LMFDB - Embedded newform 430.2.q.a.31.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, degree $12$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			31.2
Character	$\chi$	$=$	430.31
Dual form			430.2.q.a.111.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.900969 + 0.433884i) q^{2} +(-0.529721 + 0.361157i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(0.320562 - 0.555229i) q^{6} +(-1.04610 - 1.81189i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.945854 + 2.41000i) q^{9} +O(q^{10})$	\(q+(-0.900969 + 0.433884i) q^{2} +(-0.529721 + 0.361157i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(0.320562 - 0.555229i) q^{6} +(-1.04610 - 1.81189i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.945854 + 2.41000i) q^{9} +(0.955573 + 0.294755i) q^{10} +(2.03599 + 2.55305i) q^{11} +(-0.0479112 + 0.639330i) q^{12} +(1.40814 - 0.434354i) q^{13} +(1.72865 + 1.17857i) q^{14} +(0.633962 + 0.0955544i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(5.16204 - 4.78968i) q^{17} +(-0.193473 - 2.58172i) q^{18} +(0.237704 + 0.605659i) q^{19} +(-0.988831 + 0.149042i) q^{20} +(1.20852 + 0.581991i) q^{21} +(-2.94209 - 1.41684i) q^{22} +(8.69558 - 1.31065i) q^{23} +(-0.234229 - 0.596805i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-1.08023 + 1.00231i) q^{26} +(-0.797340 - 3.49337i) q^{27} +(-2.06882 - 0.311825i) q^{28} +(3.54783 + 2.41887i) q^{29} +(-0.612640 + 0.188974i) q^{30} +(-0.497328 + 6.63637i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-2.00056 - 0.617091i) q^{33} +(-2.57268 + 6.55508i) q^{34} +(-0.465556 + 2.03973i) q^{35} +(1.29448 + 2.24211i) q^{36} +(0.510629 - 0.884436i) q^{37} +(-0.476949 - 0.442544i) q^{38} +(-0.589051 + 0.738647i) q^{39} +(0.826239 - 0.563320i) q^{40} +(3.46990 - 1.67102i) q^{41} -1.34135 q^{42} +(-0.341353 + 6.54855i) q^{43} +3.26547 q^{44} +(2.33257 - 1.12331i) q^{45} +(-7.26578 + 4.95373i) q^{46} +(0.00226623 - 0.00284176i) q^{47} +(0.469976 + 0.436074i) q^{48} +(1.31137 - 2.27136i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00461 + 4.40150i) q^{51} +(0.538370 - 1.37174i) q^{52} +(7.36862 + 2.27292i) q^{53} +(2.23410 + 2.80147i) q^{54} +(0.244029 - 3.25634i) q^{55} +(1.99924 - 0.616684i) q^{56} +(-0.344655 - 0.234982i) q^{57} +(-4.24599 - 0.639981i) q^{58} +(-1.35541 - 5.93842i) q^{59} +(0.469976 - 0.436074i) q^{60} +(-0.0659657 - 0.880251i) q^{61} +(-2.43134 - 6.19495i) q^{62} +(5.35610 - 0.807302i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.32768 - 0.639375i) q^{65} +(2.07019 - 0.312031i) q^{66} +(-0.443161 - 1.12916i) q^{67} +(-0.526238 - 7.02216i) q^{68} +(-4.13288 + 3.83475i) q^{69} +(-0.465556 - 2.03973i) q^{70} +(-9.03187 - 1.36134i) q^{71} +(-2.13910 - 1.45841i) q^{72} +(-4.72258 + 1.45672i) q^{73} +(-0.0763187 + 1.01840i) q^{74} +(-0.399734 - 0.501250i) q^{75} +(0.621729 + 0.191778i) q^{76} +(2.49601 - 6.35972i) q^{77} +(0.210230 - 0.921078i) q^{78} +(5.33721 + 9.24433i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.00950 - 3.72028i) q^{81} +(-2.40125 + 3.01107i) q^{82} +(-8.62955 + 5.88353i) q^{83} +(1.20852 - 0.581991i) q^{84} -7.04185 q^{85} +(-2.53376 - 6.04815i) q^{86} -2.75295 q^{87} +(-2.94209 + 1.41684i) q^{88} +(5.36086 - 3.65498i) q^{89} +(-1.61419 + 2.02413i) q^{90} +(-2.26005 - 2.09702i) q^{91} +(4.39690 - 7.61566i) q^{92} +(-2.13333 - 3.69504i) q^{93} +(-0.000808807 + 0.00354361i) q^{94} +(0.237704 - 0.605659i) q^{95} +(-0.612640 - 0.188974i) q^{96} +(-9.62957 - 12.0751i) q^{97} +(-0.195998 + 2.61541i) q^{98} +(-8.07859 + 2.49192i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{17}{21}\right)$

Coefficient data

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

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

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

$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$2$	−0.900969	+	0.433884i	−0.637081	+	0.306802i
$3$	−0.529721	+	0.361157i	−0.305834	+	0.208514i	−0.706505	−	0.707708i	$-0.749729\pi$
$3$	−0.529721	+	0.361157i	−0.305834	+	0.208514i	0.400671	+	0.916222i	$0.368777\pi$
$4$	0.623490	−	0.781831i	0.311745	−	0.390916i
$5$	−0.733052	−	0.680173i	−0.327831	−	0.304182i
$5$	−0.733052	−	0.680173i	−0.327831	−	0.304182i
$6$	0.320562	−	0.555229i	0.130869	−	0.226671i
$7$	−1.04610	−	1.81189i	−0.395387	−	0.684830i	0.597764	−	0.801672i	$-0.296056\pi$
$7$	−1.04610	−	1.81189i	−0.395387	−	0.684830i	−0.993150	+	0.116842i	$0.962723\pi$
$8$	−0.222521	+	0.974928i	−0.0786730	+	0.344689i
$9$	−0.945854	+	2.41000i	−0.315285	+	0.803332i
$10$	0.955573	+	0.294755i	0.302179	+	0.0932098i
$11$	2.03599	+	2.55305i	0.613874	+	0.769774i	0.987468	−	0.157818i	$-0.0504461\pi$
$11$	2.03599	+	2.55305i	0.613874	+	0.769774i	−0.373594	+	0.927592i	$0.621875\pi$
$12$	−0.0479112	+	0.639330i	−0.0138308	+	0.184559i
$13$	1.40814	−	0.434354i	0.390548	−	0.120468i	−0.0932611	−	0.995642i	$-0.529729\pi$
$13$	1.40814	−	0.434354i	0.390548	−	0.120468i	0.483809	+	0.875174i	$0.339253\pi$
$14$	1.72865	+	1.17857i	0.462001	+	0.314987i
$15$	0.633962	+	0.0955544i	0.163688	+	0.0246720i
$16$	−0.222521	−	0.974928i	−0.0556302	−	0.243732i
$17$	5.16204	−	4.78968i	1.25198	−	1.16167i	0.272059	−	0.962281i	$-0.412295\pi$
$17$	5.16204	−	4.78968i	1.25198	−	1.16167i	0.979921	−	0.199387i	$-0.0638950\pi$
$18$	−0.193473	−	2.58172i	−0.0456021	−	0.608518i
$19$	0.237704	+	0.605659i	0.0545329	+	0.138948i	0.955544	−	0.294848i	$-0.0952691\pi$
$19$	0.237704	+	0.605659i	0.0545329	+	0.138948i	−0.901011	+	0.433796i	$0.857174\pi$
$20$	−0.988831	+	0.149042i	−0.221109	+	0.0333269i
$21$	1.20852	+	0.581991i	0.263720	+	0.127001i
$22$	−2.94209	−	1.41684i	−0.627256	−	0.302071i
$23$	8.69558	−	1.31065i	1.81315	−	0.273289i	0.847064	−	0.531491i	$-0.178368\pi$
$23$	8.69558	−	1.31065i	1.81315	−	0.273289i	0.966091	+	0.258202i	$0.0831301\pi$
$24$	−0.234229	−	0.596805i	−0.0478117	−	0.121822i
$25$	0.0747301	+	0.997204i	0.0149460	+	0.199441i
$26$	−1.08023	+	1.00231i	−0.211851	+	0.196569i
$27$	−0.797340	−	3.49337i	−0.153448	−	0.672300i
$28$	−2.06882	−	0.311825i	−0.390971	−	0.0589293i
$29$	3.54783	+	2.41887i	0.658816	+	0.449173i	0.846022	−	0.533148i	$-0.178991\pi$
$29$	3.54783	+	2.41887i	0.658816	+	0.449173i	−0.187206	+	0.982321i	$0.559943\pi$
$30$	−0.612640	+	0.188974i	−0.111852	+	0.0345018i
$31$	−0.497328	+	6.63637i	−0.0893227	+	1.19193i	0.754865	+	0.655880i	$0.227702\pi$
$31$	−0.497328	+	6.63637i	−0.0893227	+	1.19193i	−0.844188	+	0.536048i	$0.819917\pi$
$32$	0.623490	+	0.781831i	0.110218	+	0.138210i
$33$	−2.00056	−	0.617091i	−0.348253	−	0.107422i
$34$	−2.57268	+	6.55508i	−0.441211	+	1.12419i
$35$	−0.465556	+	2.03973i	−0.0786933	+	0.344778i
$36$	1.29448	+	2.24211i	0.215747	+	0.373684i
$37$	0.510629	−	0.884436i	0.0839469	−	0.145400i	−0.820995	−	0.570935i	$-0.806581\pi$
$37$	0.510629	−	0.884436i	0.0839469	−	0.145400i	0.904942	+	0.425535i	$0.139914\pi$
$38$	−0.476949	−	0.442544i	−0.0773713	−	0.0717901i
$39$	−0.589051	+	0.738647i	−0.0943237	+	0.118278i
$40$	0.826239	−	0.563320i	0.130640	−	0.0890687i
$41$	3.46990	−	1.67102i	0.541908	−	0.260969i	−0.142844	−	0.989745i	$-0.545625\pi$
$41$	3.46990	−	1.67102i	0.541908	−	0.260969i	0.684752	+	0.728776i	$0.259911\pi$
$42$	−1.34135			−0.206975
$43$	−0.341353	+	6.54855i	−0.0520558	+	0.998644i
$43$	−0.341353	+	6.54855i	−0.0520558	+	0.998644i
$44$	3.26547			0.492289
$45$	2.33257	−	1.12331i	0.347720	−	0.167453i
$46$	−7.26578	+	4.95373i	−1.07128	+	0.730387i
$47$	0.00226623	−	0.00284176i	0.000330563	−	0.000414513i	−0.781666	−	0.623697i	$-0.785630\pi$
$47$	0.00226623	−	0.00284176i	0.000330563	−	0.000414513i	0.781997	+	0.623283i	$0.214201\pi$
$48$	0.469976	+	0.436074i	0.0678353	+	0.0629419i
$49$	1.31137	−	2.27136i	0.187339	−	0.324480i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−1.00461	+	4.40150i	−0.140674	+	0.616334i
$52$	0.538370	−	1.37174i	0.0746585	−	0.190227i
$53$	7.36862	+	2.27292i	1.01216	+	0.312209i	0.756103	−	0.654453i	$-0.227101\pi$
$53$	7.36862	+	2.27292i	1.01216	+	0.312209i	0.256055	+	0.966662i	$0.417577\pi$
$54$	2.23410	+	2.80147i	0.304022	+	0.381232i
$55$	0.244029	−	3.25634i	0.0329049	−	0.439085i
$56$	1.99924	−	0.616684i	0.267160	−	0.0824078i
$57$	−0.344655	−	0.234982i	−0.0456506	−	0.0311241i
$58$	−4.24599	−	0.639981i	−0.557526	−	0.0840336i
$59$	−1.35541	−	5.93842i	−0.176459	−	0.773117i	−0.983247	−	0.182276i	$-0.941653\pi$
$59$	−1.35541	−	5.93842i	−0.176459	−	0.773117i	0.806788	−	0.590840i	$-0.201204\pi$
$60$	0.469976	−	0.436074i	0.0606737	−	0.0562970i
$61$	−0.0659657	−	0.880251i	−0.00844604	−	0.112705i	0.991387	−	0.130963i	$-0.0418069\pi$
$61$	−0.0659657	−	0.880251i	−0.00844604	−	0.112705i	−0.999833	+	0.0182584i	$0.994188\pi$
$62$	−2.43134	−	6.19495i	−0.308780	−	0.786759i
$63$	5.35610	−	0.807302i	0.674805	−	0.101711i
$64$	−0.900969	−	0.433884i	−0.112621	−	0.0542355i
$65$	−1.32768	−	0.639375i	−0.164678	−	0.0793047i
$66$	2.07019	−	0.312031i	0.254823	−	0.0384083i
$67$	−0.443161	−	1.12916i	−0.0541407	−	0.137948i	0.901245	−	0.433311i	$-0.142655\pi$
$67$	−0.443161	−	1.12916i	−0.0541407	−	0.137948i	−0.955385	+	0.295363i	$0.904560\pi$
$68$	−0.526238	−	7.02216i	−0.0638158	−	0.851562i
$69$	−4.13288	+	3.83475i	−0.497540	+	0.461650i
$70$	−0.465556	−	2.03973i	−0.0556446	−	0.243795i
$71$	−9.03187	−	1.36134i	−1.07189	−	0.161561i	−0.410691	−	0.911775i	$-0.634712\pi$
$71$	−9.03187	−	1.36134i	−1.07189	−	0.161561i	−0.661195	+	0.750214i	$0.729950\pi$
$72$	−2.13910	−	1.45841i	−0.252095	−	0.171876i
$73$	−4.72258	+	1.45672i	−0.552737	+	0.170497i	−0.558527	−	0.829487i	$-0.688633\pi$
$73$	−4.72258	+	1.45672i	−0.552737	+	0.170497i	0.00579008	+	0.999983i	$0.498157\pi$
$74$	−0.0763187	+	1.01840i	−0.00887187	+	0.118387i
$75$	−0.399734	−	0.501250i	−0.0461573	−	0.0578794i
$76$	0.621729	+	0.191778i	0.0713172	+	0.0219984i
$77$	2.49601	−	6.35972i	0.284446	−	0.724758i
$78$	0.210230	−	0.921078i	0.0238039	−	0.104291i
$79$	5.33721	+	9.24433i	0.600484	+	1.04007i	0.992748	+	0.120215i	$0.0383585\pi$
$79$	5.33721	+	9.24433i	0.600484	+	1.04007i	−0.392264	+	0.919853i	$0.628308\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.00950	−	3.72028i	−0.445500	−	0.413364i
$82$	−2.40125	+	3.01107i	−0.265173	+	0.332517i
$83$	−8.62955	+	5.88353i	−0.947216	+	0.645801i	−0.935198	−	0.354127i	$-0.884778\pi$
$83$	−8.62955	+	5.88353i	−0.947216	+	0.645801i	−0.0120189	+	0.999928i	$0.503826\pi$
$84$	1.20852	−	0.581991i	0.131860	−	0.0635004i
$85$	−7.04185			−0.763796
$86$	−2.53376	−	6.04815i	−0.273222	−	0.652188i
$87$	−2.75295			−0.295148
$88$	−2.94209	+	1.41684i	−0.313628	+	0.151035i
$89$	5.36086	−	3.65498i	0.568251	−	0.387427i	−0.244840	−	0.969563i	$-0.578736\pi$
$89$	5.36086	−	3.65498i	0.568251	−	0.387427i	0.813091	+	0.582137i	$0.197783\pi$
$90$	−1.61419	+	2.02413i	−0.170151	+	0.213362i
$91$	−2.26005	−	2.09702i	−0.236918	−	0.219827i
$92$	4.39690	−	7.61566i	0.458409	−	0.793987i
$93$	−2.13333	−	3.69504i	−0.221216	−	0.383158i
$94$	−0.000808807		0.00354361i	−8.34220e−5		0.000365496i
$95$	0.237704	−	0.605659i	0.0243879	−	0.0621393i
$96$	−0.612640	−	0.188974i	−0.0625273	−	0.0192871i
$97$	−9.62957	−	12.0751i	−0.977735	−	1.22604i	−0.974116	−	0.226047i	$-0.927420\pi$
$97$	−9.62957	−	12.0751i	−0.977735	−	1.22604i	−0.00361831	−	0.999993i	$-0.501152\pi$
$98$	−0.195998	+	2.61541i	−0.0197988	+	0.264196i
$99$	−8.07859	+	2.49192i	−0.811929	+	0.250447i
$100$	0.826239	+	0.563320i	0.0826239	+	0.0563320i
$101$	10.4930	+	1.58157i	1.04409	+	0.157372i	0.648625	−	0.761108i	$-0.275344\pi$
$101$	10.4930	+	1.58157i	1.04409	+	0.157372i	0.395468	+	0.918480i	$0.370582\pi$
$102$	−1.00461	−	4.40150i	−0.0994716	−	0.435814i
$103$	−1.58891	+	1.47429i	−0.156560	+	0.145266i	−0.754563	−	0.656227i	$-0.772151\pi$
$103$	−1.58891	+	1.47429i	−0.156560	+	0.145266i	0.598004	+	0.801493i	$0.295961\pi$
$104$	0.110123	+	1.46949i	0.0107984	+	0.144095i
$105$	−0.490051	−	1.24863i	−0.0478241	−	0.121854i
$106$	−7.62508	+	1.14930i	−0.740613	+	0.111629i
$107$	−15.8227	−	7.61982i	−1.52964	−	0.736636i	−0.535480	−	0.844548i	$-0.679869\pi$
$107$	−15.8227	−	7.61982i	−1.52964	−	0.736636i	−0.994160	+	0.107912i	$0.965584\pi$
$108$	−3.22836	−	1.55470i	−0.310649	−	0.149601i
$109$	15.4248	−	2.32491i	1.47742	−	0.222686i	0.639634	−	0.768679i	$-0.279086\pi$
$109$	15.4248	−	2.32491i	1.47742	−	0.222686i	0.837789	+	0.545993i	$0.183848\pi$
$110$	1.19301	+	3.03974i	0.113749	+	0.289828i
$111$	0.0489297	+	0.652922i	0.00464420	+	0.0619726i
$112$	−1.53368	+	1.42305i	−0.144920	+	0.134466i
$113$	1.38276	+	6.05827i	0.130079	+	0.569914i	0.997394	+	0.0721534i	$0.0229871\pi$
$113$	1.38276	+	6.05827i	0.130079	+	0.569914i	−0.867314	+	0.497761i	$0.834156\pi$
$114$	0.412478	+	0.0621710i	0.0386321	+	0.00582285i
$115$	−7.26578	−	4.95373i	−0.677538	−	0.461937i
$116$	4.10319	−	1.26567i	0.380971	−	0.117514i
$117$	−0.285104	+	3.80445i	−0.0263579	+	0.351721i
$118$	3.79776	+	4.76225i	0.349613	+	0.438400i
$119$	−14.0784	−	4.34260i	−1.29056	−	0.398085i
$120$	−0.234229	+	0.596805i	−0.0213820	+	0.0544806i
$121$	0.0749169	−	0.328233i	0.00681063	−	0.0298393i
$122$	0.441359	+	0.764457i	0.0399588	+	0.0692107i
$123$	−1.23458	+	2.13835i	−0.111318	+	0.192809i
$124$	4.87845	+	4.52654i	0.438098	+	0.406495i
$125$	0.623490	−	0.781831i	0.0557666	−	0.0699291i
$126$	−4.47540	+	3.05128i	−0.398701	+	0.271830i
$127$	1.19087	−	0.573494i	0.105673	−	0.0508893i	−0.380301	−	0.924863i	$-0.624179\pi$
$127$	1.19087	−	0.573494i	0.105673	−	0.0508893i	0.485973	+	0.873974i	$0.338465\pi$
$128$	1.00000			0.0883883
$129$	−2.18424	−	3.59218i	−0.192311	−	0.316274i
$130$	1.47361			0.129244
$131$	5.02410	−	2.41948i	0.438958	−	0.211391i	−0.201334	−	0.979523i	$-0.564528\pi$
$131$	5.02410	−	2.41948i	0.438958	−	0.211391i	0.640292	+	0.768132i	$0.278813\pi$
$132$	−1.72979	+	1.17935i	−0.150559	+	0.102649i
$133$	0.848726	−	1.06427i	0.0735939	−	0.0922839i
$134$	0.889196	+	0.825053i	0.0768148	+	0.0712738i
$135$	−1.79161	+	3.10315i	−0.154197	+	0.267077i
$136$	3.52093	+	6.09843i	0.301917	+	0.522936i
$137$	2.76265	−	12.1039i	0.236029	−	1.03411i	−0.708508	−	0.705703i	$-0.750631\pi$
$137$	2.76265	−	12.1039i	0.236029	−	1.03411i	0.944536	−	0.328407i	$-0.106512\pi$
$138$	2.05976	−	5.24818i	0.175338	−	0.446755i
$139$	−18.2798	−	5.63857i	−1.55047	−	0.478258i	−0.602905	−	0.797813i	$-0.705990\pi$
$139$	−18.2798	−	5.63857i	−1.55047	−	0.478258i	−0.947568	+	0.319555i	$0.896467\pi$
$140$	1.30446	+	1.63574i	0.110247	+	0.138245i
$141$	−0.000174145		0.00232380i	−1.46656e−5		0.000195699i
$142$	8.72809	−	2.69226i	0.732445	−	0.225929i
$143$	3.97589	+	2.71071i	0.332480	+	0.226681i
$144$	2.56004	+	0.385865i	0.213337	+	0.0321554i
$145$	−0.955495	−	4.18630i	−0.0793495	−	0.347653i
$146$	3.62285	−	3.36151i	0.299829	−	0.278201i
$147$	0.125659	+	1.67680i	0.0103641	+	0.138300i
$148$	−0.373108	−	0.950663i	−0.0306693	−	0.0781440i
$149$	11.0850	−	1.67080i	0.908120	−	0.136877i	0.321660	−	0.946855i	$-0.395759\pi$
$149$	11.0850	−	1.67080i	0.908120	−	0.136877i	0.586460	+	0.809978i	$0.300521\pi$
$150$	0.577632	+	0.278173i	0.0471635	+	0.0227127i
$151$	13.6670	+	6.58170i	1.11221	+	0.535611i	0.897477	−	0.441062i	$-0.145398\pi$
$151$	13.6670	+	6.58170i	1.11221	+	0.535611i	0.214731	+	0.976673i	$0.431112\pi$
$152$	−0.643368	+	0.0969721i	−0.0521840	+	0.00786547i
$153$	6.66056	+	16.9708i	0.538475	+	1.37201i
$154$	0.510556	+	6.81289i	0.0411417	+	0.548998i
$155$	4.87845	−	4.52654i	0.391846	−	0.363580i
$156$	0.210230	+	0.921078i	0.0168319	+	0.0737452i
$157$	−23.3710	−	3.52262i	−1.86521	−	0.281135i	−0.883065	−	0.469251i	$-0.844524\pi$
$157$	−23.3710	−	3.52262i	−1.86521	−	0.281135i	−0.982147	+	0.188115i	$0.939762\pi$
$158$	−8.81963	−	6.01312i	−0.701652	−	0.478378i
$159$	−4.72419	+	1.45722i	−0.374653	+	0.115565i
$160$	0.0747301	−	0.997204i	0.00590793	−	0.0788359i
$161$	−11.4712	−	14.3844i	−0.904054	−	1.13365i
$162$	5.22660	+	1.61219i	0.410641	+	0.126666i
$163$	−7.02644	+	17.9031i	−0.550353	+	1.40228i	0.337139	+	0.941455i	$0.390541\pi$
$163$	−7.02644	+	17.9031i	−0.550353	+	1.40228i	−0.887492	+	0.460822i	$0.847554\pi$
$164$	0.856995	−	3.75474i	0.0669201	−	0.293196i
$165$	1.04679	+	1.81309i	0.0814922	+	0.141149i
$166$	5.22219	−	9.04510i	0.405321	−	0.702036i
$167$	−1.22102	−	1.13294i	−0.0944854	−	0.0876696i	0.631516	−	0.775363i	$-0.282433\pi$
$167$	−1.22102	−	1.13294i	−0.0944854	−	0.0876696i	−0.726001	+	0.687693i	$0.758623\pi$
$168$	−0.836319	+	1.04871i	−0.0645234	+	0.0809098i
$169$	−8.94691	+	6.09990i	−0.688224	+	0.469223i
$170$	6.34449	−	3.05535i	0.486600	−	0.234334i
$171$	−1.68447			−0.128814
$172$	4.90703	+	4.34983i	0.374158	+	0.331672i
$173$	13.2455			1.00703			0.503517	−	0.863985i	$-0.332039\pi$
$173$	13.2455			1.00703			0.503517	+	0.863985i	$0.332039\pi$
$174$	2.48033	−	1.19446i	0.188033	−	0.0905519i
$175$	1.72865	−	1.17857i	0.130674	−	0.0890917i
$176$	2.03599	−	2.55305i	0.153469	−	0.192443i
$177$	2.86269	+	2.65619i	0.215173	+	0.199652i
$178$	−3.24414	+	5.61901i	−0.243158	+	0.421163i
$179$	12.3179	+	21.3352i	0.920681	+	1.59467i	0.798365	+	0.602174i	$0.205699\pi$
$179$	12.3179	+	21.3352i	0.920681	+	1.59467i	0.122316	+	0.992491i	$0.460968\pi$
$180$	0.576098	−	2.52405i	0.0429398	−	0.188132i
$181$	0.699175	−	1.78147i	0.0519693	−	0.132415i	−0.902532	−	0.430624i	$-0.858294\pi$
$181$	0.699175	−	1.78147i	0.0519693	−	0.132415i	0.954501	+	0.298208i	$0.0963889\pi$
$182$	2.94610	+	0.908751i	0.218379	+	0.0673611i
$183$	0.352852	+	0.442463i	0.0260836	+	0.0327078i
$184$	−0.657162	+	8.76921i	−0.0484466	+	0.646475i
$185$	−0.975887	+	0.301021i	−0.0717486	+	0.0221315i
$186$	3.52528	+	2.40350i	0.258486	+	0.176233i
$187$	22.7382	+	3.42723i	1.66278	+	0.250624i
$188$	−0.000808807	−	0.00354361i	−5.89883e−5	−	0.000258445i
$189$	−5.49551	+	5.09909i	−0.399740	+	0.370904i
$190$	0.0486220	+	0.648815i	0.00352741	+	0.0470700i
$191$	4.19575	+	10.6906i	0.303594	+	0.773545i	0.998516	+	0.0544598i	$0.0173437\pi$
$191$	4.19575	+	10.6906i	0.303594	+	0.773545i	−0.694922	+	0.719085i	$0.744561\pi$
$192$	0.633962	−	0.0955544i	0.0457523	−	0.00689605i
$193$	−3.62174	−	1.74414i	−0.260699	−	0.125546i	0.298969	−	0.954263i	$-0.403357\pi$
$193$	−3.62174	−	1.74414i	−0.260699	−	0.125546i	−0.559668	+	0.828717i	$0.689071\pi$
$194$	13.9151	+	6.70117i	0.999048	+	0.481116i
$195$	0.934212	−	0.140810i	0.0669003	−	0.0100836i
$196$	−0.958195	−	2.44144i	−0.0684425	−	0.174389i
$197$	1.34025	+	17.8844i	0.0954888	+	1.27421i	0.814891	+	0.579615i	$0.196797\pi$
$197$	1.34025	+	17.8844i	0.0954888	+	1.27421i	−0.719402	+	0.694594i	$0.755584\pi$
$198$	6.19736	−	5.75031i	0.440427	−	0.408657i
$199$	−2.26405	−	9.91946i	−0.160494	−	0.703172i	−0.989572	−	0.144039i	$-0.953991\pi$
$199$	−2.26405	−	9.91946i	−0.160494	−	0.703172i	0.829078	−	0.559134i	$-0.188866\pi$
$200$	−0.988831	−	0.149042i	−0.0699209	−	0.0105389i
$201$	0.642554	+	0.438086i	0.0453223	+	0.0309002i
$202$	−10.1401	+	3.12780i	−0.713454	+	0.220072i
$203$	0.671358	−	8.95865i	0.0471201	−	0.628774i
$204$	2.81487	+	3.52973i	0.197080	+	0.247131i
$205$	−3.68020	−	1.13519i	−0.257036	−	0.0792852i
$206$	0.791885	−	2.01769i	0.0551732	−	0.140579i
$207$	−5.06609	+	22.1960i	−0.352118	+	1.54273i
$208$	−0.736804	−	1.27618i	−0.0510882	−	0.0884874i
$209$	−1.06232	+	1.83998i	−0.0734819	+	0.127274i
$210$	0.983280	+	0.912351i	0.0678528	+	0.0629582i
$211$	7.02185	−	8.80513i	0.483404	−	0.606170i	−0.478992	−	0.877819i	$-0.658998\pi$
$211$	7.02185	−	8.80513i	0.483404	−	0.606170i	0.962396	+	0.271649i	$0.0875691\pi$
$212$	6.37130	−	4.34388i	0.437582	−	0.298339i
$213$	5.27603	−	2.54080i	0.361507	−	0.174093i
$214$	17.5619			1.20051
$215$	4.70437	−	4.56825i	0.320836	−	0.311552i
$216$	3.58321			0.243807
$217$	12.5446	−	6.04118i	0.851585	−	0.410102i
$218$	−12.8885	+	8.78722i	−0.872919	+	0.595146i
$219$	1.97554	−	2.47725i	0.133495	−	0.167397i
$220$	−2.39376	−	2.22109i	−0.161387	−	0.149746i
$221$	5.18847	−	8.98669i	0.349014	−	0.604510i
$222$	−0.327376	−	0.567032i	−0.0219720	−	0.0380567i
$223$	1.91613	−	8.39512i	0.128314	−	0.562179i	−0.869370	−	0.494161i	$-0.835475\pi$
$223$	1.91613	−	8.39512i	0.128314	−	0.562179i	0.997684	−	0.0680179i	$-0.0216675\pi$
$224$	0.764363	−	1.94756i	0.0510711	−	0.130127i
$225$	−2.47394	−	0.763110i	−0.164929	−	0.0508740i
$226$	−3.87441	−	4.85836i	−0.257722	−	0.323173i
$227$	−1.13596	+	15.1584i	−0.0753965	+	1.00610i	0.823323	+	0.567573i	$0.192117\pi$
$227$	−1.13596	+	15.1584i	−0.0753965	+	1.00610i	−0.898720	+	0.438524i	$0.855502\pi$
$228$	−0.398605	+	0.122953i	−0.0263982	+	0.00814278i
$229$	−13.8109	−	9.41614i	−0.912653	−	0.622236i	0.0132853	−	0.999912i	$-0.495771\pi$
$229$	−13.8109	−	9.41614i	−0.912653	−	0.622236i	−0.925938	+	0.377676i	$0.876723\pi$
$230$	8.69558	+	1.31065i	0.573370	+	0.0864216i
$231$	0.974675	+	4.27033i	0.0641289	+	0.280967i
$232$	−3.14769	+	2.92063i	−0.206656	+	0.191749i
$233$	−1.63104	−	21.7648i	−0.106853	−	1.42586i	−0.750670	−	0.660677i	$-0.770269\pi$
$233$	−1.63104	−	21.7648i	−0.106853	−	1.42586i	0.643817	−	0.765179i	$-0.277350\pi$
$234$	−1.39382	−	3.55139i	−0.0911168	−	0.232162i
$235$	−0.00359415		0.000541731i	−0.000234456		3.53386e-5i
$236$	−5.48793	−	2.64285i	−0.357234	−	0.172035i
$237$	−6.16589	−	2.96934i	−0.400518	−	0.192879i
$238$	14.5683	−	2.19582i	0.944326	−	0.142334i
$239$	0.532605	+	1.35706i	0.0344514	+	0.0877807i	0.947064	−	0.321044i	$-0.104034\pi$
$239$	0.532605	+	1.35706i	0.0344514	+	0.0877807i	−0.912613	+	0.408825i	$0.865939\pi$
$240$	−0.0479112	−	0.639330i	−0.00309265	−	0.0412686i
$241$	−17.0208	+	15.7930i	−1.09640	+	1.01731i	−0.0966465	+	0.995319i	$0.530812\pi$
$241$	−17.0208	+	15.7930i	−1.09640	+	1.01731i	−0.999758	+	0.0219960i	$0.992998\pi$
$242$	0.0749169	+	0.328233i	0.00481584	+	0.0210996i
$243$	14.0971	+	2.12480i	0.904329	+	0.136306i
$244$	−0.729336	−	0.497253i	−0.0466910	−	0.0318334i
$245$	−2.50622	+	0.773066i	−0.160116	+	0.0493894i
$246$	0.184520	−	2.46225i	0.0117646	−	0.156988i
$247$	0.597790	+	0.749605i	0.0380365	+	0.0476962i
$248$	−6.35932	−	1.96159i	−0.403817	−	0.124561i
$249$	2.44637	−	6.23325i	0.155033	−	0.395016i
$250$	−0.222521	+	0.974928i	−0.0140735	+	0.0616599i
$251$	8.90158	+	15.4180i	0.561863	+	0.973175i	0.997334	+	0.0729720i	$0.0232484\pi$
$251$	8.90158	+	15.4180i	0.561863	+	0.973175i	−0.435471	+	0.900203i	$0.643418\pi$
$252$	2.70830	−	4.69091i	0.170607	−	0.295500i
$253$	21.0503	+	19.5318i	1.32342	+	1.22795i
$254$	−0.824109	+	1.03340i	−0.0517092	+	0.0648413i
$255$	3.73022	−	2.54322i	0.233595	−	0.159263i
$256$	−0.900969	+	0.433884i	−0.0563106	+	0.0271177i
$257$	27.2631			1.70063			0.850313	−	0.526278i	$-0.176413\pi$
$257$	27.2631			1.70063			0.850313	+	0.526278i	$0.176413\pi$
$258$	3.52652	+	2.28874i	0.219551	+	0.142491i
$259$	−2.13667			−0.132766
$260$	−1.32768	+	0.639375i	−0.0823390	+	0.0396524i
$261$	−9.18520	+	6.26236i	−0.568550	+	0.387630i
$262$	−3.47678	+	4.35975i	−0.214796	+	0.269346i
$263$	−18.0791	−	16.7750i	−1.11481	−	1.03439i	−0.999155	−	0.0410999i	$-0.986914\pi$
$263$	−18.0791	−	16.7750i	−1.11481	−	1.03439i	−0.115652	−	0.993290i	$-0.536896\pi$
$264$	1.04679	−	1.81309i	0.0644252	−	0.111588i
$265$	−3.85560	−	6.67810i	−0.236848	−	0.410232i
$266$	−0.302907	+	1.32712i	−0.0185724	+	0.0813711i
$267$	−1.51974	+	3.87223i	−0.0930065	+	0.236977i
$268$	−1.15912	−	0.357540i	−0.0708042	−	0.0218402i
$269$	7.33684	+	9.20010i	0.447335	+	0.560940i	0.953460	−	0.301520i	$-0.0974940\pi$
$269$	7.33684	+	9.20010i	0.447335	+	0.560940i	−0.506125	+	0.862460i	$0.668923\pi$
$270$	0.267774	−	3.57319i	0.0162962	−	0.217458i
$271$	8.82231	−	2.72132i	0.535917	−	0.165309i	−0.0149705	−	0.999888i	$-0.504765\pi$
$271$	8.82231	−	2.72132i	0.535917	−	0.165309i	0.550888	+	0.834579i	$0.314289\pi$
$272$	−5.81825	−	3.96682i	−0.352783	−	0.240524i
$273$	1.95455	+	0.294601i	0.118295	+	0.0178301i
$274$	2.76265	+	12.1039i	0.166898	+	0.731226i
$275$	−2.39376	+	2.22109i	−0.144349	+	0.133937i
$276$	0.421322	+	5.62215i	0.0253606	+	0.338413i
$277$	−1.91747	−	4.88564i	−0.115210	−	0.293550i	0.861625	−	0.507546i	$-0.169447\pi$
$277$	−1.91747	−	4.88564i	−0.115210	−	0.293550i	−0.976835	+	0.213996i	$0.931352\pi$
$278$	18.9160	−	2.85113i	1.13451	−	0.171000i
$279$	−15.5232	−	7.47560i	−0.929352	−	0.447552i
$280$	−1.88500	−	0.907767i	−0.112650	−	0.0542495i
$281$	−24.2494	+	3.65501i	−1.44660	+	0.218040i	−0.824927	−	0.565239i	$-0.808784\pi$
$281$	−24.2494	+	3.65501i	−1.44660	+	0.218040i	−0.621671	+	0.783278i	$0.713546\pi$
$282$	−0.000851361	−	0.00216923i	−5.06978e−5	−	0.000129176i
$283$	0.571554	+	7.62686i	0.0339754	+	0.453370i	0.988085	+	0.153911i	$0.0491870\pi$
$283$	0.571554	+	7.62686i	0.0339754	+	0.453370i	−0.954109	+	0.299459i	$0.903194\pi$
$284$	−6.69561	+	6.21262i	−0.397312	+	0.368651i
$285$	0.0928217	+	0.406678i	0.00549828	+	0.0240896i
$286$	−4.75829	−	0.717196i	−0.281363	−	0.0424087i
$287$	−6.65755	−	4.53904i	−0.392983	−	0.267931i
$288$	−2.47394	+	0.763110i	−0.145778	+	0.0449667i
$289$	2.43528	−	32.4966i	0.143252	−	1.91156i
$290$	2.67724	+	3.35715i	0.157213	+	0.197139i
$291$	9.46200	+	2.91864i	0.554672	+	0.171094i
$292$	−1.80557	+	4.60052i	−0.105663	+	0.269225i
$293$	−2.74138	+	12.0108i	−0.160153	+	0.701677i	0.829537	+	0.558452i	$0.188604\pi$
$293$	−2.74138	+	12.0108i	−0.160153	+	0.701677i	−0.989690	+	0.143225i	$0.954253\pi$
$294$	−0.840750	−	1.45622i	−0.0490335	−	0.0849285i
$295$	−3.04557	+	5.27508i	−0.177320	+	0.307127i
$296$	0.748635	+	0.694632i	0.0435135	+	0.0403747i
$297$	7.29538	−	9.14812i	0.423321	−	0.530828i
$298$	−9.26233	+	6.31495i	−0.536552	+	0.365815i
$299$	11.6753	−	5.62254i	0.675201	−	0.325160i
$300$	−0.641123			−0.0370153
$301$	12.2223	−	6.23191i	0.704484	−	0.359201i
$302$	−15.1693			−0.872893
$303$	−6.12956	+	2.95184i	−0.352134	+	0.169579i
$304$	0.537580	−	0.366516i	0.0308323	−	0.0210211i
$305$	−0.550366	+	0.690137i	−0.0315139	+	0.0395171i
$306$	−13.3643	−	12.4003i	−0.763988	−	0.708877i
$307$	−2.41024	+	4.17465i	−0.137559	+	0.238260i	−0.926572	−	0.376117i	$-0.877259\pi$
$307$	−2.41024	+	4.17465i	−0.137559	+	0.238260i	0.789013	+	0.614377i	$0.210592\pi$
$308$	−3.41600	−	5.91668i	−0.194645	−	0.337134i
$309$	0.309226	−	1.35481i	0.0175912	−	0.0770723i
$310$	−2.43134	+	6.19495i	−0.138091	+	0.351849i
$311$	−21.4767	−	6.62470i	−1.21783	−	0.375652i	−0.381757	−	0.924263i	$-0.624681\pi$
$311$	−21.4767	−	6.62470i	−1.21783	−	0.375652i	−0.836078	+	0.548611i	$0.815157\pi$
$312$	−0.589051	−	0.738647i	−0.0333485	−	0.0418176i
$313$	0.484853	−	6.46991i	0.0274055	−	0.365701i	−0.966594	−	0.256314i	$-0.917492\pi$
$313$	0.484853	−	6.46991i	0.0274055	−	0.365701i	0.993999	−	0.109387i	$-0.0348889\pi$
$314$	22.5850	−	6.96654i	1.27454	−	0.393145i
$315$	−4.47540	−	3.05128i	−0.252160	−	0.171920i
$316$	10.5552	+	1.59094i	0.593777	+	0.0894974i
$317$	2.36512	+	10.3623i	0.132839	+	0.582004i	0.996904	+	0.0786247i	$0.0250529\pi$
$317$	2.36512	+	10.3623i	0.132839	+	0.582004i	−0.864066	+	0.503379i	$0.832090\pi$
$318$	3.62409	−	3.36266i	0.203229	−	0.188569i
$319$	1.04785	+	13.9826i	0.0586684	+	0.782875i
$320$	0.365341	+	0.930874i	0.0204232	+	0.0520374i
$321$	11.1336	−	1.67812i	0.621416	−	0.0936634i
$322$	16.5763	+	7.98273i	0.923761	+	0.444860i
$323$	4.12795	+	1.98791i	0.229685	+	0.110611i
$324$	−5.40851	+	0.815202i	−0.300473	+	0.0452890i
$325$	0.538370	+	1.37174i	0.0298634	+	0.0760907i
$326$	−1.43725	−	19.1788i	−0.0796019	−	1.06221i
$327$	−7.33116	+	6.80232i	−0.405414	+	0.376169i
$328$	0.856995	+	3.75474i	0.0473196	+	0.207321i
$329$	−0.00751964	−	0.00113340i	−0.000414571	−	6.24866e-5i
$330$	−1.72979	−	1.17935i	−0.0952218	−	0.0649211i
$331$	5.20780	−	1.60639i	0.286246	−	0.0882953i	−0.148307	−	0.988941i	$-0.547382\pi$
$331$	5.20780	−	1.60639i	0.286246	−	0.0882953i	0.434553	+	0.900646i	$0.356906\pi$
$332$	−0.780510	+	10.4152i	−0.0428360	+	0.571607i
$333$	1.64851	+	2.06716i	0.0903376	+	0.113280i
$334$	1.59167	+	0.490964i	0.0870921	+	0.0268644i
$335$	−0.443161	+	1.12916i	−0.0242125	+	0.0616923i
$336$	0.298479	−	1.30772i	0.0162834	−	0.0713420i
$337$	7.28544	+	12.6188i	0.396863	+	0.687388i	0.993337	−	0.115245i	$-0.0367653\pi$
$337$	7.28544	+	12.6188i	0.396863	+	0.687388i	−0.596474	+	0.802633i	$0.703432\pi$
$338$	5.41424	−	9.37774i	0.294496	−	0.510082i
$339$	−2.92047	−	2.70980i	−0.158618	−	0.147176i
$340$	−4.39052	+	5.50554i	−0.238110	+	0.298580i
$341$	−17.9556	+	12.2419i	−0.972348	+	0.662936i
$342$	1.51765	−	0.730863i	0.0820653	−	0.0395206i
$343$	−20.1326			−1.08706
$344$	−6.30840	−	1.78998i	−0.340126	−	0.0965094i
$345$	5.63791			0.303535
$346$	−11.9337	+	5.74699i	−0.641562	+	0.308960i
$347$	−19.2531	+	13.1266i	−1.03356	+	0.704670i	−0.956314	−	0.292342i	$-0.905566\pi$
$347$	−19.2531	+	13.1266i	−1.03356	+	0.704670i	−0.0772476	+	0.997012i	$0.524613\pi$
$348$	−1.71644	+	2.15235i	−0.0920108	+	0.115378i
$349$	−0.190563	−	0.176816i	−0.0102006	−	0.00946476i	0.675056	−	0.737767i	$-0.264119\pi$
$349$	−0.190563	−	0.176816i	−0.0102006	−	0.00946476i	−0.685257	+	0.728302i	$0.740310\pi$
$350$	−1.04610	+	1.81189i	−0.0559161	+	0.0968496i
$351$	−2.64013	−	4.57283i	−0.140920	−	0.244080i
$352$	−0.726637	+	3.18360i	−0.0387299	+	0.169687i
$353$	7.47029	−	19.0340i	0.397603	−	1.01308i	−0.582188	−	0.813054i	$-0.697803\pi$
$353$	7.47029	−	19.0340i	0.397603	−	1.01308i	0.979791	−	0.200022i	$-0.0641015\pi$
$354$	−3.73168	−	1.15107i	−0.198336	−	0.0611786i
$355$	5.69489	+	7.14116i	0.302253	+	0.379013i
$356$	0.484869	−	6.47013i	0.0256980	−	0.342916i
$357$	9.02596	−	2.78414i	0.477704	−	0.147352i
$358$	−20.3550	−	13.8778i	−1.07580	−	0.733465i
$359$	−2.33826	−	0.352436i	−0.123409	−	0.0186008i	0.0870475	−	0.996204i	$-0.472257\pi$
$359$	−2.33826	−	0.352436i	−0.123409	−	0.0186008i	−0.210456	+	0.977603i	$0.567495\pi$
$360$	0.576098	+	2.52405i	0.0303630	+	0.133029i
$361$	13.6177	−	12.6353i	0.716719	−	0.665018i
$362$	0.143015	+	1.90841i	0.00751672	+	0.100304i
$363$	0.0788586	+	0.200928i	0.00413900	+	0.0105460i
$364$	−3.04863	+	0.459508i	−0.159792	+	0.0240848i
$365$	4.45272	+	2.14432i	0.233066	+	0.112239i
$366$	−0.509887	−	0.245548i	−0.0266522	−	0.0128350i
$367$	2.42203	−	0.365062i	0.126429	−	0.0190561i	−0.0855229	−	0.996336i	$-0.527256\pi$
$367$	2.42203	−	0.365062i	0.126429	−	0.0190561i	0.211952	+	0.977280i	$0.432018\pi$
$368$	−3.21274	−	8.18592i	−0.167475	−	0.426721i
$369$	0.745124	+	9.94299i	0.0387896	+	0.517611i
$370$	0.748635	−	0.694632i	0.0389197	−	0.0361122i
$371$	−3.59000	−	15.7288i	−0.186383	−	0.816599i
$372$	−4.21901	−	0.635913i	−0.218745	−	0.0329706i
$373$	−25.8735	−	17.6403i	−1.33968	−	0.913379i	−0.340046	−	0.940409i	$-0.610443\pi$
$373$	−25.8735	−	17.6403i	−1.33968	−	0.913379i	−0.999635	+	0.0270296i	$0.991395\pi$
$374$	−21.9734	+	6.77790i	−1.13622	+	0.350477i
$375$	−0.0479112	+	0.639330i	−0.00247412	+	0.0330149i
$376$	0.00226623	+	0.00284176i	0.000116872	+	0.000146552i
$377$	6.04649	+	1.86510i	0.311410	+	0.0960573i
$378$	2.73887	−	6.97854i	0.140872	−	0.358937i
$379$	−0.636184	+	2.78730i	−0.0326786	+	0.143174i	−0.988635	−	0.150333i	$-0.951965\pi$
$379$	−0.636184	+	2.78730i	−0.0326786	+	0.143174i	0.955957	+	0.293507i	$0.0948225\pi$
$380$	−0.325317	−	0.563466i	−0.0166884	−	0.0289052i
$381$	−0.423708	+	0.733884i	−0.0217072	+	0.0375980i
$382$	−8.41872	−	7.81143i	−0.430739	−	0.399668i
$383$	18.9620	−	23.7776i	0.968912	−	1.21498i	−0.00770024	−	0.999970i	$-0.502451\pi$
$383$	18.9620	−	23.7776i	0.968912	−	1.21498i	0.976612	−	0.215007i	$-0.0689775\pi$
$384$	−0.529721	+	0.361157i	−0.0270322	+	0.0184302i
$385$	−6.15541	+	2.96429i	−0.313709	+	0.151074i
$386$	4.01983			0.204604
$387$	−15.4591	−	7.01663i	−0.785830	−	0.356675i
$388$	−15.4446			−0.784082
$389$	−15.8412	+	7.62874i	−0.803183	+	0.386793i	−0.789990	−	0.613120i	$-0.789914\pi$
$389$	−15.8412	+	7.62874i	−0.803183	+	0.386793i	−0.0131936	+	0.999913i	$0.504200\pi$
$390$	−0.780601	+	0.532205i	−0.0395273	+	0.0269492i
$391$	38.6094	−	48.4147i	1.95256	−	2.44843i
$392$	1.92260	+	1.78392i	0.0971062	+	0.0901014i
$393$	−1.78756	+	3.09614i	−0.0901703	+	0.156180i
$394$	−8.96726	−	15.5318i	−0.451764	−	0.782478i
$395$	2.37528	−	10.4068i	0.119514	−	0.523623i
$396$	−3.08866	+	7.86978i	−0.155211	+	0.395471i
$397$	23.4774	+	7.24183i	1.17830	+	0.363457i	0.821217	−	0.570616i	$-0.193295\pi$
$397$	23.4774	+	7.24183i	1.17830	+	0.363457i	0.357082	+	0.934073i	$0.383772\pi$
$398$	6.34374	+	7.95479i	0.317983	+	0.398738i
$399$	−0.0652192	+	0.870289i	−0.00326504	+	0.0435690i
$400$	0.955573	−	0.294755i	0.0477786	−	0.0147378i
$401$	−23.0300	−	15.7016i	−1.15006	−	0.784099i	−0.170523	−	0.985354i	$-0.554546\pi$
$401$	−23.0300	−	15.7016i	−1.15006	−	0.784099i	−0.979539	+	0.201254i	$0.935498\pi$
$402$	−0.769000	−	0.115908i	−0.0383542	−	0.00578097i
$403$	2.18223	+	9.56097i	0.108705	+	0.476266i
$404$	7.77880	−	7.21767i	0.387010	−	0.359093i
$405$	0.408744	+	5.45431i	0.0203107	+	0.271027i
$406$	3.28214	+	8.36275i	0.162890	+	0.415037i
$407$	3.29765	−	0.497040i	0.163458	−	0.0246374i
$408$	−4.06760	−	1.95885i	−0.201376	−	0.0969777i
$409$	−16.0884	−	7.74775i	−0.795519	−	0.383102i	−0.00844819	−	0.999964i	$-0.502689\pi$
$409$	−16.0884	−	7.74775i	−0.795519	−	0.383102i	−0.787071	+	0.616862i	$0.788403\pi$
$410$	3.80829	−	0.574007i	0.188078	−	0.0283482i
$411$	2.90800	+	7.40946i	0.143441	+	0.365482i
$412$	0.161979	+	2.16146i	0.00798014	+	0.106488i
$413$	−9.34188	+	8.66800i	−0.459684	+	0.426525i
$414$	−5.06609	−	22.1960i	−0.248985	−	1.09087i
$415$	10.3277	+	1.55665i	0.506968	+	0.0764131i
$416$	1.21755	+	0.830113i	0.0596954	+	0.0406997i
$417$	11.7196	−	3.61502i	0.573912	−	0.177028i
$418$	0.158774	−	2.11869i	0.00776589	−	0.103629i
$419$	−7.05177	−	8.84264i	−0.344502	−	0.431991i	0.579152	−	0.815219i	$-0.303384\pi$
$419$	−7.05177	−	8.84264i	−0.344502	−	0.431991i	−0.923654	+	0.383228i	$0.874812\pi$
$420$	−1.28176	−	0.395370i	−0.0625434	−	0.0192921i
$421$	−7.06028	+	17.9893i	−0.344097	+	0.876745i	0.649143	+	0.760666i	$0.275128\pi$
$421$	−7.06028	+	17.9893i	−0.344097	+	0.876745i	−0.993240	+	0.116079i	$0.962968\pi$
$422$	−2.50607	+	10.9798i	−0.121994	+	0.534489i
$423$	0.00470511	+	0.00814948i	0.000228770	+	0.000396241i
$424$	−3.85560	+	6.67810i	−0.187245	+	0.324317i
$425$	5.16204	+	4.78968i	0.250396	+	0.232333i
$426$	−3.65112	+	4.57836i	−0.176897	+	0.221822i
$427$	−1.52591	+	1.04035i	−0.0738440	+	0.0503460i
$428$	−15.8227	+	7.61982i	−0.764820	+	0.368318i
$429$	−3.08511			−0.148950
$430$	−2.25641	+	6.15700i	−0.108814	+	0.296917i
$431$	−20.6589			−0.995103			−0.497552	−	0.867434i	$-0.665767\pi$
$431$	−20.6589			−0.995103			−0.497552	+	0.867434i	$0.665767\pi$
$432$	−3.22836	+	1.55470i	−0.155325	+	0.0748004i
$433$	5.92112	−	4.03695i	0.284551	−	0.194004i	−0.412630	−	0.910899i	$-0.635390\pi$
$433$	5.92112	−	4.03695i	0.284551	−	0.194004i	0.697181	+	0.716895i	$0.254437\pi$
$434$	−8.68115	+	10.8858i	−0.416709	+	0.522536i
$435$	2.01806	+	1.87248i	0.0967585	+	0.0897787i
$436$	7.79949	−	13.5091i	0.373528	−	0.646969i
$437$	2.86078	+	4.95501i	0.136850	+	0.237030i
$438$	−0.705063	+	3.08908i	−0.0336892	+	0.147602i
$439$	−1.47768	+	3.76506i	−0.0705258	+	0.179697i	−0.961790	−	0.273787i	$-0.911724\pi$
$439$	−1.47768	+	3.76506i	−0.0705258	+	0.179697i	0.891265	+	0.453484i	$0.149819\pi$
$440$	3.12040	+	0.962516i	0.148759	+	0.0458861i
$441$	4.23360	+	5.30877i	0.201600	+	0.252799i
$442$	−0.775470	+	10.3479i	−0.0368853	+	0.492201i
$443$	3.19281	−	0.984851i	0.151695	−	0.0467917i	−0.217978	−	0.975954i	$-0.569946\pi$
$443$	3.19281	−	0.984851i	0.151695	−	0.0467917i	0.369673	+	0.929162i	$0.379470\pi$
$444$	0.540982	+	0.368835i	0.0256739	+	0.0175041i
$445$	−6.41581	−	0.967027i	−0.304138	−	0.0458415i
$446$	1.91613	+	8.39512i	0.0907315	+	0.397520i
$447$	−5.26854	+	4.88849i	−0.249194	+	0.231218i
$448$	0.156350	+	2.08634i	0.00738682	+	0.0985703i
$449$	−10.0755	−	25.6720i	−0.475492	−	1.21154i	−0.944550	−	0.328367i	$-0.893502\pi$
$449$	−10.0755	−	25.6720i	−0.475492	−	1.21154i	0.469058	−	0.883168i	$-0.344594\pi$
$450$	2.56004	−	0.385865i	0.120682	−	0.0181898i
$451$	11.3309	+	5.45666i	0.533550	+	0.256944i
$452$	5.59868	+	2.69618i	0.263340	+	0.126818i
$453$	−9.61675	+	1.44949i	−0.451834	+	0.0681030i
$454$	−5.55350	−	14.1501i	−0.260639	−	0.664097i
$455$	0.230398	+	3.07445i	0.0108012	+	0.144132i
$456$	0.305783	−	0.283725i	0.0143196	−	0.0132866i
$457$	−0.680874	−	2.98310i	−0.0318499	−	0.139544i	0.956503	−	0.291722i	$-0.0942283\pi$
$457$	−0.680874	−	2.98310i	−0.0318499	−	0.139544i	−0.988353	+	0.152179i	$0.951371\pi$
$458$	16.5287	+	2.49131i	0.772337	+	0.116411i
$459$	−20.8480	−	14.2139i	−0.973103	−	0.663450i
$460$	−8.40312	+	2.59202i	−0.391797	+	0.120854i
$461$	−2.94256	+	39.2658i	−0.137049	+	1.82879i	0.329342	+	0.944211i	$0.393173\pi$
$461$	−2.94256	+	39.2658i	−0.137049	+	1.82879i	−0.466390	+	0.884579i	$0.654446\pi$
$462$	−2.73098	−	3.42454i	−0.127057	−	0.159324i
$463$	−21.7722	−	6.71584i	−1.01184	−	0.312112i	−0.255866	−	0.966712i	$-0.582361\pi$
$463$	−21.7722	−	6.71584i	−1.01184	−	0.312112i	−0.755975	+	0.654601i	$0.772837\pi$
$464$	1.56876	−	3.99713i	0.0728277	−	0.185562i
$465$	−0.949422	+	4.15969i	−0.0440284	+	0.192901i
$466$	10.9129	+	18.9017i	0.505530	+	0.875604i
$467$	8.22735	−	14.2502i	0.380716	−	0.659420i	−0.610449	−	0.792056i	$-0.709011\pi$
$467$	8.22735	−	14.2502i	0.380716	−	0.659420i	0.991165	+	0.132636i	$0.0423442\pi$
$468$	2.79668	+	2.59494i	0.129276	+	0.119951i
$469$	−1.58232	+	1.98416i	−0.0730646	+	0.0916201i
$470$	0.00300317	−	0.00204752i	0.000138526	−	9.44453e-5i
$471$	13.6523	−	6.57462i	0.629067	−	0.302943i
$472$	6.09114			0.280367
$473$	−17.4138	+	12.4613i	−0.800686	+	0.572971i
$474$	6.84362			0.314338
$475$	−0.586202	+	0.282300i	−0.0268968	+	0.0129528i
$476$	−12.1729	+	8.29934i	−0.557944	+	0.380400i
$477$	−12.4474	+	15.6085i	−0.569925	+	0.714664i
$478$	−1.06867	−	0.991577i	−0.0488796	−	0.0453537i
$479$	17.0663	−	29.5597i	0.779780	−	1.35062i	−0.152289	−	0.988336i	$-0.548664\pi$
$479$	17.0663	−	29.5597i	0.779780	−	1.35062i	0.932068	−	0.362282i	$-0.118002\pi$
$480$	0.320562	+	0.555229i	0.0146316	+	0.0253426i
$481$	0.334880	−	1.46720i	0.0152692	−	0.0668987i
$482$	8.48288	−	21.6140i	0.386384	−	0.984491i
$483$	11.2715	+	3.47681i	0.512873	+	0.158200i
$484$	−0.209913	−	0.263222i	−0.00954148	−	0.0119646i
$485$	−1.15418	+	15.4014i	−0.0524086	+	0.699344i
$486$	−13.6230	+	4.20213i	−0.617950	+	0.190612i
$487$	−8.63052	−	5.88419i	−0.391086	−	0.266638i	0.351774	−	0.936085i	$-0.385579\pi$
$487$	−8.63052	−	5.88419i	−0.391086	−	0.266638i	−0.742860	+	0.669447i	$0.766531\pi$
$488$	0.872860	+	0.131562i	0.0395125	+	0.00595555i
$489$	−2.74378	−	12.0213i	−0.124078	−	0.543621i
$490$	1.92260	−	1.78392i	0.0868544	−	0.0805891i
$491$	−0.409539	−	5.46492i	−0.0184822	−	0.246628i	−0.998791	−	0.0491577i	$-0.984346\pi$
$491$	−0.409539	−	5.46492i	−0.0184822	−	0.246628i	0.980309	−	0.197471i	$-0.0632727\pi$
$492$	0.902085	+	2.29847i	0.0406691	+	0.103623i
$493$	29.8997	−	4.50665i	1.34661	−	0.202969i
$494$	−0.863832	−	0.416000i	−0.0388656	−	0.0187167i
$495$	7.61696	+	3.66813i	0.342357	+	0.164870i
$496$	6.58065	−	0.991874i	0.295480	−	0.0445364i
$497$	6.98160	+	17.7888i	0.313168	+	0.797938i
$498$	0.500403	+	6.67741i	0.0224236	+	0.299222i
$499$	−0.675250	+	0.626541i	−0.0302284	+	0.0280478i	−0.695142	−	0.718872i	$-0.744659\pi$
$499$	−0.675250	+	0.626541i	−0.0302284	+	0.0280478i	0.664914	+	0.746920i	$0.268468\pi$
$500$	−0.222521	−	0.974928i	−0.00995144	−	0.0436001i
$501$	1.05597	+	0.159162i	0.0471773	+	0.00711083i
$502$	−14.7097	−	10.0289i	−0.656524	−	0.447611i
$503$	11.0137	−	3.39729i	0.491078	−	0.151477i	−0.0393194	−	0.999227i	$-0.512519\pi$
$503$	11.0137	−	3.39729i	0.491078	−	0.151477i	0.530397	+	0.847749i	$0.322043\pi$
$504$	−0.404783	+	5.40145i	−0.0180305	+	0.240600i
$505$	−6.61618	−	8.29643i	−0.294416	−	0.369186i
$506$	−27.4402	−	8.46417i	−1.21986	−	0.376278i
$507$	2.53634	−	6.46249i	0.112643	−	0.287009i
$508$	0.294121	−	1.28863i	0.0130495	−	0.0571736i
$509$	4.06322	+	7.03771i	0.180099	+	0.311941i	0.941914	−	0.335854i	$-0.109025\pi$
$509$	4.06322	+	7.03771i	0.180099	+	0.311941i	−0.761815	+	0.647795i	$0.775691\pi$
$510$	−2.25735	+	3.90984i	−0.0999570	+	0.173131i
$511$	7.57969	+	7.03293i	0.335306	+	0.311118i
$512$	0.623490	−	0.781831i	0.0275546	−	0.0345524i
$513$	1.92626	−	1.31330i	0.0850465	−	0.0579837i
$514$	−24.5632	+	11.8290i	−1.08344	+	0.521756i
$515$	2.16752			0.0955125
$516$	−4.17033	−	0.531986i	−0.183589	−	0.0234194i
$517$	0.0118692			0.000522005
$518$	1.92507	−	0.927065i	0.0845827	−	0.0407329i
$519$	−7.01639	+	4.78370i	−0.307986	+	0.209981i
$520$	0.918780	−	1.15211i	0.0402912	−	0.0505235i
$521$	10.7838	+	10.0059i	0.472446	+	0.438366i	0.880112	−	0.474765i	$-0.157467\pi$
$521$	10.7838	+	10.0059i	0.472446	+	0.438366i	−0.407667	+	0.913131i	$0.633657\pi$
$522$	5.55844	−	9.62750i	0.243286	−	0.421384i
$523$	−11.3889	−	19.7262i	−0.498003	−	0.862566i	0.501995	−	0.864871i	$-0.332600\pi$
$523$	−11.3889	−	19.7262i	−0.498003	−	0.862566i	−0.999997	+	0.00230472i	$0.999266\pi$
$524$	1.24085	−	5.43652i	0.0542068	−	0.237495i
$525$	−0.490051	+	1.24863i	−0.0213876	+	0.0544946i
$526$	23.5671	+	7.26950i	1.02758	+	0.316965i
$527$	29.2189	+	36.6393i	1.27279	+	1.59603i
$528$	−0.156453	+	2.08772i	−0.00680873	+	0.0908562i
$529$	51.9172	−	16.0143i	2.25727	−	0.696275i
$530$	6.37130	+	4.34388i	0.276751	+	0.188686i
$531$	15.5936	+	2.35036i	0.676704	+	0.101997i
$532$	−0.302907	−	1.32712i	−0.0131327	−	0.0575380i
$533$	4.16030	−	3.86019i	0.180203	−	0.167204i
$534$	−0.310861	−	4.14815i	−0.0134523	−	0.179508i
$535$	6.41608	+	16.3479i	0.277391	+	0.706782i
$536$	1.19946	−	0.180789i	0.0518087	−	0.00780890i
$537$	−14.2304	−	6.85299i	−0.614086	−	0.295728i
$538$	−10.6020	−	5.10567i	−0.457086	−	0.220121i
$539$	8.46883	−	1.27647i	0.364779	−	0.0549815i
$540$	1.30909	+	3.33552i	0.0563345	+	0.143538i
$541$	3.28441	+	43.8274i	0.141208	+	1.88429i	0.397376	+	0.917656i	$0.369921\pi$
$541$	3.28441	+	43.8274i	0.141208	+	1.88429i	−0.256168	+	0.966632i	$0.582460\pi$
$542$	−6.76789	+	6.27968i	−0.290706	+	0.269736i
$543$	0.273023	+	1.19619i	0.0117165	+	0.0513336i
$544$	6.96320	+	1.04953i	0.298545	+	0.0449984i
$545$	−12.8885	−	8.78722i	−0.552082	−	0.376403i
$546$	−1.88881	+	0.582621i	−0.0808337	+	0.0249339i
$547$	1.27379	−	16.9975i	0.0544633	−	0.726763i	−0.901407	−	0.432973i	$-0.857464\pi$
$547$	1.27379	−	16.9975i	0.0544633	−	0.726763i	0.955870	−	0.293789i	$-0.0949165\pi$
$548$	−7.74076	−	9.70661i	−0.330669	−	0.414646i
$549$	2.18379	+	0.673611i	0.0932021	+	0.0287490i
$550$	1.19301	−	3.03974i	0.0508702	−	0.129615i
$551$	−0.621678	+	2.72375i	−0.0264844	+	0.116036i
$552$	−2.81896	−	4.88257i	−0.119983	−	0.207816i
$553$	11.1665	−	19.3409i	0.474847	−	0.822458i
$554$	3.84739	+	3.56985i	0.163460	+	0.151668i
$555$	0.408231	−	0.511906i	0.0173285	−	0.0217292i
$556$	−15.8057	+	10.7761i	−0.670310	+	0.457010i
$557$	28.8073	−	13.8729i	1.22060	−	0.587812i	0.291124	−	0.956685i	$-0.405971\pi$
$557$	28.8073	−	13.8729i	1.22060	−	0.587812i	0.929480	+	0.368874i	$0.120257\pi$
$558$	17.2295			0.729383
$559$	2.36371	+	9.36954i	0.0999745	+	0.396290i
$560$	2.09219			0.0884112
$561$	−13.2826	+	6.39659i	−0.560794	+	0.270064i
$562$	20.2621	−	13.8145i	0.854706	−	0.582729i
$563$	−9.89483	+	12.4077i	−0.417017	+	0.522923i	−0.945325	−	0.326130i	$-0.894255\pi$
$563$	−9.89483	+	12.4077i	−0.417017	+	0.522923i	0.528308	+	0.849053i	$0.322827\pi$
$564$	0.00170824	+	0.00158502i	7.19301e−5	+	6.67413e-5i
$565$	3.10703	−	5.38154i	0.130714	−	0.226403i
$566$	−3.82412	−	6.62358i	−0.160740	−	0.278410i
$567$	−2.54641	+	11.1565i	−0.106939	+	0.468531i
$568$	3.33698	−	8.50250i	0.140017	−	0.356757i
$569$	13.7462	+	4.24013i	0.576269	+	0.177755i	0.569171	−	0.822219i	$-0.307264\pi$
$569$	13.7462	+	4.24013i	0.576269	+	0.177755i	0.00709819	+	0.999975i	$0.497741\pi$
$570$	−0.260081	−	0.326131i	−0.0108936	−	0.0136601i
$571$	2.13217	−	28.4518i	0.0892285	−	1.19067i	−0.755380	−	0.655287i	$-0.772548\pi$
$571$	2.13217	−	28.4518i	0.0892285	−	1.19067i	0.844608	−	0.535385i	$-0.179833\pi$
$572$	4.59825	−	1.41837i	0.192262	−	0.0593051i
$573$	−6.08357	−	4.14771i	−0.254145	−	0.173273i
$574$	7.96766	+	1.20093i	0.332564	+	0.0501259i
$575$	1.95681	+	8.57332i	0.0816044	+	0.357532i
$576$	1.89784	−	1.76094i	0.0790768	−	0.0733725i
$577$	2.59782	+	34.6654i	0.108148	+	1.44314i	0.742370	+	0.669990i	$0.233702\pi$
$577$	2.59782	+	34.6654i	0.108148	+	1.44314i	−0.634222	+	0.773151i	$0.718679\pi$
$578$	11.9056	+	30.3351i	0.495209	+	1.26177i
$579$	2.54842	−	0.384113i	0.105909	−	0.0159632i
$580$	−3.86872	−	1.86308i	−0.160640	−	0.0773601i
$581$	19.6876	+	9.48107i	0.816781	+	0.393341i
$582$	−9.79131	+	1.47580i	−0.405863	+	0.0611740i
$583$	9.19956	+	23.4401i	0.381007	+	0.970790i
$584$	−0.369327	−	4.92833i	−0.0152829	−	0.203936i
$585$	2.79668	−	2.59494i	0.115628	−	0.107287i
$586$	−2.74138	−	12.0108i	−0.113245	−	0.496160i
$587$	−21.9452	−	3.30770i	−0.905773	−	0.136523i	−0.320395	−	0.947284i	$-0.603816\pi$
$587$	−21.9452	−	3.30770i	−0.905773	−	0.136523i	−0.585378	+	0.810760i	$0.699054\pi$
$588$	1.38932	+	0.947222i	0.0572946	+	0.0390628i
$589$	−4.13760	+	1.27628i	−0.170487	+	0.0525882i
$590$	0.455192	−	6.07411i	0.0187399	−	0.250067i
$591$	−7.16903	−	8.98968i	−0.294895	−	0.369786i
$592$	−0.975887	−	0.301021i	−0.0401087	−	0.0123719i
$593$	−3.88204	+	9.89127i	−0.159416	+	0.406186i	−0.988157	−	0.153447i	$-0.950963\pi$
$593$	−3.88204	+	9.89127i	−0.159416	+	0.406186i	0.828741	+	0.559633i	$0.189058\pi$
$594$	−2.60369	+	11.4075i	−0.106831	+	0.468056i
$595$	7.36645	+	12.7591i	0.301995	+	0.523071i
$596$	5.60511	−	9.70834i	0.229594	−	0.397669i
$597$	4.78180	+	4.43687i	0.195706	+	0.181589i
$598$	−8.07957	+	10.1315i	−0.330398	+	0.414306i
$599$	−6.33781	+	4.32105i	−0.258956	+	0.176553i	−0.685838	−	0.727754i	$-0.740564\pi$
$599$	−6.33781	+	4.32105i	−0.258956	+	0.176553i	0.426882	+	0.904307i	$0.359612\pi$
$600$	0.577632	−	0.278173i	0.0235817	−	0.0113564i
$601$	−12.3848			−0.505188			−0.252594	−	0.967572i	$-0.581284\pi$
$601$	−12.3848			−0.505188			−0.252594	+	0.967572i	$0.581284\pi$
$602$	−8.30802	+	10.9178i	−0.338610	+	0.444978i
$603$	3.14042			0.127888
$604$	13.6670	−	6.58170i	0.556104	−	0.267806i
$605$	−0.278173	+	0.189655i	−0.0113093	+	0.00771057i
$606$	4.24179	−	5.31903i	0.172311	−	0.216071i
$607$	3.25692	+	3.02198i	0.132194	+	0.122659i	0.743499	−	0.668737i	$-0.233165\pi$
$607$	3.25692	+	3.02198i	0.132194	+	0.122659i	−0.611305	+	0.791395i	$0.709355\pi$
$608$	−0.325317	+	0.563466i	−0.0131934	+	0.0228516i
$609$	2.87985	+	4.98805i	0.116697	+	0.202126i
$610$	0.196423	−	0.860587i	0.00795295	−	0.0348442i
$611$	0.00195684	−	0.00498594i	7.91651e−5	−	0.000201709i
$612$	17.4211	+	5.37371i	0.704208	+	0.217219i
$613$	−6.76266	−	8.48011i	−0.273141	−	0.342508i	0.626274	−	0.779603i	$-0.284579\pi$
$613$	−6.76266	−	8.48011i	−0.273141	−	0.342508i	−0.899416	+	0.437094i	$0.856008\pi$
$614$	0.360234	−	4.80699i	0.0145379	−	0.193994i
$615$	2.35946	−	0.727797i	0.0951426	−	0.0293476i
$616$	5.64486	+	3.84860i	0.227438	+	0.155064i
$617$	−34.2011	−	5.15499i	−1.37689	−	0.207532i	−0.581456	−	0.813578i	$-0.697517\pi$
$617$	−34.2011	−	5.15499i	−1.37689	−	0.207532i	−0.795430	+	0.606046i	$0.792755\pi$
$618$	0.309226	+	1.35481i	0.0124389	+	0.0544983i
$619$	−3.73614	+	3.46663i	−0.150168	+	0.139336i	−0.751679	−	0.659529i	$-0.770756\pi$
$619$	−3.73614	+	3.46663i	−0.150168	+	0.139336i	0.601511	+	0.798864i	$0.294565\pi$
$620$	−0.497328	−	6.63637i	−0.0199732	−	0.266523i
$621$	−11.5119	−	29.3319i	−0.461957	−	1.17705i
$622$	22.2242	−	3.34976i	0.891110	−	0.134313i
$623$	−12.2304	−	5.88984i	−0.490000	−	0.235972i
$624$	0.851204	+	0.409918i	0.0340754	+	0.0164099i
$625$	−0.988831	+	0.149042i	−0.0395532	+	0.00596169i
$626$	2.37035	+	6.03956i	0.0947383	+	0.241389i
$627$	−0.101794	−	1.35834i	−0.00406525	−	0.0542469i
$628$	−17.3257	+	16.0759i	−0.691371	+	0.641498i
$629$	−1.60027	−	7.01125i	−0.0638070	−	0.279557i
$630$	5.35610	+	0.807302i	0.213392	+	0.0321637i
$631$	−1.88528	−	1.28536i	−0.0750519	−	0.0511695i	0.525213	−	0.850971i	$-0.323986\pi$
$631$	−1.88528	−	1.28536i	−0.0750519	−	0.0511695i	−0.600265	+	0.799801i	$0.704938\pi$
$632$	−10.2002	+	3.14634i	−0.405742	+	0.125155i
$633$	−0.539584	+	7.20025i	−0.0214466	+	0.286184i
$634$	−6.62693	−	8.30990i	−0.263189	−	0.330028i
$635$	−1.26305	−	0.389598i	−0.0501224	−	0.0154607i
$636$	−1.80618	+	4.60208i	−0.0716199	+	0.182484i
$637$	0.860020	−	3.76799i	0.0340752	−	0.149293i
$638$	−7.01090	−	12.1432i	−0.277564	−	0.480755i
$639$	11.8236	−	20.4791i	0.467736	−	0.810142i
$640$	−0.733052	−	0.680173i	−0.0289764	−	0.0268862i
$641$	−10.9841	+	13.7736i	−0.433846	+	0.544026i	−0.949910	−	0.312524i	$-0.898825\pi$
$641$	−10.9841	+	13.7736i	−0.433846	+	0.544026i	0.516063	+	0.856550i	$0.327397\pi$
$642$	−9.30290	+	6.34261i	−0.367156	+	0.250323i
$643$	15.9983	−	7.70437i	0.630911	−	0.303831i	−0.0909640	−	0.995854i	$-0.528995\pi$
$643$	15.9983	−	7.70437i	0.630911	−	0.303831i	0.721875	+	0.692023i	$0.243281\pi$
$644$	−18.3983			−0.724995
$645$	−0.842147	+	4.11891i	−0.0331595	+	0.162182i
$646$	−4.58168			−0.180264
$647$	−10.5201	+	5.06619i	−0.413586	+	0.199173i	−0.629094	−	0.777330i	$-0.716574\pi$
$647$	−10.5201	+	5.06619i	−0.413586	+	0.199173i	0.215507	+	0.976502i	$0.430859\pi$
$648$	4.51920	−	3.08114i	0.177531	−	0.121039i
$649$	12.4015	−	15.5510i	0.486802	−	0.610430i
$650$	−1.08023	−	1.00231i	−0.0423702	−	0.0393138i
$651$	−4.46334	+	7.73072i	−0.174932	+	0.302991i
$652$	9.61628	+	16.6559i	0.376602	+	0.652295i
$653$	8.77055	−	38.4263i	0.343218	−	1.50374i	−0.449018	−	0.893523i	$-0.648226\pi$
$653$	8.77055	−	38.4263i	0.343218	−	1.50374i	0.792236	−	0.610214i	$-0.208917\pi$
$654$	3.65373	−	9.30955i	0.142872	−	0.364032i
$655$	−5.32859	−	1.64365i	−0.208205	−	0.0642228i
$656$	−2.40125	−	3.01107i	−0.0937530	−	0.117562i
$657$	0.956174	−	12.7593i	0.0373039	−	0.497786i
$658$	0.00726673	−	0.00224149i	0.000283287	−	8.73823e-5i
$659$	−7.86522	−	5.36241i	−0.306385	−	0.208890i	0.400360	−	0.916358i	$-0.368885\pi$
$659$	−7.86522	−	5.36241i	−0.306385	−	0.208890i	−0.706745	+	0.707468i	$0.749837\pi$
$660$	2.07019	+	0.312031i	0.0805820	+	0.0121458i
$661$	−5.17472	−	22.6719i	−0.201273	−	0.881835i	−0.970163	−	0.242454i	$-0.922048\pi$
$661$	−5.17472	−	22.6719i	−0.201273	−	0.881835i	0.768890	−	0.639381i	$-0.220809\pi$
$662$	−3.99508	+	3.70689i	−0.155273	+	0.144072i
$663$	0.497172	+	6.63429i	0.0193085	+	0.257655i
$664$	−3.81576	−	9.72240i	−0.148080	−	0.377302i
$665$	−1.34605	+	0.202884i	−0.0521975	+	0.00786750i
$666$	−2.38216	−	1.14719i	−0.0923068	−	0.0444526i
$667$	34.0208	+	16.3835i	1.31729	+	0.634373i
$668$	−1.64706	+	0.248255i	−0.0637268	+	0.00960527i
$669$	2.01695	+	5.13909i	0.0779796	+	0.198689i
$670$	−0.0906480	−	1.20961i	−0.00350204	−	0.0467315i
$671$	2.11302	−	1.96060i	0.0815722	−	0.0756879i
$672$	0.298479	+	1.30772i	0.0115141	+	0.0504464i
$673$	−34.5677	−	5.21025i	−1.33249	−	0.200840i	−0.556111	−	0.831108i	$-0.687707\pi$
$673$	−34.5677	−	5.21025i	−1.33249	−	0.200840i	−0.776378	+	0.630268i	$0.782945\pi$
$674$	−12.0390	−	8.20807i	−0.463726	−	0.316163i
$675$	3.42402	−	1.05617i	0.131791	−	0.0406520i
$676$	−0.809213	+	10.7982i	−0.0311236	+	0.415315i
$677$	6.51651	+	8.17144i	0.250450	+	0.314054i	0.891125	−	0.453758i	$-0.149917\pi$
$677$	6.51651	+	8.17144i	0.250450	+	0.314054i	−0.640675	+	0.767812i	$0.721345\pi$
$678$	3.80699	+	1.17430i	0.146206	+	0.0450987i
$679$	−11.8053	+	30.0794i	−0.453046	+	1.15434i
$680$	1.56696	−	6.86530i	0.0600902	−	0.263272i
$681$	−4.87282	−	8.43997i	−0.186727	−	0.323420i
$682$	10.8658	−	18.8202i	0.416075	−	0.720662i
$683$	22.4522	+	20.8326i	0.859109	+	0.797137i	0.980715	−	0.195442i	$-0.0626140\pi$
$683$	22.4522	+	20.8326i	0.859109	+	0.797137i	−0.121606	+	0.992578i	$0.538804\pi$
$684$	−1.05025	+	1.31697i	−0.0401573	+	0.0503556i
$685$	−10.2579	+	6.99374i	−0.391936	+	0.267217i
$686$	18.1388	−	8.73521i	0.692544	−	0.333512i
$687$	10.7167			0.408866
$688$	6.46032	−	1.12439i	0.246297	−	0.0428671i
$689$	11.3633			0.432907
$690$	−5.07958	+	2.44620i	−0.193376	+	0.0931251i
$691$	24.6091	−	16.7782i	0.936176	−	0.638274i	0.00388864	−	0.999992i	$-0.498762\pi$
$691$	24.6091	−	16.7782i	0.936176	−	0.638274i	0.932287	+	0.361718i	$0.117810\pi$
$692$	8.25841	−	10.3557i	0.313938	−	0.393665i
$693$	12.9661	+	12.0307i	0.492540	+	0.457010i
$694$	11.6511	−	20.1802i	0.442268	−	0.766031i
$695$	9.56484	+	16.5668i	0.362815	+	0.628414i
$696$	0.612590	−	2.68393i	0.0232202	−	0.101734i
$697$	9.90816	−	25.2456i	0.375298	−	0.956245i
$698$	0.248409	+	0.0766239i	0.00940241	+	0.00290026i
$699$	8.72450	+	10.9402i	0.329991	+	0.413796i
$700$	0.156350	−	2.08634i	0.00590946	−	0.0788562i
$701$	−30.6233	+	9.44604i	−1.15663	+	0.356772i	−0.812960	−	0.582320i	$-0.802145\pi$
$701$	−30.6233	+	9.44604i	−1.15663	+	0.356772i	−0.343667	+	0.939092i	$0.611669\pi$
$702$	4.36275	+	2.97447i	0.164661	+	0.112264i
$703$	0.657045	+	0.0990335i	0.0247809	+	0.00373512i
$704$	−0.726637	−	3.18360i	−0.0273861	−	0.119987i
$705$	0.00170824	−	0.00158502i	6.43362e−5	−	5.96953e-5i
$706$	1.52804	+	20.3903i	0.0575085	+	0.767398i
$707$	−8.11106	−	20.6666i	−0.305048	−	0.777249i
$708$	3.86155	−	0.582036i	0.145126	−	0.0218742i
$709$	−8.49381	−	4.09040i	−0.318992	−	0.153618i	0.267535	−	0.963548i	$-0.413791\pi$
$709$	−8.49381	−	4.09040i	−0.318992	−	0.153618i	−0.586527	+	0.809930i	$0.699505\pi$
$710$	−8.22935	−	3.96305i	−0.308842	−	0.148730i
$711$	−27.3270	+	4.11888i	−1.02484	+	0.154470i
$712$	2.37043	+	6.03977i	0.0888357	+	0.226350i
$713$	4.37340	+	58.3590i	0.163785	+	2.18556i
$714$	−6.92412	+	6.42464i	−0.259129	+	0.240436i
$715$	−1.07078	−	4.69139i	−0.0400448	−	0.175448i
$716$	24.3606	+	3.67177i	0.910397	+	0.137220i
$717$	−0.772243	−	0.526506i	−0.0288399	−	0.0196627i
$718$	2.25961	−	0.696999i	0.0843280	−	0.0260118i
$719$	2.97795	−	39.7380i	0.111059	−	1.48198i	−0.611817	−	0.791000i	$-0.709561\pi$
$719$	2.97795	−	39.7380i	0.111059	−	1.48198i	0.722876	−	0.690978i	$-0.242820\pi$
$720$	−1.61419	−	2.02413i	−0.0601573	−	0.0754349i
$721$	4.33340	+	1.33668i	0.161384	+	0.0497804i
$722$	−6.78682	+	17.2925i	−0.252579	+	0.643562i
$723$	3.31251	−	14.5130i	0.123194	−	0.539746i
$724$	−0.956880	−	1.65736i	−0.0355622	−	0.0615955i
$725$	−2.14698	+	3.71867i	−0.0797367	+	0.138108i
$726$	−0.158229	−	0.146815i	−0.00587242	−	0.00544881i
$727$	21.9777	−	27.5591i	0.815106	−	1.02211i	−0.184125	−	0.982903i	$-0.558945\pi$
$727$	21.9777	−	27.5591i	0.815106	−	1.02211i	0.999231	−	0.0392083i	$-0.0124836\pi$
$728$	2.54735	−	1.73676i	0.0944112	−	0.0643684i
$729$	6.54892	−	3.15379i	0.242553	−	0.116807i
$730$	−4.94215			−0.182917
$731$	29.6034	+	35.4389i	1.09492	+	1.31075i
$732$	0.565931			0.0209174
$733$	5.50291	−	2.65006i	0.203255	−	0.0978822i	−0.329487	−	0.944160i	$-0.606876\pi$
$733$	5.50291	−	2.65006i	0.203255	−	0.0978822i	0.532742	+	0.846278i	$0.321162\pi$
$734$	−2.02378	+	1.37979i	−0.0746991	+	0.0509290i
$735$	1.04840	−	1.31465i	0.0386707	−	0.0484916i
$736$	6.44631	+	5.98131i	0.237614	+	0.220474i
$737$	1.98052	−	3.43036i	0.0729534	−	0.126359i
$738$	−4.98544	−	8.63503i	−0.183516	−	0.317860i
$739$	1.95178	−	8.55131i	0.0717974	−	0.314565i	−0.926259	−	0.376889i	$-0.876994\pi$
$739$	1.95178	−	8.55131i	0.0717974	−	0.314565i	0.998056	+	0.0623237i	$0.0198511\pi$
$740$	−0.373108	+	0.950663i	−0.0137157	+	0.0349471i
$741$	−0.587387	−	0.181185i	−0.0215782	−	0.00665600i
$742$	10.0590	+	12.6135i	0.369276	+	0.463057i
$743$	−1.53886	+	20.5347i	−0.0564555	+	0.753346i	0.895099	+	0.445867i	$0.147105\pi$
$743$	−1.53886	+	20.5347i	−0.0564555	+	0.753346i	−0.951555	+	0.307479i	$0.900515\pi$
$744$	4.07711	−	1.25762i	0.149474	−	0.0461066i
$745$	−9.26233	−	6.31495i	−0.339345	−	0.231362i
$746$	30.9651	+	4.66724i	1.13371	+	0.170880i
$747$	−6.01699	−	26.3621i	−0.220150	−	0.964540i
$748$	16.8565	−	15.6406i	0.616336	−	0.571876i
$749$	2.74580	+	36.6401i	0.100329	+	1.33880i
$750$	−0.234229	−	0.596805i	−0.00855282	−	0.0217922i
$751$	29.3956	−	4.43068i	1.07266	−	0.161678i	0.411117	−	0.911583i	$-0.365139\pi$
$751$	29.3956	−	4.43068i	1.07266	−	0.161678i	0.661546	+	0.749905i	$0.269901\pi$
$752$	−0.00327479	−	0.00157706i	−0.000119419	−	5.75093e-5i
$753$	−10.2837	−	4.95236i	−0.374758	−	0.180474i
$754$	−6.25694	+	0.943081i	−0.227864	+	0.0343450i
$755$	−5.54196	−	14.1207i	−0.201692	−	0.513904i
$756$	0.560234	+	7.47580i	0.0203755	+	0.271892i
$757$	−14.4877	+	13.4426i	−0.526564	+	0.488580i	−0.898071	−	0.439850i	$-0.855032\pi$
$757$	−14.4877	+	13.4426i	−0.526564	+	0.488580i	0.371507	+	0.928430i	$0.378841\pi$
$758$	−0.636184	−	2.78730i	−0.0231072	−	0.101239i
$759$	−18.2048	−	2.74394i	−0.660793	−	0.0995986i
$760$	0.537580	+	0.366516i	0.0195001	+	0.0132949i
$761$	−39.8347	+	12.2874i	−1.44401	+	0.445417i	−0.915088	−	0.403255i	$-0.867879\pi$
$761$	−39.8347	+	12.2874i	−1.44401	+	0.445417i	−0.528920	+	0.848672i	$0.677403\pi$
$762$	0.0633275	−	0.845046i	0.00229411	−	0.0306128i
$763$	−20.3482	−	25.5159i	−0.736656	−	0.923737i
$764$	10.9743	+	3.38511i	0.397035	+	0.122469i
$765$	6.66056	−	16.9708i	0.240813	−	0.613582i
$766$	−6.76745	+	29.6502i	−0.244518	+	1.07130i
$767$	−4.48798	−	7.77341i	−0.162052	−	0.280682i
$768$	0.320562	−	0.555229i	0.0115673	−	0.0200351i
$769$	−5.66165	−	5.25325i	−0.204164	−	0.189437i	0.571463	−	0.820628i	$-0.306376\pi$
$769$	−5.66165	−	5.25325i	−0.204164	−	0.189437i	−0.775628	+	0.631191i	$0.782566\pi$
$770$	4.25968	−	5.34147i	0.153508	−	0.192493i
$771$	−14.4418	+	9.84627i	−0.520110	+	0.354605i
$772$	−3.62174	+	1.74414i	−0.130349	+	0.0627730i
$773$	−24.2744			−0.873088			−0.436544	−	0.899683i	$-0.643798\pi$
$773$	−24.2744			−0.873088			−0.436544	+	0.899683i	$0.643798\pi$
$774$	16.9726	−	0.385692i	0.610067	−	0.0138634i
$775$	−6.65498			−0.239054
$776$	13.9151	−	6.70117i	0.499524	−	0.240558i
$777$	1.13184	−	0.771673i	0.0406044	−	0.0276836i
$778$	10.9625	−	13.7465i	0.393024	−	0.492837i
$779$	1.83687	+	1.70437i	0.0658129	+	0.0610654i
$780$	0.472382	−	0.818190i	0.0169140	−	0.0292959i
$781$	−14.9132	−	25.8305i	−0.533638	−	0.924288i
$782$	−13.7795	+	60.3721i	−0.492755	+	2.15890i
$783$	5.62119	−	14.3226i	0.200885	−	0.511847i
$784$	−2.50622	−	0.773066i	−0.0895078	−	0.0276095i
$785$	14.7362	+	18.4786i	0.525957	+	0.659530i
$786$	0.267169	−	3.56512i	0.00952959	−	0.127163i
$787$	−12.5481	+	3.87058i	−0.447292	+	0.137971i	−0.510215	−	0.860047i	$-0.670434\pi$
$787$	−12.5481	+	3.87058i	−0.447292	+	0.137971i	0.0629228	+	0.998018i	$0.479958\pi$
$788$	14.8182	+	10.1029i	0.527877	+	0.359900i
$789$	15.6353	+	2.35664i	0.556631	+	0.0838987i
$790$	2.37528	+	10.4068i	0.0845088	+	0.370257i
$791$	9.53042	−	8.84294i	0.338863	−	0.314419i
$792$	−0.631782	−	8.43055i	−0.0224494	−	0.299566i
$793$	−0.475229	−	1.21086i	−0.0168759	−	0.0429990i
$794$	−24.2946	+	3.66182i	−0.862182	+	0.129953i
$795$	4.45424	+	2.14505i	0.157976	+	0.0760770i
$796$	−9.16696	−	4.41458i	−0.324914	−	0.156471i
$797$	20.4292	−	3.07920i	0.723638	−	0.109071i	0.223113	−	0.974793i	$-0.428378\pi$
$797$	20.4292	−	3.07920i	0.723638	−	0.109071i	0.500526	+	0.865722i	$0.333140\pi$
$798$	−0.318844	−	0.812401i	−0.0112870	−	0.0287587i
$799$	−0.00191274	−	0.0255238i	−6.76680e−5	−	0.000902966i
$800$	−0.733052	+	0.680173i	−0.0259173	+	0.0240477i
$801$	3.73788	+	16.3767i	0.132072	+	0.578643i
$802$	27.5620	+	4.15430i	0.973246	+	0.146693i
$803$	−13.3342	−	9.09112i	−0.470555	−	0.320819i
$804$	0.743136	−	0.229227i	0.0262084	−	0.00808421i
$805$	−1.37491	+	18.3469i	−0.0484591	+	0.646642i
$806$	−6.11447	−	7.66730i	−0.215373	−	0.270069i
$807$	−7.20916	−	2.22373i	−0.253775	−	0.0782791i
$808$	−3.87683	+	9.87800i	−0.136386	+	0.347507i
$809$	−8.41114	+	36.8516i	−0.295720	+	1.29563i	0.580713	+	0.814109i	$0.302774\pi$
$809$	−8.41114	+	36.8516i	−0.295720	+	1.29563i	−0.876432	+	0.481525i	$0.840083\pi$
$810$	−2.73480	−	4.73682i	−0.0960911	−	0.166435i
$811$	−17.6438	+	30.5600i	−0.619557	+	1.07310i	0.370009	+	0.929028i	$0.379355\pi$
$811$	−17.6438	+	30.5600i	−0.619557	+	1.07310i	−0.989567	+	0.144077i	$0.953979\pi$
$812$	−6.58557	−	6.11051i	−0.231108	−	0.214437i
$813$	−3.69054	+	4.62779i	−0.129433	+	0.162304i
$814$	−2.75542	+	1.87861i	−0.0965774	+	0.0658453i
$815$	17.3279	−	8.34469i	0.606971	−	0.292302i
$816$	4.51470			0.158046
$817$	−4.04733	+	1.34987i	−0.141598	+	0.0472260i
$818$	17.8568			0.624347
$819$	7.19149	−	3.46324i	0.251291	−	0.121015i
$820$	−3.18209	+	2.16952i	−0.111124	+	0.0757628i
$821$	−0.441229	+	0.553283i	−0.0153990	+	0.0193097i	−0.789471	−	0.613787i	$-0.789645\pi$
$821$	−0.441229	+	0.553283i	−0.0153990	+	0.0193097i	0.774072	+	0.633097i	$0.218217\pi$
$822$	−5.83486	−	5.41396i	−0.203514	−	0.188834i
$823$	−4.89456	+	8.47763i	−0.170614	+	0.295512i	−0.938635	−	0.344913i	$-0.887908\pi$
$823$	−4.89456	+	8.47763i	−0.170614	+	0.295512i	0.768021	+	0.640425i	$0.221242\pi$
$824$	−1.08376	−	1.87713i	−0.0377546	−	0.0653929i
$825$	0.465863	−	2.04108i	0.0162193	−	0.0710613i
$826$	4.65584	−	11.8629i	0.161997	−	0.412763i
$827$	−34.1697	−	10.5400i	−1.18820	−	0.366510i	−0.363235	−	0.931698i	$-0.618328\pi$
$827$	−34.1697	−	10.5400i	−1.18820	−	0.366510i	−0.824963	+	0.565187i	$0.808804\pi$
$828$	14.1949	+	17.7998i	0.493306	+	0.618586i
$829$	−2.50191	+	33.3857i	−0.0868950	+	1.15953i	0.767901	+	0.640569i	$0.221301\pi$
$829$	−2.50191	+	33.3857i	−0.0868950	+	1.15953i	−0.854796	+	0.518965i	$0.826318\pi$
$830$	−9.98037	+	3.07854i	−0.346424	+	0.106858i
$831$	2.78021	+	1.89552i	0.0964445	+	0.0657547i
$832$	−1.45715	−	0.219630i	−0.0505176	−	0.00761430i
$833$	−4.10973	−	18.0059i	−0.142394	−	0.623867i
$834$	−8.99050	+	8.34197i	−0.311316	+	0.288859i
$835$	0.124475	+	1.66101i	0.00430765	+	0.0574816i
$836$	0.776215	+	1.97776i	0.0268460	+	0.0684024i
$837$	23.5799	−	3.55409i	0.815040	−	0.122847i
$838$	10.1901	+	4.90730i	0.352011	+	0.169520i
$839$	45.3726	+	21.8503i	1.56643	+	0.754355i	0.997675	−	0.0681489i	$-0.0217093\pi$
$839$	45.3726	+	21.8503i	1.56643	+	0.754355i	0.568759	+	0.822504i	$0.307424\pi$
$840$	1.32637	−	0.199918i	0.0457641	−	0.00689783i
$841$	−3.85872	−	9.83185i	−0.133059	−	0.339029i
$842$	−1.44417	−	19.2711i	−0.0497695	−	0.664127i
$843$	11.5254	−	10.6940i	0.396955	−	0.368321i
$844$	−2.50607	−	10.9798i	−0.0862625	−	0.377941i
$845$	10.7075	+	1.61390i	0.368350	+	0.0555199i
$846$	−0.00777508	−	0.00530096i	−0.000267313	−	0.000182251i
$847$	−0.673091	+	0.207621i	−0.0231277	+	0.00713395i
$848$	0.576259	−	7.68964i	0.0197888	−	0.264063i
$849$	−3.05726	−	3.83368i	−0.104925	−	0.131572i
$850$	−6.72900	−	2.07562i	−0.230803	−	0.0711933i
$851$	3.28103	−	8.35994i	0.112472	−	0.286575i
$852$	1.30307	−	5.70913i	0.0446425	−	0.195591i
$853$	−10.8270	−	18.7529i	−0.370710	−	0.642088i	0.618965	−	0.785418i	$-0.287552\pi$
$853$	−10.8270	−	18.7529i	−0.370710	−	0.642088i	−0.989675	+	0.143330i	$0.954219\pi$
$854$	0.923408	−	1.59939i	0.0315984	−	0.0547300i
$855$	1.23480	+	1.14573i	0.0422294	+	0.0391831i
$856$	10.9497	−	13.7304i	0.374252	−	0.469297i
$857$	−43.5312	+	29.6791i	−1.48700	+	1.01382i	−0.497791	+	0.867297i	$0.665856\pi$
$857$	−43.5312	+	29.6791i	−1.48700	+	1.01382i	−0.989207	+	0.146522i	$0.953192\pi$
$858$	2.77958	−	1.33858i	0.0948934	−	0.0456983i
$859$	3.38472			0.115485			0.0577425	−	0.998332i	$-0.481610\pi$
$859$	3.38472			0.115485			0.0577425	+	0.998332i	$0.481610\pi$
$860$	−0.638470	−	6.52628i	−0.0217717	−	0.222544i
$861$	5.16595			0.176055
$862$	18.6130	−	8.96355i	0.633961	−	0.305300i
$863$	−47.0738	+	32.0944i	−1.60241	+	1.09251i	−0.663593	+	0.748094i	$0.730969\pi$
$863$	−47.0738	+	32.0944i	−1.60241	+	1.09251i	−0.938819	+	0.344412i	$0.888078\pi$
$864$	2.23410	−	2.80147i	0.0760055	−	0.0953079i
$865$	−9.70961	−	9.00920i	−0.330137	−	0.306322i
$866$	−3.58318	+	6.20625i	−0.121761	+	0.210897i
$867$	10.4464	+	18.0936i	0.354777	+	0.614492i
$868$	3.09827	−	13.5744i	0.105162	−	0.460745i
$869$	−12.7347	+	32.4475i	−0.431996	+	1.10071i
$870$	−2.63065	−	0.811447i	−0.0891873	−	0.0275106i
$871$	−1.11449	−	1.39752i	−0.0377629	−	0.0473532i
$872$	−1.16571	+	15.5554i	−0.0394760	+	0.526771i
$873$	38.2091	−	11.7859i	1.29318	−	0.398894i
$874$	−4.72737	−	3.22307i	−0.159906	−	0.109022i
$875$	−2.06882	−	0.311825i	−0.0699390	−	0.0105416i
$876$	−0.705063	−	3.08908i	−0.0238219	−	0.104370i
$877$	−1.47372	+	1.36741i	−0.0497639	+	0.0461741i	−0.704663	−	0.709542i	$-0.748902\pi$
$877$	−1.47372	+	1.36741i	−0.0497639	+	0.0461741i	0.654899	+	0.755717i	$0.272711\pi$
$878$	−0.302257	−	4.03335i	−0.0102007	−	0.136119i
$879$	−2.88561	−	7.35242i	−0.0973293	−	0.247991i
$880$	−3.22900	+	0.486694i	−0.108850	+	0.0164064i
$881$	−51.6440	−	24.8704i	−1.73993	−	0.837906i	−0.982807	−	0.184633i	$-0.940890\pi$
$881$	−51.6440	−	24.8704i	−1.73993	−	0.837906i	−0.757123	−	0.653273i	$-0.773395\pi$
$882$	−6.11773	−	2.94615i	−0.205995	−	0.0992019i
$883$	−49.9387	+	7.52705i	−1.68057	+	0.253305i	−0.918852	−	0.394601i	$-0.870883\pi$
$883$	−49.9387	+	7.52705i	−1.68057	+	0.253305i	−0.761720	+	0.647907i	$0.775645\pi$
$884$	−3.79112	−	9.65962i	−0.127509	−	0.324888i
$885$	−0.291834	−	3.89425i	−0.00980989	−	0.130904i
$886$	−2.44931	+	2.27263i	−0.0822862	+	0.0763504i
$887$	−7.00157	−	30.6759i	−0.235090	−	1.03000i	−0.945350	−	0.326056i	$-0.894280\pi$
$887$	−7.00157	−	30.6759i	−0.235090	−	1.03000i	0.710261	−	0.703939i	$-0.248577\pi$
$888$	−0.647439	−	0.0975858i	−0.0217266	−	0.00327476i
$889$	−2.28487	−	1.55780i	−0.0766322	−	0.0522469i
$890$	6.20002	−	1.91245i	0.207825	−	0.0641056i
$891$	1.33474	−	17.8109i	0.0447156	−	0.596688i
$892$	−5.36888	−	6.73236i	−0.179763	−	0.225416i
$893$	0.00225983		0.000697064i	7.56222e−5		2.33264e-5i
$894$	2.62576	−	6.69032i	0.0878184	−	0.223758i
$895$	5.48197	−	24.0181i	0.183242	−	0.802835i
$896$	−1.04610	−	1.81189i	−0.0349476	−	0.0605310i
$897$	−4.15404	+	7.19500i	−0.138699	+	0.240234i
$898$	20.2164	+	18.7580i	0.674629	+	0.625964i
$899$	−17.8170	+	22.3418i	−0.594229	+	0.745140i
$900$	−2.13910	+	1.45841i	−0.0713033	+	0.0486138i
$901$	48.9237	−	23.5604i	1.62988	−	0.784911i
$902$	−12.5763			−0.418746
$903$	−4.22372	+	7.71536i	−0.140557	+	0.256751i
$904$	−6.21407			−0.206677
$905$	−1.72424	+	0.830349i	−0.0573156	+	0.0276017i
$906$	8.03548	−	5.47850i	0.266961	−	0.182011i
$907$	−20.4626	+	25.6593i	−0.679450	+	0.852004i	−0.995303	−	0.0968044i	$-0.969138\pi$
$907$	−20.4626	+	25.6593i	−0.679450	+	0.852004i	0.315853	+	0.948808i	$0.397709\pi$
$908$	11.1430	+	10.3392i	0.369794	+	0.343119i
$909$	−13.7364	+	23.7922i	−0.455608	+	0.789137i
$910$	−1.54154	−	2.67002i	−0.0511014	−	0.0885102i
$911$	−10.0926	+	44.2187i	−0.334384	+	1.46503i	0.476163	+	0.879357i	$0.342027\pi$
$911$	−10.0926	+	44.2187i	−0.334384	+	1.46503i	−0.810547	+	0.585674i	$0.800830\pi$
$912$	−0.152397	+	0.388302i	−0.00504638	+	0.0128580i
$913$	−32.5906	−	10.0529i	−1.07859	−	0.332702i
$914$	1.90777	+	2.39226i	0.0631033	+	0.0791290i
$915$	0.0422921	−	0.564349i	0.00139813	−	0.0186568i
$916$	−15.9728	+	4.92696i	−0.527757	+	0.162791i
$917$	−9.63951	−	6.57211i	−0.318325	−	0.217030i
$918$	24.9506	+	3.76070i	0.823494	+	0.124122i
$919$	−3.22901	−	14.1472i	−0.106515	−	0.466674i	−0.999851	−	0.0172832i	$-0.994498\pi$
$919$	−3.22901	−	14.1472i	−0.106515	−	0.466674i	0.893335	−	0.449391i	$-0.148359\pi$
$920$	6.44631	−	5.98131i	0.212529	−	0.197198i
$921$	−0.230955	−	3.08187i	−0.00761021	−	0.101551i
$922$	−14.3856	−	36.6540i	−0.473765	−	1.20713i
$923$	−13.3094	+	2.00608i	−0.438086	+	0.0660308i
$924$	3.94638	+	1.90048i	0.129826	+	0.0625211i
$925$	0.920122	+	0.443107i	0.0302534	+	0.0145693i
$926$	22.5300	−	3.39585i	0.740381	−	0.111595i
$927$	−2.05016	−	5.22372i	−0.0673361	−	0.171569i
$928$	0.320888	+	4.28195i	0.0105337	+	0.140562i
$929$	27.7745	−	25.7709i	0.911251	−	0.845517i	−0.0772070	−	0.997015i	$-0.524600\pi$
$929$	27.7745	−	25.7709i	0.911251	−	0.845517i	0.988458	+	0.151498i	$0.0484098\pi$
$930$	−0.949422	−	4.15969i	−0.0311328	−	0.136402i
$931$	1.68739	+	0.254333i	0.0553019	+	0.00833541i
$932$	−18.0333	−	12.2949i	−0.590701	−	0.402733i
$933$	13.7692	−	4.24725i	0.450785	−	0.139049i
$934$	−1.22966	+	16.4087i	−0.0402357	+	0.536908i
$935$	−14.3371	−	17.9782i	−0.468875	−	0.587950i
$936$	−3.64562	−	1.12453i	−0.119161	−	0.0367563i
$937$	−19.9015	+	50.7083i	−0.650155	+	1.65657i	0.0997423	+	0.995013i	$0.468198\pi$
$937$	−19.9015	+	50.7083i	−0.650155	+	1.65657i	−0.749897	+	0.661554i	$0.769897\pi$
$938$	0.564722	−	2.47421i	0.0184388	−	0.0807858i
$939$	2.07982	+	3.60236i	0.0678724	+	0.117558i
$940$	−0.00181737	+	0.00314778i	−5.92761e−5	+	0.000102669i
$941$	−31.1263	−	28.8810i	−1.01469	−	0.941495i	−0.0163948	−	0.999866i	$-0.505219\pi$
$941$	−31.1263	−	28.8810i	−1.01469	−	0.941495i	−0.998295	+	0.0583711i	$0.981409\pi$
$942$	−9.44771	+	11.8471i	−0.307823	+	0.385998i
$943$	27.9827	−	19.0783i	0.911243	−	0.621275i
$944$	−5.48793	+	2.64285i	−0.178617	+	0.0860173i
$945$	7.49676			0.243870
$946$	10.2825	−	18.7828i	0.334313	−	0.610681i
$947$	−17.3295			−0.563132			−0.281566	−	0.959542i	$-0.590854\pi$
$947$	−17.3295			−0.563132			−0.281566	+	0.959542i	$0.590854\pi$
$948$	−6.16589	+	2.96934i	−0.200259	+	0.0964396i
$949$	−6.01733	+	4.10254i	−0.195331	+	0.133174i
$950$	0.405664	−	0.508687i	0.0131615	−	0.0165040i
$951$	−4.99527	−	4.63493i	−0.161983	−	0.150298i
$952$	7.36645	−	12.7591i	0.238748	−	0.413524i
$953$	19.2113	+	33.2749i	0.622315	+	1.07788i	0.989054	+	0.147557i	$0.0471409\pi$
$953$	19.2113	+	33.2749i	0.622315	+	1.07788i	−0.366739	+	0.930324i	$0.619526\pi$
$954$	4.44241	−	19.4635i	0.143828	−	0.630153i
$955$	4.19575	−	10.6906i	0.135771	−	0.345940i
$956$	1.39306	+	0.429703i	0.0450549	+	0.0138976i
$957$	−5.60499	−	7.02843i	−0.181183	−	0.227197i
$958$	−2.55073	+	34.0372i	−0.0824105	+	1.09969i
$959$	−24.8210	+	7.65627i	−0.801512	+	0.247234i
$960$	−0.529721	−	0.361157i	−0.0170967	−	0.0116563i
$961$	−13.1404	−	1.98059i	−0.423883	−	0.0638901i
$962$	0.334880	+	1.46720i	0.0107970	+	0.0473045i
$963$	33.3297	−	30.9255i	1.07404	−	0.996559i
$964$	1.73516	+	23.1541i	0.0558858	+	0.745745i
$965$	1.46861	+	3.74196i	0.0472762	+	0.120458i
$966$	−11.6638	+	1.75804i	−0.375278	+	0.0565640i
$967$	−51.4621	−	24.7829i	−1.65491	−	0.796963i	−0.999117	−	0.0420230i	$-0.986620\pi$
$967$	−51.4621	−	24.7829i	−1.65491	−	0.796963i	−0.655794	−	0.754940i	$-0.727666\pi$
$968$	0.303332	+	0.146077i	0.00974948	+	0.00469510i
$969$	−2.90461	+	0.437799i	−0.0933095	+	0.0140641i
$970$	−5.64256	−	14.3770i	−0.181172	−	0.461618i
$971$	−2.41983	−	32.2904i	−0.0776560	−	1.03625i	−0.890863	−	0.454272i	$-0.849899\pi$
$971$	−2.41983	−	32.2904i	−0.0776560	−	1.03625i	0.813207	−	0.581975i	$-0.197720\pi$
$972$	10.4506	−	9.69676i	0.335204	−	0.311024i
$973$	8.90594	+	39.0195i	0.285511	+	1.25091i
$974$	10.3289	+	1.55683i	0.330959	+	0.0498840i
$975$	−0.780601	−	0.532205i	−0.0249992	−	0.0170442i
$976$	−0.843502	+	0.260186i	−0.0269998	+	0.00832835i
$977$	2.71553	−	36.2362i	0.0868774	−	1.15930i	−0.767994	−	0.640457i	$-0.778745\pi$
$977$	2.71553	−	36.2362i	0.0868774	−	1.15930i	0.854871	−	0.518840i	$-0.173636\pi$
$978$	7.68790	+	9.64032i	0.245832	+	0.308263i
$979$	20.2460	+	6.24507i	0.647065	+	0.199593i
$980$	−0.958195	+	2.44144i	−0.0306084	+	0.0779889i
$981$	−8.98655	+	39.3726i	−0.286918	+	1.25707i
$982$	2.74012	+	4.74603i	0.0874408	+	0.151452i
$983$	14.3178	−	24.7991i	0.456666	−	0.790969i	−0.542116	−	0.840304i	$-0.682377\pi$
$983$	14.3178	−	24.7991i	0.456666	−	0.790969i	0.998782	+	0.0493343i	$0.0157100\pi$
$984$	−1.81002	−	1.67945i	−0.0577014	−	0.0535390i
$985$	11.1820	−	14.0218i	0.356288	−	0.446771i
$986$	−24.9833	+	17.0333i	−0.795631	+	0.542452i
$987$	0.00439265	−	0.00211539i	0.000139819	−	6.73335e-5i
$988$	0.958781			0.0305029
$989$	5.61458	+	57.3908i	0.178533	+	1.82492i
$990$	−8.45419			−0.268692
$991$	35.8483	−	17.2636i	1.13876	−	0.548397i	0.233119	−	0.972448i	$-0.425107\pi$
$991$	35.8483	−	17.2636i	1.13876	−	0.548397i	0.905638	+	0.424051i	$0.139392\pi$
$992$	−5.49861	+	3.74889i	−0.174581	+	0.119027i
$993$	−2.17852	+	2.73177i	−0.0691332	+	0.0866902i
$994$	−14.0085	−	12.9980i	−0.444323	−	0.412271i
$995$	−5.08728	+	8.81143i	−0.161278	+	0.279341i
$996$	−3.34807	−	5.79902i	−0.106088	−	0.183749i
$997$	1.45207	−	6.36193i	0.0459875	−	0.201484i	−0.946715	−	0.322072i	$-0.895621\pi$
$997$	1.45207	−	6.36193i	0.0459875	−	0.201484i	0.992703	+	0.120588i	$0.0384779\pi$
$998$	0.336534	−	0.857474i	0.0106528	−	0.0271429i
$999$	−3.49681	−	1.07862i	−0.110634	−	0.0341261i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.31.2	✓	36
43.25	even	21	inner	430.2.q.a.111.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.31.2	✓	36	1.1	even	1	trivial
430.2.q.a.111.2	yes	36	43.25	even	21	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-0.529721 + 0.361157i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(0.320562 - 0.555229i) q^{6} +(-1.04610 - 1.81189i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.945854 + 2.41000i) q^{9} +O(q^{10})\)	\(q+(-0.900969 + 0.433884i) q^{2} +(-0.529721 + 0.361157i) q^{3} +(0.623490 - 0.781831i) q^{4} +(-0.733052 - 0.680173i) q^{5} +(0.320562 - 0.555229i) q^{6} +(-1.04610 - 1.81189i) q^{7} +(-0.222521 + 0.974928i) q^{8} +(-0.945854 + 2.41000i) q^{9} +(0.955573 + 0.294755i) q^{10} +(2.03599 + 2.55305i) q^{11} +(-0.0479112 + 0.639330i) q^{12} +(1.40814 - 0.434354i) q^{13} +(1.72865 + 1.17857i) q^{14} +(0.633962 + 0.0955544i) q^{15} +(-0.222521 - 0.974928i) q^{16} +(5.16204 - 4.78968i) q^{17} +(-0.193473 - 2.58172i) q^{18} +(0.237704 + 0.605659i) q^{19} +(-0.988831 + 0.149042i) q^{20} +(1.20852 + 0.581991i) q^{21} +(-2.94209 - 1.41684i) q^{22} +(8.69558 - 1.31065i) q^{23} +(-0.234229 - 0.596805i) q^{24} +(0.0747301 + 0.997204i) q^{25} +(-1.08023 + 1.00231i) q^{26} +(-0.797340 - 3.49337i) q^{27} +(-2.06882 - 0.311825i) q^{28} +(3.54783 + 2.41887i) q^{29} +(-0.612640 + 0.188974i) q^{30} +(-0.497328 + 6.63637i) q^{31} +(0.623490 + 0.781831i) q^{32} +(-2.00056 - 0.617091i) q^{33} +(-2.57268 + 6.55508i) q^{34} +(-0.465556 + 2.03973i) q^{35} +(1.29448 + 2.24211i) q^{36} +(0.510629 - 0.884436i) q^{37} +(-0.476949 - 0.442544i) q^{38} +(-0.589051 + 0.738647i) q^{39} +(0.826239 - 0.563320i) q^{40} +(3.46990 - 1.67102i) q^{41} -1.34135 q^{42} +(-0.341353 + 6.54855i) q^{43} +3.26547 q^{44} +(2.33257 - 1.12331i) q^{45} +(-7.26578 + 4.95373i) q^{46} +(0.00226623 - 0.00284176i) q^{47} +(0.469976 + 0.436074i) q^{48} +(1.31137 - 2.27136i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-1.00461 + 4.40150i) q^{51} +(0.538370 - 1.37174i) q^{52} +(7.36862 + 2.27292i) q^{53} +(2.23410 + 2.80147i) q^{54} +(0.244029 - 3.25634i) q^{55} +(1.99924 - 0.616684i) q^{56} +(-0.344655 - 0.234982i) q^{57} +(-4.24599 - 0.639981i) q^{58} +(-1.35541 - 5.93842i) q^{59} +(0.469976 - 0.436074i) q^{60} +(-0.0659657 - 0.880251i) q^{61} +(-2.43134 - 6.19495i) q^{62} +(5.35610 - 0.807302i) q^{63} +(-0.900969 - 0.433884i) q^{64} +(-1.32768 - 0.639375i) q^{65} +(2.07019 - 0.312031i) q^{66} +(-0.443161 - 1.12916i) q^{67} +(-0.526238 - 7.02216i) q^{68} +(-4.13288 + 3.83475i) q^{69} +(-0.465556 - 2.03973i) q^{70} +(-9.03187 - 1.36134i) q^{71} +(-2.13910 - 1.45841i) q^{72} +(-4.72258 + 1.45672i) q^{73} +(-0.0763187 + 1.01840i) q^{74} +(-0.399734 - 0.501250i) q^{75} +(0.621729 + 0.191778i) q^{76} +(2.49601 - 6.35972i) q^{77} +(0.210230 - 0.921078i) q^{78} +(5.33721 + 9.24433i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.00950 - 3.72028i) q^{81} +(-2.40125 + 3.01107i) q^{82} +(-8.62955 + 5.88353i) q^{83} +(1.20852 - 0.581991i) q^{84} -7.04185 q^{85} +(-2.53376 - 6.04815i) q^{86} -2.75295 q^{87} +(-2.94209 + 1.41684i) q^{88} +(5.36086 - 3.65498i) q^{89} +(-1.61419 + 2.02413i) q^{90} +(-2.26005 - 2.09702i) q^{91} +(4.39690 - 7.61566i) q^{92} +(-2.13333 - 3.69504i) q^{93} +(-0.000808807 + 0.00354361i) q^{94} +(0.237704 - 0.605659i) q^{95} +(-0.612640 - 0.188974i) q^{96} +(-9.62957 - 12.0751i) q^{97} +(-0.195998 + 2.61541i) q^{98} +(-8.07859 + 2.49192i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

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Database

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