LMFDB - Embedded newform 231.2.j.f.169.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, 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("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (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:	$1.84454428669$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.2
Root			$1.69513 + 1.23158i$ of defining polynomial
Character	$\chi$	$=$	231.169
Dual form			231.2.j.f.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.93376 + 1.40496i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.14748 + 3.53158i) q^{4} +(2.09529 - 1.52232i) q^{5} +(-1.93376 + 1.40496i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-1.26552 + 3.89486i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(1.93376 + 1.40496i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.14748 + 3.53158i) q^{4} +(2.09529 - 1.52232i) q^{5} +(-1.93376 + 1.40496i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-1.26552 + 3.89486i) q^{8} +(-0.809017 - 0.587785i) q^{9} +6.19059 q^{10} +(-2.19098 + 2.48990i) q^{11} -3.71333 q^{12} +(-5.48555 - 3.98549i) q^{13} +(0.738630 - 2.27327i) q^{14} +(0.800331 + 2.46317i) q^{15} +(-1.91102 + 1.38844i) q^{16} +(2.54445 - 1.84865i) q^{17} +(-0.738630 - 2.27327i) q^{18} +(-0.323071 + 0.994311i) q^{19} +(7.78051 + 5.65287i) q^{20} +1.00000 q^{21} +(-7.73503 + 1.73662i) q^{22} -6.52707 q^{23} +(-3.31316 - 2.40715i) q^{24} +(0.527713 - 1.62413i) q^{25} +(-5.00829 - 15.4139i) q^{26} +(0.809017 - 0.587785i) q^{27} +(3.00415 - 2.18264i) q^{28} +(-0.187665 - 0.577574i) q^{29} +(-1.91300 + 5.88760i) q^{30} +(7.14906 + 5.19410i) q^{31} +2.54445 q^{32} +(-1.69098 - 2.85317i) q^{33} +7.51762 q^{34} +(-2.09529 - 1.52232i) q^{35} +(1.14748 - 3.53158i) q^{36} +(2.76354 + 8.50529i) q^{37} +(-2.02171 + 1.46886i) q^{38} +(5.48555 - 3.98549i) q^{39} +(3.27759 + 10.0874i) q^{40} +(2.68767 - 8.27178i) q^{41} +(1.93376 + 1.40496i) q^{42} +4.48159 q^{43} +(-11.3074 - 4.88053i) q^{44} -2.58993 q^{45} +(-12.6218 - 9.17026i) q^{46} +(1.00829 - 3.10320i) q^{47} +(-0.729944 - 2.24654i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(3.30231 - 2.39927i) q^{50} +(0.971892 + 2.99118i) q^{51} +(7.78051 - 23.9460i) q^{52} +(-1.53679 - 1.11655i) q^{53} +2.39026 q^{54} +(-0.800331 + 8.55245i) q^{55} +4.09529 q^{56} +(-0.845811 - 0.614518i) q^{57} +(0.448568 - 1.38055i) q^{58} +(-0.0537709 - 0.165490i) q^{59} +(-7.78051 + 5.65287i) q^{60} +(-6.58084 + 4.78126i) q^{61} +(6.52707 + 20.0883i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(8.74238 + 6.35171i) q^{64} -17.5610 q^{65} +(0.738630 - 7.89310i) q^{66} -7.33649 q^{67} +(9.44836 + 6.86464i) q^{68} +(2.01698 - 6.20762i) q^{69} +(-1.91300 - 5.88760i) q^{70} +(-2.18995 + 1.59109i) q^{71} +(3.31316 - 2.40715i) q^{72} +(0.182297 + 0.561053i) q^{73} +(-6.60556 + 20.3298i) q^{74} +(1.38157 + 1.00377i) q^{75} -3.88221 q^{76} +(3.04508 + 1.31433i) q^{77} +16.2072 q^{78} +(7.93534 + 5.76536i) q^{79} +(-1.89050 + 5.81836i) q^{80} +(0.309017 + 0.951057i) q^{81} +(16.8188 - 12.2196i) q^{82} +(-7.07548 + 5.14063i) q^{83} +(1.14748 + 3.53158i) q^{84} +(2.51713 - 7.74692i) q^{85} +(8.66632 + 6.29645i) q^{86} +0.607298 q^{87} +(-6.92507 - 11.6846i) q^{88} -11.6788 q^{89} +(-5.00829 - 3.63874i) q^{90} +(-2.09529 + 6.44865i) q^{91} +(-7.48970 - 23.0509i) q^{92} +(-7.14906 + 5.19410i) q^{93} +(6.30966 - 4.58423i) q^{94} +(0.836730 + 2.57519i) q^{95} +(-0.786277 + 2.41991i) q^{96} +(-9.58914 - 6.96691i) q^{97} -2.39026 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 20 q^{10} - 22 q^{11} - 6 q^{12} - 8 q^{13} + 3 q^{14} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 3 q^{18} + 20 q^{20} + 8 q^{21} - 8 q^{22} - 20 q^{23} - 7 q^{24} - 26 q^{25} - 10 q^{26} + 2 q^{27} + 9 q^{28} + 24 q^{31} - 4 q^{32} - 18 q^{33} + 36 q^{34} - 2 q^{35} + 6 q^{36} + 6 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 20 q^{41} + 2 q^{42} - 8 q^{43} - 39 q^{44} - 8 q^{45} - 43 q^{46} - 22 q^{47} + q^{48} - 2 q^{49} + 22 q^{50} + 4 q^{51} + 20 q^{52} - 20 q^{53} - 2 q^{54} + 2 q^{55} + 18 q^{56} - 10 q^{57} - 17 q^{58} + 18 q^{59} - 20 q^{60} - 2 q^{61} + 20 q^{62} + 2 q^{63} + 18 q^{64} - 56 q^{65} + 3 q^{66} - 56 q^{67} - 2 q^{68} - 10 q^{69} + 14 q^{71} + 7 q^{72} + 2 q^{73} - 12 q^{74} - 14 q^{75} - 8 q^{76} + 2 q^{77} + 40 q^{78} + 20 q^{79} + 38 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{83} + 6 q^{84} + 60 q^{85} + 55 q^{86} - 38 q^{88} - 32 q^{89} - 10 q^{90} - 2 q^{91} - 9 q^{92} - 24 q^{93} + 48 q^{94} - 28 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 20 * q^10 - 22 * q^11 - 6 * q^12 - 8 * q^13 + 3 * q^14 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 3 * q^18 + 20 * q^20 + 8 * q^21 - 8 * q^22 - 20 * q^23 - 7 * q^24 - 26 * q^25 - 10 * q^26 + 2 * q^27 + 9 * q^28 + 24 * q^31 - 4 * q^32 - 18 * q^33 + 36 * q^34 - 2 * q^35 + 6 * q^36 + 6 * q^37 + 14 * q^38 + 8 * q^39 + 12 * q^40 + 20 * q^41 + 2 * q^42 - 8 * q^43 - 39 * q^44 - 8 * q^45 - 43 * q^46 - 22 * q^47 + q^48 - 2 * q^49 + 22 * q^50 + 4 * q^51 + 20 * q^52 - 20 * q^53 - 2 * q^54 + 2 * q^55 + 18 * q^56 - 10 * q^57 - 17 * q^58 + 18 * q^59 - 20 * q^60 - 2 * q^61 + 20 * q^62 + 2 * q^63 + 18 * q^64 - 56 * q^65 + 3 * q^66 - 56 * q^67 - 2 * q^68 - 10 * q^69 + 14 * q^71 + 7 * q^72 + 2 * q^73 - 12 * q^74 - 14 * q^75 - 8 * q^76 + 2 * q^77 + 40 * q^78 + 20 * q^79 + 38 * q^80 - 2 * q^81 + 2 * q^82 - 8 * q^83 + 6 * q^84 + 60 * q^85 + 55 * q^86 - 38 * q^88 - 32 * q^89 - 10 * q^90 - 2 * q^91 - 9 * q^92 - 24 * q^93 + 48 * q^94 - 28 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

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	$0.0204493\pi$
$2$	1.93376	+	1.40496i	1.36737	+	0.993455i	0.369437	+	0.929256i	$0.379551\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	1.14748	+	3.53158i	0.573741	+	1.76579i
$5$	2.09529	−	1.52232i	0.937044	−	0.680802i	−0.0106633	−	0.999943i	$-0.503394\pi$
$5$	2.09529	−	1.52232i	0.937044	−	0.680802i	0.947707	+	0.319141i	$0.103394\pi$
$6$	−1.93376	+	1.40496i	−0.789454	+	0.573572i
$7$	−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
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	6.19059			1.95764
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$11$	−2.19098	+	2.48990i	−0.660606	+	0.750733i
$12$	−3.71333			−1.07195
$13$	−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
$15$	0.800331	+	2.46317i	0.206645	+	0.635987i
$16$	−1.91102	+	1.38844i	−0.477755	+	0.347109i
$17$	2.54445	−	1.84865i	0.617119	−	0.448363i	−0.234795	−	0.972045i	$-0.575442\pi$
$17$	2.54445	−	1.84865i	0.617119	−	0.448363i	0.851914	+	0.523682i	$0.175442\pi$
$18$	−0.738630	−	2.27327i	−0.174097	−	0.535815i
$19$	−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
$21$	1.00000			0.218218
$22$	−7.73503	+	1.73662i	−1.64911	+	0.370249i
$23$	−6.52707			−1.36099			−0.680495	−	0.732753i	$-0.738235\pi$
$23$	−6.52707			−1.36099			−0.680495	+	0.732753i	$0.738235\pi$
$24$	−3.31316	−	2.40715i	−0.676296	−	0.491358i
$25$	0.527713	−	1.62413i	0.105543	−	0.324827i
$26$	−5.00829	−	15.4139i	−0.982207	−	3.02292i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	3.00415	−	2.18264i	0.567730	−	0.412480i
$29$	−0.187665	−	0.577574i	−0.0348486	−	0.107253i	0.932119	−	0.362152i	$-0.117958\pi$
$29$	−0.187665	−	0.577574i	−0.0348486	−	0.107253i	−0.966968	+	0.254899i	$0.917958\pi$
$30$	−1.91300	+	5.88760i	−0.349264	+	1.07492i
$31$	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
$33$	−1.69098	−	2.85317i	−0.294362	−	0.496673i
$34$	7.51762			1.28926
$35$	−2.09529	−	1.52232i	−0.354169	−	0.257319i
$36$	1.14748	−	3.53158i	0.191247	−	0.588597i
$37$	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
$39$	5.48555	−	3.98549i	0.878391	−	0.638189i
$40$	3.27759	+	10.0874i	0.518233	+	1.59496i
$41$	2.68767	−	8.27178i	0.419743	−	1.29184i	−0.488196	−	0.872734i	$-0.662345\pi$
$41$	2.68767	−	8.27178i	0.419743	−	1.29184i	0.907939	−	0.419102i	$-0.137655\pi$
$42$	1.93376	+	1.40496i	0.298385	+	0.216790i
$43$	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
$45$	−2.58993			−0.386083
$46$	−12.6218	−	9.17026i	−1.86098	−	1.35208i
$47$	1.00829	−	3.10320i	0.147074	−	0.452648i	−0.850198	−	0.526464i	$-0.823518\pi$
$47$	1.00829	−	3.10320i	0.147074	−	0.452648i	0.997272	+	0.0738155i	$0.0235176\pi$
$48$	−0.729944	−	2.24654i	−0.105358	−	0.324260i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	3.30231	−	2.39927i	0.467017	−	0.339308i
$51$	0.971892	+	2.99118i	0.136092	+	0.418848i
$52$	7.78051	−	23.9460i	1.07896	−	3.32071i
$53$	−1.53679	−	1.11655i	−0.211095	−	0.153369i	0.477214	−	0.878787i	$-0.341647\pi$
$53$	−1.53679	−	1.11655i	−0.211095	−	0.153369i	−0.688309	+	0.725418i	$0.741647\pi$
$54$	2.39026			0.325273
$55$	−0.800331	+	8.55245i	−0.107917	+	1.15321i
$56$	4.09529			0.547257
$57$	−0.845811	−	0.614518i	−0.112030	−	0.0813949i
$58$	0.448568	−	1.38055i	0.0588999	−	0.181275i
$59$	−0.0537709	−	0.165490i	−0.00700037	−	0.0215449i	0.947495	−	0.319770i	$-0.103606\pi$
$59$	−0.0537709	−	0.165490i	−0.00700037	−	0.0215449i	−0.954496	+	0.298225i	$0.903606\pi$
$60$	−7.78051	+	5.65287i	−1.00446	+	0.729783i
$61$	−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
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	8.74238	+	6.35171i	1.09280	+	0.793964i
$65$	−17.5610			−2.17818
$66$	0.738630	−	7.89310i	0.0909191	−	0.971573i
$67$	−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
$69$	2.01698	−	6.20762i	0.242815	−	0.747309i
$70$	−1.91300	−	5.88760i	−0.228647	−	0.703703i
$71$	−2.18995	+	1.59109i	−0.259899	+	0.188828i	−0.710103	−	0.704098i	$-0.751351\pi$
$71$	−2.18995	+	1.59109i	−0.259899	+	0.188828i	0.450203	+	0.892926i	$0.351351\pi$
$72$	3.31316	−	2.40715i	0.390460	−	0.283686i
$73$	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
$75$	1.38157	+	1.00377i	0.159530	+	0.115905i
$76$	−3.88221			−0.445320
$77$	3.04508	+	1.31433i	0.347020	+	0.149782i
$78$	16.2072			1.83510
$79$	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
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	16.8188	−	12.2196i	1.85733	−	1.34943i
$83$	−7.07548	+	5.14063i	−0.776634	+	0.564258i	−0.903967	−	0.427602i	$-0.859358\pi$
$83$	−7.07548	+	5.14063i	−0.776634	+	0.564258i	0.127333	+	0.991860i	$0.459358\pi$
$84$	1.14748	+	3.53158i	0.125200	+	0.385327i
$85$	2.51713	−	7.74692i	0.273021	−	0.840272i
$86$	8.66632	+	6.29645i	0.934513	+	0.678964i
$87$	0.607298			0.0651091
$88$	−6.92507	−	11.6846i	−0.738215	−	1.24558i
$89$	−11.6788			−1.23795			−0.618976	−	0.785410i	$-0.712452\pi$
$89$	−11.6788			−1.23795			−0.618976	+	0.785410i	$0.712452\pi$
$90$	−5.00829	−	3.63874i	−0.527920	−	0.383556i
$91$	−2.09529	+	6.44865i	−0.219646	+	0.676002i
$92$	−7.48970	−	23.0509i	−0.780855	−	2.40322i
$93$	−7.14906	+	5.19410i	−0.741323	+	0.538603i
$94$	6.30966	−	4.58423i	0.650791	−	0.472828i
$95$	0.836730	+	2.57519i	0.0858467	+	0.264209i
$96$	−0.786277	+	2.41991i	−0.0802491	+	0.246981i
$97$	−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
$99$	3.23607	−	0.726543i	0.325237	−	0.0730203i
$100$	6.34131			0.634131
$101$	−3.00829	−	2.18565i	−0.299336	−	0.217480i	0.427971	−	0.903792i	$-0.359228\pi$
$101$	−3.00829	−	2.18565i	−0.299336	−	0.217480i	−0.727307	+	0.686312i	$0.759228\pi$
$102$	−2.32307	+	7.14968i	−0.230018	+	0.707924i
$103$	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
$105$	2.09529	−	1.52232i	0.204480	−	0.148563i
$106$	−1.40309	−	4.31826i	−0.136280	−	0.419427i
$107$	4.13477	−	12.7255i	0.399723	−	1.23022i	−0.525499	−	0.850794i	$-0.676121\pi$
$107$	4.13477	−	12.7255i	0.399723	−	1.23022i	0.925222	−	0.379427i	$-0.123879\pi$
$108$	3.00415	+	2.18264i	0.289074	+	0.210025i
$109$	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
$111$	−8.94299			−0.848831
$112$	1.91102	+	1.38844i	0.180574	+	0.131195i
$113$	−0.823071	+	2.53315i	−0.0774280	+	0.238299i	−0.982277	−	0.187433i	$-0.939983\pi$
$113$	−0.823071	+	2.53315i	−0.0774280	+	0.238299i	0.904849	+	0.425732i	$0.139983\pi$
$114$	−0.772223	−	2.37666i	−0.0723253	−	0.222594i
$115$	−13.6761	+	9.93630i	−1.27531	+	0.926564i
$116$	1.82441	−	1.32551i	0.169392	−	0.123071i
$117$	2.09529	+	6.44865i	0.193710	+	0.596178i
$118$	0.128526	−	0.395563i	0.0118318	−	0.0364145i
$119$	−2.54445	−	1.84865i	−0.233249	−	0.169465i
$120$	−10.6065			−0.968237
$121$	−1.39919	−	10.9106i	−0.127199	−	0.991877i
$122$	−19.4432			−1.76031
$123$	7.03640	+	5.11224i	0.634451	+	0.460955i
$124$	−10.1400	+	31.2077i	−0.910597	+	2.80253i
$125$	2.63492	+	8.10944i	0.235674	+	0.725331i
$126$	−1.93376	+	1.40496i	−0.172273	+	0.125164i
$127$	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
$129$	−1.38489	+	4.26225i	−0.121933	+	0.375270i
$130$	−33.9588	−	24.6725i	−2.97838	−	2.16392i
$131$	−11.6441			−1.01735			−0.508674	−	0.860959i	$-0.669864\pi$
$131$	−11.6441			−1.01735			−0.508674	+	0.860959i	$0.669864\pi$
$132$	8.13584	−	9.24581i	0.708134	−	0.804744i
$133$	1.04548			0.0906546
$134$	−14.1870	−	10.3075i	−1.22557	−	0.890428i
$135$	0.800331	−	2.46317i	0.0688815	−	0.211996i
$136$	3.98018	+	12.2497i	0.341298	+	1.05041i
$137$	12.5313	−	9.10450i	1.07062	−	0.777850i	0.0945956	−	0.995516i	$-0.469844\pi$
$137$	12.5313	−	9.10450i	1.07062	−	0.777850i	0.976023	+	0.217665i	$0.0698442\pi$
$138$	12.6218	−	9.17026i	1.07444	−	0.780625i
$139$	−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
$141$	2.63974	+	1.91788i	0.222306	+	0.161515i
$142$	−6.47025			−0.542971
$143$	21.9422	−	4.92633i	1.83490	−	0.411961i
$144$	2.36215			0.196846
$145$	−1.27247	−	0.924501i	−0.105673	−	0.0767757i
$146$	−0.435737	+	1.34106i	−0.0360618	+	0.110987i
$147$	−0.309017	−	0.951057i	−0.0254873	−	0.0784418i
$148$	−26.8661	+	19.5193i	−2.20838	+	1.60448i
$149$	11.6614	−	8.47254i	0.955343	−	0.694097i	0.00327837	−	0.999995i	$-0.498956\pi$
$149$	11.6614	−	8.47254i	0.955343	−	0.694097i	0.952064	+	0.305897i	$0.0989565\pi$
$150$	1.26137	+	3.88210i	0.102990	+	0.316972i
$151$	−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
$153$	−3.14511			−0.254267
$154$	4.04188	+	6.81981i	0.325704	+	0.549556i
$155$	22.8865			1.83829
$156$	20.3696	+	14.7994i	1.63088	+	1.18490i
$157$	−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
$159$	1.53679	−	1.11655i	0.121876	−	0.0885479i
$160$	5.33136	−	3.87346i	0.421481	−	0.306224i
$161$	2.01698	+	6.20762i	0.158960	+	0.489229i
$162$	−0.738630	+	2.27327i	−0.0580323	+	0.178605i
$163$	−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
$165$	−7.88654	−	3.40401i	−0.613967	−	0.265002i
$166$	−20.9046			−1.62251
$167$	4.11700	+	2.99118i	0.318583	+	0.231464i	0.735571	−	0.677448i	$-0.236914\pi$
$167$	4.11700	+	2.99118i	0.318583	+	0.231464i	−0.416988	+	0.908912i	$0.636914\pi$
$168$	−1.26552	+	3.89486i	−0.0976366	+	0.300495i
$169$	10.1899	+	31.3614i	0.783842	+	2.41242i
$170$	15.7516	−	11.4442i	1.20809	−	0.877731i
$171$	0.845811	−	0.614518i	0.0646808	−	0.0469933i
$172$	5.14255	+	15.8271i	0.392115	+	1.20681i
$173$	2.40250	−	7.39415i	0.182659	−	0.562167i	−0.817241	−	0.576296i	$-0.804498\pi$
$173$	2.40250	−	7.39415i	0.182659	−	0.562167i	0.999900	+	0.0141291i	$0.00449759\pi$
$174$	1.17437	+	0.853227i	0.0890285	+	0.0646830i
$175$	−1.70772			−0.129091
$176$	0.729944	−	7.80028i	0.0550216	−	0.587968i
$177$	0.174006			0.0130791
$178$	−22.5840	−	16.4082i	−1.69274	−	1.22985i
$179$	−1.89919	+	5.84510i	−0.141952	+	0.436883i	−0.996606	−	0.0823141i	$-0.973769\pi$
$179$	−1.89919	+	5.84510i	−0.141952	+	0.436883i	0.854655	+	0.519197i	$0.173769\pi$
$180$	−2.97189	−	9.14654i	−0.221512	−	0.681743i
$181$	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
$183$	−2.51366	−	7.73625i	−0.185815	−	0.571880i
$184$	8.26011	−	25.4220i	0.608944	−	1.87414i
$185$	18.7382	+	13.6141i	1.37766	+	1.00093i
$186$	−21.1221			−1.54874
$187$	−0.971892	+	10.3858i	−0.0710718	+	0.759483i
$188$	12.1162			0.883665
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	−2.00000	+	6.15537i	−0.145095	+	0.446557i
$191$	−4.52322	−	13.9210i	−0.327289	−	1.00729i	−0.970397	−	0.241515i	$-0.922356\pi$
$191$	−4.52322	−	13.9210i	−0.327289	−	1.00729i	0.643108	−	0.765775i	$-0.277644\pi$
$192$	−8.74238	+	6.35171i	−0.630927	+	0.458395i
$193$	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
$195$	5.42666	−	16.7015i	0.388611	−	1.19602i
$196$	−3.00415	−	2.18264i	−0.214582	−	0.155903i
$197$	−6.81654			−0.485658			−0.242829	−	0.970069i	$-0.578075\pi$
$197$	−6.81654			−0.485658			−0.242829	+	0.970069i	$0.578075\pi$
$198$	7.27854	+	3.14158i	0.517263	+	0.223262i
$199$	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
$201$	2.26710	−	6.97741i	0.159909	−	0.492149i
$202$	−2.74656	−	8.45304i	−0.193247	−	0.594754i
$203$	−0.491314	+	0.356961i	−0.0344835	+	0.0250537i
$204$	−9.44836	+	6.86464i	−0.661518	+	0.480621i
$205$	−6.96085	−	21.4233i	−0.486167	−	1.49627i
$206$	−5.41196	+	16.6563i	−0.377069	+	1.16050i
$207$	5.28051	+	3.83652i	0.367021	+	0.266656i
$208$	16.0166			1.11055
$209$	−1.76789	−	2.98293i	−0.122287	−	0.206334i
$210$	6.19059			0.427191
$211$	−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
$213$	−0.836486	−	2.57444i	−0.0573151	−	0.176398i
$214$	25.8744	−	18.7989i	1.76874	−	1.28506i
$215$	9.39026	−	6.82242i	0.640410	−	0.465285i
$216$	1.26552	+	3.89486i	0.0861074	+	0.265011i
$217$	2.73070	−	8.40423i	0.185372	−	0.570516i
$218$	27.3102	+	19.8420i	1.84968	+	1.34387i
$219$	−0.589926			−0.0398635
$220$	−31.1221	+	6.98734i	−2.09825	+	0.471086i
$221$	−21.3254			−1.43450
$222$	−17.2936	−	12.5645i	−1.16067	−	0.843276i
$223$	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
$225$	−1.38157	+	1.00377i	−0.0921047	+	0.0669180i
$226$	−5.15059	+	3.74212i	−0.342612	+	0.248922i
$227$	−1.72358	−	5.30462i	−0.114398	−	0.352080i	0.877423	−	0.479717i	$-0.159261\pi$
$227$	−1.72358	−	5.30462i	−0.114398	−	0.352080i	−0.991821	+	0.127637i	$0.959261\pi$
$228$	1.19967	−	3.69220i	0.0794500	−	0.244522i
$229$	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
$231$	−2.19098	+	2.48990i	−0.144156	+	0.163823i
$232$	2.48706			0.163284
$233$	−22.4151	−	16.2855i	−1.46846	−	1.06690i	−0.981055	−	0.193727i	$-0.937942\pi$
$233$	−22.4151	−	16.2855i	−1.46846	−	1.06690i	−0.487409	−	0.873174i	$-0.662058\pi$
$234$	−5.00829	+	15.4139i	−0.327402	+	1.00764i
$235$	−2.61140	−	8.03706i	−0.170349	−	0.524280i
$236$	0.522740	−	0.379793i	0.0340275	−	0.0247224i
$237$	−7.93534	+	5.76536i	−0.515456	+	0.374501i
$238$	−2.32307	−	7.14968i	−0.150582	−	0.463445i
$239$	−2.65174	+	8.16123i	−0.171527	+	0.527906i	−0.999458	−	0.0329243i	$-0.989518\pi$
$239$	−2.65174	+	8.16123i	−0.171527	+	0.527906i	0.827931	+	0.560830i	$0.189518\pi$
$240$	−4.94940	−	3.59595i	−0.319482	−	0.232117i
$241$	−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
$243$	−1.00000			−0.0641500
$244$	−24.4368	−	17.7544i	−1.56441	−	1.13661i
$245$	−0.800331	+	2.46317i	−0.0511313	+	0.157366i
$246$	6.42421	+	19.7717i	0.409593	+	1.26060i
$247$	5.73503	−	4.16675i	0.364911	−	0.265124i
$248$	−29.2775	+	21.2714i	−1.85912	+	1.35073i
$249$	−2.70259	−	8.31772i	−0.171270	−	0.527114i
$250$	−6.29813	+	19.3837i	−0.398329	+	1.22593i
$251$	24.1522	+	17.5476i	1.52448	+	1.10760i	0.959213	+	0.282685i	$0.0912252\pi$
$251$	24.1522	+	17.5476i	1.52448	+	1.10760i	0.565263	+	0.824911i	$0.308775\pi$
$252$	−3.71333			−0.233918
$253$	14.3007	−	16.2518i	0.899078	−	1.02174i
$254$	24.7710			1.55427
$255$	6.58993	+	4.78786i	0.412677	+	0.299828i
$256$	−8.64108	+	26.5945i	−0.540067	+	1.66216i
$257$	0.876598	+	2.69789i	0.0546807	+	0.168290i	0.974667	−	0.223660i	$-0.0718006\pi$
$257$	0.876598	+	2.69789i	0.0546807	+	0.168290i	−0.919987	+	0.391950i	$0.871801\pi$
$258$	−8.66632	+	6.29645i	−0.539542	+	0.392000i
$259$	7.23503	−	5.25656i	0.449563	−	0.326627i
$260$	−20.1510	−	62.0183i	−1.24971	−	3.84621i
$261$	−0.187665	+	0.577574i	−0.0116162	+	0.0357510i
$262$	−22.5168	−	16.3594i	−1.39109	−	1.01069i
$263$	10.2373			0.631262			0.315631	−	0.948882i	$-0.397784\pi$
$263$	10.2373			0.631262			0.315631	+	0.948882i	$0.397784\pi$
$264$	13.2526	−	2.97541i	0.815644	−	0.183124i
$265$	−4.91978			−0.302219
$266$	2.02171	+	1.46886i	0.123959	+	0.0900613i
$267$	3.60895	−	11.1072i	0.220864	−	0.679751i
$268$	−8.41848	−	25.9094i	−0.514241	−	1.58267i
$269$	−8.12925	+	5.90624i	−0.495649	+	0.360110i	−0.807353	−	0.590069i	$-0.799100\pi$
$269$	−8.12925	+	5.90624i	−0.495649	+	0.360110i	0.311704	+	0.950179i	$0.399100\pi$
$270$	5.00829	−	3.63874i	0.304795	−	0.221446i
$271$	−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
$273$	−5.48555	−	3.98549i	−0.332001	−	0.241213i
$274$	37.0239			2.23670
$275$	2.88772	+	4.87240i	0.174136	+	0.293817i
$276$	24.2372			1.45891
$277$	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
$279$	−2.73070	−	8.40423i	−0.163483	−	0.503148i
$280$	8.58084	−	6.23435i	0.512804	−	0.372574i
$281$	−1.65586	+	1.20305i	−0.0987805	+	0.0717682i	−0.636079	−	0.771624i	$-0.719445\pi$
$281$	−1.65586	+	1.20305i	−0.0987805	+	0.0717682i	0.537299	+	0.843392i	$0.319445\pi$
$282$	2.41007	+	7.41745i	0.143518	+	0.441702i
$283$	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
$285$	−2.70772			−0.160391
$286$	49.3522	+	21.3015i	2.91826	+	1.25959i
$287$	−8.69747			−0.513395
$288$	−2.05850	−	1.49559i	−0.121298	−	0.0881284i
$289$	−2.19658	+	6.76039i	−0.129211	+	0.397670i
$290$	−1.16176	−	3.57552i	−0.0682208	−	0.209962i
$291$	9.58914	−	6.96691i	0.562125	−	0.408408i
$292$	−1.77222	+	1.28760i	−0.103712	+	0.0753508i
$293$	−8.26173	−	25.4270i	−0.482655	−	1.48546i	−0.835348	−	0.549721i	$-0.814734\pi$
$293$	−8.26173	−	25.4270i	−0.482655	−	1.48546i	0.352693	−	0.935739i	$-0.385266\pi$
$294$	0.738630	−	2.27327i	0.0430778	−	0.132580i
$295$	−0.364594	−	0.264893i	−0.0212275	−	0.0154227i
$296$	−36.6242			−2.12874
$297$	−0.309017	+	3.30220i	−0.0179310	+	0.191613i
$298$	34.4540			1.99587
$299$	35.8046	+	26.0136i	2.07063	+	1.50440i
$300$	−1.95957	+	6.03094i	−0.113136	+	0.348197i
$301$	−1.38489	−	4.26225i	−0.0798237	−	0.245672i
$302$	−42.9625	+	31.2141i	−2.47222	+	1.79617i
$303$	3.00829	−	2.18565i	0.172822	−	0.125562i
$304$	−0.763142	−	2.34871i	−0.0437692	−	0.134708i
$305$	−6.51019	+	20.0363i	−0.372772	+	1.14728i
$306$	−6.08188	−	4.41874i	−0.347678	−	0.252603i
$307$	−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
$309$	−7.32703			−0.416820
$310$	44.2569	+	32.1545i	2.51362	+	1.82625i
$311$	8.05494	−	24.7906i	0.456754	−	1.40574i	−0.412310	−	0.911043i	$-0.635278\pi$
$311$	8.05494	−	24.7906i	0.456754	−	1.40574i	0.869064	−	0.494700i	$-0.164722\pi$
$312$	8.58084	+	26.4091i	0.485795	+	1.49512i
$313$	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
$315$	0.800331	+	2.46317i	0.0450935	+	0.138784i
$316$	−11.2552	+	34.6400i	−0.633155	+	1.94865i
$317$	20.0804	+	14.5893i	1.12783	+	0.819417i	0.985378	−	0.170385i	$-0.0545011\pi$
$317$	20.0804	+	14.5893i	1.12783	+	0.819417i	0.142453	+	0.989802i	$0.454501\pi$
$318$	4.54049			0.254618
$319$	1.84927	+	0.798188i	0.103539	+	0.0446900i
$320$	27.9872			1.56453
$321$	10.8250	+	7.86479i	0.604190	+	0.438970i
$322$	−4.82109	+	14.8378i	−0.268669	+	0.826878i
$323$	1.01609	+	3.12721i	0.0565370	+	0.174003i
$324$	−3.00415	+	2.18264i	−0.166897	+	0.121258i
$325$	−9.36776	+	6.80608i	−0.519630	+	0.377533i
$326$	−8.39365	−	25.8330i	−0.464881	−	1.43076i
$327$	−4.36420	+	13.4316i	−0.241341	+	0.742770i
$328$	28.8161	+	20.9361i	1.59110	+	1.15600i
$329$	−3.26290			−0.179889
$330$	−10.4682	−	17.6628i	−0.576254	−	0.972305i
$331$	−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
$333$	2.76354	−	8.50529i	0.151441	−	0.466087i
$334$	3.75881	+	11.5684i	0.205673	+	0.632996i
$335$	−15.3721	+	11.1685i	−0.839867	+	0.610199i
$336$	−1.91102	+	1.38844i	−0.104255	+	0.0757454i
$337$	−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
$339$	−2.15483	−	1.56557i	−0.117034	−	0.0850303i
$340$	30.2473			1.64039
$341$	−28.5963	+	6.42026i	−1.54857	+	0.347677i
$342$	2.49897			0.135129
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−5.67153	+	17.4552i	−0.305788	+	0.941119i
$345$	−5.22382	−	16.0773i	−0.281241	−	0.865571i
$346$	15.0343	−	10.9231i	0.808251	−	0.587228i
$347$	−11.3979	+	8.28107i	−0.611872	+	0.444551i	−0.850073	−	0.526665i	$-0.823442\pi$
$347$	−11.3979	+	8.28107i	−0.611872	+	0.444551i	0.238201	+	0.971216i	$0.423442\pi$
$348$	0.696863	+	2.14472i	0.0373558	+	0.114969i
$349$	−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
$351$	−6.78051			−0.361917
$352$	−5.57484	+	6.33541i	−0.297140	+	0.337679i
$353$	15.2345			0.810850			0.405425	−	0.914128i	$-0.367124\pi$
$353$	15.2345			0.810850			0.405425	+	0.914128i	$0.367124\pi$
$354$	0.336486	+	0.244471i	0.0178840	+	0.0129935i
$355$	−2.16644	+	6.66761i	−0.114983	+	0.353880i
$356$	−13.4012	−	41.2447i	−0.710264	−	2.18597i
$357$	2.54445	−	1.84865i	0.134666	−	0.0978408i
$358$	−11.8847	+	8.63473i	−0.628125	+	0.456360i
$359$	4.77379	+	14.6922i	0.251951	+	0.775425i	0.994415	+	0.105539i	$0.0336568\pi$
$359$	4.77379	+	14.6922i	0.251951	+	0.775425i	−0.742464	+	0.669886i	$0.766343\pi$
$360$	3.27759	−	10.0874i	0.172744	−	0.531652i
$361$	14.4870	+	10.5255i	0.762476	+	0.553971i
$362$	22.1290			1.16308
$363$	10.8090	+	2.04087i	0.567326	+	0.107118i
$364$	−25.1783			−1.31970
$365$	1.23607	+	0.898056i	0.0646988	+	0.0470064i
$366$	6.00829	−	18.4916i	0.314058	−	0.966572i
$367$	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
$369$	−7.03640	+	5.11224i	−0.366300	+	0.266133i
$370$	17.1079	+	52.6528i	0.889398	+	2.73729i
$371$	−0.587003	+	1.80661i	−0.0304757	+	0.0937945i
$372$	−26.5468	−	19.2874i	−1.37639	−	1.00000i
$373$	−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
$375$	−8.52677			−0.440321
$376$	10.8105	+	7.85430i	0.557510	+	0.405054i
$377$	−1.27247	+	3.91625i	−0.0655354	+	0.201697i
$378$	−0.738630	−	2.27327i	−0.0379910	−	0.116924i
$379$	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
$381$	3.20244	+	9.85610i	0.164066	+	0.504943i
$382$	10.8117	−	33.2748i	0.553172	−	1.70249i
$383$	−7.93470	−	5.76490i	−0.405444	−	0.294573i	0.366311	−	0.930493i	$-0.380621\pi$
$383$	−7.93470	−	5.76490i	−0.405444	−	0.294573i	−0.771755	+	0.635920i	$0.780621\pi$
$384$	−20.7406			−1.05842
$385$	8.38118	−	1.88169i	0.427144	−	0.0958999i
$386$	39.3707			2.00392
$387$	−3.62569	−	2.63421i	−0.184304	−	0.133905i
$388$	13.6009	−	41.8593i	0.690481	−	2.12508i
$389$	7.46028	+	22.9604i	0.378251	+	1.16414i	0.941259	+	0.337686i	$0.109644\pi$
$389$	7.46028	+	22.9604i	0.378251	+	1.16414i	−0.563007	+	0.826452i	$0.690356\pi$
$390$	33.9588	−	24.6725i	1.71957	−	1.24934i
$391$	−16.6078	+	12.0663i	−0.839892	+	0.610217i
$392$	−1.26552	−	3.89486i	−0.0639182	−	0.196720i
$393$	3.59822	−	11.0742i	0.181506	−	0.558618i
$394$	−13.1815	−	9.57694i	−0.664076	−	0.482480i
$395$	25.4036			1.27819
$396$	6.27917	+	10.5948i	0.315540	+	0.532406i
$397$	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
$399$	−0.323071	+	0.994311i	−0.0161738	+	0.0497778i
$400$	1.24654	+	3.83645i	0.0623268	+	0.191822i
$401$	20.4007	−	14.8220i	1.01876	−	0.740173i	0.0527328	−	0.998609i	$-0.483207\pi$
$401$	20.4007	−	14.8220i	1.01876	−	0.740173i	0.966029	+	0.258435i	$0.0832068\pi$
$402$	14.1870	−	10.3075i	0.707583	−	0.514089i
$403$	−18.5155	−	56.9850i	−0.922325	−	2.83862i
$404$	4.26685	−	13.1320i	0.212284	−	0.653343i
$405$	2.09529	+	1.52232i	0.104116	+	0.0756447i
$406$	−1.45160			−0.0720416
$407$	−27.2322	−	11.7540i	−1.34985	−	0.582625i
$408$	−12.8801			−0.637662
$409$	−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
$411$	4.78652	+	14.7314i	0.236102	+	0.726646i
$412$	−22.0115	+	15.9923i	−1.08443	+	0.787882i
$413$	−0.140774	+	0.102278i	−0.00692704	+	0.00503279i
$414$	4.82109	+	14.8378i	0.236944	+	0.729238i
$415$	−6.99951	+	21.5423i	−0.343593	+	1.05747i
$416$	−13.9577	−	10.1409i	−0.684332	−	0.497196i
$417$	5.81808			0.284913
$418$	0.772223	−	8.25208i	0.0377707	−	0.403622i
$419$	−28.3684			−1.38589			−0.692943	−	0.720993i	$-0.743686\pi$
$419$	−28.3684			−1.38589			−0.692943	+	0.720993i	$0.743686\pi$
$420$	7.78051	+	5.65287i	0.379650	+	0.275832i
$421$	−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
$423$	−2.63974	+	1.91788i	−0.128349	+	0.0932507i
$424$	6.29362	−	4.57259i	0.305645	−	0.222064i
$425$	−1.65971	−	5.10808i	−0.0805080	−	0.247778i
$426$	1.99942	−	6.15357i	0.0968720	−	0.298141i
$427$	6.58084	+	4.78126i	0.318469	+	0.231382i
$428$	49.6858			2.40165
$429$	−2.09529	+	22.3906i	−0.101162	+	1.08103i
$430$	27.7437			1.33792
$431$	−5.91592	−	4.29817i	−0.284960	−	0.207035i	0.436118	−	0.899889i	$-0.356353\pi$
$431$	−5.91592	−	4.29817i	−0.284960	−	0.207035i	−0.721078	+	0.692854i	$0.756353\pi$
$432$	−0.729944	+	2.24654i	−0.0351195	+	0.108087i
$433$	−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
$435$	1.27247	−	0.924501i	0.0610101	−	0.0443265i
$436$	16.2057	+	49.8760i	0.776112	+	2.38863i
$437$	2.10871	−	6.48994i	0.100873	−	0.310456i
$438$	−1.14077	−	0.828821i	−0.0545083	−	0.0396026i
$439$	−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
$441$	1.00000			0.0476190
$442$	−41.2383	−	29.9614i	−1.96150	−	1.42512i
$443$	−5.62774	+	17.3204i	−0.267382	+	0.822917i	0.723753	+	0.690059i	$0.242415\pi$
$443$	−5.62774	+	17.3204i	−0.267382	+	0.822917i	−0.991135	+	0.132858i	$0.957585\pi$
$444$	−10.2619	−	31.5829i	−0.487009	−	1.49886i
$445$	−24.4706	+	17.7789i	−1.16002	+	0.842801i
$446$	8.00433	−	5.81549i	0.379016	−	0.275371i
$447$	4.45428	+	13.7089i	0.210680	+	0.648406i
$448$	3.33929	−	10.2773i	0.157767	−	0.485556i
$449$	−3.58700	−	2.60611i	−0.169281	−	0.122990i	0.499919	−	0.866072i	$-0.333363\pi$
$449$	−3.58700	−	2.60611i	−0.169281	−	0.122990i	−0.669200	+	0.743082i	$0.733363\pi$
$450$	−4.08188			−0.192422
$451$	14.7073	+	24.8153i	0.692538	+	1.16851i
$452$	−9.89050			−0.465210
$453$	−17.9740	−	13.0589i	−0.844493	−	0.613560i
$454$	4.11979	−	12.6794i	0.193351	−	0.595074i
$455$	5.42666	+	16.7015i	0.254406	+	0.782980i
$456$	3.46385	−	2.51663i	0.162209	−	0.117852i
$457$	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
$459$	0.971892	−	2.99118i	0.0453640	−	0.139616i
$460$	−50.7840	−	36.8967i	−2.36782	−	1.72032i
$461$	−4.85723			−0.226224			−0.113112	−	0.993582i	$-0.536082\pi$
$461$	−4.85723			−0.226224			−0.113112	+	0.993582i	$0.536082\pi$
$462$	−7.73503	+	1.73662i	−0.359866	+	0.0807950i
$463$	−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
$465$	−7.07231	+	21.7663i	−0.327971	+	1.00939i
$466$	−20.4649	−	62.9846i	−0.948020	−	2.91771i
$467$	2.22175	−	1.61420i	0.102810	−	0.0746961i	−0.535192	−	0.844730i	$-0.679761\pi$
$467$	2.22175	−	1.61420i	0.102810	−	0.0746961i	0.638003	+	0.770034i	$0.279761\pi$
$468$	−20.3696	+	14.7994i	−0.941587	+	0.684103i
$469$	2.26710	+	6.97741i	0.104685	+	0.322187i
$470$	6.24191	−	19.2106i	0.287918	−	0.886120i
$471$	−7.92129	−	5.75515i	−0.364994	−	0.265183i
$472$	0.712607			0.0328004
$473$	−9.81910	+	11.1587i	−0.451483	+	0.513078i
$474$	−23.4451			−1.07687
$475$	1.44440	+	1.04942i	0.0662738	+	0.0481508i
$476$	3.60895	−	11.1072i	0.165416	−	0.509098i
$477$	0.587003	+	1.80661i	0.0268770	+	0.0827190i
$478$	−16.5940	+	12.0563i	−0.758992	+	0.551440i
$479$	14.5827	−	10.5950i	0.666302	−	0.484097i	−0.202483	−	0.979286i	$-0.564901\pi$
$479$	14.5827	−	10.5950i	0.666302	−	0.484097i	0.868785	+	0.495189i	$0.164901\pi$
$480$	2.03640	+	6.26739i	0.0929485	+	0.286066i
$481$	18.7382	−	57.6703i	0.854388	−	2.62954i
$482$	−37.9774	−	27.5922i	−1.72982	−	1.25679i
$483$	−6.52707			−0.296992
$484$	36.9263	−	17.4611i	1.67847	−	0.793687i
$485$	−30.6979			−1.39392
$486$	−1.93376	−	1.40496i	−0.0877171	−	0.0637302i
$487$	−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
$489$	9.19351	−	6.67948i	0.415745	−	0.302056i
$490$	−5.00829	+	3.63874i	−0.226252	+	0.164381i
$491$	5.13486	+	15.8035i	0.231733	+	0.713201i	0.997538	+	0.0701280i	$0.0223408\pi$
$491$	5.13486	+	15.8035i	0.231733	+	0.713201i	−0.765805	+	0.643073i	$0.777659\pi$
$492$	−9.98018	+	30.7158i	−0.449941	+	1.38478i
$493$	−1.54524	−	1.12268i	−0.0695939	−	0.0505629i
$494$	16.9443			0.762359
$495$	5.67448	−	6.44865i	0.255049	−	0.289845i
$496$	−20.8737			−0.937255
$497$	2.18995	+	1.59109i	0.0982326	+	0.0713702i
$498$	6.45989	−	19.8815i	0.289475	−	0.890911i
$499$	−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
$501$	−4.11700	+	2.99118i	−0.183934	+	0.133636i
$502$	22.0509	+	67.8657i	0.984180	+	3.02900i
$503$	2.06474	−	6.35462i	0.0920622	−	0.283338i	−0.894415	−	0.447239i	$-0.852407\pi$
$503$	2.06474	−	6.35462i	0.0920622	−	0.283338i	0.986477	+	0.163900i	$0.0524075\pi$
$504$	−3.31316	−	2.40715i	−0.147580	−	0.107223i
$505$	−9.63051			−0.428552
$506$	50.4871	−	11.3351i	2.24443	−	0.503905i
$507$	−32.9754			−1.46449
$508$	31.1329	+	22.6194i	1.38130	+	1.00357i
$509$	−5.65853	+	17.4152i	−0.250810	+	0.771914i	0.743816	+	0.668384i	$0.233014\pi$
$509$	−5.65853	+	17.4152i	−0.250810	+	0.771914i	−0.994626	+	0.103530i	$0.966986\pi$
$510$	6.01658	+	18.5171i	0.266419	+	0.819953i
$511$	0.477260	−	0.346750i	0.0211127	−	0.0153393i
$512$	−20.5148	+	14.9049i	−0.906637	+	0.658710i
$513$	0.323071	+	0.994311i	0.0142639	+	0.0438999i
$514$	−2.09529	+	6.44865i	−0.0924195	+	0.284438i
$515$	15.3523	+	11.1541i	0.676502	+	0.491508i
$516$	−16.6416			−0.732607
$517$	5.51750	+	9.30960i	0.242660	+	0.409436i
$518$	21.3761			0.939210
$519$	6.28984	+	4.56984i	0.276093	+	0.200594i
$520$	22.2238	−	68.3977i	0.974576	−	2.99944i
$521$	−0.181507	−	0.558621i	−0.00795197	−	0.0244736i	0.947002	−	0.321228i	$-0.104096\pi$
$521$	−0.181507	−	0.558621i	−0.00795197	−	0.0244736i	−0.954954	+	0.296755i	$0.904096\pi$
$522$	−1.17437	+	0.853227i	−0.0514006	+	0.0373448i
$523$	−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
$525$	0.527713	−	1.62413i	0.0230313	−	0.0708830i
$526$	19.7966	+	14.3830i	0.863171	+	0.627130i
$527$	27.7925			1.21066
$528$	7.19294	+	3.10464i	0.313033	+	0.135112i
$529$	19.6027			0.852291
$530$	−9.51366	−	6.91208i	−0.413247	−	0.300241i
$531$	−0.0537709	+	0.165490i	−0.00233346	+	0.00718164i
$532$	1.19967	+	3.69220i	0.0520122	+	0.160077i
$533$	−47.7104	+	34.6636i	−2.06657	+	1.50145i
$534$	22.5840	−	16.4082i	0.977306	−	0.710054i
$535$	−10.7087	−	32.9581i	−0.462979	−	1.42490i
$536$	9.28444	−	28.5746i	0.401027	−	1.23423i
$537$	−4.97214	−	3.61247i	−0.214564	−	0.155890i
$538$	−24.0180			−1.03549
$539$	0.309017	−	3.30220i	0.0133103	−	0.142236i
$540$	9.61724			0.413860
$541$	−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
$543$	2.86088	+	8.80489i	0.122772	+	0.377854i
$544$	6.47420	−	4.70378i	0.277579	−	0.201673i
$545$	29.5915	−	21.4995i	1.26756	−	0.920937i
$546$	−5.00829	−	15.4139i	−0.214335	−	0.659655i
$547$	−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
$549$	8.13437			0.347167
$550$	−1.26137	+	13.4792i	−0.0537850	+	0.574754i
$551$	0.634918			0.0270484
$552$	21.6253	+	15.7117i	0.920432	+	0.668733i
$553$	3.03103	−	9.32855i	0.128893	−	0.396690i
$554$	11.0136	+	33.8963i	0.467922	+	1.44011i
$555$	−18.7382	+	13.6141i	−0.795392	+	0.577886i
$556$	17.4784	−	12.6988i	0.741248	−	0.538548i
$557$	−1.85039	−	5.69491i	−0.0784035	−	0.241301i	0.904171	−	0.427171i	$-0.140490\pi$
$557$	−1.85039	−	5.69491i	−0.0784035	−	0.241301i	−0.982574	+	0.185870i	$0.940490\pi$
$558$	6.52707	−	20.0883i	0.276313	−	0.850404i
$559$	−24.5840	−	17.8613i	−1.03979	−	0.755454i
$560$	6.11779			0.258524
$561$	−9.57712	−	4.13370i	−0.404346	−	0.174525i
$562$	−4.89228			−0.206368
$563$	−29.2653	−	21.2625i	−1.23338	−	0.896106i	−0.236245	−	0.971694i	$-0.575917\pi$
$563$	−29.2653	−	21.2625i	−1.23338	−	0.896106i	−0.997139	+	0.0755874i	$0.975917\pi$
$564$	−3.74411	+	11.5232i	−0.157656	+	0.485214i
$565$	2.13169	+	6.56068i	0.0896810	+	0.276010i
$566$	33.0137	−	23.9859i	1.38767	−	1.00820i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	−3.42566	−	10.5431i	−0.143737	−	0.442378i
$569$	10.3428	−	31.8319i	0.433594	−	1.33446i	−0.460927	−	0.887438i	$-0.652483\pi$
$569$	10.3428	−	31.8319i	0.433594	−	1.33446i	0.894521	−	0.447026i	$-0.147517\pi$
$570$	−5.23607	−	3.80423i	−0.219315	−	0.159341i
$571$	−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
$573$	14.6374			0.611488
$574$	−16.8188	−	12.2196i	−0.702003	−	0.510035i
$575$	−3.44442	+	10.6008i	−0.143642	+	0.442086i
$576$	−3.33929	−	10.2773i	−0.139137	−	0.428220i
$577$	−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
$579$	5.08993	+	15.6652i	0.211530	+	0.651023i
$580$	1.80482	−	5.55467i	0.0749412	−	0.230645i
$581$	7.07548	+	5.14063i	0.293540	+	0.213269i
$582$	28.3313			1.17437
$583$	6.14718	−	1.38013i	0.254590	−	0.0571590i
$584$	−2.41592			−0.0999715
$585$	14.2072	+	10.3221i	0.587394	+	0.426767i
$586$	19.7477	−	60.7770i	0.815768	−	2.51068i
$587$	−1.48194	−	4.56094i	−0.0611661	−	0.188250i	0.915804	−	0.401625i	$-0.131554\pi$
$587$	−1.48194	−	4.56094i	−0.0611661	−	0.188250i	−0.976970	+	0.213375i	$0.931554\pi$
$588$	3.00415	−	2.18264i	0.123889	−	0.0900105i
$589$	−7.47420	+	5.43033i	−0.307969	+	0.223753i
$590$	−0.332873	−	1.02448i	−0.0137042	−	0.0421771i
$591$	2.10643	−	6.48291i	0.0866468	−	0.266671i
$592$	−17.0902	−	12.4168i	−0.702404	−	0.510326i
$593$	15.3387			0.629886			0.314943	−	0.949111i	$-0.398015\pi$
$593$	15.3387			0.629886			0.314943	+	0.949111i	$0.398015\pi$
$594$	−5.23701	+	5.95150i	−0.214877	+	0.244193i
$595$	−8.14560			−0.333937
$596$	43.3028	+	31.4613i	1.77375	+	1.28871i
$597$	−4.80711	+	14.7948i	−0.196742	+	0.605509i
$598$	32.6895	+	100.608i	1.33677	+	4.11416i
$599$	37.3303	−	27.1220i	1.52527	−	1.10818i	0.566478	−	0.824077i	$-0.308306\pi$
$599$	37.3303	−	27.1220i	1.52527	−	1.10818i	0.958795	−	0.284099i	$-0.0916944\pi$
$600$	−5.65794	+	4.11073i	−0.230984	+	0.167820i
$601$	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
$603$	5.93534	+	4.31228i	0.241706	+	0.175610i
$604$	−82.4994			−3.35685
$605$	−19.5412	−	20.7310i	−0.794463	−	0.842835i
$606$	8.88806			0.361053
$607$	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
$609$	−0.187665	−	0.577574i	−0.00760458	−	0.0234045i
$610$	−40.7393	+	29.5988i	−1.64949	+	1.19842i
$611$	−17.8988	+	13.0042i	−0.724108	+	0.526095i
$612$	−3.60895	−	11.1072i	−0.145883	−	0.448983i
$613$	−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
$615$	22.5258			0.908328
$616$	−8.97272	+	10.1969i	−0.361521	+	0.410843i
$617$	3.29610			0.132696			0.0663479	−	0.997797i	$-0.478865\pi$
$617$	3.29610			0.132696			0.0663479	+	0.997797i	$0.478865\pi$
$618$	−14.1687	−	10.2942i	−0.569949	−	0.414092i
$619$	−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
$621$	−5.28051	+	3.83652i	−0.211900	+	0.153954i
$622$	50.4060	−	36.6221i	2.02110	−	1.46841i
$623$	3.60895	+	11.1072i	0.144590	+	0.445001i
$624$	−4.94940	+	15.2327i	−0.198134	+	0.609795i
$625$	24.7739	+	17.9993i	0.990958	+	0.719973i
$626$	51.3586			2.05270
$627$	3.38324	−	0.759586i	0.135114	−	0.0303349i
$628$	−36.3581			−1.45085
$629$	22.7550	+	16.5324i	0.907300	+	0.659192i
$630$	−1.91300	+	5.88760i	−0.0762156	+	0.234568i
$631$	−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
$633$	1.26582	−	0.919672i	0.0503118	−	0.0365537i
$634$	18.3334	+	56.4244i	0.728112	+	2.24090i
$635$	8.29408	−	25.5266i	0.329141	−	1.01299i
$636$	5.70662	+	4.14610i	0.226282	+	0.164404i
$637$	6.78051			0.268654
$638$	2.45463	+	4.14165i	0.0971796	+	0.163970i
$639$	2.70693			0.107084
$640$	43.4578	+	31.5739i	1.71782	+	1.24807i
$641$	7.71648	−	23.7489i	0.304783	−	0.938025i	−0.674975	−	0.737840i	$-0.735846\pi$
$641$	7.71648	−	23.7489i	0.304783	−	0.938025i	0.979758	−	0.200185i	$-0.0641542\pi$
$642$	9.88315	+	30.4172i	0.390057	+	1.20047i
$643$	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
$645$	3.58676	+	11.0389i	0.141228	+	0.434657i
$646$	−2.42872	+	7.47485i	−0.0955569	+	0.294094i
$647$	−32.2628	−	23.4403i	−1.26838	−	0.921534i	−0.269246	−	0.963072i	$-0.586774\pi$
$647$	−32.2628	−	23.4403i	−1.26838	−	0.921534i	−0.999137	+	0.0415375i	$0.986774\pi$
$648$	−4.09529			−0.160878
$649$	0.529864	+	0.228701i	0.0207990	+	0.00897731i
$650$	−27.6772			−1.08559
$651$	7.14906	+	5.19410i	0.280194	+	0.203573i
$652$	13.0398	−	40.1322i	0.510676	−	1.57170i
$653$	0.505763	+	1.55658i	0.0197920	+	0.0609136i	0.960465	−	0.278402i	$-0.0898046\pi$
$653$	0.505763	+	1.55658i	0.0197920	+	0.0609136i	−0.940673	+	0.339315i	$0.889805\pi$
$654$	−27.3102	+	19.8420i	−1.06791	+	0.775884i
$655$	−24.3978	+	17.7260i	−0.953299	+	0.692612i
$656$	6.34867	+	19.5392i	0.247874	+	0.762877i
$657$	0.182297	−	0.561053i	0.00711209	−	0.0218888i
$658$	−6.30966	−	4.58423i	−0.245976	−	0.178712i
$659$	−7.63149			−0.297281			−0.148640	−	0.988891i	$-0.547490\pi$
$659$	−7.63149			−0.297281			−0.148640	+	0.988891i	$0.547490\pi$
$660$	2.97189	−	31.7580i	0.115681	−	1.23618i
$661$	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
$663$	6.58993	−	20.2817i	0.255932	−	0.787676i
$664$	−11.0679	−	34.0635i	−0.429518	−	1.32192i
$665$	2.19059	−	1.59156i	0.0849474	−	0.0617179i
$666$	17.2936	−	12.5645i	0.670113	−	0.486866i
$667$	1.22491	+	3.76987i	0.0474285	+	0.145970i
$668$	−5.83941	+	17.9719i	−0.225934	+	0.695352i
$669$	3.34873	+	2.43300i	0.129470	+	0.0940651i
$670$	−45.4172			−1.75462
$671$	2.51366	−	26.8613i	0.0970387	−	1.03697i
$672$	2.54445			0.0981541
$673$	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
$675$	−0.527713	−	1.62413i	−0.0203117	−	0.0625130i
$676$	−99.0628	+	71.9733i	−3.81011	+	2.76821i
$677$	6.50994	−	4.72974i	0.250197	−	0.181779i	−0.455617	−	0.890176i	$-0.650581\pi$
$677$	6.50994	−	4.72974i	0.250197	−	0.181779i	0.705814	+	0.708397i	$0.250581\pi$
$678$	−1.96735	−	6.05488i	−0.0755557	−	0.232536i
$679$	−3.66272	+	11.2727i	−0.140562	+	0.432607i
$680$	26.9877	+	19.6077i	1.03493	+	0.751921i
$681$	5.57761			0.213734
$682$	−64.3185	−	27.7613i	−2.46288	−	1.06304i
$683$	−19.2894			−0.738089			−0.369045	−	0.929412i	$-0.620315\pi$
$683$	−19.2894			−0.738089			−0.369045	+	0.929412i	$0.620315\pi$
$684$	3.14077	+	2.28191i	0.120090	+	0.0872509i
$685$	12.3967	−	38.1532i	0.473655	−	1.45776i
$686$	0.738630	+	2.27327i	0.0282010	+	0.0867938i
$687$	−0.637851	+	0.463426i	−0.0243355	+	0.0176808i
$688$	−8.56441	+	6.22241i	−0.326515	+	0.237227i
$689$	3.98018	+	12.2497i	0.151633	+	0.466678i
$690$	12.4863	−	38.4288i	0.475344	−	1.46296i
$691$	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
$693$	−1.69098	−	2.85317i	−0.0642351	−	0.108383i
$694$	−33.6753			−1.27830
$695$	−12.1906	−	8.85698i	−0.462415	−	0.335964i
$696$	−0.768545	+	2.36534i	−0.0291316	+	0.0896579i
$697$	−8.45300	−	26.0157i	−0.320180	−	0.985413i
$698$	−43.0074	+	31.2467i	−1.62786	+	1.18271i
$699$	22.4151	−	16.2855i	0.847818	−	0.615976i
$700$	−1.95957	−	6.03094i	−0.0740649	−	0.227948i
$701$	−10.8378	+	33.3555i	−0.409340	+	1.25982i	0.507877	+	0.861430i	$0.330430\pi$
$701$	−10.8378	+	33.3555i	−0.409340	+	1.25982i	−0.917217	+	0.398389i	$0.869570\pi$
$702$	−13.1119	−	9.52634i	−0.494876	−	0.359548i
$703$	−9.34972			−0.352631
$704$	−34.9695	+	7.85115i	−1.31796	+	0.295901i
$705$	8.45066			0.318270
$706$	29.4598	+	21.4038i	1.10873	+	0.805543i
$707$	−1.14906	+	3.53646i	−0.0432150	+	0.133002i
$708$	0.199669	+	0.614518i	0.00750402	+	0.0230950i
$709$	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
$711$	−3.03103	−	9.32855i	−0.113673	−	0.349848i
$712$	14.7797	−	45.4873i	0.553894	−	1.70471i
$713$	−46.6625	−	33.9023i	−1.74752	−	1.26965i
$714$	7.51762			0.281340
$715$	38.4759	−	43.7252i	1.43892	−	1.63523i
$716$	−22.8217			−0.852888
$717$	−6.94235	−	5.04392i	−0.259267	−	0.188368i
$718$	−11.4106	+	35.1181i	−0.425839	+	1.31060i
$719$	−12.6402	−	38.9026i	−0.471401	−	1.45082i	−0.850751	−	0.525570i	$-0.823852\pi$
$719$	−12.6402	−	38.9026i	−0.471401	−	1.45082i	0.379350	−	0.925253i	$-0.376148\pi$
$720$	4.94940	−	3.59595i	0.184453	−	0.134013i
$721$	5.92769	−	4.30672i	0.220759	−	0.160391i
$722$	13.2266	+	40.7074i	0.492244	+	1.51497i
$723$	6.06884	−	18.6780i	0.225703	−	0.694641i
$724$	27.8124	+	20.2069i	1.03364	+	0.750983i
$725$	−1.03709			−0.0385166
$726$	18.0347	+	19.1328i	0.669330	+	0.710083i
$727$	−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
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	1.12853	+	3.47325i	0.0417686	+	0.128551i
$731$	11.4032	−	8.28489i	0.421762	−	0.306428i
$732$	24.4368	−	17.7544i	0.903211	−	0.656222i
$733$	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
$735$	−2.09529	−	1.52232i	−0.0772861	−	0.0561516i
$736$	−16.6078			−0.612171
$737$	16.0741	−	18.2671i	0.592098	−	0.672877i
$738$	−20.7892			−0.765260
$739$	−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
$741$	2.19059	+	6.74194i	0.0804733	+	0.247671i
$742$	−3.67333	+	2.66883i	−0.134852	+	0.0979759i
$743$	34.3881	−	24.9845i	1.26158	−	0.916591i	0.262745	−	0.964865i	$-0.415372\pi$
$743$	34.3881	−	24.9845i	1.26158	−	0.916591i	0.998834	+	0.0482747i	$0.0153723\pi$
$744$	−11.1830	−	34.4178i	−0.409989	−	1.26182i
$745$	11.5362	−	35.5049i	0.422655	−	1.30080i
$746$	−1.97128	−	1.43222i	−0.0721738	−	0.0524373i
$747$	8.74577			0.319991
$748$	−37.7934	+	8.48516i	−1.38187	+	0.310248i
$749$	−13.3804			−0.488909
$750$	−16.4887	−	11.9798i	−0.602083	−	0.437439i
$751$	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
$753$	−24.1522	+	17.5476i	−0.880156	+	0.639471i
$754$	−7.96281	+	5.78532i	−0.289988	+	0.210689i
$755$	17.7810	+	54.7244i	0.647119	+	1.99163i
$756$	1.14748	−	3.53158i	0.0417335	−	0.128442i
$757$	−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
$759$	11.0372	+	18.6228i	0.400624	+	0.675967i
$760$	−11.0889			−0.402236
$761$	11.3231	+	8.22669i	0.410461	+	0.298217i	0.773788	−	0.633444i	$-0.218359\pi$
$761$	11.3231	+	8.22669i	0.410461	+	0.298217i	−0.363327	+	0.931662i	$0.618359\pi$
$762$	−7.65466	+	23.5586i	−0.277299	+	0.853438i
$763$	−4.36420	−	13.4316i	−0.157995	−	0.486257i
$764$	43.9730	−	31.9482i	1.59089	−	1.15585i
$765$	−6.58993	+	4.78786i	−0.238259	+	0.173105i
$766$	−7.24436	−	22.2958i	−0.261749	−	0.805582i
$767$	−0.364594	+	1.12211i	−0.0131647	+	0.0405169i
$768$	−22.6226	−	16.4363i	−0.816324	−	0.593094i
$769$	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
$771$	−2.83673			−0.102162
$772$	49.4823	+	35.9510i	1.78091	+	1.29391i
$773$	−13.2976	+	40.9259i	−0.478283	+	1.47200i	0.363196	+	0.931713i	$0.381686\pi$
$773$	−13.2976	+	40.9259i	−0.478283	+	1.47200i	−0.841479	+	0.540291i	$0.818314\pi$
$774$	−3.31024	−	10.1879i	−0.118984	−	0.366195i
$775$	12.2086	−	8.87005i	0.438545	−	0.318621i
$776$	39.2703	−	28.5316i	1.40972	−	1.02422i
$777$	2.76354	+	8.50529i	0.0991413	+	0.305126i
$778$	−17.8320	+	54.8812i	−0.639308	+	1.96759i
$779$	7.35641	+	5.34475i	0.263571	+	0.191495i
$780$	65.2099			2.33489
$781$	0.836486	−	8.93880i	0.0299318	−	0.319856i
$782$	−49.0680			−1.75467
$783$	−0.491314	−	0.356961i	−0.0175581	−	0.0127567i
$784$	0.729944	−	2.24654i	0.0260694	−	0.0802335i
$785$	7.83624	+	24.1175i	0.279687	+	0.860790i
$786$	22.5168	−	16.3594i	0.803149	−	0.583522i
$787$	−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
$789$	−3.16351	+	9.73629i	−0.112624	+	0.346621i
$790$	49.1244	+	35.6910i	1.74777	+	1.26983i
$791$	2.66351			0.0947037
$792$	−1.26552	+	13.5235i	−0.0449681	+	0.480536i
$793$	55.1552			1.95862
$794$	39.9765	+	29.0447i	1.41871	+	1.03076i
$795$	1.52029	−	4.67899i	0.0539193	−	0.165947i
$796$	17.8504	+	54.9378i	0.632690	+	1.94722i
$797$	5.62839	−	4.08927i	0.199368	−	0.144849i	−0.483622	−	0.875277i	$-0.660679\pi$
$797$	5.62839	−	4.08927i	0.199368	−	0.144849i	0.682990	+	0.730428i	$0.260679\pi$
$798$	−2.02171	+	1.46886i	−0.0715676	+	0.0519969i
$799$	−3.17118	−	9.75990i	−0.112188	−	0.345280i
$800$	1.34274	−	4.13252i	0.0474729	−	0.146107i
$801$	9.44836	+	6.86464i	0.333841	+	0.242550i
$802$	60.2742			2.12836
$803$	−1.79637	−	0.775356i	−0.0633927	−	0.0273617i
$804$	27.2428			0.960779
$805$	13.6761	+	9.93630i	0.482021	+	0.350208i
$806$	44.2569	−	136.209i	1.55888	−	4.79775i
$807$	−3.10510	−	9.55650i	−0.109305	−	0.336405i
$808$	12.3198	−	8.95088i	0.433410	−	0.314891i
$809$	−40.2788	+	29.2642i	−1.41613	+	1.02888i	−0.423730	+	0.905789i	$0.639279\pi$
$809$	−40.2788	+	29.2642i	−1.41613	+	1.02888i	−0.992396	+	0.123087i	$0.960721\pi$
$810$	1.91300	+	5.88760i	0.0672159	+	0.206869i
$811$	−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
$813$	2.50432			0.0878304
$814$	−36.1465	−	60.9895i	−1.26694	−	2.13768i
$815$	−29.4314			−1.03094
$816$	−6.01036	−	4.36678i	−0.210405	−	0.152868i
$817$	−1.44787	+	4.45610i	−0.0506547	+	0.155899i
$818$	−7.50141	−	23.0870i	−0.262281	−	0.807217i
$819$	5.48555	−	3.98549i	0.191681	−	0.139264i
$820$	67.6708	−	49.1657i	2.36317	−	1.71694i
$821$	5.46804	+	16.8289i	0.190836	+	0.587332i	1.00000		0.000250536i	$-7.97481e-5\pi$
$821$	5.46804	+	16.8289i	0.190836	+	0.587332i	−0.809164	+	0.587583i	$0.800080\pi$
$822$	−11.4410	+	35.2118i	−0.399051	+	1.22815i
$823$	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
$825$	−5.52628	+	1.24073i	−0.192401	+	0.0431966i
$826$	−0.415920			−0.0144717
$827$	−33.4044	−	24.2697i	−1.16158	−	0.843940i	−0.171606	−	0.985166i	$-0.554896\pi$
$827$	−33.4044	−	24.2697i	−1.16158	−	0.843940i	−0.989977	+	0.141226i	$0.954896\pi$
$828$	−7.48970	+	23.0509i	−0.260285	+	0.801075i
$829$	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
$831$	−12.0631	+	8.76435i	−0.418464	+	0.304032i
$832$	−22.6421	−	69.6853i	−0.784974	−	2.41590i
$833$	−0.971892	+	2.99118i	−0.0336741	+	0.103638i
$834$	11.2508	+	8.17416i	0.389582	+	0.283048i
$835$	13.1799			0.456108
$836$	8.50586	−	9.66631i	0.294181	−	0.334316i
$837$	8.83673			0.305442
$838$	−54.8576	−	39.8564i	−1.89502	−	1.37682i
$839$	−0.983838	+	3.02794i	−0.0339659	+	0.104536i	−0.966602	−	0.256282i	$-0.917502\pi$
$839$	−0.983838	+	3.02794i	−0.0339659	+	0.104536i	0.932636	+	0.360818i	$0.117502\pi$
$840$	3.27759	+	10.0874i	0.113088	+	0.348048i
$841$	23.1631	−	16.8290i	0.798728	−	0.580310i
$842$	−53.5339	+	38.8947i	−1.84490	+	1.34040i
$843$	−0.632483	−	1.94658i	−0.0217839	−	0.0670439i
$844$	1.79540	−	5.52566i	0.0618001	−	0.190201i
$845$	69.0931	+	50.1991i	2.37687	+	1.72690i
$846$	−7.79916			−0.268141
$847$	−9.94427	+	4.70228i	−0.341689	+	0.161572i
$848$	4.48710			0.154087
$849$	13.8118	+	10.0349i	0.474019	+	0.344395i
$850$	3.96714	−	12.2096i	0.136072	−	0.418786i
$851$	−18.0378	−	55.5147i	−0.618328	−	1.90302i
$852$	8.13200	−	5.90824i	0.278598	−	0.202413i
$853$	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
$855$	0.836730	−	2.57519i	0.0286156	−	0.0880697i
$856$	44.3314	+	32.2086i	1.51522	+	1.10087i
$857$	9.16216			0.312973			0.156487	−	0.987680i	$-0.449983\pi$
$857$	9.16216			0.312973			0.156487	+	0.987680i	$0.449983\pi$
$858$	−35.5096	+	40.3542i	−1.21228	+	1.37767i
$859$	−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
$861$	2.68767	−	8.27178i	0.0915954	−	0.281902i
$862$	−5.40122	−	16.6232i	−0.183966	−	0.566190i
$863$	−15.6086	+	11.3403i	−0.531322	+	0.386028i	−0.820852	−	0.571141i	$-0.806501\pi$
$863$	−15.6086	+	11.3403i	−0.531322	+	0.386028i	0.289530	+	0.957169i	$0.406501\pi$
$864$	2.05850	−	1.49559i	0.0700316	−	0.0508809i
$865$	−6.22231	−	19.1503i	−0.211565	−	0.651130i
$866$	7.77935	−	23.9424i	0.264353	−	0.813595i
$867$	−5.75073	−	4.17815i	−0.195305	−	0.141897i
$868$	32.8137			1.11377
$869$	−31.7414	+	7.12638i	−1.07675	+	0.241746i
$870$	3.75953			0.127460
$871$	40.2447	+	29.2395i	1.36364	+	0.990741i
$872$	−17.8727	+	55.0064i	−0.605245	+	1.86275i
$873$	3.66272	+	11.2727i	0.123964	+	0.381523i
$874$	13.1958	−	9.58733i	0.446355	−	0.324296i
$875$	6.89830	−	5.01191i	0.233205	−	0.169434i
$876$	−0.676929	−	2.08337i	−0.0228713	−	0.0703906i
$877$	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
$879$	26.7355			0.901767
$880$	−10.3451	−	17.4551i	−0.348733	−	0.588411i
$881$	6.68797			0.225324			0.112662	−	0.993633i	$-0.464062\pi$
$881$	6.68797			0.225324			0.112662	+	0.993633i	$0.464062\pi$
$882$	1.93376	+	1.40496i	0.0651130	+	0.0473074i
$883$	−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
$885$	0.364594	−	0.264893i	0.0122557	−	0.00890429i
$886$	−35.2171	+	25.5867i	−1.18314	+	0.859603i
$887$	4.35733	+	13.4105i	0.146305	+	0.450280i	0.997176	−	0.0750938i	$-0.0239256\pi$
$887$	4.35733	+	13.4105i	0.146305	+	0.450280i	−0.850872	+	0.525373i	$0.823926\pi$
$888$	11.3175	−	34.8317i	0.379790	−	1.16887i
$889$	−8.38410	−	6.09140i	−0.281194	−	0.204299i
$890$	−72.2987			−2.42346
$891$	−3.04508	−	1.31433i	−0.102014	−	0.0440316i
$892$	15.3704			0.514640
$893$	2.75980	+	2.00511i	0.0923530	+	0.0670984i
$894$	−10.6469	+	32.7677i	−0.356084	+	1.09592i
$895$	4.91875	+	15.1384i	0.164416	+	0.506020i
$896$	16.7795	−	12.1910i	0.560565	−	0.407274i
$897$	−35.8046	+	26.0136i	−1.19548	+	0.868568i
$898$	−3.27492	−	10.0792i	−0.109286	−	0.336346i
$899$	1.65835	−	5.10387i	0.0553090	−	0.170224i
$900$	−5.13023	−	3.72733i	−0.171008	−	0.124244i
$901$	−5.97439			−0.199036
$902$	−6.42421	+	68.6500i	−0.213903	+	2.28579i
$903$	4.48159			0.149138
$904$	−8.82465	−	6.41149i	−0.293504	−	0.213243i
$905$	7.40947	−	22.8040i	0.246299	−	0.758031i
$906$	−16.4102	−	50.5055i	−0.545193	−	1.67793i
$907$	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
$909$	1.14906	+	3.53646i	0.0381121	+	0.117297i
$910$	−12.9711	+	39.9209i	−0.429988	+	1.32337i
$911$	−33.6157	−	24.4232i	−1.11374	−	0.809177i	−0.130489	−	0.991450i	$-0.541655\pi$
$911$	−33.6157	−	24.4232i	−1.11374	−	0.809177i	−0.983248	+	0.182273i	$0.941655\pi$
$912$	2.46958			0.0817759
$913$	2.70259	−	28.8803i	0.0894427	−	0.955797i
$914$	48.5057			1.60442
$915$	−17.0439	−	12.3831i	−0.563454	−	0.409373i
$916$	−0.904706	+	2.78440i	−0.0298923	+	0.0919991i
$917$	3.59822	+	11.0742i	0.118824	+	0.365701i
$918$	6.08188	−	4.41874i	0.200732	−	0.145840i
$919$	−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
$921$	5.04714	−	15.5335i	0.166309	−	0.511846i
$922$	−9.39270	−	6.82420i	−0.309332	−	0.224743i
$923$	18.3543			0.604141
$924$	−11.3074	−	4.88053i	−0.371986	−	0.160558i
$925$	15.2721			0.502143
$926$	−37.7408	−	27.4203i	−1.24024	−	0.901087i
$927$	2.26418	−	6.96842i	0.0743653	−	0.228873i
$928$	−0.477504	−	1.46961i	−0.0156748	−	0.0482422i
$929$	1.24832	−	0.906954i	0.0409559	−	0.0297562i	−0.567119	−	0.823636i	$-0.691942\pi$
$929$	1.24832	−	0.906954i	0.0409559	−	0.0297562i	0.608075	+	0.793880i	$0.291942\pi$
$930$	−44.2569	+	32.1545i	−1.45124	+	1.05439i
$931$	−0.323071	−	0.994311i	−0.0105882	−	0.0325872i
$932$	31.7928	−	97.8483i	1.04141	−	3.20513i
$933$	21.0881	+	15.3214i	0.690393	+	0.501600i
$934$	6.56421			0.214788
$935$	13.7741	+	23.2408i	0.450460	+	0.760054i
$936$	−27.7682			−0.907632
$937$	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
$939$	6.63974	+	20.4350i	0.216680	+	0.666872i
$940$	25.3870	−	18.4448i	0.828033	−	0.601601i
$941$	−3.89751	+	2.83171i	−0.127055	+	0.0923111i	−0.649498	−	0.760363i	$-0.725021\pi$
$941$	−3.89751	+	2.83171i	−0.127055	+	0.0923111i	0.522443	+	0.852674i	$0.325021\pi$
$942$	−7.23211	−	22.2581i	−0.235635	−	0.725210i
$943$	−17.5426	+	53.9905i	−0.571265	+	1.75817i
$944$	0.332529	+	0.241597i	0.0108229	+	0.00786330i
$945$	−2.58993			−0.0842503
$946$	−34.6653	+	7.78284i	−1.12707	+	0.253042i
$947$	18.0449			0.586379			0.293189	−	0.956054i	$-0.405283\pi$
$947$	18.0449			0.586379			0.293189	+	0.956054i	$0.405283\pi$
$948$	−29.4665	−	21.4087i	−0.957028	−	0.695322i
$949$	1.23607	−	3.80423i	0.0401245	−	0.123490i
$950$	1.31874	+	4.05866i	0.0427855	+	0.131680i
$951$	−20.0804	+	14.5893i	−0.651153	+	0.473090i
$952$	10.4203	−	7.57076i	0.337722	−	0.245370i
$953$	−11.5977	−	35.6940i	−0.375686	−	1.15624i	−0.943015	−	0.332750i	$-0.892023\pi$
$953$	−11.5977	−	35.6940i	−0.375686	−	1.15624i	0.567329	−	0.823491i	$-0.307977\pi$
$954$	−1.40309	+	4.31826i	−0.0454267	+	0.139809i
$955$	−30.6697	−	22.2829i	−0.992449	−	0.721057i
$956$	−31.8649			−1.03058
$957$	−1.33058	+	1.51211i	−0.0430115	+	0.0488796i
$958$	43.0850			1.39201
$959$	−12.5313	−	9.10450i	−0.404656	−	0.294000i
$960$	−8.64852	+	26.6174i	−0.279130	+	0.859073i
$961$	14.5509	+	44.7832i	0.469385	+	1.44462i
$962$	117.259	−	85.1940i	3.78060	−	2.74676i
$963$	−10.8250	+	7.86479i	−0.348829	+	0.253439i
$964$	−22.5356	−	69.3574i	−0.725823	−	2.23385i
$965$	13.1825	−	40.5717i	0.424361	−	1.30605i
$966$	−12.6218	−	9.17026i	−0.406099	−	0.295048i
$967$	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
$969$	−3.28815			−0.105631
$970$	−59.3624	−	43.1293i	−1.90601	−	1.38480i
$971$	−14.1398	+	43.5180i	−0.453769	+	1.39656i	0.418805	+	0.908076i	$0.362449\pi$
$971$	−14.1398	+	43.5180i	−0.453769	+	1.39656i	−0.872574	+	0.488481i	$0.837551\pi$
$972$	−1.14748	−	3.53158i	−0.0368055	−	0.113276i
$973$	−4.70693	+	3.41978i	−0.150897	+	0.109633i
$974$	−23.9465	+	17.3982i	−0.767296	+	0.557473i
$975$	−3.57817	−	11.0125i	−0.114593	−	0.352681i
$976$	5.93764	−	18.2742i	0.190059	−	0.584942i
$977$	27.6930	+	20.1201i	0.885976	+	0.643700i	0.934826	−	0.355107i	$-0.115555\pi$
$977$	27.6930	+	20.1201i	0.885976	+	0.643700i	−0.0488494	+	0.998806i	$0.515555\pi$
$978$	27.1624			0.868558
$979$	25.5881	−	29.0791i	0.817799	−	0.929371i
$980$	−9.61724			−0.307212
$981$	−11.4256	−	8.30120i	−0.364792	−	0.265037i
$982$	−12.2736	+	37.7744i	−0.391667	+	1.20543i
$983$	−9.06625	−	27.9031i	−0.289169	−	0.889969i	−0.985118	−	0.171879i	$-0.945016\pi$
$983$	−9.06625	−	27.9031i	−0.289169	−	0.889969i	0.695950	−	0.718091i	$-0.254984\pi$
$984$	−28.8161	+	20.9361i	−0.918624	+	0.667420i
$985$	−14.2826	+	10.3770i	−0.455083	+	0.330637i
$986$	−1.41080	−	4.34198i	−0.0449289	−	0.138277i
$987$	1.00829	−	3.10320i	0.0320943	−	0.0987760i
$988$	21.2961	+	15.4725i	0.677518	+	0.492246i
$989$	−29.2517			−0.930150
$990$	20.0332	−	4.49773i	0.636696	−	0.142947i
$991$	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
$993$	9.77578	−	30.0868i	0.310225	−	0.954775i
$994$	1.99942	+	6.15357i	0.0634176	+	0.195179i
$995$	32.5947	−	23.6814i	1.03332	−	0.750752i
$996$	26.2736	−	19.0889i	0.832510	−	0.604854i
$997$	−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
$999$	7.23503	+	5.25656i	0.228906	+	0.166310i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.f.169.2	✓	8	1.1	even	1	trivial
231.2.j.f.190.2	yes	8	11.3	even	5	inner
693.2.m.f.190.1		8	33.14	odd	10
693.2.m.f.631.1		8	3.2	odd	2
2541.2.a.bm.1.4		4	11.6	odd	10
2541.2.a.bn.1.1		4	11.5	even	5
7623.2.a.ci.1.4		4	33.5	odd	10
7623.2.a.cl.1.1		4	33.17	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.93376 + 1.40496i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.14748 + 3.53158i) q^{4} +(2.09529 - 1.52232i) q^{5} +(-1.93376 + 1.40496i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-1.26552 + 3.89486i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.93376 + 1.40496i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(1.14748 + 3.53158i) q^{4} +(2.09529 - 1.52232i) q^{5} +(-1.93376 + 1.40496i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-1.26552 + 3.89486i) q^{8} +(-0.809017 - 0.587785i) q^{9} +6.19059 q^{10} +(-2.19098 + 2.48990i) q^{11} -3.71333 q^{12} +(-5.48555 - 3.98549i) q^{13} +(0.738630 - 2.27327i) q^{14} +(0.800331 + 2.46317i) q^{15} +(-1.91102 + 1.38844i) q^{16} +(2.54445 - 1.84865i) q^{17} +(-0.738630 - 2.27327i) q^{18} +(-0.323071 + 0.994311i) q^{19} +(7.78051 + 5.65287i) q^{20} +1.00000 q^{21} +(-7.73503 + 1.73662i) q^{22} -6.52707 q^{23} +(-3.31316 - 2.40715i) q^{24} +(0.527713 - 1.62413i) q^{25} +(-5.00829 - 15.4139i) q^{26} +(0.809017 - 0.587785i) q^{27} +(3.00415 - 2.18264i) q^{28} +(-0.187665 - 0.577574i) q^{29} +(-1.91300 + 5.88760i) q^{30} +(7.14906 + 5.19410i) q^{31} +2.54445 q^{32} +(-1.69098 - 2.85317i) q^{33} +7.51762 q^{34} +(-2.09529 - 1.52232i) q^{35} +(1.14748 - 3.53158i) q^{36} +(2.76354 + 8.50529i) q^{37} +(-2.02171 + 1.46886i) q^{38} +(5.48555 - 3.98549i) q^{39} +(3.27759 + 10.0874i) q^{40} +(2.68767 - 8.27178i) q^{41} +(1.93376 + 1.40496i) q^{42} +4.48159 q^{43} +(-11.3074 - 4.88053i) q^{44} -2.58993 q^{45} +(-12.6218 - 9.17026i) q^{46} +(1.00829 - 3.10320i) q^{47} +(-0.729944 - 2.24654i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(3.30231 - 2.39927i) q^{50} +(0.971892 + 2.99118i) q^{51} +(7.78051 - 23.9460i) q^{52} +(-1.53679 - 1.11655i) q^{53} +2.39026 q^{54} +(-0.800331 + 8.55245i) q^{55} +4.09529 q^{56} +(-0.845811 - 0.614518i) q^{57} +(0.448568 - 1.38055i) q^{58} +(-0.0537709 - 0.165490i) q^{59} +(-7.78051 + 5.65287i) q^{60} +(-6.58084 + 4.78126i) q^{61} +(6.52707 + 20.0883i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(8.74238 + 6.35171i) q^{64} -17.5610 q^{65} +(0.738630 - 7.89310i) q^{66} -7.33649 q^{67} +(9.44836 + 6.86464i) q^{68} +(2.01698 - 6.20762i) q^{69} +(-1.91300 - 5.88760i) q^{70} +(-2.18995 + 1.59109i) q^{71} +(3.31316 - 2.40715i) q^{72} +(0.182297 + 0.561053i) q^{73} +(-6.60556 + 20.3298i) q^{74} +(1.38157 + 1.00377i) q^{75} -3.88221 q^{76} +(3.04508 + 1.31433i) q^{77} +16.2072 q^{78} +(7.93534 + 5.76536i) q^{79} +(-1.89050 + 5.81836i) q^{80} +(0.309017 + 0.951057i) q^{81} +(16.8188 - 12.2196i) q^{82} +(-7.07548 + 5.14063i) q^{83} +(1.14748 + 3.53158i) q^{84} +(2.51713 - 7.74692i) q^{85} +(8.66632 + 6.29645i) q^{86} +0.607298 q^{87} +(-6.92507 - 11.6846i) q^{88} -11.6788 q^{89} +(-5.00829 - 3.63874i) q^{90} +(-2.09529 + 6.44865i) q^{91} +(-7.48970 - 23.0509i) q^{92} +(-7.14906 + 5.19410i) q^{93} +(6.30966 - 4.58423i) q^{94} +(0.836730 + 2.57519i) q^{95} +(-0.786277 + 2.41991i) q^{96} +(-9.58914 - 6.96691i) q^{97} -2.39026 q^{98} +(3.23607 - 0.726543i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9	\( 8 q + 2 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} - 2 q^{9} + 20 q^{10} - 22 q^{11} - 6 q^{12} - 8 q^{13} + 3 q^{14} - 2 q^{15} + 4 q^{16} - 4 q^{17} - 3 q^{18} + 20 q^{20} + 8 q^{21} - 8 q^{22} - 20 q^{23} - 7 q^{24} - 26 q^{25} - 10 q^{26} + 2 q^{27} + 9 q^{28} + 24 q^{31} - 4 q^{32} - 18 q^{33} + 36 q^{34} - 2 q^{35} + 6 q^{36} + 6 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 20 q^{41} + 2 q^{42} - 8 q^{43} - 39 q^{44} - 8 q^{45} - 43 q^{46} - 22 q^{47} + q^{48} - 2 q^{49} + 22 q^{50} + 4 q^{51} + 20 q^{52} - 20 q^{53} - 2 q^{54} + 2 q^{55} + 18 q^{56} - 10 q^{57} - 17 q^{58} + 18 q^{59} - 20 q^{60} - 2 q^{61} + 20 q^{62} + 2 q^{63} + 18 q^{64} - 56 q^{65} + 3 q^{66} - 56 q^{67} - 2 q^{68} - 10 q^{69} + 14 q^{71} + 7 q^{72} + 2 q^{73} - 12 q^{74} - 14 q^{75} - 8 q^{76} + 2 q^{77} + 40 q^{78} + 20 q^{79} + 38 q^{80} - 2 q^{81} + 2 q^{82} - 8 q^{83} + 6 q^{84} + 60 q^{85} + 55 q^{86} - 38 q^{88} - 32 q^{89} - 10 q^{90} - 2 q^{91} - 9 q^{92} - 24 q^{93} + 48 q^{94} - 28 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{98} + 8 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^5 - 2 * q^6 + 2 * q^7 + 2 * q^8 - 2 * q^9 + 20 * q^10 - 22 * q^11 - 6 * q^12 - 8 * q^13 + 3 * q^14 - 2 * q^15 + 4 * q^16 - 4 * q^17 - 3 * q^18 + 20 * q^20 + 8 * q^21 - 8 * q^22 - 20 * q^23 - 7 * q^24 - 26 * q^25 - 10 * q^26 + 2 * q^27 + 9 * q^28 + 24 * q^31 - 4 * q^32 - 18 * q^33 + 36 * q^34 - 2 * q^35 + 6 * q^36 + 6 * q^37 + 14 * q^38 + 8 * q^39 + 12 * q^40 + 20 * q^41 + 2 * q^42 - 8 * q^43 - 39 * q^44 - 8 * q^45 - 43 * q^46 - 22 * q^47 + q^48 - 2 * q^49 + 22 * q^50 + 4 * q^51 + 20 * q^52 - 20 * q^53 - 2 * q^54 + 2 * q^55 + 18 * q^56 - 10 * q^57 - 17 * q^58 + 18 * q^59 - 20 * q^60 - 2 * q^61 + 20 * q^62 + 2 * q^63 + 18 * q^64 - 56 * q^65 + 3 * q^66 - 56 * q^67 - 2 * q^68 - 10 * q^69 + 14 * q^71 + 7 * q^72 + 2 * q^73 - 12 * q^74 - 14 * q^75 - 8 * q^76 + 2 * q^77 + 40 * q^78 + 20 * q^79 + 38 * q^80 - 2 * q^81 + 2 * q^82 - 8 * q^83 + 6 * q^84 + 60 * q^85 + 55 * q^86 - 38 * q^88 - 32 * q^89 - 10 * q^90 - 2 * q^91 - 9 * q^92 - 24 * q^93 + 48 * q^94 - 28 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more