LMFDB - Embedded newform 693.2.m.f.631.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(64,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("693.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.m (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:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 231)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			631.1
Root			$1.69513 + 1.23158i$ of defining polynomial
Character	$\chi$	$=$	693.631
Dual form			693.2.m.f.190.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93376 - 1.40496i) q^{2} +(1.14748 + 3.53158i) q^{4} +(-2.09529 + 1.52232i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(1.26552 - 3.89486i) q^{8} +O(q^{10})$	\(q+(-1.93376 - 1.40496i) q^{2} +(1.14748 + 3.53158i) q^{4} +(-2.09529 + 1.52232i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(1.26552 - 3.89486i) q^{8} +6.19059 q^{10} +(2.19098 - 2.48990i) q^{11} +(-5.48555 - 3.98549i) q^{13} +(-0.738630 + 2.27327i) q^{14} +(-1.91102 + 1.38844i) q^{16} +(-2.54445 + 1.84865i) q^{17} +(-0.323071 + 0.994311i) q^{19} +(-7.78051 - 5.65287i) q^{20} +(-7.73503 + 1.73662i) q^{22} +6.52707 q^{23} +(0.527713 - 1.62413i) q^{25} +(5.00829 + 15.4139i) q^{26} +(3.00415 - 2.18264i) q^{28} +(0.187665 + 0.577574i) q^{29} +(7.14906 + 5.19410i) q^{31} -2.54445 q^{32} +7.51762 q^{34} +(2.09529 + 1.52232i) q^{35} +(2.76354 + 8.50529i) q^{37} +(2.02171 - 1.46886i) q^{38} +(3.27759 + 10.0874i) q^{40} +(-2.68767 + 8.27178i) q^{41} +4.48159 q^{43} +(11.3074 + 4.88053i) q^{44} +(-12.6218 - 9.17026i) q^{46} +(-1.00829 + 3.10320i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-3.30231 + 2.39927i) q^{50} +(7.78051 - 23.9460i) q^{52} +(1.53679 + 1.11655i) q^{53} +(-0.800331 + 8.55245i) q^{55} -4.09529 q^{56} +(0.448568 - 1.38055i) q^{58} +(0.0537709 + 0.165490i) q^{59} +(-6.58084 + 4.78126i) q^{61} +(-6.52707 - 20.0883i) q^{62} +(8.74238 + 6.35171i) q^{64} +17.5610 q^{65} -7.33649 q^{67} +(-9.44836 - 6.86464i) q^{68} +(-1.91300 - 5.88760i) q^{70} +(2.18995 - 1.59109i) q^{71} +(0.182297 + 0.561053i) q^{73} +(6.60556 - 20.3298i) q^{74} -3.88221 q^{76} +(-3.04508 - 1.31433i) q^{77} +(7.93534 + 5.76536i) q^{79} +(1.89050 - 5.81836i) q^{80} +(16.8188 - 12.2196i) q^{82} +(7.07548 - 5.14063i) q^{83} +(2.51713 - 7.74692i) q^{85} +(-8.66632 - 6.29645i) q^{86} +(-6.92507 - 11.6846i) q^{88} +11.6788 q^{89} +(-2.09529 + 6.44865i) q^{91} +(7.48970 + 23.0509i) q^{92} +(6.30966 - 4.58423i) q^{94} +(-0.836730 - 2.57519i) q^{95} +(-9.58914 - 6.96691i) q^{97} +2.39026 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	$ 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 20 q^{10} + 22 q^{11} - 8 q^{13} - 3 q^{14} + 4 q^{16} + 4 q^{17} - 20 q^{20} - 8 q^{22} + 20 q^{23} - 26 q^{25} + 10 q^{26} + 9 q^{28} + 24 q^{31} + 4 q^{32} + 36 q^{34} + 2 q^{35} + 6 q^{37} - 14 q^{38} + 12 q^{40} - 20 q^{41} - 8 q^{43} + 39 q^{44} - 43 q^{46} + 22 q^{47} - 2 q^{49} - 22 q^{50} + 20 q^{52} + 20 q^{53} + 2 q^{55} - 18 q^{56} - 17 q^{58} - 18 q^{59} - 2 q^{61} - 20 q^{62} + 18 q^{64} + 56 q^{65} - 56 q^{67} + 2 q^{68} - 14 q^{71} + 2 q^{73} + 12 q^{74} - 8 q^{76} - 2 q^{77} + 20 q^{79} - 38 q^{80} + 2 q^{82} + 8 q^{83} + 60 q^{85} - 55 q^{86} - 38 q^{88} + 32 q^{89} - 2 q^{91} + 9 q^{92} + 48 q^{94} + 28 q^{95} + 4 q^{97} - 2 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 20 * q^10 + 22 * q^11 - 8 * q^13 - 3 * q^14 + 4 * q^16 + 4 * q^17 - 20 * q^20 - 8 * q^22 + 20 * q^23 - 26 * q^25 + 10 * q^26 + 9 * q^28 + 24 * q^31 + 4 * q^32 + 36 * q^34 + 2 * q^35 + 6 * q^37 - 14 * q^38 + 12 * q^40 - 20 * q^41 - 8 * q^43 + 39 * q^44 - 43 * q^46 + 22 * q^47 - 2 * q^49 - 22 * q^50 + 20 * q^52 + 20 * q^53 + 2 * q^55 - 18 * q^56 - 17 * q^58 - 18 * q^59 - 2 * q^61 - 20 * q^62 + 18 * q^64 + 56 * q^65 - 56 * q^67 + 2 * q^68 - 14 * q^71 + 2 * q^73 + 12 * q^74 - 8 * q^76 - 2 * q^77 + 20 * q^79 - 38 * q^80 + 2 * q^82 + 8 * q^83 + 60 * q^85 - 55 * q^86 - 38 * q^88 + 32 * q^89 - 2 * q^91 + 9 * q^92 + 48 * q^94 + 28 * q^95 + 4 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	−1.93376	−	1.40496i	−1.36737	−	0.993455i	−0.997937	−	0.0641992i	$-0.979551\pi$
$2$	−1.93376	−	1.40496i	−1.36737	−	0.993455i	−0.369437	−	0.929256i	$-0.620449\pi$
$3$		0			0
$3$		0			0
$4$	1.14748	+	3.53158i	0.573741	+	1.76579i
$5$	−2.09529	+	1.52232i	−0.937044	+	0.680802i	−0.947707	−	0.319141i	$-0.896606\pi$
$5$	−2.09529	+	1.52232i	−0.937044	+	0.680802i	0.0106633	+	0.999943i	$0.496606\pi$
$6$		0			0
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	1.26552	−	3.89486i	0.447427	−	1.37704i
$9$		0			0
$10$	6.19059			1.95764
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$11$	2.19098	−	2.48990i	0.660606	−	0.750733i
$12$		0			0
$13$	−5.48555	−	3.98549i	−1.52142	−	1.10537i	−0.960779	−	0.277315i	$-0.910556\pi$
$13$	−5.48555	−	3.98549i	−1.52142	−	1.10537i	−0.560639	−	0.828060i	$-0.689444\pi$
$14$	−0.738630	+	2.27327i	−0.197407	+	0.607557i
$15$		0			0
$16$	−1.91102	+	1.38844i	−0.477755	+	0.347109i
$17$	−2.54445	+	1.84865i	−0.617119	+	0.448363i	−0.851914	−	0.523682i	$-0.824558\pi$
$17$	−2.54445	+	1.84865i	−0.617119	+	0.448363i	0.234795	+	0.972045i	$0.424558\pi$
$18$		0			0
$19$	−0.323071	+	0.994311i	−0.0741176	+	0.228110i	−0.981252	−	0.192732i	$-0.938265\pi$
$19$	−0.323071	+	0.994311i	−0.0741176	+	0.228110i	0.907134	+	0.420842i	$0.138265\pi$
$20$	−7.78051	−	5.65287i	−1.73978	−	1.26402i
$21$		0			0
$22$	−7.73503	+	1.73662i	−1.64911	+	0.370249i
$23$	6.52707			1.36099			0.680495	−	0.732753i	$-0.261765\pi$
$23$	6.52707			1.36099			0.680495	+	0.732753i	$0.261765\pi$
$24$		0			0
$25$	0.527713	−	1.62413i	0.105543	−	0.324827i
$26$	5.00829	+	15.4139i	0.982207	+	3.02292i
$27$		0			0
$28$	3.00415	−	2.18264i	0.567730	−	0.412480i
$29$	0.187665	+	0.577574i	0.0348486	+	0.107253i	0.966968	−	0.254899i	$-0.0820422\pi$
$29$	0.187665	+	0.577574i	0.0348486	+	0.107253i	−0.932119	+	0.362152i	$0.882042\pi$
$30$		0			0
$31$	7.14906	+	5.19410i	1.28401	+	0.932888i	0.999666	−	0.0258346i	$-0.00822431\pi$
$31$	7.14906	+	5.19410i	1.28401	+	0.932888i	0.284344	+	0.958722i	$0.408224\pi$
$32$	−2.54445			−0.449799
$33$		0			0
$34$	7.51762			1.28926
$35$	2.09529	+	1.52232i	0.354169	+	0.257319i
$36$		0			0
$37$	2.76354	+	8.50529i	0.454323	+	1.39826i	0.871929	+	0.489633i	$0.162869\pi$
$37$	2.76354	+	8.50529i	0.454323	+	1.39826i	−0.417606	+	0.908628i	$0.637131\pi$
$38$	2.02171	−	1.46886i	0.327964	−	0.238280i
$39$		0			0
$40$	3.27759	+	10.0874i	0.518233	+	1.59496i
$41$	−2.68767	+	8.27178i	−0.419743	+	1.29184i	0.488196	+	0.872734i	$0.337655\pi$
$41$	−2.68767	+	8.27178i	−0.419743	+	1.29184i	−0.907939	+	0.419102i	$0.862345\pi$
$42$		0			0
$43$	4.48159			0.683437			0.341718	−	0.939802i	$-0.388991\pi$
$43$	4.48159			0.683437			0.341718	+	0.939802i	$0.388991\pi$
$44$	11.3074	+	4.88053i	1.70465	+	0.735768i
$45$		0			0
$46$	−12.6218	−	9.17026i	−1.86098	−	1.35208i
$47$	−1.00829	+	3.10320i	−0.147074	+	0.452648i	−0.997272	−	0.0738155i	$-0.976482\pi$
$47$	−1.00829	+	3.10320i	−0.147074	+	0.452648i	0.850198	+	0.526464i	$0.176482\pi$
$48$		0			0
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−3.30231	+	2.39927i	−0.467017	+	0.339308i
$51$		0			0
$52$	7.78051	−	23.9460i	1.07896	−	3.32071i
$53$	1.53679	+	1.11655i	0.211095	+	0.153369i	0.688309	−	0.725418i	$-0.258353\pi$
$53$	1.53679	+	1.11655i	0.211095	+	0.153369i	−0.477214	+	0.878787i	$0.658353\pi$
$54$		0			0
$55$	−0.800331	+	8.55245i	−0.107917	+	1.15321i
$56$	−4.09529			−0.547257
$57$		0			0
$58$	0.448568	−	1.38055i	0.0588999	−	0.181275i
$59$	0.0537709	+	0.165490i	0.00700037	+	0.0215449i	0.954496	−	0.298225i	$-0.0963945\pi$
$59$	0.0537709	+	0.165490i	0.00700037	+	0.0215449i	−0.947495	+	0.319770i	$0.896394\pi$
$60$		0			0
$61$	−6.58084	+	4.78126i	−0.842591	+	0.612178i	−0.923093	−	0.384576i	$-0.874348\pi$
$61$	−6.58084	+	4.78126i	−0.842591	+	0.612178i	0.0805023	+	0.996754i	$0.474348\pi$
$62$	−6.52707	−	20.0883i	−0.828939	−	2.55121i
$63$		0			0
$64$	8.74238	+	6.35171i	1.09280	+	0.793964i
$65$	17.5610			2.17818
$66$		0			0
$67$	−7.33649			−0.896294			−0.448147	−	0.893960i	$-0.647916\pi$
$67$	−7.33649			−0.896294			−0.448147	+	0.893960i	$0.647916\pi$
$68$	−9.44836	−	6.86464i	−1.14578	−	0.832459i
$69$		0			0
$70$	−1.91300	−	5.88760i	−0.228647	−	0.703703i
$71$	2.18995	−	1.59109i	0.259899	−	0.188828i	−0.450203	−	0.892926i	$-0.648649\pi$
$71$	2.18995	−	1.59109i	0.259899	−	0.188828i	0.710103	+	0.704098i	$0.248649\pi$
$72$		0			0
$73$	0.182297	+	0.561053i	0.0213363	+	0.0656663i	0.961158	−	0.276000i	$-0.0890089\pi$
$73$	0.182297	+	0.561053i	0.0213363	+	0.0656663i	−0.939821	+	0.341666i	$0.889009\pi$
$74$	6.60556	−	20.3298i	0.767881	−	2.36330i
$75$		0			0
$76$	−3.88221			−0.445320
$77$	−3.04508	−	1.31433i	−0.347020	−	0.149782i
$78$		0			0
$79$	7.93534	+	5.76536i	0.892796	+	0.648654i	0.936605	−	0.350386i	$-0.113950\pi$
$79$	7.93534	+	5.76536i	0.892796	+	0.648654i	−0.0438097	+	0.999040i	$0.513950\pi$
$80$	1.89050	−	5.81836i	0.211364	−	0.650513i
$81$		0			0
$82$	16.8188	−	12.2196i	1.85733	−	1.34943i
$83$	7.07548	−	5.14063i	0.776634	−	0.564258i	−0.127333	−	0.991860i	$-0.540642\pi$
$83$	7.07548	−	5.14063i	0.776634	−	0.564258i	0.903967	+	0.427602i	$0.140642\pi$
$84$		0			0
$85$	2.51713	−	7.74692i	0.273021	−	0.840272i
$86$	−8.66632	−	6.29645i	−0.934513	−	0.678964i
$87$		0			0
$88$	−6.92507	−	11.6846i	−0.738215	−	1.24558i
$89$	11.6788			1.23795			0.618976	−	0.785410i	$-0.287548\pi$
$89$	11.6788			1.23795			0.618976	+	0.785410i	$0.287548\pi$
$90$		0			0
$91$	−2.09529	+	6.44865i	−0.219646	+	0.676002i
$92$	7.48970	+	23.0509i	0.780855	+	2.40322i
$93$		0			0
$94$	6.30966	−	4.58423i	0.650791	−	0.472828i
$95$	−0.836730	−	2.57519i	−0.0858467	−	0.264209i
$96$		0			0
$97$	−9.58914	−	6.96691i	−0.973629	−	0.707383i	−0.0173534	−	0.999849i	$-0.505524\pi$
$97$	−9.58914	−	6.96691i	−0.973629	−	0.707383i	−0.956276	+	0.292466i	$0.905524\pi$
$98$	2.39026			0.241452
$99$		0			0
$100$	6.34131			0.634131
$101$	3.00829	+	2.18565i	0.299336	+	0.217480i	0.727307	−	0.686312i	$-0.240772\pi$
$101$	3.00829	+	2.18565i	0.299336	+	0.217480i	−0.427971	+	0.903792i	$0.640772\pi$
$102$		0			0
$103$	2.26418	+	6.96842i	0.223096	+	0.686619i	0.998479	+	0.0551278i	$0.0175566\pi$
$103$	2.26418	+	6.96842i	0.223096	+	0.686619i	−0.775383	+	0.631491i	$0.782443\pi$
$104$	−22.4649	+	16.3217i	−2.20287	+	1.60048i
$105$		0			0
$106$	−1.40309	−	4.31826i	−0.136280	−	0.419427i
$107$	−4.13477	+	12.7255i	−0.399723	+	1.23022i	0.525499	+	0.850794i	$0.323879\pi$
$107$	−4.13477	+	12.7255i	−0.399723	+	1.23022i	−0.925222	+	0.379427i	$0.876121\pi$
$108$		0			0
$109$	14.1228			1.35272			0.676362	−	0.736570i	$-0.263556\pi$
$109$	14.1228			1.35272			0.676362	+	0.736570i	$0.263556\pi$
$110$	13.5635	−	15.4139i	1.29323	−	1.46966i
$111$		0			0
$112$	1.91102	+	1.38844i	0.180574	+	0.131195i
$113$	0.823071	−	2.53315i	0.0774280	−	0.238299i	−0.904849	−	0.425732i	$-0.860017\pi$
$113$	0.823071	−	2.53315i	0.0774280	−	0.238299i	0.982277	+	0.187433i	$0.0600167\pi$
$114$		0			0
$115$	−13.6761	+	9.93630i	−1.27531	+	0.926564i
$116$	−1.82441	+	1.32551i	−0.169392	+	0.123071i
$117$		0			0
$118$	0.128526	−	0.395563i	0.0118318	−	0.0364145i
$119$	2.54445	+	1.84865i	0.233249	+	0.169465i
$120$		0			0
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	19.4432			1.76031
$123$		0			0
$124$	−10.1400	+	31.2077i	−0.910597	+	2.80253i
$125$	−2.63492	−	8.10944i	−0.235674	−	0.725331i
$126$		0			0
$127$	8.38410	−	6.09140i	0.743968	−	0.540525i	−0.149983	−	0.988689i	$-0.547922\pi$
$127$	8.38410	−	6.09140i	0.743968	−	0.540525i	0.893951	+	0.448164i	$0.147922\pi$
$128$	−6.40921	−	19.7255i	−0.566500	−	1.74351i
$129$		0			0
$130$	−33.9588	−	24.6725i	−2.97838	−	2.16392i
$131$	11.6441			1.01735			0.508674	−	0.860959i	$-0.330136\pi$
$131$	11.6441			1.01735			0.508674	+	0.860959i	$0.330136\pi$
$132$		0			0
$133$	1.04548			0.0906546
$134$	14.1870	+	10.3075i	1.22557	+	0.890428i
$135$		0			0
$136$	3.98018	+	12.2497i	0.341298	+	1.05041i
$137$	−12.5313	+	9.10450i	−1.07062	+	0.777850i	−0.976023	−	0.217665i	$-0.930156\pi$
$137$	−12.5313	+	9.10450i	−1.07062	+	0.777850i	−0.0945956	+	0.995516i	$0.530156\pi$
$138$		0			0
$139$	−1.79789	−	5.53332i	−0.152495	−	0.469330i	0.845404	−	0.534128i	$-0.179360\pi$
$139$	−1.79789	−	5.53332i	−0.152495	−	0.469330i	−0.997898	+	0.0647974i	$0.979360\pi$
$140$	−2.97189	+	9.14654i	−0.251171	+	0.773024i
$141$		0			0
$142$	−6.47025			−0.542971
$143$	−21.9422	+	4.92633i	−1.83490	+	0.411961i
$144$		0			0
$145$	−1.27247	−	0.924501i	−0.105673	−	0.0767757i
$146$	0.435737	−	1.34106i	0.0360618	−	0.110987i
$147$		0			0
$148$	−26.8661	+	19.5193i	−2.20838	+	1.60448i
$149$	−11.6614	+	8.47254i	−0.955343	+	0.694097i	−0.952064	−	0.305897i	$-0.901044\pi$
$149$	−11.6614	+	8.47254i	−0.955343	+	0.694097i	−0.00327837	+	0.999995i	$0.501044\pi$
$150$		0			0
$151$	−6.86547	+	21.1297i	−0.558704	+	1.71951i	0.127252	+	0.991870i	$0.459384\pi$
$151$	−6.86547	+	21.1297i	−0.558704	+	1.71951i	−0.685956	+	0.727643i	$0.740616\pi$
$152$	3.46385	+	2.51663i	0.280955	+	0.204126i
$153$		0			0
$154$	4.04188	+	6.81981i	0.325704	+	0.549556i
$155$	−22.8865			−1.83829
$156$		0			0
$157$	−3.02566	+	9.31203i	−0.241474	+	0.743181i	0.754722	+	0.656045i	$0.227772\pi$
$157$	−3.02566	+	9.31203i	−0.241474	+	0.743181i	−0.996196	+	0.0871366i	$0.972228\pi$
$158$	−7.24494	−	22.2976i	−0.576377	−	1.77390i
$159$		0			0
$160$	5.33136	−	3.87346i	0.421481	−	0.306224i
$161$	−2.01698	−	6.20762i	−0.158960	−	0.489229i
$162$		0			0
$163$	−9.19351	−	6.67948i	−0.720091	−	0.523177i	0.166322	−	0.986071i	$-0.446811\pi$
$163$	−9.19351	−	6.67948i	−0.720091	−	0.523177i	−0.886413	+	0.462895i	$0.846811\pi$
$164$	−32.2965			−2.52194
$165$		0			0
$166$	−20.9046			−1.62251
$167$	−4.11700	−	2.99118i	−0.318583	−	0.231464i	0.416988	−	0.908912i	$-0.363086\pi$
$167$	−4.11700	−	2.99118i	−0.318583	−	0.231464i	−0.735571	+	0.677448i	$0.763086\pi$
$168$		0			0
$169$	10.1899	+	31.3614i	0.783842	+	2.41242i
$170$	−15.7516	+	11.4442i	−1.20809	+	0.877731i
$171$		0			0
$172$	5.14255	+	15.8271i	0.392115	+	1.20681i
$173$	−2.40250	+	7.39415i	−0.182659	+	0.562167i	−0.999900	−	0.0141291i	$-0.995502\pi$
$173$	−2.40250	+	7.39415i	−0.182659	+	0.562167i	0.817241	+	0.576296i	$0.195502\pi$
$174$		0			0
$175$	−1.70772			−0.129091
$176$	−0.729944	+	7.80028i	−0.0550216	+	0.587968i
$177$		0			0
$178$	−22.5840	−	16.4082i	−1.69274	−	1.22985i
$179$	1.89919	−	5.84510i	0.141952	−	0.436883i	−0.854655	−	0.519197i	$-0.826231\pi$
$179$	1.89919	−	5.84510i	0.141952	−	0.436883i	0.996606	+	0.0823141i	$0.0262311\pi$
$180$		0			0
$181$	7.48988	−	5.44172i	0.556719	−	0.404480i	−0.273538	−	0.961861i	$-0.588194\pi$
$181$	7.48988	−	5.44172i	0.556719	−	0.404480i	0.830257	+	0.557381i	$0.188194\pi$
$182$	13.1119	−	9.52634i	0.971917	−	0.706139i
$183$		0			0
$184$	8.26011	−	25.4220i	0.608944	−	1.87414i
$185$	−18.7382	−	13.6141i	−1.37766	−	1.00093i
$186$		0			0
$187$	−0.971892	+	10.3858i	−0.0710718	+	0.759483i
$188$	−12.1162			−0.883665
$189$		0			0
$190$	−2.00000	+	6.15537i	−0.145095	+	0.446557i
$191$	4.52322	+	13.9210i	0.327289	+	1.00729i	0.970397	+	0.241515i	$0.0776444\pi$
$191$	4.52322	+	13.9210i	0.327289	+	1.00729i	−0.643108	+	0.765775i	$0.722356\pi$
$192$		0			0
$193$	13.3256	−	9.68161i	0.959198	−	0.696898i	0.00623334	−	0.999981i	$-0.498016\pi$
$193$	13.3256	−	9.68161i	0.959198	−	0.696898i	0.952964	+	0.303083i	$0.0980159\pi$
$194$	8.75485	+	26.9447i	0.628562	+	1.93451i
$195$		0			0
$196$	−3.00415	−	2.18264i	−0.214582	−	0.155903i
$197$	6.81654			0.485658			0.242829	−	0.970069i	$-0.421925\pi$
$197$	6.81654			0.485658			0.242829	+	0.970069i	$0.421925\pi$
$198$		0			0
$199$	15.5561			1.10275			0.551373	−	0.834259i	$-0.314104\pi$
$199$	15.5561			1.10275			0.551373	+	0.834259i	$0.314104\pi$
$200$	−5.65794	−	4.11073i	−0.400077	−	0.290673i
$201$		0			0
$202$	−2.74656	−	8.45304i	−0.193247	−	0.594754i
$203$	0.491314	−	0.356961i	0.0344835	−	0.0250537i
$204$		0			0
$205$	−6.96085	−	21.4233i	−0.486167	−	1.49627i
$206$	5.41196	−	16.6563i	0.377069	−	1.16050i
$207$		0			0
$208$	16.0166			1.11055
$209$	1.76789	+	2.98293i	0.122287	+	0.206334i
$210$		0			0
$211$	−1.26582	−	0.919672i	−0.0871427	−	0.0633129i	0.543361	−	0.839499i	$-0.317152\pi$
$211$	−1.26582	−	0.919672i	−0.0871427	−	0.0633129i	−0.630504	+	0.776186i	$0.717152\pi$
$212$	−2.17974	+	6.70853i	−0.149705	+	0.460744i
$213$		0			0
$214$	25.8744	−	18.7989i	1.76874	−	1.28506i
$215$	−9.39026	+	6.82242i	−0.640410	+	0.465285i
$216$		0			0
$217$	2.73070	−	8.40423i	0.185372	−	0.570516i
$218$	−27.3102	−	19.8420i	−1.84968	−	1.34387i
$219$		0			0
$220$	−31.1221	+	6.98734i	−2.09825	+	0.471086i
$221$	21.3254			1.43450
$222$		0			0
$223$	1.27910	−	3.93667i	0.0856550	−	0.263619i	−0.899051	−	0.437844i	$-0.855742\pi$
$223$	1.27910	−	3.93667i	0.0856550	−	0.263619i	0.984706	+	0.174225i	$0.0557421\pi$
$224$	0.786277	+	2.41991i	0.0525353	+	0.161687i
$225$		0			0
$226$	−5.15059	+	3.74212i	−0.342612	+	0.248922i
$227$	1.72358	+	5.30462i	0.114398	+	0.352080i	0.991821	−	0.127637i	$-0.0407393\pi$
$227$	1.72358	+	5.30462i	0.114398	+	0.352080i	−0.877423	+	0.479717i	$0.840739\pi$
$228$		0			0
$229$	0.637851	+	0.463426i	0.0421504	+	0.0306241i	0.608661	−	0.793430i	$-0.291707\pi$
$229$	0.637851	+	0.463426i	0.0421504	+	0.0306241i	−0.566511	+	0.824054i	$0.691707\pi$
$230$	40.4064			2.66432
$231$		0			0
$232$	2.48706			0.163284
$233$	22.4151	+	16.2855i	1.46846	+	1.06690i	0.981055	+	0.193727i	$0.0620578\pi$
$233$	22.4151	+	16.2855i	1.46846	+	1.06690i	0.487409	+	0.873174i	$0.337942\pi$
$234$		0			0
$235$	−2.61140	−	8.03706i	−0.170349	−	0.524280i
$236$	−0.522740	+	0.379793i	−0.0340275	+	0.0247224i
$237$		0			0
$238$	−2.32307	−	7.14968i	−0.150582	−	0.463445i
$239$	2.65174	−	8.16123i	0.171527	−	0.527906i	−0.827931	−	0.560830i	$-0.810482\pi$
$239$	2.65174	−	8.16123i	0.171527	−	0.527906i	0.999458	+	0.0329243i	$0.0104820\pi$
$240$		0			0
$241$	−19.6392			−1.26507			−0.632535	−	0.774531i	$-0.717986\pi$
$241$	−19.6392			−1.26507			−0.632535	+	0.774531i	$0.717986\pi$
$242$	−12.6233	+	23.0644i	−0.811457	+	1.48263i
$243$		0			0
$244$	−24.4368	−	17.7544i	−1.56441	−	1.13661i
$245$	0.800331	−	2.46317i	0.0511313	−	0.157366i
$246$		0			0
$247$	5.73503	−	4.16675i	0.364911	−	0.265124i
$248$	29.2775	−	21.2714i	1.85912	−	1.35073i
$249$		0			0
$250$	−6.29813	+	19.3837i	−0.398329	+	1.22593i
$251$	−24.1522	−	17.5476i	−1.52448	−	1.10760i	−0.959213	−	0.282685i	$-0.908775\pi$
$251$	−24.1522	−	17.5476i	−1.52448	−	1.10760i	−0.565263	−	0.824911i	$-0.691225\pi$
$252$		0			0
$253$	14.3007	−	16.2518i	0.899078	−	1.02174i
$254$	−24.7710			−1.55427
$255$		0			0
$256$	−8.64108	+	26.5945i	−0.540067	+	1.66216i
$257$	−0.876598	−	2.69789i	−0.0546807	−	0.168290i	0.919987	−	0.391950i	$-0.128199\pi$
$257$	−0.876598	−	2.69789i	−0.0546807	−	0.168290i	−0.974667	+	0.223660i	$0.928199\pi$
$258$		0			0
$259$	7.23503	−	5.25656i	0.449563	−	0.326627i
$260$	20.1510	+	62.0183i	1.24971	+	3.84621i
$261$		0			0
$262$	−22.5168	−	16.3594i	−1.39109	−	1.01069i
$263$	−10.2373			−0.631262			−0.315631	−	0.948882i	$-0.602216\pi$
$263$	−10.2373			−0.631262			−0.315631	+	0.948882i	$0.602216\pi$
$264$		0			0
$265$	−4.91978			−0.302219
$266$	−2.02171	−	1.46886i	−0.123959	−	0.0900613i
$267$		0			0
$268$	−8.41848	−	25.9094i	−0.514241	−	1.58267i
$269$	8.12925	−	5.90624i	0.495649	−	0.360110i	−0.311704	−	0.950179i	$-0.600900\pi$
$269$	8.12925	−	5.90624i	0.495649	−	0.360110i	0.807353	+	0.590069i	$0.200900\pi$
$270$		0			0
$271$	−0.773878	−	2.38175i	−0.0470098	−	0.144681i	0.924796	−	0.380462i	$-0.124235\pi$
$271$	−0.773878	−	2.38175i	−0.0470098	−	0.144681i	−0.971806	+	0.235781i	$0.924235\pi$
$272$	2.29575	−	7.06560i	0.139200	−	0.428415i
$273$		0			0
$274$	37.0239			2.23670
$275$	−2.88772	−	4.87240i	−0.174136	−	0.293817i
$276$		0			0
$277$	12.0631	+	8.76435i	0.724801	+	0.526599i	0.887915	−	0.460008i	$-0.152154\pi$
$277$	12.0631	+	8.76435i	0.724801	+	0.526599i	−0.163113	+	0.986607i	$0.552154\pi$
$278$	−4.29741	+	13.2261i	−0.257741	+	0.793247i
$279$		0			0
$280$	8.58084	−	6.23435i	0.512804	−	0.372574i
$281$	1.65586	−	1.20305i	0.0987805	−	0.0717682i	−0.537299	−	0.843392i	$-0.680555\pi$
$281$	1.65586	−	1.20305i	0.0987805	−	0.0717682i	0.636079	+	0.771624i	$0.280555\pi$
$282$		0			0
$283$	5.27563	−	16.2367i	0.313604	−	0.965174i	−0.662721	−	0.748866i	$-0.730599\pi$
$283$	5.27563	−	16.2367i	0.313604	−	0.965174i	0.976325	−	0.216307i	$-0.0694014\pi$
$284$	8.13200	+	5.90824i	0.482545	+	0.350590i
$285$		0			0
$286$	49.3522	+	21.3015i	2.91826	+	1.25959i
$287$	8.69747			0.513395
$288$		0			0
$289$	−2.19658	+	6.76039i	−0.129211	+	0.397670i
$290$	1.16176	+	3.57552i	0.0682208	+	0.209962i
$291$		0			0
$292$	−1.77222	+	1.28760i	−0.103712	+	0.0753508i
$293$	8.26173	+	25.4270i	0.482655	+	1.48546i	0.835348	+	0.549721i	$0.185266\pi$
$293$	8.26173	+	25.4270i	0.482655	+	1.48546i	−0.352693	+	0.935739i	$0.614734\pi$
$294$		0			0
$295$	−0.364594	−	0.264893i	−0.0212275	−	0.0154227i
$296$	36.6242			2.12874
$297$		0			0
$298$	34.4540			1.99587
$299$	−35.8046	−	26.0136i	−2.07063	−	1.50440i
$300$		0			0
$301$	−1.38489	−	4.26225i	−0.0798237	−	0.245672i
$302$	42.9625	−	31.2141i	2.47222	−	1.79617i
$303$		0			0
$304$	−0.763142	−	2.34871i	−0.0437692	−	0.134708i
$305$	6.51019	−	20.0363i	0.372772	−	1.14728i
$306$		0			0
$307$	−16.3329			−0.932166			−0.466083	−	0.884741i	$-0.654335\pi$
$307$	−16.3329			−0.932166			−0.466083	+	0.884741i	$0.654335\pi$
$308$	1.14748	−	12.2621i	0.0653838	−	0.698700i
$309$		0			0
$310$	44.2569	+	32.1545i	2.51362	+	1.82625i
$311$	−8.05494	+	24.7906i	−0.456754	+	1.40574i	0.412310	+	0.911043i	$0.364722\pi$
$311$	−8.05494	+	24.7906i	−0.456754	+	1.40574i	−0.869064	+	0.494700i	$0.835278\pi$
$312$		0			0
$313$	17.3831	−	12.6295i	0.982549	−	0.713864i	0.0242721	−	0.999705i	$-0.492273\pi$
$313$	17.3831	−	12.6295i	0.982549	−	0.713864i	0.958277	+	0.285842i	$0.0922732\pi$
$314$	18.9339	−	13.7563i	1.06850	−	0.776313i
$315$		0			0
$316$	−11.2552	+	34.6400i	−0.633155	+	1.94865i
$317$	−20.0804	−	14.5893i	−1.12783	−	0.819417i	−0.142453	−	0.989802i	$-0.545499\pi$
$317$	−20.0804	−	14.5893i	−1.12783	−	0.819417i	−0.985378	+	0.170385i	$0.945499\pi$
$318$		0			0
$319$	1.84927	+	0.798188i	0.103539	+	0.0446900i
$320$	−27.9872			−1.56453
$321$		0			0
$322$	−4.82109	+	14.8378i	−0.268669	+	0.826878i
$323$	−1.01609	−	3.12721i	−0.0565370	−	0.174003i
$324$		0			0
$325$	−9.36776	+	6.80608i	−0.519630	+	0.377533i
$326$	8.39365	+	25.8330i	0.464881	+	1.43076i
$327$		0			0
$328$	28.8161	+	20.9361i	1.59110	+	1.15600i
$329$	3.26290			0.179889
$330$		0			0
$331$	−31.6351			−1.73882			−0.869411	−	0.494089i	$-0.835502\pi$
$331$	−31.6351			−1.73882			−0.869411	+	0.494089i	$0.835502\pi$
$332$	26.2736	+	19.0889i	1.44195	+	1.04764i
$333$		0			0
$334$	3.75881	+	11.5684i	0.205673	+	0.632996i
$335$	15.3721	−	11.1685i	0.839867	−	0.610199i
$336$		0			0
$337$	−10.1381	−	31.2018i	−0.552256	−	1.69967i	−0.703081	−	0.711110i	$-0.748193\pi$
$337$	−10.1381	−	31.2018i	−0.552256	−	1.69967i	0.150825	−	0.988560i	$-0.451807\pi$
$338$	24.3566	−	74.9619i	1.32482	−	4.07739i
$339$		0			0
$340$	30.2473			1.64039
$341$	28.5963	−	6.42026i	1.54857	−	0.347677i
$342$		0			0
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	5.67153	−	17.4552i	0.305788	−	0.941119i
$345$		0			0
$346$	15.0343	−	10.9231i	0.808251	−	0.587228i
$347$	11.3979	−	8.28107i	0.611872	−	0.444551i	−0.238201	−	0.971216i	$-0.576558\pi$
$347$	11.3979	−	8.28107i	0.611872	−	0.444551i	0.850073	+	0.526665i	$0.176558\pi$
$348$		0			0
$349$	−6.87264	+	21.1518i	−0.367884	+	1.13223i	0.580271	+	0.814423i	$0.302947\pi$
$349$	−6.87264	+	21.1518i	−0.367884	+	1.13223i	−0.948155	+	0.317807i	$0.897053\pi$
$350$	3.30231	+	2.39927i	0.176516	+	0.128246i
$351$		0			0
$352$	−5.57484	+	6.33541i	−0.297140	+	0.337679i
$353$	−15.2345			−0.810850			−0.405425	−	0.914128i	$-0.632876\pi$
$353$	−15.2345			−0.810850			−0.405425	+	0.914128i	$0.632876\pi$
$354$		0			0
$355$	−2.16644	+	6.66761i	−0.114983	+	0.353880i
$356$	13.4012	+	41.2447i	0.710264	+	2.18597i
$357$		0			0
$358$	−11.8847	+	8.63473i	−0.628125	+	0.456360i
$359$	−4.77379	−	14.6922i	−0.251951	−	0.775425i	−0.994415	−	0.105539i	$-0.966343\pi$
$359$	−4.77379	−	14.6922i	−0.251951	−	0.775425i	0.742464	−	0.669886i	$-0.233657\pi$
$360$		0			0
$361$	14.4870	+	10.5255i	0.762476	+	0.553971i
$362$	−22.1290			−1.16308
$363$		0			0
$364$	−25.1783			−1.31970
$365$	−1.23607	−	0.898056i	−0.0646988	−	0.0470064i
$366$		0			0
$367$	8.75723	+	26.9520i	0.457124	+	1.40688i	0.868624	+	0.495472i	$0.165005\pi$
$367$	8.75723	+	26.9520i	0.457124	+	1.40688i	−0.411500	+	0.911410i	$0.634995\pi$
$368$	−12.4734	+	9.06243i	−0.650219	+	0.472412i
$369$		0			0
$370$	17.1079	+	52.6528i	0.889398	+	2.73729i
$371$	0.587003	−	1.80661i	0.0304757	−	0.0937945i
$372$		0			0
$373$	−1.01940			−0.0527828			−0.0263914	−	0.999652i	$-0.508402\pi$
$373$	−1.01940			−0.0527828			−0.0263914	+	0.999652i	$0.508402\pi$
$374$	16.4710	−	18.7181i	0.851694	−	0.967890i
$375$		0			0
$376$	10.8105	+	7.85430i	0.557510	+	0.405054i
$377$	1.27247	−	3.91625i	0.0655354	−	0.201697i
$378$		0			0
$379$	7.20632	−	5.23569i	0.370164	−	0.268940i	−0.387115	−	0.922031i	$-0.626528\pi$
$379$	7.20632	−	5.23569i	0.370164	−	0.268940i	0.757279	+	0.653092i	$0.226528\pi$
$380$	8.13437	−	5.90997i	0.417284	−	0.303175i
$381$		0			0
$382$	10.8117	−	33.2748i	0.553172	−	1.70249i
$383$	7.93470	+	5.76490i	0.405444	+	0.294573i	0.771755	−	0.635920i	$-0.219379\pi$
$383$	7.93470	+	5.76490i	0.405444	+	0.294573i	−0.366311	+	0.930493i	$0.619379\pi$
$384$		0			0
$385$	8.38118	−	1.88169i	0.427144	−	0.0958999i
$386$	−39.3707			−2.00392
$387$		0			0
$388$	13.6009	−	41.8593i	0.690481	−	2.12508i
$389$	−7.46028	−	22.9604i	−0.378251	−	1.16414i	−0.941259	−	0.337686i	$-0.890356\pi$
$389$	−7.46028	−	22.9604i	−0.378251	−	1.16414i	0.563007	−	0.826452i	$-0.309644\pi$
$390$		0			0
$391$	−16.6078	+	12.0663i	−0.839892	+	0.610217i
$392$	1.26552	+	3.89486i	0.0639182	+	0.196720i
$393$		0			0
$394$	−13.1815	−	9.57694i	−0.664076	−	0.482480i
$395$	−25.4036			−1.27819
$396$		0			0
$397$	20.6730			1.03755			0.518773	−	0.854912i	$-0.326389\pi$
$397$	20.6730			1.03755			0.518773	+	0.854912i	$0.326389\pi$
$398$	−30.0818	−	21.8557i	−1.50786	−	1.09553i
$399$		0			0
$400$	1.24654	+	3.83645i	0.0623268	+	0.191822i
$401$	−20.4007	+	14.8220i	−1.01876	+	0.740173i	−0.966029	−	0.258435i	$-0.916793\pi$
$401$	−20.4007	+	14.8220i	−1.01876	+	0.740173i	−0.0527328	+	0.998609i	$0.516793\pi$
$402$		0			0
$403$	−18.5155	−	56.9850i	−0.922325	−	2.83862i
$404$	−4.26685	+	13.1320i	−0.212284	+	0.653343i
$405$		0			0
$406$	−1.45160			−0.0720416
$407$	27.2322	+	11.7540i	1.34985	+	0.582625i
$408$		0			0
$409$	−8.21625	−	5.96946i	−0.406267	−	0.295171i	0.365822	−	0.930685i	$-0.380788\pi$
$409$	−8.21625	−	5.96946i	−0.406267	−	0.295171i	−0.772089	+	0.635514i	$0.780788\pi$
$410$	−16.6382	+	51.2072i	−0.821704	+	2.52894i
$411$		0			0
$412$	−22.0115	+	15.9923i	−1.08443	+	0.787882i
$413$	0.140774	−	0.102278i	0.00692704	−	0.00503279i
$414$		0			0
$415$	−6.99951	+	21.5423i	−0.343593	+	1.05747i
$416$	13.9577	+	10.1409i	0.684332	+	0.497196i
$417$		0			0
$418$	0.772223	−	8.25208i	0.0377707	−	0.403622i
$419$	28.3684			1.38589			0.692943	−	0.720993i	$-0.256314\pi$
$419$	28.3684			1.38589			0.692943	+	0.720993i	$0.256314\pi$
$420$		0			0
$421$	−8.55479	+	26.3289i	−0.416935	+	1.28319i	0.493574	+	0.869704i	$0.335690\pi$
$421$	−8.55479	+	26.3289i	−0.416935	+	1.28319i	−0.910509	+	0.413490i	$0.864310\pi$
$422$	1.15569	+	3.55685i	0.0562581	+	0.173145i
$423$		0			0
$424$	6.29362	−	4.57259i	0.305645	−	0.222064i
$425$	1.65971	+	5.10808i	0.0805080	+	0.247778i
$426$		0			0
$427$	6.58084	+	4.78126i	0.318469	+	0.231382i
$428$	−49.6858			−2.40165
$429$		0			0
$430$	27.7437			1.33792
$431$	5.91592	+	4.29817i	0.284960	+	0.207035i	0.721078	−	0.692854i	$-0.243647\pi$
$431$	5.91592	+	4.29817i	0.284960	+	0.207035i	−0.436118	+	0.899889i	$0.643647\pi$
$432$		0			0
$433$	−3.25461	−	10.0167i	−0.156406	−	0.481369i	0.841894	−	0.539643i	$-0.181441\pi$
$433$	−3.25461	−	10.0167i	−0.156406	−	0.481369i	−0.998301	+	0.0582730i	$0.981441\pi$
$434$	−17.0881	+	12.4152i	−0.820255	+	0.595950i
$435$		0			0
$436$	16.2057	+	49.8760i	0.776112	+	2.38863i
$437$	−2.10871	+	6.48994i	−0.100873	+	0.310456i
$438$		0			0
$439$	−0.574098			−0.0274002			−0.0137001	−	0.999906i	$-0.504361\pi$
$439$	−0.574098			−0.0274002			−0.0137001	+	0.999906i	$0.504361\pi$
$440$	32.2977	+	13.9404i	1.53973	+	0.664584i
$441$		0			0
$442$	−41.2383	−	29.9614i	−1.96150	−	1.42512i
$443$	5.62774	−	17.3204i	0.267382	−	0.822917i	−0.723753	−	0.690059i	$-0.757585\pi$
$443$	5.62774	−	17.3204i	0.267382	−	0.822917i	0.991135	−	0.132858i	$-0.0424154\pi$
$444$		0			0
$445$	−24.4706	+	17.7789i	−1.16002	+	0.842801i
$446$	−8.00433	+	5.81549i	−0.379016	+	0.275371i
$447$		0			0
$448$	3.33929	−	10.2773i	0.157767	−	0.485556i
$449$	3.58700	+	2.60611i	0.169281	+	0.122990i	0.669200	−	0.743082i	$-0.266637\pi$
$449$	3.58700	+	2.60611i	0.169281	+	0.122990i	−0.499919	+	0.866072i	$0.666637\pi$
$450$		0			0
$451$	14.7073	+	24.8153i	0.692538	+	1.16851i
$452$	9.89050			0.465210
$453$		0			0
$454$	4.11979	−	12.6794i	0.193351	−	0.595074i
$455$	−5.42666	−	16.7015i	−0.254406	−	0.782980i
$456$		0			0
$457$	16.4174	−	11.9280i	0.767976	−	0.557967i	−0.133371	−	0.991066i	$-0.542580\pi$
$457$	16.4174	−	11.9280i	0.767976	−	0.557967i	0.901346	+	0.433099i	$0.142580\pi$
$458$	−0.582356	−	1.79231i	−0.0272117	−	0.0837491i
$459$		0			0
$460$	−50.7840	−	36.8967i	−2.36782	−	1.72032i
$461$	4.85723			0.226224			0.113112	−	0.993582i	$-0.463918\pi$
$461$	4.85723			0.226224			0.113112	+	0.993582i	$0.463918\pi$
$462$		0			0
$463$	−19.5168			−0.907024			−0.453512	−	0.891250i	$-0.649829\pi$
$463$	−19.5168			−0.907024			−0.453512	+	0.891250i	$0.649829\pi$
$464$	−1.16056	−	0.843194i	−0.0538775	−	0.0391443i
$465$		0			0
$466$	−20.4649	−	62.9846i	−0.948020	−	2.91771i
$467$	−2.22175	+	1.61420i	−0.102810	+	0.0746961i	−0.638003	−	0.770034i	$-0.720239\pi$
$467$	−2.22175	+	1.61420i	−0.102810	+	0.0746961i	0.535192	+	0.844730i	$0.320239\pi$
$468$		0			0
$469$	2.26710	+	6.97741i	0.104685	+	0.322187i
$470$	−6.24191	+	19.2106i	−0.287918	+	0.886120i
$471$		0			0
$472$	0.712607			0.0328004
$473$	9.81910	−	11.1587i	0.451483	−	0.513078i
$474$		0			0
$475$	1.44440	+	1.04942i	0.0662738	+	0.0481508i
$476$	−3.60895	+	11.1072i	−0.165416	+	0.509098i
$477$		0			0
$478$	−16.5940	+	12.0563i	−0.758992	+	0.551440i
$479$	−14.5827	+	10.5950i	−0.666302	+	0.484097i	−0.868785	−	0.495189i	$-0.835099\pi$
$479$	−14.5827	+	10.5950i	−0.666302	+	0.484097i	0.202483	+	0.979286i	$0.435099\pi$
$480$		0			0
$481$	18.7382	−	57.6703i	0.854388	−	2.62954i
$482$	37.9774	+	27.5922i	1.72982	+	1.25679i
$483$		0			0
$484$	36.9263	−	17.4611i	1.67847	−	0.793687i
$485$	30.6979			1.39392
$486$		0			0
$487$	−3.82668	+	11.7773i	−0.173404	+	0.533681i	−0.999557	−	0.0297639i	$-0.990524\pi$
$487$	−3.82668	+	11.7773i	−0.173404	+	0.533681i	0.826153	+	0.563445i	$0.190524\pi$
$488$	10.2942	+	31.6822i	0.465995	+	1.43419i
$489$		0			0
$490$	−5.00829	+	3.63874i	−0.226252	+	0.164381i
$491$	−5.13486	−	15.8035i	−0.231733	−	0.713201i	−0.997538	−	0.0701280i	$-0.977659\pi$
$491$	−5.13486	−	15.8035i	−0.231733	−	0.713201i	0.765805	−	0.643073i	$-0.222341\pi$
$492$		0			0
$493$	−1.54524	−	1.12268i	−0.0695939	−	0.0505629i
$494$	−16.9443			−0.762359
$495$		0			0
$496$	−20.8737			−0.937255
$497$	−2.18995	−	1.59109i	−0.0982326	−	0.0713702i
$498$		0			0
$499$	−6.29931	−	19.3873i	−0.281996	−	0.867894i	−0.987283	−	0.158972i	$-0.949182\pi$
$499$	−6.29931	−	19.3873i	−0.281996	−	0.867894i	0.705287	−	0.708922i	$-0.250818\pi$
$500$	25.6157	−	18.6109i	1.14557	−	0.832303i
$501$		0			0
$502$	22.0509	+	67.8657i	0.984180	+	3.02900i
$503$	−2.06474	+	6.35462i	−0.0920622	+	0.283338i	−0.986477	−	0.163900i	$-0.947593\pi$
$503$	−2.06474	+	6.35462i	−0.0920622	+	0.283338i	0.894415	+	0.447239i	$0.147593\pi$
$504$		0			0
$505$	−9.63051			−0.428552
$506$	−50.4871	+	11.3351i	−2.24443	+	0.503905i
$507$		0			0
$508$	31.1329	+	22.6194i	1.38130	+	1.00357i
$509$	5.65853	−	17.4152i	0.250810	−	0.771914i	−0.743816	−	0.668384i	$-0.766986\pi$
$509$	5.65853	−	17.4152i	0.250810	−	0.771914i	0.994626	−	0.103530i	$-0.0330138\pi$
$510$		0			0
$511$	0.477260	−	0.346750i	0.0211127	−	0.0153393i
$512$	20.5148	−	14.9049i	0.906637	−	0.658710i
$513$		0			0
$514$	−2.09529	+	6.44865i	−0.0924195	+	0.284438i
$515$	−15.3523	−	11.1541i	−0.676502	−	0.491508i
$516$		0			0
$517$	5.51750	+	9.30960i	0.242660	+	0.409436i
$518$	−21.3761			−0.939210
$519$		0			0
$520$	22.2238	−	68.3977i	0.974576	−	2.99944i
$521$	0.181507	+	0.558621i	0.00795197	+	0.0244736i	0.954954	−	0.296755i	$-0.0959043\pi$
$521$	0.181507	+	0.558621i	0.00795197	+	0.0244736i	−0.947002	+	0.321228i	$0.895904\pi$
$522$		0			0
$523$	−23.1458	+	16.8164i	−1.01210	+	0.735331i	−0.964648	−	0.263543i	$-0.915109\pi$
$523$	−23.1458	+	16.8164i	−1.01210	+	0.735331i	−0.0474487	+	0.998874i	$0.515109\pi$
$524$	13.3614	+	41.1220i	0.583694	+	1.79642i
$525$		0			0
$526$	19.7966	+	14.3830i	0.863171	+	0.627130i
$527$	−27.7925			−1.21066
$528$		0			0
$529$	19.6027			0.852291
$530$	9.51366	+	6.91208i	0.413247	+	0.300241i
$531$		0			0
$532$	1.19967	+	3.69220i	0.0520122	+	0.160077i
$533$	47.7104	−	34.6636i	2.06657	−	1.50145i
$534$		0			0
$535$	−10.7087	−	32.9581i	−0.462979	−	1.42490i
$536$	−9.28444	+	28.5746i	−0.401027	+	1.23423i
$537$		0			0
$538$	−24.0180			−1.03549
$539$	−0.309017	+	3.30220i	−0.0133103	+	0.142236i
$540$		0			0
$541$	−4.99897	−	3.63196i	−0.214922	−	0.156150i	0.475116	−	0.879923i	$-0.342406\pi$
$541$	−4.99897	−	3.63196i	−0.214922	−	0.156150i	−0.690038	+	0.723773i	$0.742406\pi$
$542$	−1.84977	+	5.69300i	−0.0794543	+	0.244535i
$543$		0			0
$544$	6.47420	−	4.70378i	0.277579	−	0.201673i
$545$	−29.5915	+	21.4995i	−1.26756	+	0.920937i
$546$		0			0
$547$	−1.87099	+	5.75830i	−0.0799976	+	0.246207i	−0.983054	−	0.183314i	$-0.941318\pi$
$547$	−1.87099	+	5.75830i	−0.0799976	+	0.246207i	0.903057	+	0.429521i	$0.141318\pi$
$548$	−46.5327	−	33.8080i	−1.98778	−	1.44421i
$549$		0			0
$550$	−1.26137	+	13.4792i	−0.0537850	+	0.574754i
$551$	−0.634918			−0.0270484
$552$		0			0
$553$	3.03103	−	9.32855i	0.128893	−	0.396690i
$554$	−11.0136	−	33.8963i	−0.467922	−	1.44011i
$555$		0			0
$556$	17.4784	−	12.6988i	0.741248	−	0.538548i
$557$	1.85039	+	5.69491i	0.0784035	+	0.241301i	0.982574	−	0.185870i	$-0.0595103\pi$
$557$	1.85039	+	5.69491i	0.0784035	+	0.241301i	−0.904171	+	0.427171i	$0.859510\pi$
$558$		0			0
$559$	−24.5840	−	17.8613i	−1.03979	−	0.755454i
$560$	−6.11779			−0.258524
$561$		0			0
$562$	−4.89228			−0.206368
$563$	29.2653	+	21.2625i	1.23338	+	0.896106i	0.997139	−	0.0755874i	$-0.0240832\pi$
$563$	29.2653	+	21.2625i	1.23338	+	0.896106i	0.236245	+	0.971694i	$0.424083\pi$
$564$		0			0
$565$	2.13169	+	6.56068i	0.0896810	+	0.276010i
$566$	−33.0137	+	23.9859i	−1.38767	+	1.00820i
$567$		0			0
$568$	−3.42566	−	10.5431i	−0.143737	−	0.442378i
$569$	−10.3428	+	31.8319i	−0.433594	+	1.33446i	0.460927	+	0.887438i	$0.347517\pi$
$569$	−10.3428	+	31.8319i	−0.433594	+	1.33446i	−0.894521	+	0.447026i	$0.852483\pi$
$570$		0			0
$571$	−4.96371			−0.207725			−0.103862	−	0.994592i	$-0.533120\pi$
$571$	−4.96371			−0.207725			−0.103862	+	0.994592i	$0.533120\pi$
$572$	−42.5760	−	71.8379i	−1.78019	−	3.00369i
$573$		0			0
$574$	−16.8188	−	12.2196i	−0.702003	−	0.510035i
$575$	3.44442	−	10.6008i	0.143642	−	0.442086i
$576$		0			0
$577$	−9.80923	+	7.12682i	−0.408364	+	0.296694i	−0.772939	−	0.634480i	$-0.781214\pi$
$577$	−9.80923	+	7.12682i	−0.408364	+	0.296694i	0.364575	+	0.931174i	$0.381214\pi$
$578$	13.7457	−	9.98686i	0.571747	−	0.415398i
$579$		0			0
$580$	1.80482	−	5.55467i	0.0749412	−	0.230645i
$581$	−7.07548	−	5.14063i	−0.293540	−	0.213269i
$582$		0			0
$583$	6.14718	−	1.38013i	0.254590	−	0.0571590i
$584$	2.41592			0.0999715
$585$		0			0
$586$	19.7477	−	60.7770i	0.815768	−	2.51068i
$587$	1.48194	+	4.56094i	0.0611661	+	0.188250i	0.976970	−	0.213375i	$-0.0684456\pi$
$587$	1.48194	+	4.56094i	0.0611661	+	0.188250i	−0.915804	+	0.401625i	$0.868446\pi$
$588$		0			0
$589$	−7.47420	+	5.43033i	−0.307969	+	0.223753i
$590$	0.332873	+	1.02448i	0.0137042	+	0.0421771i
$591$		0			0
$592$	−17.0902	−	12.4168i	−0.702404	−	0.510326i
$593$	−15.3387			−0.629886			−0.314943	−	0.949111i	$-0.601985\pi$
$593$	−15.3387			−0.629886			−0.314943	+	0.949111i	$0.601985\pi$
$594$		0			0
$595$	−8.14560			−0.333937
$596$	−43.3028	−	31.4613i	−1.77375	−	1.28871i
$597$		0			0
$598$	32.6895	+	100.608i	1.33677	+	4.11416i
$599$	−37.3303	+	27.1220i	−1.52527	+	1.10818i	−0.566478	+	0.824077i	$0.691694\pi$
$599$	−37.3303	+	27.1220i	−1.52527	+	1.10818i	−0.958795	+	0.284099i	$0.908306\pi$
$600$		0			0
$601$	9.65222	+	29.7065i	0.393722	+	1.21175i	0.929952	+	0.367681i	$0.119848\pi$
$601$	9.65222	+	29.7065i	0.393722	+	1.21175i	−0.536230	+	0.844072i	$0.680152\pi$
$602$	−3.31024	+	10.1879i	−0.134915	+	0.415227i
$603$		0			0
$604$	−82.4994			−3.35685
$605$	19.5412	+	20.7310i	0.794463	+	0.842835i
$606$		0			0
$607$	11.9173	+	8.65845i	0.483710	+	0.351436i	0.802760	−	0.596302i	$-0.203364\pi$
$607$	11.9173	+	8.65845i	0.483710	+	0.351436i	−0.319051	+	0.947738i	$0.603364\pi$
$608$	0.822037	−	2.52997i	0.0333380	−	0.102604i
$609$		0			0
$610$	−40.7393	+	29.5988i	−1.64949	+	1.19842i
$611$	17.8988	−	13.0042i	0.724108	−	0.526095i
$612$		0			0
$613$	−8.53268	+	26.2609i	−0.344632	+	1.06067i	0.617149	+	0.786846i	$0.288287\pi$
$613$	−8.53268	+	26.2609i	−0.344632	+	1.06067i	−0.961781	+	0.273821i	$0.911713\pi$
$614$	31.5838	+	22.9470i	1.27462	+	0.926065i
$615$		0			0
$616$	−8.97272	+	10.1969i	−0.361521	+	0.410843i
$617$	−3.29610			−0.132696			−0.0663479	−	0.997797i	$-0.521135\pi$
$617$	−3.29610			−0.132696			−0.0663479	+	0.997797i	$0.521135\pi$
$618$		0			0
$619$	−1.11467	+	3.43059i	−0.0448022	+	0.137887i	−0.970955	−	0.239261i	$-0.923095\pi$
$619$	−1.11467	+	3.43059i	−0.0448022	+	0.137887i	0.926153	+	0.377147i	$0.123095\pi$
$620$	−26.2618	−	80.8255i	−1.05470	−	3.24603i
$621$		0			0
$622$	50.4060	−	36.6221i	2.02110	−	1.46841i
$623$	−3.60895	−	11.1072i	−0.144590	−	0.445001i
$624$		0			0
$625$	24.7739	+	17.9993i	0.990958	+	0.719973i
$626$	−51.3586			−2.05270
$627$		0			0
$628$	−36.3581			−1.45085
$629$	−22.7550	−	16.5324i	−0.907300	−	0.659192i
$630$		0			0
$631$	−13.3409	−	41.0591i	−0.531093	−	1.63454i	−0.751942	−	0.659229i	$-0.770883\pi$
$631$	−13.3409	−	41.0591i	−0.531093	−	1.63454i	0.220849	−	0.975308i	$-0.429117\pi$
$632$	32.4976	−	23.6109i	1.29268	−	0.939189i
$633$		0			0
$634$	18.3334	+	56.4244i	0.728112	+	2.24090i
$635$	−8.29408	+	25.5266i	−0.329141	+	1.01299i
$636$		0			0
$637$	6.78051			0.268654
$638$	−2.45463	−	4.14165i	−0.0971796	−	0.163970i
$639$		0			0
$640$	43.4578	+	31.5739i	1.71782	+	1.24807i
$641$	−7.71648	+	23.7489i	−0.304783	+	0.938025i	0.674975	+	0.737840i	$0.264154\pi$
$641$	−7.71648	+	23.7489i	−0.304783	+	0.938025i	−0.979758	+	0.200185i	$0.935846\pi$
$642$		0			0
$643$	6.58786	−	4.78636i	0.259800	−	0.188756i	−0.450259	−	0.892898i	$-0.648668\pi$
$643$	6.58786	−	4.78636i	0.259800	−	0.188756i	0.710059	+	0.704142i	$0.248668\pi$
$644$	19.6083	−	14.2462i	0.772674	−	0.561381i
$645$		0			0
$646$	−2.42872	+	7.47485i	−0.0955569	+	0.294094i
$647$	32.2628	+	23.4403i	1.26838	+	0.921534i	0.999137	−	0.0415375i	$-0.0132256\pi$
$647$	32.2628	+	23.4403i	1.26838	+	0.921534i	0.269246	+	0.963072i	$0.413226\pi$
$648$		0			0
$649$	0.529864	+	0.228701i	0.0207990	+	0.00897731i
$650$	27.6772			1.08559
$651$		0			0
$652$	13.0398	−	40.1322i	0.510676	−	1.57170i
$653$	−0.505763	−	1.55658i	−0.0197920	−	0.0609136i	0.940673	−	0.339315i	$-0.110195\pi$
$653$	−0.505763	−	1.55658i	−0.0197920	−	0.0609136i	−0.960465	+	0.278402i	$0.910195\pi$
$654$		0			0
$655$	−24.3978	+	17.7260i	−0.953299	+	0.692612i
$656$	−6.34867	−	19.5392i	−0.247874	−	0.762877i
$657$		0			0
$658$	−6.30966	−	4.58423i	−0.245976	−	0.178712i
$659$	7.63149			0.297281			0.148640	−	0.988891i	$-0.452510\pi$
$659$	7.63149			0.297281			0.148640	+	0.988891i	$0.452510\pi$
$660$		0			0
$661$	20.4402			0.795031			0.397516	−	0.917595i	$-0.369872\pi$
$661$	20.4402			0.795031			0.397516	+	0.917595i	$0.369872\pi$
$662$	61.1746	+	44.4460i	2.37762	+	1.72744i
$663$		0			0
$664$	−11.0679	−	34.0635i	−0.429518	−	1.32192i
$665$	−2.19059	+	1.59156i	−0.0849474	+	0.0617179i
$666$		0			0
$667$	1.22491	+	3.76987i	0.0474285	+	0.145970i
$668$	5.83941	−	17.9719i	0.225934	−	0.695352i
$669$		0			0
$670$	−45.4172			−1.75462
$671$	−2.51366	+	26.8613i	−0.0970387	+	1.03697i
$672$		0			0
$673$	19.4612	+	14.1394i	0.750176	+	0.545035i	0.895881	−	0.444293i	$-0.146545\pi$
$673$	19.4612	+	14.1394i	0.750176	+	0.545035i	−0.145705	+	0.989328i	$0.546545\pi$
$674$	−24.2326	+	74.5803i	−0.933405	+	2.87273i
$675$		0			0
$676$	−99.0628	+	71.9733i	−3.81011	+	2.76821i
$677$	−6.50994	+	4.72974i	−0.250197	+	0.181779i	−0.705814	−	0.708397i	$-0.749419\pi$
$677$	−6.50994	+	4.72974i	−0.250197	+	0.181779i	0.455617	+	0.890176i	$0.349419\pi$
$678$		0			0
$679$	−3.66272	+	11.2727i	−0.140562	+	0.432607i
$680$	−26.9877	−	19.6077i	−1.03493	−	0.751921i
$681$		0			0
$682$	−64.3185	−	27.7613i	−2.46288	−	1.06304i
$683$	19.2894			0.738089			0.369045	−	0.929412i	$-0.379685\pi$
$683$	19.2894			0.738089			0.369045	+	0.929412i	$0.379685\pi$
$684$		0			0
$685$	12.3967	−	38.1532i	0.473655	−	1.45776i
$686$	−0.738630	−	2.27327i	−0.0282010	−	0.0867938i
$687$		0			0
$688$	−8.56441	+	6.22241i	−0.326515	+	0.237227i
$689$	−3.98018	−	12.2497i	−0.151633	−	0.466678i
$690$		0			0
$691$	25.7744	+	18.7262i	0.980505	+	0.712379i	0.957821	−	0.287364i	$-0.0927789\pi$
$691$	25.7744	+	18.7262i	0.980505	+	0.712379i	0.0226837	+	0.999743i	$0.492779\pi$
$692$	−28.8699			−1.09747
$693$		0			0
$694$	−33.6753			−1.27830
$695$	12.1906	+	8.85698i	0.462415	+	0.335964i
$696$		0			0
$697$	−8.45300	−	26.0157i	−0.320180	−	0.985413i
$698$	43.0074	−	31.2467i	1.62786	−	1.18271i
$699$		0			0
$700$	−1.95957	−	6.03094i	−0.0740649	−	0.227948i
$701$	10.8378	−	33.3555i	0.409340	−	1.25982i	−0.507877	−	0.861430i	$-0.669570\pi$
$701$	10.8378	−	33.3555i	0.409340	−	1.25982i	0.917217	−	0.398389i	$-0.130430\pi$
$702$		0			0
$703$	−9.34972			−0.352631
$704$	34.9695	−	7.85115i	1.31796	−	0.295901i
$705$		0			0
$706$	29.4598	+	21.4038i	1.10873	+	0.805543i
$707$	1.14906	−	3.53646i	0.0432150	−	0.133002i
$708$		0			0
$709$	11.2499	−	8.17356i	0.422500	−	0.306965i	−0.356143	−	0.934432i	$-0.615908\pi$
$709$	11.2499	−	8.17356i	0.422500	−	0.306965i	0.778643	+	0.627467i	$0.215908\pi$
$710$	13.5571	−	9.84979i	0.508788	−	0.369656i
$711$		0			0
$712$	14.7797	−	45.4873i	0.553894	−	1.70471i
$713$	46.6625	+	33.9023i	1.74752	+	1.26965i
$714$		0			0
$715$	38.4759	−	43.7252i	1.43892	−	1.63523i
$716$	22.8217			0.852888
$717$		0			0
$718$	−11.4106	+	35.1181i	−0.425839	+	1.31060i
$719$	12.6402	+	38.9026i	0.471401	+	1.45082i	0.850751	+	0.525570i	$0.176148\pi$
$719$	12.6402	+	38.9026i	0.471401	+	1.45082i	−0.379350	+	0.925253i	$0.623852\pi$
$720$		0			0
$721$	5.92769	−	4.30672i	0.220759	−	0.160391i
$722$	−13.2266	−	40.7074i	−0.492244	−	1.51497i
$723$		0			0
$724$	27.8124	+	20.2069i	1.03364	+	0.750983i
$725$	1.03709			0.0385166
$726$		0			0
$727$	−28.5963			−1.06058			−0.530288	−	0.847817i	$-0.677916\pi$
$727$	−28.5963			−1.06058			−0.530288	+	0.847817i	$0.677916\pi$
$728$	22.4649	+	16.3217i	0.832606	+	0.604924i
$729$		0			0
$730$	1.12853	+	3.47325i	0.0417686	+	0.128551i
$731$	−11.4032	+	8.28489i	−0.421762	+	0.306428i
$732$		0			0
$733$	4.74381	+	14.6000i	0.175217	+	0.539262i	0.999643	−	0.0267073i	$-0.00850221\pi$
$733$	4.74381	+	14.6000i	0.175217	+	0.539262i	−0.824427	+	0.565969i	$0.808502\pi$
$734$	20.9320	−	64.4221i	0.772615	−	2.37786i
$735$		0			0
$736$	−16.6078			−0.612171
$737$	−16.0741	+	18.2671i	−0.592098	+	0.672877i
$738$		0			0
$739$	−24.9639	−	18.1374i	−0.918313	−	0.667194i	0.0247903	−	0.999693i	$-0.492108\pi$
$739$	−24.9639	−	18.1374i	−0.918313	−	0.667194i	−0.943104	+	0.332499i	$0.892108\pi$
$740$	26.5776	−	81.7975i	0.977012	−	3.00693i
$741$		0			0
$742$	−3.67333	+	2.66883i	−0.134852	+	0.0979759i
$743$	−34.3881	+	24.9845i	−1.26158	+	0.916591i	−0.998834	−	0.0482747i	$-0.984628\pi$
$743$	−34.3881	+	24.9845i	−1.26158	+	0.916591i	−0.262745	+	0.964865i	$0.584628\pi$
$744$		0			0
$745$	11.5362	−	35.5049i	0.422655	−	1.30080i
$746$	1.97128	+	1.43222i	0.0721738	+	0.0524373i
$747$		0			0
$748$	−37.7934	+	8.48516i	−1.38187	+	0.310248i
$749$	13.3804			0.488909
$750$		0			0
$751$	6.51443	−	20.0494i	0.237715	−	0.731611i	−0.759035	−	0.651050i	$-0.774329\pi$
$751$	6.51443	−	20.0494i	0.237715	−	0.731611i	0.996750	−	0.0805613i	$-0.0256713\pi$
$752$	−2.38173	−	7.33022i	−0.0868529	−	0.267306i
$753$		0			0
$754$	−7.96281	+	5.78532i	−0.289988	+	0.210689i
$755$	−17.7810	−	54.7244i	−0.647119	−	1.99163i
$756$		0			0
$757$	−34.5741	−	25.1196i	−1.25662	−	0.912986i	−0.258031	−	0.966137i	$-0.583074\pi$
$757$	−34.5741	−	25.1196i	−1.25662	−	0.912986i	−0.998587	+	0.0531506i	$0.983074\pi$
$758$	−21.2912			−0.773331
$759$		0			0
$760$	−11.0889			−0.402236
$761$	−11.3231	−	8.22669i	−0.410461	−	0.298217i	0.363327	−	0.931662i	$-0.381641\pi$
$761$	−11.3231	−	8.22669i	−0.410461	−	0.298217i	−0.773788	+	0.633444i	$0.781641\pi$
$762$		0			0
$763$	−4.36420	−	13.4316i	−0.157995	−	0.486257i
$764$	−43.9730	+	31.9482i	−1.59089	+	1.15585i
$765$		0			0
$766$	−7.24436	−	22.2958i	−0.261749	−	0.805582i
$767$	0.364594	−	1.12211i	0.0131647	−	0.0405169i
$768$		0			0
$769$	23.8142			0.858761			0.429380	−	0.903124i	$-0.358732\pi$
$769$	23.8142			0.858761			0.429380	+	0.903124i	$0.358732\pi$
$770$	−18.8509	−	8.13646i	−0.679338	−	0.293218i
$771$		0			0
$772$	49.4823	+	35.9510i	1.78091	+	1.29391i
$773$	13.2976	−	40.9259i	0.478283	−	1.47200i	−0.363196	−	0.931713i	$-0.618314\pi$
$773$	13.2976	−	40.9259i	0.478283	−	1.47200i	0.841479	−	0.540291i	$-0.181686\pi$
$774$		0			0
$775$	12.2086	−	8.87005i	0.438545	−	0.318621i
$776$	−39.2703	+	28.5316i	−1.40972	+	1.02422i
$777$		0			0
$778$	−17.8320	+	54.8812i	−0.639308	+	1.96759i
$779$	−7.35641	−	5.34475i	−0.263571	−	0.191495i
$780$		0			0
$781$	0.836486	−	8.93880i	0.0299318	−	0.319856i
$782$	49.0680			1.75467
$783$		0			0
$784$	0.729944	−	2.24654i	0.0260694	−	0.0802335i
$785$	−7.83624	−	24.1175i	−0.279687	−	0.860790i
$786$		0			0
$787$	−25.3636	+	18.4278i	−0.904116	+	0.656878i	−0.939520	−	0.342495i	$-0.888728\pi$
$787$	−25.3636	+	18.4278i	−0.904116	+	0.656878i	0.0354042	+	0.999373i	$0.488728\pi$
$788$	7.82185	+	24.0732i	0.278642	+	0.857571i
$789$		0			0
$790$	49.1244	+	35.6910i	1.74777	+	1.26983i
$791$	−2.66351			−0.0947037
$792$		0			0
$793$	55.1552			1.95862
$794$	−39.9765	−	29.0447i	−1.41871	−	1.03076i
$795$		0			0
$796$	17.8504	+	54.9378i	0.632690	+	1.94722i
$797$	−5.62839	+	4.08927i	−0.199368	+	0.144849i	−0.682990	−	0.730428i	$-0.739321\pi$
$797$	−5.62839	+	4.08927i	−0.199368	+	0.144849i	0.483622	+	0.875277i	$0.339321\pi$
$798$		0			0
$799$	−3.17118	−	9.75990i	−0.112188	−	0.345280i
$800$	−1.34274	+	4.13252i	−0.0474729	+	0.146107i
$801$		0			0
$802$	60.2742			2.12836
$803$	1.79637	+	0.775356i	0.0633927	+	0.0273617i
$804$		0			0
$805$	13.6761	+	9.93630i	0.482021	+	0.350208i
$806$	−44.2569	+	136.209i	−1.55888	+	4.79775i
$807$		0			0
$808$	12.3198	−	8.95088i	0.433410	−	0.314891i
$809$	40.2788	−	29.2642i	1.41613	−	1.02888i	0.423730	−	0.905789i	$-0.360721\pi$
$809$	40.2788	−	29.2642i	1.41613	−	1.02888i	0.992396	−	0.123087i	$-0.0392793\pi$
$810$		0			0
$811$	−1.46897	+	4.52102i	−0.0515825	+	0.158755i	−0.973529	−	0.228562i	$-0.926598\pi$
$811$	−1.46897	+	4.52102i	−0.0515825	+	0.158755i	0.921947	+	0.387316i	$0.126598\pi$
$812$	1.82441	+	1.32551i	0.0640243	+	0.0465163i
$813$		0			0
$814$	−36.1465	−	60.9895i	−1.26694	−	2.13768i
$815$	29.4314			1.03094
$816$		0			0
$817$	−1.44787	+	4.45610i	−0.0506547	+	0.155899i
$818$	7.50141	+	23.0870i	0.262281	+	0.807217i
$819$		0			0
$820$	67.6708	−	49.1657i	2.36317	−	1.71694i
$821$	−5.46804	−	16.8289i	−0.190836	−	0.587332i	0.809164	−	0.587583i	$-0.199920\pi$
$821$	−5.46804	−	16.8289i	−0.190836	−	0.587332i	−1.00000		0.000250536i	$0.999920\pi$
$822$		0			0
$823$	20.7605	+	15.0834i	0.723667	+	0.525775i	0.887554	−	0.460704i	$-0.152403\pi$
$823$	20.7605	+	15.0834i	0.723667	+	0.525775i	−0.163887	+	0.986479i	$0.552403\pi$
$824$	30.0063			1.04532
$825$		0			0
$826$	−0.415920			−0.0144717
$827$	33.4044	+	24.2697i	1.16158	+	0.843940i	0.989977	−	0.141226i	$-0.0451044\pi$
$827$	33.4044	+	24.2697i	1.16158	+	0.843940i	0.171606	+	0.985166i	$0.445104\pi$
$828$		0			0
$829$	6.89845	+	21.2312i	0.239593	+	0.737391i	0.996479	+	0.0838443i	$0.0267198\pi$
$829$	6.89845	+	21.2312i	0.239593	+	0.737391i	−0.756886	+	0.653547i	$0.773280\pi$
$830$	43.8014	−	31.8236i	1.52037	−	1.10461i
$831$		0			0
$832$	−22.6421	−	69.6853i	−0.784974	−	2.41590i
$833$	0.971892	−	2.99118i	0.0336741	−	0.103638i
$834$		0			0
$835$	13.1799			0.456108
$836$	−8.50586	+	9.66631i	−0.294181	+	0.334316i
$837$		0			0
$838$	−54.8576	−	39.8564i	−1.89502	−	1.37682i
$839$	0.983838	−	3.02794i	0.0339659	−	0.104536i	−0.932636	−	0.360818i	$-0.882498\pi$
$839$	0.983838	−	3.02794i	0.0339659	−	0.104536i	0.966602	+	0.256282i	$0.0824975\pi$
$840$		0			0
$841$	23.1631	−	16.8290i	0.798728	−	0.580310i
$842$	53.5339	−	38.8947i	1.84490	−	1.34040i
$843$		0			0
$844$	1.79540	−	5.52566i	0.0618001	−	0.190201i
$845$	−69.0931	−	50.1991i	−2.37687	−	1.72690i
$846$		0			0
$847$	−9.94427	+	4.70228i	−0.341689	+	0.161572i
$848$	−4.48710			−0.154087
$849$		0			0
$850$	3.96714	−	12.2096i	0.136072	−	0.418786i
$851$	18.0378	+	55.5147i	0.618328	+	1.90302i
$852$		0			0
$853$	5.85527	−	4.25410i	0.200481	−	0.145658i	−0.483016	−	0.875612i	$-0.660459\pi$
$853$	5.85527	−	4.25410i	0.200481	−	0.145658i	0.683496	+	0.729954i	$0.260459\pi$
$854$	−6.00829	−	18.4916i	−0.205599	−	0.632770i
$855$		0			0
$856$	44.3314	+	32.2086i	1.51522	+	1.10087i
$857$	−9.16216			−0.312973			−0.156487	−	0.987680i	$-0.550017\pi$
$857$	−9.16216			−0.312973			−0.156487	+	0.987680i	$0.550017\pi$
$858$		0			0
$859$	−18.2015			−0.621028			−0.310514	−	0.950569i	$-0.600501\pi$
$859$	−18.2015			−0.621028			−0.310514	+	0.950569i	$0.600501\pi$
$860$	−34.8691	−	25.3339i	−1.18903	−	0.863878i
$861$		0			0
$862$	−5.40122	−	16.6232i	−0.183966	−	0.566190i
$863$	15.6086	−	11.3403i	0.531322	−	0.386028i	−0.289530	−	0.957169i	$-0.593499\pi$
$863$	15.6086	−	11.3403i	0.531322	−	0.386028i	0.820852	+	0.571141i	$0.193499\pi$
$864$		0			0
$865$	−6.22231	−	19.1503i	−0.211565	−	0.651130i
$866$	−7.77935	+	23.9424i	−0.264353	+	0.813595i
$867$		0			0
$868$	32.8137			1.11377
$869$	31.7414	−	7.12638i	1.07675	−	0.241746i
$870$		0			0
$871$	40.2447	+	29.2395i	1.36364	+	0.990741i
$872$	17.8727	−	55.0064i	0.605245	−	1.86275i
$873$		0			0
$874$	13.1958	−	9.58733i	0.446355	−	0.324296i
$875$	−6.89830	+	5.01191i	−0.233205	+	0.169434i
$876$		0			0
$877$	1.25066	−	3.84914i	0.0422318	−	0.129976i	−0.927718	−	0.373283i	$-0.878232\pi$
$877$	1.25066	−	3.84914i	0.0422318	−	0.129976i	0.969949	+	0.243307i	$0.0782321\pi$
$878$	1.11017	+	0.806584i	0.0374663	+	0.0272209i
$879$		0			0
$880$	−10.3451	−	17.4551i	−0.348733	−	0.588411i
$881$	−6.68797			−0.225324			−0.112662	−	0.993633i	$-0.535938\pi$
$881$	−6.68797			−0.225324			−0.112662	+	0.993633i	$0.535938\pi$
$882$		0			0
$883$	−0.571764	+	1.75971i	−0.0192414	+	0.0592189i	−0.960216	−	0.279258i	$-0.909912\pi$
$883$	−0.571764	+	1.75971i	−0.0192414	+	0.0592189i	0.940975	+	0.338477i	$0.109912\pi$
$884$	24.4706	+	75.3126i	0.823034	+	2.53304i
$885$		0			0
$886$	−35.2171	+	25.5867i	−1.18314	+	0.859603i
$887$	−4.35733	−	13.4105i	−0.146305	−	0.450280i	0.850872	−	0.525373i	$-0.176074\pi$
$887$	−4.35733	−	13.4105i	−0.146305	−	0.450280i	−0.997176	+	0.0750938i	$0.976074\pi$
$888$		0			0
$889$	−8.38410	−	6.09140i	−0.281194	−	0.204299i
$890$	72.2987			2.42346
$891$		0			0
$892$	15.3704			0.514640
$893$	−2.75980	−	2.00511i	−0.0923530	−	0.0670984i
$894$		0			0
$895$	4.91875	+	15.1384i	0.164416	+	0.506020i
$896$	−16.7795	+	12.1910i	−0.560565	+	0.407274i
$897$		0			0
$898$	−3.27492	−	10.0792i	−0.109286	−	0.336346i
$899$	−1.65835	+	5.10387i	−0.0553090	+	0.170224i
$900$		0			0
$901$	−5.97439			−0.199036
$902$	6.42421	−	68.6500i	0.213903	−	2.28579i
$903$		0			0
$904$	−8.82465	−	6.41149i	−0.293504	−	0.213243i
$905$	−7.40947	+	22.8040i	−0.246299	+	0.758031i
$906$		0			0
$907$	1.62569	−	1.18113i	0.0539800	−	0.0392188i	−0.560468	−	0.828176i	$-0.689379\pi$
$907$	1.62569	−	1.18113i	0.0539800	−	0.0392188i	0.614448	+	0.788957i	$0.289379\pi$
$908$	−16.7559	+	12.1739i	−0.556066	+	0.404005i
$909$		0			0
$910$	−12.9711	+	39.9209i	−0.429988	+	1.32337i
$911$	33.6157	+	24.4232i	1.11374	+	0.809177i	0.983248	−	0.182273i	$-0.0583454\pi$
$911$	33.6157	+	24.4232i	1.11374	+	0.809177i	0.130489	+	0.991450i	$0.458345\pi$
$912$		0			0
$913$	2.70259	−	28.8803i	0.0894427	−	0.955797i
$914$	−48.5057			−1.60442
$915$		0			0
$916$	−0.904706	+	2.78440i	−0.0298923	+	0.0919991i
$917$	−3.59822	−	11.0742i	−0.118824	−	0.365701i
$918$		0			0
$919$	−28.3471	+	20.5954i	−0.935085	+	0.679379i	−0.947233	−	0.320547i	$-0.896133\pi$
$919$	−28.3471	+	20.5954i	−0.935085	+	0.679379i	0.0121473	+	0.999926i	$0.496133\pi$
$920$	21.3931	+	65.8411i	0.705309	+	2.17072i
$921$		0			0
$922$	−9.39270	−	6.82420i	−0.309332	−	0.224743i
$923$	−18.3543			−0.604141
$924$		0			0
$925$	15.2721			0.502143
$926$	37.7408	+	27.4203i	1.24024	+	0.901087i
$927$		0			0
$928$	−0.477504	−	1.46961i	−0.0156748	−	0.0482422i
$929$	−1.24832	+	0.906954i	−0.0409559	+	0.0297562i	−0.608075	−	0.793880i	$-0.708058\pi$
$929$	−1.24832	+	0.906954i	−0.0409559	+	0.0297562i	0.567119	+	0.823636i	$0.308058\pi$
$930$		0			0
$931$	−0.323071	−	0.994311i	−0.0105882	−	0.0325872i
$932$	−31.7928	+	97.8483i	−1.04141	+	3.20513i
$933$		0			0
$934$	6.56421			0.214788
$935$	−13.7741	−	23.2408i	−0.450460	−	0.760054i
$936$		0			0
$937$	34.3581	+	24.9626i	1.12243	+	0.815494i	0.984576	−	0.174959i	$-0.0559792\pi$
$937$	34.3581	+	24.9626i	1.12243	+	0.815494i	0.137855	+	0.990452i	$0.455979\pi$
$938$	5.41895	−	16.6778i	0.176935	−	0.544550i
$939$		0			0
$940$	25.3870	−	18.4448i	0.828033	−	0.601601i
$941$	3.89751	−	2.83171i	0.127055	−	0.0923111i	−0.522443	−	0.852674i	$-0.674979\pi$
$941$	3.89751	−	2.83171i	0.127055	−	0.0923111i	0.649498	+	0.760363i	$0.274979\pi$
$942$		0			0
$943$	−17.5426	+	53.9905i	−0.571265	+	1.75817i
$944$	−0.332529	−	0.241597i	−0.0108229	−	0.00786330i
$945$		0			0
$946$	−34.6653	+	7.78284i	−1.12707	+	0.253042i
$947$	−18.0449			−0.586379			−0.293189	−	0.956054i	$-0.594717\pi$
$947$	−18.0449			−0.586379			−0.293189	+	0.956054i	$0.594717\pi$
$948$		0			0
$949$	1.23607	−	3.80423i	0.0401245	−	0.123490i
$950$	−1.31874	−	4.05866i	−0.0427855	−	0.131680i
$951$		0			0
$952$	10.4203	−	7.57076i	0.337722	−	0.245370i
$953$	11.5977	+	35.6940i	0.375686	+	1.15624i	0.943015	+	0.332750i	$0.107977\pi$
$953$	11.5977	+	35.6940i	0.375686	+	1.15624i	−0.567329	+	0.823491i	$0.692023\pi$
$954$		0			0
$955$	−30.6697	−	22.2829i	−0.992449	−	0.721057i
$956$	31.8649			1.03058
$957$		0			0
$958$	43.0850			1.39201
$959$	12.5313	+	9.10450i	0.404656	+	0.294000i
$960$		0			0
$961$	14.5509	+	44.7832i	0.469385	+	1.44462i
$962$	−117.259	+	85.1940i	−3.78060	+	2.74676i
$963$		0			0
$964$	−22.5356	−	69.3574i	−0.725823	−	2.23385i
$965$	−13.1825	+	40.5717i	−0.424361	+	1.30605i
$966$		0			0
$967$	1.06636			0.0342919			0.0171460	−	0.999853i	$-0.494542\pi$
$967$	1.06636			0.0342919			0.0171460	+	0.999853i	$0.494542\pi$
$968$	−44.2661	−	8.35796i	−1.42277	−	0.268635i
$969$		0			0
$970$	−59.3624	−	43.1293i	−1.90601	−	1.38480i
$971$	14.1398	−	43.5180i	0.453769	−	1.39656i	−0.418805	−	0.908076i	$-0.637551\pi$
$971$	14.1398	−	43.5180i	0.453769	−	1.39656i	0.872574	−	0.488481i	$-0.162449\pi$
$972$		0			0
$973$	−4.70693	+	3.41978i	−0.150897	+	0.109633i
$974$	23.9465	−	17.3982i	0.767296	−	0.557473i
$975$		0			0
$976$	5.93764	−	18.2742i	0.190059	−	0.584942i
$977$	−27.6930	−	20.1201i	−0.885976	−	0.643700i	0.0488494	−	0.998806i	$-0.484445\pi$
$977$	−27.6930	−	20.1201i	−0.885976	−	0.643700i	−0.934826	+	0.355107i	$0.884445\pi$
$978$		0			0
$979$	25.5881	−	29.0791i	0.817799	−	0.929371i
$980$	9.61724			0.307212
$981$		0			0
$982$	−12.2736	+	37.7744i	−0.391667	+	1.20543i
$983$	9.06625	+	27.9031i	0.289169	+	0.889969i	0.985118	+	0.171879i	$0.0549837\pi$
$983$	9.06625	+	27.9031i	0.289169	+	0.889969i	−0.695950	+	0.718091i	$0.745016\pi$
$984$		0			0
$985$	−14.2826	+	10.3770i	−0.455083	+	0.330637i
$986$	1.41080	+	4.34198i	0.0449289	+	0.138277i
$987$		0			0
$988$	21.2961	+	15.4725i	0.677518	+	0.492246i
$989$	29.2517			0.930150
$990$		0			0
$991$	19.0194			0.604171			0.302086	−	0.953281i	$-0.402317\pi$
$991$	19.0194			0.604171			0.302086	+	0.953281i	$0.402317\pi$
$992$	−18.1904	−	13.2161i	−0.577546	−	0.419612i
$993$		0			0
$994$	1.99942	+	6.15357i	0.0634176	+	0.195179i
$995$	−32.5947	+	23.6814i	−1.03332	+	0.750752i
$996$		0			0
$997$	−1.36942	−	4.21463i	−0.0433699	−	0.133479i	0.927027	−	0.374995i	$-0.122355\pi$
$997$	−1.36942	−	4.21463i	−0.0433699	−	0.133479i	−0.970397	+	0.241516i	$0.922355\pi$
$998$	−15.0570	+	46.3406i	−0.476620	+	1.46689i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.m.f.631.1		8
3.2	odd	2		231.2.j.f.169.2	✓	8
11.3	even	5	inner	693.2.m.f.190.1		8
11.5	even	5		7623.2.a.ci.1.4		4
11.6	odd	10		7623.2.a.cl.1.1		4
33.5	odd	10		2541.2.a.bn.1.1		4
33.14	odd	10		231.2.j.f.190.2	yes	8
33.17	even	10		2541.2.a.bm.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.169.2	✓	8	3.2	odd	2
231.2.j.f.190.2	yes	8	33.14	odd	10
693.2.m.f.190.1		8	11.3	even	5	inner
693.2.m.f.631.1		8	1.1	even	1	trivial
2541.2.a.bm.1.4		4	33.17	even	10
2541.2.a.bn.1.1		4	33.5	odd	10
7623.2.a.ci.1.4		4	11.5	even	5
7623.2.a.cl.1.1		4	11.6	odd	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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.m (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93376 - 1.40496i) q^{2} +(1.14748 + 3.53158i) q^{4} +(-2.09529 + 1.52232i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(1.26552 - 3.89486i) q^{8} +O(q^{10})\)	\(q+(-1.93376 - 1.40496i) q^{2} +(1.14748 + 3.53158i) q^{4} +(-2.09529 + 1.52232i) q^{5} +(-0.309017 - 0.951057i) q^{7} +(1.26552 - 3.89486i) q^{8} +6.19059 q^{10} +(2.19098 - 2.48990i) q^{11} +(-5.48555 - 3.98549i) q^{13} +(-0.738630 + 2.27327i) q^{14} +(-1.91102 + 1.38844i) q^{16} +(-2.54445 + 1.84865i) q^{17} +(-0.323071 + 0.994311i) q^{19} +(-7.78051 - 5.65287i) q^{20} +(-7.73503 + 1.73662i) q^{22} +6.52707 q^{23} +(0.527713 - 1.62413i) q^{25} +(5.00829 + 15.4139i) q^{26} +(3.00415 - 2.18264i) q^{28} +(0.187665 + 0.577574i) q^{29} +(7.14906 + 5.19410i) q^{31} -2.54445 q^{32} +7.51762 q^{34} +(2.09529 + 1.52232i) q^{35} +(2.76354 + 8.50529i) q^{37} +(2.02171 - 1.46886i) q^{38} +(3.27759 + 10.0874i) q^{40} +(-2.68767 + 8.27178i) q^{41} +4.48159 q^{43} +(11.3074 + 4.88053i) q^{44} +(-12.6218 - 9.17026i) q^{46} +(-1.00829 + 3.10320i) q^{47} +(-0.809017 + 0.587785i) q^{49} +(-3.30231 + 2.39927i) q^{50} +(7.78051 - 23.9460i) q^{52} +(1.53679 + 1.11655i) q^{53} +(-0.800331 + 8.55245i) q^{55} -4.09529 q^{56} +(0.448568 - 1.38055i) q^{58} +(0.0537709 + 0.165490i) q^{59} +(-6.58084 + 4.78126i) q^{61} +(-6.52707 - 20.0883i) q^{62} +(8.74238 + 6.35171i) q^{64} +17.5610 q^{65} -7.33649 q^{67} +(-9.44836 - 6.86464i) q^{68} +(-1.91300 - 5.88760i) q^{70} +(2.18995 - 1.59109i) q^{71} +(0.182297 + 0.561053i) q^{73} +(6.60556 - 20.3298i) q^{74} -3.88221 q^{76} +(-3.04508 - 1.31433i) q^{77} +(7.93534 + 5.76536i) q^{79} +(1.89050 - 5.81836i) q^{80} +(16.8188 - 12.2196i) q^{82} +(7.07548 - 5.14063i) q^{83} +(2.51713 - 7.74692i) q^{85} +(-8.66632 - 6.29645i) q^{86} +(-6.92507 - 11.6846i) q^{88} +11.6788 q^{89} +(-2.09529 + 6.44865i) q^{91} +(7.48970 + 23.0509i) q^{92} +(6.30966 - 4.58423i) q^{94} +(-0.836730 - 2.57519i) q^{95} +(-9.58914 - 6.96691i) q^{97} +2.39026 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8	\( 8 q - 2 q^{2} + 6 q^{4} - 2 q^{5} + 2 q^{7} - 2 q^{8} + 20 q^{10} + 22 q^{11} - 8 q^{13} - 3 q^{14} + 4 q^{16} + 4 q^{17} - 20 q^{20} - 8 q^{22} + 20 q^{23} - 26 q^{25} + 10 q^{26} + 9 q^{28} + 24 q^{31} + 4 q^{32} + 36 q^{34} + 2 q^{35} + 6 q^{37} - 14 q^{38} + 12 q^{40} - 20 q^{41} - 8 q^{43} + 39 q^{44} - 43 q^{46} + 22 q^{47} - 2 q^{49} - 22 q^{50} + 20 q^{52} + 20 q^{53} + 2 q^{55} - 18 q^{56} - 17 q^{58} - 18 q^{59} - 2 q^{61} - 20 q^{62} + 18 q^{64} + 56 q^{65} - 56 q^{67} + 2 q^{68} - 14 q^{71} + 2 q^{73} + 12 q^{74} - 8 q^{76} - 2 q^{77} + 20 q^{79} - 38 q^{80} + 2 q^{82} + 8 q^{83} + 60 q^{85} - 55 q^{86} - 38 q^{88} + 32 q^{89} - 2 q^{91} + 9 q^{92} + 48 q^{94} + 28 q^{95} + 4 q^{97} - 2 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^4 - 2 * q^5 + 2 * q^7 - 2 * q^8 + 20 * q^10 + 22 * q^11 - 8 * q^13 - 3 * q^14 + 4 * q^16 + 4 * q^17 - 20 * q^20 - 8 * q^22 + 20 * q^23 - 26 * q^25 + 10 * q^26 + 9 * q^28 + 24 * q^31 + 4 * q^32 + 36 * q^34 + 2 * q^35 + 6 * q^37 - 14 * q^38 + 12 * q^40 - 20 * q^41 - 8 * q^43 + 39 * q^44 - 43 * q^46 + 22 * q^47 - 2 * q^49 - 22 * q^50 + 20 * q^52 + 20 * q^53 + 2 * q^55 - 18 * q^56 - 17 * q^58 - 18 * q^59 - 2 * q^61 - 20 * q^62 + 18 * q^64 + 56 * q^65 - 56 * q^67 + 2 * q^68 - 14 * q^71 + 2 * q^73 + 12 * q^74 - 8 * q^76 - 2 * q^77 + 20 * q^79 - 38 * q^80 + 2 * q^82 + 8 * q^83 + 60 * q^85 - 55 * q^86 - 38 * q^88 + 32 * q^89 - 2 * q^91 + 9 * q^92 + 48 * q^94 + 28 * q^95 + 4 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more