LMFDB - Embedded newform 930.2.bg.g.421.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			421.3
Character	$\chi$	$=$	930.421
Dual form			930.2.bg.g.391.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.70884 + 3.00848i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.70884 + 3.00848i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(-0.950768 + 0.202092i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(-0.548926 + 5.22268i) q^{13} +(-3.95984 - 0.841690i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.60771 - 0.341730i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(0.387670 + 3.68843i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(3.69831 + 1.64659i) q^{21} +(0.650400 - 0.722343i) q^{22} +(1.00776 + 3.10157i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.62573 - 4.54789i) q^{26} +(0.309017 - 0.951057i) q^{27} +(3.69831 - 1.64659i) q^{28} +(2.77422 - 2.01559i) q^{29} +1.00000 q^{30} +(-5.08206 - 2.27436i) q^{31} +1.00000 q^{32} +(-0.786371 + 0.571332i) q^{33} +(1.50153 - 0.668525i) q^{34} +(1.25099 - 3.85017i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.942269 - 1.63206i) q^{37} +(-2.48164 - 2.75614i) q^{38} +(1.62279 + 4.99443i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-0.532295 - 0.236993i) q^{41} +(-3.95984 + 0.841690i) q^{42} +(1.03670 + 9.86350i) q^{43} +(-0.101603 + 0.966683i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(-2.63835 - 1.91687i) q^{46} +(4.37984 + 3.18214i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(-0.981393 + 9.33733i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-1.60771 + 0.341730i) q^{51} +(4.79744 + 2.13596i) q^{52} +(4.53184 - 5.03312i) q^{53} +(0.309017 + 0.951057i) q^{54} +(0.650400 + 0.722343i) q^{55} +(-2.02415 + 3.50593i) q^{56} +(1.85437 + 3.21187i) q^{57} +(-1.05966 + 3.26129i) q^{58} +(9.73806 - 4.33566i) q^{59} +(-0.809017 + 0.587785i) q^{60} +4.11451 q^{61} +(5.44830 - 1.14717i) q^{62} +4.04830 q^{63} +(-0.809017 + 0.587785i) q^{64} +(4.79744 - 2.13596i) q^{65} +(0.300367 - 0.924435i) q^{66} +(0.581811 + 1.00773i) q^{67} +(-0.821815 + 1.42343i) q^{68} +(2.18215 + 2.42353i) q^{69} +(1.25099 + 3.85017i) q^{70} +(-6.80061 + 7.55285i) q^{71} +(0.913545 + 0.406737i) q^{72} +(0.919533 - 0.195453i) q^{73} +(0.196988 + 1.87422i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(3.62770 + 0.771092i) q^{76} +(-3.18347 - 2.31293i) q^{77} +(-4.24851 - 3.08673i) q^{78} +(3.39466 + 0.721557i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(0.569936 - 0.121144i) q^{82} +(-4.21770 - 1.87784i) q^{83} +(2.70884 - 3.00848i) q^{84} +(0.507910 + 1.56319i) q^{85} +(-6.63632 - 7.37038i) q^{86} +(1.71456 - 2.96971i) q^{87} +(-0.486004 - 0.841784i) q^{88} +(-1.97832 + 6.08864i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-17.1993 + 12.4960i) q^{91} +3.26118 q^{92} +(-5.56775 - 0.0106683i) q^{93} -5.41378 q^{94} +(3.00044 - 2.17995i) q^{95} +(0.913545 - 0.406737i) q^{96} +(5.30797 - 16.3363i) q^{97} +(-4.69438 - 8.13091i) q^{98} +(-0.486004 + 0.841784i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{13}{15}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$3$	0.913545	−	0.406737i	0.527436	−	0.234830i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.70884	+	3.00848i	1.02385	+	1.13710i	0.990480	+	0.137654i	$0.0439562\pi$
$7$	2.70884	+	3.00848i	1.02385	+	1.13710i	0.0333665	+	0.999443i	$0.489377\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.669131	−	0.743145i	0.223044	−	0.247715i
$10$	0.913545	+	0.406737i	0.288888	+	0.128621i
$11$	−0.950768	+	0.202092i	−0.286667	+	0.0609330i	−0.349001	−	0.937122i	$-0.613479\pi$
$11$	−0.950768	+	0.202092i	−0.286667	+	0.0609330i	0.0623338	+	0.998055i	$0.480146\pi$
$12$	−0.104528	−	0.994522i	−0.0301748	−	0.287094i
$13$	−0.548926	+	5.22268i	−0.152245	+	1.44851i	0.605440	+	0.795891i	$0.292997\pi$
$13$	−0.548926	+	5.22268i	−0.152245	+	1.44851i	−0.757685	+	0.652621i	$0.773669\pi$
$14$	−3.95984	−	0.841690i	−1.05831	−	0.224951i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−1.60771	−	0.341730i	−0.389928	−	0.0828817i	0.00877596	−	0.999961i	$-0.497206\pi$
$17$	−1.60771	−	0.341730i	−0.389928	−	0.0828817i	−0.398704	+	0.917080i	$0.630540\pi$
$18$	−0.104528	+	0.994522i	−0.0246376	+	0.234411i
$19$	0.387670	+	3.68843i	0.0889376	+	0.846184i	0.944506	+	0.328494i	$0.106541\pi$
$19$	0.387670	+	3.68843i	0.0889376	+	0.846184i	−0.855568	+	0.517690i	$0.826792\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	3.69831	+	1.64659i	0.807037	+	0.359316i
$22$	0.650400	−	0.722343i	0.138666	−	0.154004i
$23$	1.00776	+	3.10157i	0.210132	+	0.646721i	0.999463	+	0.0327533i	$0.0104276\pi$
$23$	1.00776	+	3.10157i	0.210132	+	0.646721i	−0.789331	+	0.613968i	$0.789572\pi$
$24$	0.669131	+	0.743145i	0.136586	+	0.151694i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.62573	−	4.54789i	−0.514947	−	0.891915i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	3.69831	−	1.64659i	0.698915	−	0.311177i
$29$	2.77422	−	2.01559i	0.515159	−	0.374285i	−0.299618	−	0.954059i	$-0.596859\pi$
$29$	2.77422	−	2.01559i	0.515159	−	0.374285i	0.814777	+	0.579774i	$0.196859\pi$
$30$	1.00000			0.182574
$31$	−5.08206	−	2.27436i	−0.912764	−	0.408486i
$31$	−5.08206	−	2.27436i	−0.912764	−	0.408486i
$32$	1.00000			0.176777
$33$	−0.786371	+	0.571332i	−0.136890	+	0.0994562i
$34$	1.50153	−	0.668525i	0.257511	−	0.114651i
$35$	1.25099	−	3.85017i	0.211457	−	0.650797i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	0.942269	−	1.63206i	0.154908	−	0.268309i	−0.778117	−	0.628119i	$-0.783825\pi$
$37$	0.942269	−	1.63206i	0.154908	−	0.268309i	0.933026	+	0.359810i	$0.117159\pi$
$38$	−2.48164	−	2.75614i	−0.402575	−	0.447105i
$39$	1.62279	+	4.99443i	0.259854	+	0.799749i
$40$	0.669131	−	0.743145i	0.105799	−	0.117502i
$41$	−0.532295	−	0.236993i	−0.0831305	−	0.0370121i	0.364750	−	0.931105i	$-0.381154\pi$
$41$	−0.532295	−	0.236993i	−0.0831305	−	0.0370121i	−0.447881	+	0.894093i	$0.647821\pi$
$42$	−3.95984	+	0.841690i	−0.611016	+	0.129876i
$43$	1.03670	+	9.86350i	0.158095	+	1.50417i	0.729772	+	0.683691i	$0.239626\pi$
$43$	1.03670	+	9.86350i	0.158095	+	1.50417i	−0.571677	+	0.820479i	$0.693707\pi$
$44$	−0.101603	+	0.966683i	−0.0153172	+	0.145733i
$45$	−0.978148	−	0.207912i	−0.145814	−	0.0309936i
$46$	−2.63835	−	1.91687i	−0.389003	−	0.282628i
$47$	4.37984	+	3.18214i	0.638865	+	0.464162i	0.859460	−	0.511203i	$-0.170800\pi$
$47$	4.37984	+	3.18214i	0.638865	+	0.464162i	−0.220595	+	0.975365i	$0.570800\pi$
$48$	−0.978148	−	0.207912i	−0.141183	−	0.0300095i
$49$	−0.981393	+	9.33733i	−0.140199	+	1.33390i
$50$	−0.104528	−	0.994522i	−0.0147826	−	0.140647i
$51$	−1.60771	+	0.341730i	−0.225125	+	0.0478518i
$52$	4.79744	+	2.13596i	0.665285	+	0.296204i
$53$	4.53184	−	5.03312i	0.622497	−	0.691352i	−0.346606	−	0.938011i	$-0.612666\pi$
$53$	4.53184	−	5.03312i	0.622497	−	0.691352i	0.969102	+	0.246658i	$0.0793325\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	0.650400	+	0.722343i	0.0877000	+	0.0974007i
$56$	−2.02415	+	3.50593i	−0.270489	+	0.468500i
$57$	1.85437	+	3.21187i	0.245618	+	0.425423i
$58$	−1.05966	+	3.26129i	−0.139140	+	0.428228i
$59$	9.73806	−	4.33566i	1.26779	−	0.564455i	0.341008	−	0.940061i	$-0.389232\pi$
$59$	9.73806	−	4.33566i	1.26779	−	0.564455i	0.926780	+	0.375605i	$0.122565\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	4.11451			0.526809			0.263404	−	0.964685i	$-0.415155\pi$
$61$	4.11451			0.526809			0.263404	+	0.964685i	$0.415155\pi$
$62$	5.44830	−	1.14717i	0.691935	−	0.145690i
$63$	4.04830			0.510038
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	4.79744	−	2.13596i	0.595049	−	0.264933i
$66$	0.300367	−	0.924435i	0.0369726	−	0.113790i
$67$	0.581811	+	1.00773i	0.0710796	+	0.123113i	0.899375	−	0.437179i	$-0.144022\pi$
$67$	0.581811	+	1.00773i	0.0710796	+	0.123113i	−0.828295	+	0.560292i	$0.810689\pi$
$68$	−0.821815	+	1.42343i	−0.0996598	+	0.172616i
$69$	2.18215	+	2.42353i	0.262701	+	0.291759i
$70$	1.25099	+	3.85017i	0.149522	+	0.460183i
$71$	−6.80061	+	7.55285i	−0.807084	+	0.896358i	−0.996332	−	0.0855716i	$-0.972728\pi$
$71$	−6.80061	+	7.55285i	−0.807084	+	0.896358i	0.189248	+	0.981929i	$0.439395\pi$
$72$	0.913545	+	0.406737i	0.107662	+	0.0479344i
$73$	0.919533	−	0.195453i	0.107623	−	0.0228760i	−0.153785	−	0.988104i	$-0.549146\pi$
$73$	0.919533	−	0.195453i	0.107623	−	0.0228760i	0.261408	+	0.965228i	$0.415813\pi$
$74$	0.196988	+	1.87422i	0.0228994	+	0.217873i
$75$	−0.104528	+	0.994522i	−0.0120699	+	0.114837i
$76$	3.62770	+	0.771092i	0.416126	+	0.0884504i
$77$	−3.18347	−	2.31293i	−0.362790	−	0.263582i
$78$	−4.24851	−	3.08673i	−0.481049	−	0.349503i
$79$	3.39466	+	0.721557i	0.381929	+	0.0811815i	0.394875	−	0.918735i	$-0.370788\pi$
$79$	3.39466	+	0.721557i	0.381929	+	0.0811815i	−0.0129463	+	0.999916i	$0.504121\pi$
$80$	−0.104528	+	0.994522i	−0.0116866	+	0.111191i
$81$	−0.104528	−	0.994522i	−0.0116143	−	0.110502i
$82$	0.569936	−	0.121144i	0.0629390	−	0.0133781i
$83$	−4.21770	−	1.87784i	−0.462953	−	0.206120i	0.161987	−	0.986793i	$-0.448210\pi$
$83$	−4.21770	−	1.87784i	−0.462953	−	0.206120i	−0.624940	+	0.780673i	$0.714876\pi$
$84$	2.70884	−	3.00848i	0.295559	−	0.328252i
$85$	0.507910	+	1.56319i	0.0550906	+	0.169551i
$86$	−6.63632	−	7.37038i	−0.715613	−	0.794769i
$87$	1.71456	−	2.96971i	0.183820	−	0.318386i
$88$	−0.486004	−	0.841784i	−0.0518082	−	0.0897345i
$89$	−1.97832	+	6.08864i	−0.209701	+	0.645394i	0.789786	+	0.613382i	$0.210191\pi$
$89$	−1.97832	+	6.08864i	−0.209701	+	0.645394i	−0.999487	+	0.0320119i	$0.989809\pi$
$90$	0.913545	−	0.406737i	0.0962961	−	0.0428738i
$91$	−17.1993	+	12.4960i	−1.80297	+	1.30994i
$92$	3.26118			0.340001
$93$	−5.56775	−	0.0106683i	−0.577349	−	0.00110625i
$94$	−5.41378			−0.558388
$95$	3.00044	−	2.17995i	0.307839	−	0.223658i
$96$	0.913545	−	0.406737i	0.0932383	−	0.0415124i
$97$	5.30797	−	16.3363i	0.538943	−	1.65870i	−0.196029	−	0.980598i	$-0.562805\pi$
$97$	5.30797	−	16.3363i	0.538943	−	1.65870i	0.734972	−	0.678098i	$-0.237195\pi$
$98$	−4.69438	−	8.13091i	−0.474204	−	0.821346i
$99$	−0.486004	+	0.841784i	−0.0488453	+	0.0846025i
$100$	0.669131	+	0.743145i	0.0669131	+	0.0743145i
$101$	−0.0642637	−	0.197783i	−0.00639447	−	0.0196802i	0.947808	−	0.318841i	$-0.103293\pi$
$101$	−0.0642637	−	0.197783i	−0.00639447	−	0.0196802i	−0.954203	+	0.299160i	$0.903293\pi$
$102$	1.09980	−	1.22146i	0.108897	−	0.120942i
$103$	10.1486	+	4.51845i	0.999973	+	0.445217i	0.840398	−	0.541969i	$-0.182321\pi$
$103$	10.1486	+	4.51845i	0.999973	+	0.445217i	0.159574	+	0.987186i	$0.448988\pi$
$104$	−5.13670	+	1.09184i	−0.503694	+	0.107064i
$105$	−0.423163	−	4.02613i	−0.0412965	−	0.392910i
$106$	−0.707943	+	6.73563i	−0.0687615	+	0.654222i
$107$	−4.10217	−	0.871944i	−0.396572	−	0.0842940i	0.00530893	−	0.999986i	$-0.498310\pi$
$107$	−4.10217	−	0.871944i	−0.396572	−	0.0842940i	−0.401881	+	0.915692i	$0.631643\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	0.134891	+	0.0980043i	0.0129202	+	0.00938711i	0.594227	−	0.804298i	$-0.297458\pi$
$109$	0.134891	+	0.0980043i	0.0129202	+	0.00938711i	−0.581306	+	0.813685i	$0.697458\pi$
$110$	−0.950768	−	0.202092i	−0.0906521	−	0.0192687i
$111$	0.196988	−	1.87422i	0.0186973	−	0.177893i
$112$	−0.423163	−	4.02613i	−0.0399851	−	0.380433i
$113$	−12.8922	+	2.74032i	−1.21279	+	0.257787i	−0.769534	−	0.638606i	$-0.779511\pi$
$113$	−12.8922	+	2.74032i	−1.21279	+	0.257787i	−0.443260	+	0.896393i	$0.646178\pi$
$114$	−3.38811	−	1.50848i	−0.317326	−	0.141282i
$115$	2.18215	−	2.42353i	0.203487	−	0.225995i
$116$	−1.05966	−	3.26129i	−0.0983867	−	0.302803i
$117$	3.51391	+	3.90259i	0.324861	+	0.360795i
$118$	−5.32982	+	9.23151i	−0.490649	+	0.849830i
$119$	−3.32696	−	5.76246i	−0.304982	−	0.528244i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−9.18588	+	4.08982i	−0.835080	+	0.371802i
$122$	−3.32871	+	2.41845i	−0.301367	+	0.218956i
$123$	−0.582669			−0.0525375
$124$	−3.73348	+	4.13051i	−0.335277	+	0.370931i
$125$	1.00000			0.0894427
$126$	−3.27515	+	2.37953i	−0.291773	+	0.211986i
$127$	18.7908	−	8.36618i	1.66741	−	0.742379i	0.667412	−	0.744688i	$-0.267402\pi$
$127$	18.7908	−	8.36618i	1.66741	−	0.742379i	0.999997	+	0.00230989i	$0.000735262\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	4.95891	+	8.58909i	0.436608	+	0.756227i
$130$	−2.62573	+	4.54789i	−0.230291	+	0.398876i
$131$	9.31976	+	10.3506i	0.814271	+	0.904339i	0.996887	−	0.0788449i	$-0.0251232\pi$
$131$	9.31976	+	10.3506i	0.814271	+	0.904339i	−0.182616	+	0.983184i	$0.558457\pi$
$132$	0.300367	+	0.924435i	0.0261436	+	0.0804617i
$133$	−10.0464	+	11.1577i	−0.871135	+	0.967494i
$134$	−1.06302	−	0.473288i	−0.0918311	−	0.0408859i
$135$	−0.978148	+	0.207912i	−0.0841855	+	0.0178942i
$136$	−0.171806	−	1.63463i	−0.0147323	−	0.140168i
$137$	1.75683	−	16.7151i	0.150096	−	1.42807i	−0.617216	−	0.786794i	$-0.711740\pi$
$137$	1.75683	−	16.7151i	0.150096	−	1.42807i	0.767312	−	0.641274i	$-0.221594\pi$
$138$	−3.18991	−	0.678037i	−0.271544	−	0.0577184i
$139$	−6.97053	−	5.06439i	−0.591233	−	0.429556i	0.251523	−	0.967851i	$-0.419068\pi$
$139$	−6.97053	−	5.06439i	−0.591233	−	0.429556i	−0.842756	+	0.538295i	$0.819068\pi$
$140$	−3.27515	−	2.37953i	−0.276800	−	0.201107i
$141$	5.29547	+	1.12559i	0.445959	+	0.0947916i
$142$	1.06236	−	10.1077i	0.0891513	−	0.848218i
$143$	−0.533561	−	5.07649i	−0.0446186	−	0.424518i
$144$	−0.978148	+	0.207912i	−0.0815123	+	0.0173260i
$145$	−3.13266	−	1.39475i	−0.260153	−	0.115828i
$146$	−0.629033	+	0.698612i	−0.0520592	+	0.0578176i
$147$	2.90129	+	8.92925i	0.239294	+	0.736472i
$148$	−1.26100	−	1.40049i	−0.103654	−	0.115119i
$149$	−7.09575	+	12.2902i	−0.581307	+	1.00685i	0.414018	+	0.910269i	$0.364125\pi$
$149$	−7.09575	+	12.2902i	−0.581307	+	1.00685i	−0.995325	+	0.0965840i	$0.969208\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	−0.556050	+	1.71135i	−0.0452507	+	0.139267i	−0.971129	−	0.238554i	$-0.923327\pi$
$151$	−0.556050	+	1.71135i	−0.0452507	+	0.139267i	0.925879	+	0.377821i	$0.123327\pi$
$152$	−3.38811	+	1.50848i	−0.274812	+	0.122354i
$153$	−1.32973	+	0.966102i	−0.107502	+	0.0781047i
$154$	3.93498			0.317090
$155$	0.571379	+	5.53837i	0.0458943	+	0.444852i
$156$	5.25145			0.420453
$157$	5.29863	−	3.84968i	0.422877	−	0.307238i	−0.355917	−	0.934517i	$-0.615832\pi$
$157$	5.29863	−	3.84968i	0.422877	−	0.307238i	0.778794	+	0.627279i	$0.215832\pi$
$158$	−3.17046	+	1.41158i	−0.252228	+	0.112299i
$159$	2.09289	−	6.44125i	0.165977	−	0.510825i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−6.60112	+	11.4335i	−0.520241	+	0.901084i
$162$	0.669131	+	0.743145i	0.0525719	+	0.0583870i
$163$	−0.650973	−	2.00349i	−0.0509881	−	0.156925i	0.922320	−	0.386426i	$-0.126291\pi$
$163$	−0.650973	−	2.00349i	−0.0509881	−	0.156925i	−0.973308	+	0.229501i	$0.926291\pi$
$164$	−0.389882	+	0.433008i	−0.0304447	+	0.0338122i
$165$	0.887974	+	0.395351i	0.0691287	+	0.0307781i
$166$	4.51596	−	0.959897i	0.350506	−	0.0745024i
$167$	−0.651606	−	6.19962i	−0.0504228	−	0.479741i	−0.990373	−	0.138428i	$-0.955795\pi$
$167$	−0.651606	−	6.19962i	−0.0504228	−	0.479741i	0.939950	−	0.341313i	$-0.110872\pi$
$168$	−0.423163	+	4.02613i	−0.0326477	+	0.310622i
$169$	−14.2592	−	3.03088i	−1.09686	−	0.233145i
$170$	−1.32973	−	0.966102i	−0.101985	−	0.0740966i
$171$	3.00044	+	2.17995i	0.229449	+	0.166705i
$172$	9.70110	+	2.06203i	0.739702	+	0.157229i
$173$	0.495473	−	4.71411i	0.0376701	−	0.358407i	−0.959408	−	0.282021i	$-0.908995\pi$
$173$	0.495473	−	4.71411i	0.0376701	−	0.358407i	0.997078	−	0.0763860i	$-0.0243381\pi$
$174$	0.358441	+	3.41034i	0.0271733	+	0.258537i
$175$	−3.95984	+	0.841690i	−0.299336	+	0.0636258i
$176$	0.887974	+	0.395351i	0.0669335	+	0.0298007i
$177$	7.13269	−	7.92165i	0.536126	−	0.595428i
$178$	−1.97832	−	6.08864i	−0.148281	−	0.456362i
$179$	−16.1827	−	17.9727i	−1.20955	−	1.34334i	−0.922773	−	0.385344i	$-0.874083\pi$
$179$	−16.1827	−	17.9727i	−1.20955	−	1.34334i	−0.286777	−	0.957997i	$-0.592584\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	4.84715	+	8.39551i	0.360286	+	0.624033i	0.988008	−	0.154404i	$-0.0493458\pi$
$181$	4.84715	+	8.39551i	0.360286	+	0.624033i	−0.627722	+	0.778438i	$0.716013\pi$
$182$	6.56954	−	20.2190i	0.486967	−	1.49873i
$183$	3.75879	−	1.67352i	0.277858	−	0.123710i
$184$	−2.63835	+	1.91687i	−0.194502	+	0.141314i
$185$	−1.88454			−0.138554
$186$	4.51068	−	3.26401i	0.330739	−	0.239329i
$187$	1.59762			0.116830
$188$	4.37984	−	3.18214i	0.319432	−	0.232081i
$189$	3.69831	−	1.64659i	0.269012	−	0.119772i
$190$	−1.14607	+	3.52723i	−0.0831444	+	0.255892i
$191$	−11.6657	−	20.2057i	−0.844104	−	1.46203i	−0.886397	−	0.462926i	$-0.846800\pi$
$191$	−11.6657	−	20.2057i	−0.844104	−	1.46203i	0.0422932	−	0.999105i	$-0.486534\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	7.12739	+	7.91577i	0.513041	+	0.569790i	0.942887	−	0.333112i	$-0.108099\pi$
$193$	7.12739	+	7.91577i	0.513041	+	0.569790i	−0.429846	+	0.902902i	$0.641432\pi$
$194$	5.30797	+	16.3363i	0.381090	+	1.17288i
$195$	3.51391	−	3.90259i	0.251636	−	0.279470i
$196$	8.57706	+	3.81875i	0.612647	+	0.272768i
$197$	6.13672	−	1.30440i	0.437223	−	0.0929347i	0.0159591	−	0.999873i	$-0.494920\pi$
$197$	6.13672	−	1.30440i	0.437223	−	0.0929347i	0.421264	+	0.906938i	$0.361587\pi$
$198$	−0.101603	−	0.966683i	−0.00722058	−	0.0686992i
$199$	1.55917	−	14.8345i	0.110526	−	1.05159i	−0.788902	−	0.614519i	$-0.789350\pi$
$199$	1.55917	−	14.8345i	0.110526	−	1.05159i	0.899428	−	0.437069i	$-0.143983\pi$
$200$	−0.978148	−	0.207912i	−0.0691655	−	0.0147016i
$201$	0.941391	+	0.683960i	0.0664006	+	0.0482428i
$202$	0.168244	+	0.122237i	0.0118376	+	0.00860055i
$203$	13.5788	+	2.88626i	0.953043	+	0.202575i
$204$	−0.171806	+	1.63463i	−0.0120288	+	0.114447i
$205$	0.0609055	+	0.579477i	0.00425383	+	0.0404724i
$206$	−10.8663	+	2.30970i	−0.757090	+	0.160924i
$207$	2.97924	+	1.32644i	0.207071	+	0.0921940i
$208$	3.51391	−	3.90259i	0.243646	−	0.270596i
$209$	−1.11399	−	3.42850i	−0.0770560	−	0.237154i
$210$	2.70884	+	3.00848i	0.186928	+	0.207605i
$211$	4.75760	−	8.24041i	0.327527	−	0.567293i	−0.654494	−	0.756067i	$-0.727118\pi$
$211$	4.75760	−	8.24041i	0.327527	−	0.567293i	0.982020	+	0.188775i	$0.0604515\pi$
$212$	−3.38637	−	5.86536i	−0.232577	−	0.402835i
$213$	−3.14065	+	9.66593i	−0.215194	+	0.662298i
$214$	3.83124	−	1.70578i	0.261898	−	0.116605i
$215$	8.02369	−	5.82955i	0.547211	−	0.397572i
$216$	1.00000			0.0680414
$217$	−6.92416	−	21.4501i	−0.470042	−	1.45613i
$218$	−0.166735			−0.0112927
$219$	0.760537	−	0.552563i	0.0513923	−	0.0373387i
$220$	0.887974	−	0.395351i	0.0598672	−	0.0266546i
$221$	2.66726	−	8.20899i	0.179420	−	0.552197i
$222$	0.942269	+	1.63206i	0.0632410	+	0.109537i
$223$	7.15263	−	12.3887i	0.478976	−	0.829610i	−0.520734	−	0.853719i	$-0.674342\pi$
$223$	7.15263	−	12.3887i	0.478976	−	0.829610i	0.999709	+	0.0241090i	$0.00767488\pi$
$224$	2.70884	+	3.00848i	0.180992	+	0.201012i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	8.81927	−	9.79479i	0.586649	−	0.651540i
$227$	19.6999	+	8.77098i	1.30753	+	0.582151i	0.937861	−	0.347012i	$-0.112804\pi$
$227$	19.6999	+	8.77098i	1.30753	+	0.582151i	0.369671	+	0.929163i	$0.379470\pi$
$228$	3.62770	−	0.771092i	0.240251	−	0.0510668i
$229$	−1.19051	−	11.3269i	−0.0786710	−	0.748505i	−0.960752	−	0.277408i	$-0.910525\pi$
$229$	−1.19051	−	11.3269i	−0.0786710	−	0.748505i	0.882081	−	0.471097i	$-0.156142\pi$
$230$	−0.340886	+	3.24331i	−0.0224774	+	0.213858i
$231$	−3.84900	−	0.818129i	−0.253245	−	0.0538290i
$232$	2.77422	+	2.01559i	0.182136	+	0.132330i
$233$	−7.64848	−	5.55694i	−0.501068	−	0.364047i	0.308357	−	0.951271i	$-0.400221\pi$
$233$	−7.64848	−	5.55694i	−0.501068	−	0.364047i	−0.809425	+	0.587223i	$0.800221\pi$
$234$	−5.13670	−	1.09184i	−0.335796	−	0.0713757i
$235$	0.565894	−	5.38412i	0.0369148	−	0.351221i
$236$	−1.11424	−	10.6012i	−0.0725305	−	0.690082i
$237$	3.39466	−	0.721557i	0.220507	−	0.0468702i
$238$	6.07866	+	2.70639i	0.394021	+	0.175429i
$239$	8.43528	−	9.36832i	0.545633	−	0.605986i	−0.405755	−	0.913982i	$-0.632991\pi$
$239$	8.43528	−	9.36832i	0.545633	−	0.605986i	0.951388	+	0.307995i	$0.0996581\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	8.26833	+	9.18291i	0.532610	+	0.591523i	0.948060	−	0.318093i	$-0.103042\pi$
$241$	8.26833	+	9.18291i	0.532610	+	0.591523i	−0.415450	+	0.909616i	$0.636376\pi$
$242$	5.02760	−	8.70806i	0.323186	−	0.559775i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	1.27145	−	3.91313i	0.0813964	−	0.250512i
$245$	8.57706	−	3.81875i	0.547969	−	0.243971i
$246$	0.471389	−	0.342484i	0.0300547	−	0.0218360i
$247$	−19.4763			−1.23925
$248$	0.592599	−	5.53614i	0.0376301	−	0.351545i
$249$	−4.61685			−0.292581
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	−16.7592	+	7.46170i	−1.05783	+	0.470978i	−0.860549	−	0.509368i	$-0.829879\pi$
$251$	−16.7592	+	7.46170i	−1.05783	+	0.470978i	−0.197285	+	0.980346i	$0.563213\pi$
$252$	1.25099	−	3.85017i	0.0788053	−	0.242538i
$253$	−1.58495	−	2.74521i	−0.0996447	−	0.172590i
$254$	−10.2845	+	17.8133i	−0.645308	+	1.11771i
$255$	1.09980	+	1.22146i	0.0688724	+	0.0764905i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−18.2376	+	20.2550i	−1.13763	+	1.26347i	−0.177441	+	0.984132i	$0.556782\pi$
$257$	−18.2376	+	20.2550i	−1.13763	+	1.26347i	−0.960193	+	0.279338i	$0.909885\pi$
$258$	−9.06039	−	4.03394i	−0.564075	−	0.251142i
$259$	7.46247	−	1.58620i	0.463695	−	0.0985615i
$260$	−0.548926	−	5.22268i	−0.0340430	−	0.323897i
$261$	0.358441	−	3.41034i	0.0221869	−	0.211095i
$262$	−13.6238	−	2.89583i	−0.841681	−	0.178905i
$263$	−15.1431	−	11.0021i	−0.933765	−	0.678420i	0.0131466	−	0.999914i	$-0.495815\pi$
$263$	−15.1431	−	11.0021i	−0.933765	−	0.678420i	−0.946912	+	0.321493i	$0.895815\pi$
$264$	−0.786371	−	0.571332i	−0.0483978	−	0.0351631i
$265$	−6.62473	−	1.40813i	−0.406954	−	0.0865008i
$266$	1.56941	−	14.9319i	0.0962264	−	0.915533i
$267$	0.669188	+	6.36690i	0.0409536	+	0.389648i
$268$	1.13819	−	0.241931i	0.0695263	−	0.0147783i
$269$	−25.3540	−	11.2883i	−1.54586	−	0.688262i	−0.556116	−	0.831104i	$-0.687709\pi$
$269$	−25.3540	−	11.2883i	−1.54586	−	0.688262i	−0.989745	+	0.142842i	$0.954376\pi$
$270$	0.669131	−	0.743145i	0.0407220	−	0.0452264i
$271$	−6.99747	−	21.5360i	−0.425066	−	1.30822i	−0.902931	−	0.429785i	$-0.858589\pi$
$271$	−6.99747	−	21.5360i	−0.425066	−	1.30822i	0.477865	−	0.878433i	$-0.341411\pi$
$272$	1.09980	+	1.22146i	0.0666854	+	0.0740616i
$273$	−10.6297	+	18.4112i	−0.643341	+	1.11430i
$274$	8.40359	+	14.5554i	0.507679	+	0.879326i
$275$	0.300367	−	0.924435i	0.0181128	−	0.0557455i
$276$	2.97924	−	1.32644i	0.179329	−	0.0798424i
$277$	10.7788	−	7.83123i	0.647633	−	0.470533i	−0.214831	−	0.976651i	$-0.568920\pi$
$277$	10.7788	−	7.83123i	0.647633	−	0.470533i	0.862464	+	0.506118i	$0.168920\pi$
$278$	8.61605			0.516756
$279$	−5.09074	+	2.25486i	−0.304774	+	0.134995i
$280$	4.04830			0.241932
$281$	11.2111	−	8.14537i	0.668801	−	0.485912i	−0.200823	−	0.979628i	$-0.564362\pi$
$281$	11.2111	−	8.14537i	0.668801	−	0.485912i	0.869624	+	0.493715i	$0.164362\pi$
$282$	−4.94573	+	2.20198i	−0.294514	+	0.131126i
$283$	5.32754	−	16.3965i	0.316689	−	0.974670i	−0.658364	−	0.752700i	$-0.728751\pi$
$283$	5.32754	−	16.3965i	0.316689	−	0.974670i	0.975054	−	0.221970i	$-0.0712487\pi$
$284$	5.08168	+	8.80172i	0.301542	+	0.522286i
$285$	1.85437	−	3.21187i	0.109844	−	0.190255i
$286$	3.41555	+	3.79335i	0.201966	+	0.224305i
$287$	−0.728916	−	2.24337i	−0.0430266	−	0.132422i
$288$	0.669131	−	0.743145i	0.0394289	−	0.0437902i
$289$	−13.0623	−	5.81571i	−0.768371	−	0.342101i
$290$	3.35419	−	0.712954i	0.196965	−	0.0418661i
$291$	−1.79548	−	17.0829i	−0.105253	−	1.00142i
$292$	0.0982647	−	0.934926i	0.00575050	−	0.0547124i
$293$	0.266597	+	0.0566669i	0.0155747	+	0.00331051i	0.215692	−	0.976461i	$-0.430799\pi$
$293$	0.266597	+	0.0566669i	0.0155747	+	0.00331051i	−0.200118	+	0.979772i	$0.564132\pi$
$294$	−7.59567	−	5.51858i	−0.442989	−	0.321850i
$295$	−8.62382	−	6.26557i	−0.502098	−	0.364796i
$296$	1.84336	+	0.391818i	0.107143	+	0.0227739i
$297$	−0.101603	+	0.966683i	−0.00589558	+	0.0560927i
$298$	−1.48342	−	14.1138i	−0.0859320	−	0.817588i
$299$	−16.7517	+	3.56068i	−0.968775	+	0.205919i
$300$	0.913545	+	0.406737i	0.0527436	+	0.0234830i
$301$	−26.8659	+	29.8376i	−1.54852	+	1.71981i
$302$	−0.556050	−	1.71135i	−0.0319971	−	0.0984770i
$303$	−0.139153	−	0.154546i	−0.00799416	−	0.00887841i
$304$	1.85437	−	3.21187i	0.106356	−	0.184213i
$305$	−2.05725	−	3.56327i	−0.117798	−	0.204032i
$306$	0.507910	−	1.56319i	0.0290353	−	0.0893614i
$307$	25.8295	−	11.5000i	1.47417	−	0.656341i	0.496793	−	0.867869i	$-0.334511\pi$
$307$	25.8295	−	11.5000i	1.47417	−	0.656341i	0.977372	+	0.211528i	$0.0678440\pi$
$308$	−3.18347	+	2.31293i	−0.181395	+	0.131791i
$309$	11.1090			0.631971
$310$	−3.71763	−	4.14479i	−0.211147	−	0.235408i
$311$	−6.08238			−0.344900			−0.172450	−	0.985018i	$-0.555168\pi$
$311$	−6.08238			−0.344900			−0.172450	+	0.985018i	$0.555168\pi$
$312$	−4.24851	+	3.08673i	−0.240525	+	0.174751i
$313$	−20.1829	+	8.98601i	−1.14081	+	0.507920i	−0.888112	−	0.459627i	$-0.847983\pi$
$313$	−20.1829	+	8.98601i	−1.14081	+	0.507920i	−0.252694	+	0.967546i	$0.581317\pi$
$314$	−2.02390	+	6.22892i	−0.114215	+	0.351518i
$315$	−2.02415	−	3.50593i	−0.114048	−	0.197537i
$316$	1.73525	−	3.00554i	0.0976154	−	0.169075i
$317$	19.2166	+	21.3422i	1.07931	+	1.19870i	0.979025	+	0.203739i	$0.0653094\pi$
$317$	19.2166	+	21.3422i	1.07931	+	1.19870i	0.100287	+	0.994959i	$0.468024\pi$
$318$	2.09289	+	6.44125i	0.117363	+	0.361208i
$319$	−2.23030	+	2.47700i	−0.124873	+	0.138685i
$320$	0.913545	+	0.406737i	0.0510687	+	0.0227373i
$321$	−4.10217	+	0.871944i	−0.228961	+	0.0486672i
$322$	−1.38001	−	13.1299i	−0.0769050	−	0.731702i
$323$	0.637186	−	6.06242i	0.0354540	−	0.337322i
$324$	−0.978148	−	0.207912i	−0.0543415	−	0.0115506i
$325$	−4.24851	−	3.08673i	−0.235665	−	0.171221i
$326$	1.70427	+	1.23822i	0.0943907	+	0.0685789i
$327$	0.163091	+	0.0346661i	0.00901897	+	0.00191704i
$328$	0.0609055	−	0.579477i	0.00336294	−	0.0319963i
$329$	2.29091	+	21.7965i	0.126302	+	1.20168i
$330$	−0.950768	+	0.202092i	−0.0523380	+	0.0111248i
$331$	21.9306	+	9.76414i	1.20542	+	0.536686i	0.908366	−	0.418176i	$-0.137331\pi$
$331$	21.9306	+	9.76414i	1.20542	+	0.536686i	0.297050	+	0.954862i	$0.403997\pi$
$332$	−3.08927	+	3.43099i	−0.169546	+	0.188300i
$333$	−0.582354	−	1.79230i	−0.0319128	−	0.0982176i
$334$	4.17120	+	4.63259i	0.228238	+	0.253484i
$335$	0.581811	−	1.00773i	0.0317878	−	0.0550580i
$336$	−2.02415	−	3.50593i	−0.110427	−	0.191264i
$337$	1.02404	−	3.15166i	0.0557829	−	0.171682i	−0.919283	−	0.393597i	$-0.871231\pi$
$337$	1.02404	−	3.15166i	0.0557829	−	0.171682i	0.975066	+	0.221915i	$0.0712306\pi$
$338$	13.3174	−	5.92931i	0.724373	−	0.322512i
$339$	−10.6630	+	7.74712i	−0.579135	+	0.420766i
$340$	1.64363			0.0891384
$341$	5.29148	+	1.13534i	0.286550	+	0.0614822i
$342$	−3.70875			−0.200546
$343$	−7.82356	+	5.68415i	−0.422432	+	0.306915i
$344$	−9.06039	+	4.03394i	−0.488503	+	0.217496i
$345$	1.00776	−	3.10157i	0.0542560	−	0.166983i
$346$	2.37004	+	4.10502i	0.127414	+	0.220687i
$347$	1.55918	−	2.70059i	0.0837014	−	0.144975i	−0.821136	−	0.570733i	$-0.806659\pi$
$347$	1.55918	−	2.70059i	0.0837014	−	0.144975i	0.904837	+	0.425758i	$0.139992\pi$
$348$	−2.29453	−	2.54833i	−0.123000	−	0.136605i
$349$	0.635581	+	1.95612i	0.0340219	+	0.104709i	0.966625	−	0.256194i	$-0.0824686\pi$
$349$	0.635581	+	1.95612i	0.0340219	+	0.104709i	−0.932603	+	0.360903i	$0.882469\pi$
$350$	2.70884	−	3.00848i	0.144794	−	0.160810i
$351$	4.79744	+	2.13596i	0.256068	+	0.114009i
$352$	−0.950768	+	0.202092i	−0.0506761	+	0.0107715i
$353$	1.79291	+	17.0584i	0.0954272	+	0.907929i	0.932581	+	0.360961i	$0.117551\pi$
$353$	1.79291	+	17.0584i	0.0954272	+	0.907929i	−0.837154	+	0.546968i	$0.815782\pi$
$354$	−1.11424	+	10.6012i	−0.0592209	+	0.563449i
$355$	9.94126	+	2.11308i	0.527627	+	0.112151i
$356$	5.17930	+	3.76298i	0.274502	+	0.199438i
$357$	−5.38313	−	3.91107i	−0.284906	−	0.206996i
$358$	23.6561	+	5.02827i	1.25027	+	0.265752i
$359$	−0.0464218	+	0.441674i	−0.00245005	+	0.0233107i	−0.995679	−	0.0928660i	$-0.970397\pi$
$359$	−0.0464218	+	0.441674i	−0.00245005	+	0.0233107i	0.993229	+	0.116177i	$0.0370639\pi$
$360$	−0.104528	−	0.994522i	−0.00550913	−	0.0524159i
$361$	5.13056	−	1.09053i	0.270029	−	0.0573965i
$362$	−8.85618	−	3.94303i	−0.465471	−	0.207241i
$363$	−6.72824	+	7.47247i	−0.353141	+	0.392203i
$364$	6.56954	+	20.2190i	0.344337	+	1.05976i
$365$	−0.629033	−	0.698612i	−0.0329251	−	0.0365670i
$366$	−2.05725	+	3.56327i	−0.107534	+	0.186255i
$367$	−12.2797	−	21.2690i	−0.640994	−	1.11023i	−0.985211	−	0.171344i	$-0.945189\pi$
$367$	−12.2797	−	21.2690i	−0.640994	−	1.11023i	0.344218	−	0.938890i	$-0.388144\pi$
$368$	1.00776	−	3.10157i	0.0525331	−	0.161680i
$369$	−0.532295	+	0.236993i	−0.0277102	+	0.0123374i
$370$	1.52462	−	1.10770i	0.0792614	−	0.0575868i
$371$	27.4181			1.42348
$372$	−1.73068	+	5.29195i	−0.0897314	+	0.274375i
$373$	−34.0427			−1.76266			−0.881332	−	0.472498i	$-0.843353\pi$
$373$	−34.0427			−1.76266			−0.881332	+	0.472498i	$0.843353\pi$
$374$	−1.29250	+	0.939059i	−0.0668338	+	0.0485576i
$375$	0.913545	−	0.406737i	0.0471753	−	0.0210038i
$376$	−1.67295	+	5.14881i	−0.0862757	+	0.265529i
$377$	9.00393	+	15.5953i	0.463726	+	0.803197i
$378$	−2.02415	+	3.50593i	−0.104111	+	0.180326i
$379$	8.88636	+	9.86930i	0.456462	+	0.506952i	0.926811	−	0.375528i	$-0.122539\pi$
$379$	8.88636	+	9.86930i	0.456462	+	0.506952i	−0.470349	+	0.882480i	$0.655872\pi$
$380$	−1.14607	−	3.52723i	−0.0587920	−	0.180943i
$381$	13.7634	−	15.2858i	0.705119	−	0.783114i
$382$	21.3144	+	9.48977i	1.09054	+	0.485539i
$383$	27.2694	−	5.79629i	1.39340	−	0.296177i	0.550765	−	0.834660i	$-0.314336\pi$
$383$	27.2694	−	5.79629i	1.39340	−	0.296177i	0.842636	+	0.538484i	$0.181003\pi$
$384$	−0.104528	−	0.994522i	−0.00533420	−	0.0507515i
$385$	−0.411318	+	3.91343i	−0.0209627	+	0.199447i
$386$	−10.4190	−	2.21462i	−0.530311	−	0.112721i
$387$	8.02369	+	5.82955i	0.407867	+	0.296333i
$388$	−13.8965	−	10.0964i	−0.705485	−	0.512565i
$389$	−1.67774	−	0.356615i	−0.0850649	−	0.0180811i	0.165183	−	0.986263i	$-0.447179\pi$
$389$	−1.67774	−	0.356615i	−0.0850649	−	0.0180811i	−0.250248	+	0.968182i	$0.580512\pi$
$390$	−0.548926	+	5.22268i	−0.0277960	+	0.264461i
$391$	−0.560291	−	5.33081i	−0.0283351	−	0.269591i
$392$	−9.18360	+	1.95203i	−0.463842	+	0.0985926i
$393$	12.7240	+	5.66509i	0.641841	+	0.285766i
$394$	−4.19800	+	4.66236i	−0.211492	+	0.234886i
$395$	−1.07244	−	3.30064i	−0.0539605	−	0.166073i
$396$	0.650400	+	0.722343i	0.0326839	+	0.0362991i
$397$	−16.7910	+	29.0828i	−0.842714	+	1.45962i	0.0448774	+	0.998993i	$0.485710\pi$
$397$	−16.7910	+	29.0828i	−0.842714	+	1.45962i	−0.887592	+	0.460631i	$0.847623\pi$
$398$	7.45810	+	12.9178i	0.373841	+	0.647511i
$399$	−4.63963	+	14.2793i	−0.232272	+	0.714859i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	6.59117	−	4.78877i	0.329147	−	0.239140i	−0.410921	−	0.911671i	$-0.634793\pi$
$401$	6.59117	−	4.78877i	0.329147	−	0.239140i	0.740069	+	0.672531i	$0.234793\pi$
$402$	−1.16362			−0.0580362
$403$	14.6679	−	25.2935i	0.730661	−	1.25996i
$404$	−0.207962			−0.0103465
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	−12.6820	+	5.64637i	−0.629395	+	0.280225i
$407$	−0.566053	+	1.74213i	−0.0280582	+	0.0863543i
$408$	−0.821815	−	1.42343i	−0.0406859	−	0.0704701i
$409$	−4.80528	+	8.32299i	−0.237606	+	0.411545i	−0.960027	−	0.279908i	$-0.909696\pi$
$409$	−4.80528	+	8.32299i	−0.237606	+	0.411545i	0.722421	+	0.691453i	$0.243029\pi$
$410$	−0.389882	−	0.433008i	−0.0192549	−	0.0213847i
$411$	−5.19370	−	15.9846i	−0.256186	−	0.788461i
$412$	7.43340	−	8.25563i	0.366217	−	0.406726i
$413$	39.4226	+	17.5521i	1.93986	+	0.863682i
$414$	−3.18991	+	0.678037i	−0.156776	+	0.0333237i
$415$	0.482592	+	4.59156i	0.0236895	+	0.225391i
$416$	−0.548926	+	5.22268i	−0.0269133	+	0.256063i
$417$	−8.42777	−	1.79138i	−0.412710	−	0.0877241i
$418$	2.91645	+	2.11893i	0.142648	+	0.103640i
$419$	32.7282	+	23.7784i	1.59888	+	1.16165i	0.889621	+	0.456700i	$0.150969\pi$
$419$	32.7282	+	23.7784i	1.59888	+	1.16165i	0.709256	+	0.704951i	$0.249031\pi$
$420$	−3.95984	−	0.841690i	−0.193220	−	0.0410703i
$421$	−2.36124	+	22.4657i	−0.115080	+	1.09491i	0.772741	+	0.634722i	$0.218885\pi$
$421$	−2.36124	+	22.4657i	−0.115080	+	1.09491i	−0.887820	+	0.460190i	$0.847781\pi$
$422$	0.994609	+	9.46307i	0.0484168	+	0.460655i
$423$	5.29547	−	1.12559i	0.257475	−	0.0547279i
$424$	6.18720	+	2.75472i	0.300477	+	0.133781i
$425$	1.09980	−	1.22146i	0.0533483	−	0.0592493i
$426$	−3.14065	−	9.66593i	−0.152165	−	0.468316i
$427$	11.1456	+	12.3784i	0.539372	+	0.599033i
$428$	−2.09691	+	3.63195i	−0.101358	+	0.175557i
$429$	−2.55223	−	4.42059i	−0.123223	−	0.213428i
$430$	−3.06478	+	9.43242i	−0.147797	+	0.454872i
$431$	−4.90838	+	2.18535i	−0.236428	+	0.105265i	−0.521531	−	0.853232i	$-0.674639\pi$
$431$	−4.90838	+	2.18535i	−0.236428	+	0.105265i	0.285103	+	0.958497i	$0.407972\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−41.3699			−1.98811			−0.994056	−	0.108870i	$-0.965277\pi$
$433$	−41.3699			−1.98811			−0.994056	+	0.108870i	$0.965277\pi$
$434$	18.2098	+	13.2836i	0.874100	+	0.637633i
$435$	−3.42912			−0.164414
$436$	0.134891	−	0.0980043i	0.00646012	−	0.00469355i
$437$	−11.0492	+	4.91944i	−0.528557	+	0.235329i
$438$	−0.290499	+	0.894065i	−0.0138806	+	0.0427201i
$439$	−14.0386	−	24.3156i	−0.670026	−	1.16052i	−0.977896	−	0.209091i	$-0.932950\pi$
$439$	−14.0386	−	24.3156i	−0.670026	−	1.16052i	0.307870	−	0.951428i	$-0.400384\pi$
$440$	−0.486004	+	0.841784i	−0.0231693	+	0.0401305i
$441$	6.28231	+	6.97721i	0.299158	+	0.332248i
$442$	2.66726	+	8.20899i	0.126869	+	0.390462i
$443$	−24.2439	+	26.9256i	−1.15186	+	1.27927i	−0.197606	+	0.980282i	$0.563317\pi$
$443$	−24.2439	+	26.9256i	−1.15186	+	1.27927i	−0.954256	+	0.298991i	$0.903350\pi$
$444$	−1.72161	−	0.766511i	−0.0817041	−	0.0363770i
$445$	6.26207	−	1.33104i	0.296851	−	0.0630976i
$446$	1.49531	+	14.2269i	0.0708048	+	0.673663i
$447$	−1.48342	+	14.1138i	−0.0701632	+	0.667558i
$448$	−3.95984	−	0.841690i	−0.187085	−	0.0397661i
$449$	2.69486	+	1.95793i	0.127178	+	0.0924005i	0.649556	−	0.760314i	$-0.274955\pi$
$449$	2.69486	+	1.95793i	0.127178	+	0.0924005i	−0.522378	+	0.852714i	$0.674955\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	0.553983	+	0.117753i	0.0260860	+	0.00554476i
$452$	−1.37771	+	13.1080i	−0.0648018	+	0.616548i
$453$	0.188090	+	1.78956i	0.00883725	+	0.0840809i
$454$	−21.0930	+	4.48347i	−0.989946	+	0.210419i
$455$	19.4215	+	8.64701i	0.910494	+	0.405378i
$456$	−2.48164	+	2.75614i	−0.116213	+	0.129068i
$457$	−5.60946	−	17.2642i	−0.262400	−	0.807583i	−0.992281	−	0.124009i	$-0.960425\pi$
$457$	−5.60946	−	17.2642i	−0.262400	−	0.807583i	0.729881	−	0.683574i	$-0.239575\pi$
$458$	7.62095	+	8.46392i	0.356103	+	0.395493i
$459$	−0.821815	+	1.42343i	−0.0383591	+	0.0664398i
$460$	−1.63059	−	2.82426i	−0.0760266	−	0.131682i
$461$	8.55118	−	26.3178i	0.398268	−	1.22574i	−0.528119	−	0.849170i	$-0.677103\pi$
$461$	8.55118	−	26.3178i	0.398268	−	1.22574i	0.926387	−	0.376573i	$-0.122897\pi$
$462$	3.59479	−	1.60050i	0.167245	−	0.0744621i
$463$	−10.6344	+	7.72635i	−0.494223	+	0.359074i	−0.806806	−	0.590816i	$-0.798806\pi$
$463$	−10.6344	+	7.72635i	−0.494223	+	0.359074i	0.312583	+	0.949890i	$0.398806\pi$
$464$	−3.42912			−0.159193
$465$	2.77464	+	4.82715i	0.128671	+	0.223854i
$466$	9.45404			0.437950
$467$	3.60043	−	2.61587i	0.166608	−	0.121048i	−0.501357	−	0.865241i	$-0.667166\pi$
$467$	3.60043	−	2.61587i	0.166608	−	0.121048i	0.667965	+	0.744193i	$0.267166\pi$
$468$	4.79744	−	2.13596i	0.221762	−	0.0987347i
$469$	−1.45569	+	4.48014i	−0.0672173	+	0.206874i
$470$	2.70689	+	4.68847i	0.124859	+	0.216263i
$471$	3.27474	−	5.67201i	0.150892	−	0.261352i
$472$	7.13269	+	7.92165i	0.328309	+	0.364624i
$473$	−2.97899	−	9.16839i	−0.136974	−	0.421563i
$474$	−2.32222	+	2.57908i	−0.106663	+	0.118461i
$475$	−3.38811	−	1.50848i	−0.155457	−	0.0692140i
$476$	−6.50851	+	1.38343i	−0.298317	+	0.0634093i
$477$	−0.707943	−	6.73563i	−0.0324145	−	0.308403i
$478$	−1.31772	+	12.5373i	−0.0602711	+	0.573441i
$479$	−5.61199	−	1.19287i	−0.256419	−	0.0545034i	0.0779087	−	0.996960i	$-0.475176\pi$
$479$	−5.61199	−	1.19287i	−0.256419	−	0.0545034i	−0.334327	+	0.942457i	$0.608509\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	8.00649	+	5.81705i	0.365064	+	0.265235i
$482$	−12.0868	−	2.56913i	−0.550538	−	0.117021i
$483$	−1.38001	+	13.1299i	−0.0627926	+	0.597432i
$484$	1.05105	+	10.0001i	0.0477752	+	0.454551i
$485$	−16.8016	+	3.57129i	−0.762921	+	0.162164i
$486$	0.913545	+	0.406737i	0.0414393	+	0.0184499i
$487$	−10.9969	+	12.2133i	−0.498316	+	0.553436i	−0.938862	−	0.344294i	$-0.888118\pi$
$487$	−10.9969	+	12.2133i	−0.498316	+	0.553436i	0.440546	+	0.897730i	$0.354785\pi$
$488$	1.27145	+	3.91313i	0.0575560	+	0.177139i
$489$	−1.40959	−	1.56550i	−0.0637437	−	0.0707945i
$490$	−4.69438	+	8.13091i	−0.212071	+	0.367317i
$491$	16.3696	+	28.3530i	0.738751	+	1.27955i	0.953058	+	0.302788i	$0.0979174\pi$
$491$	16.3696	+	28.3530i	0.738751	+	1.27955i	−0.214307	+	0.976766i	$0.568749\pi$
$492$	−0.180055	+	0.554151i	−0.00811749	+	0.0249831i
$493$	−5.14893	+	2.29245i	−0.231896	+	0.103247i
$494$	15.7567	−	11.4479i	0.708926	−	0.515065i
$495$	0.972008			0.0436885
$496$	2.77464	+	4.82715i	0.124585	+	0.216745i
$497$	−41.1444			−1.84558
$498$	3.73511	−	2.71371i	0.167374	−	0.121604i
$499$	−9.47035	+	4.21647i	−0.423951	+	0.188755i	−0.607611	−	0.794235i	$-0.707872\pi$
$499$	−9.47035	+	4.21647i	−0.423951	+	0.188755i	0.183660	+	0.982990i	$0.441205\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	−3.11688	−	5.39860i	−0.139252	−	0.241192i
$502$	9.17264	−	15.8875i	0.409395	−	0.709093i
$503$	19.3831	+	21.5272i	0.864252	+	0.959849i	0.999521	−	0.0309602i	$-0.00985651\pi$
$503$	19.3831	+	21.5272i	0.864252	+	0.959849i	−0.135269	+	0.990809i	$0.543190\pi$
$504$	1.25099	+	3.85017i	0.0557237	+	0.171500i
$505$	−0.139153	+	0.154546i	−0.00619225	+	0.00687719i
$506$	2.89584	+	1.28931i	0.128736	+	0.0573169i
$507$	−14.2592	+	3.03088i	−0.633273	+	0.134606i
$508$	−2.15005	−	20.4564i	−0.0953930	−	0.907604i
$509$	4.34974	−	41.3850i	0.192799	−	1.83436i	−0.288121	−	0.957594i	$-0.593030\pi$
$509$	4.34974	−	41.3850i	0.192799	−	1.83436i	0.480920	−	0.876765i	$-0.340303\pi$
$510$	−1.60771	−	0.341730i	−0.0711907	−	0.0151321i
$511$	3.07889	+	2.23694i	0.136202	+	0.0989565i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	3.62770	+	0.771092i	0.160167	+	0.0340446i
$514$	2.84900	−	27.1064i	0.125664	−	1.19561i
$515$	−1.16121	−	11.0482i	−0.0511691	−	0.486841i
$516$	9.70110	−	2.06203i	0.427067	−	0.0907759i
$517$	−4.80729	−	2.14034i	−0.211424	−	0.0941322i
$518$	−5.10492	+	5.66959i	−0.224297	+	0.249107i
$519$	−1.46476	−	4.50808i	−0.0642960	−	0.197883i
$520$	3.51391	+	3.90259i	0.154095	+	0.171140i
$521$	3.70448	−	6.41636i	0.162296	−	0.281106i	−0.773395	−	0.633924i	$-0.781443\pi$
$521$	3.70448	−	6.41636i	0.162296	−	0.281106i	0.935692	+	0.352818i	$0.114777\pi$
$522$	1.71456	+	2.96971i	0.0750443	+	0.129981i
$523$	−1.93203	+	5.94618i	−0.0844819	+	0.260008i	−0.984370	−	0.176112i	$-0.943648\pi$
$523$	−1.93203	+	5.94618i	−0.0844819	+	0.260008i	0.899888	+	0.436121i	$0.143648\pi$
$524$	12.7240	−	5.66509i	0.555851	−	0.247481i
$525$	−3.27515	+	2.37953i	−0.142939	+	0.103851i
$526$	18.7179			0.816141
$527$	7.39328	+	5.39320i	0.322056	+	0.234932i
$528$	0.972008			0.0423012
$529$	10.0033	−	7.26779i	0.434924	−	0.315991i
$530$	6.18720	−	2.75472i	0.268755	−	0.119657i
$531$	3.29401	−	10.1379i	0.142948	−	0.439948i
$532$	7.50707	+	13.0026i	0.325473	+	0.563736i
$533$	1.52993	−	2.64992i	0.0662686	−	0.114781i
$534$	−4.28375	−	4.75759i	−0.185376	−	0.205881i
$535$	1.29596	+	3.98856i	0.0560293	+	0.172440i
$536$	−0.778616	+	0.864740i	−0.0336311	+	0.0373511i
$537$	−22.0938	−	9.83678i	−0.953416	−	0.424488i
$538$	27.1469	−	5.77026i	1.17039	−	0.248774i
$539$	−0.953922	−	9.07596i	−0.0410883	−	0.390929i
$540$	−0.104528	+	0.994522i	−0.00449819	+	0.0427974i
$541$	−27.8532	−	5.92037i	−1.19750	−	0.254537i	−0.434343	−	0.900748i	$-0.643019\pi$
$541$	−27.8532	−	5.92037i	−1.19750	−	0.254537i	−0.763159	+	0.646211i	$0.776353\pi$
$542$	18.3196	+	13.3100i	0.786895	+	0.571712i
$543$	7.84285	+	5.69817i	0.336569	+	0.244532i
$544$	−1.60771	−	0.341730i	−0.0689301	−	0.0146516i
$545$	0.0174285	−	0.165821i	0.000746557	−	0.00710301i
$546$	−2.22222	−	21.1430i	−0.0951022	−	0.904837i
$547$	41.3872	−	8.79712i	1.76959	−	0.376138i	0.796153	−	0.605095i	$-0.206865\pi$
$547$	41.3872	−	8.79712i	1.76959	−	0.376138i	0.973436	+	0.228957i	$0.0735316\pi$
$548$	−15.3541	−	6.83609i	−0.655895	−	0.292023i
$549$	2.75314	−	3.05768i	0.117501	−	0.130498i
$550$	0.300367	+	0.924435i	0.0128077	+	0.0394180i
$551$	8.50984	+	9.45113i	0.362531	+	0.402632i
$552$	−1.63059	+	2.82426i	−0.0694025	+	0.120209i
$553$	7.02482	+	12.1673i	0.298726	+	0.517408i
$554$	−4.11712	+	12.6712i	−0.174920	+	0.538347i
$555$	−1.72161	+	0.766511i	−0.0730784	+	0.0325366i
$556$	−6.97053	+	5.06439i	−0.295616	+	0.214778i
$557$	−32.2305			−1.36565			−0.682824	−	0.730583i	$-0.739248\pi$
$557$	−32.2305			−1.36565			−0.682824	+	0.730583i	$0.739248\pi$
$558$	2.79312	−	4.81648i	0.118242	−	0.203898i
$559$	−52.0830			−2.20288
$560$	−3.27515	+	2.37953i	−0.138400	+	0.100554i
$561$	1.45950	−	0.649812i	0.0616202	−	0.0274351i
$562$	−4.28228	+	13.1795i	−0.180637	+	0.555943i
$563$	18.0717	+	31.3011i	0.761631	+	1.31918i	0.942009	+	0.335586i	$0.108934\pi$
$563$	18.0717	+	31.3011i	0.761631	+	1.31918i	−0.180378	+	0.983597i	$0.557732\pi$
$564$	2.70689	−	4.68847i	0.113981	−	0.197420i
$565$	8.81927	+	9.79479i	0.371030	+	0.412070i
$566$	5.32754	+	16.3965i	0.223933	+	0.689195i
$567$	2.70884	−	3.00848i	0.113761	−	0.126344i
$568$	−9.28469	−	4.13381i	−0.389577	−	0.173451i
$569$	−38.5465	+	8.19331i	−1.61595	+	0.343481i	−0.925162	−	0.379574i	$-0.876071\pi$
$569$	−38.5465	+	8.19331i	−1.61595	+	0.343481i	−0.690791	+	0.723055i	$0.742737\pi$
$570$	0.387670	+	3.68843i	0.0162377	+	0.154491i
$571$	−4.49203	+	42.7388i	−0.187986	+	1.78856i	0.341132	+	0.940016i	$0.389190\pi$
$571$	−4.49203	+	42.7388i	−0.187986	+	1.78856i	−0.529117	+	0.848549i	$0.677477\pi$
$572$	−4.99291	−	1.06128i	−0.208764	−	0.0443742i
$573$	−18.8756	−	13.7139i	−0.788539	−	0.572907i
$574$	1.90833	+	1.38648i	0.0796520	+	0.0578706i
$575$	−3.18991	−	0.678037i	−0.133029	−	0.0282761i
$576$	−0.104528	+	0.994522i	−0.00435535	+	0.0414384i
$577$	−1.35890	−	12.9291i	−0.0565717	−	0.538244i	−0.985703	−	0.168493i	$-0.946110\pi$
$577$	−1.35890	−	12.9291i	−0.0565717	−	0.538244i	0.929131	−	0.369751i	$-0.120557\pi$
$578$	13.9860	−	2.97282i	0.581742	−	0.123653i
$579$	9.73083	+	4.33244i	0.404400	+	0.180050i
$580$	−2.29453	+	2.54833i	−0.0952752	+	0.105814i
$581$	−5.77565	−	17.7756i	−0.239614	−	0.737457i
$582$	11.4936	+	12.7650i	0.476426	+	0.529125i
$583$	−3.29158	+	5.70118i	−0.136323	+	0.236119i
$584$	0.470038	+	0.814129i	0.0194503	+	0.0336889i
$585$	1.62279	−	4.99443i	0.0670940	−	0.206494i
$586$	−0.248989	+	0.110857i	−0.0102857	+	0.00457947i
$587$	−15.5437	+	11.2931i	−0.641556	+	0.466118i	−0.860385	−	0.509645i	$-0.829777\pi$
$587$	−15.5437	+	11.2931i	−0.641556	+	0.466118i	0.218828	+	0.975763i	$0.429777\pi$
$588$	9.38877			0.387186
$589$	6.41865	−	19.6265i	0.264476	−	0.808697i
$590$	10.6596			0.438850
$591$	5.07563	−	3.68766i	0.208783	−	0.151690i
$592$	−1.72161	+	0.766511i	−0.0707578	+	0.0315034i
$593$	−2.79314	+	8.59641i	−0.114701	+	0.353012i	−0.991884	−	0.127142i	$-0.959419\pi$
$593$	−2.79314	+	8.59641i	−0.114701	+	0.353012i	0.877184	+	0.480155i	$0.159419\pi$
$594$	−0.486004	−	0.841784i	−0.0199410	−	0.0345388i
$595$	−3.32696	+	5.76246i	−0.136392	+	0.236238i
$596$	9.49597	+	10.5463i	0.388970	+	0.431995i
$597$	−4.60936	−	14.1861i	−0.188648	−	0.580600i
$598$	11.4595	−	12.7270i	0.468613	−	0.520448i
$599$	5.39961	+	2.40406i	0.220622	+	0.0982273i	0.514072	−	0.857747i	$-0.328137\pi$
$599$	5.39961	+	2.40406i	0.220622	+	0.0982273i	−0.293449	+	0.955975i	$0.594803\pi$
$600$	−0.978148	+	0.207912i	−0.0399327	+	0.00848796i
$601$	2.72747	+	25.9502i	0.111256	+	1.05853i	0.897621	+	0.440767i	$0.145294\pi$
$601$	2.72747	+	25.9502i	0.111256	+	1.05853i	−0.786366	+	0.617761i	$0.788040\pi$
$602$	4.19686	−	39.9304i	0.171051	−	1.62744i
$603$	1.13819	+	0.241931i	0.0463509	+	0.00985218i
$604$	1.45576	+	1.05767i	0.0592340	+	0.0430360i
$605$	8.13483	+	5.91030i	0.330728	+	0.240288i
$606$	0.203417	+	0.0432376i	0.00826326	+	0.00175641i
$607$	3.90182	−	37.1233i	0.158370	−	1.50679i	−0.570023	−	0.821629i	$-0.693066\pi$
$607$	3.90182	−	37.1233i	0.158370	−	1.50679i	0.728393	−	0.685160i	$-0.240268\pi$
$608$	0.387670	+	3.68843i	0.0157221	+	0.149586i
$609$	13.5788	−	2.88626i	0.550239	−	0.116957i
$610$	3.75879	+	1.67352i	0.152189	+	0.0677589i
$611$	−19.0235	+	21.1277i	−0.769609	+	0.854737i
$612$	0.507910	+	1.56319i	0.0205310	+	0.0631880i
$613$	16.9083	+	18.7786i	0.682921	+	0.758461i	0.980560	−	0.196218i	$-0.0628660\pi$
$613$	16.9083	+	18.7786i	0.682921	+	0.758461i	−0.297639	+	0.954678i	$0.596199\pi$
$614$	−14.1369	+	24.4859i	−0.570520	+	0.988170i
$615$	0.291335	+	0.504606i	0.0117477	+	0.0203477i
$616$	1.21598	−	3.74239i	0.0489931	−	0.150785i
$617$	4.47447	−	1.99216i	0.180135	−	0.0802014i	−0.314687	−	0.949195i	$-0.601900\pi$
$617$	4.47447	−	1.99216i	0.180135	−	0.0802014i	0.494823	+	0.868994i	$0.335233\pi$
$618$	−8.98740	+	6.52973i	−0.361526	+	0.262664i
$619$	42.7073			1.71655			0.858275	−	0.513190i	$-0.171536\pi$
$619$	42.7073			1.71655			0.858275	+	0.513190i	$0.171536\pi$
$620$	5.44387	+	1.16804i	0.218631	+	0.0469095i
$621$	3.26118			0.130867
$622$	4.92075	−	3.57514i	0.197304	−	0.143350i
$623$	−23.6765	+	10.5414i	−0.948578	+	0.422334i
$624$	1.62279	−	4.99443i	0.0649635	−	0.199937i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	11.0465	−	19.1331i	0.441506	−	0.764711i
$627$	−2.41217	−	2.67899i	−0.0963329	−	0.106988i
$628$	−2.02390	−	6.22892i	−0.0807623	−	0.248561i
$629$	−2.07262	+	2.30188i	−0.0826409	+	0.0917820i
$630$	3.69831	+	1.64659i	0.147344	+	0.0656019i
$631$	−23.1784	+	4.92672i	−0.922717	+	0.196130i	−0.644690	−	0.764444i	$-0.723014\pi$
$631$	−23.1784	+	4.92672i	−0.922717	+	0.196130i	−0.278027	+	0.960573i	$0.589680\pi$
$632$	0.362766	+	3.45149i	0.0144301	+	0.137293i
$633$	0.994609	−	9.46307i	0.0395322	−	0.376123i
$634$	−28.0912	−	5.97097i	−1.11564	−	0.237137i
$635$	−16.6407	−	12.0902i	−0.660366	−	0.479784i
$636$	−5.47926	−	3.98091i	−0.217267	−	0.157853i
$637$	−48.2272	−	10.2510i	−1.91083	−	0.406160i
$638$	0.348407	−	3.31487i	0.0137936	−	0.131237i
$639$	1.06236	+	10.1077i	0.0420263	+	0.399854i
$640$	−0.978148	+	0.207912i	−0.0386647	+	0.00821843i
$641$	30.8320	+	13.7273i	1.21779	+	0.542196i	0.912113	−	0.409938i	$-0.134450\pi$
$641$	30.8320	+	13.7273i	1.21779	+	0.542196i	0.305679	+	0.952135i	$0.401116\pi$
$642$	2.80621	−	3.11661i	0.110752	−	0.123003i
$643$	−9.85036	−	30.3163i	−0.388460	−	1.19556i	−0.933939	−	0.357433i	$-0.883652\pi$
$643$	−9.85036	−	30.3163i	−0.388460	−	1.19556i	0.545478	−	0.838125i	$-0.316348\pi$
$644$	8.83403	+	9.81118i	0.348109	+	0.386615i
$645$	4.95891	−	8.58909i	0.195257	−	0.338195i
$646$	3.04791	+	5.27913i	0.119918	+	0.207705i
$647$	−1.80429	+	5.55304i	−0.0709341	+	0.218313i	−0.980239	−	0.197819i	$-0.936614\pi$
$647$	−1.80429	+	5.55304i	−0.0709341	+	0.218313i	0.909305	+	0.416131i	$0.136614\pi$
$648$	0.913545	−	0.406737i	0.0358875	−	0.0159781i
$649$	−8.38243	+	6.09019i	−0.329039	+	0.239061i
$650$	5.25145			0.205979
$651$	−15.0501	−	16.7794i	−0.589859	−	0.657635i
$652$	−2.10659			−0.0825005
$653$	31.8061	−	23.1085i	1.24467	−	0.904306i	0.246770	−	0.969074i	$-0.420631\pi$
$653$	31.8061	−	23.1085i	1.24467	−	0.904306i	0.997900	+	0.0647681i	$0.0206308\pi$
$654$	−0.152320	+	0.0678172i	−0.00595618	+	0.00265186i
$655$	4.30404	−	13.2465i	0.168173	−	0.517582i
$656$	0.291335	+	0.504606i	0.0113747	+	0.0197016i
$657$	0.470038	−	0.814129i	0.0183379	−	0.0317622i
$658$	−14.6651	−	16.2872i	−0.571704	−	0.634942i
$659$	−3.88090	−	11.9442i	−0.151179	−	0.465280i	0.846575	−	0.532269i	$-0.178661\pi$
$659$	−3.88090	−	11.9442i	−0.151179	−	0.465280i	−0.997754	+	0.0669895i	$0.978661\pi$
$660$	0.650400	−	0.722343i	0.0253168	−	0.0281172i
$661$	13.2914	+	5.91773i	0.516977	+	0.230173i	0.648604	−	0.761126i	$-0.275353\pi$
$661$	13.2914	+	5.91773i	0.516977	+	0.230173i	−0.131626	+	0.991299i	$0.542020\pi$
$662$	−23.4815	+	4.99114i	−0.912633	+	0.193986i
$663$	−0.902232	−	8.58416i	−0.0350398	−	0.333381i
$664$	0.482592	−	4.59156i	0.0187282	−	0.178187i
$665$	14.6860	+	3.12162i	0.569501	+	0.121051i
$666$	1.52462	+	1.10770i	0.0590780	+	0.0429227i
$667$	9.04722	+	6.57319i	0.350310	+	0.254515i
$668$	−6.09754	−	1.29607i	−0.235921	−	0.0501466i
$669$	1.49531	−	14.2269i	0.0578119	−	0.550044i
$670$	0.121632	+	1.15725i	0.00469904	+	0.0447084i
$671$	−3.91194	+	0.831509i	−0.151019	+	0.0321000i
$672$	3.69831	+	1.64659i	0.142665	+	0.0635187i
$673$	−4.08176	+	4.53326i	−0.157340	+	0.174744i	−0.816661	−	0.577118i	$-0.804177\pi$
$673$	−4.08176	+	4.53326i	−0.157340	+	0.174744i	0.659321	+	0.751862i	$0.270844\pi$
$674$	1.02404	+	3.15166i	0.0394445	+	0.121398i
$675$	0.669131	+	0.743145i	0.0257548	+	0.0286037i
$676$	−7.28888	+	12.6247i	−0.280341	+	0.485565i
$677$	8.48131	+	14.6901i	0.325963	+	0.564585i	0.981707	−	0.190399i	$-0.0609781\pi$
$677$	8.48131	+	14.6901i	0.325963	+	0.564585i	−0.655744	+	0.754984i	$0.727645\pi$
$678$	4.07290	−	12.5351i	0.156419	−	0.481408i
$679$	63.5257	−	28.2835i	2.43789	−	1.08542i
$680$	−1.32973	+	0.966102i	−0.0509926	+	0.0370483i
$681$	21.5643			0.826345
$682$	−4.94824	+	2.19175i	−0.189478	+	0.0839263i
$683$	−10.1149			−0.387035			−0.193517	−	0.981097i	$-0.561990\pi$
$683$	−10.1149			−0.387035			−0.193517	+	0.981097i	$0.561990\pi$
$684$	3.00044	−	2.17995i	0.114725	−	0.0833524i
$685$	−15.3541	+	6.83609i	−0.586651	+	0.261194i
$686$	2.98833	−	9.19714i	0.114095	−	0.351149i
$687$	−5.69466	−	9.86345i	−0.217265	−	0.376314i
$688$	4.95891	−	8.58909i	0.189057	−	0.327456i
$689$	23.7988	+	26.4312i	0.906661	+	1.00695i
$690$	1.00776	+	3.10157i	0.0383648	+	0.118075i
$691$	27.1859	−	30.1930i	1.03420	−	1.14860i	0.0454595	−	0.998966i	$-0.485525\pi$
$691$	27.1859	−	30.1930i	1.03420	−	1.14860i	0.988742	−	0.149631i	$-0.0478085\pi$
$692$	−4.33027	−	1.92796i	−0.164612	−	0.0732901i
$693$	−3.84900	+	0.818129i	−0.146211	+	0.0310782i
$694$	0.325958	+	3.10129i	0.0123732	+	0.117723i
$695$	−0.900623	+	8.56885i	−0.0341626	+	0.325035i
$696$	3.35419	+	0.712954i	0.127140	+	0.0270245i
$697$	0.774790	+	0.562918i	0.0293473	+	0.0213220i
$698$	−1.66397	−	1.20895i	−0.0629823	−	0.0457593i
$699$	−9.24744	−	1.96560i	−0.349770	−	0.0743460i
$700$	−0.423163	+	4.02613i	−0.0159941	+	0.152173i
$701$	−1.81258	−	17.2456i	−0.0684603	−	0.651357i	−0.973915	−	0.226913i	$-0.927137\pi$
$701$	−1.81258	−	17.2456i	−0.0684603	−	0.651357i	0.905455	−	0.424443i	$-0.139530\pi$
$702$	−5.13670	+	1.09184i	−0.193872	+	0.0412088i
$703$	6.38503	+	2.84280i	0.240816	+	0.107218i
$704$	0.650400	−	0.722343i	0.0245129	−	0.0272243i
$705$	−1.67295	−	5.14881i	−0.0630069	−	0.193915i
$706$	−11.4772	−	12.7467i	−0.431950	−	0.479729i
$707$	0.420946	−	0.729100i	0.0158313	−	0.0274206i
$708$	−5.32982	−	9.23151i	−0.200307	−	0.346941i
$709$	3.64719	−	11.2249i	0.136973	−	0.421560i	−0.858918	−	0.512112i	$-0.828863\pi$
$709$	3.64719	−	11.2249i	0.136973	−	0.421560i	0.995892	+	0.0905520i	$0.0288631\pi$
$710$	−9.28469	+	4.13381i	−0.348448	+	0.155139i
$711$	2.80769	−	2.03991i	0.105297	−	0.0765025i
$712$	−6.40197			−0.239924
$713$	1.93257	−	18.0543i	0.0723753	−	0.676140i
$714$	6.65392			0.249017
$715$	−4.12959	+	3.00032i	−0.154438	+	0.112206i
$716$	−22.0938	+	9.83678i	−0.825683	+	0.367618i
$717$	3.89557	−	11.9893i	0.145483	−	0.447750i
$718$	−0.222053	−	0.384608i	−0.00828696	−	0.0143534i
$719$	16.2885	−	28.2125i	0.607459	−	1.05215i	−0.384199	−	0.923250i	$-0.625522\pi$
$719$	16.2885	−	28.2125i	0.607459	−	1.05215i	0.991658	−	0.128899i	$-0.0411443\pi$
$720$	0.669131	+	0.743145i	0.0249370	+	0.0276954i
$721$	13.8974	+	42.7717i	0.517564	+	1.59290i
$722$	−3.50971	+	3.89793i	−0.130618	+	0.145066i
$723$	11.2885	+	5.02597i	0.419825	+	0.186918i
$724$	9.48245	−	2.01556i	0.352413	−	0.0749076i
$725$	0.358441	+	3.41034i	0.0133122	+	0.126657i
$726$	1.05105	−	10.0001i	0.0390083	−	0.371139i
$727$	17.7095	+	3.76427i	0.656809	+	0.139609i	0.524248	−	0.851566i	$-0.324347\pi$
$727$	17.7095	+	3.76427i	0.656809	+	0.139609i	0.132561	+	0.991175i	$0.457680\pi$
$728$	−17.1993	−	12.4960i	−0.637448	−	0.463133i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	0.919533	+	0.195453i	0.0340334	+	0.00723403i
$731$	1.70394	−	16.2119i	0.0630227	−	0.599621i
$732$	−0.430083	−	4.09197i	−0.0158963	−	0.151244i
$733$	26.5641	−	5.64638i	0.981169	−	0.208554i	0.310713	−	0.950504i	$-0.399432\pi$
$733$	26.5641	−	5.64638i	0.981169	−	0.208554i	0.670455	+	0.741950i	$0.266099\pi$
$734$	22.4361	+	9.98918i	0.828131	+	0.368708i
$735$	6.28231	−	6.97721i	0.231727	−	0.257358i
$736$	1.00776	+	3.10157i	0.0371465	+	0.114325i
$737$	−0.756821	−	0.840535i	−0.0278779	−	0.0309615i
$738$	0.291335	−	0.504606i	0.0107242	−	0.0185748i
$739$	4.72916	+	8.19114i	0.173965	+	0.301316i	0.939803	−	0.341718i	$-0.111009\pi$
$739$	4.72916	+	8.19114i	0.173965	+	0.301316i	−0.765838	+	0.643034i	$0.777675\pi$
$740$	−0.582354	+	1.79230i	−0.0214078	+	0.0658864i
$741$	−17.7925	+	7.92173i	−0.653624	+	0.291012i
$742$	−22.1817	+	16.1159i	−0.814316	+	0.591635i
$743$	6.52092			0.239229			0.119615	−	0.992820i	$-0.461834\pi$
$743$	6.52092			0.239229			0.119615	+	0.992820i	$0.461834\pi$
$744$	−1.71038	−	5.29855i	−0.0627057	−	0.194254i
$745$	14.1915			0.519936
$746$	27.5411	−	20.0098i	1.00835	−	0.732611i
$747$	−4.21770	+	1.87784i	−0.154318	+	0.0687066i
$748$	0.493693	−	1.51943i	0.0180512	−	0.0555558i
$749$	−8.48893	−	14.7032i	−0.310179	−	0.537245i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	−8.54415	−	9.48924i	−0.311780	−	0.346267i	0.566805	−	0.823852i	$-0.308179\pi$
$751$	−8.54415	−	9.48924i	−0.311780	−	0.346267i	−0.878586	+	0.477585i	$0.841512\pi$
$752$	−1.67295	−	5.14881i	−0.0610062	−	0.187758i
$753$	−12.2754	+	13.6332i	−0.447340	+	0.496821i
$754$	−16.4510	−	7.32446i	−0.599110	−	0.266741i
$755$	1.76010	−	0.374120i	0.0640564	−	0.0136156i
$756$	−0.423163	−	4.02613i	−0.0153903	−	0.146429i
$757$	2.20880	−	21.0153i	0.0802801	−	0.763814i	−0.878131	−	0.478421i	$-0.841209\pi$
$757$	2.20880	−	21.0153i	0.0802801	−	0.763814i	0.958411	−	0.285393i	$-0.0921240\pi$
$758$	−12.9902	−	2.76116i	−0.471827	−	0.100290i
$759$	−2.56450	−	1.86322i	−0.0930854	−	0.0676305i
$760$	3.00044	+	2.17995i	0.108837	+	0.0790750i
$761$	−28.2039	−	5.99493i	−1.02239	−	0.217316i	−0.333937	−	0.942595i	$-0.608377\pi$
$761$	−28.2039	−	5.99493i	−1.02239	−	0.217316i	−0.688455	+	0.725279i	$0.741711\pi$
$762$	−2.15005	+	20.4564i	−0.0778881	+	0.741056i
$763$	0.0705560	+	0.671296i	0.00255430	+	0.0243025i
$764$	−22.8216	+	4.85089i	−0.825658	+	0.175499i
$765$	1.50153	+	0.668525i	0.0542880	+	0.0241706i
$766$	−18.6544	+	20.7178i	−0.674012	+	0.748566i
$767$	17.2983	+	53.2388i	0.624606	+	1.92234i
$768$	0.669131	+	0.743145i	0.0241452	+	0.0268159i
$769$	25.8654	−	44.8001i	0.932729	−	1.61553i	0.154094	−	0.988056i	$-0.450754\pi$
$769$	25.8654	−	44.8001i	0.932729	−	1.61553i	0.778635	−	0.627478i	$-0.215913\pi$
$770$	−1.96749	−	3.40780i	−0.0709035	−	0.122808i
$771$	−8.42249	+	25.9217i	−0.303328	+	0.933549i
$772$	9.73083	−	4.33244i	0.350220	−	0.155928i
$773$	27.7881	−	20.1892i	0.999467	−	0.726155i	0.0374933	−	0.999297i	$-0.488063\pi$
$773$	27.7881	−	20.1892i	0.999467	−	0.726155i	0.961974	+	0.273141i	$0.0880627\pi$
$774$	−9.91783			−0.356489
$775$	4.51068	−	3.26401i	0.162028	−	0.117247i
$776$	17.1770			0.616617
$777$	6.17214	−	4.48432i	0.221424	−	0.160874i
$778$	1.56694	−	0.697645i	0.0561774	−	0.0250118i
$779$	0.667778	−	2.05521i	0.0239256	−	0.0736355i
$780$	−2.62573	−	4.54789i	−0.0940161	−	0.162841i
$781$	4.93943	−	8.55535i	0.176747	−	0.306134i
$782$	3.58666	+	3.98339i	0.128259	+	0.142446i
$783$	−1.05966	−	3.26129i	−0.0378690	−	0.116549i
$784$	6.28231	−	6.97721i	0.224368	−	0.249186i
$785$	−5.98324	−	2.66391i	−0.213551	−	0.0950790i
$786$	−13.6238	+	2.89583i	−0.485945	+	0.103291i
$787$	−3.73248	−	35.5122i	−0.133049	−	1.26587i	−0.833639	−	0.552310i	$-0.813747\pi$
$787$	−3.73248	−	35.5122i	−0.133049	−	1.26587i	0.700590	−	0.713564i	$-0.252920\pi$
$788$	0.655793	−	6.23945i	0.0233616	−	0.222271i
$789$	−18.3089	−	3.89168i	−0.651814	−	0.138547i
$790$	2.80769	+	2.03991i	0.0998932	+	0.0725767i
$791$	−43.1671	−	31.3627i	−1.53484	−	1.11513i
$792$	−0.950768	−	0.202092i	−0.0337841	−	0.00718102i
$793$	−2.25856	+	21.4888i	−0.0802039	+	0.763089i
$794$	−3.51027	−	33.3980i	−0.124575	−	1.18525i
$795$	−6.62473	+	1.40813i	−0.234955	+	0.0499412i
$796$	−13.6266	−	6.06696i	−0.482983	−	0.215038i
$797$	−17.6139	+	19.5622i	−0.623916	+	0.692929i	−0.969397	−	0.245497i	$-0.921049\pi$
$797$	−17.6139	+	19.5622i	−0.623916	+	0.692929i	0.345481	+	0.938426i	$0.387716\pi$
$798$	−4.63963	−	14.2793i	−0.164241	−	0.505482i
$799$	−5.95409	−	6.61269i	−0.210641	−	0.233940i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	3.20098	+	5.54427i	0.113101	+	0.195897i
$802$	−2.51760	+	7.74838i	−0.0888996	+	0.273605i
$803$	−0.834762	+	0.371660i	−0.0294581	+	0.0131156i
$804$	0.941391	−	0.683960i	0.0332003	−	0.0241214i
$805$	13.2022			0.465318
$806$	3.00057	+	29.0845i	0.105691	+	1.02446i
$807$	−27.7534			−0.976967
$808$	0.168244	−	0.122237i	0.00591882	−	0.00430027i
$809$	23.7859	−	10.5902i	0.836268	−	0.372331i	0.0565029	−	0.998402i	$-0.482005\pi$
$809$	23.7859	−	10.5902i	0.836268	−	0.372331i	0.779765	+	0.626072i	$0.215338\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	−18.7471	−	32.4709i	−0.658300	−	1.14021i	−0.981056	−	0.193726i	$-0.937943\pi$
$811$	−18.7471	−	32.4709i	−0.658300	−	1.14021i	0.322756	−	0.946482i	$-0.395391\pi$
$812$	6.94106	−	12.0223i	0.243584	−	0.421899i
$813$	−15.1520	−	16.8280i	−0.531403	−	0.590183i
$814$	−0.566053	−	1.74213i	−0.0198402	−	0.0610617i
$815$	−1.40959	+	1.56550i	−0.0493756	+	0.0548372i
$816$	1.50153	+	0.668525i	0.0525641	+	0.0234031i
$817$	−35.9790	+	7.64756i	−1.25874	+	0.267554i
$818$	−1.00458	−	9.55791i	−0.0351242	−	0.334184i
$819$	−2.22222	+	21.1430i	−0.0776507	+	0.738797i
$820$	0.569936	+	0.121144i	0.0199030	+	0.00423052i
$821$	−10.8736	−	7.90010i	−0.379490	−	0.275715i	0.381645	−	0.924309i	$-0.375358\pi$
$821$	−10.8736	−	7.90010i	−0.379490	−	0.275715i	−0.761135	+	0.648593i	$0.775358\pi$
$822$	13.5973	+	9.87901i	0.474260	+	0.344570i
$823$	−8.63962	−	1.83641i	−0.301158	−	0.0640132i	0.0548542	−	0.998494i	$-0.482531\pi$
$823$	−8.63962	−	1.83641i	−0.301158	−	0.0640132i	−0.356012	+	0.934481i	$0.615864\pi$
$824$	−1.16121	+	11.0482i	−0.0404527	+	0.384882i
$825$	−0.101603	−	0.966683i	−0.00353735	−	0.0336556i
$826$	−42.2104	+	8.97210i	−1.46869	+	0.312179i
$827$	32.8857	+	14.6417i	1.14355	+	0.509140i	0.888994	−	0.457918i	$-0.151405\pi$
$827$	32.8857	+	14.6417i	1.14355	+	0.509140i	0.254554	+	0.967059i	$0.418071\pi$
$828$	2.18215	−	2.42353i	0.0758351	−	0.0842234i
$829$	8.17991	+	25.1752i	0.284100	+	0.874370i	0.986667	+	0.162753i	$0.0520372\pi$
$829$	8.17991	+	25.1752i	0.284100	+	0.874370i	−0.702567	+	0.711618i	$0.747963\pi$
$830$	−3.08927	−	3.43099i	−0.107230	−	0.119091i
$831$	6.66164	−	11.5383i	0.231090	−	0.400259i
$832$	−2.62573	−	4.54789i	−0.0910307	−	0.157670i
$833$	4.76865	−	14.6764i	0.165224	−	0.508507i
$834$	7.87115	−	3.50446i	0.272556	−	0.121350i
$835$	−5.04322	+	3.66412i	−0.174528	+	0.126802i
$836$	−3.60493			−0.124679
$837$	−3.73348	+	4.13051i	−0.129048	+	0.142771i
$838$	−40.4543			−1.39747
$839$	24.3700	−	17.7059i	0.841347	−	0.611275i	−0.0813993	−	0.996682i	$-0.525939\pi$
$839$	24.3700	−	17.7059i	0.841347	−	0.611275i	0.922747	+	0.385407i	$0.125939\pi$
$840$	3.69831	−	1.64659i	0.127604	−	0.0568129i
$841$	−5.32780	+	16.3973i	−0.183717	+	0.565424i
$842$	−11.2947	−	19.5630i	−0.389242	−	0.674187i
$843$	6.92887	−	12.0012i	0.238643	−	0.413342i
$844$	−6.36691	−	7.07117i	−0.219158	−	0.243400i
$845$	4.50477	+	13.8643i	0.154969	+	0.476945i
$846$	−3.62252	+	4.02322i	−0.124545	+	0.138321i
$847$	−37.1872	−	16.5568i	−1.27777	−	0.568899i
$848$	−6.62473	+	1.40813i	−0.227494	+	0.0483554i
$849$	−1.80210	−	17.1458i	−0.0618479	−	0.588444i
$850$	−0.171806	+	1.63463i	−0.00589290	+	0.0560672i
$851$	6.01152	+	1.27779i	0.206072	+	0.0438020i
$852$	8.22233	+	5.97387i	0.281692	+	0.204661i
$853$	12.6172	+	9.16697i	0.432006	+	0.313871i	0.782451	−	0.622713i	$-0.213969\pi$
$853$	12.6172	+	9.16697i	0.432006	+	0.313871i	−0.350444	+	0.936584i	$0.613969\pi$
$854$	−16.2928	−	3.46314i	−0.557528	−	0.118506i
$855$	0.387670	−	3.68843i	0.0132580	−	0.126142i
$856$	−0.438373	−	4.17084i	−0.0149833	−	0.142557i
$857$	37.3478	−	7.93851i	1.27578	−	0.271175i	0.480270	−	0.877121i	$-0.340539\pi$
$857$	37.3478	−	7.93851i	1.27578	−	0.271175i	0.795506	+	0.605946i	$0.207205\pi$
$858$	4.66315	+	2.07617i	0.159197	+	0.0708792i
$859$	32.5349	−	36.1337i	1.11008	−	1.23286i	0.139977	−	0.990155i	$-0.455297\pi$
$859$	32.5349	−	36.1337i	1.11008	−	1.23286i	0.970099	−	0.242710i	$-0.0780363\pi$
$860$	−3.06478	−	9.43242i	−0.104508	−	0.321643i
$861$	−1.57836	−	1.75295i	−0.0537904	−	0.0597403i
$862$	2.68645	−	4.65306i	0.0915007	−	0.158484i
$863$	−7.47108	−	12.9403i	−0.254319	−	0.440493i	0.710392	−	0.703807i	$-0.248518\pi$
$863$	−7.47108	−	12.9403i	−0.254319	−	0.440493i	−0.964710	+	0.263314i	$0.915185\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	−4.33027	+	1.92796i	−0.147234	+	0.0655527i
$866$	33.4690	−	24.3166i	1.13732	−	0.826313i
$867$	−14.2985			−0.485602
$868$	−22.5400	−	0.0431885i	−0.765056	−	0.00146591i
$869$	−3.37335			−0.114433
$870$	2.77422	−	2.01559i	0.0940548	−	0.0683348i
$871$	−5.58241	+	2.48545i	−0.189153	+	0.0842162i
$872$	−0.0515239	+	0.158574i	−0.00174482	+	0.00537000i
$873$	−8.58848	−	14.8757i	−0.290676	−	0.503466i
$874$	6.04745	−	10.4745i	0.204558	−	0.354305i
$875$	2.70884	+	3.00848i	0.0915756	+	0.101705i
$876$	−0.290499	−	0.894065i	−0.00981506	−	0.0302077i
$877$	−13.9424	+	15.4846i	−0.470800	+	0.522877i	−0.931040	−	0.364918i	$-0.881097\pi$
$877$	−13.9424	+	15.4846i	−0.470800	+	0.522877i	0.460239	+	0.887795i	$0.347764\pi$
$878$	25.6498	+	11.4200i	0.865639	+	0.385407i
$879$	0.266597	−	0.0566669i	0.00899208	−	0.00191133i
$880$	−0.101603	−	0.966683i	−0.00342502	−	0.0325869i
$881$	0.865492	−	8.23461i	0.0291592	−	0.277431i	−0.970221	−	0.242222i	$-0.922124\pi$
$881$	0.865492	−	8.23461i	0.0291592	−	0.277431i	0.999380	−	0.0352088i	$-0.0112096\pi$
$882$	−9.18360	−	1.95203i	−0.309228	−	0.0657284i
$883$	29.2429	+	21.2462i	0.984101	+	0.714991i	0.958621	−	0.284684i	$-0.0918888\pi$
$883$	29.2429	+	21.2462i	0.984101	+	0.714991i	0.0254795	+	0.999675i	$0.491889\pi$
$884$	−6.98299	−	5.07344i	−0.234863	−	0.170638i
$885$	−10.4267	−	2.21626i	−0.350489	−	0.0744988i
$886$	3.78727	−	36.0334i	0.127236	−	1.21057i
$887$	2.34168	+	22.2796i	0.0786260	+	0.748077i	0.960817	+	0.277184i	$0.0894013\pi$
$887$	2.34168	+	22.2796i	0.0786260	+	0.748077i	−0.882191	+	0.470892i	$0.843932\pi$
$888$	1.84336	−	0.391818i	0.0618590	−	0.0131485i
$889$	76.0707	+	33.8688i	2.55133	+	1.13592i
$890$	−4.28375	+	4.75759i	−0.143592	+	0.159475i
$891$	0.300367	+	0.924435i	0.0100627	+	0.0309697i
$892$	−9.57209	−	10.6309i	−0.320497	−	0.355948i
$893$	−10.0392	+	17.3884i	−0.335948	+	0.581879i
$894$	−7.09575	−	12.2902i	−0.237317	−	0.411046i
$895$	−7.47346	+	23.0010i	−0.249810	+	0.768837i
$896$	3.69831	−	1.64659i	0.123552	−	0.0550088i
$897$	−13.8552	+	10.0664i	−0.462611	+	0.336106i
$898$	−3.33103			−0.111158
$899$	−18.6829	+	3.93377i	−0.623109	+	0.131199i
$900$	1.00000			0.0333333
$901$	−9.00587	+	6.54315i	−0.300029	+	0.217984i
$902$	−0.517395	+	0.230359i	−0.0172274	+	0.00767012i
$903$	−12.4072	+	38.1853i	−0.412884	+	1.27073i
$904$	−6.59010	−	11.4144i	−0.219183	−	0.379637i
$905$	4.84715	−	8.39551i	0.161125	−	0.279076i
$906$	−1.20405	−	1.33723i	−0.0400017	−	0.0444264i
$907$	9.96570	+	30.6713i	0.330906	+	1.01842i	0.968704	+	0.248219i	$0.0798454\pi$
$907$	9.96570	+	30.6713i	0.330906	+	1.01842i	−0.637798	+	0.770204i	$0.720155\pi$
$908$	14.4293	−	16.0254i	0.478854	−	0.531821i
$909$	−0.189982	−	0.0845856i	−0.00630132	−	0.00280553i
$910$	−20.7949	+	4.42009i	−0.689344	+	0.146525i
$911$	−2.13620	−	20.3246i	−0.0707754	−	0.673383i	−0.971183	−	0.238335i	$-0.923398\pi$
$911$	−2.13620	−	20.3246i	−0.0707754	−	0.673383i	0.900408	−	0.435047i	$-0.143268\pi$
$912$	0.387670	−	3.68843i	0.0128370	−	0.122136i
$913$	4.38955	+	0.933027i	0.145273	+	0.0308787i
$914$	14.6858	+	10.6698i	0.485762	+	0.352927i
$915$	−3.32871	−	2.41845i	−0.110044	−	0.0799514i
$916$	−11.1404	−	2.36797i	−0.368091	−	0.0782401i
$917$	−5.89388	+	56.0765i	−0.194633	+	1.85181i
$918$	−0.171806	−	1.63463i	−0.00567045	−	0.0539507i
$919$	−27.9360	+	5.93799i	−0.921525	+	0.195876i	−0.644162	−	0.764889i	$-0.722794\pi$
$919$	−27.9360	+	5.93799i	−0.921525	+	0.195876i	−0.277363	+	0.960765i	$0.589460\pi$
$920$	2.97924	+	1.32644i	0.0982225	+	0.0437315i
$921$	18.9189	−	21.0116i	0.623399	−	0.692355i
$922$	8.55118	+	26.3178i	0.281618	+	0.866731i
$923$	−35.7131	−	39.6634i	−1.17551	−	1.30554i
$924$	−1.96749	+	3.40780i	−0.0647257	+	0.112108i
$925$	0.942269	+	1.63206i	0.0309816	+	0.0536618i
$926$	4.06198	−	12.5015i	0.133485	−	0.410825i
$927$	10.1486	−	4.51845i	0.333324	−	0.148406i
$928$	2.77422	−	2.01559i	0.0910681	−	0.0661649i
$929$	24.7139			0.810838			0.405419	−	0.914131i	$-0.367126\pi$
$929$	24.7139			0.810838			0.405419	+	0.914131i	$0.367126\pi$
$930$	−5.08206	−	2.27436i	−0.166647	−	0.0745791i
$931$	−34.8206			−1.14120
$932$	−7.64848	+	5.55694i	−0.250534	+	0.182024i
$933$	−5.55653	+	2.47393i	−0.181913	+	0.0809928i
$934$	−1.37524	+	4.23256i	−0.0449993	+	0.138494i
$935$	−0.798811	−	1.38358i	−0.0261239	−	0.0452480i
$936$	−2.62573	+	4.54789i	−0.0858245	+	0.148652i
$937$	−14.2961	−	15.8775i	−0.467034	−	0.518694i	0.462905	−	0.886408i	$-0.346807\pi$
$937$	−14.2961	−	15.8775i	−0.467034	−	0.518694i	−0.929939	+	0.367714i	$0.880141\pi$
$938$	−1.45569	−	4.48014i	−0.0475298	−	0.146282i
$939$	−14.7831	+	16.4183i	−0.482427	+	0.535790i
$940$	−4.94573	−	2.20198i	−0.161312	−	0.0718207i
$941$	17.9365	−	3.81251i	0.584712	−	0.124284i	0.0939481	−	0.995577i	$-0.470051\pi$
$941$	17.9365	−	3.81251i	0.584712	−	0.124284i	0.490764	+	0.871293i	$0.336718\pi$
$942$	0.684606	+	6.51359i	0.0223057	+	0.212224i
$943$	0.198624	−	1.88978i	0.00646808	−	0.0615397i
$944$	−10.4267	−	2.21626i	−0.339360	−	0.0721332i
$945$	−3.27515	−	2.37953i	−0.106541	−	0.0774062i
$946$	7.79910	+	5.66637i	0.253570	+	0.184230i
$947$	23.0454	+	4.89845i	0.748875	+	0.159178i	0.566512	−	0.824053i	$-0.308292\pi$
$947$	23.0454	+	4.89845i	0.748875	+	0.159178i	0.182362	+	0.983231i	$0.441626\pi$
$948$	0.362766	−	3.45149i	0.0117821	−	0.112099i
$949$	0.516032	+	4.90972i	0.0167511	+	0.159376i
$950$	3.62770	−	0.771092i	0.117698	−	0.0250175i
$951$	26.2359	+	11.6810i	0.850757	+	0.378782i
$952$	4.45234	−	4.94482i	0.144301	−	0.160263i
$953$	8.76780	+	26.9845i	0.284017	+	0.874114i	0.986692	+	0.162603i	$0.0519890\pi$
$953$	8.76780	+	26.9845i	0.284017	+	0.874114i	−0.702675	+	0.711511i	$0.748011\pi$
$954$	4.53184	+	5.03312i	0.146724	+	0.162953i
$955$	−11.6657	+	20.2057i	−0.377495	+	0.653840i
$956$	−6.30316	−	10.9174i	−0.203859	−	0.353094i
$957$	−1.03000	+	3.17000i	−0.0332950	+	0.102472i
$958$	5.24135	−	2.33360i	0.169340	−	0.0753951i
$959$	55.0460	−	39.9932i	1.77753	−	1.29145i
$960$	1.00000			0.0322749
$961$	20.6546	+	23.1168i	0.666278	+	0.745704i
$962$	−9.89657			−0.319078
$963$	−3.39287	+	2.46506i	−0.109334	+	0.0794356i
$964$	11.2885	−	5.02597i	0.363579	−	0.161876i
$965$	3.29156	−	10.1304i	0.105959	−	0.326109i
$966$	−6.60112	−	11.4335i	−0.212388	−	0.367866i
$967$	17.9481	−	31.0871i	0.577173	−	0.999693i	−0.418629	−	0.908158i	$-0.637489\pi$
$967$	17.9481	−	31.0871i	0.577173	−	0.999693i	0.995802	−	0.0915358i	$-0.0291776\pi$
$968$	−6.72824	−	7.47247i	−0.216254	−	0.240174i
$969$	−1.88371	−	5.79746i	−0.0605135	−	0.186241i
$970$	11.4936	−	12.7650i	0.369038	−	0.409858i
$971$	6.59440	+	2.93602i	0.211624	+	0.0942212i	0.509811	−	0.860286i	$-0.329715\pi$
$971$	6.59440	+	2.93602i	0.211624	+	0.0942212i	−0.298187	+	0.954507i	$0.596382\pi$
$972$	−0.978148	+	0.207912i	−0.0313741	+	0.00666877i
$973$	−3.64599	−	34.6893i	−0.116885	−	1.11209i
$974$	1.71788	−	16.3445i	0.0550445	−	0.523713i
$975$	−5.13670	−	1.09184i	−0.164506	−	0.0349668i
$976$	−3.32871	−	2.41845i	−0.106549	−	0.0774126i
$977$	−2.02390	−	1.47045i	−0.0647502	−	0.0470438i	0.554939	−	0.831891i	$-0.312741\pi$
$977$	−2.02390	−	1.47045i	−0.0647502	−	0.0470438i	−0.619690	+	0.784847i	$0.712741\pi$
$978$	2.06056	+	0.437985i	0.0658894	+	0.0140052i
$979$	0.650456	−	6.18868i	0.0207887	−	0.197791i
$980$	−0.981393	−	9.33733i	−0.0313495	−	0.298270i
$981$	0.163091	−	0.0346661i	0.00520710	−	0.00110680i
$982$	−29.9088	−	13.3163i	−0.954428	−	0.424939i
$983$	−27.8146	+	30.8912i	−0.887148	+	0.985278i	−0.999965	−	0.00833815i	$-0.997346\pi$
$983$	−27.8146	+	30.8912i	−0.887148	+	0.985278i	0.112817	+	0.993616i	$0.464013\pi$
$984$	−0.180055	−	0.554151i	−0.00573993	−	0.0176657i
$985$	−4.19800	−	4.66236i	−0.133760	−	0.148555i
$986$	2.81810	−	4.88110i	0.0897467	−	0.155446i
$987$	10.9583	+	18.9803i	0.348807	+	0.604151i
$988$	−6.01851	+	18.5231i	−0.191474	+	0.589298i
$989$	−29.5476	+	13.1554i	−0.939557	+	0.418318i
$990$	−0.786371	+	0.571332i	−0.0249925	+	0.0181581i
$991$	28.1479			0.894148			0.447074	−	0.894497i	$-0.352466\pi$
$991$	28.1479			0.894148			0.447074	+	0.894497i	$0.352466\pi$
$992$	−5.08206	−	2.27436i	−0.161355	−	0.0722109i
$993$	24.0060			0.761809
$994$	33.2865	−	24.1840i	1.05578	−	0.767071i
$995$	−13.6266	+	6.06696i	−0.431993	+	0.192336i
$996$	−1.42668	+	4.39088i	−0.0452062	+	0.139130i
$997$	24.6729	+	42.7348i	0.781400	+	1.35342i	0.931126	+	0.364697i	$0.118827\pi$
$997$	24.6729	+	42.7348i	0.781400	+	1.35342i	−0.149727	+	0.988727i	$0.547839\pi$
$998$	5.18330	−	8.97773i	0.164074	−	0.284185i
$999$	−1.26100	−	1.40049i	−0.0398964	−	0.0443094i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.g.421.3	yes	24
31.19	even	15	inner	930.2.bg.g.391.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.g.391.3	✓	24	31.19	even	15	inner
930.2.bg.g.421.3	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.70884 + 3.00848i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.913545 - 0.406737i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.70884 + 3.00848i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.669131 - 0.743145i) q^{9} +(0.913545 + 0.406737i) q^{10} +(-0.950768 + 0.202092i) q^{11} +(-0.104528 - 0.994522i) q^{12} +(-0.548926 + 5.22268i) q^{13} +(-3.95984 - 0.841690i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-1.60771 - 0.341730i) q^{17} +(-0.104528 + 0.994522i) q^{18} +(0.387670 + 3.68843i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(3.69831 + 1.64659i) q^{21} +(0.650400 - 0.722343i) q^{22} +(1.00776 + 3.10157i) q^{23} +(0.669131 + 0.743145i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.62573 - 4.54789i) q^{26} +(0.309017 - 0.951057i) q^{27} +(3.69831 - 1.64659i) q^{28} +(2.77422 - 2.01559i) q^{29} +1.00000 q^{30} +(-5.08206 - 2.27436i) q^{31} +1.00000 q^{32} +(-0.786371 + 0.571332i) q^{33} +(1.50153 - 0.668525i) q^{34} +(1.25099 - 3.85017i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(0.942269 - 1.63206i) q^{37} +(-2.48164 - 2.75614i) q^{38} +(1.62279 + 4.99443i) q^{39} +(0.669131 - 0.743145i) q^{40} +(-0.532295 - 0.236993i) q^{41} +(-3.95984 + 0.841690i) q^{42} +(1.03670 + 9.86350i) q^{43} +(-0.101603 + 0.966683i) q^{44} +(-0.978148 - 0.207912i) q^{45} +(-2.63835 - 1.91687i) q^{46} +(4.37984 + 3.18214i) q^{47} +(-0.978148 - 0.207912i) q^{48} +(-0.981393 + 9.33733i) q^{49} +(-0.104528 - 0.994522i) q^{50} +(-1.60771 + 0.341730i) q^{51} +(4.79744 + 2.13596i) q^{52} +(4.53184 - 5.03312i) q^{53} +(0.309017 + 0.951057i) q^{54} +(0.650400 + 0.722343i) q^{55} +(-2.02415 + 3.50593i) q^{56} +(1.85437 + 3.21187i) q^{57} +(-1.05966 + 3.26129i) q^{58} +(9.73806 - 4.33566i) q^{59} +(-0.809017 + 0.587785i) q^{60} +4.11451 q^{61} +(5.44830 - 1.14717i) q^{62} +4.04830 q^{63} +(-0.809017 + 0.587785i) q^{64} +(4.79744 - 2.13596i) q^{65} +(0.300367 - 0.924435i) q^{66} +(0.581811 + 1.00773i) q^{67} +(-0.821815 + 1.42343i) q^{68} +(2.18215 + 2.42353i) q^{69} +(1.25099 + 3.85017i) q^{70} +(-6.80061 + 7.55285i) q^{71} +(0.913545 + 0.406737i) q^{72} +(0.919533 - 0.195453i) q^{73} +(0.196988 + 1.87422i) q^{74} +(-0.104528 + 0.994522i) q^{75} +(3.62770 + 0.771092i) q^{76} +(-3.18347 - 2.31293i) q^{77} +(-4.24851 - 3.08673i) q^{78} +(3.39466 + 0.721557i) q^{79} +(-0.104528 + 0.994522i) q^{80} +(-0.104528 - 0.994522i) q^{81} +(0.569936 - 0.121144i) q^{82} +(-4.21770 - 1.87784i) q^{83} +(2.70884 - 3.00848i) q^{84} +(0.507910 + 1.56319i) q^{85} +(-6.63632 - 7.37038i) q^{86} +(1.71456 - 2.96971i) q^{87} +(-0.486004 - 0.841784i) q^{88} +(-1.97832 + 6.08864i) q^{89} +(0.913545 - 0.406737i) q^{90} +(-17.1993 + 12.4960i) q^{91} +3.26118 q^{92} +(-5.56775 - 0.0106683i) q^{93} -5.41378 q^{94} +(3.00044 - 2.17995i) q^{95} +(0.913545 - 0.406737i) q^{96} +(5.30797 - 16.3363i) q^{97} +(-4.69438 - 8.13091i) q^{98} +(-0.486004 + 0.841784i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

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