LMFDB - Embedded newform 414.2.i.h.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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 8 x^{18} + 53 x^{16} + 358 x^{14} + 1753 x^{12} + 7149 x^{10} + 23268 x^{8} + 37292 x^{6} + \cdots + 58081 $ x^20 + 8x^18 + 53x^16 + 358x^14 + 1753x^12 + 7149x^10 + 23268x^8 + 37292x^6 + 19057x^4 - 81217*x^2 + 58081
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			397.1
Root			$-1.95451 + 1.25609i$ of defining polynomial
Character	$\chi$	$=$	414.397
Dual form			414.2.i.h.73.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-3.57342 + 2.29650i) q^{5} +(0.0421569 - 0.293207i) q^{7} +(0.959493 - 0.281733i) q^{8} +O(q^{10})$	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-3.57342 + 2.29650i) q^{5} +(0.0421569 - 0.293207i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.604516 - 4.20450i) q^{10} +(-0.995855 - 2.18062i) q^{11} +(-0.357740 - 2.48813i) q^{13} +(0.249198 + 0.160150i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(2.95285 - 3.40777i) q^{17} +(-0.743787 - 0.858376i) q^{19} +(4.07567 + 1.19673i) q^{20} +2.39725 q^{22} +(-4.41244 - 1.87894i) q^{23} +(5.41836 - 11.8646i) q^{25} +(2.41190 + 0.708197i) q^{26} +(-0.249198 + 0.160150i) q^{28} +(0.626759 - 0.723318i) q^{29} +(-7.91496 + 2.32404i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(1.87316 + 4.10164i) q^{34} +(0.522706 + 1.14457i) q^{35} +(-7.02215 - 4.51286i) q^{37} +(1.08979 - 0.319990i) q^{38} +(-2.78167 + 3.21022i) q^{40} +(-3.45477 + 2.22024i) q^{41} +(3.70629 + 1.08827i) q^{43} +(-0.995855 + 2.18062i) q^{44} +(3.54214 - 3.23315i) q^{46} -3.35841 q^{47} +(6.63226 + 1.94741i) q^{49} +(8.54151 + 9.85743i) q^{50} +(-1.64614 + 1.89974i) q^{52} +(-0.689711 + 4.79705i) q^{53} +(8.56640 + 5.50529i) q^{55} +(-0.0421569 - 0.293207i) q^{56} +(0.397588 + 0.870597i) q^{58} +(-1.60963 - 11.1952i) q^{59} +(-7.45076 + 2.18774i) q^{61} +(1.17397 - 8.16514i) q^{62} +(0.841254 - 0.540641i) q^{64} +(6.99235 + 8.06961i) q^{65} +(-5.85860 + 12.8285i) q^{67} -4.50912 q^{68} -1.25827 q^{70} +(6.13536 - 13.4346i) q^{71} +(7.32867 + 8.45774i) q^{73} +(7.02215 - 4.51286i) q^{74} +(-0.161640 + 1.12423i) q^{76} +(-0.681356 + 0.200064i) q^{77} +(-1.71809 - 11.9496i) q^{79} +(-1.76457 - 3.86388i) q^{80} +(-0.584443 - 4.06489i) q^{82} +(-1.78801 - 1.14909i) q^{83} +(-2.72583 + 18.9586i) q^{85} +(-2.52957 + 2.91928i) q^{86} +(-1.56987 - 1.81172i) q^{88} +(-11.0192 - 3.23553i) q^{89} -0.744621 q^{91} +(1.46952 + 4.56514i) q^{92} +(1.39513 - 3.05491i) q^{94} +(4.62912 + 1.35923i) q^{95} +(-0.669099 + 0.430004i) q^{97} +(-4.52656 + 5.22393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	$ 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) $ 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * 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
$5$	−3.57342	+	2.29650i	−1.59808	+	1.02703i	−0.629935	+	0.776648i	$0.716918\pi$
$5$	−3.57342	+	2.29650i	−1.59808	+	1.02703i	−0.968148	+	0.250377i	$0.919445\pi$
$6$		0			0
$7$	0.0421569	−	0.293207i	0.0159338	−	0.110822i	−0.980302	−	0.197503i	$-0.936717\pi$
$7$	0.0421569	−	0.293207i	0.0159338	−	0.110822i	0.996236	+	0.0866807i	$0.0276260\pi$
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$		0			0
$10$	−0.604516	−	4.20450i	−0.191165	−	1.32958i
$11$	−0.995855	−	2.18062i	−0.300262	−	0.657481i	0.698020	−	0.716078i	$-0.254065\pi$
$11$	−0.995855	−	2.18062i	−0.300262	−	0.657481i	−0.998282	+	0.0585968i	$0.981337\pi$
$12$		0			0
$13$	−0.357740	−	2.48813i	−0.0992192	−	0.690084i	−0.977345	−	0.211654i	$-0.932115\pi$
$13$	−0.357740	−	2.48813i	−0.0992192	−	0.690084i	0.878125	−	0.478430i	$-0.158794\pi$
$14$	0.249198	+	0.160150i	0.0666010	+	0.0428019i
$15$		0			0
$16$	−0.142315	+	0.989821i	−0.0355787	+	0.247455i
$17$	2.95285	−	3.40777i	0.716170	−	0.826505i	−0.274671	−	0.961538i	$-0.588569\pi$
$17$	2.95285	−	3.40777i	0.716170	−	0.826505i	0.990841	+	0.135034i	$0.0431142\pi$
$18$		0			0
$19$	−0.743787	−	0.858376i	−0.170636	−	0.196925i	0.663990	−	0.747742i	$-0.268862\pi$
$19$	−0.743787	−	0.858376i	−0.170636	−	0.196925i	−0.834626	+	0.550817i	$0.814316\pi$
$20$	4.07567	+	1.19673i	0.911348	+	0.267596i
$21$		0			0
$22$	2.39725			0.511096
$23$	−4.41244	−	1.87894i	−0.920056	−	0.391786i
$23$	−4.41244	−	1.87894i	−0.920056	−	0.391786i
$24$		0			0
$25$	5.41836	−	11.8646i	1.08367	−	2.37291i
$26$	2.41190	+	0.708197i	0.473012	+	0.138889i
$27$		0			0
$28$	−0.249198	+	0.160150i	−0.0470940	+	0.0302655i
$29$	0.626759	−	0.723318i	0.116386	−	0.134317i	−0.694567	−	0.719428i	$-0.744404\pi$
$29$	0.626759	−	0.723318i	0.116386	−	0.134317i	0.810953	+	0.585112i	$0.198949\pi$
$30$		0			0
$31$	−7.91496	+	2.32404i	−1.42157	+	0.417410i	−0.900034	−	0.435820i	$-0.856459\pi$
$31$	−7.91496	+	2.32404i	−1.42157	+	0.417410i	−0.521535	+	0.853230i	$0.674640\pi$
$32$	−0.841254	−	0.540641i	−0.148714	−	0.0955727i
$33$		0			0
$34$	1.87316	+	4.10164i	0.321244	+	0.703426i
$35$	0.522706	+	1.14457i	0.0883535	+	0.193467i
$36$		0			0
$37$	−7.02215	−	4.51286i	−1.15443	−	0.741909i	−0.183917	−	0.982942i	$-0.558878\pi$
$37$	−7.02215	−	4.51286i	−1.15443	−	0.741909i	−0.970517	+	0.241032i	$0.922514\pi$
$38$	1.08979	−	0.319990i	0.176787	−	0.0519093i
$39$		0			0
$40$	−2.78167	+	3.21022i	−0.439821	+	0.507581i
$41$	−3.45477	+	2.22024i	−0.539544	+	0.346744i	−0.781860	−	0.623454i	$-0.785729\pi$
$41$	−3.45477	+	2.22024i	−0.539544	+	0.346744i	0.242317	+	0.970197i	$0.422093\pi$
$42$		0			0
$43$	3.70629	+	1.08827i	0.565204	+	0.165959i	0.551837	−	0.833952i	$-0.313927\pi$
$43$	3.70629	+	1.08827i	0.565204	+	0.165959i	0.0133669	+	0.999911i	$0.495745\pi$
$44$	−0.995855	+	2.18062i	−0.150131	+	0.328741i
$45$		0			0
$46$	3.54214	−	3.23315i	0.522259	−	0.476702i
$47$	−3.35841			−0.489874			−0.244937	−	0.969539i	$-0.578767\pi$
$47$	−3.35841			−0.489874			−0.244937	+	0.969539i	$0.578767\pi$
$48$		0			0
$49$	6.63226	+	1.94741i	0.947465	+	0.278201i
$50$	8.54151	+	9.85743i	1.20795	+	1.39405i
$51$		0			0
$52$	−1.64614	+	1.89974i	−0.228278	+	0.263447i
$53$	−0.689711	+	4.79705i	−0.0947391	+	0.658925i	0.886012	+	0.463662i	$0.153465\pi$
$53$	−0.689711	+	4.79705i	−0.0947391	+	0.658925i	−0.980751	+	0.195262i	$0.937444\pi$
$54$		0			0
$55$	8.56640	+	5.50529i	1.15509	+	0.742333i
$56$	−0.0421569	−	0.293207i	−0.00563345	−	0.0391815i
$57$		0			0
$58$	0.397588	+	0.870597i	0.0522059	+	0.114315i
$59$	−1.60963	−	11.1952i	−0.209556	−	1.45749i	−0.774610	−	0.632439i	$-0.782054\pi$
$59$	−1.60963	−	11.1952i	−0.209556	−	1.45749i	0.565054	−	0.825054i	$-0.308855\pi$
$60$		0			0
$61$	−7.45076	+	2.18774i	−0.953972	+	0.280111i	−0.721440	−	0.692477i	$-0.756519\pi$
$61$	−7.45076	+	2.18774i	−0.953972	+	0.280111i	−0.232532	+	0.972589i	$0.574701\pi$
$62$	1.17397	−	8.16514i	0.149094	−	1.03697i
$63$		0			0
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	6.99235	+	8.06961i	0.867295	+	1.00091i
$66$		0			0
$67$	−5.85860	+	12.8285i	−0.715742	+	1.56726i	0.104036	+	0.994574i	$0.466824\pi$
$67$	−5.85860	+	12.8285i	−0.715742	+	1.56726i	−0.819778	+	0.572682i	$0.805903\pi$
$68$	−4.50912			−0.546811
$69$		0			0
$70$	−1.25827			−0.150393
$71$	6.13536	−	13.4346i	0.728134	−	1.59439i	−0.0740088	−	0.997258i	$-0.523579\pi$
$71$	6.13536	−	13.4346i	0.728134	−	1.59439i	0.802142	−	0.597133i	$-0.203693\pi$
$72$		0			0
$73$	7.32867	+	8.45774i	0.857756	+	0.989903i	1.00000		7.15738e-5i	$2.27827e-5\pi$
$73$	7.32867	+	8.45774i	0.857756	+	0.989903i	−0.142244	+	0.989832i	$0.545432\pi$
$74$	7.02215	−	4.51286i	0.816308	−	0.524609i
$75$		0			0
$76$	−0.161640	+	1.12423i	−0.0185414	+	0.128958i
$77$	−0.681356	+	0.200064i	−0.0776477	+	0.0227994i
$78$		0			0
$79$	−1.71809	−	11.9496i	−0.193300	−	1.34443i	−0.823198	−	0.567754i	$-0.807813\pi$
$79$	−1.71809	−	11.9496i	−0.193300	−	1.34443i	0.629898	−	0.776678i	$-0.283097\pi$
$80$	−1.76457	−	3.86388i	−0.197285	−	0.431994i
$81$		0			0
$82$	−0.584443	−	4.06489i	−0.0645409	−	0.448892i
$83$	−1.78801	−	1.14909i	−0.196260	−	0.126129i	0.438820	−	0.898575i	$-0.355397\pi$
$83$	−1.78801	−	1.14909i	−0.196260	−	0.126129i	−0.635080	+	0.772446i	$0.719033\pi$
$84$		0			0
$85$	−2.72583	+	18.9586i	−0.295658	+	2.05635i
$86$	−2.52957	+	2.91928i	−0.272771	+	0.314794i
$87$		0			0
$88$	−1.56987	−	1.81172i	−0.167348	−	0.193130i
$89$	−11.0192	−	3.23553i	−1.16803	−	0.342966i	−0.360485	−	0.932765i	$-0.617389\pi$
$89$	−11.0192	−	3.23553i	−1.16803	−	0.342966i	−0.807550	+	0.589799i	$0.799207\pi$
$90$		0			0
$91$	−0.744621			−0.0780575
$92$	1.46952	+	4.56514i	0.153208	+	0.475949i
$93$		0			0
$94$	1.39513	−	3.05491i	0.143897	−	0.315090i
$95$	4.62912	+	1.35923i	0.474938	+	0.139454i
$96$		0			0
$97$	−0.669099	+	0.430004i	−0.0679367	+	0.0436603i	−0.574168	−	0.818737i	$-0.694674\pi$
$97$	−0.669099	+	0.430004i	−0.0679367	+	0.0436603i	0.506232	+	0.862398i	$0.331038\pi$
$98$	−4.52656	+	5.22393i	−0.457252	+	0.527697i
$99$		0			0
$100$	−12.5149	+	3.67471i	−1.25149	+	0.367471i
$101$	7.86602	+	5.05518i	0.782698	+	0.503009i	0.869928	−	0.493179i	$-0.164165\pi$
$101$	7.86602	+	5.05518i	0.782698	+	0.503009i	−0.0872301	+	0.996188i	$0.527802\pi$
$102$		0			0
$103$	4.11528	+	9.01120i	0.405490	+	0.887900i	0.996684	+	0.0813704i	$0.0259297\pi$
$103$	4.11528	+	9.01120i	0.405490	+	0.887900i	−0.591194	+	0.806530i	$0.701343\pi$
$104$	−1.04424	−	2.28656i	−0.102396	−	0.224216i
$105$		0			0
$106$	−4.07703	−	2.62015i	−0.395996	−	0.254491i
$107$	−17.7404	+	5.20904i	−1.71503	+	0.503577i	−0.983908	−	0.178675i	$-0.942819\pi$
$107$	−17.7404	+	5.20904i	−1.71503	+	0.503577i	−0.731117	+	0.682252i	$0.761001\pi$
$108$		0			0
$109$	−10.7930	+	12.4558i	−1.03378	+	1.19305i	−0.0528682	+	0.998602i	$0.516836\pi$
$109$	−10.7930	+	12.4558i	−1.03378	+	1.19305i	−0.980913	+	0.194446i	$0.937709\pi$
$110$	−8.56640	+	5.50529i	−0.816774	+	0.524909i
$111$		0			0
$112$	0.284223	+	0.0834555i	0.0268566	+	0.00788581i
$113$	1.77473	−	3.88611i	0.166952	−	0.365575i	−0.807601	−	0.589729i	$-0.799235\pi$
$113$	1.77473	−	3.88611i	0.166952	−	0.365575i	0.974554	+	0.224154i	$0.0719619\pi$
$114$		0			0
$115$	20.0825	−	3.41891i	1.87270	−	0.318815i
$116$	−0.957087			−0.0888633
$117$		0			0
$118$	10.8522	+	3.18649i	0.999025	+	0.293340i
$119$	−0.874700	−	1.00946i	−0.0801836	−	0.0925368i
$120$		0			0
$121$	3.44010	−	3.97008i	0.312736	−	0.360917i
$122$	1.10512	−	7.68627i	0.100053	−	0.695882i
$123$		0			0
$124$	6.93959	+	4.45980i	0.623194	+	0.400502i
$125$	4.86227	+	33.8178i	0.434895	+	3.02476i
$126$		0			0
$127$	−5.61976	−	12.3056i	−0.498673	−	1.09194i	−0.976898	−	0.213704i	$-0.931447\pi$
$127$	−5.61976	−	12.3056i	−0.498673	−	1.09194i	0.478226	−	0.878237i	$-0.341280\pi$
$128$	0.142315	+	0.989821i	0.0125790	+	0.0874887i
$129$		0			0
$130$	−10.2451	+	3.00823i	−0.898555	+	0.263839i
$131$	−1.86572	+	12.9764i	−0.163009	+	1.13375i	0.729913	+	0.683540i	$0.239561\pi$
$131$	−1.86572	+	12.9764i	−0.163009	+	1.13375i	−0.892922	+	0.450212i	$0.851348\pi$
$132$		0			0
$133$	−0.283038	+	0.181897i	−0.0245425	+	0.0157725i
$134$	−9.23550	−	10.6583i	−0.797826	−	0.920740i
$135$		0			0
$136$	1.87316	−	4.10164i	0.160622	−	0.351713i
$137$	−1.26947			−0.108458			−0.0542291	−	0.998529i	$-0.517270\pi$
$137$	−1.26947			−0.108458			−0.0542291	+	0.998529i	$0.517270\pi$
$138$		0			0
$139$	−15.5662			−1.32031			−0.660155	−	0.751129i	$-0.729509\pi$
$139$	−15.5662			−1.32031			−0.660155	+	0.751129i	$0.729509\pi$
$140$	0.522706	−	1.14457i	0.0441767	−	0.0967336i
$141$		0			0
$142$	9.67179	+	11.1618i	0.811639	+	0.936681i
$143$	−5.06942	+	3.25792i	−0.423926	+	0.272441i
$144$		0			0
$145$	−0.578574	+	4.02407i	−0.0480480	+	0.334181i
$146$	−10.7379	+	3.15292i	−0.888672	+	0.260938i
$147$		0			0
$148$	1.18794	+	8.26228i	0.0976478	+	0.679155i
$149$	−5.68369	−	12.4456i	−0.465626	−	1.01958i	−0.986169	−	0.165744i	$-0.946998\pi$
$149$	−5.68369	−	12.4456i	−0.465626	−	1.01958i	0.520543	−	0.853836i	$-0.325730\pi$
$150$		0			0
$151$	−1.08883	−	7.57299i	−0.0886079	−	0.616281i	−0.984940	−	0.172898i	$-0.944687\pi$
$151$	−1.08883	−	7.57299i	−0.0886079	−	0.616281i	0.896332	−	0.443384i	$-0.146222\pi$
$152$	−0.955491	−	0.614057i	−0.0775005	−	0.0498066i
$153$		0			0
$154$	0.101061	−	0.702893i	0.00814370	−	0.0566407i
$155$	22.9463	−	26.4815i	1.84309	−	2.12704i
$156$		0			0
$157$	−4.76430	−	5.49829i	−0.380232	−	0.438812i	0.533084	−	0.846062i	$-0.321033\pi$
$157$	−4.76430	−	5.49829i	−0.380232	−	0.438812i	−0.913316	+	0.407251i	$0.866488\pi$
$158$	11.5834	+	3.40120i	0.921528	+	0.270585i
$159$		0			0
$160$	4.24774			0.335813
$161$	−0.736933	+	1.21455i	−0.0580785	+	0.0957198i
$162$		0			0
$163$	7.31719	−	16.0224i	0.573127	−	1.25497i	−0.371989	−	0.928237i	$-0.621324\pi$
$163$	7.31719	−	16.0224i	0.573127	−	1.25497i	0.945116	−	0.326736i	$-0.105949\pi$
$164$	3.94034	+	1.15699i	0.307689	+	0.0903455i
$165$		0			0
$166$	1.78801	−	1.14909i	0.138777	−	0.0891864i
$167$	8.40388	−	9.69860i	0.650312	−	0.750500i	−0.330851	−	0.943683i	$-0.607336\pi$
$167$	8.40388	−	9.69860i	0.650312	−	0.750500i	0.981163	+	0.193183i	$0.0618812\pi$
$168$		0			0
$169$	6.41057	−	1.88231i	0.493121	−	0.144793i
$170$	−16.1130	−	10.3552i	−1.23581	−	0.794207i
$171$		0			0
$172$	−1.60465	−	3.51369i	−0.122353	−	0.267917i
$173$	3.84228	+	8.41342i	0.292123	+	0.639660i	0.997612	−	0.0690601i	$-0.0220000\pi$
$173$	3.84228	+	8.41342i	0.292123	+	0.639660i	−0.705489	+	0.708720i	$0.749273\pi$
$174$		0			0
$175$	−3.25036	−	2.08888i	−0.245704	−	0.157904i
$176$	2.30015	−	0.675385i	0.173380	−	0.0509090i
$177$		0			0
$178$	7.52069	−	8.67934i	0.563700	−	0.650544i
$179$	15.9833	−	10.2719i	1.19465	−	0.767755i	0.216628	−	0.976254i	$-0.430494\pi$
$179$	15.9833	−	10.2719i	1.19465	−	0.767755i	0.978023	+	0.208499i	$0.0668579\pi$
$180$		0			0
$181$	−2.50780	−	0.736355i	−0.186403	−	0.0547328i	0.187199	−	0.982322i	$-0.440059\pi$
$181$	−2.50780	−	0.736355i	−0.186403	−	0.0547328i	−0.373602	+	0.927589i	$0.621877\pi$
$182$	0.309327	−	0.677331i	0.0229288	−	0.0502071i
$183$		0			0
$184$	−4.76306	−	0.559703i	−0.351137	−	0.0412618i
$185$	35.4569			2.60684
$186$		0			0
$187$	−10.3716	−	3.04539i	−0.758450	−	0.222701i
$188$	2.19929	+	2.53811i	0.160400	+	0.185111i
$189$		0			0
$190$	−3.15941	+	3.64615i	−0.229208	+	0.264520i
$191$	0.840082	−	5.84290i	0.0607862	−	0.422777i	−0.936593	−	0.350420i	$-0.886039\pi$
$191$	0.840082	−	5.84290i	0.0607862	−	0.422777i	0.997379	−	0.0723570i	$-0.0230521\pi$
$192$		0			0
$193$	0.295001	+	0.189585i	0.0212346	+	0.0136467i	0.551215	−	0.834363i	$-0.314164\pi$
$193$	0.295001	+	0.189585i	0.0212346	+	0.0136467i	−0.529980	+	0.848010i	$0.677801\pi$
$194$	−0.113191	−	0.787264i	−0.00812667	−	0.0565222i
$195$		0			0
$196$	−2.87145	−	6.28761i	−0.205104	−	0.449115i
$197$	2.68310	+	18.6614i	0.191163	+	1.32957i	0.828935	+	0.559345i	$0.188947\pi$
$197$	2.68310	+	18.6614i	0.191163	+	1.32957i	−0.637772	+	0.770225i	$0.720144\pi$
$198$		0			0
$199$	15.6805	−	4.60420i	1.11156	−	0.326383i	0.326124	−	0.945327i	$-0.394257\pi$
$199$	15.6805	−	4.60420i	1.11156	−	0.326383i	0.785435	+	0.618944i	$0.212439\pi$
$200$	1.85625	−	12.9105i	0.131257	−	0.912910i
$201$		0			0
$202$	−7.86602	+	5.05518i	−0.553451	+	0.355681i
$203$	−0.185660	−	0.214263i	−0.0130308	−	0.0150383i
$204$		0			0
$205$	7.24655	−	15.8677i	0.506121	−	1.10825i
$206$	−9.90643			−0.690213
$207$		0			0
$208$	2.51372			0.174295
$209$	−1.13109	+	2.47673i	−0.0782389	+	0.171319i
$210$		0			0
$211$	−9.04551	−	10.4391i	−0.622719	−	0.718656i	0.353502	−	0.935434i	$-0.384991\pi$
$211$	−9.04551	−	10.4391i	−0.622719	−	0.718656i	−0.976221	+	0.216778i	$0.930445\pi$
$212$	4.07703	−	2.62015i	0.280012	−	0.179953i
$213$		0			0
$214$	2.63130	−	18.3011i	0.179872	−	1.25104i
$215$	−15.7434	+	4.62267i	−1.07369	+	0.315263i
$216$		0			0
$217$	0.347756	+	2.41870i	0.0236072	+	0.164192i
$218$	−6.84660	−	14.9920i	−0.463711	−	1.01538i
$219$		0			0
$220$	−1.44918	−	10.0793i	−0.0977035	−	0.679543i
$221$	−9.53533	−	6.12799i	−0.641416	−	0.412213i
$222$		0			0
$223$	−0.521460	+	3.62683i	−0.0349195	+	0.242871i	−0.999804	−	0.0198044i	$-0.993696\pi$
$223$	−0.521460	+	3.62683i	−0.0349195	+	0.242871i	0.964884	+	0.262675i	$0.0846048\pi$
$224$	−0.193984	+	0.223870i	−0.0129611	+	0.0149579i
$225$		0			0
$226$	2.79768	+	3.22870i	0.186099	+	0.214770i
$227$	0.0547420	+	0.0160737i	0.00363335	+	0.00106685i	0.283549	−	0.958958i	$-0.408488\pi$
$227$	0.0547420	+	0.0160737i	0.00363335	+	0.00106685i	−0.279915	+	0.960025i	$0.590306\pi$
$228$		0			0
$229$	6.13532			0.405433			0.202717	−	0.979237i	$-0.435023\pi$
$229$	6.13532			0.405433			0.202717	+	0.979237i	$0.435023\pi$
$230$	−5.23261	+	19.6879i	−0.345028	+	1.29818i
$231$		0			0
$232$	0.397588	−	0.870597i	0.0261030	−	0.0571575i
$233$	19.4859	+	5.72157i	1.27656	+	0.374832i	0.848634	−	0.528981i	$-0.177426\pi$
$233$	19.4859	+	5.72157i	1.27656	+	0.374832i	0.427928	+	0.903813i	$0.359244\pi$
$234$		0			0
$235$	12.0010	−	7.71257i	0.782859	−	0.503113i
$236$	−7.40670	+	8.54778i	−0.482135	+	0.556413i
$237$		0			0
$238$	1.28160	−	0.376311i	0.0830737	−	0.0243926i
$239$	3.07525	+	1.97634i	0.198921	+	0.127839i	0.636310	−	0.771434i	$-0.280460\pi$
$239$	3.07525	+	1.97634i	0.198921	+	0.127839i	−0.437388	+	0.899273i	$0.644096\pi$
$240$		0			0
$241$	−4.88168	−	10.6894i	−0.314457	−	0.688564i	0.684734	−	0.728793i	$-0.259919\pi$
$241$	−4.88168	−	10.6894i	−0.314457	−	0.688564i	−0.999190	+	0.0402291i	$0.987191\pi$
$242$	2.18225	+	4.77845i	0.140280	+	0.307171i
$243$		0			0
$244$	6.53259	+	4.19824i	0.418206	+	0.268765i
$245$	−28.1721	+	8.27207i	−1.79985	+	0.528483i
$246$		0			0
$247$	−1.86967	+	2.15772i	−0.118964	+	0.137292i
$248$	−6.93959	+	4.45980i	−0.440664	+	0.283198i
$249$		0			0
$250$	−32.7817	−	9.62556i	−2.07329	−	0.608774i
$251$	0.788016	−	1.72551i	0.0497391	−	0.108913i	−0.883131	−	0.469127i	$-0.844569\pi$
$251$	0.788016	−	1.72551i	0.0497391	−	0.108913i	0.932870	+	0.360213i	$0.117296\pi$
$252$		0			0
$253$	0.296896	+	11.4930i	0.0186657	+	0.722558i
$254$	13.5281			0.848826
$255$		0			0
$256$	−0.959493	−	0.281733i	−0.0599683	−	0.0176083i
$257$	3.56097	+	4.10958i	0.222127	+	0.256349i	0.855865	−	0.517200i	$-0.173026\pi$
$257$	3.56097	+	4.10958i	0.222127	+	0.256349i	−0.633738	+	0.773548i	$0.718480\pi$
$258$		0			0
$259$	−1.61924	+	1.86870i	−0.100614	+	0.116115i
$260$	1.51958	−	10.5689i	0.0942406	−	0.655458i
$261$		0			0
$262$	−11.0287	−	7.08771i	−0.681355	−	0.437880i
$263$	3.30010	+	22.9527i	0.203493	+	1.41533i	0.793816	+	0.608158i	$0.208091\pi$
$263$	3.30010	+	22.9527i	0.203493	+	1.41533i	−0.590323	+	0.807167i	$0.701000\pi$
$264$		0			0
$265$	−8.55178	−	18.7258i	−0.525332	−	1.15032i
$266$	−0.0478815	−	0.333023i	−0.00293580	−	0.0204190i
$267$		0			0
$268$	13.5317	−	3.97327i	0.826582	−	0.242706i
$269$	0.760980	−	5.29273i	0.0463978	−	0.322704i	−0.953383	−	0.301763i	$-0.902425\pi$
$269$	0.760980	−	5.29273i	0.0463978	−	0.322704i	0.999781	−	0.0209406i	$-0.00666608\pi$
$270$		0			0
$271$	−13.5320	+	8.69651i	−0.822012	+	0.528275i	−0.882730	−	0.469880i	$-0.844297\pi$
$271$	−13.5320	+	8.69651i	−0.822012	+	0.528275i	0.0607182	+	0.998155i	$0.480661\pi$
$272$	2.95285	+	3.40777i	0.179043	+	0.206626i
$273$		0			0
$274$	0.527357	−	1.15475i	0.0318588	−	0.0697610i
$275$	−31.2680			−1.88553
$276$		0			0
$277$	3.44954			0.207263			0.103631	−	0.994616i	$-0.466954\pi$
$277$	3.44954			0.207263			0.103631	+	0.994616i	$0.466954\pi$
$278$	6.46645	−	14.1595i	0.387832	−	0.849233i
$279$		0			0
$280$	0.823995	+	0.950941i	0.0492431	+	0.0568296i
$281$	5.41753	−	3.48164i	0.323183	−	0.207697i	−0.368982	−	0.929437i	$-0.620294\pi$
$281$	5.41753	−	3.48164i	0.323183	−	0.207697i	0.692165	+	0.721740i	$0.256657\pi$
$282$		0			0
$283$	−1.65981	+	11.5443i	−0.0986657	+	0.686235i	0.879116	+	0.476608i	$0.158134\pi$
$283$	−1.65981	+	11.5443i	−0.0986657	+	0.686235i	−0.977781	+	0.209627i	$0.932775\pi$
$284$	−14.1710	+	4.16098i	−0.840893	+	0.246908i
$285$		0			0
$286$	−0.857593	−	5.96469i	−0.0507105	−	0.352700i
$287$	0.505350	+	1.10656i	0.0298298	+	0.0653182i
$288$		0			0
$289$	−0.474218	−	3.29826i	−0.0278952	−	0.194015i
$290$	−3.42008	−	2.19795i	−0.200834	−	0.129068i
$291$		0			0
$292$	1.59267	−	11.0773i	0.0932041	−	0.648249i
$293$	3.37470	−	3.89461i	0.197152	−	0.227525i	−0.648562	−	0.761162i	$-0.724629\pi$
$293$	3.37470	−	3.89461i	0.197152	−	0.227525i	0.845714	+	0.533636i	$0.179175\pi$
$294$		0			0
$295$	31.4617	+	36.3087i	1.83177	+	2.11398i
$296$	−8.00912	−	2.35169i	−0.465521	−	0.136689i
$297$		0			0
$298$	13.6820			0.792575
$299$	−3.09655	+	11.6509i	−0.179078	+	0.673789i
$300$		0			0
$301$	0.475333	−	1.04083i	0.0273978	−	0.0599927i
$302$	7.34095	+	2.15550i	0.422424	+	0.124035i
$303$		0			0
$304$	0.955491	−	0.614057i	0.0548012	−	0.0352186i
$305$	21.6006	−	24.9284i	1.23684	−	1.42739i
$306$		0			0
$307$	14.9016	−	4.37549i	0.850477	−	0.249723i	0.172686	−	0.984977i	$-0.444755\pi$
$307$	14.9016	−	4.37549i	0.850477	−	0.249723i	0.677791	+	0.735254i	$0.262937\pi$
$308$	0.597391	+	0.383920i	0.0340395	+	0.0218759i
$309$		0			0
$310$	14.5562	+	31.8735i	0.826734	+	1.81029i
$311$	−3.15577	−	6.91017i	−0.178947	−	0.391840i	0.798809	−	0.601585i	$-0.205464\pi$
$311$	−3.15577	−	6.91017i	−0.178947	−	0.391840i	−0.977756	+	0.209745i	$0.932737\pi$
$312$		0			0
$313$	22.0077	+	14.1435i	1.24395	+	0.799439i	0.986004	−	0.166720i	$-0.0533176\pi$
$313$	22.0077	+	14.1435i	1.24395	+	0.799439i	0.257947	+	0.966159i	$0.416954\pi$
$314$	6.98058	−	2.04968i	0.393937	−	0.115670i
$315$		0			0
$316$	−7.90577	+	9.12375i	−0.444734	+	0.513251i
$317$	−20.3618	+	13.0858i	−1.14363	+	0.734969i	−0.968362	−	0.249551i	$-0.919717\pi$
$317$	−20.3618	+	13.0858i	−1.14363	+	0.734969i	−0.175273	+	0.984520i	$0.556081\pi$
$318$		0			0
$319$	−2.20144	−	0.646402i	−0.123257	−	0.0361916i
$320$	−1.76457	+	3.86388i	−0.0986426	+	0.215997i
$321$		0			0
$322$	−0.798659	−	1.17488i	−0.0445075	−	0.0654735i
$323$	−5.12143			−0.284964
$324$		0			0
$325$	−31.4590	−	9.23719i	−1.74503	−	0.512387i
$326$	11.5348	+	13.3119i	0.638855	+	0.737278i
$327$		0			0
$328$	−2.68931	+	3.10363i	−0.148492	+	0.171369i
$329$	−0.141580	+	0.984709i	−0.00780555	+	0.0542888i
$330$		0			0
$331$	−26.4346	−	16.9885i	−1.45298	−	0.933771i	−0.999087	−	0.0427121i	$-0.986400\pi$
$331$	−26.4346	−	16.9885i	−1.45298	−	0.933771i	−0.453888	−	0.891059i	$-0.649963\pi$
$332$	0.302478	+	2.10378i	0.0166006	+	0.115460i
$333$		0			0
$334$	5.33105	+	11.6734i	0.291702	+	0.638739i
$335$	−8.52549	−	59.2961i	−0.465797	−	3.23969i
$336$		0			0
$337$	−5.49420	+	1.61324i	−0.299288	+	0.0878790i	−0.427929	−	0.903812i	$-0.640757\pi$
$337$	−5.49420	+	1.61324i	−0.299288	+	0.0878790i	0.128641	+	0.991691i	$0.458939\pi$
$338$	−0.950835	+	6.61320i	−0.0517186	+	0.359711i
$339$		0			0
$340$	16.1130	−	10.3552i	0.873850	−	0.561589i
$341$	12.9500	+	14.9451i	0.701282	+	0.809323i
$342$		0			0
$343$	1.71198	−	3.74870i	0.0924380	−	0.202411i
$344$	3.86276			0.208266
$345$		0			0
$346$	−9.24925			−0.497243
$347$	8.17381	−	17.8981i	0.438793	−	0.960822i	−0.553025	−	0.833164i	$-0.686527\pi$
$347$	8.17381	−	17.8981i	0.438793	−	0.960822i	0.991818	−	0.127658i	$-0.0407460\pi$
$348$		0			0
$349$	−1.44448	−	1.66702i	−0.0773212	−	0.0892335i	0.715771	−	0.698335i	$-0.246076\pi$
$349$	−1.44448	−	1.66702i	−0.0773212	−	0.0892335i	−0.793092	+	0.609102i	$0.791530\pi$
$350$	3.25036	−	2.08888i	0.173739	−	0.111655i
$351$		0			0
$352$	−0.341165	+	2.37285i	−0.0181841	+	0.126474i
$353$	−11.3620	+	3.33619i	−0.604738	+	0.177567i	−0.569747	−	0.821820i	$-0.692959\pi$
$353$	−11.3620	+	3.33619i	−0.604738	+	0.177567i	−0.0349917	+	0.999388i	$0.511140\pi$
$354$		0			0
$355$	8.92824	+	62.0973i	0.473862	+	3.29578i
$356$	4.77080	+	10.4466i	0.252852	+	0.553668i
$357$		0			0
$358$	2.70390	+	18.8060i	0.142906	+	0.993930i
$359$	19.2028	+	12.3409i	1.01349	+	0.651328i	0.938293	−	0.345841i	$-0.112406\pi$
$359$	19.2028	+	12.3409i	1.01349	+	0.651328i	0.0751934	+	0.997169i	$0.476043\pi$
$360$		0			0
$361$	2.52039	−	17.5297i	0.132652	−	0.922616i
$362$	1.71159	−	1.97528i	0.0899591	−	0.103818i
$363$		0			0
$364$	0.487623	+	0.562747i	0.0255584	+	0.0294959i
$365$	−45.6116	−	13.3928i	−2.38742	−	0.701010i
$366$		0			0
$367$	−30.0634			−1.56930			−0.784649	−	0.619941i	$-0.787157\pi$
$367$	−30.0634			−1.56930			−0.784649	+	0.619941i	$0.787157\pi$
$368$	2.48777	−	4.10012i	0.129684	−	0.213734i
$369$		0			0
$370$	−14.7293	+	32.2527i	−0.765741	+	1.67674i
$371$	1.37745	+	0.404457i	0.0715138	+	0.0209983i
$372$		0			0
$373$	26.5713	−	17.0763i	1.37581	−	0.884179i	0.376698	−	0.926336i	$-0.377060\pi$
$373$	26.5713	−	17.0763i	1.37581	−	0.884179i	0.999111	+	0.0421577i	$0.0134232\pi$
$374$	7.07872	−	8.16928i	0.366032	−	0.422424i
$375$		0			0
$376$	−3.22237	+	0.946172i	−0.166181	+	0.0487951i
$377$	−2.02393	−	1.30070i	−0.104238	−	0.0669895i
$378$		0			0
$379$	−10.6464	−	23.3123i	−0.546867	−	1.19747i	−0.958230	−	0.286000i	$-0.907674\pi$
$379$	−10.6464	−	23.3123i	−0.546867	−	1.19747i	0.411363	−	0.911472i	$-0.365053\pi$
$380$	−2.00419	−	4.38857i	−0.102813	−	0.225129i
$381$		0			0
$382$	4.96590	+	3.19139i	0.254078	+	0.163286i
$383$	−21.9238	+	6.43741i	−1.12025	+	0.328936i	−0.788870	−	0.614560i	$-0.789334\pi$
$383$	−21.9238	+	6.43741i	−1.12025	+	0.328936i	−0.331384	+	0.943496i	$0.607515\pi$
$384$		0			0
$385$	1.97532	−	2.27965i	0.100672	−	0.116182i
$386$	−0.295001	+	0.189585i	−0.0150151	+	0.00964965i
$387$		0			0
$388$	0.763142	+	0.224079i	0.0387426	+	0.0113759i
$389$	−6.76046	+	14.8033i	−0.342769	+	0.750559i	−0.999995	−	0.00313436i	$-0.999002\pi$
$389$	−6.76046	+	14.8033i	−0.342769	+	0.750559i	0.657226	+	0.753693i	$0.271730\pi$
$390$		0			0
$391$	−19.4322	+	9.48833i	−0.982730	+	0.479845i
$392$	6.91225			0.349121
$393$		0			0
$394$	−18.0896	−	5.31159i	−0.911341	−	0.267594i
$395$	33.5816	+	38.7553i	1.68968	+	1.94999i
$396$		0			0
$397$	3.41724	−	3.94371i	0.171506	−	0.197929i	−0.663489	−	0.748186i	$-0.730925\pi$
$397$	3.41724	−	3.94371i	0.171506	−	0.197929i	0.834995	+	0.550257i	$0.185470\pi$
$398$	−2.32577	+	16.1761i	−0.116581	+	0.810835i
$399$		0			0
$400$	10.9727	+	7.05171i	0.548634	+	0.352586i
$401$	1.16900	+	8.13056i	0.0583770	+	0.406021i	0.997968	+	0.0637209i	$0.0202968\pi$
$401$	1.16900	+	8.13056i	0.0583770	+	0.406021i	−0.939591	+	0.342300i	$0.888794\pi$
$402$		0			0
$403$	8.61403	+	18.8621i	0.429095	+	0.939587i
$404$	−1.33069	−	9.25518i	−0.0662045	−	0.460462i
$405$		0			0
$406$	0.272027	−	0.0798742i	0.0135005	−	0.00396409i
$407$	−2.84779	+	19.8068i	−0.141159	+	0.981786i
$408$		0			0
$409$	−28.5919	+	18.3749i	−1.41378	+	0.908579i	−0.999998	−	0.00179855i	$-0.999428\pi$
$409$	−28.5919	+	18.3749i	−1.41378	+	0.908579i	−0.413778	+	0.910378i	$0.635791\pi$
$410$	11.4235	+	13.1834i	0.564165	+	0.651081i
$411$		0			0
$412$	4.11528	−	9.01120i	0.202745	−	0.443950i
$413$	−3.35038			−0.164861
$414$		0			0
$415$	9.02820			0.443177
$416$	−1.04424	+	2.28656i	−0.0511979	+	0.112108i
$417$		0			0
$418$	−1.78305	−	2.05775i	−0.0872117	−	0.100648i
$419$	−19.2043	+	12.3418i	−0.938191	+	0.602939i	−0.917881	−	0.396855i	$-0.870102\pi$
$419$	−19.2043	+	12.3418i	−0.938191	+	0.602939i	−0.0203095	+	0.999794i	$0.506465\pi$
$420$		0			0
$421$	−2.37183	+	16.4965i	−0.115596	+	0.803989i	0.846717	+	0.532044i	$0.178576\pi$
$421$	−2.37183	+	16.4965i	−0.115596	+	0.803989i	−0.962313	+	0.271945i	$0.912333\pi$
$422$	13.2534	−	3.89154i	0.645163	−	0.189437i
$423$		0			0
$424$	0.689711	+	4.79705i	0.0334953	+	0.232965i
$425$	−24.4321	−	53.4987i	−1.18513	−	2.59507i
$426$		0			0
$427$	0.327361	+	2.27685i	0.0158421	+	0.110184i
$428$	15.5542	+	9.99607i	0.751840	+	0.483178i
$429$		0			0
$430$	2.33510	−	16.2410i	0.112609	−	0.783210i
$431$	13.3235	−	15.3761i	0.641769	−	0.740641i	−0.337918	−	0.941176i	$-0.609723\pi$
$431$	13.3235	−	15.3761i	0.641769	−	0.740641i	0.979687	+	0.200535i	$0.0642680\pi$
$432$		0			0
$433$	19.0681	+	22.0057i	0.916354	+	1.05753i	0.998145	+	0.0608790i	$0.0193904\pi$
$433$	19.0681	+	22.0057i	0.916354	+	1.05753i	−0.0817915	+	0.996649i	$0.526064\pi$
$434$	−2.34459	−	0.688434i	−0.112544	−	0.0330459i
$435$		0			0
$436$	16.4814			0.789314
$437$	1.66908	+	5.18506i	0.0798427	+	0.248035i
$438$		0			0
$439$	−8.14649	+	17.8383i	−0.388811	+	0.851377i	0.609473	+	0.792807i	$0.291381\pi$
$439$	−8.14649	+	17.8383i	−0.388811	+	0.851377i	−0.998283	+	0.0585696i	$0.981346\pi$
$440$	9.77042	+	2.86885i	0.465787	+	0.136767i
$441$		0			0
$442$	9.53533	−	6.12799i	0.453550	−	0.291479i
$443$	−5.65770	+	6.52933i	−0.268805	+	0.310218i	−0.874064	−	0.485811i	$-0.838524\pi$
$443$	−5.65770	+	6.52933i	−0.268805	+	0.310218i	0.605259	+	0.796029i	$0.293070\pi$
$444$		0			0
$445$	46.8067	−	13.7437i	2.21885	−	0.651513i
$446$	−3.08246	−	1.98098i	−0.145959	−	0.0938020i
$447$		0			0
$448$	−0.123055	−	0.269453i	−0.00581382	−	0.0127305i
$449$	−9.26305	−	20.2832i	−0.437150	−	0.957225i	−0.992113	−	0.125350i	$-0.959995\pi$
$449$	−9.26305	−	20.2832i	−0.437150	−	0.957225i	0.554962	−	0.831875i	$-0.312733\pi$
$450$		0			0
$451$	8.28195	+	5.32249i	0.389982	+	0.250626i
$452$	−4.09913	+	1.20361i	−0.192807	+	0.0566132i
$453$		0			0
$454$	−0.0373618	+	0.0431178i	−0.00175347	+	0.00202362i
$455$	2.66084	−	1.71002i	0.124742	−	0.0801670i
$456$		0			0
$457$	−3.28839	−	0.965557i	−0.153824	−	0.0451669i	0.203914	−	0.978989i	$-0.434634\pi$
$457$	−3.28839	−	0.965557i	−0.153824	−	0.0451669i	−0.357738	+	0.933822i	$0.616452\pi$
$458$	−2.54870	+	5.58088i	−0.119093	+	0.260778i
$459$		0			0
$460$	−15.7351	−	12.9384i	−0.733651	−	0.603257i
$461$	28.9575			1.34869			0.674344	−	0.738418i	$-0.264427\pi$
$461$	28.9575			1.34869			0.674344	+	0.738418i	$0.264427\pi$
$462$		0			0
$463$	−8.72491	−	2.56186i	−0.405481	−	0.119060i	0.0726310	−	0.997359i	$-0.476860\pi$
$463$	−8.72491	−	2.56186i	−0.405481	−	0.119060i	−0.478112	+	0.878299i	$0.658679\pi$
$464$	0.626759	+	0.723318i	0.0290965	+	0.0335792i
$465$		0			0
$466$	−13.2992	+	15.3481i	−0.616075	+	0.710989i
$467$	2.98084	−	20.7322i	0.137937	−	0.959373i	−0.796853	−	0.604173i	$-0.793504\pi$
$467$	2.98084	−	20.7322i	0.137937	−	0.959373i	0.934790	−	0.355200i	$-0.115587\pi$
$468$		0			0
$469$	3.51444	+	2.25860i	0.162282	+	0.104292i
$470$	2.03021	+	14.1204i	0.0936466	+	0.651326i
$471$		0			0
$472$	−4.69848	−	10.2882i	−0.216265	−	0.473555i
$473$	−1.31784	−	9.16577i	−0.0605943	−	0.421443i
$474$		0			0
$475$	−14.2144	+	4.17371i	−0.652200	+	0.191503i
$476$	−0.190090	+	1.32211i	−0.00871278	+	0.0605987i
$477$		0			0
$478$	−3.07525	+	1.97634i	−0.140659	+	0.0903958i
$479$	−6.50193	−	7.50363i	−0.297081	−	0.342849i	0.587511	−	0.809216i	$-0.300108\pi$
$479$	−6.50193	−	7.50363i	−0.297081	−	0.342849i	−0.884591	+	0.466367i	$0.845563\pi$
$480$		0			0
$481$	−8.71650	+	19.0865i	−0.397438	+	0.870268i
$482$	11.7513			0.535259
$483$		0			0
$484$	−5.25317			−0.238781
$485$	1.40347	−	3.07317i	0.0637283	−	0.139545i
$486$		0			0
$487$	9.83563	+	11.3509i	0.445695	+	0.514359i	0.933492	−	0.358597i	$-0.116745\pi$
$487$	9.83563	+	11.3509i	0.445695	+	0.514359i	−0.487797	+	0.872957i	$0.662199\pi$
$488$	−6.53259	+	4.19824i	−0.295717	+	0.190045i
$489$		0			0
$490$	4.17857	−	29.0626i	0.188768	−	1.31291i
$491$	3.92274	−	1.15182i	0.177031	−	0.0519809i	−0.192016	−	0.981392i	$-0.561502\pi$
$491$	3.92274	−	1.15182i	0.177031	−	0.0519809i	0.369046	+	0.929411i	$0.379684\pi$
$492$		0			0
$493$	−0.614177	−	4.27169i	−0.0276611	−	0.192387i
$494$	−1.18604	−	2.59706i	−0.0533624	−	0.116847i
$495$		0			0
$496$	−1.17397	−	8.16514i	−0.0527128	−	0.366626i
$497$	−3.68047	−	2.36529i	−0.165092	−	0.106098i
$498$		0			0
$499$	2.14830	−	14.9417i	0.0961711	−	0.668885i	−0.883523	−	0.468387i	$-0.844835\pi$
$499$	2.14830	−	14.9417i	0.0961711	−	0.668885i	0.979694	−	0.200497i	$-0.0642557\pi$
$500$	22.3737	−	25.8206i	1.00058	−	1.15473i
$501$		0			0
$502$	1.24223	+	1.43361i	0.0554434	+	0.0639851i
$503$	32.0068	+	9.39805i	1.42711	+	0.419038i	0.901905	−	0.431935i	$-0.142169\pi$
$503$	32.0068	+	9.39805i	1.42711	+	0.419038i	0.525209	+	0.850973i	$0.323987\pi$
$504$		0			0
$505$	−39.7178			−1.76742
$506$	−10.5777	−	4.50430i	−0.470237	−	0.200240i
$507$		0			0
$508$	−5.61976	+	12.3056i	−0.249336	+	0.545971i
$509$	31.7848	+	9.33287i	1.40884	+	0.413672i	0.895710	−	0.444639i	$-0.146668\pi$
$509$	31.7848	+	9.33287i	1.40884	+	0.413672i	0.513129	+	0.858312i	$0.328486\pi$
$510$		0			0
$511$	2.78882	−	1.79227i	0.123370	−	0.0792853i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$		0			0
$514$	−5.21749	+	1.53199i	−0.230133	+	0.0675733i
$515$	−35.3998	−	22.7501i	−1.55990	−	1.00249i
$516$		0			0
$517$	3.34449	+	7.32340i	0.147090	+	0.322083i
$518$	−1.02717	−	2.24919i	−0.0451314	−	0.0988239i
$519$		0			0
$520$	8.98259	+	5.77276i	0.393912	+	0.253152i
$521$	13.2547	−	3.89193i	0.580699	−	0.170509i	0.0218258	−	0.999762i	$-0.493052\pi$
$521$	13.2547	−	3.89193i	0.580699	−	0.170509i	0.558873	+	0.829253i	$0.311234\pi$
$522$		0			0
$523$	−10.4911	+	12.1074i	−0.458746	+	0.529421i	−0.937247	−	0.348666i	$-0.886635\pi$
$523$	−10.4911	+	12.1074i	−0.458746	+	0.529421i	0.478501	+	0.878087i	$0.341180\pi$
$524$	11.0287	−	7.08771i	0.481791	−	0.309628i
$525$		0			0
$526$	−22.2494	−	6.53302i	−0.970122	−	0.284853i
$527$	−15.4519	+	33.8349i	−0.673094	+	1.47387i
$528$		0			0
$529$	15.9392	+	16.5814i	0.693007	+	0.720930i
$530$	20.5861			0.894204
$531$		0			0
$532$	0.322819	+	0.0947883i	0.0139960	+	0.00410959i
$533$	6.76017	+	7.80165i	0.292815	+	0.337927i
$534$		0			0
$535$	51.4312	−	59.3548i	2.22357	−	2.56613i
$536$	−2.00707	+	13.9595i	−0.0866921	+	0.602957i
$537$		0			0
$538$	4.49832	+	2.89089i	0.193936	+	0.124635i
$539$	−2.35822	−	16.4018i	−0.101576	−	0.706474i
$540$		0			0
$541$	−4.99134	−	10.9295i	−0.214595	−	0.469897i	0.771469	−	0.636267i	$-0.219522\pi$
$541$	−4.99134	−	10.9295i	−0.214595	−	0.469897i	−0.986063	+	0.166371i	$0.946795\pi$
$542$	−2.28921	−	15.9218i	−0.0983301	−	0.683901i
$543$		0			0
$544$	−4.32647	+	1.27037i	−0.185496	+	0.0544665i
$545$	9.96324	−	69.2959i	0.426778	−	2.96831i
$546$		0			0
$547$	24.9742	−	16.0500i	1.06782	−	0.686247i	0.116108	−	0.993237i	$-0.462958\pi$
$547$	24.9742	−	16.0500i	1.06782	−	0.686247i	0.951713	+	0.306989i	$0.0993216\pi$
$548$	0.831326	+	0.959402i	0.0355125	+	0.0409836i
$549$		0			0
$550$	12.9892	−	28.4424i	0.553861	−	1.21279i
$551$	−1.08705			−0.0463101
$552$		0			0
$553$	−3.57613			−0.152073
$554$	−1.43299	+	3.13781i	−0.0608819	+	0.133313i
$555$		0			0
$556$	10.1937	+	11.7642i	0.432310	+	0.498912i
$557$	−25.3904	+	16.3174i	−1.07582	+	0.691390i	−0.953589	−	0.301111i	$-0.902643\pi$
$557$	−25.3904	+	16.3174i	−1.07582	+	0.691390i	−0.122235	+	0.992501i	$0.539006\pi$
$558$		0			0
$559$	1.38186	−	9.61107i	0.0584466	−	0.406505i
$560$	−1.20731	+	0.354497i	−0.0510180	+	0.0149802i
$561$		0			0
$562$	0.916484	+	6.37428i	0.0386595	+	0.268883i
$563$	−0.902519	−	1.97624i	−0.0380367	−	0.0832887i	0.889660	−	0.456624i	$-0.150941\pi$
$563$	−0.902519	−	1.97624i	−0.0380367	−	0.0832887i	−0.927697	+	0.373335i	$0.878214\pi$
$564$		0			0
$565$	2.58260	+	17.9624i	0.108651	+	0.755683i
$566$	−9.81152	−	6.30548i	−0.412409	−	0.265039i
$567$		0			0
$568$	2.10188	−	14.6189i	0.0881930	−	0.613396i
$569$	1.37560	−	1.58752i	0.0576680	−	0.0665524i	−0.726183	−	0.687502i	$-0.758707\pi$
$569$	1.37560	−	1.58752i	0.0576680	−	0.0665524i	0.783851	+	0.620949i	$0.213253\pi$
$570$		0			0
$571$	−21.7880	−	25.1446i	−0.911797	−	1.05227i	−0.998429	−	0.0560299i	$-0.982156\pi$
$571$	−21.7880	−	25.1446i	−0.911797	−	1.05227i	0.0866317	−	0.996240i	$-0.472390\pi$
$572$	5.78193	+	1.69773i	0.241755	+	0.0709856i
$573$		0			0
$574$	−1.21649			−0.0507754
$575$	−46.2010	+	42.1708i	−1.92671	+	1.75865i
$576$		0			0
$577$	−1.49082	+	3.26444i	−0.0620637	+	0.135901i	−0.938122	−	0.346304i	$-0.887437\pi$
$577$	−1.49082	+	3.26444i	−0.0620637	+	0.135901i	0.876059	+	0.482205i	$0.160164\pi$
$578$	3.19720	+	0.938782i	0.132986	+	0.0390482i
$579$		0			0
$580$	3.42008	−	2.19795i	0.142011	−	0.0912649i
$581$	−0.412297	+	0.475817i	−0.0171050	+	0.0197402i
$582$		0			0
$583$	11.1474	−	3.27317i	0.461677	−	0.135561i
$584$	9.41463	+	6.05041i	0.389580	+	0.250368i
$585$		0			0
$586$	2.14076	+	4.68761i	0.0884340	+	0.193643i
$587$	15.5911	+	34.1396i	0.643512	+	1.40909i	0.897120	+	0.441787i	$0.145655\pi$
$587$	15.5911	+	34.1396i	0.643512	+	1.40909i	−0.253609	+	0.967307i	$0.581617\pi$
$588$		0			0
$589$	7.88195	+	5.06542i	0.324770	+	0.208717i
$590$	−46.0972	+	13.5354i	−1.89779	+	0.557242i
$591$		0			0
$592$	5.46628	−	6.30842i	0.224663	−	0.259275i
$593$	−17.5874	+	11.3028i	−0.722229	+	0.464148i	−0.849412	−	0.527731i	$-0.823043\pi$
$593$	−17.5874	+	11.3028i	−0.722229	+	0.464148i	0.127183	+	0.991879i	$0.459407\pi$
$594$		0			0
$595$	5.44389	+	1.59847i	0.223178	+	0.0655309i
$596$	−5.68369	+	12.4456i	−0.232813	+	0.509790i
$597$		0			0
$598$	−9.31168	−	7.65668i	−0.380783	−	0.313105i
$599$	−2.81949			−0.115201			−0.0576007	−	0.998340i	$-0.518345\pi$
$599$	−2.81949			−0.115201			−0.0576007	+	0.998340i	$0.518345\pi$
$600$		0			0
$601$	−28.5216	−	8.37471i	−1.16342	−	0.341612i	−0.357661	−	0.933852i	$-0.616426\pi$
$601$	−28.5216	−	8.37471i	−1.16342	−	0.341612i	−0.805762	+	0.592240i	$0.798244\pi$
$602$	0.749316	+	0.864757i	0.0305398	+	0.0352449i
$603$		0			0
$604$	−5.01025	+	5.78214i	−0.203864	+	0.235272i
$605$	−3.17563	+	22.0870i	−0.129108	+	0.897963i
$606$		0			0
$607$	−19.2966	−	12.4012i	−0.783225	−	0.503348i	0.0868775	−	0.996219i	$-0.472311\pi$
$607$	−19.2966	−	12.4012i	−0.783225	−	0.503348i	−0.870102	+	0.492871i	$0.835948\pi$
$608$	0.161640	+	1.12423i	0.00655538	+	0.0455937i
$609$		0			0
$610$	13.7024	+	30.0042i	0.554796	+	1.21483i
$611$	1.20144	+	8.35616i	0.0486049	+	0.338054i
$612$		0			0
$613$	25.6934	−	7.54427i	1.03775	−	0.304710i	0.281891	−	0.959447i	$-0.409038\pi$
$613$	25.6934	−	7.54427i	1.03775	−	0.304710i	0.755857	+	0.654736i	$0.227220\pi$
$614$	−2.21024	+	15.3726i	−0.0891982	+	0.620387i
$615$		0			0
$616$	−0.597391	+	0.383920i	−0.0240696	+	0.0154686i
$617$	−22.3887	−	25.8379i	−0.901334	−	1.04019i	−0.998988	−	0.0449743i	$-0.985679\pi$
$617$	−22.3887	−	25.8379i	−0.901334	−	1.04019i	0.0976543	−	0.995220i	$-0.468866\pi$
$618$		0			0
$619$	3.39992	−	7.44478i	0.136654	−	0.299231i	−0.828916	−	0.559373i	$-0.811042\pi$
$619$	3.39992	−	7.44478i	0.136654	−	0.299231i	0.965570	+	0.260142i	$0.0837693\pi$
$620$	−35.0400			−1.40724
$621$		0			0
$622$	7.59667			0.304599
$623$	−1.41322	+	3.09452i	−0.0566194	+	0.123979i
$624$		0			0
$625$	−52.3300	−	60.3921i	−2.09320	−	2.41568i
$626$	−22.0077	+	14.1435i	−0.879607	+	0.565289i
$627$		0			0
$628$	−1.03538	+	7.20123i	−0.0413162	+	0.287360i
$629$	−36.1141	+	10.6041i	−1.43996	+	0.422811i
$630$		0			0
$631$	−5.28765	−	36.7764i	−0.210498	−	1.46404i	−0.771499	−	0.636230i	$-0.780493\pi$
$631$	−5.28765	−	36.7764i	−0.210498	−	1.46404i	0.561002	−	0.827815i	$-0.310416\pi$
$632$	−5.01508	−	10.9815i	−0.199489	−	0.436820i
$633$		0			0
$634$	−3.44461	−	23.9578i	−0.136803	−	0.951485i
$635$	48.3415	+	31.0672i	1.91837	+	1.23286i
$636$		0			0
$637$	2.47279	−	17.1986i	0.0979754	−	0.681434i
$638$	1.50250	−	1.73398i	0.0594845	−	0.0686488i
$639$		0			0
$640$	−2.78167	−	3.21022i	−0.109955	−	0.126895i
$641$	2.00013	+	0.587293i	0.0790006	+	0.0231967i	0.320994	−	0.947081i	$-0.395983\pi$
$641$	2.00013	+	0.587293i	0.0790006	+	0.0231967i	−0.241993	+	0.970278i	$0.577801\pi$
$642$		0			0
$643$	38.7677			1.52885			0.764424	−	0.644713i	$-0.223023\pi$
$643$	38.7677			1.52885			0.764424	+	0.644713i	$0.223023\pi$
$644$	1.40048	−	0.238423i	0.0551868	−	0.00939518i
$645$		0			0
$646$	2.12752	−	4.65862i	0.0837062	−	0.183291i
$647$	7.29465	+	2.14190i	0.286782	+	0.0842068i	0.421960	−	0.906615i	$-0.361342\pi$
$647$	7.29465	+	2.14190i	0.286782	+	0.0842068i	−0.135178	+	0.990821i	$0.543161\pi$
$648$		0			0
$649$	−22.8095	+	14.6588i	−0.895353	+	0.575408i
$650$	21.4710	−	24.7788i	0.842161	−	0.971906i
$651$		0			0
$652$	−16.9007	+	4.96249i	−0.661882	+	0.194346i
$653$	−8.29815	−	5.33290i	−0.324732	−	0.208692i	0.368110	−	0.929782i	$-0.380005\pi$
$653$	−8.29815	−	5.33290i	−0.324732	−	0.208692i	−0.692841	+	0.721090i	$0.743641\pi$
$654$		0			0
$655$	−23.1333	−	50.6548i	−0.903891	−	1.97924i
$656$	−1.70598	−	3.73557i	−0.0666073	−	0.145850i
$657$		0			0
$658$	−0.836909	−	0.537849i	−0.0326261	−	0.0209675i
$659$	−17.4630	+	5.12760i	−0.680262	+	0.199743i	−0.603568	−	0.797312i	$-0.706255\pi$
$659$	−17.4630	+	5.12760i	−0.680262	+	0.199743i	−0.0766945	+	0.997055i	$0.524437\pi$
$660$		0			0
$661$	7.31461	−	8.44151i	0.284505	−	0.328337i	−0.595451	−	0.803392i	$-0.703027\pi$
$661$	7.31461	−	8.44151i	0.284505	−	0.328337i	0.879956	+	0.475055i	$0.157572\pi$
$662$	26.4346	−	16.9885i	1.02741	−	0.660276i
$663$		0			0
$664$	−2.03932	−	0.598798i	−0.0791410	−	0.0232379i
$665$	0.593687	−	1.29999i	0.0230222	−	0.0504116i
$666$		0			0
$667$	−4.12460	+	2.01395i	−0.159705	+	0.0779806i
$668$	−12.8331			−0.496527
$669$		0			0
$670$	57.4792	+	16.8774i	2.22062	+	0.652032i
$671$	12.1905	+	14.0686i	0.470609	+	0.543112i
$672$		0			0
$673$	−25.9993	+	30.0048i	−1.00220	+	1.15660i	−0.0145548	+	0.999894i	$0.504633\pi$
$673$	−25.9993	+	30.0048i	−1.00220	+	1.15660i	−0.987645	+	0.156706i	$0.949912\pi$
$674$	0.814916	−	5.66787i	0.0313894	−	0.218318i
$675$		0			0
$676$	−5.62059	−	3.61213i	−0.216177	−	0.138928i
$677$	−1.13255	−	7.87705i	−0.0435274	−	0.302740i	−0.999942	−	0.0107290i	$-0.996585\pi$
$677$	−1.13255	−	7.87705i	−0.0435274	−	0.302740i	0.956415	−	0.292011i	$-0.0943243\pi$
$678$		0			0
$679$	0.0978731	+	0.214312i	0.00375603	+	0.00822455i
$680$	2.72583	+	18.9586i	0.104531	+	0.727029i
$681$		0			0
$682$	−18.9742	+	5.57132i	−0.726559	+	0.213337i
$683$	−2.48553	+	17.2872i	−0.0951062	+	0.661478i	0.885377	+	0.464874i	$0.153900\pi$
$683$	−2.48553	+	17.2872i	−0.0951062	+	0.661478i	−0.980483	+	0.196604i	$0.937009\pi$
$684$		0			0
$685$	4.53635	−	2.91534i	0.173325	−	0.111389i
$686$	2.69876	+	3.11454i	0.103039	+	0.118914i
$687$		0			0
$688$	−1.60465	+	3.51369i	−0.0611767	+	0.133958i
$689$	12.1824			0.464114
$690$		0			0
$691$	−14.4115			−0.548240			−0.274120	−	0.961696i	$-0.588386\pi$
$691$	−14.4115			−0.548240			−0.274120	+	0.961696i	$0.588386\pi$
$692$	3.84228	−	8.41342i	0.146062	−	0.319830i
$693$		0			0
$694$	12.8852	+	14.8703i	0.489115	+	0.564469i
$695$	55.6247	−	35.7478i	2.10997	−	1.35599i
$696$		0			0
$697$	−2.63532	+	18.3291i	−0.0998199	+	0.694263i
$698$	2.11643	−	0.621441i	0.0801081	−	0.0235219i
$699$		0			0
$700$	0.549863	+	3.82438i	0.0207829	+	0.144548i
$701$	−11.2791	−	24.6978i	−0.426006	−	0.932823i	−0.993958	−	0.109761i	$-0.964991\pi$
$701$	−11.2791	−	24.6978i	−0.426006	−	0.932823i	0.567952	−	0.823062i	$-0.307736\pi$
$702$		0			0
$703$	1.34925	+	9.38425i	0.0508880	+	0.353934i
$704$	−2.01670	−	1.29605i	−0.0760072	−	0.0488469i
$705$		0			0
$706$	1.68525	−	11.7211i	0.0634251	−	0.441131i
$707$	1.81382	−	2.09326i	0.0682158	−	0.0787253i
$708$		0			0
$709$	−9.74680	−	11.2484i	−0.366049	−	0.422443i	0.542608	−	0.839986i	$-0.317437\pi$
$709$	−9.74680	−	11.2484i	−0.366049	−	0.422443i	−0.908657	+	0.417543i	$0.862891\pi$
$710$	−60.1946	−	17.6747i	−2.25906	−	0.663320i
$711$		0			0
$712$	−11.4844			−0.430397
$713$	39.2910	+	4.61705i	1.47146	+	0.172910i
$714$		0			0
$715$	10.6334	−	23.2838i	0.397665	−	0.870765i
$716$	−18.2298	−	5.35275i	−0.681280	−	0.200042i
$717$		0			0
$718$	−19.2028	+	12.3409i	−0.716643	+	0.460559i
$719$	2.15554	−	2.48763i	0.0803881	−	0.0927728i	−0.714131	−	0.700012i	$-0.753178\pi$
$719$	2.15554	−	2.48763i	0.0803881	−	0.0927728i	0.794519	+	0.607240i	$0.207723\pi$
$720$		0			0
$721$	2.81564	−	0.826746i	0.104860	−	0.0307896i
$722$	14.8986	+	9.57473i	0.554468	+	0.356335i
$723$		0			0
$724$	1.08576	+	2.37748i	0.0403518	+	0.0883582i
$725$	−5.18585	−	11.3554i	−0.192597	−	0.421730i
$726$		0			0
$727$	−27.0556	−	17.3876i	−1.00344	−	0.644869i	−0.0677491	−	0.997702i	$-0.521582\pi$
$727$	−27.0556	−	17.3876i	−1.00344	−	0.644869i	−0.935686	+	0.352834i	$0.885218\pi$
$728$	−0.714458	+	0.209784i	−0.0264796	+	0.00777511i
$729$		0			0
$730$	31.1303	−	35.9262i	1.15218	−	1.32969i
$731$	14.6527	−	9.41670i	0.541949	−	0.348289i
$732$		0			0
$733$	49.9322	+	14.6614i	1.84429	+	0.541532i	0.999984	+	0.00566632i	$0.00180365\pi$
$733$	49.9322	+	14.6614i	1.84429	+	0.541532i	0.844303	+	0.535865i	$0.180015\pi$
$734$	12.4888	−	27.3466i	0.460970	−	1.00938i
$735$		0			0
$736$	2.69615	+	3.96621i	0.0993812	+	0.146196i
$737$	33.8085			1.24535
$738$		0			0
$739$	15.9035	+	4.66969i	0.585020	+	0.171777i	0.560831	−	0.827930i	$-0.310482\pi$
$739$	15.9035	+	4.66969i	0.585020	+	0.171777i	0.0241884	+	0.999707i	$0.492300\pi$
$740$	−23.2193	−	26.7965i	−0.853559	−	0.985059i
$741$		0			0
$742$	−0.940122	+	1.08496i	−0.0345129	+	0.0398301i
$743$	1.30033	−	9.04396i	0.0477043	−	0.331791i	−0.951968	−	0.306197i	$-0.900943\pi$
$743$	1.30033	−	9.04396i	0.0477043	−	0.331791i	0.999672	−	0.0255937i	$-0.00814760\pi$
$744$		0			0
$745$	48.8914	+	31.4206i	1.79124	+	1.15116i
$746$	4.49506	+	31.2638i	0.164576	+	1.14465i
$747$		0			0
$748$	4.49043	+	9.83268i	0.164186	+	0.359518i
$749$	0.779451	+	5.42120i	0.0284805	+	0.198086i
$750$		0			0
$751$	40.3749	−	11.8551i	1.47330	−	0.432600i	0.556130	−	0.831095i	$-0.312285\pi$
$751$	40.3749	−	11.8551i	1.47330	−	0.432600i	0.917171	+	0.398495i	$0.130467\pi$
$752$	0.477951	−	3.32422i	0.0174291	−	0.121222i
$753$		0			0
$754$	2.02393	−	1.30070i	0.0737072	−	0.0473687i
$755$	21.2822	+	24.5610i	0.774539	+	0.893866i
$756$		0			0
$757$	−3.15114	+	6.90004i	−0.114530	+	0.250786i	−0.958213	−	0.286056i	$-0.907656\pi$
$757$	−3.15114	+	6.90004i	−0.114530	+	0.250786i	0.843683	+	0.536842i	$0.180383\pi$
$758$	25.6283			0.930860
$759$		0			0
$760$	4.82455			0.175005
$761$	19.1398	−	41.9103i	0.693817	−	1.51925i	−0.153493	−	0.988150i	$-0.549052\pi$
$761$	19.1398	−	41.9103i	0.693817	−	1.51925i	0.847310	−	0.531098i	$-0.178220\pi$
$762$		0			0
$763$	3.19713	+	3.68968i	0.115744	+	0.133575i
$764$	−4.96590	+	3.19139i	−0.179660	+	0.115461i
$765$		0			0
$766$	3.25180	−	22.6168i	0.117492	−	0.817178i
$767$	−27.2794	+	8.00995i	−0.985001	+	0.289222i
$768$		0			0
$769$	−1.76158	−	12.2520i	−0.0635242	−	0.441820i	−0.996617	−	0.0821849i	$-0.973810\pi$
$769$	−1.76158	−	12.2520i	−0.0635242	−	0.441820i	0.933093	−	0.359635i	$-0.117099\pi$
$770$	1.25306	+	2.74382i	0.0451571	+	0.0988803i
$771$		0			0
$772$	−0.0499053	−	0.347099i	−0.00179613	−	0.0124924i
$773$	−38.8352	−	24.9579i	−1.39680	−	0.897672i	−0.397007	−	0.917816i	$-0.629951\pi$
$773$	−38.8352	−	24.9579i	−1.39680	−	0.897672i	−0.999797	+	0.0201441i	$0.993588\pi$
$774$		0			0
$775$	−15.3124	+	106.500i	−0.550037	+	3.82559i
$776$	−0.520850	+	0.601092i	−0.0186974	+	0.0215780i
$777$		0			0
$778$	−10.6572	−	12.2991i	−0.382079	−	0.440943i
$779$	4.47541	+	1.31410i	0.160348	+	0.0470825i
$780$		0			0
$781$	−35.4056			−1.26691
$782$	−0.558447	−	21.6178i	−0.0199700	−	0.773050i
$783$		0			0
$784$	−2.87145	+	6.28761i	−0.102552	+	0.224557i
$785$	29.6517	+	8.70652i	1.05831	+	0.310749i
$786$		0			0
$787$	10.7591	−	6.91447i	0.383521	−	0.246474i	−0.334647	−	0.942344i	$-0.608617\pi$
$787$	10.7591	−	6.91447i	0.383521	−	0.246474i	0.718168	+	0.695869i	$0.244981\pi$
$788$	12.3463	−	14.2484i	0.439818	−	0.507577i
$789$		0			0
$790$	−49.2033	+	14.4474i	−1.75058	+	0.514016i
$791$	−1.06462	−	0.684190i	−0.0378535	−	0.0243270i
$792$		0			0
$793$	8.10882	+	17.7558i	0.287953	+	0.630529i
$794$	2.16775	+	4.74671i	0.0769305	+	0.168454i
$795$		0			0
$796$	−13.7481	−	8.83540i	−0.487290	−	0.313162i
$797$	17.1555	−	5.03731i	0.607679	−	0.178431i	0.0366059	−	0.999330i	$-0.488345\pi$
$797$	17.1555	−	5.03731i	0.607679	−	0.178431i	0.571073	+	0.820899i	$0.306527\pi$
$798$		0			0
$799$	−9.91686	+	11.4447i	−0.350833	+	0.404883i
$800$	−10.9727	+	7.05171i	−0.387943	+	0.249316i
$801$		0			0
$802$	−7.88144	−	2.31420i	−0.278303	−	0.0817172i
$803$	11.1448	−	24.4037i	0.393292	−	0.861189i
$804$		0			0
$805$	−0.155835	−	6.03246i	−0.00549246	−	0.212616i
$806$	−20.7360			−0.730393
$807$		0			0
$808$	8.97160	+	2.63430i	0.315620	+	0.0926743i
$809$	24.7272	+	28.5367i	0.869362	+	1.00330i	0.999930	+	0.0118575i	$0.00377446\pi$
$809$	24.7272	+	28.5367i	0.869362	+	1.00330i	−0.130568	+	0.991439i	$0.541680\pi$
$810$		0			0
$811$	−13.9486	+	16.0976i	−0.489803	+	0.565263i	−0.945813	−	0.324712i	$-0.894733\pi$
$811$	−13.9486	+	16.0976i	−0.489803	+	0.565263i	0.456010	+	0.889975i	$0.349278\pi$
$812$	−0.0403478	+	0.280625i	−0.00141593	+	0.00984801i
$813$		0			0
$814$	−16.8339	−	10.8185i	−0.590027	−	0.379187i
$815$	10.6480	+	74.0588i	0.372985	+	2.59417i
$816$		0			0
$817$	−1.82255	−	3.99083i	−0.0637630	−	0.139622i
$818$	−4.83688	−	33.6413i	−0.169118	−	1.17624i
$819$		0			0
$820$	−16.7375	+	4.91458i	−0.584499	+	0.171624i
$821$	1.11322	−	7.74258i	0.0388515	−	0.270218i	−0.961131	−	0.276092i	$-0.910961\pi$
$821$	1.11322	−	7.74258i	0.0388515	−	0.270218i	0.999983	+	0.00587381i	$0.00186970\pi$
$822$		0			0
$823$	0.0336044	−	0.0215962i	0.00117137	−	0.000752797i	−0.540055	−	0.841630i	$-0.681597\pi$
$823$	0.0336044	−	0.0215962i	0.00117137	−	0.000752797i	0.541226	+	0.840877i	$0.317960\pi$
$824$	6.48733	+	7.48678i	0.225997	+	0.260814i
$825$		0			0
$826$	1.39180	−	3.04761i	0.0484268	−	0.106040i
$827$	−35.9303			−1.24942			−0.624710	−	0.780857i	$-0.714783\pi$
$827$	−35.9303			−1.24942			−0.624710	+	0.780857i	$0.714783\pi$
$828$		0			0
$829$	11.7357			0.407597			0.203799	−	0.979013i	$-0.434671\pi$
$829$	11.7357			0.407597			0.203799	+	0.979013i	$0.434671\pi$
$830$	−3.75045	+	8.21234i	−0.130180	+	0.285054i
$831$		0			0
$832$	−1.64614	−	1.89974i	−0.0570695	−	0.0658618i
$833$	26.2203	−	16.8508i	0.908481	−	0.583845i
$834$		0			0
$835$	−7.75780	+	53.9567i	−0.268470	+	1.86725i
$836$	2.61250	−	0.767098i	0.0903550	−	0.0265306i
$837$		0			0
$838$	−3.24879	−	22.5958i	−0.112228	−	0.780560i
$839$	22.5583	+	49.3957i	0.778797	+	1.70533i	0.706249	+	0.707963i	$0.250386\pi$
$839$	22.5583	+	49.3957i	0.778797	+	1.70533i	0.0725481	+	0.997365i	$0.476887\pi$
$840$		0			0
$841$	3.99677	+	27.7981i	0.137820	+	0.958556i
$842$	−14.0204	−	9.01038i	−0.483176	−	0.310518i
$843$		0			0
$844$	−1.96578	+	13.6723i	−0.0676648	+	0.470619i
$845$	−18.5849	+	21.4482i	−0.639342	+	0.737840i
$846$		0			0
$847$	−1.01903	−	1.17603i	−0.0350144	−	0.0404088i
$848$	−4.65006	−	1.36538i	−0.159684	−	0.0468874i
$849$		0			0
$850$	58.8136			2.01729
$851$	22.5054	+	33.1069i	0.771474	+	1.13489i
$852$		0			0
$853$	18.3367	−	40.1517i	0.627836	−	1.37477i	−0.281844	−	0.959460i	$-0.590946\pi$
$853$	18.3367	−	40.1517i	0.627836	−	1.37477i	0.909680	−	0.415309i	$-0.136327\pi$
$854$	−2.20708	−	0.648058i	−0.0755248	−	0.0221761i
$855$		0			0
$856$	−15.5542	+	9.99607i	−0.531631	+	0.341659i
$857$	−16.4842	+	19.0237i	−0.563088	+	0.649839i	−0.963882	−	0.266330i	$-0.914189\pi$
$857$	−16.4842	+	19.0237i	−0.563088	+	0.649839i	0.400794	+	0.916168i	$0.368734\pi$
$858$		0			0
$859$	−16.5276	+	4.85295i	−0.563915	+	0.165580i	−0.551251	−	0.834339i	$-0.685849\pi$
$859$	−16.5276	+	4.85295i	−0.563915	+	0.165580i	−0.0126641	+	0.999920i	$0.504031\pi$
$860$	13.8033	+	8.87083i	0.470688	+	0.302493i
$861$		0			0
$862$	8.45183	+	18.5069i	0.287870	+	0.630348i
$863$	−15.6951	−	34.3674i	−0.534267	−	1.16988i	−0.963750	−	0.266806i	$-0.914032\pi$
$863$	−15.6951	−	34.3674i	−0.534267	−	1.16988i	0.429484	−	0.903075i	$-0.358696\pi$
$864$		0			0
$865$	−33.0515	−	21.2409i	−1.12378	−	0.722212i
$866$	−27.9383	+	8.20342i	−0.949382	+	0.278764i
$867$		0			0
$868$	1.60020	−	1.84673i	0.0543143	−	0.0626820i
$869$	−24.3465	+	15.6465i	−0.825898	+	0.530772i
$870$		0			0
$871$	34.0150	+	9.98770i	1.15255	+	0.338420i
$872$	−6.84660	+	14.9920i	−0.231855	+	0.507692i
$873$		0			0
$874$	−5.40986	−	0.635707i	−0.182991	−	0.0215031i
$875$	10.1206			0.342139
$876$		0			0
$877$	55.1724	+	16.2001i	1.86304	+	0.547037i	0.999053	+	0.0435206i	$0.0138574\pi$
$877$	55.1724	+	16.2001i	1.86304	+	0.547037i	0.863985	+	0.503517i	$0.167961\pi$
$878$	−12.8421	−	14.8206i	−0.433401	−	0.500171i
$879$		0			0
$880$	−6.66838	+	7.69572i	−0.224791	+	0.259423i
$881$	4.82802	−	33.5796i	0.162660	−	1.13132i	−0.730934	−	0.682448i	$-0.760915\pi$
$881$	4.82802	−	33.5796i	0.162660	−	1.13132i	0.893594	−	0.448877i	$-0.148176\pi$
$882$		0			0
$883$	−12.9359	−	8.31343i	−0.435329	−	0.279769i	0.304566	−	0.952491i	$-0.401489\pi$
$883$	−12.9359	−	8.31343i	−0.435329	−	0.279769i	−0.739895	+	0.672722i	$0.765125\pi$
$884$	1.61309	+	11.2193i	0.0542542	+	0.377346i
$885$		0			0
$886$	−3.58899	−	7.85880i	−0.120575	−	0.264022i
$887$	−1.01147	−	7.03496i	−0.0339620	−	0.236211i	0.965769	−	0.259403i	$-0.0835259\pi$
$887$	−1.01147	−	7.03496i	−0.0339620	−	0.236211i	−0.999731	+	0.0231928i	$0.992617\pi$
$888$		0			0
$889$	−3.84499	+	1.12899i	−0.128957	+	0.0378651i
$890$	−6.94251	+	48.2862i	−0.232713	+	1.61856i
$891$		0			0
$892$	3.08246	−	1.98098i	0.103208	−	0.0663281i
$893$	2.49794	+	2.88277i	0.0835903	+	0.0964684i
$894$		0			0
$895$	−33.5259	+	73.4114i	−1.12065	+	2.45387i
$896$	0.296223			0.00989610
$897$		0			0
$898$	22.2983			0.744104
$899$	−3.27975	+	7.18165i	−0.109386	+	0.239521i
$900$		0			0
$901$	14.3106	+	16.5153i	0.476755	+	0.550205i
$902$	−8.28195	+	5.32249i	−0.275759	+	0.177219i
$903$		0			0
$904$	0.607995	−	4.22870i	0.0202216	−	0.140644i
$905$	10.6524	−	3.12784i	0.354099	−	0.103973i
$906$		0			0
$907$	−4.12051	−	28.6588i	−0.136819	−	0.951600i	−0.936373	−	0.351006i	$-0.885840\pi$
$907$	−4.12051	−	28.6588i	−0.136819	−	0.951600i	0.799554	−	0.600594i	$-0.205069\pi$
$908$	−0.0237007	−	0.0518972i	−0.000786534	−	0.00172227i
$909$		0			0
$910$	0.450135	+	3.13076i	0.0149218	+	0.103784i
$911$	2.61626	+	1.68137i	0.0866805	+	0.0557062i	0.583263	−	0.812283i	$-0.301776\pi$
$911$	2.61626	+	1.68137i	0.0866805	+	0.0557062i	−0.496583	+	0.867989i	$0.665412\pi$
$912$		0			0
$913$	−0.725117	+	5.04330i	−0.0239979	+	0.166909i
$914$	2.24435	−	2.59011i	0.0742364	−	0.0856734i
$915$		0			0
$916$	−4.01778	−	4.63677i	−0.132751	−	0.153203i
$917$	3.72612	+	1.09409i	0.123047	+	0.0361300i
$918$		0			0
$919$	−14.9768			−0.494038			−0.247019	−	0.969011i	$-0.579451\pi$
$919$	−14.9768			−0.494038			−0.247019	+	0.969011i	$0.579451\pi$
$920$	18.3058	−	8.93831i	0.603524	−	0.294687i
$921$		0			0
$922$	−12.0294	+	26.3407i	−0.396167	+	0.867485i
$923$	−35.6219	−	10.4595i	−1.17251	−	0.344280i
$924$		0			0
$925$	−91.5916	+	58.8624i	−3.01151	+	1.93538i
$926$	5.95481	−	6.87222i	0.195687	−	0.225835i
$927$		0			0
$928$	−0.918318	+	0.269643i	−0.0301453	+	0.00885145i
$929$	−26.8571	−	17.2600i	−0.881154	−	0.566283i	0.0199913	−	0.999800i	$-0.493636\pi$
$929$	−26.8571	−	17.2600i	−0.881154	−	0.566283i	−0.901146	+	0.433517i	$0.857273\pi$
$930$		0			0
$931$	−3.26138	−	7.14143i	−0.106887	−	0.234051i
$932$	−8.43646	−	18.4733i	−0.276345	−	0.605112i
$933$		0			0
$934$	17.6204	+	11.3239i	0.576557	+	0.370531i
$935$	44.0560	−	12.9360i	1.44079	−	0.423053i
$936$		0			0
$937$	14.1654	−	16.3478i	0.462764	−	0.534059i	−0.475620	−	0.879651i	$-0.657776\pi$
$937$	14.1654	−	16.3478i	0.462764	−	0.534059i	0.938385	+	0.345592i	$0.112322\pi$
$938$	−3.51444	+	2.25860i	−0.114751	+	0.0737458i
$939$		0			0
$940$	−13.6878	−	4.01909i	−0.446445	−	0.131088i
$941$	−1.22869	+	2.69045i	−0.0400540	+	0.0877061i	−0.928601	−	0.371079i	$-0.878988\pi$
$941$	−1.22869	+	2.69045i	−0.0400540	+	0.0877061i	0.888547	+	0.458785i	$0.151715\pi$
$942$		0			0
$943$	19.4156	−	3.30538i	0.632260	−	0.107638i
$944$	11.3103			0.368120
$945$		0			0
$946$	8.88493	+	2.60885i	0.288874	+	0.0848210i
$947$	−1.05470	−	1.21718i	−0.0342730	−	0.0395532i	0.738354	−	0.674413i	$-0.235603\pi$
$947$	−1.05470	−	1.21718i	−0.0342730	−	0.0395532i	−0.772627	+	0.634860i	$0.781058\pi$
$948$		0			0
$949$	18.4222	−	21.2604i	0.598011	−	0.690141i
$950$	2.10832	−	14.6637i	0.0684028	−	0.475752i
$951$		0			0
$952$	−1.12367	−	0.722136i	−0.0364182	−	0.0234046i
$953$	−4.47155	−	31.1003i	−0.144848	−	1.00744i	−0.924488	−	0.381211i	$-0.875507\pi$
$953$	−4.47155	−	31.1003i	−0.144848	−	1.00744i	0.779640	−	0.626228i	$-0.215402\pi$
$954$		0			0
$955$	10.4162	+	22.8084i	0.337062	+	0.738062i
$956$	−0.520240	−	3.61835i	−0.0168258	−	0.117026i
$957$		0			0
$958$	9.52654	−	2.79724i	0.307788	−	0.0903748i
$959$	−0.0535169	+	0.372218i	−0.00172815	+	0.0120195i
$960$		0			0
$961$	31.1666	−	20.0295i	1.00537	−	0.646114i
$962$	−13.7407	−	15.8576i	−0.443018	−	0.511270i
$963$		0			0
$964$	−4.88168	+	10.6894i	−0.157228	+	0.344282i
$965$	−1.48955			−0.0479502
$966$		0			0
$967$	15.2718			0.491108			0.245554	−	0.969383i	$-0.421030\pi$
$967$	15.2718			0.491108			0.245554	+	0.969383i	$0.421030\pi$
$968$	2.18225	−	4.77845i	0.0701401	−	0.153585i
$969$		0			0
$970$	2.21243	+	2.55328i	0.0710369	+	0.0819809i
$971$	21.6752	−	13.9298i	0.695589	−	0.447028i	−0.144480	−	0.989508i	$-0.546151\pi$
$971$	21.6752	−	13.9298i	0.695589	−	0.447028i	0.840069	+	0.542480i	$0.182515\pi$
$972$		0			0
$973$	−0.656223	+	4.56413i	−0.0210376	+	0.146319i
$974$	−14.4110	+	4.23146i	−0.461759	+	0.135585i
$975$		0			0
$976$	−1.10512	−	7.68627i	−0.0353740	−	0.246031i
$977$	−3.68998	−	8.07992i	−0.118053	−	0.258500i	0.841376	−	0.540450i	$-0.181746\pi$
$977$	−3.68998	−	8.07992i	−0.118053	−	0.258500i	−0.959429	+	0.281950i	$0.909019\pi$
$978$		0			0
$979$	3.91808	+	27.2508i	0.125222	+	0.870940i
$980$	24.7004	+	15.8740i	0.789025	+	0.507076i
$981$		0			0
$982$	−0.581832	+	4.04673i	−0.0185670	+	0.129136i
$983$	2.33634	−	2.69628i	0.0745178	−	0.0859981i	−0.717266	−	0.696799i	$-0.754607\pi$
$983$	2.33634	−	2.69628i	0.0745178	−	0.0859981i	0.791784	+	0.610801i	$0.209152\pi$
$984$		0			0
$985$	−52.4437	−	60.5233i	−1.67100	−	1.92843i
$986$	4.14081	+	1.21585i	0.131870	+	0.0387206i
$987$		0			0
$988$	2.85507			0.0908319
$989$	−14.3090	−	11.7658i	−0.455000	−	0.374131i
$990$		0			0
$991$	0.194362	−	0.425594i	0.00617412	−	0.0135194i	−0.906520	−	0.422163i	$-0.861271\pi$
$991$	0.194362	−	0.425594i	0.00617412	−	0.0135194i	0.912694	+	0.408644i	$0.133998\pi$
$992$	7.91496	+	2.32404i	0.251300	+	0.0737884i
$993$		0			0
$994$	3.68047	−	2.36529i	0.116737	−	0.0750225i
$995$	−45.4594	+	52.4629i	−1.44116	+	1.66319i
$996$		0			0
$997$	−15.5806	+	4.57487i	−0.493442	+	0.144888i	−0.518980	−	0.854786i	$-0.673688\pi$
$997$	−15.5806	+	4.57487i	−0.493442	+	0.144888i	0.0255385	+	0.999674i	$0.491870\pi$
$998$	12.6991	+	8.16119i	0.401982	+	0.258338i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	414.2.i.h.397.1	yes	20
3.2	odd	2		414.2.i.g.397.2	yes	20
23.2	even	11		9522.2.a.cg.1.1		10
23.4	even	11	inner	414.2.i.h.73.1	yes	20
23.21	odd	22		9522.2.a.ch.1.10		10
69.2	odd	22		9522.2.a.cj.1.10		10
69.44	even	22		9522.2.a.ci.1.1		10
69.50	odd	22		414.2.i.g.73.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
414.2.i.g.73.2	✓	20	69.50	odd	22
414.2.i.g.397.2	yes	20	3.2	odd	2
414.2.i.h.73.1	yes	20	23.4	even	11	inner
414.2.i.h.397.1	yes	20	1.1	even	1	trivial
9522.2.a.cg.1.1		10	23.2	even	11
9522.2.a.ch.1.10		10	23.21	odd	22
9522.2.a.ci.1.1		10	69.44	even	22
9522.2.a.cj.1.10		10	69.2	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)

\(f(q)\)	\(=\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-3.57342 + 2.29650i) q^{5} +(0.0421569 - 0.293207i) q^{7} +(0.959493 - 0.281733i) q^{8} +O(q^{10})\)	\(q+(-0.415415 + 0.909632i) q^{2} +(-0.654861 - 0.755750i) q^{4} +(-3.57342 + 2.29650i) q^{5} +(0.0421569 - 0.293207i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.604516 - 4.20450i) q^{10} +(-0.995855 - 2.18062i) q^{11} +(-0.357740 - 2.48813i) q^{13} +(0.249198 + 0.160150i) q^{14} +(-0.142315 + 0.989821i) q^{16} +(2.95285 - 3.40777i) q^{17} +(-0.743787 - 0.858376i) q^{19} +(4.07567 + 1.19673i) q^{20} +2.39725 q^{22} +(-4.41244 - 1.87894i) q^{23} +(5.41836 - 11.8646i) q^{25} +(2.41190 + 0.708197i) q^{26} +(-0.249198 + 0.160150i) q^{28} +(0.626759 - 0.723318i) q^{29} +(-7.91496 + 2.32404i) q^{31} +(-0.841254 - 0.540641i) q^{32} +(1.87316 + 4.10164i) q^{34} +(0.522706 + 1.14457i) q^{35} +(-7.02215 - 4.51286i) q^{37} +(1.08979 - 0.319990i) q^{38} +(-2.78167 + 3.21022i) q^{40} +(-3.45477 + 2.22024i) q^{41} +(3.70629 + 1.08827i) q^{43} +(-0.995855 + 2.18062i) q^{44} +(3.54214 - 3.23315i) q^{46} -3.35841 q^{47} +(6.63226 + 1.94741i) q^{49} +(8.54151 + 9.85743i) q^{50} +(-1.64614 + 1.89974i) q^{52} +(-0.689711 + 4.79705i) q^{53} +(8.56640 + 5.50529i) q^{55} +(-0.0421569 - 0.293207i) q^{56} +(0.397588 + 0.870597i) q^{58} +(-1.60963 - 11.1952i) q^{59} +(-7.45076 + 2.18774i) q^{61} +(1.17397 - 8.16514i) q^{62} +(0.841254 - 0.540641i) q^{64} +(6.99235 + 8.06961i) q^{65} +(-5.85860 + 12.8285i) q^{67} -4.50912 q^{68} -1.25827 q^{70} +(6.13536 - 13.4346i) q^{71} +(7.32867 + 8.45774i) q^{73} +(7.02215 - 4.51286i) q^{74} +(-0.161640 + 1.12423i) q^{76} +(-0.681356 + 0.200064i) q^{77} +(-1.71809 - 11.9496i) q^{79} +(-1.76457 - 3.86388i) q^{80} +(-0.584443 - 4.06489i) q^{82} +(-1.78801 - 1.14909i) q^{83} +(-2.72583 + 18.9586i) q^{85} +(-2.52957 + 2.91928i) q^{86} +(-1.56987 - 1.81172i) q^{88} +(-11.0192 - 3.23553i) q^{89} -0.744621 q^{91} +(1.46952 + 4.56514i) q^{92} +(1.39513 - 3.05491i) q^{94} +(4.62912 + 1.35923i) q^{95} +(-0.669099 + 0.430004i) q^{97} +(-4.52656 + 5.22393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8}+O(q^{10}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8	\( 20 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 4 q^{7} + 2 q^{8} - 2 q^{10} - 2 q^{11} - 18 q^{14} - 2 q^{16} + 18 q^{17} + 16 q^{19} + 2 q^{20} + 24 q^{22} - 2 q^{23} + 38 q^{25} + 18 q^{28} - 30 q^{29} + 14 q^{31} + 2 q^{32} + 4 q^{34} + 48 q^{35} - 20 q^{37} - 16 q^{38} - 2 q^{40} - 12 q^{41} - 28 q^{43} - 2 q^{44} + 2 q^{46} + 32 q^{47} + 6 q^{49} + 6 q^{50} - 46 q^{53} - 28 q^{55} + 4 q^{56} - 14 q^{58} - 50 q^{61} + 8 q^{62} - 2 q^{64} + 16 q^{65} - 8 q^{67} - 48 q^{68} - 48 q^{70} + 12 q^{71} - 18 q^{73} + 20 q^{74} - 6 q^{76} - 4 q^{77} - 18 q^{79} + 2 q^{80} - 10 q^{82} - 44 q^{83} + 32 q^{85} + 28 q^{86} + 2 q^{88} + 44 q^{91} - 2 q^{92} + 12 q^{94} + 64 q^{95} + 14 q^{97} - 28 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 - 2 * q^4 + 2 * q^5 - 4 * q^7 + 2 * q^8 - 2 * q^10 - 2 * q^11 - 18 * q^14 - 2 * q^16 + 18 * q^17 + 16 * q^19 + 2 * q^20 + 24 * q^22 - 2 * q^23 + 38 * q^25 + 18 * q^28 - 30 * q^29 + 14 * q^31 + 2 * q^32 + 4 * q^34 + 48 * q^35 - 20 * q^37 - 16 * q^38 - 2 * q^40 - 12 * q^41 - 28 * q^43 - 2 * q^44 + 2 * q^46 + 32 * q^47 + 6 * q^49 + 6 * q^50 - 46 * q^53 - 28 * q^55 + 4 * q^56 - 14 * q^58 - 50 * q^61 + 8 * q^62 - 2 * q^64 + 16 * q^65 - 8 * q^67 - 48 * q^68 - 48 * q^70 + 12 * q^71 - 18 * q^73 + 20 * q^74 - 6 * q^76 - 4 * q^77 - 18 * q^79 + 2 * q^80 - 10 * q^82 - 44 * q^83 + 32 * q^85 + 28 * q^86 + 2 * q^88 + 44 * q^91 - 2 * q^92 + 12 * q^94 + 64 * q^95 + 14 * q^97 - 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more