LMFDB - Embedded newform 99.2.f.b.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(37,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("99.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.f (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ 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 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			37.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	99.37
Dual form			99.2.f.b.91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.30902 + 0.951057i) q^{2} +(0.190983 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{5} +(0.927051 + 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})$	\(q+(1.30902 + 0.951057i) q^{2} +(0.190983 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{5} +(0.927051 + 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} -0.618034 q^{10} +(-2.80902 - 1.76336i) q^{11} +(-5.04508 - 3.66547i) q^{13} +(-1.50000 + 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(-0.190983 - 0.138757i) q^{20} +(-2.00000 - 4.97980i) q^{22} +5.47214 q^{23} +(-1.50000 + 4.61653i) q^{25} +(-3.11803 - 9.59632i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(1.38197 + 4.25325i) q^{29} +(3.11803 + 2.26538i) q^{31} +3.38197 q^{32} -1.00000 q^{34} +(-0.927051 - 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(-1.11803 + 0.812299i) q^{38} +(0.263932 + 0.812299i) q^{40} +(-1.83688 + 5.65334i) q^{41} +1.76393 q^{43} +(0.500000 - 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.190983 - 0.587785i) q^{47} +(-1.61803 + 1.17557i) q^{49} +(-6.35410 + 4.61653i) q^{50} +(1.19098 - 3.66547i) q^{52} +(-5.97214 - 4.33901i) q^{53} +(1.26393 - 0.0857567i) q^{55} +6.70820 q^{56} +(-2.23607 + 6.88191i) q^{58} +(1.64590 + 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(1.92705 + 5.93085i) q^{62} +(-3.42705 - 2.48990i) q^{64} +2.38197 q^{65} +10.5623 q^{67} +(-0.309017 - 0.224514i) q^{68} +(-0.572949 - 1.76336i) q^{70} +(11.7812 - 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(2.11803 - 6.51864i) q^{74} -0.527864 q^{76} +(2.42705 - 9.64932i) q^{77} +(-0.427051 - 0.310271i) q^{79} +(-0.572949 + 1.76336i) q^{80} +(-7.78115 + 5.65334i) q^{82} +(-10.2812 + 7.46969i) q^{83} +(0.0729490 - 0.224514i) q^{85} +(2.30902 + 1.67760i) q^{86} +(-5.69098 + 4.75528i) q^{88} -9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(1.04508 + 3.21644i) q^{92} +(0.809017 - 0.587785i) q^{94} +(-0.100813 - 0.310271i) q^{95} +(-12.1631 - 8.83702i) q^{97} -3.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8	$ 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8} + 2 q^{10} - 9 q^{11} - 9 q^{13} - 6 q^{14} + 9 q^{16} - 2 q^{17} - 10 q^{19} - 3 q^{20} - 8 q^{22} + 4 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 10 q^{29} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} - 3 q^{37} + 10 q^{40} - 23 q^{41} + 16 q^{43} + 2 q^{44} + 13 q^{46} + 3 q^{47} - 2 q^{49} - 12 q^{50} + 7 q^{52} - 6 q^{53} + 14 q^{55} + 20 q^{59} + 3 q^{61} + q^{62} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{70} + 27 q^{71} + 6 q^{73} + 4 q^{74} - 20 q^{76} + 3 q^{77} + 5 q^{79} - 9 q^{80} - 11 q^{82} - 21 q^{83} + 7 q^{85} + 7 q^{86} - 25 q^{88} - 20 q^{89} + 3 q^{91} - 7 q^{92} + q^{94} - 25 q^{95} - 33 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8 + 2 * q^10 - 9 * q^11 - 9 * q^13 - 6 * q^14 + 9 * q^16 - 2 * q^17 - 10 * q^19 - 3 * q^20 - 8 * q^22 + 4 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 10 * q^29 + 8 * q^31 + 18 * q^32 - 4 * q^34 + 3 * q^35 - 3 * q^37 + 10 * q^40 - 23 * q^41 + 16 * q^43 + 2 * q^44 + 13 * q^46 + 3 * q^47 - 2 * q^49 - 12 * q^50 + 7 * q^52 - 6 * q^53 + 14 * q^55 + 20 * q^59 + 3 * q^61 + q^62 - 7 * q^64 + 14 * q^65 + 2 * q^67 + q^68 - 9 * q^70 + 27 * q^71 + 6 * q^73 + 4 * q^74 - 20 * q^76 + 3 * q^77 + 5 * q^79 - 9 * q^80 - 11 * q^82 - 21 * q^83 + 7 * q^85 + 7 * q^86 - 25 * q^88 - 20 * q^89 + 3 * q^91 - 7 * q^92 + q^94 - 25 * q^95 - 33 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	0.944915	−	0.327315i	$-0.106144\pi$
$2$	1.30902	+	0.951057i	0.925615	+	0.672499i	−0.0193004	+	0.999814i	$0.506144\pi$
$3$		0			0
$3$		0			0
$4$	0.190983	+	0.587785i	0.0954915	+	0.293893i
$5$	−0.309017	+	0.224514i	−0.138197	+	0.100406i	−0.654736	−	0.755858i	$-0.727220\pi$
$5$	−0.309017	+	0.224514i	−0.138197	+	0.100406i	0.516539	+	0.856264i	$0.327220\pi$
$6$		0			0
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	0.958633	+	0.284644i	$0.0918755\pi$
$7$	0.927051	+	2.85317i	0.350392	+	1.07840i	−0.608241	+	0.793752i	$0.708125\pi$
$8$	0.690983	−	2.12663i	0.244299	−	0.751876i
$9$		0			0
$10$	−0.618034			−0.195440
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$11$	−2.80902	−	1.76336i	−0.846950	−	0.531672i
$12$		0			0
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.994777	−	0.102070i	$-0.967453\pi$
$13$	−5.04508	−	3.66547i	−1.39925	−	1.01662i	−0.404478	−	0.914548i	$-0.632547\pi$
$14$	−1.50000	+	4.61653i	−0.400892	+	1.23382i
$15$		0			0
$16$	3.92705	−	2.85317i	0.981763	−	0.713292i
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	−0.646766	−	0.762688i	$-0.723879\pi$
$17$	−0.500000	+	0.363271i	−0.121268	+	0.0881062i	0.525498	+	0.850795i	$0.323879\pi$
$18$		0			0
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	−0.976756	−	0.214353i	$-0.931236\pi$
$19$	−0.263932	+	0.812299i	−0.0605502	+	0.186354i	0.916206	+	0.400707i	$0.131236\pi$
$20$	−0.190983	−	0.138757i	−0.0427051	−	0.0310271i
$21$		0			0
$22$	−2.00000	−	4.97980i	−0.426401	−	1.06170i
$23$	5.47214			1.14102			0.570510	−	0.821291i	$-0.306746\pi$
$23$	5.47214			1.14102			0.570510	+	0.821291i	$0.306746\pi$
$24$		0			0
$25$	−1.50000	+	4.61653i	−0.300000	+	0.923305i
$26$	−3.11803	−	9.59632i	−0.611497	−	1.88199i
$27$		0			0
$28$	−1.50000	+	1.08981i	−0.283473	+	0.205955i
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	0.993505	+	0.113787i	$0.0362980\pi$
$29$	1.38197	+	4.25325i	0.256625	+	0.789809i	−0.736881	+	0.676023i	$0.763702\pi$
$30$		0			0
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	0.831465	−	0.555578i	$-0.187503\pi$
$31$	3.11803	+	2.26538i	0.560015	+	0.406875i	−0.271449	+	0.962453i	$0.587503\pi$
$32$	3.38197			0.597853
$33$		0			0
$34$	−1.00000			−0.171499
$35$	−0.927051	−	0.673542i	−0.156700	−	0.113849i
$36$		0			0
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	−0.999139	−	0.0414819i	$-0.986792\pi$
$37$	−1.30902	−	4.02874i	−0.215201	−	0.662321i	0.783938	−	0.620839i	$-0.213208\pi$
$38$	−1.11803	+	0.812299i	−0.181369	+	0.131772i
$39$		0			0
$40$	0.263932	+	0.812299i	0.0417313	+	0.128436i
$41$	−1.83688	+	5.65334i	−0.286873	+	0.882903i	0.698958	+	0.715162i	$0.253647\pi$
$41$	−1.83688	+	5.65334i	−0.286873	+	0.882903i	−0.985831	+	0.167741i	$0.946353\pi$
$42$		0			0
$43$	1.76393			0.268997			0.134499	−	0.990914i	$-0.457058\pi$
$43$	1.76393			0.268997			0.134499	+	0.990914i	$0.457058\pi$
$44$	0.500000	−	1.98787i	0.0753778	−	0.299683i
$45$		0			0
$46$	7.16312	+	5.20431i	1.05614	+	0.767334i
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	−0.936161	−	0.351572i	$-0.885647\pi$
$47$	0.190983	−	0.587785i	0.0278577	−	0.0857373i	0.964019	+	0.265834i	$0.0856474\pi$
$48$		0			0
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$	−6.35410	+	4.61653i	−0.898606	+	0.652875i
$51$		0			0
$52$	1.19098	−	3.66547i	0.165160	−	0.508309i
$53$	−5.97214	−	4.33901i	−0.820336	−	0.596009i	0.0964728	−	0.995336i	$-0.469244\pi$
$53$	−5.97214	−	4.33901i	−0.820336	−	0.596009i	−0.916809	+	0.399327i	$0.869244\pi$
$54$		0			0
$55$	1.26393	−	0.0857567i	0.170429	−	0.0115634i
$56$	6.70820			0.896421
$57$		0			0
$58$	−2.23607	+	6.88191i	−0.293610	+	0.903639i
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	0.999204	+	0.0398899i	$0.0127007\pi$
$59$	1.64590	+	5.06555i	0.214278	+	0.659479i	−0.784926	+	0.619589i	$0.787299\pi$
$60$		0			0
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	−0.645550	−	0.763718i	$-0.723372\pi$
$61$	−0.927051	+	0.673542i	−0.118697	+	0.0862382i	0.526853	+	0.849956i	$0.323372\pi$
$62$	1.92705	+	5.93085i	0.244736	+	0.753219i
$63$		0			0
$64$	−3.42705	−	2.48990i	−0.428381	−	0.311237i
$65$	2.38197			0.295447
$66$		0			0
$67$	10.5623			1.29039			0.645196	−	0.764017i	$-0.276776\pi$
$67$	10.5623			1.29039			0.645196	+	0.764017i	$0.276776\pi$
$68$	−0.309017	−	0.224514i	−0.0374738	−	0.0272263i
$69$		0			0
$70$	−0.572949	−	1.76336i	−0.0684805	−	0.210761i
$71$	11.7812	−	8.55951i	1.39817	−	1.01583i	0.403253	−	0.915089i	$-0.367880\pi$
$71$	11.7812	−	8.55951i	1.39817	−	1.01583i	0.994913	−	0.100738i	$-0.0321204\pi$
$72$		0			0
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	0.970918	−	0.239412i	$-0.0769548\pi$
$73$	0.381966	+	1.17557i	0.0447057	+	0.137590i	−0.926212	+	0.377003i	$0.876955\pi$
$74$	2.11803	−	6.51864i	0.246216	−	0.757776i
$75$		0			0
$76$	−0.527864			−0.0605502
$77$	2.42705	−	9.64932i	0.276588	−	1.09964i
$78$		0			0
$79$	−0.427051	−	0.310271i	−0.0480470	−	0.0349082i	0.563503	−	0.826114i	$-0.309453\pi$
$79$	−0.427051	−	0.310271i	−0.0480470	−	0.0349082i	−0.611550	+	0.791206i	$0.709453\pi$
$80$	−0.572949	+	1.76336i	−0.0640576	+	0.197149i
$81$		0			0
$82$	−7.78115	+	5.65334i	−0.859285	+	0.624307i
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.985476	−	0.169813i	$-0.945684\pi$
$83$	−10.2812	+	7.46969i	−1.12850	+	0.819906i	−0.143027	+	0.989719i	$0.545684\pi$
$84$		0			0
$85$	0.0729490	−	0.224514i	0.00791243	−	0.0243520i
$86$	2.30902	+	1.67760i	0.248988	+	0.180900i
$87$		0			0
$88$	−5.69098	+	4.75528i	−0.606661	+	0.506915i
$89$	−9.47214			−1.00404			−0.502022	−	0.864855i	$-0.667410\pi$
$89$	−9.47214			−1.00404			−0.502022	+	0.864855i	$0.667410\pi$
$90$		0			0
$91$	5.78115	−	17.7926i	0.606029	−	1.86517i
$92$	1.04508	+	3.21644i	0.108958	+	0.335337i
$93$		0			0
$94$	0.809017	−	0.587785i	0.0834437	−	0.0606254i
$95$	−0.100813	−	0.310271i	−0.0103432	−	0.0318331i
$96$		0			0
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.237724	−	0.971333i	$-0.576402\pi$
$97$	−12.1631	−	8.83702i	−1.23498	−	0.897264i	−0.997253	+	0.0740689i	$0.976402\pi$
$98$	−3.23607			−0.326892
$99$		0			0
$100$	−3.00000			−0.300000
$101$	−2.42705	−	1.76336i	−0.241501	−	0.175460i	0.460451	−	0.887685i	$-0.347688\pi$
$101$	−2.42705	−	1.76336i	−0.241501	−	0.175460i	−0.701952	+	0.712225i	$0.747688\pi$
$102$		0			0
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	0.817211	−	0.576339i	$-0.195519\pi$
$103$	−1.85410	−	5.70634i	−0.182690	−	0.562262i	−0.999901	+	0.0140765i	$0.995519\pi$
$104$	−11.2812	+	8.19624i	−1.10621	+	0.803707i
$105$		0			0
$106$	−3.69098	−	11.3597i	−0.358500	−	1.10335i
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	−0.954521	−	0.298145i	$-0.903632\pi$
$107$	−0.0729490	+	0.224514i	−0.00705225	+	0.0217046i	0.947468	+	0.319849i	$0.103632\pi$
$108$		0			0
$109$		0			0			−	1.00000i	$-0.5\pi$
$109$		0			0				1.00000i	$0.5\pi$
$110$	1.73607	+	1.08981i	0.165528	+	0.103910i
$111$		0			0
$112$	11.7812	+	8.55951i	1.11321	+	0.808798i
$113$	3.92705	−	12.0862i	0.369426	−	1.13698i	−0.577737	−	0.816223i	$-0.696064\pi$
$113$	3.92705	−	12.0862i	0.369426	−	1.13698i	0.947163	−	0.320753i	$-0.103936\pi$
$114$		0			0
$115$	−1.69098	+	1.22857i	−0.157685	+	0.114565i
$116$	−2.23607	+	1.62460i	−0.207614	+	0.150840i
$117$		0			0
$118$	−2.66312	+	8.19624i	−0.245160	+	0.754525i
$119$	−1.50000	−	1.08981i	−0.137505	−	0.0999031i
$120$		0			0
$121$	4.78115	+	9.90659i	0.434650	+	0.900599i
$122$	−1.85410			−0.167863
$123$		0			0
$124$	−0.736068	+	2.26538i	−0.0661009	+	0.203438i
$125$	−1.16312	−	3.57971i	−0.104033	−	0.320179i
$126$		0			0
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	−0.878934	−	0.476944i	$-0.841745\pi$
$127$	−7.85410	+	5.70634i	−0.696939	+	0.506356i	0.181995	+	0.983299i	$0.441745\pi$
$128$	−4.20820	−	12.9515i	−0.371956	−	1.14476i
$129$		0			0
$130$	3.11803	+	2.26538i	0.273470	+	0.198687i
$131$	13.8541			1.21044			0.605219	−	0.796059i	$-0.293085\pi$
$131$	13.8541			1.21044			0.605219	+	0.796059i	$0.293085\pi$
$132$		0			0
$133$	−2.56231			−0.222180
$134$	13.8262	+	10.0453i	1.19441	+	0.867786i
$135$		0			0
$136$	0.427051	+	1.31433i	0.0366193	+	0.112703i
$137$	−1.19098	+	0.865300i	−0.101753	+	0.0739276i	−0.637498	−	0.770452i	$-0.720031\pi$
$137$	−1.19098	+	0.865300i	−0.101753	+	0.0739276i	0.535746	+	0.844379i	$0.320031\pi$
$138$		0			0
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	0.997999	−	0.0632239i	$-0.0201382\pi$
$139$	1.80902	+	5.56758i	0.153439	+	0.472236i	−0.844561	+	0.535460i	$0.820138\pi$
$140$	0.218847	−	0.673542i	0.0184960	−	0.0569247i
$141$		0			0
$142$	23.5623			1.97730
$143$	7.70820	+	19.1926i	0.644592	+	1.60497i
$144$		0			0
$145$	−1.38197	−	1.00406i	−0.114766	−	0.0833824i
$146$	−0.618034	+	1.90211i	−0.0511489	+	0.157420i
$147$		0			0
$148$	2.11803	−	1.53884i	0.174101	−	0.126492i
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.0333309	−	0.999444i	$-0.489388\pi$
$149$	12.1353	−	8.81678i	0.994159	−	0.722299i	0.960828	+	0.277146i	$0.0893885\pi$
$150$		0			0
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	−0.922755	−	0.385388i	$-0.874068\pi$
$151$	0.618034	−	1.90211i	0.0502949	−	0.154792i	0.973050	+	0.230596i	$0.0740676\pi$
$152$	1.54508	+	1.12257i	0.125323	+	0.0910524i
$153$		0			0
$154$	12.3541	−	10.3229i	0.995522	−	0.831840i
$155$	−1.47214			−0.118245
$156$		0			0
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$	−0.263932	−	0.812299i	−0.0209973	−	0.0646231i
$159$		0			0
$160$	−1.04508	+	0.759299i	−0.0826212	+	0.0600278i
$161$	5.07295	+	15.6129i	0.399804	+	1.23047i
$162$		0			0
$163$	12.3541	+	8.97578i	0.967648	+	0.703037i	0.954914	−	0.296882i	$-0.0959467\pi$
$163$	12.3541	+	8.97578i	0.967648	+	0.703037i	0.0127336	+	0.999919i	$0.495947\pi$
$164$	−3.67376			−0.286873
$165$		0			0
$166$	−20.5623			−1.59594
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.198190	−	0.980164i	$-0.563506\pi$
$167$	−15.3992	−	11.1882i	−1.19162	−	0.865766i	−0.993435	+	0.114398i	$0.963506\pi$
$168$		0			0
$169$	8.00000	+	24.6215i	0.615385	+	1.89396i
$170$	0.309017	−	0.224514i	0.0237005	−	0.0172194i
$171$		0			0
$172$	0.336881	+	1.03681i	0.0256869	+	0.0790563i
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	0.499293	+	0.866433i	$0.333593\pi$
$173$	−5.44427	+	16.7557i	−0.413920	+	1.27392i	−0.913213	+	0.407482i	$0.866407\pi$
$174$		0			0
$175$	−14.5623			−1.10081
$176$	−16.0623	+	1.08981i	−1.21074	+	0.0821478i
$177$		0			0
$178$	−12.3992	−	9.00854i	−0.929358	−	0.675218i
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	−0.973553	−	0.228460i	$-0.926631\pi$
$179$	−0.690983	+	2.12663i	−0.0516465	+	0.158952i	0.921907	+	0.387412i	$0.126631\pi$
$180$		0			0
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	−0.301077	−	0.953600i	$-0.597346\pi$
$181$	6.89919	−	5.01255i	0.512813	−	0.372580i	0.813889	+	0.581020i	$0.197346\pi$
$182$	24.4894	−	17.7926i	1.81527	−	1.31887i
$183$		0			0
$184$	3.78115	−	11.6372i	0.278750	−	0.857905i
$185$	1.30902	+	0.951057i	0.0962408	+	0.0699231i
$186$		0			0
$187$	2.04508	−	0.138757i	0.149551	−	0.0101469i
$188$	0.381966			0.0278577
$189$		0			0
$190$	0.163119	−	0.502029i	0.0118339	−	0.0364210i
$191$	−0.454915	−	1.40008i	−0.0329165	−	0.101307i	0.933248	−	0.359232i	$-0.116961\pi$
$191$	−0.454915	−	1.40008i	−0.0329165	−	0.101307i	−0.966165	+	0.257925i	$0.916961\pi$
$192$		0			0
$193$	−1.26393	+	0.918300i	−0.0909798	+	0.0661007i	−0.632345	−	0.774687i	$-0.717908\pi$
$193$	−1.26393	+	0.918300i	−0.0909798	+	0.0661007i	0.541365	+	0.840787i	$0.317908\pi$
$194$	−7.51722	−	23.1356i	−0.539705	−	1.66104i
$195$		0			0
$196$	−1.00000	−	0.726543i	−0.0714286	−	0.0518959i
$197$	−26.6180			−1.89646			−0.948228	−	0.317590i	$-0.897127\pi$
$197$	−26.6180			−1.89646			−0.948228	+	0.317590i	$0.897127\pi$
$198$		0			0
$199$	−3.29180			−0.233349			−0.116675	−	0.993170i	$-0.537223\pi$
$199$	−3.29180			−0.233349			−0.116675	+	0.993170i	$0.537223\pi$
$200$	8.78115	+	6.37988i	0.620921	+	0.451126i
$201$		0			0
$202$	−1.50000	−	4.61653i	−0.105540	−	0.324818i
$203$	−10.8541	+	7.88597i	−0.761809	+	0.553486i
$204$		0			0
$205$	−0.701626	−	2.15938i	−0.0490037	−	0.150818i
$206$	3.00000	−	9.23305i	0.209020	−	0.643297i
$207$		0			0
$208$	−30.2705			−2.09888
$209$	2.17376	−	1.81636i	0.150362	−	0.125640i
$210$		0			0
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	0.227895	−	0.973686i	$-0.426816\pi$
$211$	−9.11803	−	6.62464i	−0.627711	−	0.456059i	−0.855607	+	0.517627i	$0.826816\pi$
$212$	1.40983	−	4.33901i	0.0968275	−	0.298004i
$213$		0			0
$214$	−0.309017	+	0.224514i	−0.0211240	+	0.0153475i
$215$	−0.545085	+	0.396027i	−0.0371745	+	0.0270088i
$216$		0			0
$217$	−3.57295	+	10.9964i	−0.242548	+	0.746485i
$218$		0			0
$219$		0			0
$220$	0.291796	+	0.726543i	0.0196729	+	0.0489835i
$221$	3.85410			0.259255
$222$		0			0
$223$	−3.92705	+	12.0862i	−0.262975	+	0.809353i	0.729178	+	0.684324i	$0.239903\pi$
$223$	−3.92705	+	12.0862i	−0.262975	+	0.809353i	−0.992153	+	0.125029i	$0.960097\pi$
$224$	3.13525	+	9.64932i	0.209483	+	0.644722i
$225$		0			0
$226$	16.6353	−	12.0862i	1.10656	−	0.803963i
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	−0.998457	−	0.0555264i	$-0.982316\pi$
$227$	−3.36475	−	10.3556i	−0.223326	−	0.687327i	0.775131	−	0.631800i	$-0.217684\pi$
$228$		0			0
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	0.287467	−	0.957790i	$-0.407187\pi$
$229$	−8.09017	−	5.87785i	−0.534613	−	0.388419i	−0.822081	+	0.569371i	$0.807187\pi$
$230$	−3.38197			−0.223000
$231$		0			0
$232$	10.0000			0.656532
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	0.793419	−	0.608676i	$-0.208299\pi$
$233$	7.01722	+	5.09831i	0.459713	+	0.334001i	−0.333705	+	0.942677i	$0.608299\pi$
$234$		0			0
$235$	0.0729490	+	0.224514i	0.00475867	+	0.0146457i
$236$	−2.66312	+	1.93487i	−0.173354	+	0.125949i
$237$		0			0
$238$	−0.927051	−	2.85317i	−0.0600918	−	0.184944i
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	−0.607220	−	0.794534i	$-0.707715\pi$
$239$	5.42705	−	16.7027i	0.351047	−	1.08041i	0.958266	−	0.285877i	$-0.0922848\pi$
$240$		0			0
$241$	17.1246			1.10309			0.551547	−	0.834144i	$-0.314038\pi$
$241$	17.1246			1.10309			0.551547	+	0.834144i	$0.314038\pi$
$242$	−3.16312	+	17.5150i	−0.203333	+	1.12591i
$243$		0			0
$244$	−0.572949	−	0.416272i	−0.0366793	−	0.0266491i
$245$	0.236068	−	0.726543i	0.0150818	−	0.0464171i
$246$		0			0
$247$	4.30902	−	3.13068i	0.274176	−	0.199201i
$248$	6.97214	−	5.06555i	0.442731	−	0.321663i
$249$		0			0
$250$	1.88197	−	5.79210i	0.119026	−	0.366324i
$251$	13.5902	+	9.87384i	0.857804	+	0.623231i	0.927287	−	0.374352i	$-0.122135\pi$
$251$	13.5902	+	9.87384i	0.857804	+	0.623231i	−0.0694827	+	0.997583i	$0.522135\pi$
$252$		0			0
$253$	−15.3713	−	9.64932i	−0.966387	−	0.606648i
$254$	−15.7082			−0.985620
$255$		0			0
$256$	4.19098	−	12.8985i	0.261936	−	0.806157i
$257$	8.44427	+	25.9888i	0.526739	+	1.62114i	0.760851	+	0.648927i	$0.224782\pi$
$257$	8.44427	+	25.9888i	0.526739	+	1.62114i	−0.234112	+	0.972210i	$0.575218\pi$
$258$		0			0
$259$	10.2812	−	7.46969i	0.638840	−	0.464144i
$260$	0.454915	+	1.40008i	0.0282126	+	0.0868296i
$261$		0			0
$262$	18.1353	+	13.1760i	1.12040	+	0.814018i
$263$	0.673762			0.0415459			0.0207730	−	0.999784i	$-0.493387\pi$
$263$	0.673762			0.0415459			0.0207730	+	0.999784i	$0.493387\pi$
$264$		0			0
$265$	2.81966			0.173210
$266$	−3.35410	−	2.43690i	−0.205653	−	0.149416i
$267$		0			0
$268$	2.01722	+	6.20837i	0.123221	+	0.379236i
$269$	19.7984	−	14.3844i	1.20713	−	0.877030i	0.212161	−	0.977235i	$-0.431950\pi$
$269$	19.7984	−	14.3844i	1.20713	−	0.877030i	0.994967	+	0.100205i	$0.0319498\pi$
$270$		0			0
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	0.992502	−	0.122229i	$-0.0390043\pi$
$271$	1.93769	+	5.96361i	0.117707	+	0.362263i	−0.874795	+	0.484493i	$0.839004\pi$
$272$	−0.927051	+	2.85317i	−0.0562107	+	0.172999i
$273$		0			0
$274$	−2.38197			−0.143900
$275$	12.3541	−	10.3229i	0.744980	−	0.622492i
$276$		0			0
$277$	−8.44427	−	6.13512i	−0.507367	−	0.368624i	0.304457	−	0.952526i	$-0.401525\pi$
$277$	−8.44427	−	6.13512i	−0.507367	−	0.368624i	−0.811824	+	0.583902i	$0.801525\pi$
$278$	−2.92705	+	9.00854i	−0.175553	+	0.540296i
$279$		0			0
$280$	−2.07295	+	1.50609i	−0.123882	+	0.0900058i
$281$	−4.23607	+	3.07768i	−0.252703	+	0.183599i	−0.706924	−	0.707290i	$-0.749918\pi$
$281$	−4.23607	+	3.07768i	−0.252703	+	0.183599i	0.454221	+	0.890889i	$0.349918\pi$
$282$		0			0
$283$	−6.85410	+	21.0948i	−0.407434	+	1.25395i	0.511412	+	0.859336i	$0.329123\pi$
$283$	−6.85410	+	21.0948i	−0.407434	+	1.25395i	−0.918846	+	0.394617i	$0.870877\pi$
$284$	7.28115	+	5.29007i	0.432057	+	0.313908i
$285$		0			0
$286$	−8.16312	+	32.4544i	−0.482695	+	1.91907i
$287$	−17.8328			−1.05264
$288$		0			0
$289$	−5.13525	+	15.8047i	−0.302074	+	0.929688i
$290$	−0.854102	−	2.62866i	−0.0501546	−	0.154360i
$291$		0			0
$292$	−0.618034	+	0.449028i	−0.0361677	+	0.0262774i
$293$	−5.54508	−	17.0660i	−0.323947	−	0.997007i	−0.971914	−	0.235338i	$-0.924380\pi$
$293$	−5.54508	−	17.0660i	−0.323947	−	0.997007i	0.647966	−	0.761669i	$-0.275620\pi$
$294$		0			0
$295$	−1.64590	−	1.19581i	−0.0958279	−	0.0696230i
$296$	−9.47214			−0.550557
$297$		0			0
$298$	24.2705			1.40595
$299$	−27.6074	−	20.0579i	−1.59658	−	1.15998i
$300$		0			0
$301$	1.63525	+	5.03280i	0.0942545	+	0.290086i
$302$	2.61803	−	1.90211i	0.150651	−	0.109454i
$303$		0			0
$304$	1.28115	+	3.94298i	0.0734792	+	0.226146i
$305$	0.135255	−	0.416272i	0.00774467	−	0.0238357i
$306$		0			0
$307$	−19.5623			−1.11648			−0.558240	−	0.829680i	$-0.688523\pi$
$307$	−19.5623			−1.11648			−0.558240	+	0.829680i	$0.688523\pi$
$308$	6.13525	−	0.416272i	0.349589	−	0.0237193i
$309$		0			0
$310$	−1.92705	−	1.40008i	−0.109449	−	0.0795195i
$311$	−3.54508	+	10.9106i	−0.201023	+	0.618686i	0.798830	+	0.601557i	$0.205453\pi$
$311$	−3.54508	+	10.9106i	−0.201023	+	0.618686i	−0.999853	+	0.0171293i	$0.994547\pi$
$312$		0			0
$313$	22.5172	−	16.3597i	1.27275	−	0.924706i	0.273440	−	0.961889i	$-0.411838\pi$
$313$	22.5172	−	16.3597i	1.27275	−	0.924706i	0.999308	+	0.0371831i	$0.0118385\pi$
$314$	12.7082	−	9.23305i	0.717165	−	0.521051i
$315$		0			0
$316$	0.100813	−	0.310271i	0.00567118	−	0.0174541i
$317$	20.5172	+	14.9066i	1.15236	+	0.837240i	0.988793	−	0.149292i	$-0.0476994\pi$
$317$	20.5172	+	14.9066i	1.15236	+	0.837240i	0.163569	+	0.986532i	$0.447699\pi$
$318$		0			0
$319$	3.61803	−	14.3844i	0.202571	−	0.805370i
$320$	1.61803			0.0904508
$321$		0			0
$322$	−8.20820	+	25.2623i	−0.457425	+	1.40781i
$323$	−0.163119	−	0.502029i	−0.00907618	−	0.0279336i
$324$		0			0
$325$	24.4894	−	17.7926i	1.35843	−	0.986954i
$326$	7.63525	+	23.4989i	0.422878	+	1.30148i
$327$		0			0
$328$	10.7533	+	7.81272i	0.593751	+	0.431385i
$329$	1.85410			0.102220
$330$		0			0
$331$	−22.5967			−1.24203			−0.621015	−	0.783799i	$-0.713279\pi$
$331$	−22.5967			−1.24203			−0.621015	+	0.783799i	$0.713279\pi$
$332$	−6.35410	−	4.61653i	−0.348727	−	0.253365i
$333$		0			0
$334$	−9.51722	−	29.2910i	−0.520759	−	1.60273i
$335$	−3.26393	+	2.37139i	−0.178328	+	0.129563i
$336$		0			0
$337$	−4.23607	−	13.0373i	−0.230753	−	0.710186i	−0.997656	−	0.0684228i	$-0.978203\pi$
$337$	−4.23607	−	13.0373i	−0.230753	−	0.710186i	0.766903	−	0.641763i	$-0.221797\pi$
$338$	−12.9443	+	39.8384i	−0.704076	+	2.16692i
$339$		0			0
$340$	0.145898			0.00791243
$341$	−4.76393	−	11.8617i	−0.257981	−	0.642347i
$342$		0			0
$343$	12.1353	+	8.81678i	0.655242	+	0.476061i
$344$	1.21885	−	3.75123i	0.0657158	−	0.202253i
$345$		0			0
$346$	−23.0623	+	16.7557i	−1.23984	+	0.900794i
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	−0.652160	−	0.758081i	$-0.726137\pi$
$347$	−2.47214	+	1.79611i	−0.132711	+	0.0964203i	0.519449	+	0.854501i	$0.326137\pi$
$348$		0			0
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	−0.313449	−	0.949605i	$-0.601485\pi$
$349$	9.30902	−	28.6502i	0.498300	−	1.53361i	0.811750	−	0.584006i	$-0.198515\pi$
$350$	−19.0623	−	13.8496i	−1.01892	−	0.740291i
$351$		0			0
$352$	−9.50000	−	5.96361i	−0.506352	−	0.317861i
$353$	1.52786			0.0813200			0.0406600	−	0.999173i	$-0.487054\pi$
$353$	1.52786			0.0813200			0.0406600	+	0.999173i	$0.487054\pi$
$354$		0			0
$355$	−1.71885	+	5.29007i	−0.0912269	+	0.280768i
$356$	−1.80902	−	5.56758i	−0.0958777	−	0.295081i
$357$		0			0
$358$	−2.92705	+	2.12663i	−0.154699	+	0.112396i
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	0.987538	+	0.157379i	$0.0503044\pi$
$359$	5.32624	+	16.3925i	0.281108	+	0.865162i	−0.706430	+	0.707783i	$0.749696\pi$
$360$		0			0
$361$	14.7812	+	10.7391i	0.777955	+	0.565218i
$362$	13.7984			0.725226
$363$		0			0
$364$	11.5623			0.606029
$365$	−0.381966	−	0.277515i	−0.0199930	−	0.0145258i
$366$		0			0
$367$	−4.50000	−	13.8496i	−0.234898	−	0.722942i	−0.997135	−	0.0756437i	$-0.975899\pi$
$367$	−4.50000	−	13.8496i	−0.234898	−	0.722942i	0.762237	−	0.647298i	$-0.224101\pi$
$368$	21.4894	−	15.6129i	1.12021	−	0.813880i
$369$		0			0
$370$	0.809017	+	2.48990i	0.0420588	+	0.129444i
$371$	6.84346	−	21.0620i	0.355295	−	1.09348i
$372$		0			0
$373$	22.4164			1.16068			0.580339	−	0.814375i	$-0.302920\pi$
$373$	22.4164			1.16068			0.580339	+	0.814375i	$0.302920\pi$
$374$	2.80902	+	1.76336i	0.145251	+	0.0911810i
$375$		0			0
$376$	−1.11803	−	0.812299i	−0.0576582	−	0.0418911i
$377$	8.61803	−	26.5236i	0.443851	−	1.36603i
$378$		0			0
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.992271	−	0.124089i	$-0.960399\pi$
$379$	−22.9894	+	16.7027i	−1.18088	+	0.857962i	−0.188613	+	0.982052i	$0.560399\pi$
$380$	0.163119	−	0.118513i	0.00836783	−	0.00607958i
$381$		0			0
$382$	0.736068	−	2.26538i	0.0376605	−	0.115907i
$383$	−7.19098	−	5.22455i	−0.367442	−	0.266962i	0.388707	−	0.921361i	$-0.372922\pi$
$383$	−7.19098	−	5.22455i	−0.367442	−	0.266962i	−0.756149	+	0.654399i	$0.772922\pi$
$384$		0			0
$385$	1.41641	+	3.52671i	0.0721868	+	0.179738i
$386$	−2.52786			−0.128665
$387$		0			0
$388$	2.87132	−	8.83702i	0.145769	−	0.448632i
$389$	2.86475	+	8.81678i	0.145248	+	0.447028i	0.997043	−	0.0768476i	$-0.0244855\pi$
$389$	2.86475	+	8.81678i	0.145248	+	0.447028i	−0.851795	+	0.523876i	$0.824485\pi$
$390$		0			0
$391$	−2.73607	+	1.98787i	−0.138369	+	0.100531i
$392$	1.38197	+	4.25325i	0.0697998	+	0.214822i
$393$		0			0
$394$	−34.8435	−	25.3153i	−1.75539	−	1.27536i
$395$	0.201626			0.0101449
$396$		0			0
$397$	−25.2918			−1.26936			−0.634679	−	0.772776i	$-0.718868\pi$
$397$	−25.2918			−1.26936			−0.634679	+	0.772776i	$0.718868\pi$
$398$	−4.30902	−	3.13068i	−0.215992	−	0.156927i
$399$		0			0
$400$	7.28115	+	22.4091i	0.364058	+	1.12045i
$401$	−12.0623	+	8.76378i	−0.602363	+	0.437642i	−0.846717	−	0.532044i	$-0.821424\pi$
$401$	−12.0623	+	8.76378i	−0.602363	+	0.437642i	0.244354	+	0.969686i	$0.421424\pi$
$402$		0			0
$403$	−7.42705	−	22.8581i	−0.369968	−	1.13864i
$404$	0.572949	−	1.76336i	0.0285053	−	0.0877302i
$405$		0			0
$406$	−21.7082			−1.07736
$407$	−3.42705	+	13.6251i	−0.169873	+	0.675369i
$408$		0			0
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.989507	−	0.144486i	$-0.0461529\pi$
$409$	23.4164	+	17.0130i	1.15787	+	0.841240i	0.168360	+	0.985726i	$0.446153\pi$
$410$	1.13525	−	3.49396i	0.0560662	−	0.172554i
$411$		0			0
$412$	3.00000	−	2.17963i	0.147799	−	0.107383i
$413$	−12.9271	+	9.39205i	−0.636099	+	0.462153i
$414$		0			0
$415$	1.50000	−	4.61653i	0.0736321	−	0.226616i
$416$	−17.0623	−	12.3965i	−0.836548	−	0.607788i
$417$		0			0
$418$	4.57295	−	0.310271i	0.223670	−	0.0151758i
$419$	21.5066			1.05067			0.525333	−	0.850897i	$-0.323941\pi$
$419$	21.5066			1.05067			0.525333	+	0.850897i	$0.323941\pi$
$420$		0			0
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	−0.975205	−	0.221304i	$-0.928969\pi$
$421$	−1.15248	+	3.54696i	−0.0561682	+	0.172868i	0.919037	+	0.394172i	$0.128969\pi$
$422$	−5.63525	−	17.3435i	−0.274320	−	0.844270i
$423$		0			0
$424$	−13.3541	+	9.70232i	−0.648533	+	0.471186i
$425$	−0.927051	−	2.85317i	−0.0449686	−	0.138399i
$426$		0			0
$427$	−2.78115	−	2.02063i	−0.134589	−	0.0977849i
$428$	−0.145898			−0.00705225
$429$		0			0
$430$	−1.09017			−0.0525727
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	0.558306	−	0.829635i	$-0.311451\pi$
$431$	−1.20820	−	0.877812i	−0.0581971	−	0.0422827i	−0.616503	+	0.787352i	$0.711451\pi$
$432$		0			0
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	0.896569	−	0.442903i	$-0.146051\pi$
$433$	−1.85410	−	5.70634i	−0.0891025	−	0.274229i	−0.985672	+	0.168674i	$0.946051\pi$
$434$	−15.1353	+	10.9964i	−0.726515	+	0.527844i
$435$		0			0
$436$		0			0
$437$	−1.44427	+	4.44501i	−0.0690889	+	0.212634i
$438$		0			0
$439$	16.7082			0.797439			0.398720	−	0.917073i	$-0.369455\pi$
$439$	16.7082			0.797439			0.398720	+	0.917073i	$0.369455\pi$
$440$	0.690983	−	2.74717i	0.0329413	−	0.130966i
$441$		0			0
$442$	5.04508	+	3.66547i	0.239970	+	0.174349i
$443$	0.270510	−	0.832544i	0.0128523	−	0.0395553i	−0.944425	−	0.328728i	$-0.893380\pi$
$443$	0.270510	−	0.832544i	0.0128523	−	0.0395553i	0.957277	+	0.289172i	$0.0933801\pi$
$444$		0			0
$445$	2.92705	−	2.12663i	0.138756	−	0.100812i
$446$	−16.6353	+	12.0862i	−0.787702	+	0.572299i
$447$		0			0
$448$	3.92705	−	12.0862i	0.185536	−	0.571020i
$449$	−12.5623	−	9.12705i	−0.592852	−	0.430732i	0.250483	−	0.968121i	$-0.419411\pi$
$449$	−12.5623	−	9.12705i	−0.592852	−	0.430732i	−0.843334	+	0.537389i	$0.819411\pi$
$450$		0			0
$451$	15.1287	−	12.6412i	0.712382	−	0.595253i
$452$	7.85410			0.369426
$453$		0			0
$454$	5.44427	−	16.7557i	0.255512	−	0.786386i
$455$	2.20820	+	6.79615i	0.103522	+	0.318609i
$456$		0			0
$457$	−26.5344	+	19.2784i	−1.24123	+	0.901806i	−0.997680	−	0.0680830i	$-0.978312\pi$
$457$	−26.5344	+	19.2784i	−1.24123	+	0.901806i	−0.243549	+	0.969889i	$0.578312\pi$
$458$	−5.00000	−	15.3884i	−0.233635	−	0.719054i
$459$		0			0
$460$	−1.04508	−	0.759299i	−0.0487273	−	0.0354025i
$461$	9.90983			0.461547			0.230773	−	0.973008i	$-0.425874\pi$
$461$	9.90983			0.461547			0.230773	+	0.973008i	$0.425874\pi$
$462$		0			0
$463$	8.79837			0.408895			0.204448	−	0.978878i	$-0.434460\pi$
$463$	8.79837			0.408895			0.204448	+	0.978878i	$0.434460\pi$
$464$	17.5623	+	12.7598i	0.815310	+	0.592357i
$465$		0			0
$466$	4.33688	+	13.3475i	0.200902	+	0.618313i
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	−0.821461	−	0.570264i	$-0.806841\pi$
$467$	−11.5172	+	8.36775i	−0.532953	+	0.387213i	0.288508	+	0.957478i	$0.406841\pi$
$468$		0			0
$469$	9.79180	+	30.1360i	0.452143	+	1.39155i
$470$	−0.118034	+	0.363271i	−0.00544450	+	0.0167565i
$471$		0			0
$472$	11.9098			0.548194
$473$	−4.95492	−	3.11044i	−0.227827	−	0.143018i
$474$		0			0
$475$	−3.35410	−	2.43690i	−0.153897	−	0.111813i
$476$	0.354102	−	1.08981i	0.0162302	−	0.0499515i
$477$		0			0
$478$	22.9894	−	16.7027i	1.05151	−	0.763966i
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	−0.854689	−	0.519140i	$-0.826252\pi$
$479$	−13.6803	+	9.93935i	−0.625071	+	0.454140i	0.229618	+	0.973281i	$0.426252\pi$
$480$		0			0
$481$	−8.16312	+	25.1235i	−0.372206	+	1.14553i
$482$	22.4164	+	16.2865i	1.02104	+	0.741829i
$483$		0			0
$484$	−4.90983	+	4.70228i	−0.223174	+	0.213740i
$485$	5.74265			0.260760
$486$		0			0
$487$	12.1074	−	37.2627i	0.548638	−	1.68853i	−0.163540	−	0.986537i	$-0.552291\pi$
$487$	12.1074	−	37.2627i	0.548638	−	1.68853i	0.712179	−	0.701998i	$-0.247709\pi$
$488$	0.791796	+	2.43690i	0.0358429	+	0.110313i
$489$		0			0
$490$	1.00000	−	0.726543i	0.0451754	−	0.0328218i
$491$	8.10081	+	24.9317i	0.365585	+	1.12515i	0.949614	+	0.313421i	$0.101475\pi$
$491$	8.10081	+	24.9317i	0.365585	+	1.12515i	−0.584030	+	0.811732i	$0.698525\pi$
$492$		0			0
$493$	−2.23607	−	1.62460i	−0.100707	−	0.0731682i
$494$	8.61803			0.387744
$495$		0			0
$496$	18.7082			0.840023
$497$	35.3435	+	25.6785i	1.58537	+	1.15184i
$498$		0			0
$499$	0.791796	+	2.43690i	0.0354457	+	0.109091i	0.967214	−	0.253963i	$-0.0817342\pi$
$499$	0.791796	+	2.43690i	0.0354457	+	0.109091i	−0.931768	+	0.363054i	$0.881734\pi$
$500$	1.88197	−	1.36733i	0.0841641	−	0.0611488i
$501$		0			0
$502$	8.39919	+	25.8500i	0.374874	+	1.15374i
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	−0.498574	−	0.866847i	$-0.666143\pi$
$503$	9.29180	−	28.5972i	0.414301	−	1.27509i	0.912875	−	0.408239i	$-0.133857\pi$
$504$		0			0
$505$	1.14590			0.0509918
$506$	−10.9443	−	27.2501i	−0.486532	−	1.21142i
$507$		0			0
$508$	−4.85410	−	3.52671i	−0.215366	−	0.156473i
$509$	−6.60739	+	20.3355i	−0.292867	+	0.901353i	0.691062	+	0.722796i	$0.257143\pi$
$509$	−6.60739	+	20.3355i	−0.292867	+	0.901353i	−0.983929	+	0.178558i	$0.942857\pi$
$510$		0			0
$511$	−3.00000	+	2.17963i	−0.132712	+	0.0964210i
$512$	−4.28115	+	3.11044i	−0.189202	+	0.137463i
$513$		0			0
$514$	−13.6631	+	42.0508i	−0.602654	+	1.85478i
$515$	1.85410	+	1.34708i	0.0817015	+	0.0593596i
$516$		0			0
$517$	−1.57295	+	1.31433i	−0.0691782	+	0.0578041i
$518$	20.5623			0.903456
$519$		0			0
$520$	1.64590	−	5.06555i	0.0721774	−	0.222139i
$521$	−12.0000	−	36.9322i	−0.525730	−	1.61803i	−0.762869	−	0.646553i	$-0.776210\pi$
$521$	−12.0000	−	36.9322i	−0.525730	−	1.61803i	0.237139	−	0.971476i	$-0.423790\pi$
$522$		0			0
$523$	−28.2984	+	20.5600i	−1.23740	+	0.899025i	−0.997422	−	0.0717533i	$-0.977141\pi$
$523$	−28.2984	+	20.5600i	−1.23740	+	0.899025i	−0.239979	+	0.970778i	$0.577141\pi$
$524$	2.64590	+	8.14324i	0.115587	+	0.355739i
$525$		0			0
$526$	0.881966	+	0.640786i	0.0384555	+	0.0279396i
$527$	−2.38197			−0.103760
$528$		0			0
$529$	6.94427			0.301925
$530$	3.69098	+	2.68166i	0.160326	+	0.116484i
$531$		0			0
$532$	−0.489357	−	1.50609i	−0.0212163	−	0.0652971i
$533$	29.9894	−	21.7885i	1.29898	−	0.943767i
$534$		0			0
$535$	−0.0278640	−	0.0857567i	−0.00120467	−	0.00370759i
$536$	7.29837	−	22.4621i	0.315242	−	0.970214i
$537$		0			0
$538$	39.5967			1.70714
$539$	6.61803	−	0.449028i	0.285059	−	0.0193410i
$540$		0			0
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	0.597521	−	0.801853i	$-0.296152\pi$
$541$	0.454915	+	0.330515i	0.0195583	+	0.0142100i	−0.577963	+	0.816063i	$0.696152\pi$
$542$	−3.13525	+	9.64932i	−0.134671	+	0.414474i
$543$		0			0
$544$	−1.69098	+	1.22857i	−0.0725003	+	0.0526745i
$545$		0			0
$546$		0			0
$547$	5.98936	−	18.4333i	0.256086	−	0.788153i	−0.737527	−	0.675317i	$-0.764007\pi$
$547$	5.98936	−	18.4333i	0.256086	−	0.788153i	0.993614	−	0.112836i	$-0.0359933\pi$
$548$	−0.736068	−	0.534785i	−0.0314433	−	0.0228449i
$549$		0			0
$550$	25.9894	−	1.76336i	1.10819	−	0.0751897i
$551$	−3.81966			−0.162723
$552$		0			0
$553$	0.489357	−	1.50609i	0.0208096	−	0.0640453i
$554$	−5.21885	−	16.0620i	−0.221728	−	0.682407i
$555$		0			0
$556$	−2.92705	+	2.12663i	−0.124135	+	0.0901891i
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	−0.963373	−	0.268164i	$-0.913583\pi$
$557$	−8.06231	−	24.8132i	−0.341611	−	1.05137i	0.621762	−	0.783206i	$-0.286417\pi$
$558$		0			0
$559$	−8.89919	−	6.46564i	−0.376396	−	0.273467i
$560$	−5.56231			−0.235050
$561$		0			0
$562$	−8.47214			−0.357375
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	0.942723	−	0.333575i	$-0.108255\pi$
$563$	21.7533	+	15.8047i	0.916792	+	0.666088i	−0.0259316	+	0.999664i	$0.508255\pi$
$564$		0			0
$565$	1.50000	+	4.61653i	0.0631055	+	0.194219i
$566$	−29.0344	+	21.0948i	−1.22041	+	0.886679i
$567$		0			0
$568$	−10.0623	−	30.9686i	−0.422205	−	1.29941i
$569$	−10.5279	+	32.4014i	−0.441351	+	1.35834i	0.445085	+	0.895488i	$0.353173\pi$
$569$	−10.5279	+	32.4014i	−0.441351	+	1.35834i	−0.886436	+	0.462851i	$0.846827\pi$
$570$		0			0
$571$	−25.6869			−1.07496			−0.537482	−	0.843275i	$-0.680624\pi$
$571$	−25.6869			−1.07496			−0.537482	+	0.843275i	$0.680624\pi$
$572$	−9.80902	+	8.19624i	−0.410136	+	0.342702i
$573$		0			0
$574$	−23.3435	−	16.9600i	−0.974337	−	0.707897i
$575$	−8.20820	+	25.2623i	−0.342306	+	1.05351i
$576$		0			0
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	−0.814016	−	0.580842i	$-0.802723\pi$
$577$	−12.3262	+	8.95554i	−0.513148	+	0.372824i	0.300868	+	0.953666i	$0.402723\pi$
$578$	−21.7533	+	15.8047i	−0.904818	+	0.657388i
$579$		0			0
$580$	0.326238	−	1.00406i	0.0135463	−	0.0416912i
$581$	−30.8435	−	22.4091i	−1.27960	−	0.929685i
$582$		0			0
$583$	9.12461	+	22.7194i	0.377903	+	0.940940i
$584$	2.76393			0.114372
$585$		0			0
$586$	8.97214	−	27.6134i	0.370636	−	1.14070i
$587$	−7.51064	−	23.1154i	−0.309997	−	0.954074i	−0.977765	−	0.209704i	$-0.932750\pi$
$587$	−7.51064	−	23.1154i	−0.309997	−	0.954074i	0.667767	−	0.744370i	$-0.267250\pi$
$588$		0			0
$589$	−2.66312	+	1.93487i	−0.109732	+	0.0797249i
$590$	−1.01722	−	3.13068i	−0.0418783	−	0.128888i
$591$		0			0
$592$	−16.6353	−	12.0862i	−0.683705	−	0.496741i
$593$	29.2148			1.19971			0.599854	−	0.800110i	$-0.295225\pi$
$593$	29.2148			1.19971			0.599854	+	0.800110i	$0.295225\pi$
$594$		0			0
$595$	0.708204			0.0290335
$596$	7.50000	+	5.44907i	0.307212	+	0.223203i
$597$		0			0
$598$	−17.0623	−	52.5124i	−0.697730	−	2.14739i
$599$	−17.5623	+	12.7598i	−0.717576	+	0.521350i	−0.885609	−	0.464432i	$-0.846259\pi$
$599$	−17.5623	+	12.7598i	−0.717576	+	0.521350i	0.168033	+	0.985781i	$0.446259\pi$
$600$		0			0
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	−0.994775	−	0.102093i	$-0.967446\pi$
$601$	−6.12868	−	18.8621i	−0.249994	−	0.769402i	0.744781	−	0.667309i	$-0.232554\pi$
$602$	−2.64590	+	8.14324i	−0.107839	+	0.331894i
$603$		0			0
$604$	1.23607			0.0502949
$605$	−3.70163	−	1.98787i	−0.150493	−	0.0808184i
$606$		0			0
$607$	1.88197	+	1.36733i	0.0763866	+	0.0554981i	0.625323	−	0.780366i	$-0.284967\pi$
$607$	1.88197	+	1.36733i	0.0763866	+	0.0554981i	−0.548937	+	0.835864i	$0.684967\pi$
$608$	−0.892609	+	2.74717i	−0.0362001	+	0.111412i
$609$		0			0
$610$	0.572949	−	0.416272i	0.0231980	−	0.0168544i
$611$	−3.11803	+	2.26538i	−0.126142	+	0.0916476i
$612$		0			0
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	−0.927990	−	0.372604i	$-0.878465\pi$
$613$	1.03444	−	3.18368i	0.0417807	−	0.128588i	0.969771	+	0.244016i	$0.0784650\pi$
$614$	−25.6074	−	18.6049i	−1.03343	−	0.750831i
$615$		0			0
$616$	−18.8435	−	11.8290i	−0.759225	−	0.476602i
$617$	−46.4164			−1.86865			−0.934327	−	0.356417i	$-0.883998\pi$
$617$	−46.4164			−1.86865			−0.934327	+	0.356417i	$0.883998\pi$
$618$		0			0
$619$	−9.63525	+	29.6543i	−0.387274	+	1.19191i	0.547544	+	0.836777i	$0.315563\pi$
$619$	−9.63525	+	29.6543i	−0.387274	+	1.19191i	−0.934817	+	0.355129i	$0.884437\pi$
$620$	−0.281153	−	0.865300i	−0.0112914	−	0.0347513i
$621$		0			0
$622$	−15.0172	+	10.9106i	−0.602136	+	0.437477i
$623$	−8.78115	−	27.0256i	−0.351809	−	1.08276i
$624$		0			0
$625$	−18.4721	−	13.4208i	−0.738885	−	0.536832i
$626$	45.0344			1.79994
$627$		0			0
$628$	6.00000			0.239426
$629$	2.11803	+	1.53884i	0.0844515	+	0.0613576i
$630$		0			0
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	0.998319	−	0.0579577i	$-0.0184589\pi$
$631$	3.93363	+	12.1065i	0.156595	+	0.481951i	−0.841724	+	0.539908i	$0.818459\pi$
$632$	−0.954915	+	0.693786i	−0.0379845	+	0.0275973i
$633$		0			0
$634$	12.6803	+	39.0261i	0.503601	+	1.54992i
$635$	1.14590	−	3.52671i	0.0454736	−	0.139953i
$636$		0			0
$637$	12.4721			0.494164
$638$	18.4164	−	15.3884i	0.729113	−	0.609233i
$639$		0			0
$640$	4.20820	+	3.05744i	0.166344	+	0.120856i
$641$	2.08359	−	6.41264i	0.0822969	−	0.253284i	−0.901439	−	0.432907i	$-0.857488\pi$
$641$	2.08359	−	6.41264i	0.0822969	−	0.253284i	0.983736	+	0.179623i	$0.0574878\pi$
$642$		0			0
$643$	14.9164	−	10.8374i	0.588246	−	0.427386i	−0.253442	−	0.967351i	$-0.581563\pi$
$643$	14.9164	−	10.8374i	0.588246	−	0.427386i	0.841687	+	0.539965i	$0.181563\pi$
$644$	−8.20820	+	5.96361i	−0.323449	+	0.234999i
$645$		0			0
$646$	0.263932	−	0.812299i	0.0103843	−	0.0319595i
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	0.637535	−	0.770421i	$-0.279954\pi$
$647$	2.59017	+	1.88187i	0.101830	+	0.0739839i	−0.535705	+	0.844405i	$0.679954\pi$
$648$		0			0
$649$	4.30902	−	17.1315i	0.169144	−	0.672471i
$650$	48.9787			1.92110
$651$		0			0
$652$	−2.91641	+	8.97578i	−0.114215	+	0.351519i
$653$	−6.78773	−	20.8905i	−0.265624	−	0.817508i	−0.991549	−	0.129734i	$-0.958588\pi$
$653$	−6.78773	−	20.8905i	−0.265624	−	0.817508i	0.725924	−	0.687774i	$-0.241412\pi$
$654$		0			0
$655$	−4.28115	+	3.11044i	−0.167278	+	0.121535i
$656$	8.91641	+	27.4419i	0.348127	+	1.07143i
$657$		0			0
$658$	2.42705	+	1.76336i	0.0946163	+	0.0687428i
$659$	−20.6525			−0.804506			−0.402253	−	0.915528i	$-0.631773\pi$
$659$	−20.6525			−0.804506			−0.402253	+	0.915528i	$0.631773\pi$
$660$		0			0
$661$	−21.0902			−0.820313			−0.410156	−	0.912015i	$-0.634526\pi$
$661$	−21.0902			−0.820313			−0.410156	+	0.912015i	$0.634526\pi$
$662$	−29.5795	−	21.4908i	−1.14964	−	0.835263i
$663$		0			0
$664$	8.78115	+	27.0256i	0.340775	+	1.04880i
$665$	0.791796	−	0.575274i	0.0307045	−	0.0223082i
$666$		0			0
$667$	7.56231	+	23.2744i	0.292814	+	0.901188i
$668$	3.63525	−	11.1882i	0.140652	−	0.432883i
$669$		0			0
$670$	−6.52786			−0.252193
$671$	3.79180	−	0.257270i	0.146381	−	0.00993180i
$672$		0			0
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	0.789430	−	0.613841i	$-0.210376\pi$
$673$	11.6631	+	8.47375i	0.449580	+	0.326639i	−0.339850	+	0.940480i	$0.610376\pi$
$674$	6.85410	−	21.0948i	0.264010	−	0.812540i
$675$		0			0
$676$	−12.9443	+	9.40456i	−0.497857	+	0.361714i
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	−0.180790	−	0.983522i	$-0.557866\pi$
$677$	18.1803	−	13.2088i	0.698727	−	0.507655i	0.879517	+	0.475867i	$0.157866\pi$
$678$		0			0
$679$	13.9377	−	42.8958i	0.534880	−	1.64619i
$680$	−0.427051	−	0.310271i	−0.0163767	−	0.0118983i
$681$		0			0
$682$	5.04508	−	20.0579i	0.193186	−	0.768058i
$683$	38.8885			1.48803			0.744014	−	0.668164i	$-0.232919\pi$
$683$	38.8885			1.48803			0.744014	+	0.668164i	$0.232919\pi$
$684$		0			0
$685$	0.173762	−	0.534785i	0.00663911	−	0.0204331i
$686$	7.50000	+	23.0826i	0.286351	+	0.881299i
$687$		0			0
$688$	6.92705	−	5.03280i	0.264091	−	0.191874i
$689$	14.2254	+	43.7814i	0.541946	+	1.66794i
$690$		0			0
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.996271	−	0.0862806i	$-0.0274981\pi$
$691$	32.1246	+	23.3399i	1.22208	+	0.887892i	0.225807	+	0.974172i	$0.427498\pi$
$692$	−10.8885			−0.413920
$693$		0			0
$694$	−4.94427			−0.187682
$695$	−1.80902	−	1.31433i	−0.0686199	−	0.0498553i
$696$		0			0
$697$	−1.13525	−	3.49396i	−0.0430008	−	0.132343i
$698$	39.4336	−	28.6502i	1.49258	−	1.08443i
$699$		0			0
$700$	−2.78115	−	8.55951i	−0.105118	−	0.323519i
$701$	−15.3541	+	47.2551i	−0.579916	+	1.78480i	0.0388752	+	0.999244i	$0.487623\pi$
$701$	−15.3541	+	47.2551i	−0.579916	+	1.78480i	−0.618792	+	0.785555i	$0.712377\pi$
$702$		0			0
$703$	3.61803			0.136457
$704$	5.23607	+	13.0373i	0.197342	+	0.491361i
$705$		0			0
$706$	2.00000	+	1.45309i	0.0752710	+	0.0546876i
$707$	2.78115	−	8.55951i	0.104596	−	0.321913i
$708$		0			0
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	−0.678773	−	0.734348i	$-0.737488\pi$
$709$	−5.06231	+	3.67798i	−0.190119	+	0.138129i	0.488654	+	0.872478i	$0.337488\pi$
$710$	−7.28115	+	5.29007i	−0.273257	+	0.198533i
$711$		0			0
$712$	−6.54508	+	20.1437i	−0.245287	+	0.754917i
$713$	17.0623	+	12.3965i	0.638988	+	0.464252i
$714$		0			0
$715$	−6.69098	−	4.20025i	−0.250229	−	0.157081i
$716$	−1.38197			−0.0516465
$717$		0			0
$718$	−8.61803	+	26.5236i	−0.321622	+	0.989851i
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	0.970308	+	0.241873i	$0.0777618\pi$
$719$	8.78115	+	27.0256i	0.327482	+	1.00789i	−0.642826	+	0.766012i	$0.722238\pi$
$720$		0			0
$721$	14.5623	−	10.5801i	0.542329	−	0.394025i
$722$	9.13525	+	28.1154i	0.339979	+	1.04635i
$723$		0			0
$724$	4.26393	+	3.09793i	0.158468	+	0.115134i
$725$	−21.7082			−0.806222
$726$		0			0
$727$	32.1459			1.19223			0.596113	−	0.802901i	$-0.296711\pi$
$727$	32.1459			1.19223			0.596113	+	0.802901i	$0.296711\pi$
$728$	−33.8435	−	24.5887i	−1.25432	−	0.911318i
$729$		0			0
$730$	−0.236068	−	0.726543i	−0.00873727	−	0.0268905i
$731$	−0.881966	+	0.640786i	−0.0326207	+	0.0237003i
$732$		0			0
$733$	−7.50658	−	23.1029i	−0.277262	−	0.853324i	−0.988612	−	0.150486i	$-0.951916\pi$
$733$	−7.50658	−	23.1029i	−0.277262	−	0.853324i	0.711350	−	0.702838i	$-0.248084\pi$
$734$	7.28115	−	22.4091i	0.268752	−	0.827134i
$735$		0			0
$736$	18.5066			0.682162
$737$	−29.6697	−	18.6251i	−1.09290	−	0.686064i
$738$		0			0
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	0.893963	−	0.448142i	$-0.147914\pi$
$739$	20.2254	+	14.6946i	0.744004	+	0.540551i	−0.149958	+	0.988692i	$0.547914\pi$
$740$	−0.309017	+	0.951057i	−0.0113597	+	0.0349615i
$741$		0			0
$742$	28.9894	−	21.0620i	1.06423	−	0.773210i
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	−0.381059	−	0.924551i	$-0.624441\pi$
$743$	10.3713	−	7.53521i	0.380487	−	0.276440i	0.761546	+	0.648111i	$0.224441\pi$
$744$		0			0
$745$	−1.77051	+	5.44907i	−0.0648665	+	0.199638i
$746$	29.3435	+	21.3193i	1.07434	+	0.780554i
$747$		0			0
$748$	0.472136	+	1.17557i	0.0172630	+	0.0429831i
$749$	−0.708204			−0.0258772
$750$		0			0
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.0510571	+	0.998696i	$0.516259\pi$
$751$	−16.3541	+	50.3328i	−0.596770	+	1.83667i	−0.545713	+	0.837972i	$0.683741\pi$
$752$	−0.927051	−	2.85317i	−0.0338061	−	0.104044i
$753$		0			0
$754$	36.5066	−	26.5236i	1.32949	−	0.965932i
$755$	0.236068	+	0.726543i	0.00859139	+	0.0264416i
$756$		0			0
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	0.796985	−	0.603999i	$-0.206427\pi$
$757$	12.8992	+	9.37181i	0.468829	+	0.340624i	−0.328156	+	0.944624i	$0.606427\pi$
$758$	−45.9787			−1.67002
$759$		0			0
$760$	−0.729490			−0.0264614
$761$	3.95492	+	2.87341i	0.143366	+	0.104161i	0.657156	−	0.753754i	$-0.271759\pi$
$761$	3.95492	+	2.87341i	0.143366	+	0.104161i	−0.513791	+	0.857916i	$0.671759\pi$
$762$		0			0
$763$		0			0
$764$	0.736068	−	0.534785i	0.0266300	−	0.0193478i
$765$		0			0
$766$	−4.44427	−	13.6781i	−0.160578	−	0.494208i
$767$	10.2639	−	31.5891i	0.370609	−	1.14062i
$768$		0			0
$769$	−47.6869			−1.71963			−0.859817	−	0.510602i	$-0.829423\pi$
$769$	−47.6869			−1.71963			−0.859817	+	0.510602i	$0.829423\pi$
$770$	−1.50000	+	5.96361i	−0.0540562	+	0.214914i
$771$		0			0
$772$	−0.781153	−	0.567541i	−0.0281143	−	0.0204262i
$773$	−15.2188	+	46.8388i	−0.547384	+	1.68467i	0.167870	+	0.985809i	$0.446311\pi$
$773$	−15.2188	+	46.8388i	−0.547384	+	1.68467i	−0.715253	+	0.698865i	$0.753689\pi$
$774$		0			0
$775$	−15.1353	+	10.9964i	−0.543674	+	0.395003i
$776$	−27.1976	+	19.7602i	−0.976336	+	0.709349i
$777$		0			0
$778$	−4.63525	+	14.2658i	−0.166182	+	0.511455i
$779$	−4.10739	−	2.98419i	−0.147163	−	0.106920i
$780$		0			0
$781$	−48.1869	+	3.26944i	−1.72426	+	0.116990i
$782$	−5.47214			−0.195683
$783$		0			0
$784$	−3.00000	+	9.23305i	−0.107143	+	0.329752i
$785$	1.14590	+	3.52671i	0.0408989	+	0.125874i
$786$		0			0
$787$	19.1803	−	13.9353i	0.683705	−	0.496741i	−0.190880	−	0.981613i	$-0.561134\pi$
$787$	19.1803	−	13.9353i	0.683705	−	0.496741i	0.874585	+	0.484873i	$0.161134\pi$
$788$	−5.08359	−	15.6457i	−0.181095	−	0.557355i
$789$		0			0
$790$	0.263932	+	0.191758i	0.00939028	+	0.00682244i
$791$	38.1246			1.35556
$792$		0			0
$793$	7.14590			0.253758
$794$	−33.1074	−	24.0539i	−1.17494	−	0.853642i
$795$		0			0
$796$	−0.628677	−	1.93487i	−0.0222829	−	0.0685796i
$797$	12.3262	−	8.95554i	0.436618	−	0.317221i	−0.347672	−	0.937616i	$-0.613028\pi$
$797$	12.3262	−	8.95554i	0.436618	−	0.317221i	0.784290	+	0.620395i	$0.213028\pi$
$798$		0			0
$799$	0.118034	+	0.363271i	0.00417574	+	0.0128516i
$800$	−5.07295	+	15.6129i	−0.179356	+	0.552000i
$801$		0			0
$802$	−24.1246			−0.851870
$803$	1.00000	−	3.97574i	0.0352892	−	0.140301i
$804$		0			0
$805$	−5.07295	−	3.68571i	−0.178798	−	0.129904i
$806$	12.0172	−	36.9852i	0.423289	−	1.30275i
$807$		0			0
$808$	−5.42705	+	3.94298i	−0.190923	+	0.138714i
$809$	20.4894	−	14.8864i	0.720367	−	0.523378i	−0.166134	−	0.986103i	$-0.553128\pi$
$809$	20.4894	−	14.8864i	0.720367	−	0.523378i	0.886502	+	0.462726i	$0.153128\pi$
$810$		0			0
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	−0.318477	−	0.947931i	$-0.603171\pi$
$811$	14.1353	−	43.5038i	0.496356	−	1.52763i	0.814833	−	0.579696i	$-0.196829\pi$
$812$	−6.70820	−	4.87380i	−0.235412	−	0.171037i
$813$		0			0
$814$	−17.4443	+	14.5761i	−0.611421	+	0.510893i
$815$	−5.83282			−0.204315
$816$		0			0
$817$	−0.465558	+	1.43284i	−0.0162878	+	0.0501287i
$818$	14.4721	+	44.5407i	0.506006	+	1.55733i
$819$		0			0
$820$	1.13525	−	0.824811i	0.0396448	−	0.0288036i
$821$	−4.19756	−	12.9188i	−0.146496	−	0.450868i	0.850704	−	0.525644i	$-0.176176\pi$
$821$	−4.19756	−	12.9188i	−0.146496	−	0.450868i	−0.997200	+	0.0747763i	$0.976176\pi$
$822$		0			0
$823$	21.4615	+	15.5927i	0.748101	+	0.543527i	0.895238	−	0.445589i	$-0.147006\pi$
$823$	21.4615	+	15.5927i	0.748101	+	0.543527i	−0.147137	+	0.989116i	$0.547006\pi$
$824$	−13.4164			−0.467383
$825$		0			0
$826$	−25.8541			−0.899579
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	0.753975	−	0.656903i	$-0.228134\pi$
$827$	10.4164	+	7.56796i	0.362214	+	0.263164i	−0.391761	+	0.920067i	$0.628134\pi$
$828$		0			0
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	−0.867407	−	0.497600i	$-0.834215\pi$
$829$	−13.1910	−	40.5977i	−0.458142	−	1.41002i	0.409265	−	0.912416i	$-0.365785\pi$
$830$	6.35410	−	4.61653i	0.220554	−	0.160242i
$831$		0			0
$832$	8.16312	+	25.1235i	0.283005	+	0.871001i
$833$	0.381966	−	1.17557i	0.0132343	−	0.0407311i
$834$		0			0
$835$	7.27051			0.251606
$836$	1.48278	+	0.930812i	0.0512830	+	0.0321928i
$837$		0			0
$838$	28.1525	+	20.4540i	0.972511	+	0.706571i
$839$	7.19756	−	22.1518i	0.248487	−	0.764766i	−0.746556	−	0.665323i	$-0.768294\pi$
$839$	7.19756	−	22.1518i	0.248487	−	0.764766i	0.995043	−	0.0994428i	$-0.0317060\pi$
$840$		0			0
$841$	7.28115	−	5.29007i	0.251074	−	0.182416i
$842$	−4.88197	+	3.54696i	−0.168244	+	0.122236i
$843$		0			0
$844$	2.15248	−	6.62464i	0.0740913	−	0.228029i
$845$	−8.00000	−	5.81234i	−0.275208	−	0.199951i
$846$		0			0
$847$	−23.8328	+	22.8254i	−0.818905	+	0.784289i
$848$	−35.8328			−1.23050
$849$		0			0
$850$	1.50000	−	4.61653i	0.0514496	−	0.158346i
$851$	−7.16312	−	22.0458i	−0.245549	−	0.755721i
$852$		0			0
$853$	−6.42705	+	4.66953i	−0.220058	+	0.159882i	−0.692353	−	0.721559i	$-0.743426\pi$
$853$	−6.42705	+	4.66953i	−0.220058	+	0.159882i	0.472295	+	0.881441i	$0.343426\pi$
$854$	−1.71885	−	5.29007i	−0.0588177	−	0.181022i
$855$		0			0
$856$	0.427051	+	0.310271i	0.0145963	+	0.0106048i
$857$	41.7214			1.42517			0.712587	−	0.701584i	$-0.247523\pi$
$857$	41.7214			1.42517			0.712587	+	0.701584i	$0.247523\pi$
$858$		0			0
$859$	42.8885			1.46334			0.731669	−	0.681660i	$-0.238742\pi$
$859$	42.8885			1.46334			0.731669	+	0.681660i	$0.238742\pi$
$860$	−0.336881	−	0.244758i	−0.0114875	−	0.00834619i
$861$		0			0
$862$	−0.746711	−	2.29814i	−0.0254331	−	0.0782750i
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	−0.865944	−	0.500141i	$-0.833281\pi$
$863$	−19.3262	+	14.0413i	−0.657873	+	0.477973i	0.208071	+	0.978114i	$0.433281\pi$
$864$		0			0
$865$	−2.07953	−	6.40013i	−0.0707060	−	0.217611i
$866$	3.00000	−	9.23305i	0.101944	−	0.313752i
$867$		0			0
$868$	−7.14590			−0.242548
$869$	0.652476	+	1.62460i	0.0221337	+	0.0551107i
$870$		0			0
$871$	−53.2877	−	38.7158i	−1.80559	−	1.31183i
$872$		0			0
$873$		0			0
$874$	−6.11803	+	4.44501i	−0.206946	+	0.150355i
$875$	9.13525	−	6.63715i	0.308828	−	0.224377i
$876$		0			0
$877$	−6.30902	+	19.4172i	−0.213040	+	0.655671i	0.786247	+	0.617913i	$0.212022\pi$
$877$	−6.30902	+	19.4172i	−0.213040	+	0.655671i	−0.999287	+	0.0377579i	$0.987978\pi$
$878$	21.8713	+	15.8904i	0.738121	+	0.536277i
$879$		0			0
$880$	4.71885	−	3.94298i	0.159072	−	0.132918i
$881$	−25.0902			−0.845309			−0.422655	−	0.906291i	$-0.638902\pi$
$881$	−25.0902			−0.845309			−0.422655	+	0.906291i	$0.638902\pi$
$882$		0			0
$883$	11.5623	−	35.5851i	0.389103	−	1.19753i	−0.544358	−	0.838853i	$-0.683226\pi$
$883$	11.5623	−	35.5851i	0.389103	−	1.19753i	0.933460	−	0.358681i	$-0.116774\pi$
$884$	0.736068	+	2.26538i	0.0247566	+	0.0761931i
$885$		0			0
$886$	1.14590	−	0.832544i	0.0384972	−	0.0279699i
$887$	−0.927051	−	2.85317i	−0.0311273	−	0.0958001i	0.934286	−	0.356525i	$-0.116038\pi$
$887$	−0.927051	−	2.85317i	−0.0311273	−	0.0958001i	−0.965413	+	0.260725i	$0.916038\pi$
$888$		0			0
$889$	−23.5623	−	17.1190i	−0.790254	−	0.574153i
$890$	5.85410			0.196230
$891$		0			0
$892$	−7.85410			−0.262975
$893$	0.427051	+	0.310271i	0.0142907	+	0.0103828i
$894$		0			0
$895$	−0.263932	−	0.812299i	−0.00882227	−	0.0271522i
$896$	33.0517	−	24.0134i	1.10418	−	0.802233i
$897$		0			0
$898$	−7.76393	−	23.8949i	−0.259086	−	0.797384i
$899$	−5.32624	+	16.3925i	−0.177640	+	0.546720i
$900$		0			0
$901$	4.56231			0.151992
$902$	31.8262	−	2.15938i	1.05970	−	0.0718996i
$903$		0			0
$904$	−22.9894	−	16.7027i	−0.764615	−	0.555525i
$905$	−1.00658	+	3.09793i	−0.0334598	+	0.102979i
$906$		0			0
$907$	−3.21885	+	2.33863i	−0.106880	+	0.0776529i	−0.639942	−	0.768424i	$-0.721041\pi$
$907$	−3.21885	+	2.33863i	−0.106880	+	0.0776529i	0.533061	+	0.846077i	$0.321041\pi$
$908$	5.44427	−	3.95550i	0.180675	−	0.131268i
$909$		0			0
$910$	−3.57295	+	10.9964i	−0.118442	+	0.364527i
$911$	29.0795	+	21.1275i	0.963448	+	0.699986i	0.953949	−	0.299969i	$-0.0969764\pi$
$911$	29.0795	+	21.1275i	0.963448	+	0.699986i	0.00949880	+	0.999955i	$0.496976\pi$
$912$		0			0
$913$	42.0517	−	2.85317i	1.39171	−	0.0944261i
$914$	−53.0689			−1.75536
$915$		0			0
$916$	1.90983	−	5.87785i	0.0631026	−	0.194210i
$917$	12.8435	+	39.5281i	0.424128	+	1.30533i
$918$		0			0
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.254753	−	0.967006i	$-0.418006\pi$
$919$	37.9894	−	27.6009i	1.25315	−	0.910469i	0.998400	+	0.0565371i	$0.0180059\pi$
$920$	1.44427	+	4.44501i	0.0476162	+	0.146548i
$921$		0			0
$922$	12.9721	+	9.42481i	0.427215	+	0.310390i
$923$	−90.8115			−2.98910
$924$		0			0
$925$	20.5623			0.676084
$926$	11.5172	+	8.36775i	0.378479	+	0.274981i
$927$		0			0
$928$	4.67376	+	14.3844i	0.153424	+	0.472190i
$929$	2.33688	−	1.69784i	0.0766706	−	0.0557044i	−0.548790	−	0.835960i	$-0.684911\pi$
$929$	2.33688	−	1.69784i	0.0766706	−	0.0557044i	0.625460	+	0.780256i	$0.284911\pi$
$930$		0			0
$931$	−0.527864	−	1.62460i	−0.0173000	−	0.0532441i
$932$	−1.65654	+	5.09831i	−0.0542618	+	0.167001i
$933$		0			0
$934$	−23.0344			−0.753710
$935$	−0.600813	+	0.502029i	−0.0196487	+	0.0164181i
$936$		0			0
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	0.0667827	−	0.997768i	$-0.478727\pi$
$937$	−26.3713	−	19.1599i	−0.861514	−	0.625926i	−0.928296	+	0.371841i	$0.878727\pi$
$938$	−15.8435	+	48.7612i	−0.517307	+	1.59211i
$939$		0			0
$940$	−0.118034	+	0.0857567i	−0.00384984	+	0.00279708i
$941$	27.2082	−	19.7679i	0.886962	−	0.644416i	−0.0481221	−	0.998841i	$-0.515324\pi$
$941$	27.2082	−	19.7679i	0.886962	−	0.644416i	0.935084	+	0.354426i	$0.115324\pi$
$942$		0			0
$943$	−10.0517	+	30.9358i	−0.327327	+	1.00741i
$944$	20.9164	+	15.1967i	0.680771	+	0.494609i
$945$		0			0
$946$	−3.52786	−	8.78402i	−0.114701	−	0.285593i
$947$	−2.67376			−0.0868856			−0.0434428	−	0.999056i	$-0.513833\pi$
$947$	−2.67376			−0.0868856			−0.0434428	+	0.999056i	$0.513833\pi$
$948$		0			0
$949$	2.38197	−	7.33094i	0.0773219	−	0.237972i
$950$	−2.07295	−	6.37988i	−0.0672553	−	0.206991i
$951$		0			0
$952$	−3.35410	+	2.43690i	−0.108707	+	0.0789803i
$953$	−18.5967	−	57.2349i	−0.602408	−	1.85402i	−0.513714	−	0.857961i	$-0.671731\pi$
$953$	−18.5967	−	57.2349i	−0.602408	−	1.85402i	−0.0886937	−	0.996059i	$-0.528269\pi$
$954$		0			0
$955$	0.454915	+	0.330515i	0.0147207	+	0.0106952i
$956$	10.8541			0.351047
$957$		0			0
$958$	−27.3607			−0.883983
$959$	−3.57295	−	2.59590i	−0.115377	−	0.0838260i
$960$		0			0
$961$	−4.98936	−	15.3557i	−0.160947	−	0.495344i
$962$	−34.5795	+	25.1235i	−1.11489	+	0.810014i
$963$		0			0
$964$	3.27051	+	10.0656i	0.105336	+	0.324191i
$965$	0.184405	−	0.567541i	0.00593621	−	0.0182698i
$966$		0			0
$967$	25.6869			0.826036			0.413018	−	0.910723i	$-0.364475\pi$
$967$	25.6869			0.826036			0.413018	+	0.910723i	$0.364475\pi$
$968$	24.3713	−	3.32244i	0.783324	−	0.106787i
$969$		0			0
$970$	7.51722	+	5.46158i	0.241363	+	0.175361i
$971$	10.4377	−	32.1239i	0.334962	−	1.03091i	−0.631779	−	0.775148i	$-0.717675\pi$
$971$	10.4377	−	32.1239i	0.334962	−	1.03091i	0.966741	−	0.255757i	$-0.0823248\pi$
$972$		0			0
$973$	−14.2082	+	10.3229i	−0.455494	+	0.330936i
$974$	51.2877	−	37.2627i	1.64336	−	1.19397i
$975$		0			0
$976$	−1.71885	+	5.29007i	−0.0550190	+	0.169331i
$977$	−39.9336	−	29.0135i	−1.27759	−	0.928223i	−0.278113	−	0.960548i	$-0.589709\pi$
$977$	−39.9336	−	29.0135i	−1.27759	−	0.928223i	−0.999477	+	0.0323250i	$0.989709\pi$
$978$		0			0
$979$	26.6074	+	16.7027i	0.850376	+	0.533822i
$980$	0.472136			0.0150818
$981$		0			0
$982$	−13.1074	+	40.3404i	−0.418274	+	1.28731i
$983$	−10.9098	−	33.5770i	−0.347970	−	1.07094i	−0.959975	−	0.280086i	$-0.909637\pi$
$983$	−10.9098	−	33.5770i	−0.347970	−	1.07094i	0.612005	−	0.790854i	$-0.290363\pi$
$984$		0			0
$985$	8.22542	−	5.97612i	0.262084	−	0.190415i
$986$	−1.38197	−	4.25325i	−0.0440108	−	0.135451i
$987$		0			0
$988$	2.66312	+	1.93487i	0.0847251	+	0.0615564i
$989$	9.65248			0.306931
$990$		0			0
$991$	−12.2705			−0.389786			−0.194893	−	0.980825i	$-0.562436\pi$
$991$	−12.2705			−0.389786			−0.194893	+	0.980825i	$0.562436\pi$
$992$	10.5451	+	7.66145i	0.334807	+	0.243251i
$993$		0			0
$994$	21.8435	+	67.2273i	0.692832	+	2.13232i
$995$	1.01722	−	0.739054i	0.0322481	−	0.0234296i
$996$		0			0
$997$	10.5000	+	32.3157i	0.332538	+	1.02345i	0.967922	+	0.251251i	$0.0808420\pi$
$997$	10.5000	+	32.3157i	0.332538	+	1.02345i	−0.635384	+	0.772197i	$0.719158\pi$
$998$	−1.28115	+	3.94298i	−0.0405542	+	0.124813i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.f.b.37.1		4
3.2	odd	2		33.2.e.a.4.1	✓	4
9.2	odd	6		891.2.n.d.433.1		8
9.4	even	3		891.2.n.a.136.1		8
9.5	odd	6		891.2.n.d.136.1		8
9.7	even	3		891.2.n.a.433.1		8
11.3	even	5	inner	99.2.f.b.91.1		4
11.5	even	5		1089.2.a.m.1.1		2
11.6	odd	10		1089.2.a.s.1.2		2
12.11	even	2		528.2.y.f.433.1		4
15.2	even	4		825.2.bx.b.499.2		8
15.8	even	4		825.2.bx.b.499.1		8
15.14	odd	2		825.2.n.f.301.1		4
33.2	even	10		363.2.e.c.148.1		4
33.5	odd	10		363.2.a.h.1.2		2
33.8	even	10		363.2.e.j.124.1		4
33.14	odd	10		33.2.e.a.25.1	yes	4
33.17	even	10		363.2.a.e.1.1		2
33.20	odd	10		363.2.e.h.148.1		4
33.26	odd	10		363.2.e.h.130.1		4
33.29	even	10		363.2.e.c.130.1		4
33.32	even	2		363.2.e.j.202.1		4
99.14	odd	30		891.2.n.d.784.1		8
99.25	even	15		891.2.n.a.190.1		8
99.47	odd	30		891.2.n.d.190.1		8
99.58	even	15		891.2.n.a.784.1		8
132.47	even	10		528.2.y.f.289.1		4
132.71	even	10		5808.2.a.bl.1.2		2
132.83	odd	10		5808.2.a.bm.1.2		2
165.14	odd	10		825.2.n.f.751.1		4
165.47	even	20		825.2.bx.b.124.1		8
165.104	odd	10		9075.2.a.x.1.1		2
165.113	even	20		825.2.bx.b.124.2		8
165.149	even	10		9075.2.a.bv.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.e.a.4.1	✓	4	3.2	odd	2
33.2.e.a.25.1	yes	4	33.14	odd	10
99.2.f.b.37.1		4	1.1	even	1	trivial
99.2.f.b.91.1		4	11.3	even	5	inner
363.2.a.e.1.1		2	33.17	even	10
363.2.a.h.1.2		2	33.5	odd	10
363.2.e.c.130.1		4	33.29	even	10
363.2.e.c.148.1		4	33.2	even	10
363.2.e.h.130.1		4	33.26	odd	10
363.2.e.h.148.1		4	33.20	odd	10
363.2.e.j.124.1		4	33.8	even	10
363.2.e.j.202.1		4	33.32	even	2
528.2.y.f.289.1		4	132.47	even	10
528.2.y.f.433.1		4	12.11	even	2
825.2.n.f.301.1		4	15.14	odd	2
825.2.n.f.751.1		4	165.14	odd	10
825.2.bx.b.124.1		8	165.47	even	20
825.2.bx.b.124.2		8	165.113	even	20
825.2.bx.b.499.1		8	15.8	even	4
825.2.bx.b.499.2		8	15.2	even	4
891.2.n.a.136.1		8	9.4	even	3
891.2.n.a.190.1		8	99.25	even	15
891.2.n.a.433.1		8	9.7	even	3
891.2.n.a.784.1		8	99.58	even	15
891.2.n.d.136.1		8	9.5	odd	6
891.2.n.d.190.1		8	99.47	odd	30
891.2.n.d.433.1		8	9.2	odd	6
891.2.n.d.784.1		8	99.14	odd	30
1089.2.a.m.1.1		2	11.5	even	5
1089.2.a.s.1.2		2	11.6	odd	10
5808.2.a.bl.1.2		2	132.71	even	10
5808.2.a.bm.1.2		2	132.83	odd	10
9075.2.a.x.1.1		2	165.104	odd	10
9075.2.a.bv.1.2		2	165.149	even	10

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.30902 + 0.951057i) q^{2} +(0.190983 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{5} +(0.927051 + 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})\)	\(q+(1.30902 + 0.951057i) q^{2} +(0.190983 + 0.587785i) q^{4} +(-0.309017 + 0.224514i) q^{5} +(0.927051 + 2.85317i) q^{7} +(0.690983 - 2.12663i) q^{8} -0.618034 q^{10} +(-2.80902 - 1.76336i) q^{11} +(-5.04508 - 3.66547i) q^{13} +(-1.50000 + 4.61653i) q^{14} +(3.92705 - 2.85317i) q^{16} +(-0.500000 + 0.363271i) q^{17} +(-0.263932 + 0.812299i) q^{19} +(-0.190983 - 0.138757i) q^{20} +(-2.00000 - 4.97980i) q^{22} +5.47214 q^{23} +(-1.50000 + 4.61653i) q^{25} +(-3.11803 - 9.59632i) q^{26} +(-1.50000 + 1.08981i) q^{28} +(1.38197 + 4.25325i) q^{29} +(3.11803 + 2.26538i) q^{31} +3.38197 q^{32} -1.00000 q^{34} +(-0.927051 - 0.673542i) q^{35} +(-1.30902 - 4.02874i) q^{37} +(-1.11803 + 0.812299i) q^{38} +(0.263932 + 0.812299i) q^{40} +(-1.83688 + 5.65334i) q^{41} +1.76393 q^{43} +(0.500000 - 1.98787i) q^{44} +(7.16312 + 5.20431i) q^{46} +(0.190983 - 0.587785i) q^{47} +(-1.61803 + 1.17557i) q^{49} +(-6.35410 + 4.61653i) q^{50} +(1.19098 - 3.66547i) q^{52} +(-5.97214 - 4.33901i) q^{53} +(1.26393 - 0.0857567i) q^{55} +6.70820 q^{56} +(-2.23607 + 6.88191i) q^{58} +(1.64590 + 5.06555i) q^{59} +(-0.927051 + 0.673542i) q^{61} +(1.92705 + 5.93085i) q^{62} +(-3.42705 - 2.48990i) q^{64} +2.38197 q^{65} +10.5623 q^{67} +(-0.309017 - 0.224514i) q^{68} +(-0.572949 - 1.76336i) q^{70} +(11.7812 - 8.55951i) q^{71} +(0.381966 + 1.17557i) q^{73} +(2.11803 - 6.51864i) q^{74} -0.527864 q^{76} +(2.42705 - 9.64932i) q^{77} +(-0.427051 - 0.310271i) q^{79} +(-0.572949 + 1.76336i) q^{80} +(-7.78115 + 5.65334i) q^{82} +(-10.2812 + 7.46969i) q^{83} +(0.0729490 - 0.224514i) q^{85} +(2.30902 + 1.67760i) q^{86} +(-5.69098 + 4.75528i) q^{88} -9.47214 q^{89} +(5.78115 - 17.7926i) q^{91} +(1.04508 + 3.21644i) q^{92} +(0.809017 - 0.587785i) q^{94} +(-0.100813 - 0.310271i) q^{95} +(-12.1631 - 8.83702i) q^{97} -3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8	\( 4 q + 3 q^{2} + 3 q^{4} + q^{5} - 3 q^{7} + 5 q^{8} + 2 q^{10} - 9 q^{11} - 9 q^{13} - 6 q^{14} + 9 q^{16} - 2 q^{17} - 10 q^{19} - 3 q^{20} - 8 q^{22} + 4 q^{23} - 6 q^{25} - 8 q^{26} - 6 q^{28} + 10 q^{29} + 8 q^{31} + 18 q^{32} - 4 q^{34} + 3 q^{35} - 3 q^{37} + 10 q^{40} - 23 q^{41} + 16 q^{43} + 2 q^{44} + 13 q^{46} + 3 q^{47} - 2 q^{49} - 12 q^{50} + 7 q^{52} - 6 q^{53} + 14 q^{55} + 20 q^{59} + 3 q^{61} + q^{62} - 7 q^{64} + 14 q^{65} + 2 q^{67} + q^{68} - 9 q^{70} + 27 q^{71} + 6 q^{73} + 4 q^{74} - 20 q^{76} + 3 q^{77} + 5 q^{79} - 9 q^{80} - 11 q^{82} - 21 q^{83} + 7 q^{85} + 7 q^{86} - 25 q^{88} - 20 q^{89} + 3 q^{91} - 7 q^{92} + q^{94} - 25 q^{95} - 33 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 + 3 * q^4 + q^5 - 3 * q^7 + 5 * q^8 + 2 * q^10 - 9 * q^11 - 9 * q^13 - 6 * q^14 + 9 * q^16 - 2 * q^17 - 10 * q^19 - 3 * q^20 - 8 * q^22 + 4 * q^23 - 6 * q^25 - 8 * q^26 - 6 * q^28 + 10 * q^29 + 8 * q^31 + 18 * q^32 - 4 * q^34 + 3 * q^35 - 3 * q^37 + 10 * q^40 - 23 * q^41 + 16 * q^43 + 2 * q^44 + 13 * q^46 + 3 * q^47 - 2 * q^49 - 12 * q^50 + 7 * q^52 - 6 * q^53 + 14 * q^55 + 20 * q^59 + 3 * q^61 + q^62 - 7 * q^64 + 14 * q^65 + 2 * q^67 + q^68 - 9 * q^70 + 27 * q^71 + 6 * q^73 + 4 * q^74 - 20 * q^76 + 3 * q^77 + 5 * q^79 - 9 * q^80 - 11 * q^82 - 21 * q^83 + 7 * q^85 + 7 * q^86 - 25 * q^88 - 20 * q^89 + 3 * q^91 - 7 * q^92 + q^94 - 25 * q^95 - 33 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more