LMFDB - Embedded newform 390.2.bd.a.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (of order $12$, 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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			7.2
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	390.7
Dual form			390.2.bd.a.223.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.848387 - 1.46945i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.848387 - 1.46945i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.48356 + 1.67303i) q^{10} +(0.697977 + 2.60488i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(3.53553 - 0.707107i) q^{13} -1.69677i q^{14} +(-0.133975 + 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.49768 - 0.401302i) q^{17} -1.00000 q^{18} +(-4.02494 - 1.07848i) q^{19} +(0.448288 + 2.19067i) q^{20} +(1.19980 - 1.19980i) q^{21} +(-0.697977 + 2.60488i) q^{22} +(1.25201 - 0.335475i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(4.00000 + 3.00000i) q^{25} +(3.41542 + 1.15539i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.848387 - 1.46945i) q^{28} +(-4.85217 - 2.80140i) q^{29} +(-1.23205 + 1.86603i) q^{30} +(-5.54757 - 5.54757i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.33548 + 1.34839i) q^{33} +(-1.09638 - 1.09638i) q^{34} +(-0.760643 - 3.71707i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-1.88745 + 3.26915i) q^{37} +(-2.94646 - 2.94646i) q^{38} +(1.59808 + 3.23205i) q^{39} +(-0.707107 + 2.12132i) q^{40} +(9.96178 - 2.66925i) q^{41} +(1.63896 - 0.439158i) q^{42} +(-2.15539 + 8.04404i) q^{43} +(-1.90691 + 1.90691i) q^{44} +(-2.19067 + 0.448288i) q^{45} +(1.25201 + 0.335475i) q^{46} +6.13165 q^{47} +(-0.965926 - 0.258819i) q^{48} +(2.06048 - 3.56885i) q^{49} +(1.96410 + 4.59808i) q^{50} -1.55051i q^{51} +(2.38014 + 2.70831i) q^{52} +(4.92820 - 4.92820i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(-0.361299 + 6.01934i) q^{55} +(1.46945 - 0.848387i) q^{56} -4.16693i q^{57} +(-2.80140 - 4.85217i) q^{58} +(0.476880 - 1.77974i) q^{59} +(-2.00000 + 1.00000i) q^{60} +(-7.62070 - 13.1994i) q^{61} +(-2.03055 - 7.57812i) q^{62} +(1.46945 + 0.848387i) q^{63} -1.00000 q^{64} +(8.00000 + 1.00000i) q^{65} -2.69677 q^{66} +(-7.13834 - 4.12132i) q^{67} +(-0.401302 - 1.49768i) q^{68} +(0.648089 + 1.12252i) q^{69} +(1.19980 - 3.59940i) q^{70} +(2.59335 - 9.67851i) q^{71} +(-0.500000 - 0.866025i) q^{72} +10.6955i q^{73} +(-3.26915 + 1.88745i) q^{74} +(-1.86250 + 4.64016i) q^{75} +(-1.07848 - 4.02494i) q^{76} +(3.23559 - 3.23559i) q^{77} +(-0.232051 + 3.59808i) q^{78} -8.13505i q^{79} +(-1.67303 + 1.48356i) q^{80} +(0.500000 - 0.866025i) q^{81} +(9.96178 + 2.66925i) q^{82} -9.04184 q^{83} +(1.63896 + 0.439158i) q^{84} +(-2.89329 - 1.91031i) q^{85} +(-5.88865 + 5.88865i) q^{86} +(1.45011 - 5.41189i) q^{87} +(-2.60488 + 0.697977i) q^{88} +(-3.61571 + 0.968828i) q^{89} +(-2.12132 - 0.707107i) q^{90} +(-4.03856 - 4.59539i) q^{91} +(0.916536 + 0.916536i) q^{92} +(3.92272 - 6.79435i) q^{93} +(5.31017 + 3.06583i) q^{94} +(-7.77559 - 5.13387i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.87662 + 1.08346i) q^{97} +(3.56885 - 2.06048i) q^{98} +(-1.90691 - 1.90691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^7	$ 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$3$	0.258819	+	0.965926i	0.149429	+	0.557678i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$6$	−0.258819	+	0.965926i	−0.105662	+	0.394338i
$7$	−0.848387	−	1.46945i	−0.320660	−	0.555400i	0.659964	−	0.751297i	$-0.270571\pi$
$7$	−0.848387	−	1.46945i	−0.320660	−	0.555400i	−0.980624	+	0.195897i	$0.937238\pi$
$8$			1.00000i			0.353553i
$9$	−0.866025	+	0.500000i	−0.288675	+	0.166667i
$10$	1.48356	+	1.67303i	0.469144	+	0.529059i
$11$	0.697977	+	2.60488i	0.210448	+	0.785402i	0.987720	+	0.156237i	$0.0499364\pi$
$11$	0.697977	+	2.60488i	0.210448	+	0.785402i	−0.777272	+	0.629165i	$0.783397\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	3.53553	−	0.707107i	0.980581	−	0.196116i
$13$	3.53553	−	0.707107i	0.980581	−	0.196116i
$14$		−	1.69677i		−	0.453482i
$15$	−0.133975	+	2.23205i	−0.0345921	+	0.576313i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.49768	−	0.401302i	−0.363240	−	0.0973299i	0.0725826	−	0.997362i	$-0.476876\pi$
$17$	−1.49768	−	0.401302i	−0.363240	−	0.0973299i	−0.435823	+	0.900032i	$0.643543\pi$
$18$	−1.00000			−0.235702
$19$	−4.02494	−	1.07848i	−0.923385	−	0.247420i	−0.234354	−	0.972151i	$-0.575297\pi$
$19$	−4.02494	−	1.07848i	−0.923385	−	0.247420i	−0.689032	+	0.724731i	$0.741964\pi$
$20$	0.448288	+	2.19067i	0.100240	+	0.489849i
$21$	1.19980	−	1.19980i	0.261818	−	0.261818i
$22$	−0.697977	+	2.60488i	−0.148809	+	0.555363i
$23$	1.25201	−	0.335475i	0.261062	−	0.0699514i	−0.125914	−	0.992041i	$-0.540186\pi$
$23$	1.25201	−	0.335475i	0.261062	−	0.0699514i	0.386976	+	0.922090i	$0.373520\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$	3.41542	+	1.15539i	0.669818	+	0.226592i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	0.848387	−	1.46945i	0.160330	−	0.277700i
$29$	−4.85217	−	2.80140i	−0.901025	−	0.520207i	−0.0234925	−	0.999724i	$-0.507479\pi$
$29$	−4.85217	−	2.80140i	−0.901025	−	0.520207i	−0.877533	+	0.479517i	$0.840812\pi$
$30$	−1.23205	+	1.86603i	−0.224941	+	0.340688i
$31$	−5.54757	−	5.54757i	−0.996372	−	0.996372i	0.00362118	−	0.999993i	$-0.498847\pi$
$31$	−5.54757	−	5.54757i	−0.996372	−	0.996372i	−0.999993	+	0.00362118i	$0.998847\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−2.33548	+	1.34839i	−0.406554	+	0.234724i
$34$	−1.09638	−	1.09638i	−0.188027	−	0.188027i
$35$	−0.760643	−	3.71707i	−0.128572	−	0.628300i
$36$	−0.866025	−	0.500000i	−0.144338	−	0.0833333i
$37$	−1.88745	+	3.26915i	−0.310294	+	0.537445i	−0.978426	−	0.206598i	$-0.933761\pi$
$37$	−1.88745	+	3.26915i	−0.310294	+	0.537445i	0.668132	+	0.744043i	$0.267094\pi$
$38$	−2.94646	−	2.94646i	−0.477980	−	0.477980i
$39$	1.59808	+	3.23205i	0.255897	+	0.517542i
$40$	−0.707107	+	2.12132i	−0.111803	+	0.335410i
$41$	9.96178	−	2.66925i	1.55577	−	0.416867i	0.624448	−	0.781067i	$-0.285324\pi$
$41$	9.96178	−	2.66925i	1.55577	−	0.416867i	0.931321	+	0.364200i	$0.118657\pi$
$42$	1.63896	−	0.439158i	0.252897	−	0.0677635i
$43$	−2.15539	+	8.04404i	−0.328695	+	1.22670i	0.581851	+	0.813296i	$0.302329\pi$
$43$	−2.15539	+	8.04404i	−0.328695	+	1.22670i	−0.910545	+	0.413409i	$0.864338\pi$
$44$	−1.90691	+	1.90691i	−0.287477	+	0.287477i
$45$	−2.19067	+	0.448288i	−0.326566	+	0.0668268i
$46$	1.25201	+	0.335475i	0.184599	+	0.0494631i
$47$	6.13165			0.894393			0.447197	−	0.894436i	$-0.352422\pi$
$47$	6.13165			0.894393			0.447197	+	0.894436i	$0.352422\pi$
$48$	−0.965926	−	0.258819i	−0.139419	−	0.0373573i
$49$	2.06048	−	3.56885i	0.294354	−	0.509836i
$50$	1.96410	+	4.59808i	0.277766	+	0.650266i
$51$		−	1.55051i		−	0.217115i
$52$	2.38014	+	2.70831i	0.330066	+	0.375575i
$53$	4.92820	−	4.92820i	0.676941	−	0.676941i	−0.282366	−	0.959307i	$-0.591119\pi$
$53$	4.92820	−	4.92820i	0.676941	−	0.676941i	0.959307	+	0.282366i	$0.0911192\pi$
$54$	−0.258819	−	0.965926i	−0.0352208	−	0.131446i
$55$	−0.361299	+	6.01934i	−0.0487176	+	0.811647i
$56$	1.46945	−	0.848387i	0.196364	−	0.113371i
$57$		−	4.16693i		−	0.551923i
$58$	−2.80140	−	4.85217i	−0.367842	−	0.637121i
$59$	0.476880	−	1.77974i	0.0620845	−	0.231703i	−0.927911	−	0.372802i	$-0.878397\pi$
$59$	0.476880	−	1.77974i	0.0620845	−	0.231703i	0.989995	+	0.141099i	$0.0450637\pi$
$60$	−2.00000	+	1.00000i	−0.258199	+	0.129099i
$61$	−7.62070	−	13.1994i	−0.975730	−	1.69001i	−0.677503	−	0.735520i	$-0.736938\pi$
$61$	−7.62070	−	13.1994i	−0.975730	−	1.69001i	−0.298227	−	0.954495i	$-0.596395\pi$
$62$	−2.03055	−	7.57812i	−0.257880	−	0.962422i
$63$	1.46945	+	0.848387i	0.185133	+	0.106887i
$64$	−1.00000			−0.125000
$65$	8.00000	+	1.00000i	0.992278	+	0.124035i
$66$	−2.69677			−0.331950
$67$	−7.13834	−	4.12132i	−0.872087	−	0.503499i	−0.00404550	−	0.999992i	$-0.501288\pi$
$67$	−7.13834	−	4.12132i	−0.872087	−	0.503499i	−0.868041	+	0.496492i	$0.834621\pi$
$68$	−0.401302	−	1.49768i	−0.0486650	−	0.181620i
$69$	0.648089	+	1.12252i	0.0780207	+	0.135136i
$70$	1.19980	−	3.59940i	0.143404	−	0.430211i
$71$	2.59335	−	9.67851i	0.307774	−	1.14863i	−0.622757	−	0.782415i	$-0.713987\pi$
$71$	2.59335	−	9.67851i	0.307774	−	1.14863i	0.930531	−	0.366213i	$-0.119346\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$			10.6955i			1.25182i	0.779896	+	0.625909i	$0.215272\pi$
$73$			10.6955i			1.25182i	−0.779896	+	0.625909i	$0.784728\pi$
$74$	−3.26915	+	1.88745i	−0.380031	+	0.219411i
$75$	−1.86250	+	4.64016i	−0.215063	+	0.535800i
$76$	−1.07848	−	4.02494i	−0.123710	−	0.461693i
$77$	3.23559	−	3.23559i	0.368730	−	0.368730i
$78$	−0.232051	+	3.59808i	−0.0262746	+	0.407402i
$79$		−	8.13505i		−	0.915265i	−0.889141	−	0.457632i	$-0.848698\pi$
$79$		−	8.13505i		−	0.915265i	0.889141	−	0.457632i	$-0.151302\pi$
$80$	−1.67303	+	1.48356i	−0.187051	+	0.165867i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	9.96178	+	2.66925i	1.10009	+	0.294769i
$83$	−9.04184			−0.992471			−0.496236	−	0.868188i	$-0.665285\pi$
$83$	−9.04184			−0.992471			−0.496236	+	0.868188i	$0.665285\pi$
$84$	1.63896	+	0.439158i	0.178825	+	0.0479160i
$85$	−2.89329	−	1.91031i	−0.313822	−	0.207202i
$86$	−5.88865	+	5.88865i	−0.634989	+	0.634989i
$87$	1.45011	−	5.41189i	0.155468	−	0.580216i
$88$	−2.60488	+	0.697977i	−0.277682	+	0.0744046i
$89$	−3.61571	+	0.968828i	−0.383265	+	0.102696i	−0.445307	−	0.895378i	$-0.646905\pi$
$89$	−3.61571	+	0.968828i	−0.383265	+	0.102696i	0.0620419	+	0.998074i	$0.480239\pi$
$90$	−2.12132	−	0.707107i	−0.223607	−	0.0745356i
$91$	−4.03856	−	4.59539i	−0.423356	−	0.481728i
$92$	0.916536	+	0.916536i	0.0955554	+	0.0955554i
$93$	3.92272	−	6.79435i	0.406767	−	0.704542i
$94$	5.31017	+	3.06583i	0.547702	+	0.316216i
$95$	−7.77559	−	5.13387i	−0.797759	−	0.526724i
$96$	−0.707107	−	0.707107i	−0.0721688	−	0.0721688i
$97$	−1.87662	+	1.08346i	−0.190541	+	0.110009i	−0.592236	−	0.805765i	$-0.701755\pi$
$97$	−1.87662	+	1.08346i	−0.190541	+	0.110009i	0.401695	+	0.915774i	$0.368421\pi$
$98$	3.56885	−	2.06048i	0.360509	−	0.208140i
$99$	−1.90691	−	1.90691i	−0.191651	−	0.191651i
$100$	−0.598076	+	4.96410i	−0.0598076	+	0.496410i
$101$	10.3175	+	5.95680i	1.02663	+	0.592723i	0.916017	−	0.401141i	$-0.131386\pi$
$101$	10.3175	+	5.95680i	1.02663	+	0.592723i	0.110610	+	0.993864i	$0.464719\pi$
$102$	0.775255	−	1.34278i	0.0767617	−	0.132955i
$103$	−2.57509	−	2.57509i	−0.253731	−	0.253731i	0.568767	−	0.822498i	$-0.307420\pi$
$103$	−2.57509	−	2.57509i	−0.253731	−	0.253731i	−0.822498	+	0.568767i	$0.807420\pi$
$104$	0.707107	+	3.53553i	0.0693375	+	0.346688i
$105$	3.39355	−	1.69677i	0.331176	−	0.165588i
$106$	6.73205	−	1.80385i	0.653875	−	0.175205i
$107$	2.57545	−	0.690091i	0.248979	−	0.0667136i	−0.132171	−	0.991227i	$-0.542195\pi$
$107$	2.57545	−	0.690091i	0.248979	−	0.0667136i	0.381150	+	0.924513i	$0.375528\pi$
$108$	0.258819	−	0.965926i	0.0249049	−	0.0929463i
$109$	−8.87075	+	8.87075i	−0.849664	+	0.849664i	−0.990091	−	0.140427i	$-0.955152\pi$
$109$	−8.87075	+	8.87075i	−0.849664	+	0.849664i	0.140427	+	0.990091i	$0.455152\pi$
$110$	−3.32256	+	5.03225i	−0.316794	+	0.479806i
$111$	−3.64626	−	0.977014i	−0.346088	−	0.0927340i
$112$	1.69677			0.160330
$113$	9.77327	+	2.61874i	0.919392	+	0.246350i	0.687326	−	0.726350i	$-0.258785\pi$
$113$	9.77327	+	2.61874i	0.919392	+	0.246350i	0.232067	+	0.972700i	$0.425451\pi$
$114$	2.08346	−	3.60867i	0.195134	−	0.337983i
$115$	2.89313	+	0.173655i	0.269786	+	0.0161934i
$116$		−	5.60280i		−	0.520207i
$117$	−2.70831	+	2.38014i	−0.250383	+	0.220044i
$118$	1.30286	−	1.30286i	0.119938	−	0.119938i
$119$	0.680918	+	2.54122i	0.0624197	+	0.232953i
$120$	−2.23205	−	0.133975i	−0.203757	−	0.0122302i
$121$	3.22803	−	1.86370i	0.293457	−	0.169428i
$122$		−	15.2414i		−	1.37989i
$123$	5.15660	+	8.93149i	0.464955	+	0.805325i
$124$	2.03055	−	7.57812i	0.182349	−	0.680535i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$	0.848387	+	1.46945i	0.0755803	+	0.130909i
$127$	3.55291	+	13.2597i	0.315270	+	1.17660i	0.923738	+	0.383026i	$0.125118\pi$
$127$	3.55291	+	13.2597i	0.315270	+	1.17660i	−0.608468	+	0.793579i	$0.708215\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−8.32780			−0.733222
$130$	6.42820	+	4.86603i	0.563791	+	0.426779i
$131$	−0.603318			−0.0527121			−0.0263561	−	0.999653i	$-0.508390\pi$
$131$	−0.603318			−0.0527121			−0.0263561	+	0.999653i	$0.508390\pi$
$132$	−2.33548	−	1.34839i	−0.203277	−	0.117362i
$133$	1.82994	+	6.82942i	0.158676	+	0.592186i
$134$	−4.12132	−	7.13834i	−0.356028	−	0.616658i
$135$	−1.00000	−	2.00000i	−0.0860663	−	0.172133i
$136$	0.401302	−	1.49768i	0.0344113	−	0.128425i
$137$	−2.84536	−	4.92831i	−0.243096	−	0.421054i	0.718499	−	0.695528i	$-0.244830\pi$
$137$	−2.84536	−	4.92831i	−0.243096	−	0.421054i	−0.961594	+	0.274474i	$0.911496\pi$
$138$			1.29618i			0.110338i
$139$	−17.2140	+	9.93854i	−1.46008	+	0.842976i	−0.999014	−	0.0443922i	$-0.985865\pi$
$139$	−17.2140	+	9.93854i	−1.46008	+	0.842976i	−0.461062	+	0.887368i	$0.652532\pi$
$140$	2.83876	−	2.51727i	0.239919	−	0.212748i
$141$	1.58699	+	5.92272i	0.133649	+	0.498783i
$142$	7.08516	−	7.08516i	0.594574	−	0.594574i
$143$	4.30965	+	8.71611i	0.360391	+	0.728878i
$144$		−	1.00000i		−	0.0833333i
$145$	−8.31212	−	9.37367i	−0.690284	−	0.778441i
$146$	−5.34777	+	9.26260i	−0.442584	+	0.766578i
$147$	3.98054	+	1.06658i	0.328309	+	0.0879702i
$148$	−3.77489			−0.310294
$149$	−15.7362	−	4.21649i	−1.28916	−	0.345429i	−0.451817	−	0.892111i	$-0.649224\pi$
$149$	−15.7362	−	4.21649i	−1.28916	−	0.345429i	−0.837340	+	0.546682i	$0.815891\pi$
$150$	−3.93305	+	3.08725i	−0.321132	+	0.252073i
$151$	−2.96348	+	2.96348i	−0.241165	+	0.241165i	−0.817332	−	0.576167i	$-0.804548\pi$
$151$	−2.96348	+	2.96348i	−0.241165	+	0.241165i	0.576167	+	0.817332i	$0.304548\pi$
$152$	1.07848	−	4.02494i	0.0874763	−	0.326466i
$153$	1.49768	−	0.401302i	0.121080	−	0.0324433i
$154$	4.41990	−	1.18431i	0.356166	−	0.0954343i
$155$	−7.84544	−	15.6909i	−0.630161	−	1.26032i
$156$	−2.00000	+	3.00000i	−0.160128	+	0.240192i
$157$	16.1413	+	16.1413i	1.28821	+	1.28821i	0.935872	+	0.352341i	$0.114614\pi$
$157$	16.1413	+	16.1413i	1.28821	+	1.28821i	0.352341	+	0.935872i	$0.385386\pi$
$158$	4.06753	−	7.04516i	0.323595	−	0.560483i
$159$	6.03579	+	3.48477i	0.478669	+	0.276360i
$160$	−2.19067	+	0.448288i	−0.173188	+	0.0354403i
$161$	−1.55515	−	1.55515i	−0.122563	−	0.122563i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−1.97589	+	1.14078i	−0.154764	+	0.0893530i	−0.575382	−	0.817885i	$-0.695147\pi$
$163$	−1.97589	+	1.14078i	−0.154764	+	0.0893530i	0.420618	+	0.907238i	$0.361813\pi$
$164$	7.29253	+	7.29253i	0.569451	+	0.569451i
$165$	−5.90775	+	1.20893i	−0.459917	+	0.0941152i
$166$	−7.83047	−	4.52092i	−0.607762	−	0.350892i
$167$	−2.74969	+	4.76260i	−0.212777	+	0.368541i	−0.952583	−	0.304280i	$-0.901584\pi$
$167$	−2.74969	+	4.76260i	−0.212777	+	0.368541i	0.739805	+	0.672821i	$0.234918\pi$
$168$	1.19980	+	1.19980i	0.0925666	+	0.0925666i
$169$	12.0000	−	5.00000i	0.923077	−	0.384615i
$170$	−1.55051	−	3.10102i	−0.118919	−	0.237837i
$171$	4.02494	−	1.07848i	0.307795	−	0.0824735i
$172$	−8.04404	+	2.15539i	−0.613352	+	0.164347i
$173$	0.125333	−	0.467750i	0.00952891	−	0.0355624i	−0.960998	−	0.276556i	$-0.910807\pi$
$173$	0.125333	−	0.467750i	0.00952891	−	0.0355624i	0.970527	+	0.240994i	$0.0774734\pi$
$174$	3.96178	−	3.96178i	0.300342	−	0.300342i
$175$	1.01480	−	8.42296i	0.0767117	−	0.636716i
$176$	−2.60488	−	0.697977i	−0.196351	−	0.0526120i
$177$	1.84252			0.138493
$178$	−3.61571	−	0.968828i	−0.271009	−	0.0726167i
$179$	−6.51179	+	11.2788i	−0.486714	+	0.843014i	−0.999883	−	0.0152738i	$-0.995138\pi$
$179$	−6.51179	+	11.2788i	−0.486714	+	0.843014i	0.513169	+	0.858287i	$0.328471\pi$
$180$	−1.48356	−	1.67303i	−0.110578	−	0.124700i
$181$			3.02118i			0.224563i	0.993676	+	0.112281i	$0.0358158\pi$
$181$			3.02118i			0.224563i	−0.993676	+	0.112281i	$0.964184\pi$
$182$	−1.19980	−	5.99900i	−0.0889352	−	0.444676i
$183$	10.7773	−	10.7773i	0.796681	−	0.796681i
$184$	0.335475	+	1.25201i	0.0247316	+	0.0922995i
$185$	−6.31552	+	5.60029i	−0.464326	+	0.411742i
$186$	6.79435	−	3.92272i	0.498186	−	0.287628i
$187$		−	4.18138i		−	0.305773i
$188$	3.06583	+	5.31017i	0.223598	+	0.387284i
$189$	−0.439158	+	1.63896i	−0.0319440	+	0.119217i
$190$	−4.16693	−	8.33386i	−0.302301	−	0.604602i
$191$	9.30028	+	16.1086i	0.672945	+	1.16557i	0.977065	+	0.212941i	$0.0683042\pi$
$191$	9.30028	+	16.1086i	0.672945	+	1.16557i	−0.304120	+	0.952634i	$0.598363\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	−7.08077	−	4.08808i	−0.509685	−	0.294267i	0.223019	−	0.974814i	$-0.428409\pi$
$193$	−7.08077	−	4.08808i	−0.509685	−	0.294267i	−0.732704	+	0.680547i	$0.761742\pi$
$194$	−2.16693			−0.155576
$195$	1.10463	+	7.98623i	0.0791039	+	0.571905i
$196$	4.12096			0.294354
$197$	2.61073	+	1.50731i	0.186007	+	0.107391i	0.590112	−	0.807322i	$-0.299084\pi$
$197$	2.61073	+	1.50731i	0.186007	+	0.107391i	−0.404105	+	0.914713i	$0.632417\pi$
$198$	−0.697977	−	2.60488i	−0.0496030	−	0.185121i
$199$	−0.0399204	−	0.0691441i	−0.00282988	−	0.00490150i	0.864607	−	0.502449i	$-0.167567\pi$
$199$	−0.0399204	−	0.0691441i	−0.00282988	−	0.00490150i	−0.867437	+	0.497547i	$0.834234\pi$
$200$	−3.00000	+	4.00000i	−0.212132	+	0.282843i
$201$	2.13335	−	7.96178i	0.150475	−	0.561581i
$202$	5.95680	+	10.3175i	0.419119	+	0.725935i
$203$			9.50669i			0.667239i
$204$	1.34278	−	0.775255i	0.0940135	−	0.0542787i
$205$	23.0196	+	1.38171i	1.60776	+	0.0965025i
$206$	−0.942548	−	3.51764i	−0.0656705	−	0.245085i
$207$	−0.916536	+	0.916536i	−0.0637036	+	0.0637036i
$208$	−1.15539	+	3.41542i	−0.0801122	+	0.236816i
$209$		−	11.2373i		−	0.777298i
$210$	3.78729	+	0.227325i	0.261348	+	0.0156869i
$211$	−11.8986	+	20.6090i	−0.819134	+	1.41878i	0.0871863	+	0.996192i	$0.472212\pi$
$211$	−11.8986	+	20.6090i	−0.819134	+	1.41878i	−0.906321	+	0.422590i	$0.861121\pi$
$212$	6.73205	+	1.80385i	0.462359	+	0.123889i
$213$	10.0199			0.686555
$214$	2.57545	+	0.690091i	0.176054	+	0.0471736i
$215$	−10.2603	+	15.5399i	−0.699745	+	1.05981i
$216$	0.707107	−	0.707107i	0.0481125	−	0.0481125i
$217$	−3.44539	+	12.8584i	−0.233888	+	0.872882i
$218$	−12.1177	+	3.24692i	−0.820712	+	0.219909i
$219$	−10.3311	+	2.76821i	−0.698110	+	0.187058i
$220$	−5.39355	+	2.69677i	−0.363633	+	0.181817i
$221$	−5.57885	−	0.359797i	−0.375274	−	0.0242026i
$222$	−2.66925	−	2.66925i	−0.179148	−	0.179148i
$223$	7.19980	−	12.4704i	0.482134	−	0.835081i	−0.517655	−	0.855589i	$-0.673195\pi$
$223$	7.19980	−	12.4704i	0.482134	−	0.835081i	0.999790	+	0.0205081i	$0.00652838\pi$
$224$	1.46945	+	0.848387i	0.0981818	+	0.0566853i
$225$	−4.96410	−	0.598076i	−0.330940	−	0.0398717i
$226$	7.15453	+	7.15453i	0.475912	+	0.475912i
$227$	6.68644	−	3.86042i	0.443795	−	0.256225i	−0.261411	−	0.965228i	$-0.584188\pi$
$227$	6.68644	−	3.86042i	0.443795	−	0.256225i	0.705206	+	0.709002i	$0.250855\pi$
$228$	3.60867	−	2.08346i	0.238990	−	0.137981i
$229$	2.75787	+	2.75787i	0.182245	+	0.182245i	0.792334	−	0.610088i	$-0.208866\pi$
$229$	2.75787	+	2.75787i	0.182245	+	0.182245i	−0.610088	+	0.792334i	$0.708866\pi$
$230$	2.41870	+	1.59696i	0.159484	+	0.105300i
$231$	3.96278	+	2.28791i	0.260731	+	0.150533i
$232$	2.80140	−	4.85217i	0.183921	−	0.318561i
$233$	−8.14280	−	8.14280i	−0.533453	−	0.533453i	0.388145	−	0.921598i	$-0.373116\pi$
$233$	−8.14280	−	8.14280i	−0.533453	−	0.533453i	−0.921598	+	0.388145i	$0.873116\pi$
$234$	−3.53553	+	0.707107i	−0.231125	+	0.0462250i
$235$	13.0072	+	4.33573i	0.848496	+	0.282832i
$236$	1.77974	−	0.476880i	0.115851	−	0.0310423i
$237$	7.85786	−	2.10551i	0.510423	−	0.136767i
$238$	−0.680918	+	2.54122i	−0.0441374	+	0.164723i
$239$	−12.2061	+	12.2061i	−0.789548	+	0.789548i	−0.981420	−	0.191872i	$-0.938544\pi$
$239$	−12.2061	+	12.2061i	−0.789548	+	0.789548i	0.191872	+	0.981420i	$0.438544\pi$
$240$	−1.86603	−	1.23205i	−0.120451	−	0.0795285i
$241$	−11.3737	−	3.04757i	−0.732643	−	0.196311i	−0.126837	−	0.991924i	$-0.540482\pi$
$241$	−11.3737	−	3.04757i	−0.732643	−	0.196311i	−0.605806	+	0.795613i	$0.707149\pi$
$242$	3.72741			0.239607
$243$	0.965926	+	0.258819i	0.0619642	+	0.0166032i
$244$	7.62070	−	13.1994i	0.487865	−	0.845007i
$245$	6.89449	−	6.11370i	0.440473	−	0.390590i
$246$			10.3132i			0.657545i
$247$	−14.9929	−	0.966939i	−0.953977	−	0.0615249i
$248$	5.54757	−	5.54757i	0.352271	−	0.352271i
$249$	−2.34020	−	8.73375i	−0.148304	−	0.553479i
$250$	0.915158	+	11.1428i	0.0578797	+	0.704734i
$251$	−5.92372	+	3.42006i	−0.373902	+	0.215872i	−0.675162	−	0.737670i	$-0.735926\pi$
$251$	−5.92372	+	3.42006i	−0.373902	+	0.215872i	0.301260	+	0.953542i	$0.402593\pi$
$252$			1.69677i			0.106887i
$253$	1.74775	+	3.02719i	0.109880	+	0.190318i
$254$	−3.55291	+	13.2597i	−0.222930	+	0.831985i
$255$	1.09638	−	3.28913i	0.0686577	−	0.205973i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.98993	+	22.3547i	0.373641	+	1.39445i	0.855320	+	0.518100i	$0.173361\pi$
$257$	5.98993	+	22.3547i	0.373641	+	1.39445i	−0.481679	+	0.876348i	$0.659973\pi$
$258$	−7.21209	−	4.16390i	−0.449005	−	0.259233i
$259$	6.40514			0.397996
$260$	3.13397	+	7.42820i	0.194361	+	0.460678i
$261$	5.60280			0.346805
$262$	−0.522489	−	0.301659i	−0.0322794	−	0.0186365i
$263$	6.31187	+	23.5562i	0.389206	+	1.45254i	0.831428	+	0.555632i	$0.187524\pi$
$263$	6.31187	+	23.5562i	0.389206	+	1.45254i	−0.442222	+	0.896906i	$0.645810\pi$
$264$	−1.34839	−	2.33548i	−0.0829875	−	0.143739i
$265$	13.9391	−	6.96953i	0.856270	−	0.428135i
$266$	−1.82994	+	6.82942i	−0.112201	+	0.418739i
$267$	−1.87163	−	3.24176i	−0.114542	−	0.198393i
$268$		−	8.24264i		−	0.503499i
$269$	16.3664	−	9.44913i	0.997875	−	0.576123i	0.0902561	−	0.995919i	$-0.471231\pi$
$269$	16.3664	−	9.44913i	0.997875	−	0.576123i	0.907619	+	0.419795i	$0.137898\pi$
$270$	0.133975	−	2.23205i	0.00815343	−	0.135838i
$271$	−4.84091	−	18.0665i	−0.294064	−	1.09746i	−0.941958	−	0.335731i	$-0.891017\pi$
$271$	−4.84091	−	18.0665i	−0.294064	−	1.09746i	0.647894	−	0.761731i	$-0.275650\pi$
$272$	1.09638	−	1.09638i	0.0664776	−	0.0664776i
$273$	3.39355	−	5.09032i	0.205387	−	0.308080i
$274$		−	5.69072i		−	0.343789i
$275$	−5.02275	+	12.5135i	−0.302883	+	0.754590i
$276$	−0.648089	+	1.12252i	−0.0390103	+	0.0675679i
$277$	−0.160039	−	0.0428822i	−0.00961579	−	0.00257654i	0.254008	−	0.967202i	$-0.418251\pi$
$277$	−0.160039	−	0.0428822i	−0.00961579	−	0.00257654i	−0.263624	+	0.964626i	$0.584918\pi$
$278$	−19.8771			−1.19215
$279$	7.57812	+	2.03055i	0.453690	+	0.121566i
$280$	3.71707	−	0.760643i	0.222138	−	0.0454571i
$281$	−13.2015	+	13.2015i	−0.787534	+	0.787534i	−0.981089	−	0.193555i	$-0.937998\pi$
$281$	−13.2015	+	13.2015i	−0.787534	+	0.787534i	0.193555	+	0.981089i	$0.437998\pi$
$282$	−1.58699	+	5.92272i	−0.0945038	+	0.352693i
$283$	22.4513	−	6.01581i	1.33459	−	0.357603i	0.480167	−	0.877177i	$-0.340576\pi$
$283$	22.4513	−	6.01581i	1.33459	−	0.357603i	0.854425	+	0.519574i	$0.173909\pi$
$284$	9.67851	−	2.59335i	0.574314	−	0.153887i
$285$	2.94646	−	8.83939i	0.174533	−	0.523600i
$286$	−0.625789	+	9.70320i	−0.0370037	+	0.573762i
$287$	−12.3738	−	12.3738i	−0.730401	−	0.730401i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−12.6404	−	7.29796i	−0.743555	−	0.429292i
$290$	−2.51167	−	12.2739i	−0.147490	−	0.720748i
$291$	−1.53225	−	1.53225i	−0.0898221	−	0.0898221i
$292$	−9.26260	+	5.34777i	−0.542053	+	0.312954i
$293$	−21.5747	+	12.4562i	−1.26041	+	0.727697i	−0.973154	−	0.230157i	$-0.926076\pi$
$293$	−21.5747	+	12.4562i	−1.26041	+	0.727697i	−0.287255	+	0.957854i	$0.592743\pi$
$294$	2.91396	+	2.91396i	0.169945	+	0.169945i
$295$	2.27008	−	3.43820i	0.132169	−	0.200179i
$296$	−3.26915	−	1.88745i	−0.190016	−	0.109706i
$297$	1.34839	−	2.33548i	0.0782414	−	0.135518i
$298$	−11.5197	−	11.5197i	−0.667317	−	0.667317i
$299$	4.18931	−	2.07139i	0.242274	−	0.119792i
$300$	−4.94975	+	0.707107i	−0.285774	+	0.0408248i
$301$	13.6489	−	3.65722i	0.786711	−	0.210799i
$302$	−4.04819	+	1.08471i	−0.232947	+	0.0624180i
$303$	−3.08346	+	11.5076i	−0.177140	+	0.661097i
$304$	2.94646	−	2.94646i	0.168991	−	0.168991i
$305$	−6.83253	−	33.3889i	−0.391230	−	1.91184i
$306$	1.49768	+	0.401302i	0.0856165	+	0.0229409i
$307$	−17.6654			−1.00822			−0.504109	−	0.863640i	$-0.668179\pi$
$307$	−17.6654			−1.00822			−0.504109	+	0.863640i	$0.668179\pi$
$308$	4.41990	+	1.18431i	0.251847	+	0.0674823i
$309$	1.82086	−	3.15383i	0.103585	−	0.179415i
$310$	1.05109	−	17.5114i	0.0596979	−	0.994582i
$311$			31.6510i			1.79476i	0.441257	+	0.897381i	$0.354533\pi$
$311$			31.6510i			1.79476i	−0.441257	+	0.897381i	$0.645467\pi$
$312$	−3.23205	+	1.59808i	−0.182979	+	0.0904732i
$313$	0.521287	−	0.521287i	0.0294649	−	0.0294649i	−0.692221	−	0.721686i	$-0.743368\pi$
$313$	0.521287	−	0.521287i	0.0294649	−	0.0294649i	0.721686	+	0.692221i	$0.243368\pi$
$314$	5.90811	+	22.0494i	0.333414	+	1.24432i
$315$	2.51727	+	2.83876i	0.141832	+	0.159946i
$316$	7.04516	−	4.06753i	0.396321	−	0.228816i
$317$			6.99876i			0.393089i	0.980495	+	0.196545i	$0.0629721\pi$
$317$			6.99876i			0.393089i	−0.980495	+	0.196545i	$0.937028\pi$
$318$	3.48477	+	6.03579i	0.195416	+	0.338470i
$319$	3.91063	−	14.5947i	0.218953	−	0.817144i
$320$	−2.12132	−	0.707107i	−0.118585	−	0.0395285i
$321$	1.33315	+	2.30909i	0.0744094	+	0.128881i
$322$	−0.569226	−	2.12438i	−0.0317217	−	0.118387i
$323$	5.59527	+	3.23043i	0.311329	+	0.179746i
$324$	1.00000			0.0555556
$325$	16.2635	+	7.77817i	0.902134	+	0.431455i
$326$	−2.28157			−0.126364
$327$	−10.8644	−	6.27257i	−0.600803	−	0.346874i
$328$	2.66925	+	9.96178i	0.147385	+	0.550047i
$329$	−5.20202	−	9.01016i	−0.286796	−	0.496746i
$330$	−5.72072	−	1.90691i	−0.314915	−	0.104972i
$331$	4.77641	−	17.8258i	0.262535	−	0.979796i	−0.701206	−	0.712959i	$-0.747355\pi$
$331$	4.77641	−	17.8258i	0.262535	−	0.979796i	0.963742	−	0.266837i	$-0.0859786\pi$
$332$	−4.52092	−	7.83047i	−0.248118	−	0.429753i
$333$		−	3.77489i		−	0.206863i
$334$	−4.76260	+	2.74969i	−0.260598	+	0.150456i
$335$	−12.2285	−	13.7902i	−0.668113	−	0.753439i
$336$	0.439158	+	1.63896i	0.0239580	+	0.0894125i
$337$	6.32316	−	6.32316i	0.344445	−	0.344445i	−0.513591	−	0.858035i	$-0.671685\pi$
$337$	6.32316	−	6.32316i	0.344445	−	0.344445i	0.858035	+	0.513591i	$0.171685\pi$
$338$	12.8923	+	1.66987i	0.701249	+	0.0908291i
$339$			10.1180i			0.549536i
$340$	0.207729	−	3.46082i	0.0112657	−	0.187689i
$341$	10.5787	−	18.3228i	0.572868	−	0.992237i
$342$	4.02494	+	1.07848i	0.217644	+	0.0583175i
$343$	−18.8698			−1.01887
$344$	−8.04404	−	2.15539i	−0.433706	−	0.116211i
$345$	0.581060	+	2.83950i	0.0312832	+	0.152873i
$346$	0.342417	−	0.342417i	0.0184084	−	0.0184084i
$347$	5.71039	−	21.3115i	0.306550	−	1.14406i	−0.625053	−	0.780582i	$-0.714923\pi$
$347$	5.71039	−	21.3115i	0.306550	−	1.14406i	0.931603	−	0.363477i	$-0.118411\pi$
$348$	5.41189	−	1.45011i	0.290108	−	0.0777342i
$349$	25.5592	−	6.84858i	1.36815	−	0.366596i	0.501350	−	0.865244i	$-0.332837\pi$
$349$	25.5592	−	6.84858i	1.36815	−	0.366596i	0.866804	+	0.498649i	$0.166170\pi$
$350$	5.09032	−	6.78710i	0.272089	−	0.362786i
$351$	−3.00000	−	2.00000i	−0.160128	−	0.106752i
$352$	−1.90691	−	1.90691i	−0.101639	−	0.101639i
$353$	2.67095	−	4.62622i	0.142160	−	0.246229i	−0.786150	−	0.618036i	$-0.787928\pi$
$353$	2.67095	−	4.62622i	0.142160	−	0.246229i	0.928310	+	0.371807i	$0.121262\pi$
$354$	1.59567	+	0.921262i	0.0848090	+	0.0489645i
$355$	12.3451	−	18.6975i	0.655208	−	0.992358i
$356$	−2.64689	−	2.64689i	−0.140285	−	0.140285i
$357$	−2.27840	+	1.31543i	−0.120586	+	0.0696201i
$358$	−11.2788	+	6.51179i	−0.596101	+	0.344159i
$359$	2.49886	+	2.49886i	0.131885	+	0.131885i	0.769968	−	0.638083i	$-0.220272\pi$
$359$	2.49886	+	2.49886i	0.131885	+	0.131885i	−0.638083	+	0.769968i	$0.720272\pi$
$360$	−0.448288	−	2.19067i	−0.0236268	−	0.115458i
$361$	−1.41743	−	0.818353i	−0.0746015	−	0.0430712i
$362$	−1.51059	+	2.61642i	−0.0793948	+	0.137516i
$363$	2.63567	+	2.63567i	0.138337	+	0.138337i
$364$	1.96044	−	5.79519i	0.102755	−	0.303751i
$365$	−7.56288	+	22.6886i	−0.395859	+	1.18758i
$366$	14.7221	−	3.94476i	0.769534	−	0.206196i
$367$	22.8055	−	6.11072i	1.19044	−	0.318977i	0.391379	−	0.920229i	$-0.371998\pi$
$367$	22.8055	−	6.11072i	1.19044	−	0.318977i	0.799059	+	0.601252i	$0.205331\pi$
$368$	−0.335475	+	1.25201i	−0.0174879	+	0.0652656i
$369$	−7.29253	+	7.29253i	−0.379634	+	0.379634i
$370$	−8.26954	+	1.69224i	−0.429913	+	0.0879752i
$371$	−11.4228	−	3.06072i	−0.593041	−	0.158905i
$372$	7.84544			0.406767
$373$	−13.0281	−	3.49086i	−0.674568	−	0.180750i	−0.0947563	−	0.995501i	$-0.530207\pi$
$373$	−13.0281	−	3.49086i	−0.674568	−	0.180750i	−0.579812	+	0.814751i	$0.696874\pi$
$374$	2.09069	−	3.62118i	0.108107	−	0.187247i
$375$	−7.23205	+	8.52628i	−0.373461	+	0.440295i
$376$			6.13165i			0.316216i
$377$	−19.1359	−	6.47345i	−0.985549	−	0.333399i
$378$	−1.19980	+	1.19980i	−0.0617111	+	0.0617111i
$379$	−1.32301	−	4.93754i	−0.0679584	−	0.253624i	0.923586	−	0.383391i	$-0.125244\pi$
$379$	−1.32301	−	4.93754i	−0.0679584	−	0.253624i	−0.991545	+	0.129767i	$0.958577\pi$
$380$	0.558263	−	9.30080i	0.0286383	−	0.477121i
$381$	−11.8883	+	6.86370i	−0.609055	+	0.351638i
$382$			18.6006i			0.951688i
$383$	−13.0887	−	22.6703i	−0.668802	−	1.15840i	−0.978240	−	0.207479i	$-0.933474\pi$
$383$	−13.0887	−	22.6703i	−0.668802	−	1.15840i	0.309438	−	0.950920i	$-0.399859\pi$
$384$	0.258819	−	0.965926i	0.0132078	−	0.0492922i
$385$	9.15164	−	4.57582i	0.466411	−	0.233205i
$386$	−4.08808	−	7.08077i	−0.208078	−	0.360402i
$387$	−2.15539	−	8.04404i	−0.109565	−	0.408902i
$388$	−1.87662	−	1.08346i	−0.0952707	−	0.0550046i
$389$	1.79931			0.0912285			0.0456142	−	0.998959i	$-0.485476\pi$
$389$	1.79931			0.0912285			0.0456142	+	0.998959i	$0.485476\pi$
$390$	−3.03648	+	7.46859i	−0.153758	+	0.378187i
$391$	−2.00974			−0.101637
$392$	3.56885	+	2.06048i	0.180254	+	0.104070i
$393$	−0.156150	−	0.582760i	−0.00787673	−	0.0293964i
$394$	1.50731	+	2.61073i	0.0759370	+	0.131527i
$395$	5.75235	−	17.2571i	0.289432	−	0.868297i
$396$	0.697977	−	2.60488i	0.0350746	−	0.130900i
$397$	12.1867	+	21.1079i	0.611631	+	1.05938i	0.990966	+	0.134116i	$0.0428195\pi$
$397$	12.1867	+	21.1079i	0.611631	+	1.05938i	−0.379335	+	0.925259i	$0.623847\pi$
$398$		−	0.0798408i		−	0.00400206i
$399$	−6.12309	+	3.53517i	−0.306538	+	0.176980i
$400$	−4.59808	+	1.96410i	−0.229904	+	0.0982051i
$401$	−2.21557	−	8.26863i	−0.110640	−	0.412916i	0.888283	−	0.459296i	$-0.151898\pi$
$401$	−2.21557	−	8.26863i	−0.110640	−	0.412916i	−0.998924	+	0.0463800i	$0.985231\pi$
$402$	5.82843	−	5.82843i	0.290696	−	0.290696i
$403$	−23.5363	−	15.6909i	−1.17243	−	0.781619i
$404$			11.9136i			0.592723i
$405$	1.67303	−	1.48356i	0.0831337	−	0.0737189i
$406$	−4.75335	+	8.23304i	−0.235905	+	0.408599i
$407$	−9.83315	−	2.63479i	−0.487411	−	0.130601i
$408$	1.55051			0.0767617
$409$	33.6546	+	9.01772i	1.66411	+	0.445898i	0.963514	−	0.267658i	$-0.0862498\pi$
$409$	33.6546	+	9.01772i	1.66411	+	0.445898i	0.700598	+	0.713556i	$0.252916\pi$
$410$	19.2447	+	12.7064i	0.950427	+	0.627523i
$411$	4.02395	−	4.02395i	0.198487	−	0.198487i
$412$	0.942548	−	3.51764i	0.0464360	−	0.173302i
$413$	−3.01982	+	0.809158i	−0.148596	+	0.0398161i
$414$	−1.25201	+	0.335475i	−0.0615330	+	0.0164877i
$415$	−19.1806	−	6.39355i	−0.941541	−	0.313847i
$416$	−2.70831	+	2.38014i	−0.132786	+	0.116696i
$417$	−14.0552	−	14.0552i	−0.688287	−	0.688287i
$418$	5.61863	−	9.73176i	0.274816	−	0.475996i
$419$	25.3053	+	14.6100i	1.23624	+	0.713745i	0.968324	−	0.249696i	$-0.0803308\pi$
$419$	25.3053	+	14.6100i	1.23624	+	0.713745i	0.267919	+	0.963441i	$0.413664\pi$
$420$	3.16622	+	2.09051i	0.154496	+	0.102007i
$421$	−24.7802	−	24.7802i	−1.20771	−	1.20771i	−0.971766	−	0.235948i	$-0.924180\pi$
$421$	−24.7802	−	24.7802i	−1.20771	−	1.20771i	−0.235948	−	0.971766i	$-0.575820\pi$
$422$	−20.6090	+	11.8986i	−1.00323	+	0.579216i
$423$	−5.31017	+	3.06583i	−0.258189	+	0.149066i
$424$	4.92820	+	4.92820i	0.239335	+	0.239335i
$425$	−4.78681	−	6.09824i	−0.232194	−	0.295808i
$426$	8.67752	+	5.00997i	0.420427	+	0.242734i
$427$	−12.9306	+	22.3965i	−0.625756	+	1.08384i
$428$	1.88536	+	1.88536i	0.0911325	+	0.0911325i
$429$	−7.30370	+	6.41870i	−0.352626	+	0.309898i
$430$	−16.6556	+	8.32780i	−0.803205	+	0.401602i
$431$	10.5376	−	2.82353i	0.507577	−	0.136005i	0.00406274	−	0.999992i	$-0.498707\pi$
$431$	10.5376	−	2.82353i	0.507577	−	0.136005i	0.503514	+	0.863987i	$0.332040\pi$
$432$	0.965926	−	0.258819i	0.0464731	−	0.0124524i
$433$	−6.04800	+	22.5714i	−0.290648	+	1.08471i	0.653964	+	0.756526i	$0.273105\pi$
$433$	−6.04800	+	22.5714i	−0.290648	+	1.08471i	−0.944612	+	0.328189i	$0.893562\pi$
$434$	−9.41297	+	9.41297i	−0.451837	+	0.451837i
$435$	6.90294	−	10.4550i	0.330971	−	0.501278i
$436$	−12.1177	−	3.24692i	−0.580331	−	0.155499i
$437$	−5.40108			−0.258369
$438$	−10.3311	−	2.76821i	−0.493639	−	0.132270i
$439$	14.4096	−	24.9581i	0.687731	−	1.19119i	−0.284839	−	0.958575i	$-0.591940\pi$
$439$	14.4096	−	24.9581i	0.687731	−	1.19119i	0.972570	−	0.232610i	$-0.0747266\pi$
$440$	−6.01934	−	0.361299i	−0.286961	−	0.0172243i
$441$			4.12096i			0.196236i
$442$	−4.65153	−	3.10102i	−0.221251	−	0.147501i
$443$	15.0528	−	15.0528i	0.715180	−	0.715180i	−0.252434	−	0.967614i	$-0.581231\pi$
$443$	15.0528	−	15.0528i	0.715180	−	0.715180i	0.967614	+	0.252434i	$0.0812310\pi$
$444$	−0.977014	−	3.64626i	−0.0463670	−	0.173044i
$445$	−8.35515	−	0.501502i	−0.396072	−	0.0237735i
$446$	12.4704	−	7.19980i	0.590492	−	0.340920i
$447$		−	16.2913i		−	0.770551i
$448$	0.848387	+	1.46945i	0.0400825	+	0.0694250i
$449$	10.7162	−	39.9934i	0.505728	−	1.88740i	0.0468573	−	0.998902i	$-0.485079\pi$
$449$	10.7162	−	39.9934i	0.505728	−	1.88740i	0.458871	−	0.888503i	$-0.348254\pi$
$450$	−4.00000	−	3.00000i	−0.188562	−	0.141421i
$451$	13.9062	+	24.0862i	0.654816	+	1.13418i
$452$	2.61874	+	9.77327i	0.123175	+	0.459696i
$453$	−3.62951	−	2.09550i	−0.170529	−	0.0984550i
$454$	7.72084			0.362357
$455$	−5.31765	−	12.6040i	−0.249295	−	0.590884i
$456$	4.16693			0.195134
$457$	−30.5787	−	17.6546i	−1.43041	−	0.825848i	−0.433259	−	0.901269i	$-0.642636\pi$
$457$	−30.5787	−	17.6546i	−1.43041	−	0.825848i	−0.997152	+	0.0754215i	$0.975970\pi$
$458$	1.00945	+	3.76733i	0.0471686	+	0.176036i
$459$	0.775255	+	1.34278i	0.0361858	+	0.0626757i
$460$	1.29618	+	2.59235i	0.0604346	+	0.120869i
$461$	6.99442	−	26.1035i	0.325763	−	1.21576i	−0.587780	−	0.809021i	$-0.699998\pi$
$461$	6.99442	−	26.1035i	0.325763	−	1.21576i	0.913543	−	0.406742i	$-0.133335\pi$
$462$	2.28791	+	3.96278i	0.106443	+	0.184365i
$463$		−	15.2724i		−	0.709768i	−0.934910	−	0.354884i	$-0.884520\pi$
$463$		−	15.2724i		−	0.709768i	0.934910	−	0.354884i	$-0.115480\pi$
$464$	4.85217	−	2.80140i	0.225256	−	0.130052i
$465$	13.1257	−	11.6392i	0.608689	−	0.539756i
$466$	−2.98047	−	11.1233i	−0.138068	−	0.515276i
$467$	4.30839	−	4.30839i	0.199368	−	0.199368i	−0.600361	−	0.799729i	$-0.704976\pi$
$467$	4.30839	−	4.30839i	0.199368	−	0.199368i	0.799729	+	0.600361i	$0.204976\pi$
$468$	−3.41542	−	1.15539i	−0.157878	−	0.0534081i
$469$			13.9859i			0.645809i
$470$	9.09670	+	10.2585i	0.419599	+	0.473187i
$471$	−11.4136	+	19.7689i	−0.525911	+	0.910904i
$472$	1.77974	+	0.476880i	0.0819192	+	0.0219502i
$473$	−22.4582			−1.03263
$474$	7.85786	+	2.10551i	0.360923	+	0.0967091i
$475$	−12.8643	−	16.3888i	−0.590256	−	0.751968i
$476$	−1.86030	+	1.86030i	−0.0852669	+	0.0852669i
$477$	−1.80385	+	6.73205i	−0.0825925	+	0.308239i
$478$	−16.6739	+	4.46775i	−0.762645	+	0.204350i
$479$	26.0927	−	6.99152i	1.19221	−	0.319451i	0.392449	−	0.919774i	$-0.371628\pi$
$479$	26.0927	−	6.99152i	1.19221	−	0.319451i	0.799757	+	0.600323i	$0.204961\pi$
$480$	−1.00000	−	2.00000i	−0.0456435	−	0.0912871i
$481$	−4.36149	+	12.8928i	−0.198867	+	0.587862i
$482$	−8.32611	−	8.32611i	−0.379244	−	0.379244i
$483$	1.09966	−	1.90467i	0.0500363	−	0.0866654i
$484$	3.22803	+	1.86370i	0.146729	+	0.0847138i
$485$	−4.74703	+	0.971408i	−0.215551	+	0.0441093i
$486$	0.707107	+	0.707107i	0.0320750	+	0.0320750i
$487$	10.0533	−	5.80430i	0.455561	−	0.263018i	−0.254615	−	0.967042i	$-0.581949\pi$
$487$	10.0533	−	5.80430i	0.455561	−	0.263018i	0.710176	+	0.704024i	$0.248615\pi$
$488$	13.1994	−	7.62070i	0.597510	−	0.344973i
$489$	−1.61331	−	1.61331i	−0.0729564	−	0.0729564i
$490$	9.02766	−	1.84737i	0.407828	−	0.0834558i
$491$	19.4549	+	11.2323i	0.877989	+	0.506907i	0.869995	−	0.493061i	$-0.164122\pi$
$491$	19.4549	+	11.2323i	0.877989	+	0.506907i	0.00799395	+	0.999968i	$0.497455\pi$
$492$	−5.15660	+	8.93149i	−0.232477	+	0.402663i
$493$	6.14278	+	6.14278i	0.276657	+	0.276657i
$494$	−12.5008	−	8.33386i	−0.562437	−	0.374958i
$495$	−2.69677	−	5.39355i	−0.121211	−	0.242422i
$496$	7.57812	−	2.03055i	0.340267	−	0.0911744i
$497$	−16.4223	+	4.40033i	−0.736639	+	0.197382i
$498$	2.34020	−	8.73375i	0.104867	−	0.391369i
$499$	−12.4096	+	12.4096i	−0.555529	+	0.555529i	−0.928031	−	0.372503i	$-0.878500\pi$
$499$	−12.4096	+	12.4096i	−0.555529	+	0.555529i	0.372503	+	0.928031i	$0.378500\pi$
$500$	−4.77886	+	10.1075i	−0.213717	+	0.452023i
$501$	−5.31199	−	1.42334i	−0.237322	−	0.0635903i
$502$	−6.84012			−0.305289
$503$	33.7510	+	9.04354i	1.50488	+	0.403232i	0.914732	−	0.404062i	$-0.132402\pi$
$503$	33.7510	+	9.04354i	1.50488	+	0.403232i	0.590150	+	0.807294i	$0.299069\pi$
$504$	−0.848387	+	1.46945i	−0.0377902	+	0.0654545i
$505$	17.6746	+	19.9318i	0.786508	+	0.886955i
$506$			3.49550i			0.155394i
$507$	7.93546	+	10.2970i	0.352426	+	0.457306i
$508$	−9.70674	+	9.70674i	−0.430667	+	0.430667i
$509$	10.7481	+	40.1125i	0.476402	+	1.77796i	0.615999	+	0.787747i	$0.288753\pi$
$509$	10.7481	+	40.1125i	0.476402	+	1.77796i	−0.139597	+	0.990208i	$0.544581\pi$
$510$	2.59405	−	2.30028i	0.114867	−	0.101858i
$511$	15.7165	−	9.07395i	0.695259	−	0.401408i
$512$		−	1.00000i		−	0.0441942i
$513$	2.08346	+	3.60867i	0.0919872	+	0.159327i
$514$	−5.98993	+	22.3547i	−0.264204	+	0.986024i
$515$	−3.64173	−	7.28345i	−0.160474	−	0.320947i
$516$	−4.16390	−	7.21209i	−0.183306	−	0.317495i
$517$	4.27975	+	15.9722i	0.188223	+	0.702459i
$518$	5.54701	+	3.20257i	0.243722	+	0.140713i
$519$	0.484250			0.0212562
$520$	−1.00000	+	8.00000i	−0.0438529	+	0.350823i
$521$	−22.8036			−0.999045			−0.499523	−	0.866301i	$-0.666491\pi$
$521$	−22.8036			−0.999045			−0.499523	+	0.866301i	$0.666491\pi$
$522$	4.85217	+	2.80140i	0.212374	+	0.122614i
$523$	−7.97815	−	29.7748i	−0.348860	−	1.30196i	−0.888037	−	0.459771i	$-0.847931\pi$
$523$	−7.97815	−	29.7748i	−0.348860	−	1.30196i	0.539177	−	0.842192i	$-0.318735\pi$
$524$	−0.301659	−	0.522489i	−0.0131780	−	0.0228250i
$525$	8.39861	−	1.19980i	0.366545	−	0.0523636i
$526$	−6.31187	+	23.5562i	−0.275210	+	1.02710i
$527$	6.08222	+	10.5347i	0.264946	+	0.458899i
$528$		−	2.69677i		−	0.117362i
$529$	−18.4636	+	10.6600i	−0.802765	+	0.463477i
$530$	15.5563	+	0.933740i	0.675725	+	0.0405591i
$531$	0.476880	+	1.77974i	0.0206948	+	0.0772342i
$532$	−4.99948	+	4.99948i	−0.216755	+	0.216755i
$533$	33.3328	−	16.4813i	1.44380	−	0.713883i
$534$		−	3.74326i		−	0.161987i
$535$	5.95133	+	0.357217i	0.257298	+	0.0154439i
$536$	4.12132	−	7.13834i	0.178014	−	0.308329i
$537$	−12.5798	−	3.37075i	−0.542859	−	0.145459i
$538$	18.8983			0.814761
$539$	10.7346	+	2.87633i	0.462373	+	0.123892i
$540$	1.23205	−	1.86603i	0.0530190	−	0.0803009i
$541$	−13.7642	+	13.7642i	−0.591769	+	0.591769i	−0.938109	−	0.346340i	$-0.887424\pi$
$541$	−13.7642	+	13.7642i	−0.591769	+	0.591769i	0.346340	+	0.938109i	$0.387424\pi$
$542$	4.84091	−	18.0665i	0.207935	−	0.776023i
$543$	−2.91824	+	0.781939i	−0.125233	+	0.0335562i
$544$	1.49768	−	0.401302i	0.0642124	−	0.0172057i
$545$	−25.0903	+	12.5451i	−1.07475	+	0.537375i
$546$	5.48406	−	2.71158i	0.234696	−	0.116045i
$547$	7.17814	+	7.17814i	0.306915	+	0.306915i	0.843712	−	0.536797i	$-0.180366\pi$
$547$	7.17814	+	7.17814i	0.306915	+	0.306915i	−0.536797	+	0.843712i	$0.680366\pi$
$548$	2.84536	−	4.92831i	0.121548	−	0.210527i
$549$	13.1994	+	7.62070i	0.563338	+	0.325243i
$550$	−10.6066	+	8.32561i	−0.452265	+	0.355005i
$551$	16.5085	+	16.5085i	0.703284	+	0.703284i
$552$	−1.12252	+	0.648089i	−0.0477777	+	0.0275845i
$553$	−11.9541	+	6.90168i	−0.508338	+	0.293489i
$554$	−0.117156	−	0.117156i	−0.00497750	−	0.00497750i
$555$	−7.04404	−	4.65086i	−0.299003	−	0.197418i
$556$	−17.2140	−	9.93854i	−0.730038	−	0.421488i
$557$	−22.3736	+	38.7521i	−0.947998	+	1.64198i	−0.198365	+	0.980128i	$0.563563\pi$
$557$	−22.3736	+	38.7521i	−0.947998	+	1.64198i	−0.749634	+	0.661853i	$0.769770\pi$
$558$	5.54757	+	5.54757i	0.234847	+	0.234847i
$559$	−1.93247	+	29.9641i	−0.0817349	+	1.26735i
$560$	3.59940	+	1.19980i	0.152103	+	0.0507008i
$561$	4.03890	−	1.08222i	0.170522	−	0.0456914i
$562$	−18.0336	+	4.83208i	−0.760699	+	0.203829i
$563$	8.06903	−	30.1140i	0.340069	−	1.26915i	−0.558199	−	0.829707i	$-0.688507\pi$
$563$	8.06903	−	30.1140i	0.340069	−	1.26915i	0.898268	−	0.439448i	$-0.144826\pi$
$564$	−4.33573	+	4.33573i	−0.182567	+	0.182567i
$565$	18.8805	+	12.4659i	0.794309	+	0.524446i
$566$	22.4513	+	6.01581i	0.943699	+	0.252864i
$567$	−1.69677			−0.0712578
$568$	9.67851	+	2.59335i	0.406101	+	0.108815i
$569$	9.06350	−	15.6984i	0.379962	−	0.658113i	−0.611094	−	0.791558i	$-0.709270\pi$
$569$	9.06350	−	15.6984i	0.379962	−	0.658113i	0.991056	+	0.133444i	$0.0426038\pi$
$570$	6.97141	−	6.18191i	0.292000	−	0.258932i
$571$			32.6068i			1.36455i	0.731096	+	0.682275i	$0.239009\pi$
$571$			32.6068i			1.36455i	−0.731096	+	0.682275i	$0.760991\pi$
$572$	−5.39355	+	8.09032i	−0.225516	+	0.338273i
$573$	−13.1526	+	13.1526i	−0.549457	+	0.549457i
$574$	−4.52912	−	16.9029i	−0.189042	−	0.705513i
$575$	6.01447	+	2.41413i	0.250821	+	0.100676i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$			31.9270i			1.32914i	0.747227	+	0.664568i	$0.231385\pi$
$577$			31.9270i			1.32914i	−0.747227	+	0.664568i	$0.768615\pi$
$578$	−7.29796	−	12.6404i	−0.303555	−	0.525773i
$579$	2.11615	−	7.89757i	0.0879441	−	0.328212i
$580$	3.96178	−	11.8853i	0.164504	−	0.493512i
$581$	7.67099	+	13.2865i	0.318246	+	0.551218i
$582$	−0.560842	−	2.09309i	−0.0232477	−	0.0867615i
$583$	16.2772	+	9.39763i	0.674131	+	0.389210i
$584$	−10.6955			−0.442584
$585$	−7.42820	+	3.13397i	−0.307118	+	0.129574i
$586$	−24.9123			−1.02912
$587$	−10.6325	−	6.13870i	−0.438852	−	0.253371i	0.264259	−	0.964452i	$-0.414873\pi$
$587$	−10.6325	−	6.13870i	−0.438852	−	0.253371i	−0.703111	+	0.711081i	$0.748206\pi$
$588$	1.06658	+	3.98054i	0.0439851	+	0.164155i
$589$	16.3457	+	28.3116i	0.673513	+	1.16656i
$590$	3.68505	−	1.84252i	0.151711	−	0.0758555i
$591$	−0.780239	+	2.91189i	−0.0320947	+	0.119779i
$592$	−1.88745	−	3.26915i	−0.0775735	−	0.134361i
$593$		−	3.25357i		−	0.133608i	−0.997766	−	0.0668040i	$-0.978720\pi$
$593$		−	3.25357i		−	0.133608i	0.997766	−	0.0668040i	$-0.0212802\pi$
$594$	2.33548	−	1.34839i	0.0958257	−	0.0553250i
$595$	−0.352469	+	5.87223i	−0.0144498	+	0.240738i
$596$	−4.21649	−	15.7362i	−0.172714	−	0.644579i
$597$	0.0564559	−	0.0564559i	0.00231059	−	0.00231059i
$598$	4.66374	+	0.300779i	0.190715	+	0.0122998i
$599$			7.03279i			0.287352i	0.989625	+	0.143676i	$0.0458923\pi$
$599$			7.03279i			0.287352i	−0.989625	+	0.143676i	$0.954108\pi$
$600$	−4.64016	−	1.86250i	−0.189434	−	0.0760363i
$601$	7.57447	−	13.1194i	0.308969	−	0.535150i	−0.669168	−	0.743111i	$-0.733349\pi$
$601$	7.57447	−	13.1194i	0.308969	−	0.535150i	0.978137	+	0.207961i	$0.0666827\pi$
$602$	13.6489	+	3.65722i	0.556289	+	0.149057i
$603$	8.24264			0.335666
$604$	−4.04819	−	1.08471i	−0.164718	−	0.0441362i
$605$	8.16552	−	1.67095i	0.331976	−	0.0679338i
$606$	−8.42418	+	8.42418i	−0.342209	+	0.342209i
$607$	3.91308	−	14.6038i	0.158827	−	0.592750i	−0.839920	−	0.542710i	$-0.817398\pi$
$607$	3.91308	−	14.6038i	0.158827	−	0.592750i	0.998747	−	0.0500402i	$-0.0159349\pi$
$608$	4.02494	−	1.07848i	0.163233	−	0.0437382i
$609$	−9.18276	+	2.46051i	−0.372104	+	0.0997050i
$610$	10.7773	−	32.3319i	0.436360	−	1.30908i
$611$	21.6787	−	4.33573i	0.877025	−	0.175405i
$612$	1.09638	+	1.09638i	0.0443184	+	0.0443184i
$613$	6.78402	−	11.7503i	0.274004	−	0.474589i	−0.695879	−	0.718159i	$-0.744985\pi$
$613$	6.78402	−	11.7503i	0.274004	−	0.474589i	0.969883	+	0.243570i	$0.0783185\pi$
$614$	−15.2987	−	8.83271i	−0.617405	−	0.356459i
$615$	4.62328	+	22.5928i	0.186429	+	0.911030i
$616$	3.23559	+	3.23559i	0.130366	+	0.130366i
$617$	−6.88329	+	3.97407i	−0.277111	+	0.159990i	−0.632115	−	0.774875i	$-0.717813\pi$
$617$	−6.88329	+	3.97407i	−0.277111	+	0.159990i	0.355004	+	0.934865i	$0.384480\pi$
$618$	3.15383	−	1.82086i	0.126866	−	0.0732459i
$619$	−10.8722	−	10.8722i	−0.436989	−	0.436989i	0.454008	−	0.890997i	$-0.349994\pi$
$619$	−10.8722	−	10.8722i	−0.436989	−	0.436989i	−0.890997	+	0.454008i	$0.849994\pi$
$620$	9.66598	−	14.6398i	0.388195	−	0.587948i
$621$	−1.12252	−	0.648089i	−0.0450453	−	0.0260069i
$622$	−15.8255	+	27.4105i	−0.634544	+	1.09906i
$623$	4.49117	+	4.49117i	0.179935	+	0.179935i
$624$	−3.59808	−	0.232051i	−0.144038	−	0.00928947i
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$	0.712091	−	0.190804i	0.0284609	−	0.00762607i
$627$	10.8544	−	2.90842i	0.433482	−	0.116151i
$628$	−5.90811	+	22.0494i	−0.235759	+	0.879865i
$629$	4.13870	−	4.13870i	0.165021	−	0.165021i
$630$	0.760643	+	3.71707i	0.0303048	+	0.148092i
$631$	21.6093	+	5.79021i	0.860254	+	0.230504i	0.661869	−	0.749620i	$-0.269764\pi$
$631$	21.6093	+	5.79021i	0.860254	+	0.230504i	0.198386	+	0.980124i	$0.436430\pi$
$632$	8.13505			0.323595
$633$	−22.9864	−	6.15918i	−0.913626	−	0.244805i
$634$	−3.49938	+	6.06110i	−0.138978	+	0.240717i
$635$	−1.83912	+	30.6403i	−0.0729834	+	1.21592i
$636$			6.96953i			0.276360i
$637$	4.76133	−	14.0748i	0.188651	−	0.557663i
$638$	10.6840	−	10.6840i	0.422985	−	0.422985i
$639$	2.59335	+	9.67851i	0.102591	+	0.382876i
$640$	−1.48356	−	1.67303i	−0.0586430	−	0.0661324i
$641$	−16.5419	+	9.55049i	−0.653367	+	0.377221i	−0.789745	−	0.613435i	$-0.789787\pi$
$641$	−16.5419	+	9.55049i	−0.653367	+	0.377221i	0.136378	+	0.990657i	$0.456454\pi$
$642$			2.66631i			0.105231i
$643$	11.1775	+	19.3600i	0.440799	+	0.763486i	0.997749	−	0.0670602i	$-0.0213619\pi$
$643$	11.1775	+	19.3600i	0.440799	+	0.763486i	−0.556950	+	0.830546i	$0.688029\pi$
$644$	0.569226	−	2.12438i	0.0224306	−	0.0837123i
$645$	−17.6659	−	5.88865i	−0.695596	−	0.231865i
$646$	3.23043	+	5.59527i	0.127100	+	0.220143i
$647$	10.4617	+	39.0435i	0.411291	+	1.53496i	0.792151	+	0.610325i	$0.208961\pi$
$647$	10.4617	+	39.0435i	0.411291	+	1.53496i	−0.380860	+	0.924633i	$0.624372\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$	4.96887			0.195045
$650$	10.1955	+	14.8678i	0.399900	+	0.583164i
$651$	−13.3119			−0.521736
$652$	−1.97589	−	1.14078i	−0.0773820	−	0.0446765i
$653$	−7.99018	−	29.8198i	−0.312680	−	1.16694i	−0.926130	−	0.377204i	$-0.876885\pi$
$653$	−7.99018	−	29.8198i	−0.312680	−	1.16694i	0.613450	−	0.789734i	$-0.289781\pi$
$654$	−6.27257	−	10.8644i	−0.245277	−	0.424832i
$655$	−1.27983	−	0.426610i	−0.0500071	−	0.0166690i
$656$	−2.66925	+	9.96178i	−0.104217	+	0.388942i
$657$	−5.34777	−	9.26260i	−0.208636	−	0.361368i
$658$		−	10.4040i		−	0.405591i
$659$	26.6621	−	15.3934i	1.03861	−	0.599641i	0.119170	−	0.992874i	$-0.461977\pi$
$659$	26.6621	−	15.3934i	1.03861	−	0.599641i	0.919439	+	0.393232i	$0.128643\pi$
$660$	−4.00084	−	4.51179i	−0.155732	−	0.175621i
$661$	−6.56325	−	24.4944i	−0.255281	−	0.952721i	−0.967934	−	0.251204i	$-0.919173\pi$
$661$	−6.56325	−	24.4944i	−0.255281	−	0.952721i	0.712653	−	0.701516i	$-0.247493\pi$
$662$	13.0494	−	13.0494i	0.507180	−	0.507180i
$663$	−1.09638	−	5.48188i	−0.0425797	−	0.212899i
$664$		−	9.04184i		−	0.350892i
$665$	−0.947246	+	15.7814i	−0.0367326	+	0.611975i
$666$	1.88745	−	3.26915i	0.0731370	−	0.126677i
$667$	−7.01477	−	1.87960i	−0.271613	−	0.0727785i
$668$	−5.49938			−0.212777
$669$	13.9089	+	3.72689i	0.537751	+	0.144090i
$670$	−3.69507	−	18.0569i	−0.142753	−	0.697599i
$671$	29.0639	−	29.0639i	1.12200	−	1.12200i
$672$	−0.439158	+	1.63896i	−0.0169409	+	0.0632242i
$673$	−13.3943	+	3.58898i	−0.516311	+	0.138345i	−0.507559	−	0.861617i	$-0.669452\pi$
$673$	−13.3943	+	3.58898i	−0.516311	+	0.138345i	−0.00875104	+	0.999962i	$0.502786\pi$
$674$	8.63760	−	2.31444i	0.332708	−	0.0891488i
$675$	−0.707107	−	4.94975i	−0.0272166	−	0.190516i
$676$	10.3301	+	7.89230i	0.397313	+	0.303550i
$677$	33.2390	+	33.2390i	1.27748	+	1.27748i	0.942074	+	0.335404i	$0.108873\pi$
$677$	33.2390	+	33.2390i	1.27748	+	1.27748i	0.335404	+	0.942074i	$0.391127\pi$
$678$	−5.05902	+	8.76248i	−0.194290	+	0.336521i
$679$	3.18419	+	1.83839i	0.122198	+	0.0705511i
$680$	1.91031	−	2.89329i	0.0732569	−	0.110953i
$681$	5.45946	+	5.45946i	0.209207	+	0.209207i
$682$	18.3228	−	10.5787i	0.701618	−	0.405079i
$683$	−21.9649	+	12.6814i	−0.840463	+	0.485242i	−0.857422	−	0.514615i	$-0.827935\pi$
$683$	−21.9649	+	12.6814i	−0.840463	+	0.485242i	0.0169585	+	0.999856i	$0.494602\pi$
$684$	2.94646	+	2.94646i	0.112661	+	0.112661i
$685$	−2.55108	−	12.4665i	−0.0974718	−	0.476320i
$686$	−16.3417	−	9.43488i	−0.623929	−	0.360225i
$687$	−1.95011	+	3.37769i	−0.0744014	+	0.128867i
$688$	−5.88865	−	5.88865i	−0.224503	−	0.224503i
$689$	13.9391	−	20.9086i	0.531036	−	0.796554i
$690$	−0.916536	+	2.74961i	−0.0348919	+	0.104676i
$691$	7.70110	−	2.06350i	0.292964	−	0.0784994i	−0.109344	−	0.994004i	$-0.534875\pi$
$691$	7.70110	−	2.06350i	0.292964	−	0.0784994i	0.402308	+	0.915505i	$0.368208\pi$
$692$	0.467750	−	0.125333i	0.0177812	−	0.00476446i
$693$	−1.18431	+	4.41990i	−0.0449882	+	0.167898i
$694$	15.6011	−	15.6011i	0.592209	−	0.592209i
$695$	−43.5441	+	8.91065i	−1.65172	+	0.338000i
$696$	5.41189	+	1.45011i	0.205137	+	0.0549664i
$697$	−15.9907			−0.605691
$698$	25.5592	+	6.84858i	0.967431	+	0.259222i
$699$	5.75783	−	9.97286i	0.217781	−	0.377208i
$700$	7.80190	−	3.33264i	0.294884	−	0.125962i
$701$			28.7457i			1.08571i	0.839827	+	0.542855i	$0.182657\pi$
$701$			28.7457i			1.08571i	−0.839827	+	0.542855i	$0.817343\pi$
$702$	−1.59808	−	3.23205i	−0.0603155	−	0.121986i
$703$	11.1226	−	11.1226i	0.419496	−	0.419496i
$704$	−0.697977	−	2.60488i	−0.0263060	−	0.0981753i
$705$	−0.821486	+	13.6862i	−0.0309389	+	0.515451i
$706$	4.62622	−	2.67095i	0.174110	−	0.100523i
$707$		−	20.2147i		−	0.760251i
$708$	0.921262	+	1.59567i	0.0346231	+	0.0599690i
$709$	−8.43944	+	31.4964i	−0.316950	+	1.18287i	0.605211	+	0.796065i	$0.293089\pi$
$709$	−8.43944	+	31.4964i	−0.316950	+	1.18287i	−0.922161	+	0.386807i	$0.873578\pi$
$710$	20.0399	−	10.0199i	0.752083	−	0.376041i
$711$	4.06753	+	7.04516i	0.152544	+	0.264214i
$712$	−0.968828	−	3.61571i	−0.0363084	−	0.135505i
$713$	−8.80669	−	5.08454i	−0.329813	−	0.190418i
$714$	−2.63087			−0.0984577
$715$	2.97893	+	21.5371i	0.111406	+	0.805440i
$716$	−13.0236			−0.486714
$717$	−14.9494	−	8.63103i	−0.558295	−	0.322332i
$718$	0.914647	+	3.41351i	0.0341343	+	0.127391i
$719$	−25.4137	−	44.0178i	−0.947770	−	1.64159i	−0.750108	−	0.661316i	$-0.769998\pi$
$719$	−25.4137	−	44.0178i	−0.947770	−	1.64159i	−0.197662	−	0.980270i	$-0.563335\pi$
$720$	0.707107	−	2.12132i	0.0263523	−	0.0790569i
$721$	−1.59929	+	5.96864i	−0.0595607	+	0.222284i
$722$	−0.818353	−	1.41743i	−0.0304559	−	0.0527512i
$723$		−	11.7749i		−	0.437913i
$724$	−2.61642	+	1.51059i	−0.0972384	+	0.0561406i
$725$	−11.0045	−	25.7621i	−0.408696	−	0.956781i
$726$	0.964724	+	3.60040i	0.0358043	+	0.133623i
$727$	23.6281	−	23.6281i	0.876319	−	0.876319i	−0.116832	−	0.993152i	$-0.537274\pi$
$727$	23.6281	−	23.6281i	0.876319	−	0.876319i	0.993152	+	0.116832i	$0.0372740\pi$
$728$	4.59539	−	4.03856i	0.170316	−	0.149679i
$729$			1.00000i			0.0370370i
$730$	−17.8940	+	15.8675i	−0.662286	+	0.587283i
$731$	6.45617	−	11.1824i	0.238790	−	0.413597i
$732$	14.7221	+	3.94476i	0.544143	+	0.145803i
$733$	−21.6103			−0.798195			−0.399098	−	0.916908i	$-0.630677\pi$
$733$	−21.6103			−0.798195			−0.399098	+	0.916908i	$0.630677\pi$
$734$	22.8055	+	6.11072i	0.841767	+	0.225551i
$735$	7.68981	+	5.07723i	0.283643	+	0.187276i
$736$	−0.916536	+	0.916536i	−0.0337840	+	0.0337840i
$737$	5.75317	−	21.4711i	0.211921	−	0.790899i
$738$	−9.96178	+	2.66925i	−0.366698	+	0.0982565i
$739$	−43.3940	+	11.6274i	−1.59627	+	0.427720i	−0.943914	−	0.330190i	$-0.892887\pi$
$739$	−43.3940	+	11.6274i	−1.59627	+	0.427720i	−0.652359	+	0.757910i	$0.726220\pi$
$740$	−8.00775	−	2.66925i	−0.294371	−	0.0981236i
$741$	−2.94646	−	14.7323i	−0.108241	−	0.541205i
$742$	−8.36205	−	8.36205i	−0.306981	−	0.306981i
$743$	−20.4586	+	35.4354i	−0.750555	+	1.30000i	0.196999	+	0.980404i	$0.436880\pi$
$743$	−20.4586	+	35.4354i	−0.750555	+	1.30000i	−0.947554	+	0.319596i	$0.896453\pi$
$744$	6.79435	+	3.92272i	0.249093	+	0.143814i
$745$	−30.4000	−	20.0717i	−1.11377	−	0.735370i
$746$	−9.53721	−	9.53721i	−0.349182	−	0.349182i
$747$	7.83047	−	4.52092i	0.286502	−	0.165412i
$748$	3.62118	−	2.09069i	0.132403	−	0.0764431i
$749$	−3.19904	−	3.19904i	−0.116890	−	0.116890i
$750$	−10.5263	+	3.76795i	−0.384365	+	0.137586i
$751$	−22.0629	−	12.7380i	−0.805087	−	0.464817i	0.0401601	−	0.999193i	$-0.487213\pi$
$751$	−22.0629	−	12.7380i	−0.805087	−	0.464817i	−0.845247	+	0.534376i	$0.820547\pi$
$752$	−3.06583	+	5.31017i	−0.111799	+	0.193642i
$753$	−4.83669	−	4.83669i	−0.176259	−	0.176259i
$754$	−13.3355	−	15.1741i	−0.485648	−	0.552609i
$755$	−8.38199	+	4.19099i	−0.305052	+	0.152526i
$756$	−1.63896	+	0.439158i	−0.0596083	+	0.0159720i
$757$	25.2307	−	6.76055i	0.917025	−	0.245716i	0.230712	−	0.973022i	$-0.425895\pi$
$757$	25.2307	−	6.76055i	0.917025	−	0.245716i	0.686313	+	0.727306i	$0.259228\pi$
$758$	1.32301	−	4.93754i	0.0480539	−	0.179340i
$759$	−2.47169	+	2.47169i	−0.0897167	+	0.0897167i
$760$	5.13387	−	7.77559i	0.186225	−	0.282050i
$761$	−23.5677	−	6.31495i	−0.854329	−	0.228917i	−0.195030	−	0.980797i	$-0.562480\pi$
$761$	−23.5677	−	6.31495i	−0.854329	−	0.228917i	−0.659299	+	0.751880i	$0.729147\pi$
$762$	−13.7274			−0.497291
$763$	20.5610	+	5.50929i	0.744357	+	0.199450i
$764$	−9.30028	+	16.1086i	−0.336472	+	0.582787i
$765$	3.46082	+	0.207729i	0.125126	+	0.00751046i
$766$		−	26.1774i		−	0.945828i
$767$	0.427559	−	6.62954i	0.0154383	−	0.239379i
$768$	0.707107	−	0.707107i	0.0255155	−	0.0255155i
$769$	−1.41386	−	5.27662i	−0.0509853	−	0.190280i	0.935736	−	0.352700i	$-0.114736\pi$
$769$	−1.41386	−	5.27662i	−0.0509853	−	0.190280i	−0.986722	+	0.162421i	$0.948070\pi$
$770$	10.2135	+	0.613043i	0.368068	+	0.0220926i
$771$	−20.0427	+	11.5716i	−0.721820	+	0.416743i
$772$		−	8.17617i		−	0.294267i
$773$	8.18519	+	14.1772i	0.294401	+	0.509917i	0.974845	−	0.222882i	$-0.0715466\pi$
$773$	8.18519	+	14.1772i	0.294401	+	0.509917i	−0.680445	+	0.732800i	$0.738213\pi$
$774$	2.15539	−	8.04404i	0.0774741	−	0.289137i
$775$	−5.54757	−	38.8330i	−0.199274	−	1.39492i
$776$	−1.08346	−	1.87662i	−0.0388941	−	0.0673666i
$777$	1.65777	+	6.18689i	0.0594722	+	0.221953i
$778$	1.55825	+	0.899653i	0.0558658	+	0.0322541i
$779$	−42.9743			−1.53972
$780$	−6.36396	+	4.94975i	−0.227866	+	0.177229i
$781$	27.0215			0.966906
$782$	−1.74048	−	1.00487i	−0.0622395	−	0.0359340i
$783$	1.45011	+	5.41189i	0.0518228	+	0.193405i
$784$	2.06048	+	3.56885i	0.0735885	+	0.127459i
$785$	22.8272	+	45.6544i	0.814737	+	1.62947i
$786$	0.156150	−	0.582760i	0.00556969	−	0.0207864i
$787$	−15.5016	−	26.8496i	−0.552573	−	0.957084i	−0.998088	−	0.0618097i	$-0.980313\pi$
$787$	−15.5016	−	26.8496i	−0.552573	−	0.957084i	0.445515	−	0.895274i	$-0.353021\pi$
$788$			3.01461i			0.107391i
$789$	−21.1199	+	12.1936i	−0.751889	+	0.434103i
$790$	13.6102	−	12.0689i	0.484229	−	0.429391i
$791$	−4.44341	−	16.5830i	−0.157990	−	0.589625i
$792$	1.90691	−	1.90691i	0.0677590	−	0.0677590i
$793$	−36.2766	−	41.2784i	−1.28822	−	1.46584i
$794$			24.3733i			0.864977i
$795$	10.3397	+	11.6603i	0.366713	+	0.413547i
$796$	0.0399204	−	0.0691441i	0.00141494	−	0.00245075i
$797$	27.8385	+	7.45931i	0.986091	+	0.264222i	0.715608	−	0.698503i	$-0.246150\pi$
$797$	27.8385	+	7.45931i	0.986091	+	0.264222i	0.270483	+	0.962725i	$0.412817\pi$
$798$	−7.07034			−0.250287
$799$	−9.18324	−	2.46064i	−0.324880	−	0.0870513i
$800$	−4.96410	−	0.598076i	−0.175507	−	0.0211452i
$801$	2.64689	−	2.64689i	0.0935231	−	0.0935231i
$802$	2.21557	−	8.26863i	0.0782346	−	0.291975i
$803$	−27.8606	+	7.46523i	−0.983180	+	0.263442i
$804$	7.96178	−	2.13335i	0.280790	−	0.0752375i
$805$	−2.19932	−	4.39864i	−0.0775159	−	0.155032i
$806$	−12.5376	−	25.3569i	−0.441619	−	0.893158i
$807$	13.3631	+	13.3631i	0.470403	+	0.470403i
$808$	−5.95680	+	10.3175i	−0.209559	+	0.362967i
$809$	−39.3730	−	22.7320i	−1.38428	−	0.799215i	−0.391619	−	0.920128i	$-0.628085\pi$
$809$	−39.3730	−	22.7320i	−1.38428	−	0.799215i	−0.992663	+	0.120912i	$0.961418\pi$
$810$	2.19067	−	0.448288i	0.0769723	−	0.0157512i
$811$	33.7831	+	33.7831i	1.18629	+	1.18629i	0.978087	+	0.208198i	$0.0667600\pi$
$811$	33.7831	+	33.7831i	1.18629	+	1.18629i	0.208198	+	0.978087i	$0.433240\pi$
$812$	−8.23304	+	4.75335i	−0.288923	+	0.166810i
$813$	16.1980	−	9.35191i	0.568088	−	0.327986i
$814$	−7.19837	−	7.19837i	−0.252303	−	0.252303i
$815$	−4.99816	+	1.02280i	−0.175078	+	0.0358270i
$816$	1.34278	+	0.775255i	0.0470067	+	0.0271394i
$817$	17.3507	−	30.0523i	0.607024	−	1.05140i
$818$	24.6369	+	24.6369i	0.861408	+	0.861408i
$819$	5.79519	+	1.96044i	0.202500	+	0.0685035i
$820$	10.3132	+	20.6264i	0.360152	+	0.720305i
$821$	−30.7466	+	8.23853i	−1.07306	+	0.287527i	−0.751752	−	0.659446i	$-0.770791\pi$
$821$	−30.7466	+	8.23853i	−1.07306	+	0.287527i	−0.321313	+	0.946973i	$0.604124\pi$
$822$	5.49682	−	1.47287i	0.191723	−	0.0513721i
$823$	3.81257	−	14.2287i	0.132898	−	0.495982i	−0.867100	−	0.498134i	$-0.834019\pi$
$823$	3.81257	−	14.2287i	0.132898	−	0.495982i	0.999998	+	0.00215284i	$0.000685271\pi$
$824$	2.57509	−	2.57509i	0.0897075	−	0.0897075i
$825$	−13.3871	−	1.61288i	−0.466078	−	0.0561532i
$826$	−3.01982	−	0.809158i	−0.105073	−	0.0281542i
$827$	28.3497			0.985816			0.492908	−	0.870081i	$-0.335934\pi$
$827$	28.3497			0.985816			0.492908	+	0.870081i	$0.335934\pi$
$828$	−1.25201	−	0.335475i	−0.0435104	−	0.0116586i
$829$	−3.58970	+	6.21755i	−0.124675	+	0.215944i	−0.921606	−	0.388127i	$-0.873122\pi$
$829$	−3.58970	+	6.21755i	−0.124675	+	0.215944i	0.796931	+	0.604071i	$0.206456\pi$
$830$	−13.4142	−	15.1273i	−0.465612	−	0.525076i
$831$		−	0.165684i		−	0.00574752i
$832$	−3.53553	+	0.707107i	−0.122573	+	0.0245145i
$833$	−4.51812	+	4.51812i	−0.156544	+	0.156544i
$834$	−5.14456	−	19.1998i	−0.178142	−	0.664834i
$835$	−9.20064	+	8.15868i	−0.318401	+	0.282343i
$836$	9.73176	−	5.61863i	0.336580	−	0.194325i
$837$			7.84544i			0.271178i
$838$	14.6100	+	25.3053i	0.504694	+	0.874156i
$839$	1.18716	−	4.43053i	0.0409852	−	0.152959i	−0.942401	−	0.334486i	$-0.891437\pi$
$839$	1.18716	−	4.43053i	0.0409852	−	0.152959i	0.983386	+	0.181527i	$0.0581040\pi$
$840$	1.69677	+	3.39355i	0.0585443	+	0.117089i
$841$	1.19570	+	2.07101i	0.0412309	+	0.0714141i
$842$	−9.07019	−	33.8504i	−0.312579	−	1.16656i
$843$	−16.1684	−	9.33485i	−0.556871	−	0.321509i
$844$	−23.7972			−0.819134
$845$	28.9914	−	2.12132i	0.997334	−	0.0729756i
$846$	−6.13165			−0.210811
$847$	−5.47724	−	3.16228i	−0.188200	−	0.108657i
$848$	1.80385	+	6.73205i	0.0619444	+	0.231180i
$849$	11.6217	+	20.1293i	0.398854	+	0.690836i
$850$	−1.09638	−	7.67463i	−0.0376054	−	0.263238i
$851$	−1.26638	+	4.72620i	−0.0434110	+	0.162012i
$852$	5.00997	+	8.67752i	0.171639	+	0.297287i
$853$			42.4467i			1.45335i	0.686983	+	0.726673i	$0.258935\pi$
$853$			42.4467i			1.45335i	−0.686983	+	0.726673i	$0.741065\pi$
$854$	−22.3965	+	12.9306i	−0.766391	+	0.442476i
$855$	9.30080	+	0.558263i	0.318081	+	0.0190922i
$856$	0.690091	+	2.57545i	0.0235868	+	0.0880272i
$857$	25.6454	−	25.6454i	0.876029	−	0.876029i	−0.117092	−	0.993121i	$-0.537357\pi$
$857$	25.6454	−	25.6454i	0.876029	−	0.876029i	0.993121	+	0.117092i	$0.0373572\pi$
$858$	−9.53454	+	1.90691i	−0.325504	+	0.0651008i
$859$		−	36.2147i		−	1.23563i	−0.786324	−	0.617814i	$-0.788018\pi$
$859$		−	36.2147i		−	1.23563i	0.786324	−	0.617814i	$-0.211982\pi$
$860$	−18.5881	−	1.11571i	−0.633848	−	0.0380455i
$861$	8.74958	−	15.1547i	0.298185	−	0.516472i
$862$	10.5376	+	2.82353i	0.358911	+	0.0961700i
$863$	8.04560			0.273875			0.136938	−	0.990580i	$-0.456274\pi$
$863$	8.04560			0.273875			0.136938	+	0.990580i	$0.456274\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	0.596621	−	0.903624i	0.0202857	−	0.0307241i
$866$	−16.5234	+	16.5234i	−0.561489	+	0.561489i
$867$	3.77770	−	14.0986i	0.128297	−	0.478813i
$868$	−12.8584	+	3.44539i	−0.436441	+	0.116944i
$869$	21.1909	−	5.67808i	0.718851	−	0.192616i
$870$	11.2056	−	5.60280i	0.379906	−	0.189953i
$871$	−28.1520	−	9.52350i	−0.953896	−	0.322692i
$872$	−8.87075	−	8.87075i	−0.300402	−	0.300402i
$873$	1.08346	−	1.87662i	0.0366697	−	0.0635138i
$874$	−4.67747	−	2.70054i	−0.158218	−	0.0913471i
$875$	8.10865	−	17.1502i	0.274122	−	0.579784i
$876$	−7.56288	−	7.56288i	−0.255526	−	0.255526i
$877$	1.39522	−	0.805530i	0.0471132	−	0.0272008i	−0.476258	−	0.879305i	$-0.658007\pi$
$877$	1.39522	−	0.805530i	0.0471132	−	0.0272008i	0.523372	+	0.852105i	$0.324674\pi$
$878$	24.9581	−	14.4096i	0.842295	−	0.486299i
$879$	−17.6157	−	17.6157i	−0.594162	−	0.594162i
$880$	−5.03225	−	3.32256i	−0.169637	−	0.112004i
$881$	−29.5852	−	17.0810i	−0.996751	−	0.575475i	−0.0894659	−	0.995990i	$-0.528516\pi$
$881$	−29.5852	−	17.0810i	−0.996751	−	0.575475i	−0.907286	+	0.420515i	$0.861849\pi$
$882$	−2.06048	+	3.56885i	−0.0693799	+	0.120170i
$883$	35.7131	+	35.7131i	1.20184	+	1.20184i	0.973606	+	0.228236i	$0.0732958\pi$
$883$	35.7131	+	35.7131i	1.20184	+	1.20184i	0.228236	+	0.973606i	$0.426704\pi$
$884$	−2.47783	−	5.01133i	−0.0833386	−	0.168549i
$885$	3.90858	+	1.30286i	0.131386	+	0.0437952i
$886$	20.5625	−	5.50971i	0.690811	−	0.185102i
$887$	−4.75331	+	1.27365i	−0.159601	+	0.0427649i	−0.337735	−	0.941241i	$-0.609661\pi$
$887$	−4.75331	+	1.27365i	−0.159601	+	0.0427649i	0.178134	+	0.984006i	$0.442994\pi$
$888$	0.977014	−	3.64626i	0.0327864	−	0.122361i
$889$	16.4702	−	16.4702i	0.552391	−	0.552391i
$890$	−6.98502	−	4.61189i	−0.234139	−	0.154591i
$891$	2.60488	+	0.697977i	0.0872669	+	0.0233831i
$892$	14.3996			0.482134
$893$	−24.6796	−	6.61287i	−0.825870	−	0.221291i
$894$	8.14564	−	14.1087i	0.272431	−	0.471864i
$895$	−21.7889	+	19.3213i	−0.728322	+	0.645840i
$896$			1.69677i			0.0566853i
$897$	3.08508	+	3.51045i	0.103008	+	0.117210i
$898$	29.2772	−	29.2772i	0.976992	−	0.976992i
$899$	11.3768	+	42.4587i	0.379437	+	1.41608i
$900$	−1.96410	−	4.59808i	−0.0654701	−	0.153269i
$901$	−9.35856	+	5.40317i	−0.311779	+	0.180006i
$902$			27.8124i			0.926050i
$903$	7.06520	+	12.2373i	0.235115	+	0.407232i
$904$	−2.61874	+	9.77327i	−0.0870980	+	0.325054i
$905$	−2.13630	+	6.40889i	−0.0710129	+	0.213039i
$906$	−2.09550	−	3.62951i	−0.0696182	−	0.120582i
$907$	5.73768	+	21.4133i	0.190517	+	0.711018i	0.993382	+	0.114857i	$0.0366411\pi$
$907$	5.73768	+	21.4133i	0.190517	+	0.711018i	−0.802865	+	0.596160i	$0.796692\pi$
$908$	6.68644	+	3.86042i	0.221897	+	0.128113i
$909$	−11.9136			−0.395149
$910$	1.69677	−	13.5742i	0.0562475	−	0.449980i
$911$	41.2800			1.36767			0.683834	−	0.729638i	$-0.260311\pi$
$911$	41.2800			1.36767			0.683834	+	0.729638i	$0.260311\pi$
$912$	3.60867	+	2.08346i	0.119495	+	0.0689904i
$913$	−6.31100	−	23.5530i	−0.208863	−	0.779489i
$914$	−17.6546	−	30.5787i	−0.583963	−	1.01145i
$915$	30.4828	−	15.2414i	1.00773	−	0.503865i
$916$	−1.00945	+	3.76733i	−0.0333532	+	0.124476i
$917$	0.511847	+	0.886545i	0.0169027	+	0.0292763i
$918$			1.55051i			0.0511745i
$919$	−4.23675	+	2.44609i	−0.139758	+	0.0806891i	−0.568248	−	0.822857i	$-0.692379\pi$
$919$	−4.23675	+	2.44609i	−0.139758	+	0.0806891i	0.428491	+	0.903546i	$0.359045\pi$
$920$	−0.173655	+	2.89313i	−0.00572523	+	0.0953838i
$921$	−4.57215	−	17.0635i	−0.150657	−	0.562261i
$922$	19.1091	−	19.1091i	0.629325	−	0.629325i
$923$	2.32513	−	36.0525i	0.0765327	−	1.18668i
$924$			4.57582i			0.150533i
$925$	−17.3572	+	7.41427i	−0.570702	+	0.243780i
$926$	7.63619	−	13.2263i	0.250941	−	0.434642i
$927$	3.51764	+	0.942548i	0.115534	+	0.0309573i
$928$	5.60280			0.183921
$929$	1.34584	+	0.360617i	0.0441556	+	0.0118315i	0.280829	−	0.959758i	$-0.409391\pi$
$929$	1.34584	+	0.360617i	0.0441556	+	0.0118315i	−0.236674	+	0.971589i	$0.576057\pi$
$930$	17.1868	−	3.51702i	0.563577	−	0.115327i
$931$	−12.1422	+	12.1422i	−0.397946	+	0.397946i
$932$	2.98047	−	11.1233i	0.0976287	−	0.364355i
$933$	−30.5725	+	8.19187i	−1.00090	+	0.268190i
$934$	5.88536	−	1.57698i	0.192575	−	0.0516003i
$935$	2.95668	−	8.87004i	0.0966938	−	0.290081i
$936$	−2.38014	−	2.70831i	−0.0777973	−	0.0885238i
$937$	−29.9091	−	29.9091i	−0.977088	−	0.977088i	0.0226553	−	0.999743i	$-0.492788\pi$
$937$	−29.9091	−	29.9091i	−0.977088	−	0.977088i	−0.999743	+	0.0226553i	$0.992788\pi$
$938$	−6.99295	+	12.1121i	−0.228328	+	0.395476i
$939$	0.638443	+	0.368605i	0.0208348	+	0.0120290i
$940$	2.74874	+	13.4324i	0.0896542	+	0.438118i
$941$	−34.3258	−	34.3258i	−1.11899	−	1.11899i	−0.991890	−	0.127100i	$-0.959433\pi$
$941$	−34.3258	−	34.3258i	−1.11899	−	1.11899i	−0.127100	−	0.991890i	$-0.540567\pi$
$942$	−19.7689	+	11.4136i	−0.644106	+	0.371875i
$943$	11.5768	−	6.68386i	0.376992	−	0.217657i
$944$	1.30286	+	1.30286i	0.0424045	+	0.0424045i
$945$	−2.09051	+	3.16622i	−0.0680044	+	0.102997i
$946$	−19.4494	−	11.2291i	−0.632354	−	0.365090i
$947$	26.9011	−	46.5941i	0.874169	−	1.51411i	0.0165245	−	0.999863i	$-0.494740\pi$
$947$	26.9011	−	46.5941i	0.874169	−	1.51411i	0.857645	−	0.514242i	$-0.171927\pi$
$948$	5.75235	+	5.75235i	0.186828	+	0.186828i
$949$	7.56288	+	37.8144i	0.245502	+	1.22751i
$950$	−2.94646	−	20.6252i	−0.0955959	−	0.669171i
$951$	−6.76028	+	1.81141i	−0.219217	+	0.0587390i
$952$	−2.54122	+	0.680918i	−0.0823615	+	0.0220687i
$953$	−8.70086	+	32.4720i	−0.281848	+	1.05187i	0.669263	+	0.743025i	$0.266610\pi$
$953$	−8.70086	+	32.4720i	−0.281848	+	1.05187i	−0.951112	+	0.308847i	$0.900057\pi$
$954$	−4.92820	+	4.92820i	−0.159556	+	0.159556i
$955$	8.33840	+	40.7477i	0.269824	+	1.31856i
$956$	−16.6739	−	4.46775i	−0.539271	−	0.144497i
$957$	15.1095			0.488421
$958$	26.0927	+	6.99152i	0.843017	+	0.225886i
$959$	−4.82794	+	8.36223i	−0.155902	+	0.270031i
$960$	0.133975	−	2.23205i	0.00432401	−	0.0720391i
$961$			30.5510i			0.985515i
$962$	−10.2236	+	8.98477i	−0.329621	+	0.289680i
$963$	−1.88536	+	1.88536i	−0.0607550	+	0.0607550i
$964$	−3.04757	−	11.3737i	−0.0981555	−	0.366321i
$965$	−12.1299	−	13.6790i	−0.390474	−	0.440342i
$966$	1.90467	−	1.09966i	0.0612817	−	0.0353810i
$967$		−	42.1480i		−	1.35539i	−0.735344	−	0.677694i	$-0.762980\pi$
$967$		−	42.1480i		−	1.35539i	0.735344	−	0.677694i	$-0.237020\pi$
$968$	1.86370	+	3.22803i	0.0599017	+	0.103753i
$969$	−1.67220	+	6.24072i	−0.0537186	+	0.200481i
$970$	−4.59675	−	1.53225i	−0.147593	−	0.0491976i
$971$	7.84873	+	13.5944i	0.251878	+	0.436265i	0.964043	−	0.265747i	$-0.0856186\pi$
$971$	7.84873	+	13.5944i	0.251878	+	0.436265i	−0.712165	+	0.702012i	$0.752285\pi$
$972$	0.258819	+	0.965926i	0.00830162	+	0.0309821i
$973$	29.2084	+	16.8635i	0.936377	+	0.540618i
$974$	11.6086			0.371964
$975$	−3.30385	+	17.7224i	−0.105808	+	0.567572i
$976$	15.2414			0.487865
$977$	9.47861	+	5.47248i	0.303247	+	0.175080i	0.643901	−	0.765109i	$-0.277315\pi$
$977$	9.47861	+	5.47248i	0.303247	+	0.175080i	−0.340653	+	0.940189i	$0.610648\pi$
$978$	−0.590513	−	2.20382i	−0.0188825	−	0.0704705i
$979$	−5.04737	−	8.74230i	−0.161315	−	0.279405i
$980$	8.74187	+	2.91396i	0.279249	+	0.0930829i
$981$	3.24692	−	12.1177i	0.103666	−	0.386887i
$982$	11.2323	+	19.4549i	0.358437	+	0.620832i
$983$			59.8088i			1.90760i	0.300437	+	0.953802i	$0.402868\pi$
$983$			59.8088i			1.90760i	−0.300437	+	0.953802i	$0.597132\pi$
$984$	−8.93149	+	5.15660i	−0.284725	+	0.164386i
$985$	4.47237	+	5.04354i	0.142502	+	0.160701i
$986$	2.24841	+	8.39119i	0.0716041	+	0.267230i
$987$	7.35676	−	7.35676i	0.234168	−	0.234168i
$988$	−6.65907	−	13.4677i	−0.211853	−	0.428465i
$989$			10.7943i			0.343239i
$990$	0.361299	−	6.01934i	0.0114828	−	0.191307i
$991$	22.0072	−	38.1175i	0.699081	−	1.21084i	−0.269705	−	0.962943i	$-0.586926\pi$
$991$	22.0072	−	38.1175i	0.699081	−	1.21084i	0.968786	−	0.247900i	$-0.0797405\pi$
$992$	7.57812	+	2.03055i	0.240605	+	0.0644700i
$993$	18.4546			0.585641
$994$	−16.4223	−	4.40033i	−0.520882	−	0.139570i
$995$	−0.0357916	−	0.174905i	−0.00113467	−	0.00554486i
$996$	6.39355	−	6.39355i	0.202587	−	0.202587i
$997$	5.38675	−	20.1036i	0.170600	−	0.636688i	−0.826659	−	0.562703i	$-0.809762\pi$
$997$	5.38675	−	20.1036i	0.170600	−	0.636688i	0.997259	−	0.0739853i	$-0.0235718\pi$
$998$	−16.9518	+	4.54222i	−0.536599	+	0.143781i
$999$	3.64626	−	0.977014i	0.115363	−	0.0309113i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.a.7.2	✓	8
5.3	odd	4		390.2.bn.a.163.1	yes	8
13.2	odd	12		390.2.bn.a.67.1	yes	8
65.28	even	12	inner	390.2.bd.a.223.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.a.7.2	✓	8	1.1	even	1	trivial
390.2.bd.a.223.2	yes	8	65.28	even	12	inner
390.2.bn.a.67.1	yes	8	13.2	odd	12
390.2.bn.a.163.1	yes	8	5.3	odd	4

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.848387 - 1.46945i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.258819 + 0.965926i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 + 0.707107i) q^{5} +(-0.258819 + 0.965926i) q^{6} +(-0.848387 - 1.46945i) q^{7} +1.00000i q^{8} +(-0.866025 + 0.500000i) q^{9} +(1.48356 + 1.67303i) q^{10} +(0.697977 + 2.60488i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(3.53553 - 0.707107i) q^{13} -1.69677i q^{14} +(-0.133975 + 2.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.49768 - 0.401302i) q^{17} -1.00000 q^{18} +(-4.02494 - 1.07848i) q^{19} +(0.448288 + 2.19067i) q^{20} +(1.19980 - 1.19980i) q^{21} +(-0.697977 + 2.60488i) q^{22} +(1.25201 - 0.335475i) q^{23} +(-0.965926 + 0.258819i) q^{24} +(4.00000 + 3.00000i) q^{25} +(3.41542 + 1.15539i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(0.848387 - 1.46945i) q^{28} +(-4.85217 - 2.80140i) q^{29} +(-1.23205 + 1.86603i) q^{30} +(-5.54757 - 5.54757i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-2.33548 + 1.34839i) q^{33} +(-1.09638 - 1.09638i) q^{34} +(-0.760643 - 3.71707i) q^{35} +(-0.866025 - 0.500000i) q^{36} +(-1.88745 + 3.26915i) q^{37} +(-2.94646 - 2.94646i) q^{38} +(1.59808 + 3.23205i) q^{39} +(-0.707107 + 2.12132i) q^{40} +(9.96178 - 2.66925i) q^{41} +(1.63896 - 0.439158i) q^{42} +(-2.15539 + 8.04404i) q^{43} +(-1.90691 + 1.90691i) q^{44} +(-2.19067 + 0.448288i) q^{45} +(1.25201 + 0.335475i) q^{46} +6.13165 q^{47} +(-0.965926 - 0.258819i) q^{48} +(2.06048 - 3.56885i) q^{49} +(1.96410 + 4.59808i) q^{50} -1.55051i q^{51} +(2.38014 + 2.70831i) q^{52} +(4.92820 - 4.92820i) q^{53} +(-0.258819 - 0.965926i) q^{54} +(-0.361299 + 6.01934i) q^{55} +(1.46945 - 0.848387i) q^{56} -4.16693i q^{57} +(-2.80140 - 4.85217i) q^{58} +(0.476880 - 1.77974i) q^{59} +(-2.00000 + 1.00000i) q^{60} +(-7.62070 - 13.1994i) q^{61} +(-2.03055 - 7.57812i) q^{62} +(1.46945 + 0.848387i) q^{63} -1.00000 q^{64} +(8.00000 + 1.00000i) q^{65} -2.69677 q^{66} +(-7.13834 - 4.12132i) q^{67} +(-0.401302 - 1.49768i) q^{68} +(0.648089 + 1.12252i) q^{69} +(1.19980 - 3.59940i) q^{70} +(2.59335 - 9.67851i) q^{71} +(-0.500000 - 0.866025i) q^{72} +10.6955i q^{73} +(-3.26915 + 1.88745i) q^{74} +(-1.86250 + 4.64016i) q^{75} +(-1.07848 - 4.02494i) q^{76} +(3.23559 - 3.23559i) q^{77} +(-0.232051 + 3.59808i) q^{78} -8.13505i q^{79} +(-1.67303 + 1.48356i) q^{80} +(0.500000 - 0.866025i) q^{81} +(9.96178 + 2.66925i) q^{82} -9.04184 q^{83} +(1.63896 + 0.439158i) q^{84} +(-2.89329 - 1.91031i) q^{85} +(-5.88865 + 5.88865i) q^{86} +(1.45011 - 5.41189i) q^{87} +(-2.60488 + 0.697977i) q^{88} +(-3.61571 + 0.968828i) q^{89} +(-2.12132 - 0.707107i) q^{90} +(-4.03856 - 4.59539i) q^{91} +(0.916536 + 0.916536i) q^{92} +(3.92272 - 6.79435i) q^{93} +(5.31017 + 3.06583i) q^{94} +(-7.77559 - 5.13387i) q^{95} +(-0.707107 - 0.707107i) q^{96} +(-1.87662 + 1.08346i) q^{97} +(3.56885 - 2.06048i) q^{98} +(-1.90691 - 1.90691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^7	\( 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Introduction

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