LMFDB - Embedded newform 930.2.n.h.721.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(481,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("930.481");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 5 x^{14} - 60 x^{13} + 480 x^{12} - 1202 x^{11} - 147 x^{10} - 2185 x^{9} + \cdots + 12851 $ x^16 - 4x^15 + 5x^14 - 60x^13 + 480x^12 - 1202x^11 - 147x^10 - 2185x^9 + 62400x^8 - 289745x^7 + 699483x^6 - 1042897x^5 + 1014415x^4 - 652345x^3 + 274580x^2 - 73519*x + 12851
Coefficient ring:	$\Z[a_1, \ldots, a_{31}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			721.2
Root			$0.109569 - 0.374923i$ of defining polynomial
Character	$\chi$	$=$	930.721
Dual form			930.2.n.h.841.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.0930287 - 0.0675893i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.0930287 - 0.0675893i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-4.78166 - 3.47408i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-0.0677171 - 0.208412i) q^{13} +(0.0930287 - 0.0675893i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(6.20586 - 4.50882i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.223166 + 0.686835i) q^{19} +(0.809017 + 0.587785i) q^{20} +(0.0355338 - 0.109362i) q^{21} +(4.78166 - 3.47408i) q^{22} +(3.30922 - 2.40429i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +0.219137 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.0355338 + 0.109362i) q^{28} +(1.40382 - 4.32050i) q^{29} +1.00000 q^{30} +(4.30204 + 3.53446i) q^{31} -1.00000 q^{32} +(1.82643 - 5.62117i) q^{33} +(2.37043 + 7.29543i) q^{34} +(0.0930287 + 0.0675893i) q^{35} +1.00000 q^{36} -11.2087 q^{37} +(-0.584257 - 0.424488i) q^{38} +(0.177286 - 0.128806i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(1.05858 - 3.25798i) q^{41} +(0.0930287 + 0.0675893i) q^{42} +(0.732047 - 2.25301i) q^{43} +(1.82643 + 5.62117i) q^{44} +(0.809017 - 0.587785i) q^{45} +(1.26401 + 3.89022i) q^{46} +(-0.348918 - 1.07386i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-2.15903 - 6.64482i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(6.20586 + 4.50882i) q^{51} +(-0.0677171 + 0.208412i) q^{52} +(7.59258 - 5.51633i) q^{53} +(0.809017 - 0.587785i) q^{54} +(4.78166 + 3.47408i) q^{55} -0.114990 q^{56} -0.722181 q^{57} +(3.67524 + 2.67022i) q^{58} +(-0.911338 - 2.80481i) q^{59} +(-0.309017 + 0.951057i) q^{60} +8.33985 q^{61} +(-4.69088 + 2.99928i) q^{62} +0.114990 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.0677171 + 0.208412i) q^{65} +(4.78166 + 3.47408i) q^{66} -13.7930 q^{67} -7.67087 q^{68} +(3.30922 + 2.40429i) q^{69} +(-0.0930287 + 0.0675893i) q^{70} +(4.55851 - 3.31195i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(7.02631 + 5.10492i) q^{73} +(3.46369 - 10.6601i) q^{74} +(0.309017 + 0.951057i) q^{75} +(0.584257 - 0.424488i) q^{76} +(0.210021 + 0.646378i) q^{77} +(0.0677171 + 0.208412i) q^{78} +(0.118704 - 0.0862438i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.77140 + 2.01354i) q^{82} +(2.78839 - 8.58179i) q^{83} +(-0.0930287 + 0.0675893i) q^{84} +(-6.20586 + 4.50882i) q^{85} +(1.91652 + 1.39244i) q^{86} +4.54284 q^{87} -5.91045 q^{88} +(10.9436 + 7.95101i) q^{89} +(0.309017 + 0.951057i) q^{90} +(-0.00778678 + 0.0239652i) q^{91} -4.09042 q^{92} +(-2.03207 + 5.18369i) q^{93} +1.12912 q^{94} +(0.223166 - 0.686835i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-2.42867 - 1.76453i) q^{97} +6.98678 q^{98} +5.91045 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−1.00000			−0.408248
$7$	−0.0930287	−	0.0675893i	−0.0351616	−	0.0255464i	0.570066	−	0.821599i	$-0.306918\pi$
$7$	−0.0930287	−	0.0675893i	−0.0351616	−	0.0255464i	−0.605227	+	0.796053i	$0.706918\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	0.309017	−	0.951057i	0.0977198	−	0.300750i
$11$	−4.78166	−	3.47408i	−1.44172	−	1.04747i	−0.987679	−	0.156494i	$-0.949981\pi$
$11$	−4.78166	−	3.47408i	−1.44172	−	1.04747i	−0.454045	−	0.890979i	$-0.650019\pi$
$12$	0.309017	−	0.951057i	0.0892055	−	0.274546i
$13$	−0.0677171	−	0.208412i	−0.0187813	−	0.0578030i	0.941227	−	0.337776i	$-0.109675\pi$
$13$	−0.0677171	−	0.208412i	−0.0187813	−	0.0578030i	−0.960008	+	0.279973i	$0.909675\pi$
$14$	0.0930287	−	0.0675893i	0.0248630	−	0.0180640i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	6.20586	−	4.50882i	1.50514	−	1.09355i	0.536867	−	0.843667i	$-0.319608\pi$
$17$	6.20586	−	4.50882i	1.50514	−	1.09355i	0.968276	−	0.249884i	$-0.0803924\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$	−0.223166	+	0.686835i	−0.0511979	+	0.157571i	−0.973387	−	0.229169i	$-0.926399\pi$
$19$	−0.223166	+	0.686835i	−0.0511979	+	0.157571i	0.922189	+	0.386740i	$0.126399\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	0.0355338	−	0.109362i	0.00775411	−	0.0238647i
$22$	4.78166	−	3.47408i	1.01945	−	0.740676i
$23$	3.30922	−	2.40429i	0.690020	−	0.501329i	−0.186647	−	0.982427i	$-0.559762\pi$
$23$	3.30922	−	2.40429i	0.690020	−	0.501329i	0.876667	+	0.481098i	$0.159762\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	1.00000			0.200000
$26$	0.219137			0.0429763
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.0355338	+	0.109362i	0.00671526	+	0.0206674i
$29$	1.40382	−	4.32050i	0.260682	−	0.802296i	−0.731975	−	0.681332i	$-0.761401\pi$
$29$	1.40382	−	4.32050i	0.260682	−	0.802296i	0.992657	−	0.120965i	$-0.0385988\pi$
$30$	1.00000			0.182574
$31$	4.30204	+	3.53446i	0.772669	+	0.634809i
$31$	4.30204	+	3.53446i	0.772669	+	0.634809i
$32$	−1.00000			−0.176777
$33$	1.82643	−	5.62117i	0.317941	−	0.978521i
$34$	2.37043	+	7.29543i	0.406525	+	1.25116i
$35$	0.0930287	+	0.0675893i	0.0157247	+	0.0114247i
$36$	1.00000			0.166667
$37$	−11.2087			−1.84271			−0.921353	−	0.388728i	$-0.872915\pi$
$37$	−11.2087			−1.84271			−0.921353	+	0.388728i	$0.872915\pi$
$38$	−0.584257	−	0.424488i	−0.0947790	−	0.0688610i
$39$	0.177286	−	0.128806i	0.0283884	−	0.0206254i
$40$	−0.809017	+	0.587785i	−0.127917	+	0.0929370i
$41$	1.05858	−	3.25798i	0.165323	−	0.508810i	−0.833737	−	0.552161i	$-0.813803\pi$
$41$	1.05858	−	3.25798i	0.165323	−	0.508810i	0.999060	+	0.0433508i	$0.0138033\pi$
$42$	0.0930287	+	0.0675893i	0.0143546	+	0.0104293i
$43$	0.732047	−	2.25301i	0.111636	−	0.343580i	−0.879594	−	0.475724i	$-0.842186\pi$
$43$	0.732047	−	2.25301i	0.111636	−	0.343580i	0.991231	+	0.132144i	$0.0421860\pi$
$44$	1.82643	+	5.62117i	0.275345	+	0.847424i
$45$	0.809017	−	0.587785i	0.120601	−	0.0876219i
$46$	1.26401	+	3.89022i	0.186368	+	0.573582i
$47$	−0.348918	−	1.07386i	−0.0508949	−	0.156638i	0.922379	−	0.386287i	$-0.126242\pi$
$47$	−0.348918	−	1.07386i	−0.0508949	−	0.156638i	−0.973274	+	0.229648i	$0.926242\pi$
$48$	−0.809017	+	0.587785i	−0.116772	+	0.0848395i
$49$	−2.15903	−	6.64482i	−0.308433	−	0.949260i
$50$	−0.309017	+	0.951057i	−0.0437016	+	0.134500i
$51$	6.20586	+	4.50882i	0.868995	+	0.631362i
$52$	−0.0677171	+	0.208412i	−0.00939067	+	0.0289015i
$53$	7.59258	−	5.51633i	1.04292	−	0.757727i	0.0720676	−	0.997400i	$-0.477040\pi$
$53$	7.59258	−	5.51633i	1.04292	−	0.757727i	0.970854	+	0.239673i	$0.0770403\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	4.78166	+	3.47408i	0.644758	+	0.468444i
$56$	−0.114990			−0.0153662
$57$	−0.722181			−0.0956553
$58$	3.67524	+	2.67022i	0.482582	+	0.350616i
$59$	−0.911338	−	2.80481i	−0.118646	−	0.365155i	0.874044	−	0.485847i	$-0.161489\pi$
$59$	−0.911338	−	2.80481i	−0.118646	−	0.365155i	−0.992690	+	0.120692i	$0.961489\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	8.33985			1.06781			0.533904	−	0.845545i	$-0.320724\pi$
$61$	8.33985			1.06781			0.533904	+	0.845545i	$0.320724\pi$
$62$	−4.69088	+	2.99928i	−0.595742	+	0.380908i
$63$	0.114990			0.0144874
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.0677171	+	0.208412i	0.00839927	+	0.0258503i
$66$	4.78166	+	3.47408i	0.588581	+	0.427629i
$67$	−13.7930			−1.68509			−0.842544	−	0.538627i	$-0.818943\pi$
$67$	−13.7930			−1.68509			−0.842544	+	0.538627i	$0.818943\pi$
$68$	−7.67087			−0.930230
$69$	3.30922	+	2.40429i	0.398383	+	0.289442i
$70$	−0.0930287	+	0.0675893i	−0.0111191	+	0.00807847i
$71$	4.55851	−	3.31195i	0.540996	−	0.393056i	−0.283459	−	0.958984i	$-0.591482\pi$
$71$	4.55851	−	3.31195i	0.540996	−	0.393056i	0.824455	+	0.565928i	$0.191482\pi$
$72$	−0.309017	+	0.951057i	−0.0364180	+	0.112083i
$73$	7.02631	+	5.10492i	0.822368	+	0.597485i	0.917390	−	0.397990i	$-0.130292\pi$
$73$	7.02631	+	5.10492i	0.822368	+	0.597485i	−0.0950219	+	0.995475i	$0.530292\pi$
$74$	3.46369	−	10.6601i	0.402646	−	1.23922i
$75$	0.309017	+	0.951057i	0.0356822	+	0.109819i
$76$	0.584257	−	0.424488i	0.0670189	−	0.0486921i
$77$	0.210021	+	0.646378i	0.0239341	+	0.0736616i
$78$	0.0677171	+	0.208412i	0.00766745	+	0.0235980i
$79$	0.118704	−	0.0862438i	0.0133553	−	0.00970318i	−0.581088	−	0.813841i	$-0.697373\pi$
$79$	0.118704	−	0.0862438i	0.0133553	−	0.00970318i	0.594443	+	0.804138i	$0.297373\pi$
$80$	−0.309017	−	0.951057i	−0.0345492	−	0.106331i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	2.77140	+	2.01354i	0.306050	+	0.222358i
$83$	2.78839	−	8.58179i	0.306066	−	0.941973i	−0.673212	−	0.739450i	$-0.735086\pi$
$83$	2.78839	−	8.58179i	0.306066	−	0.941973i	0.979277	−	0.202524i	$-0.0649143\pi$
$84$	−0.0930287	+	0.0675893i	−0.0101503	+	0.00737460i
$85$	−6.20586	+	4.50882i	−0.673120	+	0.489051i
$86$	1.91652	+	1.39244i	0.206664	+	0.150150i
$87$	4.54284			0.487044
$88$	−5.91045			−0.630056
$89$	10.9436	+	7.95101i	1.16002	+	0.842806i	0.989781	−	0.142597i	$-0.0455452\pi$
$89$	10.9436	+	7.95101i	1.16002	+	0.842806i	0.170241	+	0.985402i	$0.445545\pi$
$90$	0.309017	+	0.951057i	0.0325733	+	0.100250i
$91$	−0.00778678	+	0.0239652i	−0.000816276	+	0.00251224i
$92$	−4.09042			−0.426456
$93$	−2.03207	+	5.18369i	−0.210716	+	0.537524i
$94$	1.12912			0.116460
$95$	0.223166	−	0.686835i	0.0228964	−	0.0704678i
$96$	−0.309017	−	0.951057i	−0.0315389	−	0.0970668i
$97$	−2.42867	−	1.76453i	−0.246594	−	0.179161i	0.457622	−	0.889147i	$-0.348701\pi$
$97$	−2.42867	−	1.76453i	−0.246594	−	0.179161i	−0.704216	+	0.709986i	$0.748701\pi$
$98$	6.98678			0.705771
$99$	5.91045			0.594023
$100$	−0.809017	−	0.587785i	−0.0809017	−	0.0587785i
$101$	−10.9221	+	7.93540i	−1.08679	+	0.789601i	−0.978855	−	0.204556i	$-0.934425\pi$
$101$	−10.9221	+	7.93540i	−1.08679	+	0.789601i	−0.107938	+	0.994158i	$0.534425\pi$
$102$	−6.20586	+	4.50882i	−0.614472	+	0.446440i
$103$	3.94237	−	12.1334i	0.388454	−	1.19554i	−0.545490	−	0.838117i	$-0.683656\pi$
$103$	3.94237	−	12.1334i	0.388454	−	1.19554i	0.933944	−	0.357420i	$-0.116344\pi$
$104$	−0.177286	−	0.128806i	−0.0173843	−	0.0126304i
$105$	−0.0355338	+	0.109362i	−0.00346774	+	0.0106726i
$106$	2.90011	+	8.92561i	0.281683	+	0.866932i
$107$	−13.0973	+	9.51575i	−1.26616	+	0.919923i	−0.999043	−	0.0437401i	$-0.986073\pi$
$107$	−13.0973	+	9.51575i	−1.26616	+	0.919923i	−0.267122	+	0.963663i	$0.586073\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	1.01182	+	3.11405i	0.0969144	+	0.298272i	0.987748	−	0.156058i	$-0.0498787\pi$
$109$	1.01182	+	3.11405i	0.0969144	+	0.298272i	−0.890833	+	0.454330i	$0.849879\pi$
$110$	−4.78166	+	3.47408i	−0.455913	+	0.331240i
$111$	−3.46369	−	10.6601i	−0.328759	−	1.01182i
$112$	0.0355338	−	0.109362i	0.00335763	−	0.0103337i
$113$	−9.67487	−	7.02920i	−0.910135	−	0.661252i	0.0309139	−	0.999522i	$-0.490158\pi$
$113$	−9.67487	−	7.02920i	−0.910135	−	0.661252i	−0.941049	+	0.338270i	$0.890158\pi$
$114$	0.223166	−	0.686835i	0.0209014	−	0.0643280i
$115$	−3.30922	+	2.40429i	−0.308586	+	0.224201i
$116$	−3.67524	+	2.67022i	−0.341237	+	0.247923i
$117$	0.177286	+	0.128806i	0.0163901	+	0.0119081i
$118$	2.94915			0.271492
$119$	−0.882072			−0.0808594
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	7.39584	+	22.7620i	0.672349	+	2.06928i
$122$	−2.57716	+	7.93167i	−0.233325	+	0.718100i
$123$	3.42564			0.308879
$124$	−1.40292	−	5.38812i	−0.125986	−	0.483867i
$125$	−1.00000			−0.0894427
$126$	−0.0355338	+	0.109362i	−0.00316560	+	0.00974273i
$127$	4.35633	+	13.4074i	0.386562	+	1.18972i	0.935341	+	0.353748i	$0.115093\pi$
$127$	4.35633	+	13.4074i	0.386562	+	1.18972i	−0.548779	+	0.835968i	$0.684907\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	2.36895			0.208575
$130$	−0.219137			−0.0192196
$131$	−11.0538	−	8.03105i	−0.965774	−	0.701676i	−0.0112893	−	0.999936i	$-0.503594\pi$
$131$	−11.0538	−	8.03105i	−0.965774	−	0.701676i	−0.954484	+	0.298261i	$0.903594\pi$
$132$	−4.78166	+	3.47408i	−0.416190	+	0.302380i
$133$	0.0671836	−	0.0488117i	0.00582556	−	0.00423252i
$134$	4.26228	−	13.1180i	0.368205	−	1.13322i
$135$	0.809017	+	0.587785i	0.0696291	+	0.0505885i
$136$	2.37043	−	7.29543i	0.203263	−	0.625578i
$137$	−5.19552	−	15.9902i	−0.443883	−	1.36613i	−0.883704	−	0.468046i	$-0.844958\pi$
$137$	−5.19552	−	15.9902i	−0.443883	−	1.36613i	0.439821	−	0.898085i	$-0.355042\pi$
$138$	−3.30922	+	2.40429i	−0.281699	+	0.204667i
$139$	3.28420	+	10.1077i	0.278562	+	0.857326i	0.988255	+	0.152815i	$0.0488338\pi$
$139$	3.28420	+	10.1077i	0.278562	+	0.857326i	−0.709693	+	0.704511i	$0.751166\pi$
$140$	−0.0355338	−	0.109362i	−0.00300316	−	0.00924276i
$141$	0.913479	−	0.663681i	0.0769288	−	0.0558920i
$142$	1.74120	+	5.35885i	0.146118	+	0.449705i
$143$	−0.400239	+	1.23181i	−0.0334696	+	0.103009i
$144$	−0.809017	−	0.587785i	−0.0674181	−	0.0489821i
$145$	−1.40382	+	4.32050i	−0.116581	+	0.358798i
$146$	−7.02631	+	5.10492i	−0.581502	+	0.422486i
$147$	5.65242	−	4.10672i	0.466204	−	0.338717i
$148$	9.06806	+	6.58833i	0.745390	+	0.541558i
$149$	1.32978			0.108940			0.0544701	−	0.998515i	$-0.482653\pi$
$149$	1.32978			0.108940			0.0544701	+	0.998515i	$0.482653\pi$
$150$	−1.00000			−0.0816497
$151$	−19.2308	−	13.9720i	−1.56498	−	1.13703i	−0.931770	−	0.363050i	$-0.881736\pi$
$151$	−19.2308	−	13.9720i	−1.56498	−	1.13703i	−0.633213	−	0.773977i	$-0.718264\pi$
$152$	0.223166	+	0.686835i	0.0181012	+	0.0557097i
$153$	−2.37043	+	7.29543i	−0.191638	+	0.589801i
$154$	−0.679642			−0.0547671
$155$	−4.30204	−	3.53446i	−0.345548	−	0.283895i
$156$	−0.219137			−0.0175450
$157$	5.47032	−	16.8359i	0.436579	−	1.34365i	−0.454880	−	0.890553i	$-0.650318\pi$
$157$	5.47032	−	16.8359i	0.436579	−	1.34365i	0.891460	−	0.453100i	$-0.149682\pi$
$158$	0.0453410	+	0.139545i	0.00360714	+	0.0111016i
$159$	7.59258	+	5.51633i	0.602131	+	0.437474i
$160$	1.00000			0.0790569
$161$	−0.470357			−0.0370693
$162$	0.809017	+	0.587785i	0.0635624	+	0.0461808i
$163$	1.24688	−	0.905912i	0.0976632	−	0.0709565i	−0.537882	−	0.843020i	$-0.680775\pi$
$163$	1.24688	−	0.905912i	0.0976632	−	0.0709565i	0.635545	+	0.772064i	$0.280775\pi$
$164$	−2.77140	+	2.01354i	−0.216410	+	0.157231i
$165$	−1.82643	+	5.62117i	−0.142187	+	0.437608i
$166$	7.30010	+	5.30384i	0.566598	+	0.411657i
$167$	−0.316215	+	0.973208i	−0.0244694	+	0.0753091i	−0.962546	−	0.271120i	$-0.912606\pi$
$167$	−0.316215	+	0.973208i	−0.0244694	+	0.0753091i	0.938076	+	0.346429i	$0.112606\pi$
$168$	−0.0355338	−	0.109362i	−0.00274149	−	0.00843745i
$169$	10.4784	−	7.61298i	0.806029	−	0.585614i
$170$	−2.37043	−	7.29543i	−0.181804	−	0.559534i
$171$	−0.223166	−	0.686835i	−0.0170660	−	0.0525236i
$172$	−1.91652	+	1.39244i	−0.146134	+	0.106172i
$173$	−7.08860	−	21.8165i	−0.538936	−	1.65868i	−0.734986	−	0.678082i	$-0.762811\pi$
$173$	−7.08860	−	21.8165i	−0.538936	−	1.65868i	0.196050	−	0.980594i	$-0.437189\pi$
$174$	−1.40382	+	4.32050i	−0.106423	+	0.327536i
$175$	−0.0930287	−	0.0675893i	−0.00703231	−	0.00510927i
$176$	1.82643	−	5.62117i	0.137672	−	0.423712i
$177$	2.38591	−	1.73347i	0.179336	−	0.130295i
$178$	−10.9436	+	7.95101i	−0.820260	+	0.595954i
$179$	−0.0645815	−	0.0469212i	−0.00482705	−	0.00350706i	0.585369	−	0.810767i	$-0.300950\pi$
$179$	−0.0645815	−	0.0469212i	−0.00482705	−	0.00350706i	−0.590196	+	0.807260i	$0.700950\pi$
$180$	−1.00000			−0.0745356
$181$	21.4832			1.59684			0.798418	−	0.602103i	$-0.205670\pi$
$181$	21.4832			1.59684			0.798418	+	0.602103i	$0.205670\pi$
$182$	−0.0203860	−	0.0148113i	−0.00151111	−	0.00109789i
$183$	2.57716	+	7.93167i	0.190509	+	0.586326i
$184$	1.26401	−	3.89022i	0.0931840	−	0.286791i
$185$	11.2087			0.824083
$186$	−4.30204	−	3.53446i	−0.315441	−	0.259159i
$187$	−45.3383			−3.31547
$188$	−0.348918	+	1.07386i	−0.0254475	+	0.0783192i
$189$	0.0355338	+	0.109362i	0.00258470	+	0.00795490i
$190$	0.584257	+	0.424488i	0.0423865	+	0.0307956i
$191$	0.234859			0.0169938			0.00849691	−	0.999964i	$-0.497295\pi$
$191$	0.234859			0.0169938			0.00849691	+	0.999964i	$0.497295\pi$
$192$	1.00000			0.0721688
$193$	0.322736	+	0.234481i	0.0232310	+	0.0168783i	0.599340	−	0.800494i	$-0.295430\pi$
$193$	0.322736	+	0.234481i	0.0232310	+	0.0168783i	−0.576109	+	0.817373i	$0.695430\pi$
$194$	2.42867	−	1.76453i	0.174368	−	0.126686i
$195$	−0.177286	+	0.128806i	−0.0126957	+	0.00922396i
$196$	−2.15903	+	6.64482i	−0.154217	+	0.474630i
$197$	−11.9693	−	8.69620i	−0.852776	−	0.619578i	0.0731337	−	0.997322i	$-0.476700\pi$
$197$	−11.9693	−	8.69620i	−0.852776	−	0.619578i	−0.925910	+	0.377744i	$0.876700\pi$
$198$	−1.82643	+	5.62117i	−0.129799	+	0.399479i
$199$	−2.55645	−	7.86795i	−0.181222	−	0.557745i	0.818641	−	0.574306i	$-0.194728\pi$
$199$	−2.55645	−	7.86795i	−0.181222	−	0.557745i	−0.999863	+	0.0165615i	$0.994728\pi$
$200$	0.809017	−	0.587785i	0.0572061	−	0.0415627i
$201$	−4.26228	−	13.1180i	−0.300638	−	0.925270i
$202$	−4.17188	−	12.8397i	−0.293533	−	0.903401i
$203$	−0.422615	+	0.307048i	−0.0296617	+	0.0215505i
$204$	−2.37043	−	7.29543i	−0.165963	−	0.510782i
$205$	−1.05858	+	3.25798i	−0.0739345	+	0.227547i
$206$	10.3213	+	7.49884i	0.719117	+	0.522469i
$207$	−1.26401	+	3.89022i	−0.0878547	+	0.270389i
$208$	0.177286	−	0.128806i	0.0122926	−	0.00893106i
$209$	3.45322	−	2.50891i	0.238864	−	0.173545i
$210$	−0.0930287	−	0.0675893i	−0.00641959	−	0.00466411i
$211$	10.8392			0.746202			0.373101	−	0.927791i	$-0.378295\pi$
$211$	10.8392			0.746202			0.373101	+	0.927791i	$0.378295\pi$
$212$	−9.38495			−0.644561
$213$	4.55851	+	3.31195i	0.312344	+	0.226931i
$214$	−5.00273	−	15.3968i	−0.341979	−	1.05250i
$215$	−0.732047	+	2.25301i	−0.0499252	+	0.153654i
$216$	−1.00000			−0.0680414
$217$	−0.161321	−	0.619579i	−0.0109512	−	0.0420597i
$218$	−3.27431			−0.221764
$219$	−2.68381	+	8.25993i	−0.181355	+	0.558154i
$220$	−1.82643	−	5.62117i	−0.123138	−	0.378979i
$221$	−1.35994	−	0.988051i	−0.0914792	−	0.0664635i
$222$	11.2087			0.752281
$223$	−11.0819			−0.742097			−0.371049	−	0.928613i	$-0.621002\pi$
$223$	−11.0819			−0.742097			−0.371049	+	0.928613i	$0.621002\pi$
$224$	0.0930287	+	0.0675893i	0.00621574	+	0.00451600i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	9.67487	−	7.02920i	0.643563	−	0.467576i
$227$	−3.47941	+	10.7085i	−0.230936	+	0.710749i	0.766698	+	0.642008i	$0.221898\pi$
$227$	−3.47941	+	10.7085i	−0.230936	+	0.710749i	−0.997635	+	0.0687413i	$0.978102\pi$
$228$	0.584257	+	0.424488i	0.0386934	+	0.0281124i
$229$	−5.51721	+	16.9802i	−0.364588	+	1.12209i	0.585651	+	0.810563i	$0.300839\pi$
$229$	−5.51721	+	16.9802i	−0.364588	+	1.12209i	−0.950239	+	0.311522i	$0.899161\pi$
$230$	−1.26401	−	3.89022i	−0.0833463	−	0.256514i
$231$	−0.549842	+	0.399483i	−0.0361769	+	0.0262841i
$232$	−1.40382	−	4.32050i	−0.0921650	−	0.283655i
$233$	1.19585	+	3.68044i	0.0783427	+	0.241114i	0.982556	−	0.185967i	$-0.0595419\pi$
$233$	1.19585	+	3.68044i	0.0783427	+	0.241114i	−0.904213	+	0.427081i	$0.859542\pi$
$234$	−0.177286	+	0.128806i	−0.0115895	+	0.00842028i
$235$	0.348918	+	1.07386i	0.0227609	+	0.0700508i
$236$	−0.911338	+	2.80481i	−0.0593231	+	0.182578i
$237$	0.118704	+	0.0862438i	0.00771068	+	0.00560214i
$238$	0.272575	−	0.838900i	0.0176684	−	0.0543778i
$239$	−15.7662	+	11.4548i	−1.01983	+	0.740952i	−0.966249	−	0.257611i	$-0.917065\pi$
$239$	−15.7662	+	11.4548i	−1.01983	+	0.740952i	−0.0535846	+	0.998563i	$0.517065\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	−9.22264	−	6.70064i	−0.594082	−	0.431626i	0.249691	−	0.968326i	$-0.419671\pi$
$241$	−9.22264	−	6.70064i	−0.594082	−	0.431626i	−0.843773	+	0.536699i	$0.819671\pi$
$242$	−23.9334			−1.53850
$243$	1.00000			0.0641500
$244$	−6.74708	−	4.90204i	−0.431938	−	0.313821i
$245$	2.15903	+	6.64482i	0.137936	+	0.424522i
$246$	−1.05858	+	3.25798i	−0.0674926	+	0.207721i
$247$	0.158257			0.0100696
$248$	5.55793	+	0.330765i	0.352929	+	0.0210036i
$249$	9.02342			0.571836
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	3.50913	+	10.8000i	0.221495	+	0.681690i	0.998629	+	0.0523549i	$0.0166727\pi$
$251$	3.50913	+	10.8000i	0.221495	+	0.681690i	−0.777134	+	0.629335i	$0.783327\pi$
$252$	−0.0930287	−	0.0675893i	−0.00586026	−	0.00425773i
$253$	−24.1762			−1.51995
$254$	−14.0974			−0.884549
$255$	−6.20586	−	4.50882i	−0.388626	−	0.282354i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−16.2044	+	11.7732i	−1.01080	+	0.734390i	−0.964377	−	0.264532i	$-0.914782\pi$
$257$	−16.2044	+	11.7732i	−1.01080	+	0.734390i	−0.0464236	+	0.998922i	$0.514782\pi$
$258$	−0.732047	+	2.25301i	−0.0455752	+	0.140266i
$259$	1.04273	+	0.757591i	0.0647924	+	0.0470744i
$260$	0.0677171	−	0.208412i	0.00419964	−	0.0129252i
$261$	1.40382	+	4.32050i	0.0868940	+	0.267432i
$262$	11.0538	−	8.03105i	0.682905	−	0.496160i
$263$	0.394943	+	1.21551i	0.0243532	+	0.0749515i	0.962494	−	0.271301i	$-0.0874540\pi$
$263$	0.394943	+	1.21551i	0.0243532	+	0.0749515i	−0.938141	+	0.346253i	$0.887454\pi$
$264$	−1.82643	−	5.62117i	−0.112409	−	0.345959i
$265$	−7.59258	+	5.51633i	−0.466409	+	0.338866i
$266$	0.0256619	+	0.0789791i	0.00157343	+	0.00484252i
$267$	−4.18009	+	12.8650i	−0.255818	+	0.787326i
$268$	11.1588	+	8.10735i	0.681633	+	0.495235i
$269$	−1.28518	+	3.95536i	−0.0783585	+	0.241163i	−0.982561	−	0.185942i	$-0.940466\pi$
$269$	−1.28518	+	3.95536i	−0.0783585	+	0.241163i	0.904202	+	0.427105i	$0.140466\pi$
$270$	−0.809017	+	0.587785i	−0.0492352	+	0.0357715i
$271$	−22.8458	+	16.5984i	−1.38778	+	1.00828i	−0.391679	+	0.920102i	$0.628106\pi$
$271$	−22.8458	+	16.5984i	−1.38778	+	1.00828i	−0.996104	+	0.0881822i	$0.971894\pi$
$272$	6.20586	+	4.50882i	0.376286	+	0.273388i
$273$	−0.0251985			−0.00152509
$274$	16.8130			1.01571
$275$	−4.78166	−	3.47408i	−0.288345	−	0.209495i
$276$	−1.26401	−	3.89022i	−0.0760844	−	0.234164i
$277$	4.36595	−	13.4370i	0.262325	−	0.807353i	−0.729973	−	0.683476i	$-0.760467\pi$
$277$	4.36595	−	13.4370i	0.262325	−	0.807353i	0.992298	−	0.123876i	$-0.0395327\pi$
$278$	−10.6279			−0.637419
$279$	−5.55793	−	0.330765i	−0.332745	−	0.0198024i
$280$	0.114990			0.00687196
$281$	−1.26741	+	3.90069i	−0.0756074	+	0.232696i	−0.981717	−	0.190348i	$-0.939038\pi$
$281$	−1.26741	+	3.90069i	−0.0756074	+	0.232696i	0.906109	+	0.423044i	$0.139038\pi$
$282$	0.348918	+	1.07386i	0.0207778	+	0.0639474i
$283$	12.6973	+	9.22512i	0.754775	+	0.548376i	0.897303	−	0.441414i	$-0.145523\pi$
$283$	12.6973	+	9.22512i	0.754775	+	0.548376i	−0.142528	+	0.989791i	$0.545523\pi$
$284$	−5.63463			−0.334354
$285$	0.722181			0.0427783
$286$	−1.04784	−	0.761299i	−0.0619600	−	0.0450166i
$287$	−0.318683	+	0.231537i	−0.0188113	+	0.0136672i
$288$	0.809017	−	0.587785i	0.0476718	−	0.0346356i
$289$	12.9300	−	39.7943i	0.760586	−	2.34084i
$290$	−3.67524	−	2.67022i	−0.215817	−	0.156800i
$291$	0.927668	−	2.85507i	0.0543809	−	0.167367i
$292$	−2.68381	−	8.25993i	−0.157058	−	0.483376i
$293$	27.5912	−	20.0462i	1.61190	−	1.17111i	0.754804	−	0.655950i	$-0.227732\pi$
$293$	27.5912	−	20.0462i	1.61190	−	1.17111i	0.857093	−	0.515161i	$-0.172268\pi$
$294$	2.15903	+	6.64482i	0.125917	+	0.387534i
$295$	0.911338	+	2.80481i	0.0530602	+	0.163302i
$296$	−9.06806	+	6.58833i	−0.527070	+	0.382939i
$297$	1.82643	+	5.62117i	0.105980	+	0.326174i
$298$	−0.410926	+	1.26470i	−0.0238043	+	0.0732621i
$299$	−0.725173	−	0.526869i	−0.0419378	−	0.0304696i
$300$	0.309017	−	0.951057i	0.0178411	−	0.0549093i
$301$	−0.220381	+	0.160116i	−0.0127025	+	0.00922893i
$302$	19.2308	−	13.9720i	1.10661	−	0.803999i
$303$	−10.9221	−	7.93540i	−0.627460	−	0.455877i
$304$	−0.722181			−0.0414199
$305$	−8.33985			−0.477539
$306$	−6.20586	−	4.50882i	−0.354766	−	0.257752i
$307$	8.07118	+	24.8405i	0.460646	+	1.41772i	0.864376	+	0.502846i	$0.167714\pi$
$307$	8.07118	+	24.8405i	0.460646	+	1.41772i	−0.403730	+	0.914878i	$0.632286\pi$
$308$	0.210021	−	0.646378i	0.0119670	−	0.0368308i
$309$	12.7578			0.725765
$310$	4.69088	−	2.99928i	0.266424	−	0.170347i
$311$	25.3953			1.44004			0.720018	−	0.693955i	$-0.244134\pi$
$311$	25.3953			1.44004			0.720018	+	0.693955i	$0.244134\pi$
$312$	0.0677171	−	0.208412i	0.00383373	−	0.0117990i
$313$	5.95565	+	18.3296i	0.336633	+	1.03605i	0.965912	+	0.258871i	$0.0833504\pi$
$313$	5.95565	+	18.3296i	0.336633	+	1.03605i	−0.629279	+	0.777180i	$0.716650\pi$
$314$	14.3215	+	10.4052i	0.808209	+	0.587198i
$315$	−0.114990			−0.00647894
$316$	−0.146727			−0.00825402
$317$	3.09305	+	2.24724i	0.173723	+	0.126217i	0.671249	−	0.741232i	$-0.265758\pi$
$317$	3.09305	+	2.24724i	0.173723	+	0.126217i	−0.497526	+	0.867449i	$0.665758\pi$
$318$	−7.59258	+	5.51633i	−0.425771	+	0.309341i
$319$	−21.7223	+	15.7822i	−1.21622	+	0.883632i
$320$	−0.309017	+	0.951057i	−0.0172746	+	0.0531657i
$321$	−13.0973	−	9.51575i	−0.731021	−	0.531118i
$322$	0.145348	−	0.447336i	0.00809994	−	0.0249291i
$323$	1.71188	+	5.26862i	0.0952515	+	0.293154i
$324$	−0.809017	+	0.587785i	−0.0449454	+	0.0326547i
$325$	−0.0677171	−	0.208412i	−0.00375627	−	0.0115606i
$326$	0.476266	+	1.46580i	0.0263779	+	0.0811829i
$327$	−2.64897	+	1.92459i	−0.146488	+	0.106430i
$328$	−1.05858	−	3.25798i	−0.0584503	−	0.179892i
$329$	−0.0401220	+	0.123483i	−0.00221200	+	0.00680783i
$330$	−4.78166	−	3.47408i	−0.263221	−	0.191242i
$331$	1.41967	−	4.36928i	0.0780319	−	0.240158i	−0.904430	−	0.426623i	$-0.859703\pi$
$331$	1.41967	−	4.36928i	0.0780319	−	0.240158i	0.982462	+	0.186465i	$0.0597032\pi$
$332$	−7.30010	+	5.30384i	−0.400645	+	0.291086i
$333$	9.06806	−	6.58833i	0.496927	−	0.361038i
$334$	−0.827860	−	0.601476i	−0.0452985	−	0.0329113i
$335$	13.7930			0.753594
$336$	0.114990			0.00627321
$337$	−16.8309	−	12.2284i	−0.916840	−	0.666123i	0.0258954	−	0.999665i	$-0.491756\pi$
$337$	−16.8309	−	12.2284i	−0.916840	−	0.666123i	−0.942735	+	0.333541i	$0.891756\pi$
$338$	4.00238	+	12.3181i	0.217701	+	0.670014i
$339$	3.69547	−	11.3735i	0.200710	−	0.617723i
$340$	7.67087			0.416011
$341$	−8.29188	−	31.8462i	−0.449031	−	1.72457i
$342$	0.722181			0.0390511
$343$	−0.497003	+	1.52962i	−0.0268357	+	0.0825917i
$344$	−0.732047	−	2.25301i	−0.0394693	−	0.121474i
$345$	−3.30922	−	2.40429i	−0.178162	−	0.129443i
$346$	22.9392			1.23322
$347$	−11.4732			−0.615914			−0.307957	−	0.951400i	$-0.599645\pi$
$347$	−11.4732			−0.615914			−0.307957	+	0.951400i	$0.599645\pi$
$348$	−3.67524	−	2.67022i	−0.197013	−	0.143139i
$349$	3.63178	−	2.63864i	0.194405	−	0.141243i	−0.486325	−	0.873778i	$-0.661663\pi$
$349$	3.63178	−	2.63864i	0.194405	−	0.141243i	0.680730	+	0.732535i	$0.261663\pi$
$350$	0.0930287	−	0.0675893i	0.00497259	−	0.00361280i
$351$	−0.0677171	+	0.208412i	−0.00361447	+	0.0111242i
$352$	4.78166	+	3.47408i	0.254863	+	0.185169i
$353$	−2.45186	+	7.54603i	−0.130499	+	0.401635i	−0.994863	−	0.101232i	$-0.967721\pi$
$353$	−2.45186	+	7.54603i	−0.130499	+	0.401635i	0.864364	+	0.502867i	$0.167721\pi$
$354$	0.911338	+	2.80481i	0.0484371	+	0.149074i
$355$	−4.55851	+	3.31195i	−0.241941	+	0.175780i
$356$	−4.18009	−	12.8650i	−0.221545	−	0.681844i
$357$	−0.272575	−	0.838900i	−0.0144262	−	0.0443993i
$358$	0.0645815	−	0.0469212i	0.00341324	−	0.00247986i
$359$	4.59394	+	14.1387i	0.242459	+	0.746212i	0.996044	+	0.0888618i	$0.0283229\pi$
$359$	4.59394	+	14.1387i	0.242459	+	0.746212i	−0.753585	+	0.657351i	$0.771677\pi$
$360$	0.309017	−	0.951057i	0.0162866	−	0.0501251i
$361$	14.9494	+	10.8614i	0.786810	+	0.571651i
$362$	−6.63869	+	20.4318i	−0.348922	+	1.07387i
$363$	−19.3626	+	14.0677i	−1.01627	+	0.738364i
$364$	0.0203860	−	0.0148113i	0.00106852	−	0.000776325i
$365$	−7.02631	−	5.10492i	−0.367774	−	0.267204i
$366$	−8.33985			−0.435931
$367$	−5.91628			−0.308828			−0.154414	−	0.988006i	$-0.549349\pi$
$367$	−5.91628			−0.308828			−0.154414	+	0.988006i	$0.549349\pi$
$368$	3.30922	+	2.40429i	0.172505	+	0.125332i
$369$	1.05858	+	3.25798i	0.0551075	+	0.169603i
$370$	−3.46369	+	10.6601i	−0.180069	+	0.554195i
$371$	−1.07917			−0.0560279
$372$	4.69088	−	2.99928i	0.243211	−	0.155505i
$373$	21.5106			1.11377			0.556887	−	0.830588i	$-0.311996\pi$
$373$	21.5106			1.11377			0.556887	+	0.830588i	$0.311996\pi$
$374$	14.0103	−	43.1193i	0.724456	−	2.22965i
$375$	−0.309017	−	0.951057i	−0.0159576	−	0.0491123i
$376$	−0.913479	−	0.663681i	−0.0471091	−	0.0342267i
$377$	−0.995505			−0.0512711
$378$	−0.114990			−0.00591444
$379$	6.29090	+	4.57060i	0.323142	+	0.234776i	0.737515	−	0.675331i	$-0.235999\pi$
$379$	6.29090	+	4.57060i	0.323142	+	0.234776i	−0.414373	+	0.910107i	$0.635999\pi$
$380$	−0.584257	+	0.424488i	−0.0299717	+	0.0217758i
$381$	−11.4050	+	8.28624i	−0.584297	+	0.424517i
$382$	−0.0725755	+	0.223365i	−0.00371329	+	0.0114283i
$383$	11.7059	+	8.50485i	0.598145	+	0.434578i	0.845220	−	0.534419i	$-0.179469\pi$
$383$	11.7059	+	8.50485i	0.598145	+	0.434578i	−0.247075	+	0.968996i	$0.579469\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−0.210021	−	0.646378i	−0.0107037	−	0.0329425i
$386$	−0.322736	+	0.234481i	−0.0164268	+	0.0119348i
$387$	0.732047	+	2.25301i	0.0372120	+	0.114527i
$388$	0.927668	+	2.85507i	0.0470952	+	0.144944i
$389$	14.1844	−	10.3056i	0.719180	−	0.522515i	−0.166942	−	0.985967i	$-0.553389\pi$
$389$	14.1844	−	10.3056i	0.719180	−	0.522515i	0.886122	+	0.463452i	$0.153389\pi$
$390$	−0.0677171	−	0.208412i	−0.00342899	−	0.0105533i
$391$	9.69605	−	29.8414i	0.490350	−	1.50914i
$392$	−5.65242	−	4.10672i	−0.285490	−	0.207421i
$393$	4.22217	−	12.9945i	0.212980	−	0.655486i
$394$	11.9693	−	8.69620i	0.603004	−	0.438108i
$395$	−0.118704	+	0.0862438i	−0.00597267	+	0.00433940i
$396$	−4.78166	−	3.47408i	−0.240287	−	0.174579i
$397$	13.7536			0.690275			0.345138	−	0.938552i	$-0.387832\pi$
$397$	13.7536			0.690275			0.345138	+	0.938552i	$0.387832\pi$
$398$	8.27286			0.414681
$399$	0.0671836	+	0.0488117i	0.00336339	+	0.00244364i
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−10.0785	+	31.0186i	−0.503298	+	1.54899i	0.300314	+	0.953840i	$0.402908\pi$
$401$	−10.0785	+	31.0186i	−0.503298	+	1.54899i	−0.803613	+	0.595153i	$0.797092\pi$
$402$	13.7930			0.687934
$403$	0.445302	−	1.13594i	0.0221821	−	0.0565852i
$404$	13.5005			0.671675
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	−0.161424	−	0.496813i	−0.00801136	−	0.0246564i
$407$	53.5963	+	38.9400i	2.65667	+	1.93018i
$408$	7.67087			0.379765
$409$	3.92458			0.194058			0.0970289	−	0.995282i	$-0.469066\pi$
$409$	3.92458			0.194058			0.0970289	+	0.995282i	$0.469066\pi$
$410$	−2.77140	−	2.01354i	−0.136870	−	0.0994417i
$411$	13.6020	−	9.88246i	0.670939	−	0.487466i
$412$	−10.3213	+	7.49884i	−0.508492	+	0.369441i
$413$	−0.104795	+	0.322525i	−0.00515661	+	0.0158704i
$414$	−3.30922	−	2.40429i	−0.162639	−	0.118164i
$415$	−2.78839	+	8.58179i	−0.136877	+	0.421263i
$416$	0.0677171	+	0.208412i	0.00332010	+	0.0102182i
$417$	−8.59815	+	6.24692i	−0.421053	+	0.305913i
$418$	1.31901	+	4.05951i	0.0645151	+	0.198557i
$419$	2.52642	+	7.77551i	0.123424	+	0.379859i	0.993611	−	0.112863i	$-0.0360021\pi$
$419$	2.52642	+	7.77551i	0.123424	+	0.379859i	−0.870187	+	0.492722i	$0.836002\pi$
$420$	0.0930287	−	0.0675893i	0.00453934	−	0.00329802i
$421$	3.42582	+	10.5436i	0.166964	+	0.513863i	0.999176	−	0.0405953i	$-0.0129254\pi$
$421$	3.42582	+	10.5436i	0.166964	+	0.513863i	−0.832211	+	0.554458i	$0.812925\pi$
$422$	−3.34950	+	10.3087i	−0.163051	+	0.501820i
$423$	0.913479	+	0.663681i	0.0444149	+	0.0322693i
$424$	2.90011	−	8.92561i	0.140842	−	0.433466i
$425$	6.20586	−	4.50882i	0.301029	−	0.218710i
$426$	−4.55851	+	3.31195i	−0.220861	+	0.160465i
$427$	−0.775846	−	0.563685i	−0.0375458	−	0.0272786i
$428$	16.1892			0.782533
$429$	−1.29520			−0.0625328
$430$	−1.91652	−	1.39244i	−0.0924229	−	0.0671492i
$431$	−0.235039	−	0.723375i	−0.0113214	−	0.0348438i	0.945236	−	0.326387i	$-0.105831\pi$
$431$	−0.235039	−	0.723375i	−0.0113214	−	0.0348438i	−0.956558	+	0.291543i	$0.905831\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	26.9477			1.29502			0.647511	−	0.762056i	$-0.275810\pi$
$433$	26.9477			1.29502			0.647511	+	0.762056i	$0.275810\pi$
$434$	0.639105	+	0.0380346i	0.0306780	+	0.00182572i
$435$	−4.54284			−0.217813
$436$	1.01182	−	3.11405i	0.0484572	−	0.149136i
$437$	0.912844	+	2.80944i	0.0436673	+	0.134394i
$438$	−7.02631	−	5.10492i	−0.335730	−	0.243922i
$439$	0.765930			0.0365559			0.0182779	−	0.999833i	$-0.494182\pi$
$439$	0.765930			0.0365559			0.0182779	+	0.999833i	$0.494182\pi$
$440$	5.91045			0.281770
$441$	5.65242	+	4.10672i	0.269163	+	0.195558i
$442$	1.35994	−	0.988051i	0.0646855	−	0.0469968i
$443$	−18.7162	+	13.5981i	−0.889235	+	0.646067i	−0.935678	−	0.352854i	$-0.885211\pi$
$443$	−18.7162	+	13.5981i	−0.889235	+	0.646067i	0.0464434	+	0.998921i	$0.485211\pi$
$444$	−3.46369	+	10.6601i	−0.164380	+	0.505908i
$445$	−10.9436	−	7.95101i	−0.518778	−	0.376914i
$446$	3.42449	−	10.5395i	0.162154	−	0.499059i
$447$	0.410926	+	1.26470i	0.0194361	+	0.0598183i
$448$	−0.0930287	+	0.0675893i	−0.00439519	+	0.00319330i
$449$	0.377280	+	1.16115i	0.0178050	+	0.0547980i	0.959564	−	0.281490i	$-0.0908285\pi$
$449$	0.377280	+	1.16115i	0.0178050	+	0.0547980i	−0.941759	+	0.336288i	$0.890829\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	−16.3802	+	11.9009i	−0.771315	+	0.560393i
$452$	3.69547	+	11.3735i	0.173820	+	0.534964i
$453$	7.34553	−	22.6072i	0.345123	−	1.06218i
$454$	−9.10921	−	6.61822i	−0.427516	−	0.310609i
$455$	0.00778678	−	0.0239652i	0.000365050	−	0.00112351i
$456$	−0.584257	+	0.424488i	−0.0273603	+	0.0198784i
$457$	8.25537	−	5.99788i	0.386170	−	0.280569i	−0.377714	−	0.925922i	$-0.623290\pi$
$457$	8.25537	−	5.99788i	0.386170	−	0.280569i	0.763884	+	0.645353i	$0.223290\pi$
$458$	−14.4442	−	10.4944i	−0.674935	−	0.490369i
$459$	−7.67087			−0.358046
$460$	4.09042			0.190717
$461$	−15.1986	−	11.0424i	−0.707869	−	0.514297i	0.174617	−	0.984636i	$-0.444131\pi$
$461$	−15.1986	−	11.0424i	−0.707869	−	0.514297i	−0.882485	+	0.470340i	$0.844131\pi$
$462$	−0.210021	−	0.646378i	−0.00977105	−	0.0300722i
$463$	2.48700	−	7.65421i	0.115581	−	0.355721i	−0.876487	−	0.481426i	$-0.840119\pi$
$463$	2.48700	−	7.65421i	0.115581	−	0.355721i	0.992068	+	0.125704i	$0.0401191\pi$
$464$	4.54284			0.210896
$465$	2.03207	−	5.18369i	0.0942351	−	0.240388i
$466$	−3.86985			−0.179267
$467$	−0.375552	+	1.15583i	−0.0173785	+	0.0534855i	−0.959370	−	0.282152i	$-0.908952\pi$
$467$	−0.375552	+	1.15583i	−0.0173785	+	0.0534855i	0.941991	+	0.335638i	$0.108952\pi$
$468$	−0.0677171	−	0.208412i	−0.00313022	−	0.00963384i
$469$	1.28315	+	0.932262i	0.0592503	+	0.0430479i
$470$	−1.12912			−0.0520825
$471$	17.7023			0.815681
$472$	−2.38591	−	1.73347i	−0.109821	−	0.0797894i
$473$	−11.3275	+	8.22992i	−0.520840	+	0.378412i
$474$	−0.118704	+	0.0862438i	−0.00545227	+	0.00396131i
$475$	−0.223166	+	0.686835i	−0.0102396	+	0.0315142i
$476$	0.713611	+	0.518469i	0.0327083	+	0.0237640i
$477$	−2.90011	+	8.92561i	−0.132787	+	0.408676i
$478$	−6.02217	−	18.5343i	−0.275448	−	0.847740i
$479$	22.2482	−	16.1643i	1.01655	−	0.738565i	0.0509752	−	0.998700i	$-0.483767\pi$
$479$	22.2482	−	16.1643i	1.01655	−	0.738565i	0.965572	+	0.260135i	$0.0837671\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	0.759023	+	2.33603i	0.0346085	+	0.106514i
$482$	9.22264	−	6.70064i	0.420080	−	0.305206i
$483$	−0.145348	−	0.447336i	−0.00661357	−	0.0203545i
$484$	7.39584	−	22.7620i	0.336174	−	1.03464i
$485$	2.42867	+	1.76453i	0.110280	+	0.0801231i
$486$	−0.309017	+	0.951057i	−0.0140173	+	0.0431408i
$487$	9.96097	−	7.23707i	0.451375	−	0.327943i	−0.338764	−	0.940871i	$-0.610009\pi$
$487$	9.96097	−	7.23707i	0.451375	−	0.327943i	0.790138	+	0.612929i	$0.210009\pi$
$488$	6.74708	−	4.90204i	0.305426	−	0.221905i
$489$	1.24688	+	0.905912i	0.0563859	+	0.0409667i
$490$	−6.98678			−0.315630
$491$	23.7912			1.07368			0.536840	−	0.843684i	$-0.319618\pi$
$491$	23.7912			1.07368			0.536840	+	0.843684i	$0.319618\pi$
$492$	−2.77140	−	2.01354i	−0.124944	−	0.0907774i
$493$	−10.7685	−	33.1420i	−0.484988	−	1.49264i
$494$	−0.0489040	+	0.150511i	−0.00220030	+	0.00677182i
$495$	−5.91045			−0.265655
$496$	−2.03207	+	5.18369i	−0.0912427	+	0.232755i
$497$	−0.647925			−0.0290634
$498$	−2.78839	+	8.58179i	−0.124951	+	0.384559i
$499$	3.97513	+	12.2342i	0.177951	+	0.547677i	0.999756	−	0.0220919i	$-0.00703264\pi$
$499$	3.97513	+	12.2342i	0.177951	+	0.547677i	−0.821805	+	0.569769i	$0.807033\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−1.02329			−0.0457173
$502$	−11.3558			−0.506834
$503$	9.20152	+	6.68529i	0.410275	+	0.298082i	0.773713	−	0.633536i	$-0.218397\pi$
$503$	9.20152	+	6.68529i	0.410275	+	0.298082i	−0.363438	+	0.931618i	$0.618397\pi$
$504$	0.0930287	−	0.0675893i	0.00414383	−	0.00301067i
$505$	10.9221	−	7.93540i	0.486029	−	0.353121i
$506$	7.47087	−	22.9930i	0.332121	−	1.02216i
$507$	10.4784	+	7.61298i	0.465361	+	0.338104i
$508$	4.35633	−	13.4074i	0.193281	−	0.594858i
$509$	5.42197	+	16.6871i	0.240324	+	0.739643i	0.996370	+	0.0851241i	$0.0271287\pi$
$509$	5.42197	+	16.6871i	0.240324	+	0.739643i	−0.756046	+	0.654519i	$0.772871\pi$
$510$	6.20586	−	4.50882i	0.274800	−	0.199654i
$511$	−0.308611	−	0.949808i	−0.0136522	−	0.0420170i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	0.584257	−	0.424488i	0.0257956	−	0.0187416i
$514$	−6.18952	−	19.0494i	−0.273008	−	0.840232i
$515$	−3.94237	+	12.1334i	−0.173722	+	0.534661i
$516$	−1.91652	−	1.39244i	−0.0843702	−	0.0612986i
$517$	−2.06226	+	6.34699i	−0.0906982	+	0.279140i
$518$	−1.04273	+	0.757591i	−0.0458151	+	0.0332866i
$519$	18.5582	−	13.4833i	0.814615	−	0.591852i
$520$	0.177286	+	0.128806i	0.00777449	+	0.00564850i
$521$	−22.4861			−0.985133			−0.492566	−	0.870275i	$-0.663941\pi$
$521$	−22.4861			−0.985133			−0.492566	+	0.870275i	$0.663941\pi$
$522$	−4.54284			−0.198835
$523$	−34.7453	−	25.2439i	−1.51930	−	1.10384i	−0.961831	−	0.273644i	$-0.911771\pi$
$523$	−34.7453	−	25.2439i	−1.51930	−	1.10384i	−0.557473	−	0.830195i	$-0.688229\pi$
$524$	4.22217	+	12.9945i	0.184446	+	0.567668i
$525$	0.0355338	−	0.109362i	0.00155082	−	0.00477294i
$526$	−1.27806			−0.0557261
$527$	42.6342	+	2.53726i	1.85717	+	0.110525i
$528$	5.91045			0.257219
$529$	−1.93706	+	5.96166i	−0.0842200	+	0.259203i
$530$	−2.90011	−	8.92561i	−0.125973	−	0.387704i
$531$	2.38591	+	1.73347i	0.103540	+	0.0752261i
$532$	−0.0830435			−0.00360039
$533$	−0.750685			−0.0325158
$534$	−10.9436	−	7.95101i	−0.473577	−	0.344074i
$535$	13.0973	−	9.51575i	0.566246	−	0.411402i
$536$	−11.1588	+	8.10735i	−0.481987	+	0.350184i
$537$	0.0246679	−	0.0759201i	0.00106450	−	0.00327620i
$538$	−3.36463	−	2.44455i	−0.145060	−	0.105392i
$539$	−12.7609	+	39.2739i	−0.549649	+	1.69165i
$540$	−0.309017	−	0.951057i	−0.0132980	−	0.0409270i
$541$	33.2081	−	24.1271i	1.42773	−	1.03731i	0.437295	−	0.899318i	$-0.355936\pi$
$541$	33.2081	−	24.1271i	1.42773	−	1.03731i	0.990434	−	0.137988i	$-0.0440635\pi$
$542$	−8.72632	−	26.8569i	−0.374828	−	1.15360i
$543$	6.63869	+	20.4318i	0.284893	+	0.876811i
$544$	−6.20586	+	4.50882i	−0.266074	+	0.193314i
$545$	−1.01182	−	3.11405i	−0.0433414	−	0.133391i
$546$	0.00778678	−	0.0239652i	0.000333243	−	0.00102562i
$547$	−21.9381	−	15.9390i	−0.938005	−	0.681501i	0.00993438	−	0.999951i	$-0.496838\pi$
$547$	−21.9381	−	15.9390i	−0.938005	−	0.681501i	−0.947940	+	0.318450i	$0.896838\pi$
$548$	−5.19552	+	15.9902i	−0.221941	+	0.683066i
$549$	−6.74708	+	4.90204i	−0.287958	+	0.209214i
$550$	4.78166	−	3.47408i	0.203890	−	0.148135i
$551$	2.65419	+	1.92838i	0.113072	+	0.0821517i
$552$	4.09042			0.174100
$553$	−0.0168721			−0.000717474
$554$	11.4302	+	8.30454i	0.485623	+	0.352826i
$555$	3.46369	+	10.6601i	0.147025	+	0.452498i
$556$	3.28420	−	10.1077i	0.139281	−	0.428663i
$557$	36.6109			1.55125			0.775627	−	0.631192i	$-0.217434\pi$
$557$	36.6109			1.55125			0.775627	+	0.631192i	$0.217434\pi$
$558$	2.03207	−	5.18369i	0.0860244	−	0.219443i
$559$	−0.519126			−0.0219567
$560$	−0.0355338	+	0.109362i	−0.00150158	+	0.00462138i
$561$	−14.0103	−	43.1193i	−0.591516	−	1.82050i
$562$	−3.31813	−	2.41076i	−0.139967	−	0.101692i
$563$	38.1521			1.60792			0.803961	−	0.594683i	$-0.202722\pi$
$563$	38.1521			1.60792			0.803961	+	0.594683i	$0.202722\pi$
$564$	−1.12912			−0.0475446
$565$	9.67487	+	7.02920i	0.407025	+	0.295721i
$566$	−12.6973	+	9.22512i	−0.533707	+	0.387761i
$567$	−0.0930287	+	0.0675893i	−0.00390684	+	0.00283848i
$568$	1.74120	−	5.35885i	0.0730590	−	0.224852i
$569$	31.0227	+	22.5393i	1.30054	+	0.944898i	0.999961	−	0.00885810i	$-0.00281966\pi$
$569$	31.0227	+	22.5393i	1.30054	+	0.944898i	0.300580	+	0.953757i	$0.402820\pi$
$570$	−0.223166	+	0.686835i	−0.00934741	+	0.0287684i
$571$	6.95290	+	21.3988i	0.290970	+	0.895513i	0.984545	+	0.175129i	$0.0560343\pi$
$571$	6.95290	+	21.3988i	0.290970	+	0.895513i	−0.693576	+	0.720384i	$0.743966\pi$
$572$	1.04784	−	0.761299i	0.0438123	−	0.0318315i
$573$	0.0725755	+	0.223365i	0.00303189	+	0.00933119i
$574$	−0.121726	−	0.374634i	−0.00508075	−	0.0156369i
$575$	3.30922	−	2.40429i	0.138004	−	0.100266i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	3.08339	−	9.48969i	0.128363	−	0.395061i	−0.866136	−	0.499809i	$-0.833404\pi$
$577$	3.08339	−	9.48969i	0.128363	−	0.395061i	0.994499	+	0.104748i	$0.0334036\pi$
$578$	33.8511	+	24.5943i	1.40802	+	1.02299i
$579$	−0.123274	+	0.379399i	−0.00512310	+	0.0157673i
$580$	3.67524	−	2.67022i	0.152606	−	0.110875i
$581$	−0.839438	+	0.609887i	−0.0348257	+	0.0253024i
$582$	2.42867	+	1.76453i	0.100671	+	0.0731421i
$583$	−55.4693			−2.29730
$584$	8.68500			0.359388
$585$	−0.177286	−	0.128806i	−0.00732986	−	0.00532546i
$586$	10.5389	+	32.4354i	0.435359	+	1.33990i
$587$	5.76966	−	17.7572i	0.238139	−	0.732917i	−0.758550	−	0.651615i	$-0.774092\pi$
$587$	5.76966	−	17.7572i	0.238139	−	0.732917i	0.996689	−	0.0813027i	$-0.0259080\pi$
$588$	−6.98678			−0.288130
$589$	−3.38767	+	2.16602i	−0.139586	+	0.0892493i
$590$	−2.94915			−0.121415
$591$	4.57186	−	14.0707i	0.188061	−	0.578793i
$592$	−3.46369	−	10.6601i	−0.142357	−	0.438129i
$593$	19.7487	+	14.3483i	0.810983	+	0.589213i	0.914115	−	0.405454i	$-0.132887\pi$
$593$	19.7487	+	14.3483i	0.810983	+	0.589213i	−0.103133	+	0.994668i	$0.532887\pi$
$594$	−5.91045			−0.242509
$595$	0.882072			0.0361614
$596$	−1.07582	−	0.781628i	−0.0440672	−	0.0320167i
$597$	6.69288	−	4.86266i	0.273921	−	0.199016i
$598$	0.725173	−	0.526869i	0.0296545	−	0.0215453i
$599$	7.16565	−	22.0536i	0.292781	−	0.901086i	−0.691177	−	0.722685i	$-0.742908\pi$
$599$	7.16565	−	22.0536i	0.292781	−	0.901086i	0.983958	−	0.178401i	$-0.0570924\pi$
$600$	0.809017	+	0.587785i	0.0330280	+	0.0239962i
$601$	−10.6759	+	32.8570i	−0.435479	+	1.34027i	0.457117	+	0.889407i	$0.348882\pi$
$601$	−10.6759	+	32.8570i	−0.435479	+	1.34027i	−0.892595	+	0.450859i	$0.851118\pi$
$602$	−0.0841779	−	0.259073i	−0.00343084	−	0.0105590i
$603$	11.1588	−	8.10735i	0.454422	−	0.330157i
$604$	7.34553	+	22.6072i	0.298885	+	0.919874i
$605$	−7.39584	−	22.7620i	−0.300684	−	0.925409i
$606$	10.9221	−	7.93540i	0.443681	−	0.322353i
$607$	−1.34037	−	4.12522i	−0.0544038	−	0.167438i	0.920163	−	0.391536i	$-0.128056\pi$
$607$	−1.34037	−	4.12522i	−0.0544038	−	0.167438i	−0.974566	+	0.224099i	$0.928056\pi$
$608$	0.223166	−	0.686835i	0.00905059	−	0.0278548i
$609$	−0.422615	−	0.307048i	−0.0171252	−	0.0124422i
$610$	2.57716	−	7.93167i	0.104346	−	0.321144i
$611$	−0.200177	+	0.145437i	−0.00809830	+	0.00588376i
$612$	6.20586	−	4.50882i	0.250857	−	0.182258i
$613$	12.0708	+	8.76998i	0.487537	+	0.354216i	0.804236	−	0.594310i	$-0.202575\pi$
$613$	12.0708	+	8.76998i	0.487537	+	0.354216i	−0.316699	+	0.948526i	$0.602575\pi$
$614$	−26.1189			−1.05407
$615$	−3.42564			−0.138135
$616$	0.549842	+	0.399483i	0.0221538	+	0.0160956i
$617$	1.39958	+	4.30746i	0.0563449	+	0.173412i	0.975268	−	0.221024i	$-0.0709400\pi$
$617$	1.39958	+	4.30746i	0.0563449	+	0.173412i	−0.918923	+	0.394436i	$0.870940\pi$
$618$	−3.94237	+	12.1334i	−0.158586	+	0.488076i
$619$	−35.2018			−1.41488			−0.707439	−	0.706774i	$-0.750150\pi$
$619$	−35.2018			−1.41488			−0.707439	+	0.706774i	$0.750150\pi$
$620$	1.40292	+	5.38812i	0.0563426	+	0.216392i
$621$	−4.09042			−0.164143
$622$	−7.84758	+	24.1524i	−0.314659	+	0.968422i
$623$	−0.480668	−	1.47934i	−0.0192576	−	0.0592687i
$624$	0.177286	+	0.128806i	0.00709711	+	0.00515635i
$625$	1.00000			0.0400000
$626$	−19.2729			−0.770300
$627$	3.45322	+	2.50891i	0.137908	+	0.100196i
$628$	−14.3215	+	10.4052i	−0.571490	+	0.415212i
$629$	−69.5599	+	50.5382i	−2.77354	+	2.01509i
$630$	0.0355338	−	0.109362i	0.00141570	−	0.00435708i
$631$	19.3039	+	14.0251i	0.768476	+	0.558331i	0.901498	−	0.432782i	$-0.142468\pi$
$631$	19.3039	+	14.0251i	0.768476	+	0.558331i	−0.133022	+	0.991113i	$0.542468\pi$
$632$	0.0453410	−	0.139545i	0.00180357	−	0.00555082i
$633$	3.34950	+	10.3087i	0.133131	+	0.409734i
$634$	−3.09305	+	2.24724i	−0.122841	+	0.0892491i
$635$	−4.35633	−	13.4074i	−0.172876	−	0.532057i
$636$	−2.90011	−	8.92561i	−0.114997	−	0.353924i
$637$	−1.23866	+	0.899936i	−0.0490773	+	0.0356568i
$638$	−8.29718	−	25.5361i	−0.328489	−	1.01098i
$639$	−1.74120	+	5.35885i	−0.0688806	+	0.211993i
$640$	−0.809017	−	0.587785i	−0.0319792	−	0.0232343i
$641$	5.44345	−	16.7532i	0.215003	−	0.661712i	−0.784150	−	0.620571i	$-0.786901\pi$
$641$	5.44345	−	16.7532i	0.215003	−	0.661712i	0.999153	−	0.0411407i	$-0.0130992\pi$
$642$	13.0973	−	9.51575i	0.516910	−	0.375557i
$643$	−0.481095	+	0.349536i	−0.0189726	+	0.0137844i	−0.597231	−	0.802069i	$-0.703732\pi$
$643$	−0.481095	+	0.349536i	−0.0189726	+	0.0137844i	0.578259	+	0.815854i	$0.303732\pi$
$644$	0.380527	+	0.276469i	0.0149948	+	0.0108944i
$645$	−2.36895			−0.0932774
$646$	−5.53976			−0.217959
$647$	−5.90767	−	4.29218i	−0.232255	−	0.168743i	0.465571	−	0.885011i	$-0.345849\pi$
$647$	−5.90767	−	4.29218i	−0.232255	−	0.168743i	−0.697826	+	0.716268i	$0.745849\pi$
$648$	−0.309017	−	0.951057i	−0.0121393	−	0.0373610i
$649$	−5.38642	+	16.5777i	−0.211436	+	0.650732i
$650$	0.219137			0.00859527
$651$	0.539403	−	0.344886i	0.0211409	−	0.0135172i
$652$	−1.54123			−0.0603592
$653$	12.7860	−	39.3513i	0.500356	−	1.53994i	−0.308085	−	0.951359i	$-0.599688\pi$
$653$	12.7860	−	39.3513i	0.500356	−	1.53994i	0.808441	−	0.588578i	$-0.200312\pi$
$654$	−1.01182	−	3.11405i	−0.0395651	−	0.121769i
$655$	11.0538	+	8.03105i	0.431907	+	0.313799i
$656$	3.42564			0.133749
$657$	−8.68500			−0.338834
$658$	−0.105041	−	0.0763166i	−0.00409492	−	0.00297513i
$659$	−32.6187	+	23.6988i	−1.27064	+	0.923176i	−0.999228	−	0.0392865i	$-0.987491\pi$
$659$	−32.6187	+	23.6988i	−1.27064	+	0.923176i	−0.271415	+	0.962462i	$0.587491\pi$
$660$	4.78166	−	3.47408i	0.186126	−	0.135228i
$661$	1.28330	−	3.94960i	0.0499147	−	0.153622i	−0.922992	−	0.384818i	$-0.874264\pi$
$661$	1.28330	−	3.94960i	0.0499147	−	0.153622i	0.972907	+	0.231197i	$0.0742641\pi$
$662$	3.71674	+	2.70037i	0.144455	+	0.104953i
$663$	0.519449	−	1.59870i	0.0201737	−	0.0620884i
$664$	−2.78839	−	8.58179i	−0.108211	−	0.333038i
$665$	−0.0671836	+	0.0488117i	−0.00260527	+	0.00189284i
$666$	3.46369	+	10.6601i	0.134215	+	0.413072i
$667$	−5.74219	−	17.6727i	−0.222339	−	0.684288i
$668$	0.827860	−	0.601476i	0.0320309	−	0.0232718i
$669$	−3.42449	−	10.5395i	−0.132398	−	0.407480i
$670$	−4.26228	+	13.1180i	−0.164666	+	0.506791i
$671$	−39.8783	−	28.9733i	−1.53948	−	1.11850i
$672$	−0.0355338	+	0.109362i	−0.00137075	+	0.00421872i
$673$	−27.4966	+	19.9774i	−1.05991	+	0.770073i	−0.974073	−	0.226235i	$-0.927358\pi$
$673$	−27.4966	+	19.9774i	−1.05991	+	0.770073i	−0.0858423	+	0.996309i	$0.527358\pi$
$674$	16.8309	−	12.2284i	0.648304	−	0.471020i
$675$	−0.809017	−	0.587785i	−0.0311391	−	0.0226239i
$676$	−12.9520			−0.498153
$677$	21.4488			0.824346			0.412173	−	0.911106i	$-0.364770\pi$
$677$	21.4488			0.824346			0.412173	+	0.911106i	$0.364770\pi$
$678$	9.67487	+	7.02920i	0.371561	+	0.269955i
$679$	0.106672	+	0.328304i	0.00409371	+	0.0125991i
$680$	−2.37043	+	7.29543i	−0.0909018	+	0.279767i
$681$	−11.2596			−0.431469
$682$	32.8499	+	1.95497i	1.25789	+	0.0748597i
$683$	−31.9991			−1.22441			−0.612206	−	0.790699i	$-0.709718\pi$
$683$	−31.9991			−1.22441			−0.612206	+	0.790699i	$0.709718\pi$
$684$	−0.223166	+	0.686835i	−0.00853298	+	0.0262618i
$685$	5.19552	+	15.9902i	0.198511	+	0.610953i
$686$	−1.30117	−	0.945357i	−0.0496790	−	0.0360939i
$687$	−17.8541			−0.681175
$688$	2.36895			0.0903155
$689$	−1.66382	−	1.20883i	−0.0633864	−	0.0460529i
$690$	3.30922	−	2.40429i	0.125980	−	0.0915297i
$691$	0.277693	−	0.201756i	0.0105639	−	0.00767514i	−0.582491	−	0.812837i	$-0.697922\pi$
$691$	0.277693	−	0.201756i	0.0105639	−	0.00767514i	0.593055	+	0.805162i	$0.297922\pi$
$692$	−7.08860	+	21.8165i	−0.269468	+	0.829338i
$693$	−0.549842	−	0.399483i	−0.0208868	−	0.0151751i
$694$	3.54542	−	10.9117i	0.134582	−	0.414201i
$695$	−3.28420	−	10.1077i	−0.124577	−	0.383408i
$696$	3.67524	−	2.67022i	0.139309	−	0.101214i
$697$	−8.12023	−	24.9915i	−0.307576	−	0.946621i
$698$	1.38722	+	4.26941i	0.0525069	+	0.161600i
$699$	−3.13077	+	2.27464i	−0.118417	+	0.0860348i
$700$	0.0355338	+	0.109362i	0.00134305	+	0.00413349i
$701$	−7.68125	+	23.6405i	−0.290117	+	0.892888i	0.694701	+	0.719299i	$0.255537\pi$
$701$	−7.68125	+	23.6405i	−0.290117	+	0.892888i	−0.984818	+	0.173590i	$0.944463\pi$
$702$	−0.177286	−	0.128806i	−0.00669122	−	0.00486145i
$703$	2.50141	−	7.69856i	0.0943426	−	0.290357i
$704$	−4.78166	+	3.47408i	−0.180215	+	0.130934i
$705$	−0.913479	+	0.663681i	−0.0344036	+	0.0249957i
$706$	−6.41904	−	4.66371i	−0.241584	−	0.175521i
$707$	1.55242			0.0583848
$708$	−2.94915			−0.110836
$709$	22.3915	+	16.2683i	0.840929	+	0.610970i	0.922630	−	0.385686i	$-0.126035\pi$
$709$	22.3915	+	16.2683i	0.840929	+	0.610970i	−0.0817012	+	0.996657i	$0.526035\pi$
$710$	−1.74120	−	5.35885i	−0.0653459	−	0.201114i
$711$	−0.0453410	+	0.139545i	−0.00170042	+	0.00523336i
$712$	13.5271			0.506948
$713$	22.7343	+	1.35297i	0.851405	+	0.0506691i
$714$	0.882072			0.0330107
$715$	0.400239	−	1.23181i	0.0149681	−	0.0460670i
$716$	0.0246679	+	0.0759201i	0.000921884	+	0.00283727i
$717$	−15.7662	−	11.4548i	−0.588801	−	0.427789i
$718$	−14.8663			−0.554806
$719$	24.6479			0.919210			0.459605	−	0.888123i	$-0.347991\pi$
$719$	24.6479			0.919210			0.459605	+	0.888123i	$0.347991\pi$
$720$	0.809017	+	0.587785i	0.0301503	+	0.0219055i
$721$	−1.18684	+	0.862290i	−0.0442003	+	0.0321134i
$722$	−14.9494	+	10.8614i	−0.556358	+	0.404218i
$723$	3.52273	−	10.8419i	0.131012	−	0.403213i
$724$	−17.3803	−	12.6275i	−0.645934	−	0.469298i
$725$	1.40382	−	4.32050i	0.0521364	−	0.160459i
$726$	−7.39584	−	22.7620i	−0.274485	−	0.844779i
$727$	−36.8708	+	26.7882i	−1.36746	+	0.993518i	−0.369530	+	0.929219i	$0.620481\pi$
$727$	−36.8708	+	26.7882i	−1.36746	+	0.993518i	−0.997931	+	0.0642994i	$0.979519\pi$
$728$	0.00778678	+	0.0239652i	0.000288597	+	0.000888211i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	7.02631	−	5.10492i	0.260056	−	0.188941i
$731$	−5.61543	−	17.2825i	−0.207694	−	0.639217i
$732$	2.57716	−	7.93167i	0.0952544	−	0.293163i
$733$	−2.74566	−	1.99484i	−0.101413	−	0.0736811i	0.535923	−	0.844267i	$-0.319964\pi$
$733$	−2.74566	−	1.99484i	−0.101413	−	0.0736811i	−0.637336	+	0.770586i	$0.719964\pi$
$734$	1.82823	−	5.62672i	0.0674813	−	0.207686i
$735$	−5.65242	+	4.10672i	−0.208493	+	0.151479i
$736$	−3.30922	+	2.40429i	−0.121979	+	0.0886233i
$737$	65.9536	+	47.9181i	2.42943	+	1.76509i
$738$	−3.42564			−0.126100
$739$	14.0026			0.515094			0.257547	−	0.966266i	$-0.417086\pi$
$739$	14.0026			0.515094			0.257547	+	0.966266i	$0.417086\pi$
$740$	−9.06806	−	6.58833i	−0.333349	−	0.242192i
$741$	0.0489040	+	0.150511i	0.00179653	+	0.00552916i
$742$	0.333483	−	1.02635i	0.0122425	−	0.0376787i
$743$	−32.3049			−1.18515			−0.592576	−	0.805515i	$-0.701889\pi$
$743$	−32.3049			−1.18515			−0.592576	+	0.805515i	$0.701889\pi$
$744$	1.40292	+	5.38812i	0.0514335	+	0.197538i
$745$	−1.32978			−0.0487195
$746$	−6.64713	+	20.4578i	−0.243369	+	0.749011i
$747$	2.78839	+	8.58179i	0.102022	+	0.313991i
$748$	36.6795	+	26.6492i	1.34113	+	0.974391i
$749$	1.86159			0.0680210
$750$	1.00000			0.0365148
$751$	10.9530	+	7.95779i	0.399679	+	0.290384i	0.769410	−	0.638755i	$-0.220550\pi$
$751$	10.9530	+	7.95779i	0.399679	+	0.290384i	−0.369731	+	0.929139i	$0.620550\pi$
$752$	0.913479	−	0.663681i	0.0333111	−	0.0242020i
$753$	−9.18703	+	6.67477i	−0.334794	+	0.243242i
$754$	0.307628	−	0.946782i	0.0112032	−	0.0344798i
$755$	19.2308	+	13.9720i	0.699882	+	0.508494i
$756$	0.0355338	−	0.109362i	0.00129235	−	0.00397745i
$757$	−10.3107	−	31.7332i	−0.374750	−	1.15336i	−0.943647	−	0.330953i	$-0.892630\pi$
$757$	−10.3107	−	31.7332i	−0.374750	−	1.15336i	0.568898	−	0.822408i	$-0.307370\pi$
$758$	−6.29090	+	4.57060i	−0.228496	+	0.166012i
$759$	−7.47087	−	22.9930i	−0.271175	−	0.834592i
$760$	−0.223166	−	0.686835i	−0.00809509	−	0.0249141i
$761$	14.6923	−	10.6746i	0.532595	−	0.386953i	−0.288733	−	0.957410i	$-0.593234\pi$
$761$	14.6923	−	10.6746i	0.532595	−	0.386953i	0.821328	+	0.570457i	$0.193234\pi$
$762$	−4.35633	−	13.4074i	−0.157813	−	0.485699i
$763$	0.116349	−	0.358084i	0.00421210	−	0.0129635i
$764$	−0.190005	−	0.138047i	−0.00687415	−	0.00499436i
$765$	2.37043	−	7.29543i	0.0857030	−	0.263767i
$766$	−11.7059	+	8.50485i	−0.422952	+	0.307293i
$767$	−0.522843	+	0.379867i	−0.0188788	+	0.0137162i
$768$	−0.809017	−	0.587785i	−0.0291929	−	0.0212099i
$769$	21.8977			0.789651			0.394825	−	0.918756i	$-0.370805\pi$
$769$	21.8977			0.789651			0.394825	+	0.918756i	$0.370805\pi$
$770$	0.679642			0.0244926
$771$	−16.2044	−	11.7732i	−0.583586	−	0.424000i
$772$	−0.123274	−	0.379399i	−0.00443673	−	0.0136549i
$773$	6.49584	−	19.9922i	0.233639	−	0.719068i	−0.763660	−	0.645619i	$-0.776599\pi$
$773$	6.49584	−	19.9922i	0.233639	−	0.719068i	0.997299	−	0.0734488i	$-0.0234006\pi$
$774$	−2.36895			−0.0851502
$775$	4.30204	+	3.53446i	0.154534	+	0.126962i
$776$	−3.00200			−0.107765
$777$	−0.398289	+	1.22581i	−0.0142885	+	0.0439756i
$778$	5.41797	+	16.6748i	0.194244	+	0.597821i
$779$	2.00145	+	1.45414i	0.0717095	+	0.0521000i
$780$	0.219137			0.00784637
$781$	−33.3032			−1.19168
$782$	25.3846	+	18.4430i	0.907751	+	0.659520i
$783$	−3.67524	+	2.67022i	−0.131342	+	0.0954257i
$784$	5.65242	−	4.10672i	0.201872	−	0.146669i
$785$	−5.47032	+	16.8359i	−0.195244	+	0.600900i
$786$	11.0538	+	8.03105i	0.394275	+	0.286458i
$787$	15.1603	−	46.6587i	0.540408	−	1.66320i	−0.191258	−	0.981540i	$-0.561257\pi$
$787$	15.1603	−	46.6587i	0.540408	−	1.66320i	0.731666	−	0.681664i	$-0.238743\pi$
$788$	4.57186	+	14.0707i	0.162866	+	0.501249i
$789$	−1.03397	+	0.751226i	−0.0368104	+	0.0267443i
$790$	−0.0453410	−	0.139545i	−0.00161316	−	0.00496480i
$791$	0.424942	+	1.30784i	0.0151092	+	0.0465013i
$792$	4.78166	−	3.47408i	0.169909	−	0.123446i
$793$	−0.564751	−	1.73812i	−0.0200549	−	0.0617226i
$794$	−4.25011	+	13.0805i	−0.150831	+	0.464209i
$795$	−7.59258	−	5.51633i	−0.269281	−	0.195644i
$796$	−2.55645	+	7.86795i	−0.0906111	+	0.278872i
$797$	−2.45193	+	1.78143i	−0.0868518	+	0.0631015i	−0.630364	−	0.776300i	$-0.717094\pi$
$797$	−2.45193	+	1.78143i	−0.0868518	+	0.0631015i	0.543512	+	0.839401i	$0.317094\pi$
$798$	−0.0671836	+	0.0488117i	−0.00237827	+	0.00172792i
$799$	−7.00718	−	5.09101i	−0.247896	−	0.180107i
$800$	−1.00000			−0.0353553
$801$	−13.5271			−0.477955
$802$	−26.3860	−	19.1705i	−0.931721	−	0.676935i
$803$	−15.8625	−	48.8199i	−0.559777	−	1.72282i
$804$	−4.26228	+	13.1180i	−0.150319	+	0.462635i
$805$	0.470357			0.0165779
$806$	0.942737	+	0.774532i	0.0332065	+	0.0272817i
$807$	−4.15892			−0.146401
$808$	−4.17188	+	12.8397i	−0.146766	+	0.451701i
$809$	−11.4879	−	35.3561i	−0.403893	−	1.24305i	−0.921816	−	0.387628i	$-0.873295\pi$
$809$	−11.4879	−	35.3561i	−0.403893	−	1.24305i	0.517923	−	0.855427i	$-0.326705\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	6.55499			0.230177			0.115088	−	0.993355i	$-0.463285\pi$
$811$	6.55499			0.230177			0.115088	+	0.993355i	$0.463285\pi$
$812$	0.522381			0.0183320
$813$	−22.8458	−	16.5984i	−0.801237	−	0.582133i
$814$	−53.5963	+	38.9400i	−1.87855	+	1.36485i
$815$	−1.24688	+	0.905912i	−0.0436763	+	0.0317327i
$816$	−2.37043	+	7.29543i	−0.0829816	+	0.255391i
$817$	1.38408	+	1.00559i	0.0484227	+	0.0351812i
$818$	−1.21276	+	3.73249i	−0.0424032	+	0.130504i
$819$	−0.00778678	−	0.0239652i	−0.000272092	−	0.000837413i
$820$	2.77140	−	2.01354i	0.0967815	−	0.0703159i
$821$	−4.30702	−	13.2557i	−0.150316	−	0.462626i	0.847340	−	0.531051i	$-0.178203\pi$
$821$	−4.30702	−	13.2557i	−0.150316	−	0.462626i	−0.997656	+	0.0684251i	$0.978203\pi$
$822$	5.19552	+	15.9902i	0.181214	+	0.557721i
$823$	37.4991	−	27.2447i	1.30714	−	0.949690i	0.307138	−	0.951665i	$-0.400629\pi$
$823$	37.4991	−	27.2447i	1.30714	−	0.949690i	0.999998	+	0.00197544i	$0.000628802\pi$
$824$	−3.94237	−	12.1334i	−0.137339	−	0.422686i
$825$	1.82643	−	5.62117i	0.0635881	−	0.195704i
$826$	−0.274356	−	0.199331i	−0.00954606	−	0.00693562i
$827$	−10.2340	+	31.4971i	−0.355873	+	1.09526i	0.599629	+	0.800278i	$0.295315\pi$
$827$	−10.2340	+	31.4971i	−0.355873	+	1.09526i	−0.955502	+	0.294985i	$0.904685\pi$
$828$	3.30922	−	2.40429i	0.115003	−	0.0835548i
$829$	−14.5356	+	10.5607i	−0.504842	+	0.366789i	−0.810863	−	0.585235i	$-0.801002\pi$
$829$	−14.5356	+	10.5607i	−0.504842	+	0.366789i	0.306021	+	0.952025i	$0.401002\pi$
$830$	−7.30010	−	5.30384i	−0.253390	−	0.184099i
$831$	14.1285			0.490113
$832$	−0.219137			−0.00759721
$833$	−43.3590	−	31.5022i	−1.50230	−	1.09148i
$834$	−3.28420	−	10.1077i	−0.113723	−	0.350002i
$835$	0.316215	−	0.973208i	0.0109431	−	0.0336793i
$836$	−4.26842			−0.147626
$837$	−1.40292	−	5.38812i	−0.0484920	−	0.186241i
$838$	−8.17566			−0.282423
$839$	−3.47704	+	10.7012i	−0.120041	+	0.369448i	−0.992965	−	0.118408i	$-0.962221\pi$
$839$	−3.47704	+	10.7012i	−0.120041	+	0.369448i	0.872924	+	0.487856i	$0.162221\pi$
$840$	0.0355338	+	0.109362i	0.00122603	+	0.00377334i
$841$	6.76548	+	4.91541i	0.233292	+	0.169497i
$842$	−11.0862			−0.382055
$843$	−4.10143			−0.141261
$844$	−8.76910	−	6.37113i	−0.301845	−	0.219303i
$845$	−10.4784	+	7.61298i	−0.360467	+	0.261895i
$846$	−0.913479	+	0.663681i	−0.0314061	+	0.0228178i
$847$	0.850446	−	2.61740i	0.0292217	−	0.0899351i
$848$	7.59258	+	5.51633i	0.260730	+	0.189432i
$849$	−4.84993	+	14.9266i	−0.166449	+	0.512278i
$850$	2.37043	+	7.29543i	0.0813050	+	0.250231i
$851$	−37.0922	+	26.9490i	−1.27150	+	0.923801i
$852$	−1.74120	−	5.35885i	−0.0596524	−	0.183591i
$853$	−10.9562	−	33.7197i	−0.375133	−	1.15454i	−0.943389	−	0.331689i	$-0.892382\pi$
$853$	−10.9562	−	33.7197i	−0.375133	−	1.15454i	0.568256	−	0.822852i	$-0.307618\pi$
$854$	0.775846	−	0.563685i	0.0265489	−	0.0192889i
$855$	0.223166	+	0.686835i	0.00763213	+	0.0234893i
$856$	−5.00273	+	15.3968i	−0.170990	+	0.526252i
$857$	−8.00373	−	5.81505i	−0.273402	−	0.198638i	0.442632	−	0.896703i	$-0.354045\pi$
$857$	−8.00373	−	5.81505i	−0.273402	−	0.198638i	−0.716034	+	0.698065i	$0.754045\pi$
$858$	0.400239	−	1.23181i	0.0136639	−	0.0420532i
$859$	−43.7973	+	31.8206i	−1.49434	+	1.08570i	−0.521775	+	0.853083i	$0.674730\pi$
$859$	−43.7973	+	31.8206i	−1.49434	+	1.08570i	−0.972568	+	0.232621i	$0.925270\pi$
$860$	1.91652	−	1.39244i	0.0653529	−	0.0474817i
$861$	−0.318683	−	0.231537i	−0.0108607	−	0.00789075i
$862$	0.760602			0.0259062
$863$	0.702544			0.0239149			0.0119574	−	0.999929i	$-0.496194\pi$
$863$	0.702544			0.0239149			0.0119574	+	0.999929i	$0.496194\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	7.08860	+	21.8165i	0.241020	+	0.741782i
$866$	−8.32729	+	25.6288i	−0.282973	+	0.870901i
$867$	41.8422			1.42104
$868$	−0.233668	+	0.596072i	−0.00793119	+	0.0202320i
$869$	−0.867221			−0.0294185
$870$	1.40382	−	4.32050i	0.0475938	−	0.146479i
$871$	0.934025	+	2.87463i	0.0316482	+	0.0974032i
$872$	2.64897	+	1.92459i	0.0897054	+	0.0651748i
$873$	3.00200			0.101602
$874$	−2.95403			−0.0999214
$875$	0.0930287	+	0.0675893i	0.00314494	+	0.00228494i
$876$	7.02631	−	5.10492i	0.237397	−	0.172479i
$877$	1.30938	−	0.951319i	0.0442146	−	0.0321238i	−0.565458	−	0.824777i	$-0.691301\pi$
$877$	1.30938	−	0.951319i	0.0442146	−	0.0321238i	0.609673	+	0.792653i	$0.291301\pi$
$878$	−0.236685	+	0.728443i	−0.00798775	+	0.0245838i
$879$	27.5912	+	20.0462i	0.930629	+	0.676142i
$880$	−1.82643	+	5.62117i	−0.0615689	+	0.189490i
$881$	−2.90576	−	8.94301i	−0.0978975	−	0.301298i	0.890100	−	0.455764i	$-0.150634\pi$
$881$	−2.90576	−	8.94301i	−0.0978975	−	0.301298i	−0.987998	+	0.154467i	$0.950634\pi$
$882$	−5.65242	+	4.10672i	−0.190327	+	0.138281i
$883$	11.9541	+	36.7909i	0.402287	+	1.23811i	0.923140	+	0.384465i	$0.125614\pi$
$883$	11.9541	+	36.7909i	0.402287	+	1.23811i	−0.520853	+	0.853646i	$0.674386\pi$
$884$	0.519449	+	1.59870i	0.0174710	+	0.0537701i
$885$	−2.38591	+	1.73347i	−0.0802016	+	0.0582699i
$886$	−7.14897	−	22.0023i	−0.240174	−	0.739180i
$887$	−0.673618	+	2.07318i	−0.0226179	+	0.0696107i	−0.961728	−	0.274005i	$-0.911652\pi$
$887$	−0.673618	+	2.07318i	−0.0226179	+	0.0696107i	0.939110	+	0.343615i	$0.111652\pi$
$888$	−9.06806	−	6.58833i	−0.304304	−	0.221090i
$889$	0.500934	−	1.54172i	0.0168008	−	0.0517075i
$890$	10.9436	−	7.95101i	0.366831	−	0.266519i
$891$	−4.78166	+	3.47408i	−0.160191	+	0.116386i
$892$	8.96543	+	6.51376i	0.300185	+	0.218097i
$893$	0.815431			0.0272874
$894$	−1.32978			−0.0444747
$895$	0.0645815	+	0.0469212i	0.00215872	+	0.00156840i
$896$	−0.0355338	−	0.109362i	−0.00118710	−	0.00365352i
$897$	0.276991	−	0.852492i	0.00924847	−	0.0284639i
$898$	−1.22090			−0.0407421
$899$	21.3099	−	13.6252i	0.710726	−	0.454427i
$900$	1.00000			0.0333333
$901$	22.2463	−	68.4672i	0.741133	−	2.28097i
$902$	−6.25669	−	19.2561i	−0.208325	−	0.641158i
$903$	−0.220381	−	0.160116i	−0.00733381	−	0.00532832i
$904$	−11.9588			−0.397744
$905$	−21.4832			−0.714127
$906$	19.2308	+	13.9720i	0.638902	+	0.464189i
$907$	−29.4383	+	21.3882i	−0.977482	+	0.710182i	−0.957144	−	0.289611i	$-0.906474\pi$
$907$	−29.4383	+	21.3882i	−0.977482	+	0.710182i	−0.0203373	+	0.999793i	$0.506474\pi$
$908$	9.10921	−	6.61822i	0.302300	−	0.219634i
$909$	4.17188	−	12.8397i	0.138373	−	0.425867i
$910$	0.0203860	+	0.0148113i	0.000675791	+	0.000490991i
$911$	−0.410526	+	1.26347i	−0.0136013	+	0.0418606i	−0.957627	−	0.288012i	$-0.907006\pi$
$911$	−0.410526	+	1.26347i	−0.0136013	+	0.0418606i	0.944026	+	0.329872i	$0.107006\pi$
$912$	−0.223166	−	0.686835i	−0.00738977	−	0.0227434i
$913$	−43.1469	+	31.3481i	−1.42795	+	1.03747i
$914$	3.15327	+	9.70477i	0.104301	+	0.321005i
$915$	−2.57716	−	7.93167i	−0.0851982	−	0.262213i
$916$	14.4442	−	10.4944i	0.477251	−	0.346743i
$917$	0.485507	+	1.49424i	0.0160328	+	0.0493440i
$918$	2.37043	−	7.29543i	0.0782358	−	0.240785i
$919$	19.6738	+	14.2939i	0.648979	+	0.471511i	0.862923	−	0.505335i	$-0.168631\pi$
$919$	19.6738	+	14.2939i	0.648979	+	0.471511i	−0.213944	+	0.976846i	$0.568631\pi$
$920$	−1.26401	+	3.89022i	−0.0416732	+	0.128257i
$921$	−21.1306	+	15.3523i	−0.696277	+	0.505875i
$922$	15.1986	−	11.0424i	0.500539	−	0.363663i
$923$	−0.998939	−	0.725772i	−0.0328805	−	0.0238891i
$924$	0.679642			0.0223586
$925$	−11.2087			−0.368541
$926$	6.51106	+	4.73056i	0.213967	+	0.155456i
$927$	3.94237	+	12.1334i	0.129485	+	0.398512i
$928$	−1.40382	+	4.32050i	−0.0460825	+	0.141827i
$929$	−32.5415			−1.06765			−0.533825	−	0.845595i	$-0.679246\pi$
$929$	−32.5415			−1.06765			−0.533825	+	0.845595i	$0.679246\pi$
$930$	4.30204	+	3.53446i	0.141070	+	0.115900i
$931$	5.04572			0.165367
$932$	1.19585	−	3.68044i	0.0391713	−	0.120557i
$933$	7.84758	+	24.1524i	0.256918	+	0.790713i
$934$	−0.983209	−	0.714343i	−0.0321716	−	0.0233740i
$935$	45.3383			1.48272
$936$	0.219137			0.00716272
$937$	2.33797	+	1.69864i	0.0763782	+	0.0554920i	0.625319	−	0.780369i	$-0.284969\pi$
$937$	2.33797	+	1.69864i	0.0763782	+	0.0554920i	−0.548941	+	0.835861i	$0.684969\pi$
$938$	−1.28315	+	0.932262i	−0.0418963	+	0.0304394i
$939$	−15.5921	+	11.3283i	−0.508829	+	0.369686i
$940$	0.348918	−	1.07386i	0.0113804	−	0.0350254i
$941$	45.3082	+	32.9183i	1.47700	+	1.07311i	0.978507	+	0.206215i	$0.0661146\pi$
$941$	45.3082	+	32.9183i	1.47700	+	1.07311i	0.498497	+	0.866891i	$0.333885\pi$
$942$	−5.47032	+	16.8359i	−0.178233	+	0.548544i
$943$	−4.33004	−	13.3265i	−0.141006	−	0.433970i
$944$	2.38591	−	1.73347i	0.0776549	−	0.0564196i
$945$	−0.0355338	−	0.109362i	−0.00115591	−	0.00355754i
$946$	−4.32673	−	13.3163i	−0.140674	−	0.432950i
$947$	−9.99453	+	7.26145i	−0.324779	+	0.235965i	−0.738212	−	0.674569i	$-0.764330\pi$
$947$	−9.99453	+	7.26145i	−0.324779	+	0.235965i	0.413433	+	0.910534i	$0.364330\pi$
$948$	−0.0453410	−	0.139545i	−0.00147261	−	0.00453222i
$949$	0.588123	−	1.81006i	0.0190913	−	0.0587569i
$950$	−0.584257	−	0.424488i	−0.0189558	−	0.0137722i
$951$	−1.18144	+	3.63610i	−0.0383109	+	0.117909i
$952$	−0.713611	+	0.518469i	−0.0231283	+	0.0168037i
$953$	−38.4254	+	27.9177i	−1.24472	+	0.904343i	−0.997904	−	0.0647185i	$-0.979385\pi$
$953$	−38.4254	+	27.9177i	−1.24472	+	0.904343i	−0.246818	+	0.969062i	$0.579385\pi$
$954$	−7.59258	−	5.51633i	−0.245819	−	0.178598i
$955$	−0.234859			−0.00759987
$956$	19.4881			0.630292
$957$	−21.7223	−	15.7822i	−0.702182	−	0.510165i
$958$	8.49807	+	26.1544i	0.274560	+	0.845009i
$959$	−0.597432	+	1.83871i	−0.0192921	+	0.0593749i
$960$	−1.00000			−0.0322749
$961$	6.01512	+	30.4108i	0.194036	+	0.980994i
$962$	−2.45625			−0.0791927
$963$	5.00273	−	15.3968i	0.161211	−	0.496155i
$964$	3.52273	+	10.8419i	0.113460	+	0.349193i
$965$	−0.322736	−	0.234481i	−0.0103892	−	0.00754822i
$966$	0.470357			0.0151335
$967$	28.1068			0.903853			0.451926	−	0.892055i	$-0.350737\pi$
$967$	28.1068			0.903853			0.451926	+	0.892055i	$0.350737\pi$
$968$	19.3626	+	14.0677i	0.622336	+	0.452154i
$969$	−4.48176	+	3.25619i	−0.143975	+	0.104604i
$970$	−2.42867	+	1.76453i	−0.0779798	+	0.0566556i
$971$	19.0826	−	58.7301i	0.612389	−	1.88474i	0.177946	−	0.984040i	$-0.443055\pi$
$971$	19.0826	−	58.7301i	0.612389	−	1.88474i	0.434443	−	0.900699i	$-0.356945\pi$
$972$	−0.809017	−	0.587785i	−0.0259492	−	0.0188532i
$973$	0.377650	−	1.16229i	0.0121069	−	0.0372612i
$974$	3.80475	+	11.7098i	0.121912	+	0.375207i
$975$	0.177286	−	0.128806i	0.00567769	−	0.00412508i
$976$	2.57716	+	7.93167i	0.0824928	+	0.253887i
$977$	−14.6457	−	45.0748i	−0.468558	−	1.44207i	−0.854453	−	0.519529i	$-0.826107\pi$
$977$	−14.6457	−	45.0748i	−0.468558	−	1.44207i	0.385895	−	0.922543i	$-0.373893\pi$
$978$	−1.24688	+	0.905912i	−0.0398708	+	0.0289679i
$979$	−24.7062	−	76.0380i	−0.789615	−	2.43019i
$980$	2.15903	−	6.64482i	0.0689678	−	0.212261i
$981$	−2.64897	−	1.92459i	−0.0845751	−	0.0614474i
$982$	−7.35187	+	22.6267i	−0.234608	+	0.722048i
$983$	31.7610	−	23.0757i	1.01302	−	0.736001i	0.0481783	−	0.998839i	$-0.484658\pi$
$983$	31.7610	−	23.0757i	1.01302	−	0.736001i	0.964840	+	0.262838i	$0.0846584\pi$
$984$	2.77140	−	2.01354i	0.0883490	−	0.0641893i
$985$	11.9693	+	8.69620i	0.381373	+	0.277084i
$986$	34.8475			1.10977
$987$	−0.129838			−0.00413277
$988$	−0.128032	−	0.0930210i	−0.00407325	−	0.00295939i
$989$	−2.99438	−	9.21575i	−0.0952157	−	0.293044i
$990$	1.82643	−	5.62117i	0.0580478	−	0.178653i
$991$	−17.7944			−0.565257			−0.282629	−	0.959229i	$-0.591206\pi$
$991$	−17.7944			−0.565257			−0.282629	+	0.959229i	$0.591206\pi$
$992$	−4.30204	−	3.53446i	−0.136590	−	0.112219i
$993$	4.59414			0.145791
$994$	0.200220	−	0.616213i	0.00635059	−	0.0195451i
$995$	2.55645	+	7.86795i	0.0810450	+	0.249431i
$996$	−7.30010	−	5.30384i	−0.231313	−	0.168058i
$997$	−5.37169			−0.170123			−0.0850616	−	0.996376i	$-0.527109\pi$
$997$	−5.37169			−0.170123			−0.0850616	+	0.996376i	$0.527109\pi$
$998$	−12.8638			−0.407196
$999$	9.06806	+	6.58833i	0.286901	+	0.208446i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.n.h.721.2	✓	16
31.4	even	5	inner	930.2.n.h.841.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.n.h.721.2	✓	16	1.1	even	1	trivial
930.2.n.h.841.2	yes	16	31.4	even	5	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.0930287 - 0.0675893i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.809017 - 0.587785i) q^{4} -1.00000 q^{5} -1.00000 q^{6} +(-0.0930287 - 0.0675893i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(0.309017 - 0.951057i) q^{10} +(-4.78166 - 3.47408i) q^{11} +(0.309017 - 0.951057i) q^{12} +(-0.0677171 - 0.208412i) q^{13} +(0.0930287 - 0.0675893i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(6.20586 - 4.50882i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-0.223166 + 0.686835i) q^{19} +(0.809017 + 0.587785i) q^{20} +(0.0355338 - 0.109362i) q^{21} +(4.78166 - 3.47408i) q^{22} +(3.30922 - 2.40429i) q^{23} +(0.809017 + 0.587785i) q^{24} +1.00000 q^{25} +0.219137 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.0355338 + 0.109362i) q^{28} +(1.40382 - 4.32050i) q^{29} +1.00000 q^{30} +(4.30204 + 3.53446i) q^{31} -1.00000 q^{32} +(1.82643 - 5.62117i) q^{33} +(2.37043 + 7.29543i) q^{34} +(0.0930287 + 0.0675893i) q^{35} +1.00000 q^{36} -11.2087 q^{37} +(-0.584257 - 0.424488i) q^{38} +(0.177286 - 0.128806i) q^{39} +(-0.809017 + 0.587785i) q^{40} +(1.05858 - 3.25798i) q^{41} +(0.0930287 + 0.0675893i) q^{42} +(0.732047 - 2.25301i) q^{43} +(1.82643 + 5.62117i) q^{44} +(0.809017 - 0.587785i) q^{45} +(1.26401 + 3.89022i) q^{46} +(-0.348918 - 1.07386i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(-2.15903 - 6.64482i) q^{49} +(-0.309017 + 0.951057i) q^{50} +(6.20586 + 4.50882i) q^{51} +(-0.0677171 + 0.208412i) q^{52} +(7.59258 - 5.51633i) q^{53} +(0.809017 - 0.587785i) q^{54} +(4.78166 + 3.47408i) q^{55} -0.114990 q^{56} -0.722181 q^{57} +(3.67524 + 2.67022i) q^{58} +(-0.911338 - 2.80481i) q^{59} +(-0.309017 + 0.951057i) q^{60} +8.33985 q^{61} +(-4.69088 + 2.99928i) q^{62} +0.114990 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.0677171 + 0.208412i) q^{65} +(4.78166 + 3.47408i) q^{66} -13.7930 q^{67} -7.67087 q^{68} +(3.30922 + 2.40429i) q^{69} +(-0.0930287 + 0.0675893i) q^{70} +(4.55851 - 3.31195i) q^{71} +(-0.309017 + 0.951057i) q^{72} +(7.02631 + 5.10492i) q^{73} +(3.46369 - 10.6601i) q^{74} +(0.309017 + 0.951057i) q^{75} +(0.584257 - 0.424488i) q^{76} +(0.210021 + 0.646378i) q^{77} +(0.0677171 + 0.208412i) q^{78} +(0.118704 - 0.0862438i) q^{79} +(-0.309017 - 0.951057i) q^{80} +(0.309017 - 0.951057i) q^{81} +(2.77140 + 2.01354i) q^{82} +(2.78839 - 8.58179i) q^{83} +(-0.0930287 + 0.0675893i) q^{84} +(-6.20586 + 4.50882i) q^{85} +(1.91652 + 1.39244i) q^{86} +4.54284 q^{87} -5.91045 q^{88} +(10.9436 + 7.95101i) q^{89} +(0.309017 + 0.951057i) q^{90} +(-0.00778678 + 0.0239652i) q^{91} -4.09042 q^{92} +(-2.03207 + 5.18369i) q^{93} +1.12912 q^{94} +(0.223166 - 0.686835i) q^{95} +(-0.309017 - 0.951057i) q^{96} +(-2.42867 - 1.76453i) q^{97} +6.98678 q^{98} +5.91045 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9	\( 16 q + 4 q^{2} - 4 q^{3} - 4 q^{4} - 16 q^{5} - 16 q^{6} - 7 q^{7} + 4 q^{8} - 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} + 7 q^{14} + 4 q^{15} - 4 q^{16} + 5 q^{17} + 4 q^{18} - 2 q^{19} + 4 q^{20} + 8 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{24} + 16 q^{25} + 8 q^{26} - 4 q^{27} + 8 q^{28} + 5 q^{29} + 16 q^{30} - q^{31} - 16 q^{32} - q^{33} - 5 q^{34} + 7 q^{35} + 16 q^{36} - 20 q^{37} - 3 q^{38} + 2 q^{39} - 4 q^{40} - 17 q^{41} + 7 q^{42} - 4 q^{43} - q^{44} + 4 q^{45} - 6 q^{46} + 2 q^{47} - 4 q^{48} - 21 q^{49} + 4 q^{50} + 5 q^{51} + 2 q^{52} + 9 q^{53} + 4 q^{54} - 4 q^{55} + 2 q^{56} - 2 q^{57} - 5 q^{58} - 3 q^{59} + 4 q^{60} + 70 q^{61} - 4 q^{62} - 2 q^{63} - 4 q^{64} - 2 q^{65} - 4 q^{66} - 66 q^{67} - 20 q^{68} - 4 q^{69} - 7 q^{70} - 25 q^{71} + 4 q^{72} - 10 q^{73} - 15 q^{74} - 4 q^{75} + 3 q^{76} + 26 q^{77} - 2 q^{78} + 14 q^{79} + 4 q^{80} - 4 q^{81} + 17 q^{82} + 20 q^{83} - 7 q^{84} - 5 q^{85} - 6 q^{86} - 20 q^{87} + 6 q^{88} - 13 q^{89} - 4 q^{90} - 4 q^{91} - 4 q^{92} + 4 q^{93} - 12 q^{94} + 2 q^{95} + 4 q^{96} + 55 q^{97} - 14 q^{98} - 6 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 - 4 * q^3 - 4 * q^4 - 16 * q^5 - 16 * q^6 - 7 * q^7 + 4 * q^8 - 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 + 7 * q^14 + 4 * q^15 - 4 * q^16 + 5 * q^17 + 4 * q^18 - 2 * q^19 + 4 * q^20 + 8 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^24 + 16 * q^25 + 8 * q^26 - 4 * q^27 + 8 * q^28 + 5 * q^29 + 16 * q^30 - q^31 - 16 * q^32 - q^33 - 5 * q^34 + 7 * q^35 + 16 * q^36 - 20 * q^37 - 3 * q^38 + 2 * q^39 - 4 * q^40 - 17 * q^41 + 7 * q^42 - 4 * q^43 - q^44 + 4 * q^45 - 6 * q^46 + 2 * q^47 - 4 * q^48 - 21 * q^49 + 4 * q^50 + 5 * q^51 + 2 * q^52 + 9 * q^53 + 4 * q^54 - 4 * q^55 + 2 * q^56 - 2 * q^57 - 5 * q^58 - 3 * q^59 + 4 * q^60 + 70 * q^61 - 4 * q^62 - 2 * q^63 - 4 * q^64 - 2 * q^65 - 4 * q^66 - 66 * q^67 - 20 * q^68 - 4 * q^69 - 7 * q^70 - 25 * q^71 + 4 * q^72 - 10 * q^73 - 15 * q^74 - 4 * q^75 + 3 * q^76 + 26 * q^77 - 2 * q^78 + 14 * q^79 + 4 * q^80 - 4 * q^81 + 17 * q^82 + 20 * q^83 - 7 * q^84 - 5 * q^85 - 6 * q^86 - 20 * q^87 + 6 * q^88 - 13 * q^89 - 4 * q^90 - 4 * q^91 - 4 * q^92 + 4 * q^93 - 12 * q^94 + 2 * q^95 + 4 * q^96 + 55 * q^97 - 14 * q^98 - 6 * q^99

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