544845	−	1.19304i	0.414303	−	0.910139i	$-0.364025\pi$
$564$		0			0
$565$	−3.79327	−	26.3828i	−0.159584	−	1.10993i
$566$	11.5682	+	7.43441i	0.486246	+	0.312491i
$567$		0			0
$568$	−0.914379	+	6.35964i	−0.0383665	+	0.266845i
$569$	17.0555	−	19.6831i	0.715003	−	0.825157i	−0.275694	−	0.961245i	$-0.588908\pi$
$569$	17.0555	−	19.6831i	0.715003	−	0.825157i	0.990697	+	0.136088i	$0.0434531\pi$
$570$		0			0
$571$	−3.29341	−	3.80080i	−0.137825	−	0.159059i	0.682641	−	0.730754i	$-0.260831\pi$
$571$	−3.29341	−	3.80080i	−0.137825	−	0.159059i	−0.820466	+	0.571695i	$0.806286\pi$
$572$	23.6129	+	6.93338i	0.987306	+	0.289899i
$573$		0			0
$574$	4.66099			0.194546
$575$	17.5796	−	0.578539i	0.733122	−	0.0241268i
$576$		0			0
$577$	−11.7759	+	25.7855i	−0.490236	+	1.07347i	0.489285	+	0.872124i	$0.337258\pi$
$577$	−11.7759	+	25.7855i	−0.490236	+	1.07347i	−0.979521	+	0.201343i	$0.935470\pi$
$578$	−11.3288	−	3.32645i	−0.471218	−	0.138362i
$579$		0			0
$580$	−22.3333	+	14.3528i	−0.927341	+	0.595966i
$581$	9.10569	−	10.5085i	0.377768	−	0.435967i
$582$		0			0
$583$	11.5932	−	3.40407i	0.480141	−	0.140982i
$584$	−11.2738	−	7.24526i	−0.466515	−	0.299811i
$585$		0			0
$586$	0.353332	+	0.773688i	0.0145960	+	0.0319608i
$587$	−4.70486	−	10.3022i	−0.194191	−	0.425218i	0.787341	−	0.616518i	$-0.211457\pi$
$587$	−4.70486	−	10.3022i	−0.194191	−	0.425218i	−0.981532	+	0.191300i	$0.938730\pi$
$588$		0			0
$589$	9.39099	+	6.03522i	0.386949	+	0.248677i
$590$	−1.21921	+	0.357992i	−0.0501940	+	0.0147383i
$591$		0			0
$592$	5.62301	−	6.48930i	0.231104	−	0.266709i
$593$	−2.99628	+	1.92559i	−0.123042	+	0.0790746i	−0.600714	−	0.799464i	$-0.705117\pi$
$593$	−2.99628	+	1.92559i	−0.123042	+	0.0790746i	0.477672	+	0.878538i	$0.341481\pi$
$594$		0			0
$595$	−16.1820	−	4.75145i	−0.663396	−	0.194791i
$596$	1.46152	−	3.20028i	0.0598661	−	0.131088i
$597$		0			0
$598$	4.91678	+	27.6958i	0.201062	+	1.13257i
$599$	28.0028			1.14417			0.572083	−	0.820196i	$-0.306136\pi$
$599$	28.0028			1.14417			0.572083	+	0.820196i	$0.306136\pi$
$600$		0			0
$601$	21.3296	+	6.26294i	0.870054	+	0.255471i	0.686138	−	0.727471i	$-0.259305\pi$
$601$	21.3296	+	6.26294i	0.870054	+	0.255471i	0.183916	+	0.982942i	$0.441123\pi$
$602$	0.379638	+	0.438126i	0.0154729	+	0.0178567i
$603$		0			0
$604$	−12.5286	+	14.4588i	−0.509781	+	0.588319i
$605$	2.76745	−	19.2480i	0.112513	−	0.782543i
$606$		0			0
$607$	12.7781	+	8.21198i	0.518647	+	0.333314i	0.773636	−	0.633630i	$-0.218436\pi$
$607$	12.7781	+	8.21198i	0.518647	+	0.333314i	−0.254990	+	0.966944i	$0.582072\pi$
$608$	−0.346156	−	2.40757i	−0.0140385	−	0.0976397i
$609$		0			0
$610$	1.32641	+	2.90443i	0.0537047	+	0.117597i
$611$	1.34498	+	9.35451i	0.0544119	+	0.378443i
$612$		0			0
$613$	−16.4705	+	4.83616i	−0.665235	+	0.195331i	−0.596880	−	0.802330i	$-0.703593\pi$
$613$	−16.4705	+	4.83616i	−0.665235	+	0.195331i	−0.0683551	+	0.997661i	$0.521775\pi$
$614$	−0.967604	+	6.72983i	−0.0390493	+	0.271594i
$615$		0			0
$616$	3.76735	−	2.42113i	0.151791	−	0.0975502i
$617$	25.5443	+	29.4797i	1.02837	+	1.18681i	0.982193	+	0.187873i	$0.0601594\pi$
$617$	25.5443	+	29.4797i	1.02837	+	1.18681i	0.0461802	+	0.998933i	$0.485295\pi$
$618$		0			0
$619$	−4.54357	+	9.94902i	−0.182621	+	0.399885i	−0.978696	−	0.205313i	$-0.934179\pi$
$619$	−4.54357	+	9.94902i	−0.182621	+	0.399885i	0.796075	+	0.605198i	$0.206906\pi$
$620$	−13.5118			−0.542646
$621$		0			0
$622$	14.3525			0.575484
$623$	−3.19423	+	6.99439i	−0.127974	+	0.280224i
$624$		0			0
$625$	19.5716	+	22.5869i	0.782866	+	0.903475i
$626$	2.78966	−	1.79280i	0.111497	−	0.0716548i
$627$		0			0
$628$	3.27942	−	22.8089i	0.130863	−	0.910172i
$629$	−44.2193	+	12.9840i	−1.76314	+	0.517704i
$630$		0			0
$631$	−4.60826	−	32.0511i	−0.183452	−	1.27594i	−0.848524	−	0.529156i	$-0.822508\pi$
$631$	−4.60826	−	32.0511i	−0.183452	−	1.27594i	0.665072	−	0.746779i	$-0.268401\pi$
$632$	−0.545343	−	1.19414i	−0.0216926	−	0.0475002i
$633$		0			0
$634$	−2.78612	−	19.3779i	−0.110651	−	0.769595i
$635$	−30.4199	−	19.5497i	−1.20718	−	0.775806i
$636$		0			0
$637$	−4.89215	+	34.0256i	−0.193834	+	1.34814i
$638$	−24.7768	+	28.5940i	−0.980924	+	1.13205i
$639$		0			0
$640$	1.92796	+	2.22499i	0.0762093	+	0.0879503i
$641$	−25.5918	−	7.51443i	−1.01081	−	0.296802i	−0.265928	−	0.963993i	$-0.585678\pi$
$641$	−25.5918	−	7.51443i	−1.01081	−	0.296802i	−0.744887	+	0.667191i	$0.767497\pi$
$642$		0			0
$643$	4.32227			0.170454			0.0852268	−	0.996362i	$-0.472839\pi$
$643$	4.32227			0.170454			0.0852268	+	0.996362i	$0.472839\pi$
$644$	4.39476	+	2.62421i	0.173178	+	0.103408i
$645$		0			0
$646$	−5.42317	+	11.8751i	−0.213372	+	0.467219i
$647$	36.5856	+	10.7425i	1.43833	+	0.422331i	0.905664	−	0.423996i	$-0.139373\pi$
$647$	36.5856	+	10.7425i	1.43833	+	0.422331i	0.532664	+	0.846327i	$0.321191\pi$
$648$		0			0
$649$	−1.52347	+	0.979072i	−0.0598013	+	0.0384319i
$650$	14.0870	−	16.2573i	0.552538	−	0.637663i
$651$		0			0
$652$	8.60820	−	2.52760i	0.337123	−	0.0989883i
$653$	−8.85523	−	5.69091i	−0.346532	−	0.222703i	0.355784	−	0.934568i	$-0.384214\pi$
$653$	−8.85523	−	5.69091i	−0.346532	−	0.222703i	−0.702315	+	0.711866i	$0.747850\pi$
$654$		0			0
$655$	27.4302	+	60.0638i	1.07179	+	2.34689i
$656$	1.81414	+	3.97241i	0.0708301	+	0.155096i
$657$		0			0
$658$	1.44675	+	0.929768i	0.0564001	+	0.0362461i
$659$	19.9109	−	5.84637i	0.775619	−	0.227742i	0.130115	−	0.991499i	$-0.458465\pi$
$659$	19.9109	−	5.84637i	0.775619	−	0.227742i	0.645504	+	0.763757i	$0.276647\pi$
$660$		0			0
$661$	7.65931	−	8.83932i	0.297913	−	0.343810i	−0.586983	−	0.809600i	$-0.699684\pi$
$661$	7.65931	−	8.83932i	0.297913	−	0.343810i	0.884895	+	0.465790i	$0.154230\pi$
$662$	3.01005	−	1.93444i	0.116989	−	0.0751843i
$663$		0			0
$664$	12.5002	+	3.67038i	0.485100	+	0.142438i
$665$	−3.17499	+	6.95227i	−0.123121	+	0.269597i
$666$		0			0
$667$	−41.8721	−	10.8123i	−1.62129	−	0.418653i
$668$	−4.97958			−0.192666
$669$		0			0
$670$	−8.13017	−	2.38723i	−0.314096	−	0.0922268i
$671$	2.97999	+	3.43909i	0.115041	+	0.132764i
$672$		0			0
$673$	9.25493	−	10.6808i	0.356751	−	0.411713i	−0.548797	−	0.835955i	$-0.684914\pi$
$673$	9.25493	−	10.6808i	0.356751	−	0.411713i	0.905549	+	0.424243i	$0.139460\pi$
$674$	−3.88318	+	27.0081i	−0.149575	+	1.04031i
$675$		0			0
$676$	18.0041	+	11.5705i	0.692464	+	0.445019i
$677$	0.486078	+	3.38075i	0.0186815	+	0.129933i	0.997028	−	0.0770416i	$-0.0245474\pi$
$677$	0.486078	+	3.38075i	0.0186815	+	0.129933i	−0.978346	+	0.206974i	$0.933638\pi$
$678$		0			0
$679$	5.08698	+	11.1389i	0.195220	+	0.427473i
$680$	−2.24879	−	15.6407i	−0.0862372	−	0.599793i
$681$		0			0
$682$	−18.4767	+	5.42525i	−0.707509	+	0.207743i
$683$	0.593229	−	4.12600i	0.0226993	−	0.157877i	−0.975319	−	0.220800i	$-0.929133\pi$
$683$	0.593229	−	4.12600i	0.0226993	−	0.157877i	0.998018	+	0.0629231i	$0.0200423\pi$
$684$		0			0
$685$	10.4737	−	6.73101i	0.400178	−	0.257179i
$686$	8.98895	+	10.3738i	0.343200	+	0.396073i
$687$		0			0
$688$	−0.225638	+	0.494079i	−0.00860238	+	0.0188366i
$689$	16.8900			0.643459
$690$		0			0
$691$	36.7618			1.39849			0.699243	−	0.714884i	$-0.253520\pi$
$691$	36.7618			1.39849			0.699243	+	0.714884i	$0.253520\pi$
$692$	5.06771	−	11.0967i	0.192646	−	0.421835i
$693$		0			0
$694$	17.0994	+	19.7338i	0.649085	+	0.749084i
$695$	−16.3933	+	10.5353i	−0.621832	+	0.399627i
$696$		0			0
$697$	3.33571	−	23.2004i	0.126349	−	0.878776i
$698$	−15.8763	+	4.66171i	−0.600928	+	0.176448i
$699$		0			0
$700$	−0.557085	−	3.87461i	−0.0210558	−	0.146447i
$701$	−4.71530	−	10.3251i	−0.178095	−	0.389973i	0.799441	−	0.600745i	$-0.205129\pi$
$701$	−4.71530	−	10.3251i	−0.178095	−	0.389973i	−0.977535	+	0.210772i	$0.932402\pi$
$702$		0			0
$703$	2.97229	+	20.6728i	0.112102	+	0.779688i
$704$	3.52977	+	2.26844i	0.133033	+	0.0854952i
$705$		0			0
$706$	−1.06782	+	7.42687i	−0.0401881	+	0.279514i
$707$	−10.8488	+	12.5202i	−0.408011	+	0.470870i
$708$		0			0
$709$	18.2818	+	21.0983i	0.686586	+	0.792363i	0.986875	−	0.161486i	$-0.0516285\pi$
$709$	18.2818	+	21.0983i	0.686586	+	0.792363i	−0.300289	+	0.953848i	$0.597083\pi$
$710$	18.1496	+	5.32920i	0.681142	+	0.200001i
$711$		0			0
$712$	−7.20433			−0.269994
$713$	−14.9531	−	16.1512i	−0.559996	−	0.604868i
$714$		0			0
$715$	30.0981	−	65.9057i	1.12561	−	2.46473i
$716$	10.1568	+	2.98230i	0.379577	+	0.111454i
$717$		0			0
$718$	2.88413	−	1.85351i	0.107635	−	0.0691726i
$719$	−3.60399	+	4.15923i	−0.134406	+	0.155113i	−0.818963	−	0.573847i	$-0.805450\pi$
$719$	−3.60399	+	4.15923i	−0.134406	+	0.155113i	0.684556	+	0.728960i	$0.259996\pi$
$720$		0			0
$721$	17.9987	−	5.28488i	0.670305	−	0.196819i
$722$	−11.0068	−	7.07364i	−0.409631	−	0.263254i
$723$		0			0
$724$	−9.31604	−	20.3993i	−0.346228	−	0.758133i
$725$	13.7386	+	30.0832i	0.510237	+	1.11726i
$726$		0			0
$727$	−6.36734	−	4.09204i	−0.236151	−	0.151765i	0.417213	−	0.908809i	$-0.363007\pi$
$727$	−6.36734	−	4.09204i	−0.236151	−	0.151765i	−0.653365	+	0.757043i	$0.726643\pi$
$728$	6.00648	−	1.76366i	0.222615	−	0.0653657i
$729$		0			0
$730$	−25.8371	+	29.8176i	−0.956273	+	1.10360i
$731$	2.45249	−	1.57612i	0.0907087	−	0.0582949i
$732$		0			0
$733$	−46.3321	−	13.6043i	−1.71132	−	0.502488i	−0.728184	−	0.685382i	$-0.759635\pi$
$733$	−46.3321	−	13.6043i	−1.71132	−	0.502488i	−0.983133	+	0.182894i	$0.941454\pi$
$734$	−2.60618	+	5.70674i	−0.0961958	+	0.210639i
$735$		0			0
$736$	−0.526011	+	4.76690i	−0.0193890	+	0.175710i
$737$	−12.0761			−0.444830
$738$		0			0
$739$	36.9215	+	10.8411i	1.35818	+	0.398798i	0.878121	−	0.478439i	$-0.158797\pi$
$739$	36.9215	+	10.8411i	1.35818	+	0.398798i	0.480059	+	0.877236i	$0.340615\pi$
$740$	−16.5546	−	19.1050i	−0.608559	−	0.702314i
$741$		0			0
$742$	2.01271	−	2.32279i	0.0738889	−	0.0852723i
$743$	4.87878	−	33.9327i	0.178985	−	1.24487i	−0.680132	−	0.733090i	$-0.738078\pi$
$743$	4.87878	−	33.9327i	0.178985	−	1.24487i	0.859117	−	0.511779i	$-0.171013\pi$
$744$		0			0
$745$	−8.71361	−	5.59990i	−0.319242	−	0.205164i
$746$	1.45917	+	10.1488i	0.0534242	+	0.371573i
$747$		0			0
$748$	−9.35516	−	20.4850i	−0.342059	−	0.749004i
$749$	−1.47377	−	10.2503i	−0.0538503	−	0.374537i
$750$		0			0
$751$	−24.8177	+	7.28714i	−0.905611	+	0.265911i	−0.701192	−	0.712972i	$-0.747349\pi$
$751$	−24.8177	+	7.28714i	−0.905611	+	0.265911i	−0.204419	+	0.978884i	$0.565530\pi$
$752$	−0.229312	+	1.59490i	−0.00836213	+	0.0581599i
$753$		0			0
$754$	−44.4931	+	28.5940i	−1.62034	+	1.04133i
$755$	36.8852	+	42.5678i	1.34239	+	1.54920i
$756$		0			0
$757$	6.84038	−	14.9783i	0.248618	−	0.544397i	−0.743642	−	0.668578i	$-0.766903\pi$
$757$	6.84038	−	14.9783i	0.248618	−	0.544397i	0.992260	+	0.124181i	$0.0396304\pi$
$758$	−19.8019			−0.719238
$759$		0			0
$760$	−7.16095			−0.259755
$761$	12.8854	−	28.2150i	0.467094	−	1.02279i	−0.518719	−	0.854945i	$-0.673591\pi$
$761$	12.8854	−	28.2150i	0.467094	−	1.02279i	0.985813	−	0.167848i	$-0.0536817\pi$
$762$		0			0
$763$	6.90087	+	7.96402i	0.249828	+	0.288317i
$764$	4.77274	−	3.06725i	0.172672	−	0.110969i
$765$		0			0
$766$	−0.954965	+	6.64193i	−0.0345043	+	0.239983i
$767$	−2.42894	+	0.713201i	−0.0877039	+	0.0257522i
$768$		0			0
$769$	−1.06161	−	7.38365i	−0.0382826	−	0.266261i	0.961686	−	0.274152i	$-0.0883973\pi$
$769$	−1.06161	−	7.38365i	−0.0382826	−	0.266261i	−0.999969	+	0.00789110i	$0.997488\pi$
$770$	−5.47698	−	11.9929i	−0.197377	−	0.432194i
$771$		0			0
$772$	−0.272900	−	1.89806i	−0.00982190	−	0.0683128i
$773$	7.36262	+	4.73167i	0.264815	+	0.170186i	0.666310	−	0.745675i	$-0.267873\pi$
$773$	7.36262	+	4.73167i	0.264815	+	0.170186i	−0.401495	+	0.915861i	$0.631509\pi$
$774$		0			0
$775$	−2.39549	+	16.6610i	−0.0860486	+	0.598481i
$776$	−7.51340	+	8.67093i	−0.269715	+	0.311268i
$777$		0			0
$778$	−7.77164	−	8.96895i	−0.278627	−	0.321552i
$779$	−10.1918	−	2.99258i	−0.365159	−	0.107220i
$780$		0			0
$781$	26.9585			0.964650
$782$	16.2073	−	19.9971i	0.579574	−	0.715096i
$783$		0			0
$784$	−2.43469	+	5.33122i	−0.0869531	+	0.190401i
$785$	−65.0935	−	19.1132i	−2.32329	−	0.682179i
$786$		0			0
$787$	−17.7866	+	11.4307i	−0.634023	+	0.407462i	−0.817797	−	0.575507i	$-0.804805\pi$
$787$	−17.7866	+	11.4307i	−0.634023	+	0.407462i	0.183774	+	0.982968i	$0.441168\pi$
$788$	5.25280	−	6.06205i	0.187123	−	0.215952i
$789$		0			0
$790$	−3.70833	+	1.08887i	−0.131937	+	0.0387401i
$791$	−8.12889	−	5.22412i	−0.289030	−	0.185748i
$792$		0			0
$793$	2.64251	+	5.78629i	0.0938382	+	0.205477i
$794$	1.99487	+	4.36815i	0.0707952	+	0.155020i
$795$		0			0
$796$	−12.6939	−	8.15787i	−0.449923	−	0.289148i
$797$	22.1110	−	6.49239i	0.783214	−	0.229972i	0.134408	−	0.990926i	$-0.457087\pi$
$797$	22.1110	−	6.49239i	0.783214	−	0.229972i	0.648806	+	0.760954i	$0.275269\pi$
$798$		0			0
$799$	5.66336	−	6.53587i	0.200355	−	0.231222i
$800$	3.08538	−	1.98285i	0.109085	−	0.0701044i
$801$		0			0
$802$	15.5699	+	4.57175i	0.549794	+	0.161434i
$803$	−23.3586	+	51.1482i	−0.824306	+	1.80498i
$804$		0			0
$805$	9.48858	−	11.7073i	0.334429	−	0.412629i
$806$	−26.9185			−0.948165
$807$		0			0
$808$	−14.8931	−	4.37300i	−0.523936	−	0.153842i
$809$	8.35194	+	9.63865i	0.293639	+	0.338877i	0.883330	−	0.468752i	$-0.155296\pi$
$809$	8.35194	+	9.63865i	0.293639	+	0.338877i	−0.589691	+	0.807629i	$0.700751\pi$
$810$		0			0
$811$	16.3239	−	18.8388i	0.573210	−	0.661520i	−0.392921	−	0.919572i	$-0.628535\pi$
$811$	16.3239	−	18.8388i	0.573210	−	0.661520i	0.966131	+	0.258053i	$0.0830808\pi$
$812$	−1.36968	+	9.52631i	−0.0480662	+	0.334308i
$813$		0			0
$814$	−30.3086	−	19.4782i	−1.06232	−	0.682710i
$815$	−3.75898	−	26.1443i	−0.131671	−	0.915794i
$816$		0			0
$817$	−0.548825	−	1.20176i	−0.0192010	−	0.0420443i
$818$	−3.65842	−	25.4449i	−0.127914	−	0.889659i
$819$		0			0
$820$	12.3361	−	3.62221i	0.430796	−	0.126493i
$821$	−2.74707	+	19.1063i	−0.0958733	+	0.666813i	0.884043	+	0.467405i	$0.154811\pi$
$821$	−2.74707	+	19.1063i	−0.0958733	+	0.666813i	−0.979917	+	0.199408i	$0.936098\pi$
$822$		0			0
$823$	19.8677	−	12.7682i	0.692546	−	0.445072i	−0.146444	−	0.989219i	$-0.546783\pi$
$823$	19.8677	−	12.7682i	0.692546	−	0.445072i	0.838990	+	0.544147i	$0.183146\pi$
$824$	11.5095	+	13.2827i	0.400953	+	0.462724i
$825$		0			0
$826$	−0.191363	+	0.419027i	−0.00665838	+	0.0145798i
$827$	8.84206			0.307469			0.153734	−	0.988112i	$-0.450870\pi$
$827$	8.84206			0.307469			0.153734	+	0.988112i	$0.450870\pi$
$828$		0			0
$829$	19.0563			0.661853			0.330926	−	0.943657i	$-0.392639\pi$
$829$	19.0563			0.661853			0.330926	+	0.943657i	$0.392639\pi$
$830$	15.9333	−	34.8890i	0.553052	−	1.21102i
$831$		0			0
$832$	3.84094	+	4.43268i	0.133161	+	0.153676i
$833$	26.4629	−	17.0067i	0.916885	−	0.589246i
$834$		0			0
$835$	−2.08638	+	14.5111i	−0.0722020	+	0.502176i
$836$	−9.79225	+	2.87526i	−0.338672	+	0.0994431i
$837$		0			0
$838$	−0.217344	−	1.51166i	−0.00750802	−	0.0522194i
$839$	18.8332	+	41.2389i	0.650194	+	1.42373i	0.891384	+	0.453249i	$0.149735\pi$
$839$	18.8332	+	41.2389i	0.650194	+	1.42373i	−0.241190	+	0.970478i	$0.577538\pi$
$840$		0			0
$841$	−7.44478	−	51.7796i	−0.256717	−	1.78550i
$842$	−12.8404	−	8.25201i	−0.442508	−	0.284383i
$843$		0			0
$844$	3.13159	−	21.7807i	0.107794	−	0.749721i
$845$	41.2612	−	47.6179i	1.41943	−	1.63811i
$846$		0			0
$847$	−4.61657	−	5.32780i	−0.158627	−	0.183065i
$848$	2.76302	+	0.811296i	0.0948825	+	0.0278600i
$849$		0			0
$850$	−19.6848			−0.675183
$851$	4.51663	−	40.9313i	0.154828	−	1.40311i
$852$		0			0
$853$	18.5846	−	40.6945i	0.636324	−	1.39335i	−0.266707	−	0.963778i	$-0.585936\pi$
$853$	18.5846	−	40.6945i	0.636324	−	1.39335i	0.903030	−	0.429577i	$-0.141337\pi$
$854$	1.11065	+	0.326117i	0.0380057	+	0.0111595i
$855$		0			0
$856$	8.16236	−	5.24563i	0.278984	−	0.179292i
$857$	−0.538599	+	0.621576i	−0.0183982	+	0.0212326i	−0.764874	−	0.644180i	$-0.777199\pi$
$857$	−0.538599	+	0.621576i	−0.0183982	+	0.0212326i	0.746476	+	0.665412i	$0.231744\pi$
$858$		0			0
$859$	−23.1852	+	6.80778i	−0.791067	+	0.232278i	−0.652214	−	0.758035i	$-0.726160\pi$
$859$	−23.1852	+	6.80778i	−0.791067	+	0.232278i	−0.138853	+	0.990313i	$0.544342\pi$
$860$	1.34526	+	0.864548i	0.0458731	+	0.0294808i
$861$		0			0
$862$	−0.700522	−	1.53393i	−0.0238599	−	0.0522458i
$863$	−9.08323	−	19.8895i	−0.309197	−	0.677046i	0.689696	−	0.724099i	$-0.257744\pi$
$863$	−9.08323	−	19.8895i	−0.309197	−	0.677046i	−0.998892	+	0.0470531i	$0.985017\pi$
$864$		0			0
$865$	−30.2138	−	19.4173i	−1.02730	−	0.660207i
$866$	−14.5336	+	4.26744i	−0.493870	+	0.145013i
$867$		0			0
$868$	−3.20776	+	3.70196i	−0.108879	+	0.125653i
$869$	−4.63377	+	2.97794i	−0.157190	+	0.101020i
$870$		0			0
$871$	−16.1971	−	4.75591i	−0.548819	−	0.161148i
$872$	−4.10154	+	8.98111i	−0.138896	+	0.304139i
$873$		0			0
$874$	−7.92479	−	8.55980i	−0.268060	−	0.289539i
$875$	4.18674			0.141538
$876$		0			0
$877$	−33.5280	−	9.84472i	−1.13216	−	0.332432i	−0.338604	−	0.940929i	$-0.609955\pi$
$877$	−33.5280	−	9.84472i	−1.13216	−	0.332432i	−0.793557	+	0.608496i	$0.791773\pi$
$878$	11.1366	+	12.8524i	0.375843	+	0.433746i
$879$		0			0
$880$	8.08942	−	9.33569i	0.272694	−	0.314706i
$881$	−1.64055	+	11.4103i	−0.0552716	+	0.384423i	0.943344	+	0.331817i	$0.107662\pi$
$881$	−1.64055	+	11.4103i	−0.0552716	+	0.384423i	−0.998615	+	0.0526055i	$0.983247\pi$
$882$		0			0
$883$	47.0000	+	30.2050i	1.58167	+	1.01648i	0.975186	+	0.221388i	$0.0710588\pi$
$883$	47.0000	+	30.2050i	1.58167	+	1.01648i	0.606489	+	0.795092i	$0.292578\pi$
$884$	−4.48011	−	31.1598i	−0.150682	−	1.04802i
$885$		0			0
$886$	6.33116	+	13.8633i	0.212699	+	0.465747i
$887$	−6.59756	−	45.8871i	−0.221525	−	1.54074i	−0.732276	−	0.681008i	$-0.761542\pi$
$887$	−6.59756	−	45.8871i	−0.221525	−	1.54074i	0.510751	−	0.859729i	$-0.329367\pi$
$888$		0			0
$889$	−12.5781	+	3.69325i	−0.421855	+	0.123868i
$890$	−3.01851	+	20.9942i	−0.101181	+	0.703728i
$891$		0			0
$892$	−18.7083	+	12.0231i	−0.626400	+	0.402563i
$893$	−2.56653	−	2.96193i	−0.0858856	−	0.0991172i
$894$		0			0
$895$	12.9463	−	28.3485i	0.432747	−	0.947585i
$896$	1.06731			0.0356563
$897$		0			0
$898$	0.498442			0.0166332
$899$	17.1919	−	37.6449i	0.573381	−	1.25553i
$900$		0			0
$901$	−10.1214	−	11.6807i	−0.337193	−	0.389141i
$902$	15.4147	−	9.90640i	0.513252	−	0.329847i
$903$		0			0
$904$	1.28844	−	8.96130i	0.0428529	−	0.298049i
$905$	−63.3491	+	18.6010i	−2.10579	+	0.618317i
$906$		0			0
$907$	2.84332	+	19.7758i	0.0944110	+	0.656643i	0.980989	+	0.194064i	$0.0621669\pi$
$907$	2.84332	+	19.7758i	0.0944110	+	0.656643i	−0.886578	+	0.462579i	$0.846924\pi$
$908$	−5.85974	−	12.8310i	−0.194462	−	0.425813i
$909$		0			0
$910$	−2.62288	−	18.2425i	−0.0869475	−	0.604733i
$911$	11.7821	+	7.57188i	0.390357	+	0.250867i	0.721067	−	0.692865i	$-0.243652\pi$
$911$	11.7821	+	7.57188i	0.390357	+	0.250867i	−0.330710	+	0.943732i	$0.607288\pi$
$912$		0			0
$913$	7.77935	−	54.1066i	0.257459	−	1.79067i
$914$	4.98823	−	5.75672i	0.164996	−	0.190415i
$915$		0			0
$916$	5.81011	+	6.70523i	0.191972	+	0.221547i
$917$	22.9683	+	6.74411i	0.758481	+	0.222710i
$918$		0			0
$919$	44.6314			1.47226			0.736128	−	0.676843i	$-0.236652\pi$
$919$	44.6314			1.47226			0.736128	+	0.676843i	$0.236652\pi$
$920$	13.6709	+	3.53012i	0.450716	+	0.116385i
$921$		0			0
$922$	−6.06256	+	13.2751i	−0.199660	+	0.437194i
$923$	36.1581	+	10.6170i	1.19016	+	0.349462i
$924$		0			0
$925$	−26.4928	+	17.0259i	−0.871079	+	0.559808i
$926$	−22.8414	+	26.3603i	−0.750614	+	0.866254i
$927$		0			0
$928$	−8.65206	+	2.54047i	−0.284018	+	0.0833951i
$929$	−0.500592	−	0.321711i	−0.0164239	−	0.0105550i	0.532403	−	0.846491i	$-0.321289\pi$
$929$	−0.500592	−	0.321711i	−0.0164239	−	0.0105550i	−0.548827	+	0.835936i	$0.684925\pi$
$930$		0			0
$931$	−5.92194	−	12.9672i	−0.194084	−	0.424984i
$932$	−2.97540	−	6.51521i	−0.0974623	−	0.213413i
$933$		0			0
$934$	−10.7040	−	6.87906i	−0.350247	−	0.225090i
$935$	−63.6151	+	18.6791i	−2.08044	+	0.610871i
$936$		0			0
$937$	−25.7146	+	29.6762i	−0.840059	+	0.969480i	−0.999844	−	0.0176717i	$-0.994375\pi$
$937$	−25.7146	+	29.6762i	−0.840059	+	0.969480i	0.159784	+	0.987152i	$0.448920\pi$
$938$	−2.58420	+	1.66076i	−0.0843770	+	0.0542258i
$939$		0			0
$940$	4.55163	+	1.33648i	0.148458	+	0.0435911i
$941$	−9.65946	+	21.1513i	−0.314889	+	0.689511i	−0.999213	−	0.0396670i	$-0.987370\pi$
$941$	−9.65946	+	21.1513i	−0.314889	+	0.689511i	0.684324	+	0.729178i	$0.260098\pi$
$942$		0			0
$943$	17.9818	+	10.7373i	0.585568	+	0.349656i
$944$	−0.431605			−0.0140475
$945$		0			0
$946$	2.18671	+	0.642077i	0.0710962	+	0.0208757i
$947$	−0.176041	−	0.203162i	−0.00572056	−	0.00660188i	0.752882	−	0.658155i	$-0.228663\pi$
$947$	−0.176041	−	0.203162i	−0.00572056	−	0.00660188i	−0.758603	+	0.651554i	$0.774118\pi$
$948$		0			0
$949$	−51.4733	+	59.4034i	−1.67090	+	1.92832i
$950$	−1.26956	+	8.82997i	−0.0411899	+	0.286482i
$951$		0			0
$952$	−4.81911	−	3.09705i	−0.156188	−	0.100376i
$953$	−6.53924	−	45.4814i	−0.211827	−	1.47329i	−0.767050	−	0.641587i	$-0.778276\pi$
$953$	−6.53924	−	45.4814i	−0.211827	−	1.47329i	0.555223	−	0.831701i	$-0.312633\pi$
$954$		0			0
$955$	−6.93861	−	15.1934i	−0.224528	−	0.491648i
$956$	3.03544	+	21.1119i	0.0981730	+	0.682808i
$957$		0			0
$958$	6.43376	−	1.88912i	0.207865	−	0.0610347i
$959$	0.642336	−	4.46755i	0.0207421	−	0.144265i
$960$		0			0
$961$	−8.35929	+	5.37219i	−0.269654	+	0.173296i
$962$	−32.9805	−	38.0616i	−1.06333	−	1.22715i
$963$		0			0
$964$	−7.03867	+	15.4125i	−0.226700	+	0.496404i
$965$	−5.64551			−0.181735
$966$		0			0
$967$	19.3102			0.620974			0.310487	−	0.950578i	$-0.399508\pi$
$967$	19.3102			0.620974			0.310487	+	0.950578i	$0.399508\pi$
$968$	2.74386	−	6.00822i	0.0881910	−	0.193111i
$969$		0			0
$970$	22.1200	+	25.5279i	0.710232	+	0.819651i
$971$	10.9655	−	7.04713i	0.351901	−	0.226153i	−0.352733	−	0.935724i	$-0.614748\pi$
$971$	10.9655	−	7.04713i	0.351901	−	0.226153i	0.704634	+	0.709571i	$0.251111\pi$
$972$		0			0
$973$	−1.00538	+	6.99256i	−0.0322310	+	0.224171i
$974$	28.6487	−	8.41203i	0.917965	−	0.269539i
$975$		0			0
$976$	0.154346	+	1.07350i	0.00494050	+	0.0343620i
$977$	19.1077	+	41.8400i	0.611310	+	1.33858i	0.921674	+	0.387964i	$0.126822\pi$
$977$	19.1077	+	41.8400i	0.611310	+	1.33858i	−0.310365	+	0.950618i	$0.600451\pi$
$978$		0			0
$979$	4.30193	+	29.9206i	0.137490	+	0.956266i
$980$	14.5157	+	9.32865i	0.463686	+	0.297993i
$981$		0			0
$982$	0.739925	−	5.14629i	0.0236119	−	0.164225i
$983$	−25.8151	+	29.7922i	−0.823374	+	0.950224i	−0.999416	−	0.0341584i	$-0.989125\pi$
$983$	−25.8151	+	29.7922i	−0.823374	+	0.950224i	0.176043	+	0.984383i	$0.443670\pi$
$984$		0			0
$985$	−15.4646	−	17.8472i	−0.492745	−	0.568658i
$986$	46.4375	+	13.6353i	1.47887	+	0.434236i
$987$		0			0
$988$	−14.2662			−0.453870
$989$	0.455327	+	2.56482i	0.0144786	+	0.0815565i
$990$		0			0
$991$	1.26185	−	2.76308i	0.0400841	−	0.0877720i	−0.888531	−	0.458817i	$-0.848273\pi$
$991$	1.26185	−	2.76308i	0.0400841	−	0.0877720i	0.928615	+	0.371045i	$0.121001\pi$
$992$	−4.40357	−	1.29301i	−0.139814	−	0.0410530i
$993$		0			0
$994$	5.76890	−	3.70745i	0.182978	−	0.117593i
$995$	−29.0915	+	33.5734i	−0.922263	+	1.06435i
$996$		0			0
$997$	54.9991	−	16.1492i	1.74184	−	0.511450i	0.752691	−	0.658374i	$-0.228756\pi$
$997$	54.9991	−	16.1492i	1.74184	−	0.511450i	0.989148	+	0.146925i	$0.0469375\pi$
$998$	−11.8303	−	7.60285i	−0.374480	−	0.240664i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.a.397.1		10
3.2	odd	2		138.2.e.d.121.1	yes	10
23.2	even	11		9522.2.a.bx.1.1		5
23.4	even	11	inner	414.2.i.a.73.1		10
23.21	odd	22		9522.2.a.by.1.5		5
69.2	odd	22		3174.2.a.x.1.5		5
69.44	even	22		3174.2.a.w.1.1		5
69.50	odd	22		138.2.e.d.73.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.73.1	✓	10	69.50	odd	22
138.2.e.d.121.1	yes	10	3.2	odd	2
414.2.i.a.73.1		10	23.4	even	11	inner
414.2.i.a.397.1		10	1.1	even	1	trivial
3174.2.a.w.1.1		5	69.44	even	22
3174.2.a.x.1.5		5	69.2	odd	22
9522.2.a.bx.1.1		5	23.2	even	11
9522.2.a.by.1.5		5	23.21	odd	22

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:	\( N \)	\(=\)	\( 414 = 2 \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	414.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.47672 + 1.59169i) q^{5} +(-0.151894 + 1.05645i) q^{7} +(-0.959493 + 0.281733i) q^{8} +O(q^{10})\)	\(q+(0.415415 - 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-2.47672 + 1.59169i) q^{5} +(-0.151894 + 1.05645i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(0.418986 + 2.91411i) q^{10} +(1.74302 + 3.81667i) q^{11} +(0.834716 + 5.80558i) q^{13} +(0.897877 + 0.577031i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(3.51479 - 4.05628i) q^{17} +(-1.59283 - 1.83823i) q^{19} +(2.82482 + 0.829443i) q^{20} +4.19584 q^{22} +(2.13467 + 4.29455i) q^{23} +(1.52357 - 3.33616i) q^{25} +(5.62769 + 1.65244i) q^{26} +(0.897877 - 0.577031i) q^{28} +(-5.90509 + 6.81484i) q^{29} +(-4.40357 + 1.29301i) q^{31} +(0.841254 + 0.540641i) q^{32} +(-2.22963 - 4.88220i) q^{34} +(-1.30533 - 2.85828i) q^{35} +(-7.22349 - 4.64226i) q^{37} +(-2.33380 + 0.685265i) q^{38} +(1.92796 - 2.22499i) q^{40} +(3.67379 - 2.36100i) q^{41} +(0.521162 + 0.153027i) q^{43} +(1.74302 - 3.81667i) q^{44} +(4.79324 - 0.157744i) q^{46} +1.61130 q^{47} +(5.62345 + 1.65119i) q^{49} +(-2.40176 - 2.77178i) q^{50} +(3.84094 - 4.43268i) q^{52} +(0.409819 - 2.85036i) q^{53} +(-10.3919 - 6.67848i) q^{55} +(-0.151894 - 1.05645i) q^{56} +(3.74593 + 8.20244i) q^{58} +(0.0614238 + 0.427212i) q^{59} +(1.04061 - 0.305550i) q^{61} +(-0.653151 + 4.54276i) q^{62} +(0.841254 - 0.540641i) q^{64} +(-11.3080 - 13.0502i) q^{65} +(-1.19561 + 2.61803i) q^{67} -5.36723 q^{68} -3.14224 q^{70} +(2.66906 - 5.84442i) q^{71} +(8.77594 + 10.1280i) q^{73} +(-7.22349 + 4.64226i) q^{74} +(-0.346156 + 2.40757i) q^{76} +(-4.29686 + 1.26167i) q^{77} +(0.186826 + 1.29941i) q^{79} +(-1.22301 - 2.67803i) q^{80} +(-0.621496 - 4.32260i) q^{82} +(-10.9598 - 7.04340i) q^{83} +(-2.24879 + 15.6407i) q^{85} +(0.355697 - 0.410496i) q^{86} +(-2.74769 - 3.17101i) q^{88} +(6.91251 + 2.02970i) q^{89} -6.26006 q^{91} +(1.84769 - 4.42561i) q^{92} +(0.669357 - 1.46569i) q^{94} +(6.87088 + 2.01747i) q^{95} +(9.65194 - 6.20292i) q^{97} +(3.83804 - 4.42934i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8}+O(q^{10}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8	\( 10 q - q^{2} - q^{4} - 2 q^{5} + 2 q^{7} - q^{8} - 13 q^{10} + 5 q^{11} + 13 q^{13} - 9 q^{14} - q^{16} + 9 q^{20} - 6 q^{22} + 32 q^{23} + q^{25} + 13 q^{26} - 9 q^{28} - 27 q^{29} - 8 q^{31} - q^{32} - 11 q^{34} + 26 q^{35} - 11 q^{37} - 11 q^{38} + 9 q^{40} + 10 q^{41} + 34 q^{43} + 5 q^{44} - q^{46} - 8 q^{47} + 25 q^{49} - 21 q^{50} + 2 q^{52} - 9 q^{53} - 23 q^{55} + 2 q^{56} - 5 q^{58} + 21 q^{59} - 4 q^{61} - 8 q^{62} - q^{64} - 29 q^{65} - 32 q^{67} - 22 q^{68} - 18 q^{70} - 22 q^{71} + 43 q^{73} - 11 q^{74} - 10 q^{77} - 16 q^{79} - 2 q^{80} + 32 q^{82} + 3 q^{83} + 33 q^{85} - 32 q^{86} - 6 q^{88} + 11 q^{89} - 70 q^{91} + 21 q^{92} + 3 q^{94} + 39 q^{97} + 14 q^{98}+O(q^{100}) \) 10 * q - q^2 - q^4 - 2 * q^5 + 2 * q^7 - q^8 - 13 * q^10 + 5 * q^11 + 13 * q^13 - 9 * q^14 - q^16 + 9 * q^20 - 6 * q^22 + 32 * q^23 + q^25 + 13 * q^26 - 9 * q^28 - 27 * q^29 - 8 * q^31 - q^32 - 11 * q^34 + 26 * q^35 - 11 * q^37 - 11 * q^38 + 9 * q^40 + 10 * q^41 + 34 * q^43 + 5 * q^44 - q^46 - 8 * q^47 + 25 * q^49 - 21 * q^50 + 2 * q^52 - 9 * q^53 - 23 * q^55 + 2 * q^56 - 5 * q^58 + 21 * q^59 - 4 * q^61 - 8 * q^62 - q^64 - 29 * q^65 - 32 * q^67 - 22 * q^68 - 18 * q^70 - 22 * q^71 + 43 * q^73 - 11 * q^74 - 10 * q^77 - 16 * q^79 - 2 * q^80 + 32 * q^82 + 3 * q^83 + 33 * q^85 - 32 * q^86 - 6 * q^88 + 11 * q^89 - 70 * q^91 + 21 * q^92 + 3 * q^94 + 39 * q^97 + 14 * q^98

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