LMFDB - Embedded newform 390.2.bn.c.67.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(67,390)]

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, 1]))

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

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

chi := DirichletCharacter("390.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bn (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:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			67.6
Character	$\chi$	$=$	390.67
Dual form			390.2.bn.c.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.64894 + 1.51030i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-3.98101 - 2.29844i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.64894 + 1.51030i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-3.98101 - 2.29844i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(2.13243 + 0.672876i) q^{10} +(0.765017 - 2.85508i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.40726 - 1.17923i) q^{13} +4.59687i q^{14} +(-1.98365 + 1.03206i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.55871 - 5.81718i) q^{17} -1.00000i q^{18} +(-5.14503 + 1.37861i) q^{19} +(-0.483485 - 2.18317i) q^{20} +(-3.25048 - 3.25048i) q^{21} +(-2.85508 + 0.765017i) q^{22} +(-1.14936 + 4.28946i) q^{23} +(0.965926 + 0.258819i) q^{24} +(0.438009 - 4.98078i) q^{25} +(0.682387 + 3.54039i) q^{26} +(0.707107 + 0.707107i) q^{27} +(3.98101 - 2.29844i) q^{28} +(8.57255 - 4.94936i) q^{29} +(1.88561 + 1.20186i) q^{30} +(-2.23737 + 2.23737i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.47790 - 2.55980i) q^{33} +(-4.25847 + 4.25847i) q^{34} +(10.0358 - 2.22252i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-3.14020 + 1.81300i) q^{37} +(3.76642 + 3.76642i) q^{38} +(-2.98595 - 2.02091i) q^{39} +(-1.64894 + 1.51030i) q^{40} +(-1.71172 - 0.458653i) q^{41} +(-1.18976 + 4.44024i) q^{42} +(-5.26896 + 1.41181i) q^{43} +(2.09006 + 2.09006i) q^{44} +(-2.18317 + 0.483485i) q^{45} +(4.28946 - 1.14936i) q^{46} +6.65049i q^{47} +(-0.258819 - 0.965926i) q^{48} +(7.06563 + 12.2380i) q^{49} +(-4.53248 + 2.11106i) q^{50} -6.02239i q^{51} +(2.72487 - 2.36116i) q^{52} +(0.101422 - 0.101422i) q^{53} +(0.258819 - 0.965926i) q^{54} +(3.05055 + 5.86326i) q^{55} +(-3.98101 - 2.29844i) q^{56} -5.32652 q^{57} +(-8.57255 - 4.94936i) q^{58} +(0.305647 + 1.14069i) q^{59} +(0.0980360 - 2.23392i) q^{60} +(-3.63442 + 6.29500i) q^{61} +(3.05630 + 0.818933i) q^{62} +(-2.29844 - 3.98101i) q^{63} +1.00000 q^{64} +(7.39935 - 3.20149i) q^{65} -2.95580 q^{66} +(-6.53996 - 11.3276i) q^{67} +(5.81718 + 1.55871i) q^{68} +(-2.22039 + 3.84583i) q^{69} +(-6.94264 - 7.57997i) q^{70} +(1.20885 + 4.51148i) q^{71} +(0.866025 + 0.500000i) q^{72} +15.1512 q^{73} +(3.14020 + 1.81300i) q^{74} +(1.71220 - 4.69770i) q^{75} +(1.37861 - 5.14503i) q^{76} +(-9.60776 + 9.60776i) q^{77} +(-0.257185 + 3.59637i) q^{78} -6.34359i q^{79} +(2.13243 + 0.672876i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.458653 + 1.71172i) q^{82} -8.15139i q^{83} +(4.44024 - 1.18976i) q^{84} +(11.3559 + 7.23807i) q^{85} +(3.85715 + 3.85715i) q^{86} +(9.56144 - 2.56198i) q^{87} +(0.765017 - 2.85508i) q^{88} +(2.30891 + 0.618671i) q^{89} +(1.51030 + 1.64894i) q^{90} +(10.8539 + 12.5259i) q^{91} +(-3.14010 - 3.14010i) q^{92} +(-2.74020 + 1.58206i) q^{93} +(5.75949 - 3.32524i) q^{94} +(6.40174 - 10.0438i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(6.36980 - 11.0328i) q^{97} +(7.06563 - 12.2380i) q^{98} +(2.09006 - 2.09006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	$ 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) $ 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.64894	+	1.51030i	−0.737429	+	0.675425i
$5$	−1.64894	+	1.51030i	−0.737429	+	0.675425i
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	−3.98101	−	2.29844i	−1.50468	−	0.868728i	−0.999985	−	0.00542980i	$-0.998272\pi$
$7$	−3.98101	−	2.29844i	−1.50468	−	0.868728i	−0.504695	−	0.863298i	$-0.668395\pi$
$8$	1.00000			0.353553
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	2.13243	+	0.672876i	0.674332	+	0.212782i
$11$	0.765017	−	2.85508i	0.230661	−	0.860839i	−0.749396	−	0.662122i	$-0.769656\pi$
$11$	0.765017	−	2.85508i	0.230661	−	0.860839i	0.980057	−	0.198717i	$-0.0636775\pi$
$12$	−0.707107	+	0.707107i	−0.204124	+	0.204124i
$13$	−3.40726	−	1.17923i	−0.945004	−	0.327060i
$13$	−3.40726	−	1.17923i	−0.945004	−	0.327060i
$14$			4.59687i			1.22857i
$15$	−1.98365	+	1.03206i	−0.512176	+	0.266476i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.55871	−	5.81718i	−0.378042	−	1.41087i	−0.848848	−	0.528636i	$-0.822704\pi$
$17$	−1.55871	−	5.81718i	−0.378042	−	1.41087i	0.470806	−	0.882237i	$-0.343963\pi$
$18$		−	1.00000i		−	0.235702i
$19$	−5.14503	+	1.37861i	−1.18035	+	0.316274i	−0.795065	−	0.606524i	$-0.792563\pi$
$19$	−5.14503	+	1.37861i	−1.18035	+	0.316274i	−0.385285	+	0.922798i	$0.625897\pi$
$20$	−0.483485	−	2.18317i	−0.108111	−	0.488172i
$21$	−3.25048	−	3.25048i	−0.709313	−	0.709313i
$22$	−2.85508	+	0.765017i	−0.608705	+	0.163102i
$23$	−1.14936	+	4.28946i	−0.239658	+	0.894415i	0.736336	+	0.676616i	$0.236554\pi$
$23$	−1.14936	+	4.28946i	−0.239658	+	0.894415i	−0.975994	+	0.217799i	$0.930112\pi$
$24$	0.965926	+	0.258819i	0.197169	+	0.0528312i
$25$	0.438009	−	4.98078i	0.0876017	−	0.996156i
$26$	0.682387	+	3.54039i	0.133827	+	0.694327i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	3.98101	−	2.29844i	0.752340	−	0.434364i
$29$	8.57255	−	4.94936i	1.59188	−	0.919074i	0.598899	−	0.800825i	$-0.295605\pi$
$29$	8.57255	−	4.94936i	1.59188	−	0.919074i	0.992984	−	0.118249i	$-0.0377281\pi$
$30$	1.88561	+	1.20186i	0.344264	+	0.219429i
$31$	−2.23737	+	2.23737i	−0.401843	+	0.401843i	−0.878882	−	0.477039i	$-0.841710\pi$
$31$	−2.23737	+	2.23737i	−0.401843	+	0.401843i	0.477039	+	0.878882i	$0.341710\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	1.47790	−	2.55980i	0.257269	−	0.445603i
$34$	−4.25847	+	4.25847i	−0.730322	+	0.730322i
$35$	10.0358	−	2.22252i	1.69635	−	0.375674i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−3.14020	+	1.81300i	−0.516246	+	0.298055i	−0.735397	−	0.677636i	$-0.763004\pi$
$37$	−3.14020	+	1.81300i	−0.516246	+	0.298055i	0.219151	+	0.975691i	$0.429671\pi$
$38$	3.76642	+	3.76642i	0.610994	+	0.610994i
$39$	−2.98595	−	2.02091i	−0.478135	−	0.323605i
$40$	−1.64894	+	1.51030i	−0.260720	+	0.238799i
$41$	−1.71172	−	0.458653i	−0.267325	−	0.0716295i	0.122667	−	0.992448i	$-0.460855\pi$
$41$	−1.71172	−	0.458653i	−0.267325	−	0.0716295i	−0.389992	+	0.920818i	$0.627522\pi$
$42$	−1.18976	+	4.44024i	−0.183584	+	0.685144i
$43$	−5.26896	+	1.41181i	−0.803509	+	0.215300i	−0.637124	−	0.770761i	$-0.719876\pi$
$43$	−5.26896	+	1.41181i	−0.803509	+	0.215300i	−0.166385	+	0.986061i	$0.553210\pi$
$44$	2.09006	+	2.09006i	0.315089	+	0.315089i
$45$	−2.18317	+	0.483485i	−0.325448	+	0.0720737i
$46$	4.28946	−	1.14936i	0.632447	−	0.169464i
$47$			6.65049i			0.970073i	0.874494	+	0.485037i	$0.161194\pi$
$47$			6.65049i			0.970073i	−0.874494	+	0.485037i	$0.838806\pi$
$48$	−0.258819	−	0.965926i	−0.0373573	−	0.139419i
$49$	7.06563	+	12.2380i	1.00938	+	1.74829i
$50$	−4.53248	+	2.11106i	−0.640990	+	0.298549i
$51$		−	6.02239i		−	0.843303i
$52$	2.72487	−	2.36116i	0.377872	−	0.327434i
$53$	0.101422	−	0.101422i	0.0139314	−	0.0139314i	−0.700107	−	0.714038i	$-0.746864\pi$
$53$	0.101422	−	0.101422i	0.0139314	−	0.0139314i	0.714038	+	0.700107i	$0.246864\pi$
$54$	0.258819	−	0.965926i	0.0352208	−	0.131446i
$55$	3.05055	+	5.86326i	0.411336	+	0.790602i
$56$	−3.98101	−	2.29844i	−0.531985	−	0.307142i
$57$	−5.32652			−0.705515
$58$	−8.57255	−	4.94936i	−1.12563	−	0.649883i
$59$	0.305647	+	1.14069i	0.0397919	+	0.148505i	0.982964	−	0.183800i	$-0.0588400\pi$
$59$	0.305647	+	1.14069i	0.0397919	+	0.148505i	−0.943172	+	0.332306i	$0.892173\pi$
$60$	0.0980360	−	2.23392i	0.0126564	−	0.288398i
$61$	−3.63442	+	6.29500i	−0.465340	+	0.805992i	−0.999217	−	0.0395698i	$-0.987401\pi$
$61$	−3.63442	+	6.29500i	−0.465340	+	0.805992i	0.533877	+	0.845562i	$0.320735\pi$
$62$	3.05630	+	0.818933i	0.388150	+	0.104005i
$63$	−2.29844	−	3.98101i	−0.289576	−	0.501560i
$64$	1.00000			0.125000
$65$	7.39935	−	3.20149i	0.917777	−	0.397096i
$66$	−2.95580			−0.363834
$67$	−6.53996	−	11.3276i	−0.798984	−	1.38388i	−0.920278	−	0.391264i	$-0.872038\pi$
$67$	−6.53996	−	11.3276i	−0.798984	−	1.38388i	0.121295	−	0.992617i	$-0.461295\pi$
$68$	5.81718	+	1.55871i	0.705436	+	0.189021i
$69$	−2.22039	+	3.84583i	−0.267303	+	0.462983i
$70$	−6.94264	−	7.57997i	−0.829805	−	0.905980i
$71$	1.20885	+	4.51148i	0.143464	+	0.535414i	0.999819	+	0.0190268i	$0.00605678\pi$
$71$	1.20885	+	4.51148i	0.143464	+	0.535414i	−0.856355	+	0.516387i	$0.827277\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	15.1512			1.77332			0.886659	−	0.462424i	$-0.153020\pi$
$73$	15.1512			1.77332			0.886659	+	0.462424i	$0.153020\pi$
$74$	3.14020	+	1.81300i	0.365041	+	0.210756i
$75$	1.71220	−	4.69770i	0.197708	−	0.542443i
$76$	1.37861	−	5.14503i	0.158137	−	0.590175i
$77$	−9.60776	+	9.60776i	−1.09491	+	1.09491i
$78$	−0.257185	+	3.59637i	−0.0291205	+	0.407208i
$79$		−	6.34359i		−	0.713710i	−0.934160	−	0.356855i	$-0.883849\pi$
$79$		−	6.34359i		−	0.713710i	0.934160	−	0.356855i	$-0.116151\pi$
$80$	2.13243	+	0.672876i	0.238412	+	0.0752298i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	0.458653	+	1.71172i	0.0506497	+	0.189027i
$83$		−	8.15139i		−	0.894731i	−0.894351	−	0.447365i	$-0.852362\pi$
$83$		−	8.15139i		−	0.894731i	0.894351	−	0.447365i	$-0.147638\pi$
$84$	4.44024	−	1.18976i	0.484470	−	0.129813i
$85$	11.3559	+	7.23807i	1.23172	+	0.785079i
$86$	3.85715	+	3.85715i	0.415927	+	0.415927i
$87$	9.56144	−	2.56198i	1.02509	−	0.274673i
$88$	0.765017	−	2.85508i	0.0815511	−	0.304353i
$89$	2.30891	+	0.618671i	0.244744	+	0.0655790i	0.379106	−	0.925353i	$-0.376232\pi$
$89$	2.30891	+	0.618671i	0.244744	+	0.0655790i	−0.134361	+	0.990932i	$0.542898\pi$
$90$	1.51030	+	1.64894i	0.159199	+	0.173814i
$91$	10.8539	+	12.5259i	1.13780	+	1.31307i
$92$	−3.14010	−	3.14010i	−0.327379	−	0.327379i
$93$	−2.74020	+	1.58206i	−0.284146	+	0.164052i
$94$	5.75949	−	3.32524i	0.594046	−	0.342973i
$95$	6.40174	−	10.0438i	0.656805	−	1.03047i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	6.36980	−	11.0328i	0.646755	−	1.12021i	−0.337138	−	0.941455i	$-0.609459\pi$
$97$	6.36980	−	11.0328i	0.646755	−	1.12021i	0.983893	−	0.178757i	$-0.0572076\pi$
$98$	7.06563	−	12.2380i	0.713736	−	1.23623i
$99$	2.09006	−	2.09006i	0.210059	−	0.210059i
$100$	4.09448	+	2.86972i	0.409448	+	0.286972i
$101$	−7.02836	+	4.05783i	−0.699348	+	0.403769i	−0.807105	−	0.590408i	$-0.798967\pi$
$101$	−7.02836	+	4.05783i	−0.699348	+	0.403769i	0.107756	+	0.994177i	$0.465633\pi$
$102$	−5.21554	+	3.01119i	−0.516415	+	0.298153i
$103$	−4.36852	−	4.36852i	−0.430443	−	0.430443i	0.458336	−	0.888779i	$-0.348446\pi$
$103$	−4.36852	−	4.36852i	−0.430443	−	0.430443i	−0.888779	+	0.458336i	$0.848446\pi$
$104$	−3.40726	−	1.17923i	−0.334109	−	0.115633i
$105$	10.2690	+	0.450659i	1.00216	+	0.0439798i
$106$	−0.138545	−	0.0371230i	−0.0134567	−	0.00360570i
$107$	0.939386	−	3.50584i	0.0908139	−	0.338922i	−0.905538	−	0.424266i	$-0.860532\pi$
$107$	0.939386	−	3.50584i	0.0908139	−	0.338922i	0.996352	+	0.0853439i	$0.0271989\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	−7.90565	−	7.90565i	−0.757224	−	0.757224i	0.218593	−	0.975816i	$-0.429853\pi$
$109$	−7.90565	−	7.90565i	−0.757224	−	0.757224i	−0.975816	+	0.218593i	$0.929853\pi$
$110$	3.55246	−	5.57349i	0.338713	−	0.531411i
$111$	−3.50244	+	0.938476i	−0.332437	+	0.0890762i
$112$			4.59687i			0.434364i
$113$	−1.60947	−	6.00662i	−0.151406	−	0.565055i	−0.999386	−	0.0350273i	$-0.988848\pi$
$113$	−1.60947	−	6.00662i	−0.151406	−	0.565055i	0.847980	−	0.530028i	$-0.177818\pi$
$114$	2.66326	+	4.61291i	0.249437	+	0.432038i
$115$	−4.58314	−	8.80894i	−0.427380	−	0.821438i
$116$			9.89873i			0.919074i
$117$	−2.36116	−	2.72487i	−0.218289	−	0.251915i
$118$	0.835044	−	0.835044i	0.0768721	−	0.0768721i
$119$	−7.16519	+	26.7408i	−0.656831	+	2.45133i
$120$	−1.98365	+	1.03206i	−0.181081	+	0.0942135i
$121$	1.96004	+	1.13163i	0.178185	+	0.102875i
$122$	7.26884			0.658090
$123$	−1.53468	−	0.886049i	−0.138378	−	0.0798923i
$124$	−0.818933	−	3.05630i	−0.0735423	−	0.274464i
$125$	6.80020	+	8.87453i	0.608229	+	0.793762i
$126$	−2.29844	+	3.98101i	−0.204761	+	0.354657i
$127$	2.51133	+	0.672910i	0.222845	+	0.0597111i	0.368514	−	0.929622i	$-0.379867\pi$
$127$	2.51133	+	0.672910i	0.222845	+	0.0597111i	−0.145669	+	0.989333i	$0.546533\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−5.45483			−0.480271
$130$	−6.47225	−	4.80728i	−0.567654	−	0.421627i
$131$	5.64958			0.493606			0.246803	−	0.969066i	$-0.420620\pi$
$131$	5.64958			0.493606			0.246803	+	0.969066i	$0.420620\pi$
$132$	1.47790	+	2.55980i	0.128635	+	0.222802i
$133$	23.6510	+	6.33728i	2.05081	+	0.549512i
$134$	−6.53996	+	11.3276i	−0.564967	+	0.978551i
$135$	−2.23392	−	0.0980360i	−0.192265	−	0.00843759i
$136$	−1.55871	−	5.81718i	−0.133658	−	0.498819i
$137$	−11.6846	−	6.74609i	−0.998280	−	0.576357i	−0.0905409	−	0.995893i	$-0.528860\pi$
$137$	−11.6846	−	6.74609i	−0.998280	−	0.576357i	−0.907739	+	0.419536i	$0.862193\pi$
$138$	4.44078			0.378024
$139$	−3.59959	−	2.07823i	−0.305314	−	0.176273i	0.339514	−	0.940601i	$-0.389737\pi$
$139$	−3.59959	−	2.07823i	−0.305314	−	0.176273i	−0.644827	+	0.764328i	$0.723071\pi$
$140$	−3.09313	+	9.80249i	−0.261417	+	0.828462i
$141$	−1.72127	+	6.42388i	−0.144957	+	0.540988i
$142$	3.30263	−	3.30263i	0.277151	−	0.277151i
$143$	−5.97341	+	8.82587i	−0.499521	+	0.738057i
$144$		−	1.00000i		−	0.0833333i
$145$	−6.66062	+	21.1083i	−0.553134	+	1.75295i
$146$	−7.57562	−	13.1214i	−0.626963	−	1.08593i
$147$	3.65744	+	13.6497i	0.301660	+	1.12581i
$148$		−	3.62599i		−	0.298055i
$149$	21.2750	−	5.70061i	1.74291	−	0.467013i	0.759823	−	0.650130i	$-0.225285\pi$
$149$	21.2750	−	5.70061i	1.74291	−	0.467013i	0.983091	+	0.183117i	$0.0586187\pi$
$150$	−4.92443	+	0.866036i	−0.402078	+	0.0707116i
$151$	−10.2034	−	10.2034i	−0.830339	−	0.830339i	0.157224	−	0.987563i	$-0.449745\pi$
$151$	−10.2034	−	10.2034i	−0.830339	−	0.830339i	−0.987563	+	0.157224i	$0.949745\pi$
$152$	−5.14503	+	1.37861i	−0.417317	+	0.111820i
$153$	1.55871	−	5.81718i	0.126014	−	0.470291i
$154$	13.1245	+	3.51669i	1.05760	+	0.283383i
$155$	0.310197	−	7.06837i	0.0249156	−	0.567745i
$156$	3.24314	−	1.57545i	0.259659	−	0.126137i
$157$	−11.0575	−	11.0575i	−0.882488	−	0.882488i	0.111299	−	0.993787i	$-0.464499\pi$
$157$	−11.0575	−	11.0575i	−0.882488	−	0.882488i	−0.993787	+	0.111299i	$0.964499\pi$
$158$	−5.49371	+	3.17180i	−0.437056	+	0.252334i
$159$	0.124216	−	0.0717161i	0.00985097	−	0.00568746i
$160$	−0.483485	−	2.18317i	−0.0382228	−	0.172595i
$161$	14.4347	−	14.4347i	1.13761	−	1.13761i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	1.42513	−	2.46840i	0.111625	−	0.193340i	−0.804801	−	0.593545i	$-0.797728\pi$
$163$	1.42513	−	2.46840i	0.111625	−	0.193340i	0.916426	+	0.400205i	$0.131061\pi$
$164$	1.25306	−	1.25306i	0.0978477	−	0.0978477i
$165$	1.42908	+	6.45302i	0.111254	+	0.502367i
$166$	−7.05931	+	4.07569i	−0.547908	+	0.316335i
$167$	2.13765	−	1.23417i	0.165416	−	0.0955033i	−0.415006	−	0.909819i	$-0.636221\pi$
$167$	2.13765	−	1.23417i	0.165416	−	0.0955033i	0.580423	+	0.814315i	$0.302887\pi$
$168$	−3.25048	−	3.25048i	−0.250780	−	0.250780i
$169$	10.2188	+	8.03588i	0.786064	+	0.618145i
$170$	0.590410	−	13.4535i	0.0452824	−	1.03184i
$171$	−5.14503	−	1.37861i	−0.393450	−	0.105425i
$172$	1.41181	−	5.26896i	0.107650	−	0.401755i
$173$	−15.9230	+	4.26655i	−1.21060	+	0.324380i	−0.806998	−	0.590554i	$-0.798909\pi$
$173$	−15.9230	+	4.26655i	−1.21060	+	0.324380i	−0.403604	+	0.914934i	$0.632242\pi$
$174$	−6.99946	−	6.99946i	−0.530628	−	0.530628i
$175$	−13.1917	+	18.8218i	−0.997200	+	1.42279i
$176$	−2.85508	+	0.765017i	−0.215210	+	0.0576653i
$177$			1.18093i			0.0887642i
$178$	−0.618671	−	2.30891i	−0.0463714	−	0.173060i
$179$	−8.02350	−	13.8971i	−0.599704	−	1.03872i	−0.992864	−	0.119248i	$-0.961951\pi$
$179$	−8.02350	−	13.8971i	−0.599704	−	1.03872i	0.393160	−	0.919470i	$-0.371382\pi$
$180$	0.672876	−	2.13243i	0.0501532	−	0.158942i
$181$			3.17943i			0.236325i	0.992994	+	0.118163i	$0.0377004\pi$
$181$			3.17943i			0.236325i	−0.992994	+	0.118163i	$0.962300\pi$
$182$	5.42077	−	15.6627i	0.401814	−	1.16100i
$183$	−5.13985	+	5.13985i	−0.379948	+	0.379948i
$184$	−1.14936	+	4.28946i	−0.0847318	+	0.316223i
$185$	2.43984	−	7.73216i	0.179381	−	0.568479i
$186$	2.74020	+	1.58206i	0.200921	+	0.116002i
$187$	−17.8010			−1.30173
$188$	−5.75949	−	3.32524i	−0.420054	−	0.242518i
$189$	−1.18976	−	4.44024i	−0.0865422	−	0.322980i
$190$	−11.8990	−	0.522191i	−0.863245	−	0.0378837i
$191$	−1.14647	+	1.98574i	−0.0829556	+	0.143683i	−0.904518	−	0.426435i	$-0.859769\pi$
$191$	−1.14647	+	1.98574i	−0.0829556	+	0.143683i	0.821563	+	0.570118i	$0.193103\pi$
$192$	0.965926	+	0.258819i	0.0697097	+	0.0186787i
$193$	8.60288	+	14.9006i	0.619249	+	1.07257i	0.989623	+	0.143687i	$0.0458960\pi$
$193$	8.60288	+	14.9006i	0.619249	+	1.07257i	−0.370375	+	0.928882i	$0.620771\pi$
$194$	−12.7396			−0.914649
$195$	7.97583	−	1.17731i	0.571161	−	0.0843090i
$196$	−14.1313			−1.00938
$197$	3.19513	+	5.53413i	0.227644	+	0.394290i	0.957109	−	0.289727i	$-0.0935645\pi$
$197$	3.19513	+	5.53413i	0.227644	+	0.394290i	−0.729466	+	0.684017i	$0.760231\pi$
$198$	−2.85508	−	0.765017i	−0.202902	−	0.0543674i
$199$	−9.31661	+	16.1368i	−0.660437	+	1.14391i	0.320064	+	0.947396i	$0.396296\pi$
$199$	−9.31661	+	16.1368i	−0.660437	+	1.14391i	−0.980501	+	0.196515i	$0.937038\pi$
$200$	0.438009	−	4.98078i	0.0309719	−	0.352194i
$201$	−3.38533	−	12.6342i	−0.238783	−	0.891151i
$202$	7.02836	+	4.05783i	0.494514	+	0.285508i
$203$	−45.5032			−3.19370
$204$	5.21554	+	3.01119i	0.365161	+	0.210826i
$205$	3.51522	−	1.82891i	0.245513	−	0.127736i
$206$	−1.59899	+	5.96751i	−0.111407	+	0.415776i
$207$	−3.14010	+	3.14010i	−0.218252	+	0.218252i
$208$	0.682387	+	3.54039i	0.0473150	+	0.245482i
$209$			15.7441i			1.08904i
$210$	−4.74424	−	9.11858i	−0.327383	−	0.629242i
$211$	0.672697	+	1.16515i	0.0463104	+	0.0802119i	0.888251	−	0.459358i	$-0.151920\pi$
$211$	0.672697	+	1.16515i	0.0463104	+	0.0802119i	−0.841941	+	0.539570i	$0.818587\pi$
$212$	0.0371230	+	0.138545i	0.00254962	+	0.00951530i
$213$			4.67063i			0.320026i
$214$	−3.50584	+	0.939386i	−0.239654	+	0.0642151i
$215$	6.55595	−	10.2857i	0.447112	−	0.701479i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	14.0494	−	3.76453i	0.953737	−	0.255553i
$218$	−2.89367	+	10.7993i	−0.195984	+	0.731422i
$219$	14.6350	+	3.92143i	0.988940	+	0.264986i
$220$	−6.60301	−	0.289774i	−0.445175	−	0.0195366i
$221$	−1.54887	+	21.6587i	−0.104188	+	1.45692i
$222$	2.56396	+	2.56396i	0.172082	+	0.172082i
$223$	−9.96232	+	5.75175i	−0.667126	+	0.385166i	−0.794987	−	0.606627i	$-0.792522\pi$
$223$	−9.96232	+	5.75175i	−0.667126	+	0.385166i	0.127861	+	0.991792i	$0.459189\pi$
$224$	3.98101	−	2.29844i	0.265992	−	0.153571i
$225$	2.86972	−	4.09448i	0.191314	−	0.272965i
$226$	−4.39715	+	4.39715i	−0.292494	+	0.292494i
$227$	−7.04004	+	12.1937i	−0.467264	+	0.809325i	−0.999301	−	0.0373963i	$-0.988094\pi$
$227$	−7.04004	+	12.1937i	−0.467264	+	0.809325i	0.532036	+	0.846721i	$0.321427\pi$
$228$	2.66326	−	4.61291i	0.176379	−	0.305497i
$229$	11.2603	−	11.2603i	0.744104	−	0.744104i	−0.229261	−	0.973365i	$-0.573631\pi$
$229$	11.2603	−	11.2603i	0.744104	−	0.744104i	0.973365	+	0.229261i	$0.0736309\pi$
$230$	−5.33720	+	8.37358i	−0.351924	+	0.552138i
$231$	−11.7671	+	6.79372i	−0.774216	+	0.446994i
$232$	8.57255	−	4.94936i	0.562815	−	0.324942i
$233$	−7.72487	−	7.72487i	−0.506073	−	0.506073i	0.407246	−	0.913319i	$-0.366489\pi$
$233$	−7.72487	−	7.72487i	−0.506073	−	0.506073i	−0.913319	+	0.407246i	$0.866489\pi$
$234$	−1.17923	+	3.40726i	−0.0770887	+	0.222740i
$235$	−10.0442	−	10.9663i	−0.655212	−	0.715360i
$236$	−1.14069	−	0.305647i	−0.0742527	−	0.0198960i
$237$	1.64184	−	6.12744i	0.106649	−	0.398020i
$238$	26.7408	−	7.16519i	1.73335	−	0.464450i
$239$	−19.7087	−	19.7087i	−1.27485	−	1.27485i	−0.943514	−	0.331334i	$-0.892501\pi$
$239$	−19.7087	−	19.7087i	−1.27485	−	1.27485i	−0.331334	−	0.943514i	$-0.607499\pi$
$240$	1.88561	+	1.20186i	0.121716	+	0.0775798i
$241$	−12.4519	+	3.33647i	−0.802096	+	0.214921i	−0.636504	−	0.771274i	$-0.719620\pi$
$241$	−12.4519	+	3.33647i	−0.802096	+	0.214921i	−0.165592	+	0.986194i	$0.552953\pi$
$242$		−	2.26326i		−	0.145488i
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	−3.63442	−	6.29500i	−0.232670	−	0.402996i
$245$	−30.1338	−	9.50858i	−1.92518	−	0.607481i
$246$			1.77210i			0.112985i
$247$	19.1561	+	1.36990i	1.21888	+	0.0871648i
$248$	−2.23737	+	2.23737i	−0.142073	+	0.142073i
$249$	2.10973	−	7.87363i	0.133699	−	0.498971i
$250$	4.28547	−	10.3264i	0.271037	−	0.653100i
$251$	−3.69951	−	2.13591i	−0.233511	−	0.134818i	0.378680	−	0.925528i	$-0.376378\pi$
$251$	−3.69951	−	2.13591i	−0.233511	−	0.134818i	−0.612191	+	0.790710i	$0.709711\pi$
$252$	4.59687			0.289576
$253$	11.3675	+	6.56302i	0.714668	+	0.412614i
$254$	−0.672910	−	2.51133i	−0.0422221	−	0.157575i
$255$	9.09559	+	9.93056i	0.569588	+	0.621875i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	28.6699	+	7.68208i	1.78838	+	0.479195i	0.992069	−	0.125691i	$-0.0401149\pi$
$257$	28.6699	+	7.68208i	1.78838	+	0.479195i	0.796312	+	0.604887i	$0.206782\pi$
$258$	2.72742	+	4.72402i	0.169802	+	0.294105i
$259$	16.6682			1.03571
$260$	−0.927103	+	8.00878i	−0.0574965	+	0.496683i
$261$	9.89873			0.612716
$262$	−2.82479	−	4.89268i	−0.174516	−	0.302271i
$263$	16.1989	+	4.34047i	0.998864	+	0.267645i	0.720970	−	0.692967i	$-0.243697\pi$
$263$	16.1989	+	4.34047i	0.998864	+	0.267645i	0.277895	+	0.960612i	$0.410363\pi$
$264$	1.47790	−	2.55980i	0.0909584	−	0.157545i
$265$	−0.0140615	+	0.320416i	−0.000863792	+	0.0196830i
$266$	−6.33728	−	23.6510i	−0.388563	−	1.45014i
$267$	2.07011	+	1.19518i	0.126689	+	0.0731439i
$268$	13.0799			0.798984
$269$	−20.4461	−	11.8046i	−1.24662	−	0.719738i	−0.276189	−	0.961103i	$-0.589072\pi$
$269$	−20.4461	−	11.8046i	−1.24662	−	0.719738i	−0.970434	+	0.241365i	$0.922405\pi$
$270$	1.03206	+	1.98365i	0.0628090	+	0.120721i
$271$	5.85290	−	21.8433i	0.355538	−	1.32689i	−0.524268	−	0.851553i	$-0.675661\pi$
$271$	5.85290	−	21.8433i	0.355538	−	1.32689i	0.879806	−	0.475333i	$-0.157672\pi$
$272$	−4.25847	+	4.25847i	−0.258208	+	0.258208i
$273$	7.24217	+	14.9083i	0.438316	+	0.902291i
$274$			13.4922i			0.815092i
$275$	−13.8854	−	5.06093i	−0.837324	−	0.305185i
$276$	−2.22039	−	3.84583i	−0.133652	−	0.231492i
$277$	−2.03378	−	7.59016i	−0.122198	−	0.456048i	0.877527	−	0.479528i	$-0.159192\pi$
$277$	−2.03378	−	7.59016i	−0.122198	−	0.456048i	−0.999724	+	0.0234798i	$0.992525\pi$
$278$			4.15645i			0.249288i
$279$	−3.05630	+	0.818933i	−0.182976	+	0.0490282i
$280$	10.0358	−	2.22252i	0.599752	−	0.132821i
$281$	7.42903	+	7.42903i	0.443179	+	0.443179i	0.893079	−	0.449900i	$-0.148540\pi$
$281$	7.42903	+	7.42903i	0.443179	+	0.443179i	−0.449900	+	0.893079i	$0.648540\pi$
$282$	6.42388	−	1.72127i	0.382536	−	0.102500i
$283$	−6.51872	+	24.3282i	−0.387497	+	1.44616i	0.446695	+	0.894686i	$0.352601\pi$
$283$	−6.51872	+	24.3282i	−0.387497	+	1.44616i	−0.834192	+	0.551474i	$0.814066\pi$
$284$	−4.51148	−	1.20885i	−0.267707	−	0.0717319i
$285$	8.78312	−	8.04463i	0.520267	−	0.476523i
$286$	10.6301	+	0.760187i	0.628573	+	0.0449508i
$287$	5.76017	+	5.76017i	0.340012	+	0.340012i
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	−16.6876	+	9.63457i	−0.981621	+	0.566739i
$290$	21.6106	−	4.78589i	1.26902	−	0.281037i
$291$	9.00825	−	9.00825i	0.528073	−	0.528073i
$292$	−7.57562	+	13.1214i	−0.443329	+	0.767869i
$293$	2.25262	−	3.90166i	0.131600	−	0.227937i	−0.792694	−	0.609620i	$-0.791322\pi$
$293$	2.25262	−	3.90166i	0.131600	−	0.227937i	0.924293	+	0.381683i	$0.124655\pi$
$294$	9.99230	−	9.99230i	0.582763	−	0.582763i
$295$	−2.22678	−	1.41931i	−0.129648	−	0.0826357i
$296$	−3.14020	+	1.81300i	−0.182520	+	0.105378i
$297$	2.55980	−	1.47790i	0.148534	−	0.0857564i
$298$	−15.5744	−	15.5744i	−0.902199	−	0.902199i
$299$	8.97442	−	13.2600i	0.519004	−	0.766843i
$300$	3.21222	+	3.83166i	0.185458	+	0.221221i
$301$	24.2208	+	6.48993i	1.39606	+	0.374074i
$302$	−3.73469	+	13.9381i	−0.214907	+	0.802046i
$303$	−7.83912	+	2.10049i	−0.450346	+	0.120670i
$304$	3.76642	+	3.76642i	0.216019	+	0.216019i
$305$	−3.51438	−	15.8691i	−0.201233	−	0.908664i
$306$	−5.81718	+	1.55871i	−0.332546	+	0.0891054i
$307$			21.5547i			1.23019i	0.788452	+	0.615096i	$0.210883\pi$
$307$			21.5547i			1.23019i	−0.788452	+	0.615096i	$0.789117\pi$
$308$	−3.51669	−	13.1245i	−0.200382	−	0.747835i
$309$	−3.08901	−	5.35032i	−0.175728	−	0.304369i
$310$	−6.27648	+	3.26555i	−0.356480	+	0.185471i
$311$		−	25.6923i		−	1.45687i	−0.685112	−	0.728437i	$-0.740247\pi$
$311$		−	25.6923i		−	1.45687i	0.685112	−	0.728437i	$-0.259753\pi$
$312$	−2.98595	−	2.02091i	−0.169046	−	0.114412i
$313$	3.79060	−	3.79060i	0.214258	−	0.214258i	−0.591816	−	0.806073i	$-0.701589\pi$
$313$	3.79060	−	3.79060i	0.214258	−	0.214258i	0.806073	+	0.591816i	$0.201589\pi$
$314$	−4.04734	+	15.1049i	−0.228405	+	0.852418i
$315$	9.80249	+	3.09313i	0.552308	+	0.174278i
$316$	5.49371	+	3.17180i	0.309045	+	0.178427i
$317$	18.7112			1.05093			0.525463	−	0.850817i	$-0.323892\pi$
$317$	18.7112			1.05093			0.525463	+	0.850817i	$0.323892\pi$
$318$	−0.124216	−	0.0717161i	−0.00696569	−	0.00402164i
$319$	−7.57269	−	28.2617i	−0.423989	−	1.58235i
$320$	−1.64894	+	1.51030i	−0.0921786	+	0.0844281i
$321$	1.81475	−	3.14325i	0.101290	−	0.175439i
$322$	−19.7181	−	5.28345i	−1.09885	−	0.294435i
$323$	16.0392	+	27.7807i	0.892444	+	1.54576i
$324$	−1.00000			−0.0555556
$325$	−7.36589	+	16.4543i	−0.408586	+	0.912720i
$326$	−2.85026			−0.157861
$327$	−5.59014	−	9.68240i	−0.309135	−	0.535438i
$328$	−1.71172	−	0.458653i	−0.0945137	−	0.0253249i
$329$	15.2857	−	26.4757i	0.842729	−	1.45965i
$330$	4.87393	−	4.46413i	0.268301	−	0.245742i
$331$	4.37394	+	16.3238i	0.240414	+	0.897236i	0.975633	+	0.219407i	$0.0704122\pi$
$331$	4.37394	+	16.3238i	0.240414	+	0.897236i	−0.735220	+	0.677829i	$0.762921\pi$
$332$	7.05931	+	4.07569i	0.387430	+	0.223683i
$333$	−3.62599			−0.198703
$334$	−2.13765	−	1.23417i	−0.116967	−	0.0675310i
$335$	27.8920	+	8.80117i	1.52390	+	0.480859i
$336$	−1.18976	+	4.44024i	−0.0649067	+	0.242235i
$337$	8.50566	−	8.50566i	0.463333	−	0.463333i	−0.436414	−	0.899746i	$-0.643752\pi$
$337$	8.50566	−	8.50566i	0.463333	−	0.463333i	0.899746	+	0.436414i	$0.143752\pi$
$338$	1.84986	−	12.8677i	0.100619	−	0.699911i
$339$		−	6.21851i		−	0.337743i
$340$	−11.9463	+	6.21545i	−0.647879	+	0.337080i
$341$	4.67624	+	8.09948i	0.253233	+	0.438612i
$342$	1.37861	+	5.14503i	0.0745465	+	0.278211i
$343$		−	32.7815i		−	1.77003i
$344$	−5.26896	+	1.41181i	−0.284083	+	0.0761199i
$345$	−2.14705	−	9.69499i	−0.115593	−	0.521960i
$346$	11.6564	+	11.6564i	0.626653	+	0.626653i
$347$	−7.81767	+	2.09474i	−0.419674	+	0.112451i	−0.462475	−	0.886632i	$-0.653039\pi$
$347$	−7.81767	+	2.09474i	−0.419674	+	0.112451i	0.0428008	+	0.999084i	$0.486372\pi$
$348$	−2.56198	+	9.56144i	−0.137337	+	0.512547i
$349$	−19.9015	−	5.33258i	−1.06530	−	0.285446i	−0.316740	−	0.948512i	$-0.602588\pi$
$349$	−19.9015	−	5.33258i	−1.06530	−	0.285446i	−0.748561	+	0.663066i	$0.769255\pi$
$350$	22.8960	+	2.01347i	1.22384	+	0.107625i
$351$	−1.57545	−	3.24314i	−0.0840916	−	0.173106i
$352$	2.09006	+	2.09006i	0.111401	+	0.111401i
$353$	6.14970	−	3.55053i	0.327316	−	0.188976i	−0.327333	−	0.944909i	$-0.606150\pi$
$353$	6.14970	−	3.55053i	0.327316	−	0.188976i	0.654649	+	0.755933i	$0.272817\pi$
$354$	1.02272	−	0.590466i	0.0543568	−	0.0313829i
$355$	−8.80699	−	5.61344i	−0.467426	−	0.297931i
$356$	−1.69024	+	1.69024i	−0.0895826	+	0.0895826i
$357$	−13.8421	+	23.9752i	−0.732600	+	1.26890i
$358$	−8.02350	+	13.8971i	−0.424055	+	0.734485i
$359$	11.4302	−	11.4302i	0.603263	−	0.603263i	−0.337914	−	0.941177i	$-0.609721\pi$
$359$	11.4302	−	11.4302i	0.603263	−	0.603263i	0.941177	+	0.337914i	$0.109721\pi$
$360$	−2.18317	+	0.483485i	−0.115063	+	0.0254819i
$361$	8.11627	−	4.68593i	0.427172	−	0.246628i
$362$	2.75347	−	1.58972i	0.144719	−	0.0835536i
$363$	1.60037	+	1.60037i	0.0839974	+	0.0839974i
$364$	−16.2747	+	3.13685i	−0.853027	+	0.164415i
$365$	−24.9835	+	22.8829i	−1.30770	+	1.19774i
$366$	7.02116	+	1.88131i	0.367002	+	0.0983379i
$367$	−1.09325	+	4.08007i	−0.0570673	+	0.212978i	−0.988572	−	0.150752i	$-0.951830\pi$
$367$	−1.09325	+	4.08007i	−0.0570673	+	0.212978i	0.931504	+	0.363730i	$0.118497\pi$
$368$	4.28946	−	1.14936i	0.223604	−	0.0599144i
$369$	−1.25306	−	1.25306i	−0.0652318	−	0.0652318i
$370$	−7.91617	+	1.75311i	−0.411542	+	0.0911400i
$371$	−0.636874	+	0.170650i	−0.0330648	+	0.00885969i
$372$		−	3.16411i		−	0.164052i
$373$	−0.132907	−	0.496018i	−0.00688169	−	0.0256828i	0.962400	−	0.271638i	$-0.0875652\pi$
$373$	−0.132907	−	0.496018i	−0.00688169	−	0.0256828i	−0.969281	+	0.245955i	$0.920899\pi$
$374$	8.90048	+	15.4161i	0.460233	+	0.797147i
$375$	4.27159	+	10.3322i	0.220584	+	0.533550i
$376$			6.65049i			0.342973i
$377$	−35.0453	+	6.75476i	−1.80493	+	0.347888i
$378$	−3.25048	+	3.25048i	−0.167187	+	0.167187i
$379$	−0.219532	+	0.819303i	−0.0112766	+	0.0420848i	−0.971335	−	0.237715i	$-0.923601\pi$
$379$	−0.219532	+	0.819303i	−0.0112766	+	0.0420848i	0.960058	+	0.279800i	$0.0902682\pi$
$380$	5.49728	+	10.5659i	0.282004	+	0.542022i
$381$	2.25160	+	1.29996i	0.115353	+	0.0665991i
$382$	2.29294			0.117317
$383$	13.2538	+	7.65209i	0.677238	+	0.391003i	0.798814	−	0.601579i	$-0.205461\pi$
$383$	13.2538	+	7.65209i	0.677238	+	0.391003i	−0.121576	+	0.992582i	$0.538795\pi$
$384$	−0.258819	−	0.965926i	−0.0132078	−	0.0492922i
$385$	1.33206	−	30.3532i	0.0678879	−	1.54694i
$386$	8.60288	−	14.9006i	0.437875	−	0.758422i
$387$	−5.26896	−	1.41181i	−0.267836	−	0.0717666i
$388$	6.36980	+	11.0328i	0.323377	+	0.560106i
$389$	−4.06547			−0.206128			−0.103064	−	0.994675i	$-0.532865\pi$
$389$	−4.06547			−0.206128			−0.103064	+	0.994675i	$0.532865\pi$
$390$	−5.00750	−	6.31862i	−0.253565	−	0.319956i
$391$	26.7441			1.35251
$392$	7.06563	+	12.2380i	0.356868	+	0.618113i
$393$	5.45708	+	1.46222i	0.275273	+	0.0737592i
$394$	3.19513	−	5.53413i	0.160968	−	0.278805i
$395$	9.58070	+	10.4602i	0.482057	+	0.526310i
$396$	0.765017	+	2.85508i	0.0384435	+	0.143473i
$397$	−27.8338	−	16.0699i	−1.39694	−	0.806523i	−0.402868	−	0.915258i	$-0.631987\pi$
$397$	−27.8338	−	16.0699i	−1.39694	−	0.806523i	−0.994071	+	0.108735i	$0.965320\pi$
$398$	18.6332			0.933999
$399$	21.2049	+	12.2427i	1.06157	+	0.612901i
$400$	−4.53248	+	2.11106i	−0.226624	+	0.105553i
$401$	3.69019	−	13.7720i	0.184279	−	0.687740i	−0.810504	−	0.585733i	$-0.800807\pi$
$401$	3.69019	−	13.7720i	0.184279	−	0.687740i	0.994784	−	0.102007i	$-0.0325265\pi$
$402$	−9.24891	+	9.24891i	−0.461294	+	0.461294i
$403$	10.2617	−	4.98492i	0.511169	−	0.248316i
$404$		−	8.11566i		−	0.403769i
$405$	−2.13243	−	0.672876i	−0.105961	−	0.0334355i
$406$	22.7516	+	39.4069i	1.12914	+	1.95573i
$407$	2.77394	+	10.3525i	0.137499	+	0.513155i
$408$		−	6.02239i		−	0.298153i
$409$	−17.6429	+	4.72741i	−0.872387	+	0.233755i	−0.667120	−	0.744951i	$-0.732473\pi$
$409$	−17.6429	+	4.72741i	−0.872387	+	0.233755i	−0.205267	+	0.978706i	$0.565806\pi$
$410$	−3.34149	−	2.12981i	−0.165024	−	0.105184i
$411$	−9.54041	−	9.54041i	−0.470594	−	0.470594i
$412$	5.96751	−	1.59899i	0.293998	−	0.0787766i
$413$	1.40502	−	5.24362i	0.0691367	−	0.258022i
$414$	4.28946	+	1.14936i	0.210816	+	0.0564879i
$415$	12.3110	+	13.4411i	0.604324	+	0.659800i
$416$	2.72487	−	2.36116i	0.133598	−	0.115765i
$417$	−2.93906	−	2.93906i	−0.143926	−	0.143926i
$418$	13.6348	−	7.87206i	0.666901	−	0.385035i
$419$	13.1690	−	7.60312i	0.643347	−	0.371437i	−0.142556	−	0.989787i	$-0.545532\pi$
$419$	13.1690	−	7.60312i	0.643347	−	0.371437i	0.785903	+	0.618350i	$0.212199\pi$
$420$	−5.52480	+	8.66792i	−0.269583	+	0.422951i
$421$	13.0605	−	13.0605i	0.636530	−	0.636530i	−0.313168	−	0.949698i	$-0.601390\pi$
$421$	13.0605	−	13.0605i	0.636530	−	0.636530i	0.949698	+	0.313168i	$0.101390\pi$
$422$	0.672697	−	1.16515i	0.0327464	−	0.0567184i
$423$	−3.32524	+	5.75949i	−0.161679	+	0.280036i
$424$	0.101422	−	0.101422i	0.00492548	−	0.00492548i
$425$	−29.6568	+	5.21561i	−1.43857	+	0.252994i
$426$	4.04488	−	2.33531i	0.195975	−	0.113146i
$427$	28.9373	−	16.7070i	1.40038	−	0.808507i
$428$	2.56645	+	2.56645i	0.124054	+	0.124054i
$429$	−8.05417	+	6.97911i	−0.388859	+	0.336954i
$430$	−12.1856	−	0.534770i	−0.587644	−	0.0257889i
$431$	3.65389	+	0.979056i	0.176001	+	0.0471595i	0.345743	−	0.938329i	$-0.387627\pi$
$431$	3.65389	+	0.979056i	0.176001	+	0.0471595i	−0.169742	+	0.985489i	$0.554293\pi$
$432$	0.258819	−	0.965926i	0.0124524	−	0.0464731i
$433$	−23.2211	+	6.22209i	−1.11594	+	0.299014i	−0.769238	−	0.638962i	$-0.779364\pi$
$433$	−23.2211	+	6.22209i	−1.11594	+	0.299014i	−0.346699	+	0.937977i	$0.612697\pi$
$434$	−10.2849	−	10.2849i	−0.493690	−	0.493690i
$435$	−11.8969	+	18.6652i	−0.570412	+	0.894926i
$436$	10.7993	−	2.89367i	0.517193	−	0.138582i
$437$		−	23.6539i		−	1.13152i
$438$	−3.92143	−	14.6350i	−0.187373	−	0.699286i
$439$	−9.25275	−	16.0262i	−0.441610	−	0.764890i	0.556200	−	0.831049i	$-0.312259\pi$
$439$	−9.25275	−	16.0262i	−0.441610	−	0.764890i	−0.997809	+	0.0661585i	$0.978926\pi$
$440$	3.05055	+	5.86326i	0.145429	+	0.279520i
$441$			14.1313i			0.672917i
$442$	19.5314	−	9.48800i	0.929015	−	0.451298i
$443$	−12.6893	+	12.6893i	−0.602889	+	0.602889i	−0.941078	−	0.338189i	$-0.890186\pi$
$443$	−12.6893	+	12.6893i	−0.602889	+	0.602889i	0.338189	+	0.941078i	$0.390186\pi$
$444$	0.938476	−	3.50244i	0.0445381	−	0.166218i
$445$	−4.74164	+	2.46699i	−0.224775	+	0.116947i
$446$	9.96232	+	5.75175i	0.471730	+	0.272353i
$447$	22.0255			1.04177
$448$	−3.98101	−	2.29844i	−0.188085	−	0.108591i
$449$	2.90568	+	10.8441i	0.137127	+	0.511766i	0.999980	+	0.00631086i	$0.00200882\pi$
$449$	2.90568	+	10.8441i	0.137127	+	0.511766i	−0.862853	+	0.505455i	$0.831325\pi$
$450$	−4.98078	−	0.438009i	−0.234796	−	0.0206479i
$451$	−2.61898	+	4.53621i	−0.123323	+	0.213602i
$452$	6.00662	+	1.60947i	0.282528	+	0.0757030i
$453$	−7.21488	−	12.4965i	−0.338984	−	0.587138i
$454$	14.0801			0.660811
$455$	−36.8153	−	4.26178i	−1.72593	−	0.199795i
$456$	−5.32652			−0.249437
$457$	−10.1150	−	17.5197i	−0.473159	−	0.819535i	0.526369	−	0.850256i	$-0.323553\pi$
$457$	−10.1150	−	17.5197i	−0.473159	−	0.819535i	−0.999528	+	0.0307208i	$0.990220\pi$
$458$	−15.3819	−	4.12157i	−0.718749	−	0.192588i
$459$	3.01119	−	5.21554i	0.140550	−	0.243441i
$460$	9.92033	+	0.435356i	0.462538	+	0.0202986i
$461$	−1.51106	−	5.63934i	−0.0703769	−	0.262650i	0.921768	−	0.387741i	$-0.126744\pi$
$461$	−1.51106	−	5.63934i	−0.0703769	−	0.262650i	−0.992145	+	0.125091i	$0.960078\pi$
$462$	11.7671	+	6.79372i	0.547453	+	0.316072i
$463$	28.4397			1.32170			0.660852	−	0.750516i	$-0.270195\pi$
$463$	28.4397			1.32170			0.660852	+	0.750516i	$0.270195\pi$
$464$	−8.57255	−	4.94936i	−0.397971	−	0.229768i
$465$	2.12906	−	6.74723i	0.0987326	−	0.312895i
$466$	−2.82750	+	10.5524i	−0.130981	+	0.488829i
$467$	−11.8221	+	11.8221i	−0.547060	+	0.547060i	−0.925589	−	0.378529i	$-0.876430\pi$
$467$	−11.8221	+	11.8221i	−0.547060	+	0.547060i	0.378529	+	0.925589i	$0.376430\pi$
$468$	3.54039	−	0.682387i	0.163655	−	0.0315433i
$469$			60.1268i			2.77640i
$470$	−4.47495	+	14.1817i	−0.206414	+	0.654152i
$471$	−7.81887	−	13.5427i	−0.360274	−	0.624014i
$472$	0.305647	+	1.14069i	0.0140686	+	0.0525046i
$473$			16.1234i			0.741354i
$474$	−6.12744	+	1.64184i	−0.281443	+	0.0754123i
$475$	4.61296	+	26.2301i	0.211657	+	1.20352i
$476$	−19.5756	−	19.5756i	−0.897248	−	0.897248i
$477$	0.138545	−	0.0371230i	0.00634354	−	0.00169975i
$478$	−7.21387	+	26.9225i	−0.329955	+	1.23141i
$479$	−8.52777	−	2.28501i	−0.389644	−	0.104405i	0.0586781	−	0.998277i	$-0.481311\pi$
$479$	−8.52777	−	2.28501i	−0.389644	−	0.104405i	−0.448322	+	0.893872i	$0.647978\pi$
$480$	0.0980360	−	2.23392i	0.00447471	−	0.101964i
$481$	12.8374	−	2.47433i	0.585336	−	0.112820i
$482$	9.11540	+	9.11540i	0.415195	+	0.415195i
$483$	17.6788	−	10.2068i	0.804412	−	0.464428i
$484$	−1.96004	+	1.13163i	−0.0890927	+	0.0514377i
$485$	6.15940	+	27.8127i	0.279684	+	1.26291i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	3.24416	−	5.61906i	0.147007	−	0.254624i	−0.783113	−	0.621880i	$-0.786369\pi$
$487$	3.24416	−	5.61906i	0.147007	−	0.254624i	0.930120	+	0.367256i	$0.119703\pi$
$488$	−3.63442	+	6.29500i	−0.164523	+	0.284961i
$489$	2.01544	−	2.01544i	0.0911413	−	0.0911413i
$490$	6.83225	+	30.8510i	0.308650	+	1.39370i
$491$	−6.14710	+	3.54903i	−0.277415	+	0.160165i	−0.632252	−	0.774762i	$-0.717869\pi$
$491$	−6.14710	+	3.54903i	−0.277415	+	0.160165i	0.354838	+	0.934928i	$0.384536\pi$
$492$	1.53468	−	0.886049i	0.0691888	−	0.0399462i
$493$	−42.1534	−	42.1534i	−1.89850	−	1.89850i
$494$	−8.39170	−	17.2747i	−0.377560	−	0.777223i
$495$	−0.289774	+	6.60301i	−0.0130244	+	0.296783i
$496$	3.05630	+	0.818933i	0.137232	+	0.0367712i
$497$	5.55692	−	20.7387i	0.249262	−	0.930258i
$498$	−7.87363	+	2.10973i	−0.352826	+	0.0945394i
$499$	−19.5215	−	19.5215i	−0.873902	−	0.873902i	0.118993	−	0.992895i	$-0.462033\pi$
$499$	−19.5215	−	19.5215i	−0.873902	−	0.873902i	−0.992895	+	0.118993i	$0.962033\pi$
$500$	−11.0857	+	1.45188i	−0.495766	+	0.0649302i
$501$	2.38424	−	0.638856i	0.106520	−	0.0285420i
$502$			4.27182i			0.190661i
$503$	−8.37597	−	31.2596i	−0.373466	−	1.39379i	−0.855573	−	0.517682i	$-0.826795\pi$
$503$	−8.37597	−	31.2596i	−0.373466	−	1.39379i	0.482107	−	0.876113i	$-0.339872\pi$
$504$	−2.29844	−	3.98101i	−0.102381	−	0.177328i
$505$	5.46083	−	17.3060i	0.243004	−	0.770108i
$506$		−	13.1260i		−	0.583524i
$507$	7.79080	+	10.4069i	0.346001	+	0.462187i
$508$	−1.83842	+	1.83842i	−0.0815669	+	0.0815669i
$509$	−0.381312	+	1.42307i	−0.0169013	+	0.0630767i	−0.973861	−	0.227143i	$-0.927062\pi$
$509$	−0.381312	+	1.42307i	−0.0169013	+	0.0630767i	0.956960	+	0.290219i	$0.0937283\pi$
$510$	4.05232	−	12.8423i	0.179440	−	0.568666i
$511$	−60.3172	−	34.8242i	−2.66828	−	1.54053i
$512$	1.00000			0.0441942
$513$	−4.61291	−	2.66326i	−0.203665	−	0.117586i
$514$	−7.68208	−	28.6699i	−0.338842	−	1.26458i
$515$	13.8012	+	0.605668i	0.608153	+	0.0266889i
$516$	2.72742	−	4.72402i	0.120068	−	0.207964i
$517$	18.9877	+	5.08773i	0.835077	+	0.223758i
$518$	−8.33411	−	14.4351i	−0.366180	−	0.634242i
$519$	−16.4847			−0.723597
$520$	7.39935	−	3.20149i	0.324483	−	0.140395i
$521$	35.0983			1.53768			0.768842	−	0.639439i	$-0.220833\pi$
$521$	35.0983			1.53768			0.768842	+	0.639439i	$0.220833\pi$
$522$	−4.94936	−	8.57255i	−0.216628	−	0.375210i
$523$	6.81350	+	1.82567i	0.297934	+	0.0798311i	0.404689	−	0.914454i	$-0.367380\pi$
$523$	6.81350	+	1.82567i	0.297934	+	0.0798311i	−0.106756	+	0.994285i	$0.534046\pi$
$524$	−2.82479	+	4.89268i	−0.123402	+	0.213738i
$525$	−17.6137	+	14.7662i	−0.768723	+	0.644449i
$526$	−4.34047	−	16.1989i	−0.189253	−	0.706304i
$527$	16.5026	+	9.52775i	0.718862	+	0.415035i
$528$	−2.95580			−0.128635
$529$	2.84012	+	1.63974i	0.123483	+	0.0712932i
$530$	0.284519	−	0.148030i	0.0123587	−	0.00643003i
$531$	−0.305647	+	1.14069i	−0.0132640	+	0.0495018i
$532$	−17.3138	+	17.3138i	−0.750647	+	0.750647i
$533$	5.29140	+	3.58125i	0.229196	+	0.155121i
$534$		−	2.39036i		−	0.103441i
$535$	3.74586	+	7.19966i	0.161948	+	0.311269i
$536$	−6.53996	−	11.3276i	−0.282483	−	0.489276i
$537$	−4.15327	−	15.5002i	−0.179227	−	0.668883i
$538$			23.6092i			1.01786i
$539$	40.3459	−	10.8106i	1.73782	−	0.465647i
$540$	1.20186	−	1.88561i	0.0517198	−	0.0811438i
$541$	17.0764	+	17.0764i	0.734172	+	0.734172i	0.971443	−	0.237272i	$-0.0762532\pi$
$541$	17.0764	+	17.0764i	0.734172	+	0.734172i	−0.237272	+	0.971443i	$0.576253\pi$
$542$	−21.8433	+	5.85290i	−0.938250	+	0.251403i
$543$	−0.822898	+	3.07110i	−0.0353139	+	0.131793i
$544$	5.81718	+	1.55871i	0.249409	+	0.0668291i
$545$	24.9758	+	1.09607i	1.06985	+	0.0469504i
$546$	9.28988	−	13.7260i	0.397570	−	0.587421i
$547$	−21.4057	−	21.4057i	−0.915241	−	0.915241i	0.0814372	−	0.996678i	$-0.474049\pi$
$547$	−21.4057	−	21.4057i	−0.915241	−	0.915241i	−0.996678	+	0.0814372i	$0.974049\pi$
$548$	11.6846	−	6.74609i	0.499140	−	0.288179i
$549$	−6.29500	+	3.63442i	−0.268664	+	0.155113i
$550$	2.55983	+	14.5556i	0.109151	+	0.620653i
$551$	−37.2828	+	37.2828i	−1.58830	+	1.58830i
$552$	−2.22039	+	3.84583i	−0.0945060	+	0.163689i
$553$	−14.5803	+	25.2539i	−0.620019	+	1.07390i
$554$	−5.55638	+	5.55638i	−0.236068	+	0.236068i
$555$	4.35794	−	6.83721i	0.184984	−	0.290224i
$556$	3.59959	−	2.07823i	0.152657	−	0.0881365i
$557$	−18.7527	+	10.8269i	−0.794578	+	0.458750i	−0.841572	−	0.540145i	$-0.818369\pi$
$557$	−18.7527	+	10.8269i	−0.794578	+	0.458750i	0.0469938	+	0.998895i	$0.485036\pi$
$558$	2.23737	+	2.23737i	0.0947152	+	0.0947152i
$559$	19.6176	+	1.40290i	0.829735	+	0.0593364i
$560$	−6.94264	−	7.57997i	−0.293380	−	0.320312i
$561$	−17.1944	−	4.60723i	−0.725948	−	0.194517i
$562$	2.71921	−	10.1482i	0.114703	−	0.428078i
$563$	28.1878	−	7.55290i	1.18797	−	0.318317i	0.389889	−	0.920862i	$-0.372513\pi$
$563$	28.1878	−	7.55290i	1.18797	−	0.318317i	0.798085	+	0.602545i	$0.205847\pi$
$564$	−4.70260	−	4.70260i	−0.198015	−	0.198015i
$565$	11.7257	+	7.47378i	0.493304	+	0.314424i
$566$	24.3282	−	6.51872i	1.02259	−	0.274002i
$567$		−	4.59687i		−	0.193051i
$568$	1.20885	+	4.51148i	0.0507221	+	0.189297i
$569$	8.13503	+	14.0903i	0.341038	+	0.590695i	0.984626	−	0.174677i	$-0.0558882\pi$
$569$	8.13503	+	14.0903i	0.341038	+	0.590695i	−0.643588	+	0.765372i	$0.722555\pi$
$570$	−11.3584	−	3.58409i	−0.475752	−	0.150121i
$571$			2.10496i			0.0880898i	0.999030	+	0.0440449i	$0.0140245\pi$
$571$			2.10496i			0.0880898i	−0.999030	+	0.0440449i	$0.985976\pi$
$572$	−4.65673	−	9.58606i	−0.194708	−	0.400813i
$573$	−1.62135	+	1.62135i	−0.0677330	+	0.0677330i
$574$	2.10837	−	7.86854i	0.0880016	−	0.328426i
$575$	20.8614	+	7.60352i	0.869982	+	0.317089i
$576$	0.866025	+	0.500000i	0.0360844	+	0.0208333i
$577$	44.6554			1.85903			0.929515	−	0.368785i	$-0.120226\pi$
$577$	44.6554			1.85903			0.929515	+	0.368785i	$0.120226\pi$
$578$	16.6876	+	9.63457i	0.694111	+	0.400745i
$579$	4.45318	+	16.6195i	0.185068	+	0.690682i
$580$	−14.9500	−	16.3224i	−0.620766	−	0.677751i
$581$	−18.7354	+	32.4507i	−0.777277	+	1.34628i
$582$	−12.3055	−	3.29725i	−0.510079	−	0.136675i
$583$	−0.211978	−	0.367157i	−0.00877925	−	0.0152061i
$584$	15.1512			0.626963
$585$	8.00878	+	0.927103i	0.331122	+	0.0383310i
$586$	−4.50524			−0.186110
$587$	17.5431	+	30.3855i	0.724080	+	1.25414i	0.959352	+	0.282213i	$0.0910686\pi$
$587$	17.5431	+	30.3855i	0.724080	+	1.25414i	−0.235272	+	0.971930i	$0.575598\pi$
$588$	−13.6497	−	3.65744i	−0.562906	−	0.150830i
$589$	8.42686	−	14.5958i	0.347223	−	0.601407i
$590$	−0.115774	+	2.63810i	−0.00476633	+	0.108609i
$591$	1.65392	+	6.17252i	0.0680332	+	0.253903i
$592$	3.14020	+	1.81300i	0.129061	+	0.0745137i
$593$	−7.78083			−0.319520			−0.159760	−	0.987156i	$-0.551072\pi$
$593$	−7.78083			−0.319520			−0.159760	+	0.987156i	$0.551072\pi$
$594$	−2.55980	−	1.47790i	−0.105030	−	0.0606389i
$595$	−28.5716	−	54.9156i	−1.17132	−	2.25132i
$596$	−5.70061	+	21.2750i	−0.233506	+	0.871457i
$597$	−13.1757	+	13.1757i	−0.539245	+	0.539245i
$598$	−15.9707	−	1.14210i	−0.653089	−	0.0467040i
$599$		−	24.3612i		−	0.995374i	−0.867357	−	0.497687i	$-0.834183\pi$
$599$		−	24.3612i		−	0.995374i	0.867357	−	0.497687i	$-0.165817\pi$
$600$	1.71220	−	4.69770i	0.0699004	−	0.191783i
$601$	−11.2773	−	19.5328i	−0.460009	−	0.796759i	0.538952	−	0.842337i	$-0.318820\pi$
$601$	−11.2773	−	19.5328i	−0.460009	−	0.796759i	−0.998961	+	0.0455778i	$0.985487\pi$
$602$	−6.48993	−	24.2208i	−0.264510	−	0.987165i
$603$		−	13.0799i		−	0.532656i
$604$	13.9381	−	3.73469i	0.567132	−	0.151963i
$605$	−4.94108	+	1.09425i	−0.200884	+	0.0444876i
$606$	5.73864	+	5.73864i	0.233116	+	0.233116i
$607$	−15.9299	+	4.26840i	−0.646574	+	0.173249i	−0.567179	−	0.823594i	$-0.691965\pi$
$607$	−15.9299	+	4.26840i	−0.646574	+	0.173249i	−0.0793944	+	0.996843i	$0.525299\pi$
$608$	1.37861	−	5.14503i	0.0559099	−	0.208658i
$609$	−43.9527	−	11.7771i	−1.78105	−	0.477232i
$610$	−11.9859	+	10.9781i	−0.485294	+	0.444491i
$611$	7.84245	−	22.6599i	0.317272	−	0.916723i
$612$	4.25847	+	4.25847i	0.172138	+	0.172138i
$613$	16.9999	−	9.81491i	0.686620	−	0.396420i	−0.115724	−	0.993281i	$-0.536919\pi$
$613$	16.9999	−	9.81491i	0.686620	−	0.396420i	0.802345	+	0.596861i	$0.203586\pi$
$614$	18.6669	−	10.7774i	0.753336	−	0.434939i
$615$	3.86880	−	0.856783i	0.156005	−	0.0345488i
$616$	−9.60776	+	9.60776i	−0.387108	+	0.387108i
$617$	0.814632	−	1.41098i	0.0327958	−	0.0568041i	−0.849162	−	0.528133i	$-0.822892\pi$
$617$	0.814632	−	1.41098i	0.0327958	−	0.0568041i	0.881957	+	0.471329i	$0.156226\pi$
$618$	−3.08901	+	5.35032i	−0.124258	+	0.215222i
$619$	−0.215346	+	0.215346i	−0.00865550	+	0.00865550i	−0.711421	−	0.702766i	$-0.751948\pi$
$619$	−0.215346	+	0.215346i	−0.00865550	+	0.00865550i	0.702766	+	0.711421i	$0.251948\pi$
$620$	5.96629	+	3.80282i	0.239612	+	0.152725i
$621$	−3.84583	+	2.22039i	−0.154328	+	0.0891011i
$622$	−22.2502	+	12.8461i	−0.892150	+	0.515083i
$623$	−7.76983	−	7.76983i	−0.311292	−	0.311292i
$624$	−0.257185	+	3.59637i	−0.0102956	+	0.143970i
$625$	−24.6163	−	4.36325i	−0.984652	−	0.174530i
$626$	−5.17806	−	1.38746i	−0.206957	−	0.0554539i
$627$	−4.07488	+	15.2077i	−0.162735	+	0.607335i
$628$	15.1049	−	4.04734i	0.602751	−	0.161507i
$629$	15.4412	+	15.4412i	0.615680	+	0.615680i
$630$	−2.22252	−	10.0358i	−0.0885473	−	0.399835i
$631$	21.4779	−	5.75499i	0.855023	−	0.229103i	0.195422	−	0.980719i	$-0.437392\pi$
$631$	21.4779	−	5.75499i	0.855023	−	0.229103i	0.659600	+	0.751617i	$0.270726\pi$
$632$		−	6.34359i		−	0.252334i
$633$	0.348214	+	1.29955i	0.0138402	+	0.0516525i
$634$	−9.35560	−	16.2044i	−0.371558	−	0.643558i
$635$	−5.15733	+	2.68327i	−0.204663	+	0.106482i
$636$			0.143432i			0.00568746i
$637$	−9.64298	−	50.0301i	−0.382069	−	1.98227i
$638$	−20.6890	+	20.6890i	−0.819085	+	0.819085i
$639$	−1.20885	+	4.51148i	−0.0478212	+	0.178471i
$640$	2.13243	+	0.672876i	0.0842915	+	0.0265978i
$641$	−34.3854	−	19.8524i	−1.35814	−	0.784122i	−0.368767	−	0.929522i	$-0.620220\pi$
$641$	−34.3854	−	19.8524i	−1.35814	−	0.784122i	−0.989373	+	0.145399i	$0.953553\pi$
$642$	−3.62951			−0.143245
$643$	−42.3847	−	24.4708i	−1.67149	−	0.965035i	−0.966805	−	0.255516i	$-0.917755\pi$
$643$	−42.3847	−	24.4708i	−1.67149	−	0.965035i	−0.704686	−	0.709520i	$-0.748912\pi$
$644$	5.28345	+	19.7181i	0.208197	+	0.777003i
$645$	8.99469	−	8.23842i	0.354166	−	0.324387i
$646$	16.0392	−	27.7807i	0.631054	−	1.09302i
$647$	20.4842	+	5.48872i	0.805316	+	0.215784i	0.637917	−	0.770105i	$-0.279796\pi$
$647$	20.4842	+	5.48872i	0.805316	+	0.215784i	0.167399	+	0.985889i	$0.446463\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	3.49059			0.137018
$650$	17.9328	−	1.84810i	0.703381	−	0.0724883i
$651$	14.5450			0.570065
$652$	1.42513	+	2.46840i	0.0558124	+	0.0966699i
$653$	10.9760	+	2.94101i	0.429524	+	0.115091i	0.467103	−	0.884203i	$-0.345298\pi$
$653$	10.9760	+	2.94101i	0.429524	+	0.115091i	−0.0375788	+	0.999294i	$0.511965\pi$
$654$	−5.59014	+	9.68240i	−0.218592	+	0.378612i
$655$	−9.31582	+	8.53254i	−0.363999	+	0.333394i
$656$	0.458653	+	1.71172i	0.0179074	+	0.0668312i
$657$	13.1214	+	7.57562i	0.511913	+	0.295553i
$658$	−30.5715			−1.19180
$659$	2.68153	+	1.54818i	0.104458	+	0.0603086i	0.551319	−	0.834295i	$-0.314125\pi$
$659$	2.68153	+	1.54818i	0.104458	+	0.0603086i	−0.446861	+	0.894603i	$0.647458\pi$
$660$	−6.30302	−	1.98889i	−0.245345	−	0.0774173i
$661$	−2.66194	+	9.93449i	−0.103537	+	0.386407i	−0.998175	−	0.0603853i	$-0.980767\pi$
$661$	−2.66194	+	9.93449i	−0.103537	+	0.386407i	0.894638	+	0.446792i	$0.147434\pi$
$662$	11.9498	−	11.9498i	0.464443	−	0.464443i
$663$	−7.10178	+	20.5198i	−0.275810	+	0.796924i
$664$		−	8.15139i		−	0.316335i
$665$	−48.5703	+	25.2703i	−1.88348	+	0.979940i
$666$	1.81300	+	3.14020i	0.0702522	+	0.121680i
$667$	11.3772	+	42.4602i	0.440526	+	1.64407i
$668$			2.46835i			0.0955033i
$669$	−11.1115	+	2.97732i	−0.429596	+	0.115110i
$670$	−6.32395	−	28.5557i	−0.244315	−	1.10320i
$671$	15.1924	+	15.1924i	0.586494	+	0.586494i
$672$	4.44024	−	1.18976i	0.171286	−	0.0458959i
$673$	7.36238	−	27.4768i	0.283799	−	1.05915i	−0.665914	−	0.746029i	$-0.731958\pi$
$673$	7.36238	−	27.4768i	0.283799	−	1.05915i	0.949713	−	0.313123i	$-0.101375\pi$
$674$	−11.6189	−	3.11329i	−0.447545	−	0.119919i
$675$	3.83166	−	3.21222i	0.147481	−	0.123639i
$676$	−12.0687	+	4.83183i	−0.464181	+	0.185840i
$677$	−1.16662	−	1.16662i	−0.0448369	−	0.0448369i	0.684333	−	0.729170i	$-0.260094\pi$
$677$	−1.16662	−	1.16662i	−0.0448369	−	0.0448369i	−0.729170	+	0.684333i	$0.760094\pi$
$678$	−5.38539	+	3.10925i	−0.206824	+	0.119410i
$679$	−50.7164	+	29.2812i	−1.94632	+	1.12371i
$680$	11.3559	+	7.23807i	0.435478	+	0.277567i
$681$	−9.95612	+	9.95612i	−0.381520	+	0.381520i
$682$	4.67624	−	8.09948i	0.179062	−	0.310145i
$683$	−21.0715	+	36.4969i	−0.806277	+	1.39651i	0.109148	+	0.994025i	$0.465188\pi$
$683$	−21.0715	+	36.4969i	−0.806277	+	1.39651i	−0.915425	+	0.402488i	$0.868146\pi$
$684$	3.76642	−	3.76642i	0.144013	−	0.144013i
$685$	29.4557	−	6.52326i	1.12545	−	0.249241i
$686$	−28.3896	+	16.3907i	−1.08392	+	0.625801i
$687$	13.7910	−	7.96226i	0.526161	−	0.303779i
$688$	3.85715	+	3.85715i	0.147052	+	0.147052i
$689$	−0.465171	+	0.225971i	−0.0177216	+	0.00860881i
$690$	−7.32258	+	6.70689i	−0.278766	+	0.255327i
$691$	−24.8600	−	6.66123i	−0.945721	−	0.253405i	−0.247175	−	0.968971i	$-0.579502\pi$
$691$	−24.8600	−	6.66123i	−0.945721	−	0.253405i	−0.698545	+	0.715566i	$0.746169\pi$
$692$	4.26655	−	15.9230i	0.162190	−	0.605301i
$693$	−13.1245	+	3.51669i	−0.498557	+	0.133588i
$694$	5.72293	+	5.72293i	0.217239	+	0.217239i
$695$	9.07426	−	2.00958i	0.344206	−	0.0762278i
$696$	9.56144	−	2.56198i	0.362425	−	0.0971116i
$697$			10.6723i			0.404241i
$698$	5.33258	+	19.9015i	0.201841	+	0.753281i
$699$	−5.46231	−	9.46099i	−0.206603	−	0.357848i
$700$	−9.70429	−	20.8353i	−0.366788	−	0.787499i
$701$		−	24.6239i		−	0.930033i	−0.885302	−	0.465017i	$-0.846048\pi$
$701$		−	24.6239i		−	0.930033i	0.885302	−	0.465017i	$-0.153952\pi$
$702$	−2.02091	+	2.98595i	−0.0762744	+	0.112698i
$703$	13.6570	−	13.6570i	0.515084	−	0.515084i
$704$	0.765017	−	2.85508i	0.0288327	−	0.107605i
$705$	−6.86368	−	13.1922i	−0.258501	−	0.496848i
$706$	−6.14970	−	3.55053i	−0.231447	−	0.133626i
$707$	37.3067			1.40306
$708$	−1.02272	−	0.590466i	−0.0384360	−	0.0221911i
$709$	12.5815	+	46.9549i	0.472509	+	1.76343i	0.630709	+	0.776020i	$0.282764\pi$
$709$	12.5815	+	46.9549i	0.472509	+	1.76343i	−0.158200	+	0.987407i	$0.550569\pi$
$710$	−0.457889	+	10.4338i	−0.0171843	+	0.391573i
$711$	3.17180	−	5.49371i	0.118952	−	0.206030i
$712$	2.30891	+	0.618671i	0.0865302	+	0.0231857i
$713$	−7.02556	−	12.1686i	−0.263109	−	0.455719i
$714$	27.6841			1.03605
$715$	−3.47989	−	23.5750i	−0.130141	−	0.881653i
$716$	16.0470			0.599704
$717$	−13.9361	−	24.1381i	−0.520454	−	0.901453i
$718$	−15.6140	−	4.18375i	−0.582708	−	0.156136i
$719$	17.9868	−	31.1540i	0.670794	−	1.16185i	−0.306885	−	0.951746i	$-0.599287\pi$
$719$	17.9868	−	31.1540i	0.670794	−	1.16185i	0.977679	−	0.210103i	$-0.0673799\pi$
$720$	1.51030	+	1.64894i	0.0562854	+	0.0614524i
$721$	7.35036	+	27.4319i	0.273742	+	1.02162i
$722$	−8.11627	−	4.68593i	−0.302056	−	0.174392i
$723$	−12.8911			−0.479426
$724$	−2.75347	−	1.58972i	−0.102332	−	0.0590813i
$725$	−20.8968	−	44.8658i	−0.776089	−	1.66628i
$726$	0.585774	−	2.18614i	0.0217401	−	0.0811352i
$727$	−22.9023	+	22.9023i	−0.849398	+	0.849398i	−0.990058	−	0.140660i	$-0.955078\pi$
$727$	−22.9023	+	22.9023i	−0.849398	+	0.849398i	0.140660	+	0.990058i	$0.455078\pi$
$728$	10.8539	+	12.5259i	0.402274	+	0.464241i
$729$			1.00000i			0.0370370i
$730$	32.3089	+	10.1949i	1.19581	+	0.377330i
$731$	16.4256	+	28.4499i	0.607521	+	1.05226i
$732$	−1.88131	−	7.02116i	−0.0695354	−	0.259510i
$733$			13.0687i			0.482705i	0.970438	+	0.241352i	$0.0775910\pi$
$733$			13.0687i			0.482705i	−0.970438	+	0.241352i	$0.922409\pi$
$734$	4.08007	−	1.09325i	0.150598	−	0.0403527i
$735$	−26.6461	−	16.9838i	−0.982854	−	0.626457i
$736$	−3.14010	−	3.14010i	−0.115746	−	0.115746i
$737$	−37.3443	+	10.0064i	−1.37559	+	0.368589i
$738$	−0.458653	+	1.71172i	−0.0168832	+	0.0630091i
$739$	9.71768	+	2.60384i	0.357471	+	0.0957840i	0.433085	−	0.901353i	$-0.357425\pi$
$739$	9.71768	+	2.60384i	0.357471	+	0.0957840i	−0.0756141	+	0.997137i	$0.524092\pi$
$740$	5.47632	+	5.97904i	0.201314	+	0.219794i
$741$	18.1488	+	6.28120i	0.666715	+	0.230746i
$742$	0.466224	+	0.466224i	0.0171156	+	0.0171156i
$743$	9.02528	−	5.21075i	0.331106	−	0.191164i	−0.325226	−	0.945636i	$-0.605440\pi$
$743$	9.02528	−	5.21075i	0.331106	−	0.191164i	0.656332	+	0.754472i	$0.272107\pi$
$744$	−2.74020	+	1.58206i	−0.100461	+	0.0580010i
$745$	−26.4716	+	41.5315i	−0.969843	+	1.52160i
$746$	−0.363110	+	0.363110i	−0.0132944	+	0.0132944i
$747$	4.07569	−	7.05931i	0.149122	−	0.258287i
$748$	8.90048	−	15.4161i	0.325434	−	0.563668i
$749$	−11.7976	+	11.7976i	−0.431077	+	0.431077i
$750$	6.81211	−	8.86539i	0.248743	−	0.323718i
$751$	4.49090	−	2.59282i	0.163875	−	0.0946134i	−0.415819	−	0.909447i	$-0.636505\pi$
$751$	4.49090	−	2.59282i	0.163875	−	0.0946134i	0.579695	+	0.814834i	$0.303172\pi$
$752$	5.75949	−	3.32524i	0.210027	−	0.121259i
$753$	−3.02064	−	3.02064i	−0.110078	−	0.110078i
$754$	23.3725	+	26.9728i	0.851175	+	0.982290i
$755$	32.2349	+	1.41463i	1.17315	+	0.0514838i
$756$	4.44024	+	1.18976i	0.161490	+	0.0432711i
$757$	−10.7723	+	40.2027i	−0.391526	+	1.46119i	0.436093	+	0.899902i	$0.356362\pi$
$757$	−10.7723	+	40.2027i	−0.391526	+	1.46119i	−0.827618	+	0.561291i	$0.810305\pi$
$758$	0.819303	−	0.219532i	0.0297584	−	0.00797375i
$759$	9.28151	+	9.28151i	0.336898	+	0.336898i
$760$	6.40174	−	10.0438i	0.232215	−	0.364325i
$761$	18.4576	−	4.94569i	0.669086	−	0.179281i	0.0917428	−	0.995783i	$-0.470756\pi$
$761$	18.4576	−	4.94569i	0.669086	−	0.179281i	0.577343	+	0.816502i	$0.304090\pi$
$762$		−	2.59992i		−	0.0941853i
$763$	13.3018	+	49.6431i	0.481558	+	1.79720i
$764$	−1.14647	−	1.98574i	−0.0414778	−	0.0718417i
$765$	6.21545	+	11.9463i	0.224720	+	0.431919i
$766$		−	15.3042i		−	0.552962i
$767$	0.303718	−	4.24706i	0.0109666	−	0.153353i
$768$	−0.707107	+	0.707107i	−0.0255155	+	0.0255155i
$769$	8.92252	−	33.2993i	0.321754	−	1.20080i	−0.595780	−	0.803147i	$-0.703157\pi$
$769$	8.92252	−	33.2993i	0.321754	−	1.20080i	0.917535	−	0.397656i	$-0.130176\pi$
$770$	−26.9527	+	14.0230i	−0.971307	+	0.505354i
$771$	25.7048	+	14.8406i	0.925734	+	0.534473i
$772$	−17.2058			−0.619249
$773$	29.4252	+	16.9886i	1.05835	+	0.611039i	0.924975	−	0.380027i	$-0.124085\pi$
$773$	29.4252	+	16.9886i	1.05835	+	0.611039i	0.133375	+	0.991066i	$0.457419\pi$
$774$	1.41181	+	5.26896i	0.0507466	+	0.189389i
$775$	10.1638	+	12.1238i	0.365096	+	0.435500i
$776$	6.36980	−	11.0328i	0.228662	−	0.396055i
$777$	16.1003	+	4.31405i	0.577594	+	0.154766i
$778$	2.03274	+	3.52080i	0.0728771	+	0.126227i
$779$	9.43912			0.338192
$780$	−2.96834	+	7.49593i	−0.106283	+	0.268397i
$781$	13.8054			0.493997
$782$	−13.3720	−	23.1611i	−0.478183	−	0.828238i
$783$	9.56144	+	2.56198i	0.341698	+	0.0915577i
$784$	7.06563	−	12.2380i	0.252344	−	0.437072i
$785$	34.9334	+	1.53306i	1.24683	+	0.0547173i
$786$	−1.46222	−	5.45708i	−0.0521556	−	0.194648i
$787$	−3.81659	−	2.20351i	−0.136047	−	0.0785465i	0.430432	−	0.902623i	$-0.358361\pi$
$787$	−3.81659	−	2.20351i	−0.136047	−	0.0785465i	−0.566479	+	0.824076i	$0.691695\pi$
$788$	−6.39026			−0.227644
$789$	14.5235	+	8.38514i	0.517050	+	0.298519i
$790$	4.26845	−	13.5272i	0.151865	−	0.481277i
$791$	−7.39852	+	27.6117i	−0.263061	+	0.981758i
$792$	2.09006	−	2.09006i	0.0742672	−	0.0742672i
$793$	19.8067	−	17.1629i	0.703355	−	0.609472i
$794$			32.1397i			1.14060i
$795$	−0.0965121	+	0.305859i	−0.00342293	+	0.0108477i
$796$	−9.31661	−	16.1368i	−0.330219	−	0.571955i
$797$	6.89585	+	25.7356i	0.244263	+	0.911603i	0.973752	+	0.227611i	$0.0730913\pi$
$797$	6.89585	+	25.7356i	0.244263	+	0.911603i	−0.729489	+	0.683993i	$0.760242\pi$
$798$		−	24.4854i		−	0.866772i
$799$	38.6871	−	10.3662i	1.36865	−	0.366729i
$800$	4.09448	+	2.86972i	0.144762	+	0.101460i
$801$	1.69024	+	1.69024i	0.0597218	+	0.0597218i
$802$	−13.7720	+	3.69019i	−0.486305	+	0.130305i
$803$	11.5909	−	43.2580i	0.409036	−	1.52654i
$804$	12.6342	+	3.38533i	0.445575	+	0.119392i
$805$	−2.00128	+	45.6025i	−0.0705357	+	1.60728i
$806$	−9.44789	−	6.39439i	−0.332788	−	0.225233i
$807$	−16.6942	−	16.6942i	−0.587664	−	0.587664i
$808$	−7.02836	+	4.05783i	−0.247257	+	0.142754i
$809$	−6.30984	+	3.64299i	−0.221842	+	0.128081i	−0.606803	−	0.794852i	$-0.707548\pi$
$809$	−6.30984	+	3.64299i	−0.221842	+	0.128081i	0.384961	+	0.922933i	$0.374215\pi$
$810$	0.483485	+	2.18317i	0.0169879	+	0.0767089i
$811$	−28.4553	+	28.4553i	−0.999201	+	0.999201i	−1.00000		0.000798642i	$-0.999746\pi$
$811$	−28.4553	+	28.4553i	−0.999201	+	0.999201i	0.000798642		1.00000i	$0.499746\pi$
$812$	22.7516	−	39.4069i	0.798425	−	1.38291i
$813$	11.3069	−	19.5842i	0.396551	−	0.686847i
$814$	7.57856	−	7.57856i	0.265628	−	0.265628i
$815$	1.37806	+	6.22261i	0.0482713	+	0.217968i
$816$	−5.21554	+	3.01119i	−0.182580	+	0.105413i
$817$	25.1626	−	14.5276i	0.880329	−	0.508258i
$818$	12.9155	+	12.9155i	0.451581	+	0.451581i
$819$	3.13685	+	16.2747i	0.109610	+	0.568685i
$820$	−0.173729	+	3.95872i	−0.00606689	+	0.138245i
$821$	6.02599	+	1.61466i	0.210309	+	0.0563520i	0.362435	−	0.932009i	$-0.381945\pi$
$821$	6.02599	+	1.61466i	0.210309	+	0.0563520i	−0.152127	+	0.988361i	$0.548612\pi$
$822$	−3.49203	+	13.0324i	−0.121799	+	0.454559i
$823$	31.1564	−	8.34834i	1.08604	−	0.291005i	0.328975	−	0.944339i	$-0.393297\pi$
$823$	31.1564	−	8.34834i	1.08604	−	0.291005i	0.757070	+	0.653334i	$0.226630\pi$
$824$	−4.36852	−	4.36852i	−0.152185	−	0.152185i
$825$	−12.1024	−	8.48230i	−0.421353	−	0.295316i
$826$	−5.24362	+	1.40502i	−0.182449	+	0.0488870i
$827$			48.9222i			1.70119i	0.525819	+	0.850597i	$0.323759\pi$
$827$			48.9222i			1.70119i	−0.525819	+	0.850597i	$0.676241\pi$
$828$	−1.14936	−	4.28946i	−0.0399430	−	0.149069i
$829$	4.97052	+	8.60920i	0.172633	+	0.299010i	0.939340	−	0.342988i	$-0.111439\pi$
$829$	4.97052	+	8.60920i	0.172633	+	0.299010i	−0.766706	+	0.641998i	$0.778106\pi$
$830$	5.48487	−	17.3822i	0.190383	−	0.603346i
$831$		−	7.85791i		−	0.272588i
$832$	−3.40726	−	1.17923i	−0.118125	−	0.0408824i
$833$	60.1775	−	60.1775i	2.08503	−	2.08503i
$834$	−1.07577	+	4.01483i	−0.0372508	+	0.139022i
$835$	−1.66089	+	5.26357i	−0.0574775	+	0.182153i
$836$	−13.6348	−	7.87206i	−0.471570	−	0.272261i
$837$	−3.16411			−0.109368
$838$	−13.1690	−	7.60312i	−0.454915	−	0.262645i
$839$	4.65389	+	17.3686i	0.160670	+	0.599629i	0.998553	+	0.0537788i	$0.0171266\pi$
$839$	4.65389	+	17.3686i	0.160670	+	0.599629i	−0.837883	+	0.545850i	$0.816207\pi$
$840$	10.2690	+	0.450659i	0.354316	+	0.0155492i
$841$	34.4924	−	59.7426i	1.18939	−	2.06009i
$842$	−17.8410	−	4.78048i	−0.614841	−	0.164746i
$843$	5.25312	+	9.09866i	0.180927	+	0.313375i
$844$	−1.34539			−0.0463104
$845$	−28.9868	+	2.18278i	−0.997177	+	0.0750898i
$846$	6.65049			0.228648
$847$	−5.20196	−	9.01005i	−0.178741	−	0.309589i
$848$	−0.138545	−	0.0371230i	−0.00475765	−	0.00127481i
$849$	−12.5932	+	21.8120i	−0.432197	+	0.748588i
$850$	19.3452	+	23.0757i	0.663536	+	0.791491i
$851$	−4.16756	−	15.5536i	−0.142862	−	0.533169i
$852$	−4.04488	−	2.33531i	−0.138575	−	0.0800065i
$853$	−34.0445			−1.16566			−0.582831	−	0.812593i	$-0.698055\pi$
$853$	−34.0445			−1.16566			−0.582831	+	0.812593i	$0.698055\pi$
$854$	−28.9373	−	16.7070i	−0.990215	−	0.571701i
$855$	10.5659	−	5.49728i	0.361348	−	0.188003i
$856$	0.939386	−	3.50584i	0.0321075	−	0.119827i
$857$	−19.9291	+	19.9291i	−0.680764	+	0.680764i	−0.960172	−	0.279408i	$-0.909862\pi$
$857$	−19.9291	+	19.9291i	−0.680764	+	0.680764i	0.279408	+	0.960172i	$0.409862\pi$
$858$	10.0712	+	3.48557i	0.343824	+	0.118995i
$859$			14.8748i			0.507522i	0.967267	+	0.253761i	$0.0816677\pi$
$859$			14.8748i			0.507522i	−0.967267	+	0.253761i	$0.918332\pi$
$860$	5.62970	+	10.8205i	0.191971	+	0.368975i
$861$	4.07306	+	7.05474i	0.138809	+	0.240425i
$862$	−0.979056	−	3.65389i	−0.0333468	−	0.124452i
$863$			36.0992i			1.22883i	0.788983	+	0.614415i	$0.210608\pi$
$863$			36.0992i			1.22883i	−0.788983	+	0.614415i	$0.789392\pi$
$864$	−0.965926	+	0.258819i	−0.0328615	+	0.00880520i
$865$	19.8123	−	31.0837i	0.673638	−	1.05688i
$866$	16.9991	+	16.9991i	0.577652	+	0.577652i
$867$	−18.6126	+	4.98722i	−0.632115	+	0.169375i
$868$	−3.76453	+	14.0494i	−0.127776	+	0.476868i
$869$	−18.1115	−	4.85295i	−0.614390	−	0.164625i
$870$	22.1129	+	0.970431i	0.749699	+	0.0329007i
$871$	8.92557	+	46.3080i	0.302431	+	1.56909i
$872$	−7.90565	−	7.90565i	−0.267719	−	0.267719i
$873$	11.0328	−	6.36980i	0.373404	−	0.215585i
$874$	−20.4849	+	11.8270i	−0.692912	+	0.400053i
$875$	−6.67412	−	50.9594i	−0.225627	−	1.72274i
$876$	−10.7135	+	10.7135i	−0.361977	+	0.361977i
$877$	−11.5735	+	20.0460i	−0.390811	+	0.676904i	−0.992557	−	0.121783i	$-0.961139\pi$
$877$	−11.5735	+	20.0460i	−0.390811	+	0.676904i	0.601746	+	0.798688i	$0.294472\pi$
$878$	−9.25275	+	16.0262i	−0.312265	+	0.540859i
$879$	3.18569	−	3.18569i	0.107451	−	0.107451i
$880$	3.55246	−	5.57349i	0.119753	−	0.187882i
$881$	−37.9214	+	21.8940i	−1.27761	+	0.737626i	−0.976408	−	0.215935i	$-0.930720\pi$
$881$	−37.9214	+	21.8940i	−1.27761	+	0.737626i	−0.301198	+	0.953561i	$0.597387\pi$
$882$	12.2380	−	7.06563i	0.412076	−	0.237912i
$883$	19.8590	+	19.8590i	0.668308	+	0.668308i	0.957324	−	0.289016i	$-0.0933282\pi$
$883$	19.8590	+	19.8590i	0.668308	+	0.668308i	−0.289016	+	0.957324i	$0.593328\pi$
$884$	−17.9826	−	12.1707i	−0.604819	−	0.409345i
$885$	−1.78356	−	1.94728i	−0.0599536	−	0.0654573i
$886$	17.3340	+	4.64462i	0.582346	+	0.156039i
$887$	6.30533	−	23.5318i	0.211712	−	0.790120i	−0.775586	−	0.631242i	$-0.782546\pi$
$887$	6.30533	−	23.5318i	0.211712	−	0.790120i	0.987298	−	0.158878i	$-0.0507878\pi$
$888$	−3.50244	+	0.938476i	−0.117534	+	0.0314932i
$889$	−8.45100	−	8.45100i	−0.283438	−	0.283438i
$890$	4.50730	+	2.87288i	0.151085	+	0.0962992i
$891$	2.85508	−	0.765017i	0.0956488	−	0.0256290i
$892$		−	11.5035i		−	0.385166i
$893$	−9.16840	−	34.2169i	−0.306809	−	1.14503i
$894$	−11.0127	−	19.0746i	−0.368321	−	0.637951i
$895$	34.2190	+	10.7976i	1.14382	+	0.360925i
$896$			4.59687i			0.153571i
$897$	12.1006	−	10.4854i	0.404026	−	0.350097i
$898$	7.93846	−	7.93846i	0.264910	−	0.264910i
$899$	−8.10639	+	30.2535i	−0.270363	+	1.00901i
$900$	2.11106	+	4.53248i	0.0703687	+	0.151083i
$901$	−0.748077	−	0.431902i	−0.0249220	−	0.0143887i
$902$	5.23796			0.174405
$903$	21.7157	+	12.5376i	0.722655	+	0.417225i
$904$	−1.60947	−	6.00662i	−0.0535301	−	0.199777i
$905$	−4.80189	−	5.24270i	−0.159620	−	0.174273i
$906$	−7.21488	+	12.4965i	−0.239698	+	0.415169i
$907$	−0.208308	−	0.0558159i	−0.00691675	−	0.00185334i	0.255359	−	0.966846i	$-0.417806\pi$
$907$	−0.208308	−	0.0558159i	−0.00691675	−	0.00185334i	−0.262276	+	0.964993i	$0.584473\pi$
$908$	−7.04004	−	12.1937i	−0.233632	−	0.404663i
$909$	−8.11566			−0.269179
$910$	14.7169	+	34.0139i	0.487859	+	1.12755i
$911$	−16.0483			−0.531705			−0.265852	−	0.964014i	$-0.585653\pi$
$911$	−16.0483			−0.531705			−0.265852	+	0.964014i	$0.585653\pi$
$912$	2.66326	+	4.61291i	0.0881894	+	0.152749i
$913$	−23.2729	−	6.23595i	−0.770220	−	0.206380i
$914$	−10.1150	+	17.5197i	−0.334574	+	0.579499i
$915$	0.712608	−	16.2380i	0.0235581	−	0.536812i
$916$	4.12157	+	15.3819i	0.136181	+	0.508233i
$917$	−22.4910	−	12.9852i	−0.742720	−	0.428809i
$918$	−6.02239			−0.198768
$919$	−21.8784	−	12.6315i	−0.721702	−	0.416675i	0.0936766	−	0.995603i	$-0.470138\pi$
$919$	−21.8784	−	12.6315i	−0.721702	−	0.416675i	−0.815379	+	0.578928i	$0.803471\pi$
$920$	−4.58314	−	8.80894i	−0.151102	−	0.290422i
$921$	−5.57877	+	20.8202i	−0.183827	+	0.686050i
$922$	−4.12828	+	4.12828i	−0.135958	+	0.135958i
$923$	1.20121	−	16.7973i	0.0395385	−	0.552889i
$924$		−	13.5874i		−	0.446994i
$925$	7.65470	+	16.4348i	0.251685	+	0.540371i
$926$	−14.2198	−	24.6295i	−0.467293	−	0.809375i
$927$	−1.59899	−	5.96751i	−0.0525177	−	0.195999i
$928$			9.89873i			0.324942i
$929$	−22.8017	+	6.10971i	−0.748101	+	0.200453i	−0.612675	−	0.790335i	$-0.709907\pi$
$929$	−22.8017	+	6.10971i	−0.748101	+	0.200453i	−0.135425	+	0.990788i	$0.543240\pi$
$930$	−6.90780	+	1.52980i	−0.226516	+	0.0501642i
$931$	−53.2242	−	53.2242i	−1.74435	−	1.74435i
$932$	10.5524	−	2.82750i	0.345654	−	0.0926178i
$933$	6.64965	−	24.8168i	0.217700	−	0.812466i
$934$	16.1493	+	4.32718i	0.528420	+	0.141590i
$935$	29.3527	−	26.8847i	0.959936	−	0.879224i
$936$	−2.36116	−	2.72487i	−0.0771769	−	0.0890653i
$937$	8.60797	+	8.60797i	0.281210	+	0.281210i	0.833592	−	0.552381i	$-0.186281\pi$
$937$	8.60797	+	8.60797i	0.281210	+	0.281210i	−0.552381	+	0.833592i	$0.686281\pi$
$938$	52.0713	−	30.0634i	1.70019	−	0.981605i
$939$	4.64252	−	2.68036i	0.151503	−	0.0874703i
$940$	14.5192	−	3.21541i	0.473563	−	0.104875i
$941$	−7.14287	+	7.14287i	−0.232851	+	0.232851i	−0.813882	−	0.581031i	$-0.802650\pi$
$941$	−7.14287	+	7.14287i	−0.232851	+	0.232851i	0.581031	+	0.813882i	$0.302650\pi$
$942$	−7.81887	+	13.5427i	−0.254752	+	0.441244i
$943$	3.93475	−	6.81518i	0.128133	−	0.221933i
$944$	0.835044	−	0.835044i	0.0271784	−	0.0271784i
$945$	8.66792	+	5.52480i	0.281967	+	0.179722i
$946$	13.9633	−	8.06169i	0.453985	−	0.262108i
$947$	46.3595	−	26.7657i	1.50648	−	0.869768i	0.506510	−	0.862234i	$-0.330935\pi$
$947$	46.3595	−	26.7657i	1.50648	−	0.869768i	0.999972	−	0.00753336i	$-0.00239797\pi$
$948$	4.48560	+	4.48560i	0.145685	+	0.145685i
$949$	−51.6242	−	17.8668i	−1.67579	−	0.579980i
$950$	20.4094	−	17.1100i	0.662169	−	0.555121i
$951$	18.0736	+	4.84282i	0.586078	+	0.157039i
$952$	−7.16519	+	26.7408i	−0.232225	+	0.866675i
$953$	20.7004	−	5.54666i	0.670553	−	0.179674i	0.0925489	−	0.995708i	$-0.470499\pi$
$953$	20.7004	−	5.54666i	0.670553	−	0.179674i	0.578004	+	0.816034i	$0.303832\pi$
$954$	−0.101422	−	0.101422i	−0.00328366	−	0.00328366i
$955$	−1.10860	−	5.00588i	−0.0358735	−	0.161987i
$956$	26.9225	−	7.21387i	0.870737	−	0.233313i
$957$		−	29.2586i		−	0.945798i
$958$	2.28501	+	8.52777i	0.0738253	+	0.275520i
$959$	31.0109	+	53.7125i	1.00139	+	1.73447i
$960$	−1.98365	+	1.03206i	−0.0640220	+	0.0333095i
$961$			20.9884i			0.677045i
$962$	−8.56154	−	9.88037i	−0.276035	−	0.318556i
$963$	2.56645	−	2.56645i	0.0827027	−	0.0827027i
$964$	3.33647	−	12.4519i	0.107460	−	0.401048i
$965$	−36.6900	−	11.5773i	−1.18109	−	0.372688i
$966$	−17.6788	−	10.2068i	−0.568805	−	0.328400i
$967$	6.13266			0.197213			0.0986066	−	0.995126i	$-0.468561\pi$
$967$	6.13266			0.197213			0.0986066	+	0.995126i	$0.468561\pi$
$968$	1.96004	+	1.13163i	0.0629980	+	0.0363719i
$969$	8.30250	+	30.9853i	0.266715	+	0.995392i
$970$	21.0068	−	19.2406i	0.674489	−	0.617777i
$971$	−2.28743	+	3.96194i	−0.0734070	+	0.127145i	−0.900392	−	0.435079i	$-0.856721\pi$
$971$	−2.28743	+	3.96194i	−0.0734070	+	0.127145i	0.826985	+	0.562223i	$0.190054\pi$
$972$	−0.965926	−	0.258819i	−0.0309821	−	0.00830162i
$973$	9.55335	+	16.5469i	0.306266	+	0.530469i
$974$	−6.48833			−0.207899
$975$	−11.3736	+	13.9872i	−0.364246	+	0.447949i
$976$	7.26884			0.232670
$977$	−11.8392	−	20.5061i	−0.378769	−	0.656048i	0.612114	−	0.790769i	$-0.290319\pi$
$977$	−11.8392	−	20.5061i	−0.378769	−	0.656048i	−0.990883	+	0.134722i	$0.956986\pi$
$978$	−2.75314	−	0.737701i	−0.0880357	−	0.0235891i
$979$	3.53271	−	6.11884i	0.112906	−	0.195559i
$980$	23.3016	−	21.3424i	0.744342	−	0.681757i
$981$	−2.89367	−	10.7993i	−0.0923877	−	0.344796i
$982$	6.14710	+	3.54903i	0.196162	+	0.113254i
$983$	−5.50733			−0.175657			−0.0878283	−	0.996136i	$-0.527993\pi$
$983$	−5.50733			−0.175657			−0.0878283	+	0.996136i	$0.527993\pi$
$984$	−1.53468	−	0.886049i	−0.0489239	−	0.0282462i
$985$	−13.6268	−	4.29985i	−0.434185	−	0.137005i
$986$	−15.4292	+	57.5827i	−0.491367	+	1.83381i
$987$	21.6173	−	21.6173i	0.688086	−	0.688086i
$988$	−10.7644	+	15.9047i	−0.342462	+	0.505997i
$989$		−	24.2237i		−	0.770269i
$990$	5.86326	−	3.05055i	0.186347	−	0.0969529i
$991$	−10.8425	−	18.7797i	−0.344423	−	0.596558i	0.640826	−	0.767686i	$-0.278592\pi$
$991$	−10.8425	−	18.7797i	−0.344423	−	0.596558i	−0.985249	+	0.171128i	$0.945259\pi$
$992$	−0.818933	−	3.05630i	−0.0260011	−	0.0970376i
$993$			16.8996i			0.536293i
$994$	−20.7387	+	5.55692i	−0.657792	+	0.176255i
$995$	−9.00888	−	40.6795i	−0.285601	−	1.28963i
$996$	5.76390	+	5.76390i	0.182636	+	0.182636i
$997$	4.58284	−	1.22797i	0.145140	−	0.0388901i	−0.185518	−	0.982641i	$-0.559396\pi$
$997$	4.58284	−	1.22797i	0.145140	−	0.0388901i	0.330658	+	0.943751i	$0.392729\pi$
$998$	−7.14536	+	26.6669i	−0.226183	+	0.844125i
$999$	−3.50244	−	0.938476i	−0.110812	−	0.0296921i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bn.c.67.6	yes	32
5.3	odd	4		390.2.bd.c.223.1	yes	32
13.7	odd	12		390.2.bd.c.7.1	✓	32
65.33	even	12	inner	390.2.bn.c.163.6	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.c.7.1	✓	32	13.7	odd	12
390.2.bd.c.223.1	yes	32	5.3	odd	4
390.2.bn.c.67.6	yes	32	1.1	even	1	trivial
390.2.bn.c.163.6	yes	32	65.33	even	12	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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.64894 + 1.51030i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-3.98101 - 2.29844i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.64894 + 1.51030i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-3.98101 - 2.29844i) q^{7} +1.00000 q^{8} +(0.866025 + 0.500000i) q^{9} +(2.13243 + 0.672876i) q^{10} +(0.765017 - 2.85508i) q^{11} +(-0.707107 + 0.707107i) q^{12} +(-3.40726 - 1.17923i) q^{13} +4.59687i q^{14} +(-1.98365 + 1.03206i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.55871 - 5.81718i) q^{17} -1.00000i q^{18} +(-5.14503 + 1.37861i) q^{19} +(-0.483485 - 2.18317i) q^{20} +(-3.25048 - 3.25048i) q^{21} +(-2.85508 + 0.765017i) q^{22} +(-1.14936 + 4.28946i) q^{23} +(0.965926 + 0.258819i) q^{24} +(0.438009 - 4.98078i) q^{25} +(0.682387 + 3.54039i) q^{26} +(0.707107 + 0.707107i) q^{27} +(3.98101 - 2.29844i) q^{28} +(8.57255 - 4.94936i) q^{29} +(1.88561 + 1.20186i) q^{30} +(-2.23737 + 2.23737i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(1.47790 - 2.55980i) q^{33} +(-4.25847 + 4.25847i) q^{34} +(10.0358 - 2.22252i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-3.14020 + 1.81300i) q^{37} +(3.76642 + 3.76642i) q^{38} +(-2.98595 - 2.02091i) q^{39} +(-1.64894 + 1.51030i) q^{40} +(-1.71172 - 0.458653i) q^{41} +(-1.18976 + 4.44024i) q^{42} +(-5.26896 + 1.41181i) q^{43} +(2.09006 + 2.09006i) q^{44} +(-2.18317 + 0.483485i) q^{45} +(4.28946 - 1.14936i) q^{46} +6.65049i q^{47} +(-0.258819 - 0.965926i) q^{48} +(7.06563 + 12.2380i) q^{49} +(-4.53248 + 2.11106i) q^{50} -6.02239i q^{51} +(2.72487 - 2.36116i) q^{52} +(0.101422 - 0.101422i) q^{53} +(0.258819 - 0.965926i) q^{54} +(3.05055 + 5.86326i) q^{55} +(-3.98101 - 2.29844i) q^{56} -5.32652 q^{57} +(-8.57255 - 4.94936i) q^{58} +(0.305647 + 1.14069i) q^{59} +(0.0980360 - 2.23392i) q^{60} +(-3.63442 + 6.29500i) q^{61} +(3.05630 + 0.818933i) q^{62} +(-2.29844 - 3.98101i) q^{63} +1.00000 q^{64} +(7.39935 - 3.20149i) q^{65} -2.95580 q^{66} +(-6.53996 - 11.3276i) q^{67} +(5.81718 + 1.55871i) q^{68} +(-2.22039 + 3.84583i) q^{69} +(-6.94264 - 7.57997i) q^{70} +(1.20885 + 4.51148i) q^{71} +(0.866025 + 0.500000i) q^{72} +15.1512 q^{73} +(3.14020 + 1.81300i) q^{74} +(1.71220 - 4.69770i) q^{75} +(1.37861 - 5.14503i) q^{76} +(-9.60776 + 9.60776i) q^{77} +(-0.257185 + 3.59637i) q^{78} -6.34359i q^{79} +(2.13243 + 0.672876i) q^{80} +(0.500000 + 0.866025i) q^{81} +(0.458653 + 1.71172i) q^{82} -8.15139i q^{83} +(4.44024 - 1.18976i) q^{84} +(11.3559 + 7.23807i) q^{85} +(3.85715 + 3.85715i) q^{86} +(9.56144 - 2.56198i) q^{87} +(0.765017 - 2.85508i) q^{88} +(2.30891 + 0.618671i) q^{89} +(1.51030 + 1.64894i) q^{90} +(10.8539 + 12.5259i) q^{91} +(-3.14010 - 3.14010i) q^{92} +(-2.74020 + 1.58206i) q^{93} +(5.75949 - 3.32524i) q^{94} +(6.40174 - 10.0438i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(6.36980 - 11.0328i) q^{97} +(7.06563 - 12.2380i) q^{98} +(2.09006 - 2.09006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8}+O(q^{10}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8	\( 32 q - 16 q^{2} - 16 q^{4} - 12 q^{7} + 32 q^{8} - 4 q^{11} + 8 q^{13} - 4 q^{15} - 16 q^{16} - 4 q^{17} + 20 q^{19} + 8 q^{21} + 8 q^{22} - 16 q^{23} - 8 q^{25} - 4 q^{26} + 12 q^{28} + 24 q^{29} + 8 q^{30} + 12 q^{31} - 16 q^{32} - 16 q^{34} + 12 q^{35} - 24 q^{37} - 4 q^{38} - 20 q^{39} - 28 q^{41} - 16 q^{42} + 4 q^{43} - 4 q^{44} - 4 q^{46} + 20 q^{49} - 8 q^{50} - 4 q^{52} - 4 q^{53} + 68 q^{55} - 12 q^{56} + 16 q^{57} - 24 q^{58} + 36 q^{59} - 4 q^{60} - 28 q^{61} - 48 q^{62} + 32 q^{64} - 28 q^{65} - 28 q^{67} + 20 q^{68} - 20 q^{69} - 24 q^{70} - 4 q^{71} - 48 q^{73} + 24 q^{74} + 24 q^{75} - 16 q^{76} + 20 q^{77} + 4 q^{78} + 16 q^{81} + 44 q^{82} + 8 q^{84} + 64 q^{85} - 8 q^{86} + 20 q^{87} - 4 q^{88} - 16 q^{89} - 40 q^{91} + 20 q^{92} - 24 q^{93} - 24 q^{94} + 68 q^{95} + 8 q^{97} + 20 q^{98} - 4 q^{99}+O(q^{100}) \) 32 * q - 16 * q^2 - 16 * q^4 - 12 * q^7 + 32 * q^8 - 4 * q^11 + 8 * q^13 - 4 * q^15 - 16 * q^16 - 4 * q^17 + 20 * q^19 + 8 * q^21 + 8 * q^22 - 16 * q^23 - 8 * q^25 - 4 * q^26 + 12 * q^28 + 24 * q^29 + 8 * q^30 + 12 * q^31 - 16 * q^32 - 16 * q^34 + 12 * q^35 - 24 * q^37 - 4 * q^38 - 20 * q^39 - 28 * q^41 - 16 * q^42 + 4 * q^43 - 4 * q^44 - 4 * q^46 + 20 * q^49 - 8 * q^50 - 4 * q^52 - 4 * q^53 + 68 * q^55 - 12 * q^56 + 16 * q^57 - 24 * q^58 + 36 * q^59 - 4 * q^60 - 28 * q^61 - 48 * q^62 + 32 * q^64 - 28 * q^65 - 28 * q^67 + 20 * q^68 - 20 * q^69 - 24 * q^70 - 4 * q^71 - 48 * q^73 + 24 * q^74 + 24 * q^75 - 16 * q^76 + 20 * q^77 + 4 * q^78 + 16 * q^81 + 44 * q^82 + 8 * q^84 + 64 * q^85 - 8 * q^86 + 20 * q^87 - 4 * q^88 - 16 * q^89 - 40 * q^91 + 20 * q^92 - 24 * q^93 - 24 * q^94 + 68 * q^95 + 8 * q^97 + 20 * q^98 - 4 * q^99

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