LMFDB - Embedded newform 418.2.h.b.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (of order $6$, degree $2$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.4
Root			$0.634765i$ of defining polynomial
Character	$\chi$	$=$	418.65
Dual form			418.2.h.b.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.549723 - 0.317383i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.464143 + 0.803919i) q^{5} +(-0.549723 + 0.317383i) q^{6} +0.602460i q^{7} -1.00000 q^{8} +(-1.29854 - 2.24913i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.549723 - 0.317383i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.464143 + 0.803919i) q^{5} +(-0.549723 + 0.317383i) q^{6} +0.602460i q^{7} -1.00000 q^{8} +(-1.29854 - 2.24913i) q^{9} +(0.464143 + 0.803919i) q^{10} +(1.50282 - 2.95661i) q^{11} +0.634765i q^{12} +(-3.38075 - 5.85563i) q^{13} +(0.521746 + 0.301230i) q^{14} +(0.510300 - 0.294622i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.731463 + 0.422310i) q^{17} -2.59707 q^{18} +(-2.11195 - 3.81309i) q^{19} +0.928285 q^{20} +(0.191210 - 0.331186i) q^{21} +(-1.80909 - 2.77978i) q^{22} +(-1.03330 - 1.78973i) q^{23} +(0.549723 + 0.317383i) q^{24} +(2.06914 + 3.58386i) q^{25} -6.76150 q^{26} +3.55283i q^{27} +(0.521746 - 0.301230i) q^{28} +(-0.0793963 - 0.137518i) q^{29} -0.589244i q^{30} -1.30358i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.76451 + 1.14835i) q^{33} +(0.731463 - 0.422310i) q^{34} +(-0.484329 - 0.279627i) q^{35} +(-1.29854 + 2.24913i) q^{36} +9.87159i q^{37} +(-4.35821 - 0.0775409i) q^{38} +4.29197i q^{39} +(0.464143 - 0.803919i) q^{40} +(2.44091 - 4.22778i) q^{41} +(-0.191210 - 0.331186i) q^{42} +(-1.19431 - 0.689537i) q^{43} +(-3.31191 + 0.176827i) q^{44} +2.41082 q^{45} -2.06660 q^{46} +(-0.0217933 - 0.0377472i) q^{47} +(0.549723 - 0.317383i) q^{48} +6.63704 q^{49} +4.13829 q^{50} +(-0.268068 - 0.464308i) q^{51} +(-3.38075 + 5.85563i) q^{52} +(5.68217 - 3.28060i) q^{53} +(3.07684 + 1.77641i) q^{54} +(1.67935 + 2.58043i) q^{55} -0.602460i q^{56} +(-0.0492203 + 2.76644i) q^{57} -0.158793 q^{58} +(-7.69762 - 4.44422i) q^{59} +(-0.510300 - 0.294622i) q^{60} +(5.81059 - 3.35475i) q^{61} +(-1.12893 - 0.651790i) q^{62} +(1.35501 - 0.782316i) q^{63} +1.00000 q^{64} +6.27660 q^{65} +(0.112243 + 2.10228i) q^{66} +(6.79379 - 3.92240i) q^{67} -0.844621i q^{68} +1.31181i q^{69} +(-0.484329 + 0.279627i) q^{70} +(-6.08474 - 3.51303i) q^{71} +(1.29854 + 2.24913i) q^{72} +(6.47869 + 3.74048i) q^{73} +(8.54905 + 4.93580i) q^{74} -2.62684i q^{75} +(-2.24626 + 3.73555i) q^{76} +(1.78124 + 0.905387i) q^{77} +(3.71695 + 2.14598i) q^{78} +(-8.17598 + 14.1612i) q^{79} +(-0.464143 - 0.803919i) q^{80} +(-2.76800 + 4.79432i) q^{81} +(-2.44091 - 4.22778i) q^{82} -2.37669i q^{83} -0.382421 q^{84} +(-0.679007 + 0.392025i) q^{85} +(-1.19431 + 0.689537i) q^{86} +0.100796i q^{87} +(-1.50282 + 2.95661i) q^{88} +(11.9810 - 6.91725i) q^{89} +(1.20541 - 2.08784i) q^{90} +(3.52778 - 2.03677i) q^{91} +(-1.03330 + 1.78973i) q^{92} +(-0.413734 + 0.716608i) q^{93} -0.0435867 q^{94} +(4.04566 + 0.0719801i) q^{95} -0.634765i q^{96} +(10.0334 + 5.79276i) q^{97} +(3.31852 - 5.74785i) q^{98} +(-8.60127 + 0.459231i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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
$3$	−0.549723	−	0.317383i	−0.317383	−	0.183241i	0.332843	−	0.942982i	$-0.391992\pi$
$3$	−0.549723	−	0.317383i	−0.317383	−	0.183241i	−0.650225	+	0.759741i	$0.725326\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.464143	+	0.803919i	−0.207571	+	0.359523i	−0.950949	−	0.309348i	$-0.899889\pi$
$5$	−0.464143	+	0.803919i	−0.207571	+	0.359523i	0.743378	+	0.668872i	$0.233222\pi$
$6$	−0.549723	+	0.317383i	−0.224423	+	0.129571i
$7$			0.602460i			0.227708i	0.993497	+	0.113854i	$0.0363197\pi$
$7$			0.602460i			0.227708i	−0.993497	+	0.113854i	$0.963680\pi$
$8$	−1.00000			−0.353553
$9$	−1.29854	−	2.24913i	−0.432845	−	0.749710i
$10$	0.464143	+	0.803919i	0.146775	+	0.254221i
$11$	1.50282	−	2.95661i	0.453117	−	0.891451i
$11$	1.50282	−	2.95661i	0.453117	−	0.891451i
$12$			0.634765i			0.183241i
$13$	−3.38075	−	5.85563i	−0.937651	−	1.62406i	−0.769836	−	0.638241i	$-0.779662\pi$
$13$	−3.38075	−	5.85563i	−0.937651	−	1.62406i	−0.167815	−	0.985818i	$-0.553671\pi$
$14$	0.521746	+	0.301230i	0.139442	+	0.0805071i
$15$	0.510300	−	0.294622i	0.131759	−	0.0760710i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.731463	+	0.422310i	0.177406	+	0.102425i	0.586073	−	0.810258i	$-0.300673\pi$
$17$	0.731463	+	0.422310i	0.177406	+	0.102425i	−0.408667	+	0.912683i	$0.634006\pi$
$18$	−2.59707			−0.612136
$19$	−2.11195	−	3.81309i	−0.484515	−	0.874783i
$19$	−2.11195	−	3.81309i	−0.484515	−	0.874783i
$20$	0.928285			0.207571
$21$	0.191210	−	0.331186i	0.0417255	−	0.0722707i
$22$	−1.80909	−	2.77978i	−0.385699	−	0.592652i
$23$	−1.03330	−	1.78973i	−0.215458	−	0.373184i	0.737956	−	0.674849i	$-0.235791\pi$
$23$	−1.03330	−	1.78973i	−0.215458	−	0.373184i	−0.953414	+	0.301664i	$0.902458\pi$
$24$	0.549723	+	0.317383i	0.112212	+	0.0647855i
$25$	2.06914	+	3.58386i	0.413829	+	0.716772i
$26$	−6.76150			−1.32604
$27$			3.55283i			0.683742i
$28$	0.521746	−	0.301230i	0.0986007	−	0.0569271i
$29$	−0.0793963	−	0.137518i	−0.0147435	−	0.0255365i	0.858560	−	0.512714i	$-0.171360\pi$
$29$	−0.0793963	−	0.137518i	−0.0147435	−	0.0255365i	−0.873303	+	0.487177i	$0.838027\pi$
$30$		−	0.589244i		−	0.107581i
$31$		−	1.30358i		−	0.234130i	−0.993124	−	0.117065i	$-0.962651\pi$
$31$		−	1.30358i		−	0.234130i	0.993124	−	0.117065i	$-0.0373486\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.76451	+	1.14835i	−0.307162	+	0.199902i
$34$	0.731463	−	0.422310i	0.125445	−	0.0724257i
$35$	−0.484329	−	0.279627i	−0.0818665	−	0.0472657i
$36$	−1.29854	+	2.24913i	−0.216423	+	0.374855i
$37$			9.87159i			1.62288i	0.584436	+	0.811440i	$0.301316\pi$
$37$			9.87159i			1.62288i	−0.584436	+	0.811440i	$0.698684\pi$
$38$	−4.35821	−	0.0775409i	−0.706995	−	0.0125788i
$39$			4.29197i			0.687265i
$40$	0.464143	−	0.803919i	0.0733874	−	0.127111i
$41$	2.44091	−	4.22778i	0.381206	−	0.660268i	−0.610029	−	0.792379i	$-0.708842\pi$
$41$	2.44091	−	4.22778i	0.381206	−	0.660268i	0.991235	+	0.132111i	$0.0421755\pi$
$42$	−0.191210	−	0.331186i	−0.0295044	−	0.0511031i
$43$	−1.19431	−	0.689537i	−0.182131	−	0.105153i	0.406162	−	0.913801i	$-0.366867\pi$
$43$	−1.19431	−	0.689537i	−0.182131	−	0.105153i	−0.588294	+	0.808647i	$0.700200\pi$
$44$	−3.31191	+	0.176827i	−0.499289	+	0.0266576i
$45$	2.41082			0.359385
$46$	−2.06660			−0.304704
$47$	−0.0217933	−	0.0377472i	−0.00317888	−	0.00550599i	0.864432	−	0.502750i	$-0.167679\pi$
$47$	−0.0217933	−	0.0377472i	−0.00317888	−	0.00550599i	−0.867610	+	0.497244i	$0.834345\pi$
$48$	0.549723	−	0.317383i	0.0793457	−	0.0458103i
$49$	6.63704			0.948149
$50$	4.13829			0.585242
$51$	−0.268068	−	0.464308i	−0.0375370	−	0.0650161i
$52$	−3.38075	+	5.85563i	−0.468826	+	0.812030i
$53$	5.68217	−	3.28060i	0.780506	−	0.450625i	−0.0561038	−	0.998425i	$-0.517868\pi$
$53$	5.68217	−	3.28060i	0.780506	−	0.450625i	0.836609	+	0.547800i	$0.184534\pi$
$54$	3.07684	+	1.77641i	0.418705	+	0.241739i
$55$	1.67935	+	2.58043i	0.226444	+	0.347945i
$56$		−	0.602460i		−	0.0805071i
$57$	−0.0492203	+	2.76644i	−0.00651938	+	0.366424i
$58$	−0.158793			−0.0208505
$59$	−7.69762	−	4.44422i	−1.00214	−	0.578589i	−0.0932628	−	0.995642i	$-0.529730\pi$
$59$	−7.69762	−	4.44422i	−1.00214	−	0.578589i	−0.908882	+	0.417053i	$0.863063\pi$
$60$	−0.510300	−	0.294622i	−0.0658794	−	0.0380355i
$61$	5.81059	−	3.35475i	0.743970	−	0.429531i	−0.0795411	−	0.996832i	$-0.525345\pi$
$61$	5.81059	−	3.35475i	0.743970	−	0.429531i	0.823511	+	0.567300i	$0.192012\pi$
$62$	−1.12893	−	0.651790i	−0.143375	−	0.0827774i
$63$	1.35501	−	0.782316i	0.170715	−	0.0985626i
$64$	1.00000			0.125000
$65$	6.27660			0.778517
$66$	0.112243	+	2.10228i	0.0138162	+	0.258773i
$67$	6.79379	−	3.92240i	0.829994	−	0.479197i	−0.0238567	−	0.999715i	$-0.507595\pi$
$67$	6.79379	−	3.92240i	0.829994	−	0.479197i	0.853851	+	0.520518i	$0.174261\pi$
$68$		−	0.844621i		−	0.102425i
$69$			1.31181i			0.157923i
$70$	−0.484329	+	0.279627i	−0.0578884	+	0.0334219i
$71$	−6.08474	−	3.51303i	−0.722126	−	0.416920i	0.0934087	−	0.995628i	$-0.470224\pi$
$71$	−6.08474	−	3.51303i	−0.722126	−	0.416920i	−0.815535	+	0.578708i	$0.803557\pi$
$72$	1.29854	+	2.24913i	0.153034	+	0.265063i
$73$	6.47869	+	3.74048i	0.758274	+	0.437790i	0.828676	−	0.559729i	$-0.189095\pi$
$73$	6.47869	+	3.74048i	0.758274	+	0.437790i	−0.0704018	+	0.997519i	$0.522428\pi$
$74$	8.54905	+	4.93580i	0.993807	+	0.573775i
$75$		−	2.62684i		−	0.303321i
$76$	−2.24626	+	3.73555i	−0.257663	+	0.428497i
$77$	1.78124	+	0.905387i	0.202991	+	0.103178i
$78$	3.71695	+	2.14598i	0.420862	+	0.242985i
$79$	−8.17598	+	14.1612i	−0.919870	+	1.59326i	−0.120259	+	0.992743i	$0.538373\pi$
$79$	−8.17598	+	14.1612i	−0.919870	+	1.59326i	−0.799611	+	0.600519i	$0.794961\pi$
$80$	−0.464143	−	0.803919i	−0.0518927	−	0.0898809i
$81$	−2.76800	+	4.79432i	−0.307556	+	0.532702i
$82$	−2.44091	−	4.22778i	−0.269553	−	0.466880i
$83$		−	2.37669i		−	0.260876i	−0.991456	−	0.130438i	$-0.958362\pi$
$83$		−	2.37669i		−	0.260876i	0.991456	−	0.130438i	$-0.0416383\pi$
$84$	−0.382421			−0.0417255
$85$	−0.679007	+	0.392025i	−0.0736486	+	0.0425210i
$86$	−1.19431	+	0.689537i	−0.128786	+	0.0743547i
$87$			0.100796i			0.0108065i
$88$	−1.50282	+	2.95661i	−0.160201	+	0.315176i
$89$	11.9810	−	6.91725i	1.26999	−	0.733227i	0.295001	−	0.955497i	$-0.404680\pi$
$89$	11.9810	−	6.91725i	1.26999	−	0.733227i	0.974985	+	0.222270i	$0.0713466\pi$
$90$	1.20541	−	2.08784i	0.127062	−	0.220077i
$91$	3.52778	−	2.03677i	0.369812	−	0.213511i
$92$	−1.03330	+	1.78973i	−0.107729	+	0.186592i
$93$	−0.413734	+	0.716608i	−0.0429022	+	0.0743088i
$94$	−0.0435867			−0.00449562
$95$	4.04566	+	0.0719801i	0.415076	+	0.00738500i
$96$		−	0.634765i		−	0.0647855i
$97$	10.0334	+	5.79276i	1.01873	+	0.588165i	0.913737	−	0.406307i	$-0.133184\pi$
$97$	10.0334	+	5.79276i	1.01873	+	0.588165i	0.104996	+	0.994473i	$0.466517\pi$
$98$	3.31852	−	5.74785i	0.335221	−	0.580620i
$99$	−8.60127	+	0.459231i	−0.864460	+	0.0461545i
$100$	2.06914	−	3.58386i	0.206914	−	0.358386i
$101$	2.26554	−	1.30801i	0.225430	−	0.130152i	−0.383032	−	0.923735i	$-0.625120\pi$
$101$	2.26554	−	1.30801i	0.225430	−	0.130152i	0.608462	+	0.793583i	$0.291787\pi$
$102$	−0.536136			−0.0530854
$103$		−	11.4386i		−	1.12708i	−0.826090	−	0.563539i	$-0.809439\pi$
$103$		−	11.4386i		−	1.12708i	0.826090	−	0.563539i	$-0.190561\pi$
$104$	3.38075	+	5.85563i	0.331510	+	0.574192i
$105$	0.177498	+	0.307435i	0.0173220	+	0.0300026i
$106$		−	6.56120i		−	0.637280i
$107$	−10.5569			−1.02057			−0.510286	−	0.860004i	$-0.670461\pi$
$107$	−10.5569			−1.02057			−0.510286	+	0.860004i	$0.670461\pi$
$108$	3.07684	−	1.77641i	0.296069	−	0.170936i
$109$	−1.23781	+	2.14395i	−0.118561	+	0.205354i	−0.919198	−	0.393797i	$-0.871161\pi$
$109$	−1.23781	+	2.14395i	−0.118561	+	0.205354i	0.800637	+	0.599150i	$0.204495\pi$
$110$	3.07440	−	0.164146i	0.293132	−	0.0156507i
$111$	3.13307	−	5.42664i	0.297378	−	0.515074i
$112$	−0.521746	−	0.301230i	−0.0493003	−	0.0284636i
$113$			14.2392i			1.33951i	0.742580	+	0.669757i	$0.233602\pi$
$113$			14.2392i			1.33951i	−0.742580	+	0.669757i	$0.766398\pi$
$114$	2.37120	+	1.42585i	0.222083	+	0.133543i
$115$	1.91840			0.178891
$116$	−0.0793963	+	0.137518i	−0.00737176	+	0.0127683i
$117$	−8.78005	+	15.2075i	−0.811716	+	1.40593i
$118$	−7.69762	+	4.44422i	−0.708624	+	0.409124i
$119$	−0.254425	+	0.440677i	−0.0233231	+	0.0403968i
$120$	−0.510300	+	0.294622i	−0.0465838	+	0.0268952i
$121$	−6.48308	−	8.88649i	−0.589371	−	0.807863i
$122$		−	6.70949i		−	0.607449i
$123$	−2.68365	+	1.54941i	−0.241976	+	0.139705i
$124$	−1.12893	+	0.651790i	−0.101381	+	0.0585325i
$125$	−8.48294			−0.758737
$126$		−	1.56463i		−	0.139389i
$127$	5.17110	+	8.95660i	0.458860	+	0.794770i	0.998901	−	0.0468693i	$-0.0149244\pi$
$127$	5.17110	+	8.95660i	0.458860	+	0.794770i	−0.540041	+	0.841639i	$0.681591\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.437694	+	0.758109i	0.0385368	+	0.0667478i
$130$	3.13830	−	5.43570i	0.275247	−	0.476742i
$131$	13.1829	+	7.61114i	1.15179	+	0.664988i	0.949324	−	0.314300i	$-0.101770\pi$
$131$	13.1829	+	7.61114i	1.15179	+	0.664988i	0.202470	+	0.979289i	$0.435103\pi$
$132$	1.87675	+	0.953937i	0.163350	+	0.0830295i
$133$	2.29723	−	1.27237i	0.199195	−	0.110328i
$134$		−	7.84480i		−	0.677687i
$135$	−2.85619	−	1.64902i	−0.245821	−	0.141925i
$136$	−0.731463	−	0.422310i	−0.0627225	−	0.0362128i
$137$	−4.82759	−	8.36163i	−0.412449	−	0.714382i	0.582708	−	0.812682i	$-0.301993\pi$
$137$	−4.82759	−	8.36163i	−0.412449	−	0.714382i	−0.995157	+	0.0982992i	$0.968660\pi$
$138$	1.13606	+	0.655904i	0.0967077	+	0.0558342i
$139$	12.8588	−	7.42405i	1.09067	−	0.629700i	0.156917	−	0.987612i	$-0.449845\pi$
$139$	12.8588	−	7.42405i	1.09067	−	0.629700i	0.933755	+	0.357912i	$0.116511\pi$
$140$			0.559255i			0.0472657i
$141$			0.0276673i			0.00233001i
$142$	−6.08474	+	3.51303i	−0.510620	+	0.294807i
$143$	−22.3935	+	1.19561i	−1.87264	+	0.0999822i
$144$	2.59707			0.216423
$145$	0.147405			0.0122413
$146$	6.47869	−	3.74048i	0.536181	−	0.309564i
$147$	−3.64853	−	2.10648i	−0.300926	−	0.173740i
$148$	8.54905	−	4.93580i	0.702728	−	0.405720i
$149$	2.60063	+	1.50148i	0.213052	+	0.123006i	0.602729	−	0.797946i	$-0.294080\pi$
$149$	2.60063	+	1.50148i	0.213052	+	0.123006i	−0.389677	+	0.920952i	$0.627413\pi$
$150$	−2.27491	−	1.31342i	−0.185746	−	0.107240i
$151$	−0.782222			−0.0636563			−0.0318281	−	0.999493i	$-0.510133\pi$
$151$	−0.782222			−0.0636563			−0.0318281	+	0.999493i	$0.510133\pi$
$152$	2.11195	+	3.81309i	0.171302	+	0.309282i
$153$		−	2.19354i		−	0.177337i
$154$	1.67471	−	1.08990i	0.134952	−	0.0878270i
$155$	1.04797	+	0.605047i	0.0841752	+	0.0485986i
$156$	3.71695	−	2.14598i	0.297594	−	0.171816i
$157$	3.27664	−	5.67530i	0.261504	−	0.452938i	−0.705138	−	0.709070i	$-0.749115\pi$
$157$	3.27664	−	5.67530i	0.261504	−	0.452938i	0.966642	+	0.256132i	$0.0824482\pi$
$158$	8.17598	+	14.1612i	0.650446	+	1.12661i
$159$	−4.16482			−0.330292
$160$	−0.928285			−0.0733874
$161$	1.07824	−	0.622522i	0.0849773	−	0.0490616i
$162$	2.76800	+	4.79432i	0.217475	+	0.376677i
$163$	18.4385			1.44421			0.722106	−	0.691782i	$-0.243174\pi$
$163$	18.4385			1.44421			0.722106	+	0.691782i	$0.243174\pi$
$164$	−4.88182			−0.381206
$165$	−0.104194	−	1.95152i	−0.00811149	−	0.151926i
$166$	−2.05828	−	1.18835i	−0.159753	−	0.0922335i
$167$	−6.20883	−	10.7540i	−0.480453	−	0.832170i	0.519295	−	0.854595i	$-0.326195\pi$
$167$	−6.20883	−	10.7540i	−0.480453	−	0.832170i	−0.999749	+	0.0224253i	$0.992861\pi$
$168$	−0.191210	+	0.331186i	−0.0147522	+	0.0255516i
$169$	−16.3589	+	28.3345i	−1.25838	+	2.17958i
$170$			0.784049i			0.0601338i
$171$	−5.83369	+	9.70149i	−0.446114	+	0.741892i
$172$			1.37907i			0.105153i
$173$	11.5737	−	20.0462i	0.879929	−	1.52408i	0.0285118	−	0.999593i	$-0.490923\pi$
$173$	11.5737	−	20.0462i	0.879929	−	1.52408i	0.851417	−	0.524489i	$-0.175743\pi$
$174$	0.0872919	+	0.0503980i	0.00661758	+	0.00382066i
$175$	−2.15913	+	1.24658i	−0.163215	+	0.0942323i
$176$	1.80909	+	2.77978i	0.136365	+	0.209534i
$177$	2.82104	+	4.88618i	0.212042	+	0.367268i
$178$		−	13.8345i		−	1.03694i
$179$		−	19.9245i		−	1.48923i	−0.667496	−	0.744614i	$-0.732634\pi$
$179$		−	19.9245i		−	1.48923i	0.667496	−	0.744614i	$-0.267366\pi$
$180$	−1.20541	−	2.08784i	−0.0898461	−	0.155618i
$181$	−18.6778	+	10.7836i	−1.38831	+	0.801542i	−0.993125	−	0.117059i	$-0.962653\pi$
$181$	−18.6778	+	10.7836i	−1.38831	+	0.801542i	−0.395186	+	0.918601i	$0.629320\pi$
$182$		−	4.07353i		−	0.301950i
$183$	−4.25895			−0.314831
$184$	1.03330	+	1.78973i	0.0761760	+	0.131941i
$185$	−7.93596	−	4.58183i	−0.583463	−	0.336863i
$186$	0.413734	+	0.716608i	0.0303364	+	0.0525443i
$187$	2.34786	−	1.52800i	0.171693	−	0.111738i
$188$	−0.0217933	+	0.0377472i	−0.00158944	+	0.00275300i
$189$	−2.14044			−0.155694
$190$	2.08517	−	3.46766i	0.151274	−	0.251570i
$191$	−21.9330			−1.58702			−0.793510	−	0.608558i	$-0.791748\pi$
$191$	−21.9330			−1.58702			−0.793510	+	0.608558i	$0.791748\pi$
$192$	−0.549723	−	0.317383i	−0.0396728	−	0.0229051i
$193$	−5.93879	+	10.2863i	−0.427483	+	0.740423i	−0.996649	−	0.0818001i	$-0.973933\pi$
$193$	−5.93879	+	10.2863i	−0.427483	+	0.740423i	0.569165	+	0.822223i	$0.307266\pi$
$194$	10.0334	−	5.79276i	0.720353	−	0.415896i
$195$	−3.45039	−	1.99209i	−0.247088	−	0.142656i
$196$	−3.31852	−	5.74785i	−0.237037	−	0.410560i
$197$			6.58335i			0.469045i	0.972111	+	0.234522i	$0.0753526\pi$
$197$			6.58335i			0.469045i	−0.972111	+	0.234522i	$0.924647\pi$
$198$	−3.90293	+	7.67853i	−0.277369	+	0.545689i
$199$	5.40236	+	9.35717i	0.382963	+	0.663312i	0.991484	−	0.130226i	$-0.0415702\pi$
$199$	5.40236	+	9.35717i	0.382963	+	0.663312i	−0.608521	+	0.793538i	$0.708237\pi$
$200$	−2.06914	−	3.58386i	−0.146311	−	0.253417i
$201$	−4.97961			−0.351234
$202$		−	2.61602i		−	0.184063i
$203$	0.0828493	−	0.0478331i	0.00581488	−	0.00335722i
$204$	−0.268068	+	0.464308i	−0.0187685	+	0.0325080i
$205$	2.26586	+	3.92459i	0.158255	+	0.274105i
$206$	−9.90611	−	5.71930i	−0.690191	−	0.398482i
$207$	−2.68356	+	4.64806i	−0.186520	+	0.323062i
$208$	6.76150			0.468826
$209$	−14.4477	+	0.513839i	−0.999368	+	0.0355430i
$210$	0.354996			0.0244970
$211$	0.0415210	−	0.0719165i	0.00285842	−	0.00495093i	−0.864593	−	0.502473i	$-0.832423\pi$
$211$	0.0415210	−	0.0719165i	0.00285842	−	0.00495093i	0.867451	+	0.497522i	$0.165757\pi$
$212$	−5.68217	−	3.28060i	−0.390253	−	0.225313i
$213$	2.22995	+	3.86238i	0.152794	+	0.264646i
$214$	−5.27844	+	9.14253i	−0.360827	+	0.624971i
$215$	1.10866	−	0.640087i	0.0756103	−	0.0436536i
$216$		−	3.55283i		−	0.241739i
$217$	0.785355			0.0533134
$218$	1.23781	+	2.14395i	0.0838353	+	0.145207i
$219$	−2.37433	−	4.11245i	−0.160442	−	0.277894i
$220$	1.39504	−	2.74458i	0.0940538	−	0.185039i
$221$		−	5.71090i		−	0.384157i
$222$	−3.13307	−	5.42664i	−0.210278	−	0.364212i
$223$	−3.70697	−	2.14022i	−0.248237	−	0.143320i	0.370720	−	0.928745i	$-0.379111\pi$
$223$	−3.70697	−	2.14022i	−0.248237	−	0.143320i	−0.618957	+	0.785425i	$0.712444\pi$
$224$	−0.521746	+	0.301230i	−0.0348606	+	0.0201268i
$225$	5.37372	−	9.30755i	0.358248	−	0.620503i
$226$	12.3315	+	7.11962i	0.820282	+	0.473590i
$227$	−20.2869			−1.34649			−0.673245	−	0.739420i	$-0.735100\pi$
$227$	−20.2869			−1.34649			−0.673245	+	0.739420i	$0.735100\pi$
$228$	2.42042	−	1.34059i	0.160296	−	0.0887830i
$229$	19.1288			1.26406			0.632032	−	0.774942i	$-0.282221\pi$
$229$	19.1288			1.26406			0.632032	+	0.774942i	$0.282221\pi$
$230$	0.959198	−	1.66138i	0.0632477	−	0.109548i
$231$	−0.691834	−	1.06305i	−0.0455193	−	0.0699433i
$232$	0.0793963	+	0.137518i	0.00521262	+	0.00902852i
$233$	17.3799	+	10.0343i	1.13859	+	0.657367i	0.946082	−	0.323928i	$-0.105004\pi$
$233$	17.3799	+	10.0343i	1.13859	+	0.657367i	0.192511	+	0.981295i	$0.438337\pi$
$234$	8.78005	+	15.2075i	0.573970	+	0.994145i
$235$	0.0404609			0.00263938
$236$			8.88845i			0.578589i
$237$	8.98905	−	5.18983i	0.583902	−	0.337116i
$238$	0.254425	+	0.440677i	0.0164919	+	0.0285649i
$239$		−	16.8213i		−	1.08808i	−0.839060	−	0.544040i	$-0.816894\pi$
$239$		−	16.8213i		−	1.08808i	0.839060	−	0.544040i	$-0.183106\pi$
$240$			0.589244i			0.0380355i
$241$	−9.20489	−	15.9433i	−0.592939	−	1.02700i	−0.993834	−	0.110877i	$-0.964634\pi$
$241$	−9.20489	−	15.9433i	−0.592939	−	1.02700i	0.400895	−	0.916124i	$-0.368699\pi$
$242$	−10.9375	+	1.17127i	−0.703087	+	0.0752919i
$243$	12.2738	−	7.08628i	0.787364	−	0.454585i
$244$	−5.81059	−	3.35475i	−0.371985	−	0.214766i
$245$	−3.08053	+	5.33564i	−0.196808	+	0.340882i
$246$			3.09881i			0.197573i
$247$	−15.1881	+	25.2579i	−0.966394	+	1.60712i
$248$			1.30358i			0.0827774i
$249$	−0.754321	+	1.30652i	−0.0478031	+	0.0827975i
$250$	−4.24147	+	7.34644i	−0.268254	+	0.464630i
$251$	−8.60900	−	14.9112i	−0.543395	−	0.941188i	−0.998706	−	0.0508555i	$-0.983805\pi$
$251$	−8.60900	−	14.9112i	−0.543395	−	0.941188i	0.455311	−	0.890333i	$-0.349528\pi$
$252$	−1.35501	−	0.782316i	−0.0853577	−	0.0492813i
$253$	−6.84439	+	0.365430i	−0.430303	+	0.0229744i
$254$	10.3422			0.648927
$255$	0.497687			0.0311664
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	13.4952	−	7.79148i	0.841810	−	0.486019i	−0.0160689	−	0.999871i	$-0.505115\pi$
$257$	13.4952	−	7.79148i	0.841810	−	0.486019i	0.857879	+	0.513852i	$0.171782\pi$
$258$	0.875389			0.0544993
$259$	−5.94724			−0.369544
$260$	−3.13830	−	5.43570i	−0.194629	−	0.337108i
$261$	−0.206198	+	0.357145i	−0.0127633	+	0.0221067i
$262$	13.1829	−	7.61114i	0.814441	−	0.470218i
$263$	3.18777	+	1.84046i	0.196566	+	0.113488i	0.595053	−	0.803687i	$-0.297131\pi$
$263$	3.18777	+	1.84046i	0.196566	+	0.113488i	−0.398487	+	0.917174i	$0.630464\pi$
$264$	1.76451	−	1.14835i	0.108598	−	0.0706759i
$265$			6.09067i			0.374147i
$266$	0.0467153	−	2.62565i	0.00286430	−	0.160989i
$267$	−8.78166			−0.537429
$268$	−6.79379	−	3.92240i	−0.414997	−	0.239599i
$269$	−4.47493	−	2.58360i	−0.272841	−	0.157525i	0.357337	−	0.933976i	$-0.383685\pi$
$269$	−4.47493	−	2.58360i	−0.272841	−	0.157525i	−0.630178	+	0.776451i	$0.717018\pi$
$270$	−2.85619	+	1.64902i	−0.173822	+	0.100356i
$271$	1.20366	+	0.694932i	0.0731169	+	0.0422141i	0.536113	−	0.844146i	$-0.319892\pi$
$271$	1.20366	+	0.694932i	0.0731169	+	0.0422141i	−0.462996	+	0.886360i	$0.653226\pi$
$272$	−0.731463	+	0.422310i	−0.0443515	+	0.0256063i
$273$	−2.58574			−0.156496
$274$	−9.65518			−0.583291
$275$	13.7056	−	0.731759i	0.826480	−	0.0441267i
$276$	1.13606	−	0.655904i	0.0683827	−	0.0394808i
$277$			15.6925i			0.942869i	0.881901	+	0.471435i	$0.156264\pi$
$277$			15.6925i			0.942869i	−0.881901	+	0.471435i	$0.843736\pi$
$278$		−	14.8481i		−	0.890530i
$279$	−2.93192	+	1.69275i	−0.175530	+	0.101342i
$280$	0.484329	+	0.279627i	0.0289442	+	0.0167109i
$281$	−13.5361	−	23.4453i	−0.807498	−	1.39863i	−0.914592	−	0.404378i	$-0.867488\pi$
$281$	−13.5361	−	23.4453i	−0.807498	−	1.39863i	0.107094	−	0.994249i	$-0.465845\pi$
$282$	0.0239606	+	0.0138337i	0.00142683	+	0.000823782i
$283$	−8.82881	−	5.09732i	−0.524819	−	0.303004i	0.214085	−	0.976815i	$-0.431323\pi$
$283$	−8.82881	−	5.09732i	−0.524819	−	0.303004i	−0.738904	+	0.673811i	$0.764656\pi$
$284$			7.02605i			0.416920i
$285$	−2.20115	−	1.32359i	−0.130385	−	0.0784029i
$286$	−10.1613	+	19.9911i	−0.600850	+	1.18210i
$287$	2.54707	+	1.47055i	0.150349	+	0.0868038i
$288$	1.29854	−	2.24913i	0.0765170	−	0.132531i
$289$	−8.14331	−	14.1046i	−0.479018	−	0.829684i
$290$	0.0737024	−	0.127656i	0.00432795	−	0.00749624i
$291$	−3.67704	−	6.36883i	−0.215552	−	0.373347i
$292$		−	7.48095i		−	0.437790i
$293$	−8.08264			−0.472193			−0.236096	−	0.971730i	$-0.575868\pi$
$293$	−8.08264			−0.472193			−0.236096	+	0.971730i	$0.575868\pi$
$294$	−3.64853	+	2.10648i	−0.212787	+	0.122853i
$295$	7.14559	−	4.12551i	0.416032	−	0.240196i
$296$		−	9.87159i		−	0.573775i
$297$	10.5043	+	5.33925i	0.609523	+	0.309815i
$298$	2.60063	−	1.50148i	0.150651	−	0.0869782i
$299$	−6.98666	+	12.1013i	−0.404049	+	0.699834i
$300$	−2.27491	+	1.31342i	−0.131342	+	0.0758304i
$301$	0.415419	−	0.719526i	0.0239443	−	0.0414728i
$302$	−0.391111	+	0.677424i	−0.0225059	+	0.0389814i
$303$	−1.66056			−0.0953968
$304$	4.35821	+	0.0775409i	0.249960	+	0.00444727i
$305$			6.22832i			0.356633i
$306$	−1.89966	−	1.09677i	−0.108597	−	0.0626982i
$307$	0.142057	−	0.246049i	0.00810760	−	0.0140428i	−0.861943	−	0.507005i	$-0.830753\pi$
$307$	0.142057	−	0.246049i	0.00810760	−	0.0140428i	0.870051	+	0.492962i	$0.164086\pi$
$308$	−0.106531	−	1.99529i	−0.00607016	−	0.113692i
$309$	−3.63041	+	6.28806i	−0.206527	+	0.357715i
$310$	1.04797	−	0.605047i	0.0595208	−	0.0343644i
$311$	14.8851			0.844056			0.422028	−	0.906583i	$-0.361318\pi$
$311$	14.8851			0.844056			0.422028	+	0.906583i	$0.361318\pi$
$312$		−	4.29197i		−	0.242985i
$313$	4.53872	+	7.86129i	0.256544	+	0.444346i	0.965314	−	0.261093i	$-0.0840830\pi$
$313$	4.53872	+	7.86129i	0.256544	+	0.444346i	−0.708770	+	0.705440i	$0.750750\pi$
$314$	−3.27664	−	5.67530i	−0.184911	−	0.320276i
$315$			1.45243i			0.0818349i
$316$	16.3520			0.919870
$317$	13.0069	−	7.50951i	0.730538	−	0.421776i	−0.0880809	−	0.996113i	$-0.528073\pi$
$317$	13.0069	−	7.50951i	0.730538	−	0.421776i	0.818619	+	0.574337i	$0.194740\pi$
$318$	−2.08241	+	3.60684i	−0.116776	+	0.202262i
$319$	−0.525906	+	0.0280787i	−0.0294451	+	0.00157211i
$320$	−0.464143	+	0.803919i	−0.0259464	+	0.0449404i
$321$	5.80336	+	3.35057i	0.323912	+	0.187011i
$322$		−	1.24504i		−	0.0693836i
$323$	0.0654926	−	3.68103i	0.00364411	−	0.204818i
$324$	5.53601			0.307556
$325$	13.9905	−	24.2323i	0.776054	−	1.34416i
$326$	9.21924	−	15.9682i	0.510606	−	0.884396i
$327$	1.36091	−	0.785721i	0.0752584	−	0.0434505i
$328$	−2.44091	+	4.22778i	−0.134777	+	0.233440i
$329$	0.0227412	−	0.0131296i	0.00125376	−	0.000723859i
$330$	−1.74216	−	0.885526i	−0.0959029	−	0.0487466i
$331$		−	23.7354i		−	1.30461i	−0.757955	−	0.652307i	$-0.773801\pi$
$331$		−	23.7354i		−	1.30461i	0.757955	−	0.652307i	$-0.226199\pi$
$332$	−2.05828	+	1.18835i	−0.112963	+	0.0652189i
$333$	22.2025	−	12.8186i	1.21669	−	0.702456i
$334$	−12.4177			−0.679464
$335$			7.28221i			0.397870i
$336$	0.191210	+	0.331186i	0.0104314	+	0.0180677i
$337$	−12.4439	+	21.5534i	−0.677861	+	1.17409i	0.297763	+	0.954640i	$0.403759\pi$
$337$	−12.4439	+	21.5534i	−0.677861	+	1.17409i	−0.975624	+	0.219449i	$0.929574\pi$
$338$	16.3589	+	28.3345i	0.889809	+	1.54119i
$339$	4.51929	−	7.82763i	0.245454	−	0.425139i
$340$	0.679007	+	0.392025i	0.0368243	+	0.0212605i
$341$	−3.85418	−	1.95904i	−0.208715	−	0.106088i
$342$	5.48489	+	9.90287i	0.296589	+	0.535486i
$343$			8.21577i			0.443610i
$344$	1.19431	+	0.689537i	0.0643931	+	0.0371774i
$345$	−1.05459	−	0.608866i	−0.0567770	−	0.0327802i
$346$	−11.5737	−	20.0462i	−0.622204	−	1.07769i
$347$	10.9807	+	6.33973i	0.589477	+	0.340335i	0.764891	−	0.644160i	$-0.222793\pi$
$347$	10.9807	+	6.33973i	0.589477	+	0.340335i	−0.175414	+	0.984495i	$0.556126\pi$
$348$	0.0872919	−	0.0503980i	0.00467934	−	0.00270162i
$349$			9.21385i			0.493206i	0.969117	+	0.246603i	$0.0793143\pi$
$349$			9.21385i			0.493206i	−0.969117	+	0.246603i	$0.920686\pi$
$350$			2.49315i			0.133265i
$351$	20.8041	−	12.0112i	1.11044	−	0.641112i
$352$	3.31191	−	0.176827i	0.176525	−	0.00942489i
$353$	23.9085			1.27252			0.636261	−	0.771474i	$-0.280480\pi$
$353$	23.9085			1.27252			0.636261	+	0.771474i	$0.280480\pi$
$354$	5.64208			0.299873
$355$	5.64838	−	3.26109i	0.299785	−	0.173081i
$356$	−11.9810	−	6.91725i	−0.634993	−	0.366614i
$357$	0.279727	−	0.161500i	0.0148047	−	0.00854750i
$358$	−17.2551	−	9.96225i	−0.911962	−	0.526521i
$359$	22.3441	+	12.9004i	1.17928	+	0.680857i	0.955848	−	0.293863i	$-0.0949409\pi$
$359$	22.3441	+	12.9004i	1.17928	+	0.680857i	0.223431	+	0.974720i	$0.428274\pi$
$360$	−2.41082			−0.127062
$361$	−10.0793	+	16.1061i	−0.530490	+	0.847691i
$362$			21.5673i			1.13355i
$363$	0.743480	+	6.94273i	0.0390226	+	0.364399i
$364$	−3.52778	−	2.03677i	−0.184906	−	0.106756i
$365$	−6.01408	+	3.47223i	−0.314791	+	0.181745i
$366$	−2.12948	+	3.68836i	−0.111310	+	0.192794i
$367$	17.2796	+	29.9292i	0.901989	+	1.56229i	0.824909	+	0.565266i	$0.191226\pi$
$367$	17.2796	+	29.9292i	0.901989	+	1.56229i	0.0770799	+	0.997025i	$0.475440\pi$
$368$	2.06660			0.107729
$369$	−12.6784			−0.660013
$370$	−7.93596	+	4.58183i	−0.412571	+	0.238198i
$371$	1.97643	+	3.42328i	0.102611	+	0.177728i
$372$	0.827468			0.0429022
$373$	8.31805			0.430692			0.215346	−	0.976538i	$-0.430912\pi$
$373$	8.31805			0.430692			0.215346	+	0.976538i	$0.430912\pi$
$374$	−0.149351	−	2.79731i	−0.00772278	−	0.144645i
$375$	4.66327	+	2.69234i	0.240810	+	0.139032i
$376$	0.0217933	+	0.0377472i	0.00112391	+	0.00194666i
$377$	−0.536838	+	0.929830i	−0.0276486	+	0.0478887i
$378$	−1.07022	+	1.85367i	−0.0550461	+	0.0953426i
$379$		−	28.9556i		−	1.48735i	−0.668541	−	0.743676i	$-0.733081\pi$
$379$		−	28.9556i		−	1.48735i	0.668541	−	0.743676i	$-0.266919\pi$
$380$	−1.96049	−	3.53964i	−0.100571	−	0.181580i
$381$		−	6.56487i		−	0.336328i
$382$	−10.9665	+	18.9946i	−0.561096	+	0.971847i
$383$	−3.17405	−	1.83254i	−0.162186	−	0.0936382i	0.416710	−	0.909039i	$-0.363183\pi$
$383$	−3.17405	−	1.83254i	−0.162186	−	0.0936382i	−0.578896	+	0.815401i	$0.696516\pi$
$384$	−0.549723	+	0.317383i	−0.0280529	+	0.0161964i
$385$	−1.55461	+	1.01174i	−0.0792301	+	0.0515632i
$386$	5.93879	+	10.2863i	0.302276	+	0.523558i
$387$			3.58156i			0.182061i
$388$		−	11.5855i		−	0.588165i
$389$	−7.89975	−	13.6828i	−0.400533	−	0.693744i	0.593257	−	0.805013i	$-0.297842\pi$
$389$	−7.89975	−	13.6828i	−0.400533	−	0.693744i	−0.993790	+	0.111269i	$0.964508\pi$
$390$	−3.45039	+	1.99209i	−0.174717	+	0.100873i
$391$		−	1.74550i		−	0.0882735i
$392$	−6.63704			−0.335221
$393$	−4.83129	−	8.36804i	−0.243706	−	0.422112i
$394$	5.70135	+	3.29168i	0.287230	+	0.165832i
$395$	−7.58965	−	13.1457i	−0.381876	−	0.661429i
$396$	4.69834	+	7.21930i	0.236100	+	0.362783i
$397$	0.172652	−	0.299043i	0.00866517	−	0.0150085i	−0.861660	−	0.507485i	$-0.830575\pi$
$397$	0.172652	−	0.299043i	0.00866517	−	0.0150085i	0.870325	+	0.492477i	$0.163908\pi$
$398$	10.8047			0.541592
$399$	−1.66667	−	0.0296532i	−0.0834379	−	0.00148452i
$400$	−4.13829			−0.206914
$401$	22.5610	+	13.0256i	1.12664	+	0.650468i	0.943089	−	0.332541i	$-0.107906\pi$
$401$	22.5610	+	13.0256i	1.12664	+	0.650468i	0.183555	+	0.983009i	$0.441239\pi$
$402$	−2.48980	+	4.31247i	−0.124180	+	0.215086i
$403$	−7.63328	+	4.40708i	−0.380241	+	0.219532i
$404$	−2.26554	−	1.30801i	−0.112715	−	0.0650760i
$405$	−2.56950	−	4.45050i	−0.127679	−	0.221147i
$406$		−	0.0956661i		−	0.00474783i
$407$	29.1864	+	14.8352i	1.44672	+	0.735354i
$408$	0.268068	+	0.464308i	0.0132713	+	0.0229867i
$409$	6.56127	+	11.3645i	0.324434	+	0.561936i	0.981398	−	0.191986i	$-0.0614928\pi$
$409$	6.56127	+	11.3645i	0.324434	+	0.561936i	−0.656964	+	0.753922i	$0.728159\pi$
$410$	4.53172			0.223806
$411$			6.12877i			0.302310i
$412$	−9.90611	+	5.71930i	−0.488039	+	0.281769i
$413$	2.67747	−	4.63751i	0.131750	−	0.228197i
$414$	2.68356	+	4.64806i	0.131890	+	0.228440i
$415$	1.91067	+	1.10312i	0.0937910	+	0.0541502i
$416$	3.38075	−	5.85563i	0.165755	−	0.287096i
$417$	−9.42506			−0.461547
$418$	−6.77885	+	12.7690i	−0.331564	+	0.624552i
$419$	−10.3360			−0.504945			−0.252472	−	0.967604i	$-0.581244\pi$
$419$	−10.3360			−0.504945			−0.252472	+	0.967604i	$0.581244\pi$
$420$	0.177498	−	0.307435i	0.00866101	−	0.0150013i
$421$	6.47288	+	3.73712i	0.315469	+	0.182136i	0.649371	−	0.760472i	$-0.275032\pi$
$421$	6.47288	+	3.73712i	0.315469	+	0.182136i	−0.333902	+	0.942608i	$0.608366\pi$
$422$	−0.0415210	−	0.0719165i	−0.00202121	−	0.00350084i
$423$	−0.0565989	+	0.0980321i	−0.00275193	+	0.00476649i
$424$	−5.68217	+	3.28060i	−0.275950	+	0.159320i
$425$			3.49528i			0.169546i
$426$	4.45990			0.216083
$427$	2.02110	+	3.50065i	0.0978079	+	0.169408i
$428$	5.27844	+	9.14253i	0.255143	+	0.441921i
$429$	12.6897	+	6.45004i	0.612663	+	0.311411i
$430$		−	1.28017i		−	0.0617355i
$431$	17.9329	+	31.0607i	0.863799	+	1.49614i	0.868235	+	0.496153i	$0.165254\pi$
$431$	17.9329	+	31.0607i	0.863799	+	1.49614i	−0.00443646	+	0.999990i	$0.501412\pi$
$432$	−3.07684	−	1.77641i	−0.148035	−	0.0854678i
$433$	12.9536	−	7.47879i	0.622512	−	0.359408i	−0.155334	−	0.987862i	$-0.549645\pi$
$433$	12.9536	−	7.47879i	0.622512	−	0.359408i	0.777846	+	0.628454i	$0.216312\pi$
$434$	0.392677	−	0.680137i	0.0188491	−	0.0326476i
$435$	−0.0810318	−	0.0467837i	−0.00388518	−	0.00224311i
$436$	2.47563			0.118561
$437$	−4.64212	+	7.71989i	−0.222063	+	0.369293i
$438$	−4.74865			−0.226899
$439$	−8.92756	+	15.4630i	−0.426089	+	0.738008i	−0.996521	−	0.0833368i	$-0.973442\pi$
$439$	−8.92756	+	15.4630i	−0.426089	+	0.738008i	0.570432	+	0.821344i	$0.306776\pi$
$440$	−1.67935	−	2.58043i	−0.0800600	−	0.123017i
$441$	−8.61844	−	14.9276i	−0.410402	−	0.710837i
$442$	−4.94579	−	2.85545i	−0.235247	−	0.135820i
$443$	14.5297	+	25.1662i	0.690329	+	1.19568i	0.971730	+	0.236094i	$0.0758674\pi$
$443$	14.5297	+	25.1662i	0.690329	+	1.19568i	−0.281401	+	0.959590i	$0.590799\pi$
$444$	−6.26615			−0.297378
$445$			12.8424i			0.608787i
$446$	−3.70697	+	2.14022i	−0.175530	+	0.101342i
$447$	−0.953086	−	1.65079i	−0.0450794	−	0.0780798i
$448$			0.602460i			0.0284636i
$449$		−	2.64573i		−	0.124860i	−0.998049	−	0.0624299i	$-0.980115\pi$
$449$		−	2.64573i		−	0.124860i	0.998049	−	0.0624299i	$-0.0198850\pi$
$450$	−5.37372	−	9.30755i	−0.253319	−	0.438762i
$451$	−8.83165	−	13.5704i	−0.415866	−	0.639005i
$452$	12.3315	−	7.11962i	0.580027	−	0.334879i
$453$	0.430005	+	0.248264i	0.0202034	+	0.0116644i
$454$	−10.1435	+	17.5690i	−0.476056	+	0.824553i
$455$			3.78140i			0.177275i
$456$	0.0492203	−	2.76644i	0.00230495	−	0.129550i
$457$			27.1774i			1.27130i	0.771976	+	0.635652i	$0.219268\pi$
$457$			27.1774i			1.27130i	−0.771976	+	0.635652i	$0.780732\pi$
$458$	9.56438	−	16.5660i	0.446914	−	0.774078i
$459$	−1.50040	+	2.59876i	−0.0700325	+	0.121300i
$460$	−0.959198	−	1.66138i	−0.0447228	−	0.0774622i
$461$	−16.4403	−	9.49182i	−0.765701	−	0.442078i	0.0656376	−	0.997844i	$-0.479092\pi$
$461$	−16.4403	−	9.49182i	−0.765701	−	0.442078i	−0.831339	+	0.555766i	$0.812425\pi$
$462$	−1.26654	+	0.0676222i	−0.0589249	+	0.00314607i
$463$	−14.5710			−0.677170			−0.338585	−	0.940936i	$-0.609948\pi$
$463$	−14.5710			−0.677170			−0.338585	+	0.940936i	$0.609948\pi$
$464$	0.158793			0.00737176
$465$	−0.384063	−	0.665217i	−0.0178105	−	0.0308487i
$466$	17.3799	−	10.0343i	0.805106	−	0.464828i
$467$	22.9049			1.05991			0.529956	−	0.848025i	$-0.322208\pi$
$467$	22.9049			1.05991			0.529956	+	0.848025i	$0.322208\pi$
$468$	17.5601			0.811716
$469$	2.36309	+	4.09299i	0.109117	+	0.188997i
$470$	0.0202304	−	0.0350401i	0.000933161	−	0.00161628i
$471$	−3.60248	+	2.07990i	−0.165994	+	0.0958365i
$472$	7.69762	+	4.44422i	0.354312	+	0.204562i
$473$	−3.83353	+	2.49487i	−0.176266	+	0.114714i
$474$		−	10.3797i		−	0.476754i
$475$	9.29565	−	15.4588i	0.426514	−	0.709297i
$476$	0.508850			0.0233231
$477$	−14.7570	−	8.51996i	−0.675677	−	0.390102i
$478$	−14.5677	−	8.41065i	−0.666310	−	0.384694i
$479$	−20.7246	+	11.9653i	−0.946929	+	0.546710i	−0.892126	−	0.451787i	$-0.850787\pi$
$479$	−20.7246	+	11.9653i	−0.946929	+	0.546710i	−0.0548037	+	0.998497i	$0.517453\pi$
$480$	0.510300	+	0.294622i	0.0232919	+	0.0134476i
$481$	57.8044	−	33.3734i	2.63565	−	1.52170i
$482$	−18.4098			−0.838543
$483$	−0.790312			−0.0359604
$484$	−4.45439	+	10.0578i	−0.202472	+	0.457171i
$485$	−9.31381	+	5.37733i	−0.422919	+	0.244172i
$486$		−	14.1726i		−	0.642880i
$487$			18.1772i			0.823687i	0.911255	+	0.411843i	$0.135115\pi$
$487$			18.1772i			0.823687i	−0.911255	+	0.411843i	$0.864885\pi$
$488$	−5.81059	+	3.35475i	−0.263033	+	0.151862i
$489$	−10.1361	−	5.85205i	−0.458368	−	0.264639i
$490$	3.08053	+	5.33564i	0.139164	+	0.241040i
$491$	3.87871	+	2.23937i	0.175044	+	0.101062i	0.584962	−	0.811061i	$-0.301109\pi$
$491$	3.87871	+	2.23937i	0.175044	+	0.101062i	−0.409918	+	0.912122i	$0.634443\pi$
$492$	2.68365	+	1.54941i	0.120988	+	0.0698526i
$493$		−	0.134120i		−	0.00604044i
$494$	14.2800	+	25.7822i	0.642486	+	1.16000i
$495$	3.62303	−	7.12787i	0.162843	−	0.320374i
$496$	1.12893	+	0.651790i	0.0506906	+	0.0292662i
$497$	2.11646	−	3.66581i	0.0949361	−	0.164434i
$498$	0.754321	+	1.30652i	0.0338019	+	0.0585467i
$499$	−2.66879	+	4.62248i	−0.119471	+	0.206931i	−0.919558	−	0.392953i	$-0.871453\pi$
$499$	−2.66879	+	4.62248i	−0.119471	+	0.206931i	0.800087	+	0.599884i	$0.204787\pi$
$500$	4.24147	+	7.34644i	0.189684	+	0.328543i
$501$			7.88230i			0.352155i
$502$	−17.2180			−0.768477
$503$	−13.6499	+	7.88078i	−0.608620	+	0.351387i	−0.772425	−	0.635106i	$-0.780956\pi$
$503$	−13.6499	+	7.88078i	−0.608620	+	0.351387i	0.163805	+	0.986493i	$0.447623\pi$
$504$	−1.35501	+	0.782316i	−0.0603570	+	0.0348471i
$505$			2.42842i			0.108063i
$506$	−3.10573	+	6.11013i	−0.138066	+	0.271629i
$507$	17.9858	−	10.3841i	0.798776	−	0.461174i
$508$	5.17110	−	8.95660i	0.229430	−	0.397385i
$509$	3.39218	−	1.95848i	0.150356	−	0.0868079i	−0.422935	−	0.906160i	$-0.639000\pi$
$509$	3.39218	−	1.95848i	0.150356	−	0.0868079i	0.573290	+	0.819352i	$0.305667\pi$
$510$	0.248844	−	0.431010i	0.0110190	−	0.0190854i
$511$	−2.25349	+	3.90315i	−0.0996884	+	0.172665i
$512$	−1.00000			−0.0441942
$513$	13.5473	−	7.50340i	0.598126	−	0.331283i
$514$		−	15.5830i		−	0.687335i
$515$	9.19570	+	5.30914i	0.405211	+	0.233949i
$516$	0.437694	−	0.758109i	0.0192684	−	0.0333739i
$517$	−0.144355	+	0.00770728i	−0.00634873	+	0.000338966i
$518$	−2.97362	+	5.15046i	−0.130653	+	0.226298i
$519$	−12.7246	+	7.34656i	−0.558549	+	0.322478i
$520$	−6.27660			−0.275247
$521$		−	37.3766i		−	1.63750i	−0.574151	−	0.818749i	$-0.694668\pi$
$521$		−	37.3766i		−	1.63750i	0.574151	−	0.818749i	$-0.305332\pi$
$522$	0.206198	+	0.357145i	0.00902504	+	0.0156318i
$523$	−9.95848	−	17.2486i	−0.435454	−	0.754228i	0.561879	−	0.827220i	$-0.310079\pi$
$523$	−9.95848	−	17.2486i	−0.435454	−	0.754228i	−0.997333	+	0.0729916i	$0.976745\pi$
$524$		−	15.2223i		−	0.664988i
$525$	1.58257			0.0690689
$526$	3.18777	−	1.84046i	0.138993	−	0.0802479i
$527$	0.550516	−	0.953521i	0.0239808	−	0.0415360i
$528$	−0.112243	−	2.10228i	−0.00488477	−	0.0914902i
$529$	9.36458	−	16.2199i	0.407156	−	0.705214i
$530$	5.27467	+	3.04533i	0.229117	+	0.132281i
$531$			23.0839i			1.00176i
$532$	−2.25052	−	1.35328i	−0.0975724	−	0.0586721i
$533$	−33.0084			−1.42975
$534$	−4.39083	+	7.60514i	−0.190010	+	0.329107i
$535$	4.89990	−	8.48688i	0.211841	−	0.366920i
$536$	−6.79379	+	3.92240i	−0.293447	+	0.169422i
$537$	−6.32369	+	10.9530i	−0.272888	+	0.472655i
$538$	−4.47493	+	2.58360i	−0.192928	+	0.111387i
$539$	9.97426	−	19.6231i	0.429622	−	0.845229i
$540$			3.29804i			0.141925i
$541$	13.1913	−	7.61598i	0.567137	−	0.327436i	−0.188868	−	0.982002i	$-0.560482\pi$
$541$	13.1913	−	7.61598i	0.567137	−	0.327436i	0.756005	+	0.654566i	$0.227149\pi$
$542$	1.20366	−	0.694932i	0.0517015	−	0.0298499i
$543$	13.6902			0.587501
$544$			0.844621i			0.0362128i
$545$	−1.14904	−	1.99020i	−0.0492196	−	0.0852509i
$546$	−1.29287	+	2.23932i	−0.0553297	+	0.0958338i
$547$	−12.3655	−	21.4176i	−0.528709	−	0.915750i	−0.999440	−	0.0334733i	$-0.989343\pi$
$547$	−12.3655	−	21.4176i	−0.528709	−	0.915750i	0.470731	−	0.882277i	$-0.343990\pi$
$548$	−4.82759	+	8.36163i	−0.206224	+	0.357191i
$549$	−15.0905	−	8.71252i	−0.644048	−	0.371841i
$550$	6.21909	−	12.2353i	0.265183	−	0.521715i
$551$	−0.356689	+	0.593177i	−0.0151955	+	0.0252702i
$552$		−	1.31181i		−	0.0558342i
$553$	−8.53157	−	4.92570i	−0.362799	−	0.209462i
$554$	13.5901	+	7.84624i	0.577387	+	0.333355i
$555$	2.90839	+	5.03747i	0.123454	+	0.213829i
$556$	−12.8588	−	7.42405i	−0.545336	−	0.314850i
$557$	−4.50379	+	2.60026i	−0.190832	+	0.110177i	−0.592372	−	0.805665i	$-0.701808\pi$
$557$	−4.50379	+	2.60026i	−0.190832	+	0.110177i	0.401540	+	0.915841i	$0.368475\pi$
$558$			3.38549i			0.143319i
$559$			9.32461i			0.394389i
$560$	0.484329	−	0.279627i	0.0204666	−	0.0118164i
$561$	−1.77563	+	0.0948031i	−0.0749673	+	0.00400259i
$562$	−27.0723			−1.14197
$563$	−26.7354			−1.12676			−0.563381	−	0.826197i	$-0.690500\pi$
$563$	−26.7354			−1.12676			−0.563381	+	0.826197i	$0.690500\pi$
$564$	0.0239606	−	0.0138337i	0.00100892	−	0.000582502i
$565$	−11.4472	−	6.60904i	−0.481587	−	0.278044i
$566$	−8.82881	+	5.09732i	−0.371103	+	0.214256i
$567$	−2.88839	−	1.66761i	−0.121301	−	0.0700331i
$568$	6.08474	+	3.51303i	0.255310	+	0.147403i
$569$	10.6578			0.446800			0.223400	−	0.974727i	$-0.428284\pi$
$569$	10.6578			0.446800			0.223400	+	0.974727i	$0.428284\pi$
$570$	−2.24684	+	1.24445i	−0.0941097	+	0.0521245i
$571$		−	36.9708i		−	1.54718i	−0.633686	−	0.773590i	$-0.718459\pi$
$571$		−	36.9708i		−	1.54718i	0.633686	−	0.773590i	$-0.281541\pi$
$572$	12.2322	+	18.7955i	0.511452	+	0.785879i
$573$	12.0571	+	6.96117i	0.503693	+	0.290807i
$574$	2.54707	−	1.47055i	0.106313	−	0.0613796i
$575$	4.27609	−	7.40641i	0.178325	−	0.308869i
$576$	−1.29854	−	2.24913i	−0.0541057	−	0.0937138i
$577$	8.71645			0.362871			0.181435	−	0.983403i	$-0.441926\pi$
$577$	8.71645			0.362871			0.181435	+	0.983403i	$0.441926\pi$
$578$	−16.2866			−0.677434
$579$	6.52938	−	3.76974i	0.271352	−	0.156665i
$580$	−0.0737024	−	0.127656i	−0.00306033	−	0.00530064i
$581$	1.43186			0.0594036
$582$	−7.35409			−0.304837
$583$	−1.16019	−	21.7301i	−0.0480504	−	0.899968i
$584$	−6.47869	−	3.74048i	−0.268090	−	0.154782i
$585$	−8.15040	−	14.1169i	−0.336977	−	0.583662i
$586$	−4.04132	+	6.99977i	−0.166945	+	0.289158i
$587$	1.19828	−	2.07548i	0.0494582	−	0.0856640i	−0.840236	−	0.542220i	$-0.817584\pi$
$587$	1.19828	−	2.07548i	0.0494582	−	0.0856640i	0.889695	+	0.456556i	$0.150917\pi$
$588$			4.21297i			0.173740i
$589$	−4.97067	+	2.75310i	−0.204813	+	0.113439i
$590$		−	8.25102i		−	0.339689i
$591$	2.08944	−	3.61902i	0.0859482	−	0.148867i
$592$	−8.54905	−	4.93580i	−0.351364	−	0.202860i
$593$	−31.6901	+	18.2963i	−1.30136	+	0.751340i	−0.980637	−	0.195834i	$-0.937259\pi$
$593$	−31.6901	+	18.2963i	−1.30136	+	0.751340i	−0.320721	+	0.947174i	$0.603925\pi$
$594$	9.87609	−	6.42739i	0.405221	−	0.263719i
$595$	−0.236179	−	0.409074i	−0.00968240	−	0.0167704i
$596$		−	3.00295i		−	0.123006i
$597$		−	6.85847i		−	0.280698i
$598$	6.98666	+	12.1013i	0.285706	+	0.494857i
$599$	13.3718	−	7.72019i	0.546355	−	0.315438i	−0.201295	−	0.979531i	$-0.564515\pi$
$599$	13.3718	−	7.72019i	0.546355	−	0.315438i	0.747651	+	0.664092i	$0.231182\pi$
$600$			2.62684i			0.107240i
$601$	−36.9537			−1.50737			−0.753687	−	0.657234i	$-0.771726\pi$
$601$	−36.9537			−1.50737			−0.753687	+	0.657234i	$0.771726\pi$
$602$	−0.415419	−	0.719526i	−0.0169312	−	0.0293257i
$603$	−17.6440	−	10.1868i	−0.718518	−	0.414837i
$604$	0.391111	+	0.677424i	0.0159141	+	0.0275640i
$605$	10.1531	−	1.08727i	0.412782	−	0.0442038i
$606$	−0.830281	+	1.43809i	−0.0337279	+	0.0584184i
$607$	22.0261			0.894011			0.447006	−	0.894531i	$-0.352490\pi$
$607$	22.0261			0.894011			0.447006	+	0.894531i	$0.352490\pi$
$608$	2.24626	−	3.73555i	0.0910977	−	0.151497i
$609$	−0.0607256			−0.00246072
$610$	5.39389	+	3.11416i	0.218392	+	0.126089i
$611$	−0.147356	+	0.255227i	−0.00596137	+	0.0103254i
$612$	−1.89966	+	1.09677i	−0.0767893	+	0.0443343i
$613$	23.9194	+	13.8099i	0.966096	+	0.557776i	0.898044	−	0.439906i	$-0.144988\pi$
$613$	23.9194	+	13.8099i	0.966096	+	0.557776i	0.0680520	+	0.997682i	$0.478322\pi$
$614$	−0.142057	−	0.246049i	−0.00573294	−	0.00992974i
$615$		−	2.87658i		−	0.115995i
$616$	−1.78124	−	0.905387i	−0.0717682	−	0.0364791i
$617$	2.50286	+	4.33508i	0.100761	+	0.174524i	0.911999	−	0.410194i	$-0.134539\pi$
$617$	2.50286	+	4.33508i	0.100761	+	0.174524i	−0.811237	+	0.584717i	$0.801206\pi$
$618$	3.63041	+	6.28806i	0.146037	+	0.252943i
$619$	−20.7905			−0.835641			−0.417820	−	0.908530i	$-0.637206\pi$
$619$	−20.7905			−0.835641			−0.417820	+	0.908530i	$0.637206\pi$
$620$		−	1.21009i		−	0.0485986i
$621$	6.35860	−	3.67114i	0.255162	−	0.147318i
$622$	7.44255	−	12.8909i	0.298419	−	0.516877i
$623$	4.16737	+	7.21809i	0.166962	+	0.289187i
$624$	−3.71695	−	2.14598i	−0.148797	−	0.0859081i
$625$	−6.40842	+	11.0997i	−0.256337	+	0.443988i
$626$	9.07744			0.362807
$627$	8.10532	+	4.30298i	0.323695	+	0.171845i
$628$	−6.55327			−0.261504
$629$	−4.16888	+	7.22071i	−0.166224	+	0.287908i
$630$	1.25784	+	0.726213i	0.0501134	+	0.0289330i
$631$	1.44194	+	2.49751i	0.0574027	+	0.0994244i	0.893299	−	0.449463i	$-0.148385\pi$
$631$	1.44194	+	2.49751i	0.0574027	+	0.0994244i	−0.835896	+	0.548888i	$0.815051\pi$
$632$	8.17598	−	14.1612i	0.325223	−	0.563303i
$633$	−0.0456501	+	0.0263561i	−0.00181443	+	0.00104756i
$634$		−	15.0190i		−	0.596482i
$635$	−9.60050			−0.380984
$636$	2.08241	+	3.60684i	0.0825730	+	0.143021i
$637$	−22.4382	−	38.8641i	−0.889033	−	1.53985i
$638$	−0.238636	+	0.469487i	−0.00944770	+	0.0185872i
$639$			18.2472i			0.721847i
$640$	0.464143	+	0.803919i	0.0183469	+	0.0317777i
$641$	−18.7751	−	10.8398i	−0.741572	−	0.428147i	0.0810684	−	0.996709i	$-0.474167\pi$
$641$	−18.7751	−	10.8398i	−0.741572	−	0.428147i	−0.822641	+	0.568562i	$0.807500\pi$
$642$	5.80336	−	3.35057i	0.229041	−	0.132237i
$643$	5.12115	−	8.87009i	0.201958	−	0.349802i	−0.747201	−	0.664598i	$-0.768603\pi$
$643$	5.12115	−	8.87009i	0.201958	−	0.349802i	0.949159	+	0.314796i	$0.101936\pi$
$644$	−1.07824	−	0.622522i	−0.0424886	−	0.0245308i
$645$	−0.812611			−0.0319965
$646$	−3.15512	−	1.89724i	−0.124137	−	0.0746457i
$647$	−28.1993			−1.10863			−0.554315	−	0.832307i	$-0.687020\pi$
$647$	−28.1993			−1.10863			−0.554315	+	0.832307i	$0.687020\pi$
$648$	2.76800	−	4.79432i	0.108737	−	0.188339i
$649$	−24.7080	+	16.0800i	−0.969872	+	0.631195i
$650$	−13.9905	−	24.2323i	−0.548753	−	0.950468i
$651$	−0.431728	−	0.249258i	−0.0169207	−	0.00976919i
$652$	−9.21924	−	15.9682i	−0.361053	−	0.625362i
$653$	18.4948			0.723756			0.361878	−	0.932225i	$-0.382136\pi$
$653$	18.4948			0.723756			0.361878	+	0.932225i	$0.382136\pi$
$654$		−	1.57144i		−	0.0614482i
$655$	−12.2375	+	7.06531i	−0.478158	+	0.276064i
$656$	2.44091	+	4.22778i	0.0953015	+	0.165067i
$657$		−	19.4286i		−	0.757981i
$658$		−	0.0262592i		−	0.00102369i
$659$	2.23581	+	3.87255i	0.0870950	+	0.150853i	0.906282	−	0.422674i	$-0.138908\pi$
$659$	2.23581	+	3.87255i	0.0870950	+	0.150853i	−0.819187	+	0.573526i	$0.805575\pi$
$660$	−1.63797	+	1.06599i	−0.0637579	+	0.0414938i
$661$	−37.8980	+	21.8804i	−1.47406	+	0.851049i	−0.999573	−	0.0292136i	$-0.990700\pi$
$661$	−37.8980	+	21.8804i	−1.47406	+	0.851049i	−0.474487	+	0.880263i	$0.657366\pi$
$662$	−20.5554	−	11.8677i	−0.798910	−	0.461251i
$663$	−1.81254	+	3.13942i	−0.0703933	+	0.121925i
$664$			2.37669i			0.0922335i
$665$	−0.0433651	+	2.43735i	−0.00168163	+	0.0945164i
$666$		−	25.6372i		−	0.993423i
$667$	−0.164080	+	0.284196i	−0.00635322	+	0.0110041i
$668$	−6.20883	+	10.7540i	−0.240227	+	0.416085i
$669$	1.35854	+	2.35305i	0.0525240	+	0.0909743i
$670$	6.30658	+	3.64110i	0.243644	+	0.140668i
$671$	−1.18642	−	22.2212i	−0.0458011	−	0.857841i
$672$	0.382421			0.0147522
$673$	7.44367			0.286932			0.143466	−	0.989655i	$-0.454175\pi$
$673$	7.44367			0.286932			0.143466	+	0.989655i	$0.454175\pi$
$674$	12.4439	+	21.5534i	0.479320	+	0.830206i
$675$	−12.7328	+	7.35131i	−0.490087	+	0.282952i
$676$	32.7179			1.25838
$677$	10.5563			0.405712			0.202856	−	0.979209i	$-0.434978\pi$
$677$	10.5563			0.405712			0.202856	+	0.979209i	$0.434978\pi$
$678$	−4.51929	−	7.82763i	−0.173562	−	0.300618i
$679$	−3.48990	+	6.04469i	−0.133930	+	0.231974i
$680$	0.679007	−	0.392025i	0.0260387	−	0.0150335i
$681$	11.1522	+	6.43872i	0.427353	+	0.246732i
$682$	−3.62367	+	2.35829i	−0.138757	+	0.0903037i
$683$			10.2292i			0.391408i	0.980663	+	0.195704i	$0.0626991\pi$
$683$			10.2292i			0.391408i	−0.980663	+	0.195704i	$0.937301\pi$
$684$	11.3186	+	0.201379i	0.432777	+	0.00769993i
$685$	8.96276			0.342450
$686$	7.11507	+	4.10789i	0.271655	+	0.156840i
$687$	−10.5155	−	6.07114i	−0.401192	−	0.231628i
$688$	1.19431	−	0.689537i	0.0455328	−	0.0262884i
$689$	−38.4200	−	22.1818i	−1.46368	−	0.845059i
$690$	−1.05459	+	0.608866i	−0.0401474	+	0.0231791i
$691$	35.6187			1.35500			0.677500	−	0.735522i	$-0.263063\pi$
$691$	35.6187			1.35500			0.677500	+	0.735522i	$0.263063\pi$
$692$	−23.1473			−0.879929
$693$	−0.276669	−	5.18192i	−0.0105098	−	0.196845i
$694$	10.9807	−	6.33973i	0.416823	−	0.240653i
$695$			13.7833i			0.522829i
$696$		−	0.100796i		−	0.00382066i
$697$	3.57087	−	2.06164i	0.135256	−	0.0780903i
$698$	7.97942	+	4.60692i	0.302026	+	0.174375i
$699$	−6.36941	−	11.0321i	−0.240913	−	0.417274i
$700$	2.15913	+	1.24658i	0.0816075	+	0.0471161i
$701$	−39.2399	−	22.6552i	−1.48207	−	0.855673i	−0.482277	−	0.876019i	$-0.660190\pi$
$701$	−39.2399	−	22.6552i	−1.48207	−	0.855673i	−0.999793	+	0.0203458i	$0.993523\pi$
$702$		−	24.0225i		−	0.906669i
$703$	37.6413	−	20.8483i	1.41967	−	0.786310i
$704$	1.50282	−	2.95661i	0.0566396	−	0.111431i
$705$	−0.0222423	−	0.0128416i	−0.000837693	−	0.000483642i
$706$	11.9543	−	20.7054i	0.449905	−	0.779257i
$707$	0.788025	+	1.36490i	0.0296367	+	0.0513323i
$708$	2.82104	−	4.88618i	0.106021	−	0.183634i
$709$	−2.02309	−	3.50410i	−0.0759789	−	0.131599i	0.825533	−	0.564354i	$-0.190875\pi$
$709$	−2.02309	−	3.50410i	−0.0759789	−	0.131599i	−0.901512	+	0.432755i	$0.857541\pi$
$710$		−	6.52218i		−	0.244773i
$711$	42.4672			1.59265
$712$	−11.9810	+	6.91725i	−0.449008	+	0.259235i
$713$	−2.33306	+	1.34699i	−0.0873736	+	0.0504452i
$714$		−	0.323001i		−	0.0120880i
$715$	9.43259	−	18.5575i	0.352759	−	0.694010i
$716$	−17.2551	+	9.96225i	−0.644854	+	0.372307i
$717$	−5.33879	+	9.24705i	−0.199381	+	0.345338i
$718$	22.3441	−	12.9004i	0.833876	−	0.481438i
$719$	−10.3276	+	17.8880i	−0.385155	+	0.667108i	−0.991791	−	0.127872i	$-0.959185\pi$
$719$	−10.3276	+	17.8880i	−0.385155	+	0.667108i	0.606636	+	0.794980i	$0.292519\pi$
$720$	−1.20541	+	2.08784i	−0.0449231	+	0.0778090i
$721$	6.89129			0.256645
$722$	8.90866	+	16.7820i	0.331546	+	0.624562i
$723$			11.6859i			0.434603i
$724$	18.6778	+	10.7836i	0.694156	+	0.400771i
$725$	0.328564	−	0.569090i	0.0122026	−	0.0211355i
$726$	6.38432	+	2.82749i	0.236944	+	0.104938i
$727$	−11.9901	+	20.7674i	−0.444687	+	0.770220i	−0.998030	−	0.0627328i	$-0.980018\pi$
$727$	−11.9901	+	20.7674i	−0.444687	+	0.770220i	0.553343	+	0.832953i	$0.313352\pi$
$728$	−3.52778	+	2.03677i	−0.130748	+	0.0754876i
$729$	7.61177			0.281917
$730$			6.94446i			0.257026i
$731$	−0.582398	−	1.00874i	−0.0215408	−	0.0373097i
$732$	2.12948	+	3.68836i	0.0787077	+	0.136326i
$733$			48.6858i			1.79825i	0.437692	+	0.899125i	$0.355796\pi$
$733$			48.6858i			1.79825i	−0.437692	+	0.899125i	$0.644204\pi$
$734$	34.5592			1.27560
$735$	3.38688	−	1.95542i	0.124927	−	0.0721266i
$736$	1.03330	−	1.78973i	0.0380880	−	0.0659703i
$737$	−1.38717	−	25.9812i	−0.0510970	−	0.957031i
$738$	−6.33922	+	10.9799i	−0.233350	+	0.404174i
$739$	8.72473	+	5.03723i	0.320944	+	0.185297i	0.651813	−	0.758379i	$-0.274009\pi$
$739$	8.72473	+	5.03723i	0.320944	+	0.185297i	−0.330869	+	0.943677i	$0.607342\pi$
$740$			9.16366i			0.336863i
$741$	16.3657	−	9.06443i	0.601207	−	0.332990i
$742$	3.95286			0.145114
$743$	20.3525	−	35.2516i	0.746663	−	1.29326i	−0.202751	−	0.979230i	$-0.564988\pi$
$743$	20.3525	−	35.2516i	0.746663	−	1.29326i	0.949414	−	0.314027i	$-0.101678\pi$
$744$	0.413734	−	0.716608i	0.0151682	−	0.0262721i
$745$	−2.41413	+	1.39380i	−0.0884469	+	0.0510649i
$746$	4.15902	−	7.20364i	0.152273	−	0.263744i
$747$	−5.34549	+	3.08622i	−0.195581	+	0.112919i
$748$	−2.49721	−	1.26931i	−0.0913072	−	0.0464106i
$749$		−	6.36010i		−	0.232393i
$750$	4.66327	−	2.69234i	0.170278	−	0.0983103i
$751$	−25.6076	+	14.7846i	−0.934436	+	0.539497i	−0.888212	−	0.459434i	$-0.848052\pi$
$751$	−25.6076	+	14.7846i	−0.934436	+	0.539497i	−0.0462240	+	0.998931i	$0.514719\pi$
$752$	0.0435867			0.00158944
$753$			10.9294i			0.398289i
$754$	0.536838	+	0.929830i	0.0195505	+	0.0338624i
$755$	0.363063	−	0.628843i	0.0132132	−	0.0228859i
$756$	1.07022	+	1.85367i	0.0389235	+	0.0674174i
$757$	−1.40203	+	2.42839i	−0.0509578	+	0.0882615i	−0.890379	−	0.455220i	$-0.849561\pi$
$757$	−1.40203	+	2.42839i	−0.0509578	+	0.0882615i	0.839421	+	0.543481i	$0.182894\pi$
$758$	−25.0763	−	14.4778i	−0.910813	−	0.525858i
$759$	3.87850	+	1.97141i	0.140781	+	0.0715576i
$760$	−4.04566	−	0.0719801i	−0.146752	−	0.00261099i
$761$			29.8573i			1.08233i	0.840917	+	0.541164i	$0.182016\pi$
$761$			29.8573i			1.08233i	−0.840917	+	0.541164i	$0.817984\pi$
$762$	−5.68534	−	3.28243i	−0.205958	−	0.118910i
$763$	−1.29165	−	0.745733i	−0.0467608	−	0.0269973i
$764$	10.9665	+	18.9946i	0.396755	+	0.687199i
$765$	1.76343	+	1.01812i	0.0637569	+	0.0368101i
$766$	−3.17405	+	1.83254i	−0.114683	+	0.0662122i
$767$			60.0992i			2.17006i
$768$			0.634765i			0.0229051i
$769$	25.5648	−	14.7599i	0.921891	−	0.532254i	0.0376534	−	0.999291i	$-0.488012\pi$
$769$	25.5648	−	14.7599i	0.921891	−	0.532254i	0.884238	+	0.467037i	$0.154678\pi$
$770$	0.0988911	+	1.85220i	0.00356379	+	0.0667487i
$771$	−9.89153			−0.356235
$772$	11.8776			0.427483
$773$	−33.3560	+	19.2581i	−1.19973	+	0.692665i	−0.960495	−	0.278296i	$-0.910230\pi$
$773$	−33.3560	+	19.2581i	−1.19973	+	0.692665i	−0.239236	+	0.970961i	$0.576897\pi$
$774$	3.10172	+	1.79078i	0.111489	+	0.0643682i
$775$	4.67185	−	2.69729i	0.167818	−	0.0968897i
$776$	−10.0334	−	5.79276i	−0.360176	−	0.207948i
$777$	3.26933	+	1.88755i	0.117287	+	0.0677155i
$778$	−15.7995			−0.566440
$779$	−21.2760	−	0.378540i	−0.762291	−	0.0135626i
$780$			3.98417i			0.142656i
$781$	−19.5309	+	12.7108i	−0.698871	+	0.454827i
$782$	−1.51164	−	0.872748i	−0.0540563	−	0.0312094i
$783$	0.488579	−	0.282081i	0.0174604	−	0.0100808i
$784$	−3.31852	+	5.74785i	−0.118519	+	0.205280i
$785$	3.04165	+	5.26830i	0.108561	+	0.188034i
$786$	−9.66257			−0.344653
$787$	−8.06386			−0.287445			−0.143723	−	0.989618i	$-0.545907\pi$
$787$	−8.06386			−0.287445			−0.143723	+	0.989618i	$0.545907\pi$
$788$	5.70135	−	3.29168i	0.203102	−	0.117261i
$789$	−1.16826	−	2.02349i	−0.0415912	−	0.0720380i
$790$	−15.1793			−0.540055
$791$	−8.57857			−0.305019
$792$	8.60127	−	0.459231i	0.305633	−	0.0163181i
$793$	−39.2883	−	22.6831i	−1.39517	−	0.805501i
$794$	−0.172652	−	0.299043i	−0.00612720	−	0.0106126i
$795$	1.93307	−	3.34818i	0.0685590	−	0.118748i
$796$	5.40236	−	9.35717i	0.191482	−	0.331656i
$797$			12.8794i			0.456213i	0.973636	+	0.228106i	$0.0732534\pi$
$797$			12.8794i			0.456213i	−0.973636	+	0.228106i	$0.926747\pi$
$798$	−0.859015	+	1.42855i	−0.0304088	+	0.0505702i
$799$		−	0.0368142i		−	0.00130239i
$800$	−2.06914	+	3.58386i	−0.0731553	+	0.126709i
$801$	−31.1156	−	17.9646i	−1.09942	−	0.634748i
$802$	22.5610	−	13.0256i	0.796658	−	0.459950i
$803$	20.7954	−	13.5337i	0.733855	−	0.477595i
$804$	2.48980	+	4.31247i	0.0878086	+	0.152089i
$805$			1.15576i			0.0407351i
$806$			8.81416i			0.310465i
$807$	1.63998	+	2.84053i	0.0577301	+	0.0999915i
$808$	−2.26554	+	1.30801i	−0.0797015	+	0.0460157i
$809$			10.6404i			0.374097i	0.982351	+	0.187049i	$0.0598922\pi$
$809$			10.6404i			0.374097i	−0.982351	+	0.187049i	$0.940108\pi$
$810$	−5.13899			−0.180566
$811$	8.32345	+	14.4166i	0.292276	+	0.506237i	0.974348	−	0.225049i	$-0.0722541\pi$
$811$	8.32345	+	14.4166i	0.292276	+	0.506237i	−0.682072	+	0.731285i	$0.738921\pi$
$812$	−0.0828493	−	0.0478331i	−0.00290744	−	0.00167861i
$813$	−0.441119	−	0.764040i	−0.0154707	−	0.0267960i
$814$	27.4409	−	17.8586i	0.961803	−	0.625944i
$815$	−8.55808	+	14.8230i	−0.299777	+	0.519228i
$816$	0.536136			0.0187685
$817$	−0.106935	+	6.01030i	−0.00374117	+	0.210274i
$818$	13.1225			0.458819
$819$	−9.16191	−	5.28963i	−0.320143	−	0.184835i
$820$	2.26586	−	3.92459i	0.0791273	−	0.137052i
$821$	28.1136	−	16.2314i	0.981170	−	0.566479i	0.0785468	−	0.996910i	$-0.474972\pi$
$821$	28.1136	−	16.2314i	0.981170	−	0.566479i	0.902623	+	0.430432i	$0.141639\pi$
$822$	5.30767	+	3.06439i	0.185126	+	0.106883i
$823$	5.34469	+	9.25728i	0.186304	+	0.322688i	0.944015	−	0.329902i	$-0.107016\pi$
$823$	5.34469	+	9.25728i	0.186304	+	0.322688i	−0.757711	+	0.652590i	$0.773682\pi$
$824$			11.4386i			0.398482i
$825$	−7.76654	−	3.94766i	−0.270396	−	0.137440i
$826$	−2.67747	−	4.63751i	−0.0931610	−	0.161360i
$827$	22.6071	+	39.1567i	0.786126	+	1.36161i	0.928324	+	0.371772i	$0.121250\pi$
$827$	22.6071	+	39.1567i	0.786126	+	1.36161i	−0.142198	+	0.989838i	$0.545417\pi$
$828$	5.36712			0.186520
$829$			2.68894i			0.0933908i	0.998909	+	0.0466954i	$0.0148690\pi$
$829$			2.68894i			0.0933908i	−0.998909	+	0.0466954i	$0.985131\pi$
$830$	1.91067	−	1.10312i	0.0663202	−	0.0382900i
$831$	4.98052	−	8.62651i	0.172772	−	0.299250i
$832$	−3.38075	−	5.85563i	−0.117206	−	0.203007i
$833$	4.85475	+	2.80289i	0.168207	+	0.0971145i
$834$	−4.71253	+	8.16234i	−0.163182	+	0.282639i
$835$	11.5271			0.398913
$836$	7.66885	+	12.2552i	0.265233	+	0.423853i
$837$	4.63140			0.160084
$838$	−5.16798	+	8.95121i	−0.178525	+	0.309214i
$839$	25.5817	+	14.7696i	0.883177	+	0.509903i	0.871705	−	0.490032i	$-0.163015\pi$
$839$	25.5817	+	14.7696i	0.883177	+	0.509903i	0.0114725	+	0.999934i	$0.496348\pi$
$840$	−0.177498	−	0.307435i	−0.00612426	−	0.0106075i
$841$	14.4874	−	25.0929i	0.499565	−	0.865272i
$842$	6.47288	−	3.73712i	0.223070	−	0.128790i
$843$			17.1845i			0.591867i
$844$	−0.0830420			−0.00285842
$845$	−15.1858	−	26.3025i	−0.522406	−	0.904834i
$846$	0.0565989	+	0.0980321i	0.00194591	+	0.00337041i
$847$	5.35375	−	3.90580i	0.183957	−	0.134205i
$848$			6.56120i			0.225313i
$849$	3.23560	+	5.60423i	0.111046	+	0.192337i
$850$	3.02700	+	1.74764i	0.103825	+	0.0599436i
$851$	17.6675	−	10.2003i	0.605634	−	0.349663i
$852$	2.22995	−	3.86238i	0.0763968	−	0.132323i
$853$	−10.5886	−	6.11332i	−0.362546	−	0.209316i	0.307651	−	0.951499i	$-0.400457\pi$
$853$	−10.5886	−	6.11332i	−0.362546	−	0.209316i	−0.670197	+	0.742183i	$0.733790\pi$
$854$	4.04220			0.138321
$855$	−5.09155	−	9.19269i	−0.174127	−	0.314383i
$856$	10.5569			0.360827
$857$	−25.6630	+	44.4496i	−0.876630	+	1.51837i	−0.0216140	+	0.999766i	$0.506880\pi$
$857$	−25.6630	+	44.4496i	−0.876630	+	1.51837i	−0.855016	+	0.518601i	$0.826453\pi$
$858$	11.9307	−	7.76456i	0.407309	−	0.265078i
$859$	14.3854	+	24.9162i	0.490823	+	0.850131i	0.999944	−	0.0105641i	$-0.00336273\pi$
$859$	14.3854	+	24.9162i	0.490823	+	0.850131i	−0.509121	+	0.860695i	$0.670029\pi$
$860$	−1.10866	−	0.640087i	−0.0378051	−	0.0218268i
$861$	−0.933455	−	1.61679i	−0.0318120	−	0.0551001i
$862$	35.8659			1.22160
$863$			1.96238i			0.0668003i	0.999442	+	0.0334002i	$0.0106336\pi$
$863$			1.96238i			0.0668003i	−0.999442	+	0.0334002i	$0.989366\pi$
$864$	−3.07684	+	1.77641i	−0.104676	+	0.0604348i
$865$	10.7437	+	18.6086i	0.365295	+	0.632710i
$866$		−	14.9576i		−	0.508279i
$867$			10.3382i			0.351103i
$868$	−0.392677	−	0.680137i	−0.0133283	−	0.0230854i
$869$	29.5822	+	45.4549i	1.00351	+	1.54195i
$870$	−0.0810318	+	0.0467837i	−0.00274724	+	0.00158612i
$871$	−45.9362	−	26.5213i	−1.55649	−	0.898640i
$872$	1.23781	−	2.14395i	0.0419176	−	0.0726035i
$873$		−	30.0884i		−	1.01834i
$874$	4.36456	+	7.88014i	0.147634	+	0.266550i
$875$		−	5.11063i		−	0.172771i
$876$	−2.37433	+	4.11245i	−0.0802210	+	0.138947i
$877$	5.71117	−	9.89203i	0.192852	−	0.334030i	−0.753342	−	0.657629i	$-0.771559\pi$
$877$	5.71117	−	9.89203i	0.192852	−	0.334030i	0.946194	+	0.323599i	$0.104893\pi$
$878$	8.92756	+	15.4630i	0.301290	+	0.521850i
$879$	4.44321	+	2.56529i	0.149866	+	0.0865251i
$880$	−3.07440	+	0.164146i	−0.103638	+	0.00553334i
$881$	1.66096			0.0559593			0.0279796	−	0.999608i	$-0.491093\pi$
$881$	1.66096			0.0559593			0.0279796	+	0.999608i	$0.491093\pi$
$882$	−17.2369			−0.580396
$883$	−25.3387	−	43.8880i	−0.852717	−	1.47695i	−0.878747	−	0.477287i	$-0.841620\pi$
$883$	−25.3387	−	43.8880i	−0.852717	−	1.47695i	0.0260306	−	0.999661i	$-0.491713\pi$
$884$	−4.94579	+	2.85545i	−0.166345	+	0.0960393i
$885$	−5.23746			−0.176055
$886$	29.0595			0.976272
$887$	−15.2423	−	26.4005i	−0.511788	−	0.886442i	−0.999907	−	0.0136649i	$-0.995650\pi$
$887$	−15.2423	−	26.4005i	−0.511788	−	0.886442i	0.488119	−	0.872777i	$-0.337683\pi$
$888$	−3.13307	+	5.42664i	−0.105139	+	0.182106i
$889$	−5.39599	+	3.11538i	−0.180976	+	0.104486i
$890$	11.1218	+	6.42118i	0.372804	+	0.215239i
$891$	10.0151	+	15.3889i	0.335520	+	0.515547i
$892$			4.28044i			0.143320i
$893$	−0.0979069	+	0.162820i	−0.00327633	+	0.00544857i
$894$	−1.90617			−0.0637519
$895$	16.0177	+	9.24781i	0.535412	+	0.309120i
$896$	0.521746	+	0.301230i	0.0174303	+	0.0100634i
$897$	7.68146	−	4.43489i	0.256477	−	0.148077i
$898$	−2.29127	−	1.32287i	−0.0764607	−	0.0441446i
$899$	−0.179266	+	0.103499i	−0.00597886	+	0.00345190i
$900$	−10.7474			−0.358248
$901$	5.54173			0.184622
$902$	−16.1681	+	0.863235i	−0.538340	+	0.0287426i
$903$	−0.456730	+	0.263693i	−0.0151990	+	0.00877517i
$904$		−	14.2392i		−	0.473590i
$905$		−	20.0206i		−	0.665507i
$906$	0.430005	−	0.248264i	0.0142860	−	0.00824801i
$907$	28.7387	+	16.5923i	0.954254	+	0.550939i	0.894400	−	0.447269i	$-0.147603\pi$
$907$	28.7387	+	16.5923i	0.954254	+	0.550939i	0.0598539	+	0.998207i	$0.480937\pi$
$908$	10.1435	+	17.5690i	0.336622	+	0.583047i
$909$	−5.88378	−	3.39700i	−0.195153	−	0.112671i
$910$	3.27479	+	1.89070i	0.108558	+	0.0626761i
$911$			52.7851i			1.74885i	0.485161	+	0.874425i	$0.338761\pi$
$911$			52.7851i			1.74885i	−0.485161	+	0.874425i	$0.661239\pi$
$912$	−2.37120	−	1.42585i	−0.0785182	−	0.0472145i
$913$	−7.02695	−	3.57173i	−0.232558	−	0.118207i
$914$	23.5363	+	13.5887i	0.778511	+	0.449474i
$915$	1.97676	−	3.42385i	0.0653498	−	0.113189i
$916$	−9.56438	−	16.5660i	−0.316016	−	0.547356i
$917$	−4.58541	+	7.94216i	−0.151423	+	0.262273i
$918$	1.50040	+	2.59876i	0.0495205	+	0.0857720i
$919$			53.6412i			1.76946i	0.466105	+	0.884730i	$0.345657\pi$
$919$			53.6412i			1.76946i	−0.466105	+	0.884730i	$0.654343\pi$
$920$	−1.91840			−0.0632477
$921$	−0.156184	+	0.0901727i	−0.00514643	+	0.00297129i
$922$	−16.4403	+	9.49182i	−0.541433	+	0.312596i
$923$			47.5067i			1.56370i
$924$	−0.574709	+	1.13067i	−0.0189065	+	0.0371963i
$925$	−35.3784	+	20.4257i	−1.16324	+	0.671594i
$926$	−7.28548	+	12.6188i	−0.239416	+	0.414680i
$927$	−25.7269	+	14.8534i	−0.844982	+	0.487851i
$928$	0.0793963	−	0.137518i	0.00260631	−	0.00451426i
$929$	8.99340	−	15.5770i	0.295064	−	0.511066i	−0.679936	−	0.733272i	$-0.737992\pi$
$929$	8.99340	−	15.5770i	0.295064	−	0.511066i	0.975000	+	0.222206i	$0.0713257\pi$
$930$	−0.768126			−0.0251879
$931$	−14.0171	−	25.3076i	−0.459392	−	0.829424i
$932$		−	20.0685i		−	0.657367i
$933$	−8.18268	−	4.72427i	−0.267889	−	0.154666i
$934$	11.4525	−	19.8362i	0.374736	−	0.649061i
$935$	0.138641	+	2.59670i	0.00453404	+	0.0849211i
$936$	8.78005	−	15.2075i	0.286985	−	0.497073i
$937$	18.8590	−	10.8882i	0.616096	−	0.355703i	−0.159251	−	0.987238i	$-0.550908\pi$
$937$	18.8590	−	10.8882i	0.616096	−	0.355703i	0.775348	+	0.631535i	$0.217575\pi$
$938$	4.72618			0.154315
$939$		−	5.76204i		−	0.188037i
$940$	−0.0202304	−	0.0350401i	−0.000659844	−	0.00114288i
$941$	27.0467	+	46.8462i	0.881696	+	1.52714i	0.849454	+	0.527662i	$0.176931\pi$
$941$	27.0467	+	46.8462i	0.881696	+	1.52714i	0.0322420	+	0.999480i	$0.489735\pi$
$942$			4.15979i			0.135533i
$943$	−10.0888			−0.328536
$944$	7.69762	−	4.44422i	0.250536	−	0.144647i
$945$	0.993468	−	1.72074i	0.0323175	−	0.0559756i
$946$	0.243857	+	4.56737i	0.00792848	+	0.148498i
$947$	−24.0775	+	41.7035i	−0.782414	+	1.35518i	0.148117	+	0.988970i	$0.452679\pi$
$947$	−24.0775	+	41.7035i	−0.782414	+	1.35518i	−0.930532	+	0.366211i	$0.880655\pi$
$948$	−8.98905	−	5.18983i	−0.291951	−	0.168558i
$949$		−	50.5825i		−	1.64198i
$950$	−8.73986	−	15.7797i	−0.283559	−	0.511960i
$951$	−9.53356			−0.309147
$952$	0.254425	−	0.440677i	0.00824597	−	0.0142824i
$953$	−15.6907	+	27.1771i	−0.508272	+	0.880353i	0.491682	+	0.870775i	$0.336382\pi$
$953$	−15.6907	+	27.1771i	−0.508272	+	0.880353i	−0.999954	+	0.00957831i	$0.996951\pi$
$954$	−14.7570	+	8.51996i	−0.477776	+	0.275844i
$955$	10.1801	−	17.6324i	0.329419	−	0.570571i
$956$	−14.5677	+	8.41065i	−0.471152	+	0.272020i
$957$	0.298014	+	0.151478i	0.00963344	+	0.00489659i
$958$			23.9307i			0.773165i
$959$	5.03755	−	2.90843i	0.162671	−	0.0939181i
$960$	0.510300	−	0.294622i	0.0164699	−	0.00950888i
$961$	29.3007			0.945183
$962$		−	66.7468i		−	2.15200i
$963$	13.7085	+	23.7438i	0.441750	+	0.765134i
$964$	−9.20489	+	15.9433i	−0.296470	+	0.513500i
$965$	−5.51289	−	9.54861i	−0.177466	−	0.307381i
$966$	−0.395156	+	0.684430i	−0.0127139	+	0.0220212i
$967$	24.5680	+	14.1844i	0.790055	+	0.456139i	0.839982	−	0.542614i	$-0.182565\pi$
$967$	24.5680	+	14.1844i	0.790055	+	0.456139i	−0.0499269	+	0.998753i	$0.515899\pi$
$968$	6.48308	+	8.88649i	0.208374	+	0.285623i
$969$	−1.20430	+	2.00276i	−0.0386877	+	0.0643380i
$970$			10.7547i			0.345312i
$971$	41.7471	+	24.1027i	1.33973	+	0.773493i	0.986767	−	0.162145i	$-0.0518411\pi$
$971$	41.7471	+	24.1027i	1.33973	+	0.773493i	0.352962	+	0.935638i	$0.385174\pi$
$972$	−12.2738	−	7.08628i	−0.393682	−	0.227292i
$973$	4.47269	+	7.74693i	0.143388	+	0.248355i
$974$	15.7419	+	9.08859i	0.504403	+	0.291217i
$975$	−15.3818	+	8.88069i	−0.492612	+	0.284410i
$976$			6.70949i			0.214766i
$977$		−	7.26942i		−	0.232569i	−0.993216	−	0.116285i	$-0.962902\pi$
$977$		−	7.26942i		−	0.232569i	0.993216	−	0.116285i	$-0.0370985\pi$
$978$	−10.1361	+	5.85205i	−0.324115	+	0.187128i
$979$	−2.44631	−	45.8186i	−0.0781843	−	1.46437i
$980$	6.16107			0.196808
$981$	6.42938			0.205274
$982$	3.87871	−	2.23937i	0.123775	−	0.0714613i
$983$	−3.66981	−	2.11877i	−0.117049	−	0.0675782i	0.440333	−	0.897835i	$-0.354861\pi$
$983$	−3.66981	−	2.11877i	−0.117049	−	0.0675782i	−0.557381	+	0.830257i	$0.688194\pi$
$984$	2.68365	−	1.54941i	0.0855516	−	0.0493932i
$985$	−5.29248	−	3.05562i	−0.168632	−	0.0973600i
$986$	−0.116151	−	0.0670598i	−0.00369900	−	0.00213562i
$987$	−0.0166685			−0.000530563
$988$	29.4680	+	0.524293i	0.937503	+	0.0166800i
$989$			2.85000i			0.0906247i
$990$	−4.36140	−	6.70157i	−0.138614	−	0.212990i
$991$	−40.8906	−	23.6082i	−1.29893	−	0.749940i	−0.318714	−	0.947851i	$-0.603251\pi$
$991$	−40.8906	−	23.6082i	−1.29893	−	0.749940i	−0.980220	+	0.197911i	$0.936584\pi$
$992$	1.12893	−	0.651790i	0.0358437	−	0.0206944i
$993$	−7.53320	+	13.0479i	−0.239059	+	0.414062i
$994$	−2.11646	−	3.66581i	−0.0671300	−	0.116273i
$995$	−10.0299			−0.317968
$996$	1.50864			0.0478031
$997$	30.9244	−	17.8542i	0.979385	−	0.565448i	0.0773004	−	0.997008i	$-0.475370\pi$
$997$	30.9244	−	17.8542i	0.979385	−	0.565448i	0.902084	+	0.431560i	$0.142037\pi$
$998$	2.66879	+	4.62248i	0.0844791	+	0.146322i
$999$	−35.0721			−1.10963

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.65.4	yes	20
11.10	odd	2		418.2.h.a.65.4	✓	20
19.12	odd	6		418.2.h.a.373.4	yes	20
209.164	even	6	inner	418.2.h.b.373.4	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.4	✓	20	11.10	odd	2
418.2.h.a.373.4	yes	20	19.12	odd	6
418.2.h.b.65.4	yes	20	1.1	even	1	trivial
418.2.h.b.373.4	yes	20	209.164	even	6	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.549723 - 0.317383i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.464143 + 0.803919i) q^{5} +(-0.549723 + 0.317383i) q^{6} +0.602460i q^{7} -1.00000 q^{8} +(-1.29854 - 2.24913i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.549723 - 0.317383i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.464143 + 0.803919i) q^{5} +(-0.549723 + 0.317383i) q^{6} +0.602460i q^{7} -1.00000 q^{8} +(-1.29854 - 2.24913i) q^{9} +(0.464143 + 0.803919i) q^{10} +(1.50282 - 2.95661i) q^{11} +0.634765i q^{12} +(-3.38075 - 5.85563i) q^{13} +(0.521746 + 0.301230i) q^{14} +(0.510300 - 0.294622i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(0.731463 + 0.422310i) q^{17} -2.59707 q^{18} +(-2.11195 - 3.81309i) q^{19} +0.928285 q^{20} +(0.191210 - 0.331186i) q^{21} +(-1.80909 - 2.77978i) q^{22} +(-1.03330 - 1.78973i) q^{23} +(0.549723 + 0.317383i) q^{24} +(2.06914 + 3.58386i) q^{25} -6.76150 q^{26} +3.55283i q^{27} +(0.521746 - 0.301230i) q^{28} +(-0.0793963 - 0.137518i) q^{29} -0.589244i q^{30} -1.30358i q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.76451 + 1.14835i) q^{33} +(0.731463 - 0.422310i) q^{34} +(-0.484329 - 0.279627i) q^{35} +(-1.29854 + 2.24913i) q^{36} +9.87159i q^{37} +(-4.35821 - 0.0775409i) q^{38} +4.29197i q^{39} +(0.464143 - 0.803919i) q^{40} +(2.44091 - 4.22778i) q^{41} +(-0.191210 - 0.331186i) q^{42} +(-1.19431 - 0.689537i) q^{43} +(-3.31191 + 0.176827i) q^{44} +2.41082 q^{45} -2.06660 q^{46} +(-0.0217933 - 0.0377472i) q^{47} +(0.549723 - 0.317383i) q^{48} +6.63704 q^{49} +4.13829 q^{50} +(-0.268068 - 0.464308i) q^{51} +(-3.38075 + 5.85563i) q^{52} +(5.68217 - 3.28060i) q^{53} +(3.07684 + 1.77641i) q^{54} +(1.67935 + 2.58043i) q^{55} -0.602460i q^{56} +(-0.0492203 + 2.76644i) q^{57} -0.158793 q^{58} +(-7.69762 - 4.44422i) q^{59} +(-0.510300 - 0.294622i) q^{60} +(5.81059 - 3.35475i) q^{61} +(-1.12893 - 0.651790i) q^{62} +(1.35501 - 0.782316i) q^{63} +1.00000 q^{64} +6.27660 q^{65} +(0.112243 + 2.10228i) q^{66} +(6.79379 - 3.92240i) q^{67} -0.844621i q^{68} +1.31181i q^{69} +(-0.484329 + 0.279627i) q^{70} +(-6.08474 - 3.51303i) q^{71} +(1.29854 + 2.24913i) q^{72} +(6.47869 + 3.74048i) q^{73} +(8.54905 + 4.93580i) q^{74} -2.62684i q^{75} +(-2.24626 + 3.73555i) q^{76} +(1.78124 + 0.905387i) q^{77} +(3.71695 + 2.14598i) q^{78} +(-8.17598 + 14.1612i) q^{79} +(-0.464143 - 0.803919i) q^{80} +(-2.76800 + 4.79432i) q^{81} +(-2.44091 - 4.22778i) q^{82} -2.37669i q^{83} -0.382421 q^{84} +(-0.679007 + 0.392025i) q^{85} +(-1.19431 + 0.689537i) q^{86} +0.100796i q^{87} +(-1.50282 + 2.95661i) q^{88} +(11.9810 - 6.91725i) q^{89} +(1.20541 - 2.08784i) q^{90} +(3.52778 - 2.03677i) q^{91} +(-1.03330 + 1.78973i) q^{92} +(-0.413734 + 0.716608i) q^{93} -0.0435867 q^{94} +(4.04566 + 0.0719801i) q^{95} -0.634765i q^{96} +(10.0334 + 5.79276i) q^{97} +(3.31852 - 5.74785i) q^{98} +(-8.60127 + 0.459231i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

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