LMFDB - Embedded newform 385.2.i.d.221.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [385,2,Mod(221,385)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(385, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("385.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 385 = 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	385.i (of order $3$, 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:	$3.07424047782$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 241 x^{16} - 411 x^{15} + 1702 x^{14} - 2261 x^{13} + \cdots + 441 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 241x^16 - 411x^15 + 1702x^14 - 2261x^13 + 7837x^12 - 9160x^11 + 25160x^10 - 22890x^9 + 51017x^8 - 39775x^7 + 67640x^6 - 31197x^5 + 36799x^4 - 6043x^3 + 13120x^2 - 2289*x + 441
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			221.5
Root			$0.533037 + 0.923247i$ of defining polynomial
Character	$\chi$	$=$	385.221
Dual form			385.2.i.d.331.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.533037 - 0.923247i) q^{2} +(-1.53745 + 2.66295i) q^{3} +(0.431743 - 0.747801i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.27808 q^{6} +(-2.62595 + 0.323104i) q^{7} -3.05269 q^{8} +(-3.22753 - 5.59025i) q^{9} +O(q^{10})$	\(q+(-0.533037 - 0.923247i) q^{2} +(-1.53745 + 2.66295i) q^{3} +(0.431743 - 0.747801i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.27808 q^{6} +(-2.62595 + 0.323104i) q^{7} -3.05269 q^{8} +(-3.22753 - 5.59025i) q^{9} +(0.533037 - 0.923247i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.32757 + 2.29942i) q^{12} +2.06228 q^{13} +(1.69803 + 2.25217i) q^{14} -3.07491 q^{15} +(0.763711 + 1.32279i) q^{16} +(0.561652 - 0.972810i) q^{17} +(-3.44079 + 5.95963i) q^{18} +(-4.23532 - 7.33580i) q^{19} +0.863486 q^{20} +(3.17687 - 7.48953i) q^{21} +1.06607 q^{22} +(-1.99963 - 3.46346i) q^{23} +(4.69337 - 8.12916i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.09927 - 1.90399i) q^{26} +10.6240 q^{27} +(-0.892117 + 2.10318i) q^{28} -4.01868 q^{29} +(1.63904 + 2.83890i) q^{30} +(0.162793 - 0.281965i) q^{31} +(-2.23852 + 3.87722i) q^{32} +(-1.53745 - 2.66295i) q^{33} -1.19753 q^{34} +(-1.59279 - 2.11259i) q^{35} -5.57386 q^{36} +(-2.70461 - 4.68452i) q^{37} +(-4.51517 + 7.82050i) q^{38} +(-3.17066 + 5.49174i) q^{39} +(-1.52634 - 2.64371i) q^{40} +1.23247 q^{41} +(-8.60807 + 1.05916i) q^{42} -12.0838 q^{43} +(0.431743 + 0.747801i) q^{44} +(3.22753 - 5.59025i) q^{45} +(-2.13175 + 3.69230i) q^{46} +(0.526841 + 0.912516i) q^{47} -4.69668 q^{48} +(6.79121 - 1.69691i) q^{49} +1.06607 q^{50} +(1.72703 + 2.99130i) q^{51} +(0.890373 - 1.54217i) q^{52} +(0.442221 - 0.765949i) q^{53} +(-5.66300 - 9.80860i) q^{54} -1.00000 q^{55} +(8.01620 - 0.986335i) q^{56} +26.0465 q^{57} +(2.14211 + 3.71024i) q^{58} +(-6.93461 + 12.0111i) q^{59} +(-1.32757 + 2.29942i) q^{60} +(-0.819335 - 1.41913i) q^{61} -0.347098 q^{62} +(10.2816 + 13.6369i) q^{63} +7.82769 q^{64} +(1.03114 + 1.78598i) q^{65} +(-1.63904 + 2.83890i) q^{66} +(-5.37852 + 9.31587i) q^{67} +(-0.484978 - 0.840007i) q^{68} +12.2974 q^{69} +(-1.10142 + 2.59663i) q^{70} +8.18682 q^{71} +(9.85266 + 17.0653i) q^{72} +(6.48062 - 11.2248i) q^{73} +(-2.88332 + 4.99405i) q^{74} +(-1.53745 - 2.66295i) q^{75} -7.31428 q^{76} +(1.03316 - 2.43569i) q^{77} +6.76031 q^{78} +(-3.71992 - 6.44309i) q^{79} +(-0.763711 + 1.32279i) q^{80} +(-6.65135 + 11.5205i) q^{81} +(-0.656953 - 1.13788i) q^{82} +4.20154 q^{83} +(-4.22908 - 5.60921i) q^{84} +1.12330 q^{85} +(6.44111 + 11.1563i) q^{86} +(6.17854 - 10.7015i) q^{87} +(1.52634 - 2.64371i) q^{88} +(7.04583 + 12.2037i) q^{89} -6.88158 q^{90} +(-5.41543 + 0.666329i) q^{91} -3.45330 q^{92} +(0.500573 + 0.867017i) q^{93} +(0.561652 - 0.972810i) q^{94} +(4.23532 - 7.33580i) q^{95} +(-6.88323 - 11.9221i) q^{96} -16.8254 q^{97} +(-5.18663 - 5.36545i) q^{98} +6.45507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 3 q^{3} - 15 q^{4} + 10 q^{5} + 10 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 3 * q^3 - 15 * q^4 + 10 * q^5 + 10 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 20 q - 3 q^{2} + 3 q^{3} - 15 q^{4} + 10 q^{5} + 10 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} + 3 q^{10} - 10 q^{11} + 3 q^{12} - 12 q^{13} + 15 q^{14} + 6 q^{15} - 21 q^{16} + 5 q^{17} - q^{18} - q^{19} - 30 q^{20} + 24 q^{21} + 6 q^{22} - 18 q^{23} - 10 q^{24} - 10 q^{25} - 13 q^{26} - 30 q^{27} + 18 q^{28} + 28 q^{29} + 5 q^{30} - 10 q^{31} - 46 q^{32} + 3 q^{33} - 4 q^{34} + q^{35} + 52 q^{36} - 13 q^{37} - 9 q^{38} - 3 q^{39} + 9 q^{40} - 14 q^{41} + 76 q^{42} + 12 q^{43} - 15 q^{44} + 19 q^{45} - 10 q^{46} - q^{47} - 70 q^{48} + 11 q^{49} + 6 q^{50} - 9 q^{51} + 17 q^{52} - 16 q^{53} - 73 q^{54} - 20 q^{55} + 6 q^{56} + 24 q^{57} + 9 q^{58} - 13 q^{59} - 3 q^{60} - 18 q^{61} + 28 q^{62} + 17 q^{63} + 86 q^{64} - 6 q^{65} - 5 q^{66} - 29 q^{67} - 13 q^{68} + 3 q^{70} + 38 q^{71} + 48 q^{72} + 31 q^{73} + 8 q^{74} + 3 q^{75} - 16 q^{76} + 2 q^{77} + 6 q^{78} + 21 q^{80} - 42 q^{81} - q^{82} - 4 q^{83} - 12 q^{84} + 10 q^{85} - 10 q^{86} + 50 q^{87} - 9 q^{88} - 23 q^{89} - 2 q^{90} - 15 q^{91} + 28 q^{92} - 4 q^{93} + 5 q^{94} + q^{95} - 39 q^{96} - 86 q^{97} + 72 q^{98} + 38 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 3 * q^3 - 15 * q^4 + 10 * q^5 + 10 * q^6 - q^7 + 18 * q^8 - 19 * q^9 + 3 * q^10 - 10 * q^11 + 3 * q^12 - 12 * q^13 + 15 * q^14 + 6 * q^15 - 21 * q^16 + 5 * q^17 - q^18 - q^19 - 30 * q^20 + 24 * q^21 + 6 * q^22 - 18 * q^23 - 10 * q^24 - 10 * q^25 - 13 * q^26 - 30 * q^27 + 18 * q^28 + 28 * q^29 + 5 * q^30 - 10 * q^31 - 46 * q^32 + 3 * q^33 - 4 * q^34 + q^35 + 52 * q^36 - 13 * q^37 - 9 * q^38 - 3 * q^39 + 9 * q^40 - 14 * q^41 + 76 * q^42 + 12 * q^43 - 15 * q^44 + 19 * q^45 - 10 * q^46 - q^47 - 70 * q^48 + 11 * q^49 + 6 * q^50 - 9 * q^51 + 17 * q^52 - 16 * q^53 - 73 * q^54 - 20 * q^55 + 6 * q^56 + 24 * q^57 + 9 * q^58 - 13 * q^59 - 3 * q^60 - 18 * q^61 + 28 * q^62 + 17 * q^63 + 86 * q^64 - 6 * q^65 - 5 * q^66 - 29 * q^67 - 13 * q^68 + 3 * q^70 + 38 * q^71 + 48 * q^72 + 31 * q^73 + 8 * q^74 + 3 * q^75 - 16 * q^76 + 2 * q^77 + 6 * q^78 + 21 * q^80 - 42 * q^81 - q^82 - 4 * q^83 - 12 * q^84 + 10 * q^85 - 10 * q^86 + 50 * q^87 - 9 * q^88 - 23 * q^89 - 2 * q^90 - 15 * q^91 + 28 * q^92 - 4 * q^93 + 5 * q^94 + q^95 - 39 * q^96 - 86 * q^97 + 72 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/385\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$276$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.533037	−	0.923247i	−0.376914	−	0.652834i	0.613697	−	0.789541i	$-0.289681\pi$
$2$	−0.533037	−	0.923247i	−0.376914	−	0.652834i	−0.990612	+	0.136707i	$0.956348\pi$
$3$	−1.53745	+	2.66295i	−0.887650	+	1.53745i	−0.0450040	+	0.998987i	$0.514330\pi$
$3$	−1.53745	+	2.66295i	−0.887650	+	1.53745i	−0.842646	+	0.538468i	$0.819003\pi$
$4$	0.431743	−	0.747801i	0.215871	−	0.373900i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	3.27808			1.33827
$7$	−2.62595	+	0.323104i	−0.992515	+	0.122122i
$7$	−2.62595	+	0.323104i	−0.992515	+	0.122122i
$8$	−3.05269			−1.07929
$9$	−3.22753	−	5.59025i	−1.07584	−	1.86342i
$10$	0.533037	−	0.923247i	0.168561	−	0.291956i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	1.32757	+	2.29942i	0.383236	+	0.663785i
$13$	2.06228			0.571973			0.285986	−	0.958234i	$-0.407679\pi$
$13$	2.06228			0.571973			0.285986	+	0.958234i	$0.407679\pi$
$14$	1.69803	+	2.25217i	0.453818	+	0.601919i
$15$	−3.07491			−0.793938
$16$	0.763711	+	1.32279i	0.190928	+	0.330696i
$17$	0.561652	−	0.972810i	0.136221	−	0.235941i	−0.789842	−	0.613310i	$-0.789838\pi$
$17$	0.561652	−	0.972810i	0.136221	−	0.235941i	0.926063	+	0.377369i	$0.123171\pi$
$18$	−3.44079	+	5.95963i	−0.811002	+	1.40470i
$19$	−4.23532	−	7.33580i	−0.971650	−	1.68295i	−0.690574	−	0.723262i	$-0.742642\pi$
$19$	−4.23532	−	7.33580i	−0.971650	−	1.68295i	−0.281076	−	0.959685i	$-0.590691\pi$
$20$	0.863486			0.193081
$21$	3.17687	−	7.48953i	0.693249	−	1.63435i
$22$	1.06607			0.227288
$23$	−1.99963	−	3.46346i	−0.416951	−	0.722181i	0.578680	−	0.815555i	$-0.303568\pi$
$23$	−1.99963	−	3.46346i	−0.416951	−	0.722181i	−0.995631	+	0.0933740i	$0.970235\pi$
$24$	4.69337	−	8.12916i	0.958030	−	1.65936i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.09927	−	1.90399i	−0.215585	−	0.373403i
$27$	10.6240			2.04459
$28$	−0.892117	+	2.10318i	−0.168594	+	0.397464i
$29$	−4.01868			−0.746250			−0.373125	−	0.927781i	$-0.621714\pi$
$29$	−4.01868			−0.746250			−0.373125	+	0.927781i	$0.621714\pi$
$30$	1.63904	+	2.83890i	0.299247	+	0.518310i
$31$	0.162793	−	0.281965i	0.0292384	−	0.0506424i	−0.851036	−	0.525107i	$-0.824025\pi$
$31$	0.162793	−	0.281965i	0.0292384	−	0.0506424i	0.880274	+	0.474465i	$0.157358\pi$
$32$	−2.23852	+	3.87722i	−0.395717	+	0.685403i
$33$	−1.53745	−	2.66295i	−0.267637	−	0.463560i
$34$	−1.19753			−0.205374
$35$	−1.59279	−	2.11259i	−0.269231	−	0.357092i
$36$	−5.57386			−0.928977
$37$	−2.70461	−	4.68452i	−0.444635	−	0.770131i	0.553392	−	0.832921i	$-0.313333\pi$
$37$	−2.70461	−	4.68452i	−0.444635	−	0.770131i	−0.998027	+	0.0627905i	$0.980000\pi$
$38$	−4.51517	+	7.82050i	−0.732457	+	1.26865i
$39$	−3.17066	+	5.49174i	−0.507711	+	0.879382i
$40$	−1.52634	−	2.64371i	−0.241336	−	0.418007i
$41$	1.23247			0.192480			0.0962399	−	0.995358i	$-0.469318\pi$
$41$	1.23247			0.192480			0.0962399	+	0.995358i	$0.469318\pi$
$42$	−8.60807	+	1.05916i	−1.32825	+	0.163432i
$43$	−12.0838			−1.84276			−0.921381	−	0.388660i	$-0.872938\pi$
$43$	−12.0838			−1.84276			−0.921381	+	0.388660i	$0.872938\pi$
$44$	0.431743	+	0.747801i	0.0650877	+	0.112735i
$45$	3.22753	−	5.59025i	0.481132	−	0.833346i
$46$	−2.13175	+	3.69230i	−0.314310	+	0.544400i
$47$	0.526841	+	0.912516i	0.0768477	+	0.133104i	0.901888	−	0.431969i	$-0.142181\pi$
$47$	0.526841	+	0.912516i	0.0768477	+	0.133104i	−0.825041	+	0.565073i	$0.808848\pi$
$48$	−4.69668			−0.677908
$49$	6.79121	−	1.69691i	0.970173	−	0.242415i
$50$	1.06607			0.150766
$51$	1.72703	+	2.99130i	0.241832	+	0.418866i
$52$	0.890373	−	1.54217i	0.123473	−	0.213861i
$53$	0.442221	−	0.765949i	0.0607437	−	0.105211i	−0.834054	−	0.551682i	$-0.813986\pi$
$53$	0.442221	−	0.765949i	0.0607437	−	0.105211i	0.894798	+	0.446471i	$0.147319\pi$
$54$	−5.66300	−	9.80860i	−0.770637	−	1.33478i
$55$	−1.00000			−0.134840
$56$	8.01620	−	0.986335i	1.07121	−	0.131805i
$57$	26.0465			3.44994
$58$	2.14211	+	3.71024i	0.281272	+	0.487178i
$59$	−6.93461	+	12.0111i	−0.902809	+	1.56371i	−0.0789785	+	0.996876i	$0.525166\pi$
$59$	−6.93461	+	12.0111i	−0.902809	+	1.56371i	−0.823831	+	0.566836i	$0.808167\pi$
$60$	−1.32757	+	2.29942i	−0.171389	+	0.296854i
$61$	−0.819335	−	1.41913i	−0.104905	−	0.181701i	0.808794	−	0.588092i	$-0.200121\pi$
$61$	−0.819335	−	1.41913i	−0.104905	−	0.181701i	−0.913699	+	0.406391i	$0.866787\pi$
$62$	−0.347098			−0.0440815
$63$	10.2816	+	13.6369i	1.29536	+	1.71809i
$64$	7.82769			0.978461
$65$	1.03114	+	1.78598i	0.127897	+	0.221524i
$66$	−1.63904	+	2.83890i	−0.201752	+	0.349445i
$67$	−5.37852	+	9.31587i	−0.657091	+	1.13811i	0.324274	+	0.945963i	$0.394880\pi$
$67$	−5.37852	+	9.31587i	−0.657091	+	1.13811i	−0.981365	+	0.192152i	$0.938453\pi$
$68$	−0.484978	−	0.840007i	−0.0588123	−	0.101866i
$69$	12.2974			1.48043
$70$	−1.10142	+	2.59663i	−0.131645	+	0.310356i
$71$	8.18682			0.971597			0.485799	−	0.874071i	$-0.338529\pi$
$71$	8.18682			0.971597			0.485799	+	0.874071i	$0.338529\pi$
$72$	9.85266	+	17.0653i	1.16115	+	2.01117i
$73$	6.48062	−	11.2248i	0.758499	−	1.31376i	−0.185117	−	0.982717i	$-0.559266\pi$
$73$	6.48062	−	11.2248i	0.758499	−	1.31376i	0.943616	−	0.331043i	$-0.107400\pi$
$74$	−2.88332	+	4.99405i	−0.335179	+	0.580546i
$75$	−1.53745	−	2.66295i	−0.177530	−	0.307491i
$76$	−7.31428			−0.839006
$77$	1.03316	−	2.43569i	0.117739	−	0.277573i
$78$	6.76031			0.765454
$79$	−3.71992	−	6.44309i	−0.418523	−	0.724904i	0.577268	−	0.816555i	$-0.304119\pi$
$79$	−3.71992	−	6.44309i	−0.418523	−	0.724904i	−0.995791	+	0.0916511i	$0.970786\pi$
$80$	−0.763711	+	1.32279i	−0.0853854	+	0.147892i
$81$	−6.65135	+	11.5205i	−0.739039	+	1.28005i
$82$	−0.656953	−	1.13788i	−0.0725484	−	0.125657i
$83$	4.20154			0.461179			0.230590	−	0.973051i	$-0.425935\pi$
$83$	4.20154			0.461179			0.230590	+	0.973051i	$0.425935\pi$
$84$	−4.22908	−	5.60921i	−0.461431	−	0.612015i
$85$	1.12330			0.121839
$86$	6.44111	+	11.1563i	0.694563	+	1.20302i
$87$	6.17854	−	10.7015i	0.662409	−	1.14733i
$88$	1.52634	−	2.64371i	0.162709	−	0.281820i
$89$	7.04583	+	12.2037i	0.746856	+	1.29359i	0.949323	+	0.314303i	$0.101771\pi$
$89$	7.04583	+	12.2037i	0.746856	+	1.29359i	−0.202467	+	0.979289i	$0.564896\pi$
$90$	−6.88158			−0.725383
$91$	−5.41543	+	0.666329i	−0.567691	+	0.0698503i
$92$	−3.45330			−0.360031
$93$	0.500573	+	0.867017i	0.0519070	+	0.0899055i
$94$	0.561652	−	0.972810i	0.0579300	−	0.100338i
$95$	4.23532	−	7.33580i	0.434535	−	0.752637i
$96$	−6.88323	−	11.9221i	−0.702517	−	1.21680i
$97$	−16.8254			−1.70836			−0.854180	−	0.519977i	$-0.825940\pi$
$97$	−16.8254			−1.70836			−0.854180	+	0.519977i	$0.825940\pi$
$98$	−5.18663	−	5.36545i	−0.523929	−	0.541992i
$99$	6.45507			0.648759
$100$	0.431743	+	0.747801i	0.0431743	+	0.0747801i
$101$	−7.12645	+	12.3434i	−0.709109	+	1.22821i	0.256079	+	0.966656i	$0.417569\pi$
$101$	−7.12645	+	12.3434i	−0.709109	+	1.22821i	−0.965188	+	0.261557i	$0.915764\pi$
$102$	1.84114	−	3.18895i	0.182300	−	0.315753i
$103$	8.12911	+	14.0800i	0.800985	+	1.38735i	0.918968	+	0.394332i	$0.129024\pi$
$103$	8.12911	+	14.0800i	0.800985	+	1.38735i	−0.117983	+	0.993016i	$0.537643\pi$
$104$	−6.29549			−0.617323
$105$	8.07455	−	0.993515i	0.787996	−	0.0969571i
$106$	−0.942881			−0.0915807
$107$	−4.29016	−	7.43078i	−0.414745	−	0.718360i	0.580656	−	0.814149i	$-0.302796\pi$
$107$	−4.29016	−	7.43078i	−0.414745	−	0.718360i	−0.995402	+	0.0957886i	$0.969463\pi$
$108$	4.58685	−	7.94465i	0.441369	−	0.764474i
$109$	−2.07085	+	3.58681i	−0.198351	+	0.343555i	−0.947994	−	0.318288i	$-0.896892\pi$
$109$	−2.07085	+	3.58681i	−0.198351	+	0.343555i	0.749643	+	0.661843i	$0.230225\pi$
$110$	0.533037	+	0.923247i	0.0508231	+	0.0880282i
$111$	16.6329			1.57872
$112$	−2.43286	−	3.22681i	−0.229884	−	0.304905i
$113$	2.95520			0.278002			0.139001	−	0.990292i	$-0.455611\pi$
$113$	2.95520			0.278002			0.139001	+	0.990292i	$0.455611\pi$
$114$	−13.8837	−	24.0473i	−1.30033	−	2.25224i
$115$	1.99963	−	3.46346i	0.186466	−	0.322969i
$116$	−1.73504	+	3.00517i	−0.161094	+	0.279023i
$117$	−6.65607	−	11.5286i	−0.615354	−	1.06582i
$118$	14.7856			1.36113
$119$	−1.16055	+	2.73602i	−0.106388	+	0.250811i
$120$	9.38674			0.856888
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−0.873471	+	1.51290i	−0.0790804	+	0.136971i
$123$	−1.89487	+	3.28201i	−0.170855	+	0.295929i
$124$	−0.140569	−	0.243473i	−0.0126235	−	0.0218645i
$125$	−1.00000			−0.0894427
$126$	7.10976	−	16.7614i	0.633388	−	1.49322i
$127$	−6.78852			−0.602383			−0.301192	−	0.953564i	$-0.597384\pi$
$127$	−6.78852			−0.602383			−0.301192	+	0.953564i	$0.597384\pi$
$128$	0.304582	+	0.527552i	0.0269215	+	0.0466294i
$129$	18.5783	−	32.1786i	1.63573	−	2.83316i
$130$	1.09927	−	1.90399i	0.0964123	−	0.166991i
$131$	2.06094	+	3.56966i	0.180065	+	0.311883i	0.941903	−	0.335886i	$-0.109036\pi$
$131$	2.06094	+	3.56966i	0.180065	+	0.311883i	−0.761837	+	0.647769i	$0.775702\pi$
$132$	−2.65514			−0.231100
$133$	13.4920	+	17.8950i	1.16990	+	1.55169i
$134$	11.4678			0.990668
$135$	5.31201	+	9.20067i	0.457185	+	0.791868i
$136$	−1.71455	+	2.96969i	−0.147021	+	0.254648i
$137$	−5.75396	+	9.96615i	−0.491594	+	0.851465i	−0.999953	−	0.00967958i	$-0.996919\pi$
$137$	−5.75396	+	9.96615i	−0.491594	+	0.851465i	0.508359	+	0.861145i	$0.330252\pi$
$138$	−6.55495	−	11.3535i	−0.557994	−	0.966474i
$139$	−0.783249			−0.0664343			−0.0332172	−	0.999448i	$-0.510575\pi$
$139$	−0.783249			−0.0664343			−0.0332172	+	0.999448i	$0.510575\pi$
$140$	−2.26747	+	0.278995i	−0.191636	+	0.0235794i
$141$	−3.23998			−0.272855
$142$	−4.36388	−	7.55846i	−0.366209	−	0.634292i
$143$	−1.03114	+	1.78598i	−0.0862281	+	0.149351i
$144$	4.92980	−	8.53867i	0.410817	−	0.711556i
$145$	−2.00934	−	3.48028i	−0.166867	−	0.289022i
$146$	−13.8176			−1.14356
$147$	−5.92240	+	20.6936i	−0.488471	+	1.70678i
$148$	−4.67078			−0.383936
$149$	−5.48695	−	9.50368i	−0.449509	−	0.778572i	0.548845	−	0.835924i	$-0.315068\pi$
$149$	−5.48695	−	9.50368i	−0.449509	−	0.778572i	−0.998354	+	0.0573521i	$0.981734\pi$
$150$	−1.63904	+	2.83890i	−0.133827	+	0.231795i
$151$	4.81317	−	8.33666i	0.391691	−	0.678428i	−0.600982	−	0.799263i	$-0.705224\pi$
$151$	4.81317	−	8.33666i	0.391691	−	0.678428i	0.992673	+	0.120834i	$0.0385570\pi$
$152$	12.9291	+	22.3939i	1.04869	+	1.81639i
$153$	−7.25101			−0.586209
$154$	−2.79946	+	0.344453i	−0.225587	+	0.0277568i
$155$	0.325585			0.0261516
$156$	2.73782	+	4.74204i	0.219201	+	0.379667i
$157$	9.67603	−	16.7594i	0.772231	−	1.33754i	−0.164106	−	0.986443i	$-0.552474\pi$
$157$	9.67603	−	16.7594i	0.772231	−	1.33754i	0.936337	−	0.351101i	$-0.114193\pi$
$158$	−3.96571	+	6.86881i	−0.315495	+	0.546453i
$159$	1.35979	+	2.35522i	0.107838	+	0.186781i
$160$	−4.47703			−0.353940
$161$	6.36998	+	8.44877i	0.502024	+	0.665857i
$162$	14.1817			1.11422
$163$	−8.05931	−	13.9591i	−0.631254	−	1.09336i	−0.987296	−	0.158894i	$-0.949207\pi$
$163$	−8.05931	−	13.9591i	−0.631254	−	1.09336i	0.356042	−	0.934470i	$-0.384126\pi$
$164$	0.532111	−	0.921643i	0.0415509	−	0.0719682i
$165$	1.53745	−	2.66295i	0.119691	−	0.207310i
$166$	−2.23958	−	3.87906i	−0.173825	−	0.301074i
$167$	−9.27253			−0.717530			−0.358765	−	0.933428i	$-0.616802\pi$
$167$	−9.27253			−0.717530			−0.358765	+	0.933428i	$0.616802\pi$
$168$	−9.69799	+	22.8632i	−0.748216	+	1.76393i
$169$	−8.74702			−0.672847
$170$	−0.598763	−	1.03709i	−0.0459230	−	0.0795410i
$171$	−27.3393	+	47.3531i	−2.09069	+	3.62118i
$172$	−5.21709	+	9.03627i	−0.397800	+	0.689009i
$173$	9.62070	+	16.6635i	0.731448	+	1.26691i	0.956264	+	0.292505i	$0.0944887\pi$
$173$	9.62070	+	16.6635i	0.731448	+	1.26691i	−0.224816	+	0.974401i	$0.572178\pi$
$174$	−13.1736			−0.998685
$175$	1.03316	−	2.43569i	0.0780994	−	0.184121i
$176$	−1.52742			−0.115134
$177$	−21.3233	−	36.9330i	−1.60276	−	2.77606i
$178$	7.51137	−	13.0101i	0.563001	−	0.975147i
$179$	4.17161	−	7.22544i	0.311801	−	0.540055i	−0.666952	−	0.745101i	$-0.732401\pi$
$179$	4.17161	−	7.22544i	0.311801	−	0.540055i	0.978752	+	0.205046i	$0.0657345\pi$
$180$	−2.78693	−	4.82710i	−0.207725	−	0.359791i
$181$	−18.9132			−1.40580			−0.702902	−	0.711287i	$-0.748113\pi$
$181$	−18.9132			−1.40580			−0.702902	+	0.711287i	$0.748113\pi$
$182$	3.50181	+	4.64460i	0.259572	+	0.344281i
$183$	5.03876			0.372476
$184$	6.10424	+	10.5729i	0.450011	+	0.779441i
$185$	2.70461	−	4.68452i	0.198847	−	0.344413i
$186$	0.533648	−	0.924305i	0.0391289	−	0.0677733i
$187$	0.561652	+	0.972810i	0.0410721	+	0.0711389i
$188$	0.909840			0.0663569
$189$	−27.8981	+	3.43266i	−2.02929	+	0.249689i
$190$	−9.03034			−0.655130
$191$	−0.597017	−	1.03406i	−0.0431986	−	0.0748222i	0.843618	−	0.536944i	$-0.180421\pi$
$191$	−0.597017	−	1.03406i	−0.0431986	−	0.0748222i	−0.886816	+	0.462122i	$0.847088\pi$
$192$	−12.0347	+	20.8447i	−0.868531	+	1.50434i
$193$	11.1045	−	19.2335i	0.799319	−	1.38446i	−0.120741	−	0.992684i	$-0.538527\pi$
$193$	11.1045	−	19.2335i	0.799319	−	1.38446i	0.920060	−	0.391777i	$-0.128140\pi$
$194$	8.96856	+	15.5340i	0.643905	+	1.11528i
$195$	−6.34131			−0.454111
$196$	1.66311	−	5.81110i	0.118793	−	0.415078i
$197$	−5.35087			−0.381234			−0.190617	−	0.981664i	$-0.561049\pi$
$197$	−5.35087			−0.381234			−0.190617	+	0.981664i	$0.561049\pi$
$198$	−3.44079	−	5.95963i	−0.244526	−	0.423532i
$199$	5.51146	−	9.54613i	0.390697	−	0.676707i	−0.601845	−	0.798613i	$-0.705567\pi$
$199$	5.51146	−	9.54613i	0.390697	−	0.676707i	0.992542	+	0.121906i	$0.0389007\pi$
$200$	1.52634	−	2.64371i	0.107929	−	0.186938i
$201$	−16.5385	−	28.6455i	−1.16653	−	2.02050i
$202$	15.1947			1.06909
$203$	10.5528	−	1.29845i	0.740665	−	0.0911334i
$204$	2.98253			0.208819
$205$	0.616236	+	1.06735i	0.0430398	+	0.0745471i
$206$	8.66624	−	15.0104i	0.603805	−	1.04582i
$207$	−12.9077	+	22.3569i	−0.897150	+	1.55391i
$208$	1.57498	+	2.72795i	0.109205	+	0.189149i
$209$	8.47065			0.585927
$210$	−5.22130	−	6.92523i	−0.360304	−	0.477886i
$211$	4.84291			0.333400			0.166700	−	0.986008i	$-0.446689\pi$
$211$	4.84291			0.333400			0.166700	+	0.986008i	$0.446689\pi$
$212$	−0.381851	−	0.661386i	−0.0262257	−	0.0454242i
$213$	−12.5869	+	21.8011i	−0.862438	+	1.49379i
$214$	−4.57363	+	7.92176i	−0.312647	+	0.541520i
$215$	−6.04190	−	10.4649i	−0.412054	−	0.713699i
$216$	−32.4318			−2.20671
$217$	−0.336381	+	0.793025i	−0.0228350	+	0.0538340i
$218$	4.41536			0.299046
$219$	19.9273	+	34.5151i	1.34656	+	2.33232i
$220$	−0.431743	+	0.747801i	−0.0291081	+	0.0504167i
$221$	1.15828	−	2.00620i	0.0779145	−	0.134952i
$222$	−8.86593	−	15.3562i	−0.595042	−	1.03064i
$223$	−10.7581			−0.720412			−0.360206	−	0.932873i	$-0.617294\pi$
$223$	−10.7581			−0.720412			−0.360206	+	0.932873i	$0.617294\pi$
$224$	4.62548	−	10.9047i	0.309053	−	0.728598i
$225$	6.45507			0.430338
$226$	−1.57523	−	2.72838i	−0.104783	−	0.181489i
$227$	−2.31224	+	4.00491i	−0.153469	+	0.265815i	−0.932500	−	0.361169i	$-0.882378\pi$
$227$	−2.31224	+	4.00491i	−0.153469	+	0.265815i	0.779032	+	0.626984i	$0.215711\pi$
$228$	11.2454	−	19.4776i	0.744744	−	1.28993i
$229$	0.827005	+	1.43241i	0.0546500	+	0.0946566i	0.892056	−	0.451924i	$-0.149262\pi$
$229$	0.827005	+	1.43241i	0.0546500	+	0.0946566i	−0.837406	+	0.546581i	$0.815929\pi$
$230$	−4.26350			−0.281127
$231$	4.89769	+	6.49601i	0.322244	+	0.427406i
$232$	12.2678			0.805419
$233$	−1.04515	−	1.81025i	−0.0684700	−	0.118594i	0.829758	−	0.558123i	$-0.188478\pi$
$233$	−1.04515	−	1.81025i	−0.0684700	−	0.118594i	−0.898228	+	0.439530i	$0.855145\pi$
$234$	−7.09586	+	12.2904i	−0.463871	+	0.803448i
$235$	−0.526841	+	0.912516i	−0.0343673	+	0.0595260i
$236$	5.98794	+	10.3714i	0.389782	+	0.675121i
$237$	22.8768			1.48601
$238$	3.14464	−	0.386925i	0.203837	−	0.0250806i
$239$	−13.1060			−0.847754			−0.423877	−	0.905720i	$-0.639331\pi$
$239$	−13.1060			−0.847754			−0.423877	+	0.905720i	$0.639331\pi$
$240$	−2.34834	−	4.06745i	−0.151585	−	0.262553i
$241$	−2.96322	+	5.13244i	−0.190877	+	0.330609i	−0.945541	−	0.325502i	$-0.894467\pi$
$241$	−2.96322	+	5.13244i	−0.190877	+	0.330609i	0.754664	+	0.656112i	$0.227800\pi$
$242$	−0.533037	+	0.923247i	−0.0342649	+	0.0593486i
$243$	−4.51627	−	7.82242i	−0.289719	−	0.501808i
$244$	−1.41497			−0.0905840
$245$	4.86517	+	5.03290i	0.310824	+	0.321540i
$246$	4.04014			0.257590
$247$	−8.73441	−	15.1284i	−0.555757	−	0.962600i
$248$	−0.496955	+	0.860752i	−0.0315567	+	0.0546578i
$249$	−6.45968	+	11.1885i	−0.409366	+	0.709042i
$250$	0.533037	+	0.923247i	0.0337122	+	0.0583913i
$251$	8.12067			0.512572			0.256286	−	0.966601i	$-0.417501\pi$
$251$	8.12067			0.512572			0.256286	+	0.966601i	$0.417501\pi$
$252$	14.6367	−	1.80093i	0.922023	−	0.113448i
$253$	3.99926			0.251431
$254$	3.61853	+	6.26748i	0.227047	+	0.393257i
$255$	−1.72703	+	2.99130i	−0.108151	+	0.187323i
$256$	8.15240	−	14.1204i	0.509525	−	0.882523i
$257$	−13.1908	−	22.8471i	−0.822818	−	1.42516i	−0.903575	−	0.428429i	$-0.859067\pi$
$257$	−13.1908	−	22.8471i	−0.822818	−	1.42516i	0.0807568	−	0.996734i	$-0.474266\pi$
$258$	−39.6117			−2.46612
$259$	8.61575	+	11.4274i	0.535357	+	0.710067i
$260$	1.78075			0.110437
$261$	12.9704	+	22.4654i	0.802850	+	1.39058i
$262$	2.19712	−	3.80552i	0.135738	−	0.235106i
$263$	10.3845	−	17.9865i	0.640337	−	1.10910i	−0.345021	−	0.938595i	$-0.612128\pi$
$263$	10.3845	−	17.9865i	0.640337	−	1.10910i	0.985358	−	0.170501i	$-0.0545385\pi$
$264$	4.69337	+	8.12916i	0.288857	+	0.500315i
$265$	0.884442			0.0543308
$266$	9.32977	−	21.9951i	0.572045	−	1.34861i
$267$	−43.3306			−2.65179
$268$	4.64428	+	8.04412i	0.283694	+	0.491373i
$269$	5.33628	−	9.24271i	0.325359	−	0.563538i	−0.656226	−	0.754564i	$-0.727848\pi$
$269$	5.33628	−	9.24271i	0.325359	−	0.563538i	0.981585	+	0.191026i	$0.0611816\pi$
$270$	5.66300	−	9.80860i	0.344639	−	0.596933i
$271$	2.62181	+	4.54110i	0.159263	+	0.275852i	0.934603	−	0.355692i	$-0.115755\pi$
$271$	2.62181	+	4.54110i	0.159263	+	0.275852i	−0.775340	+	0.631544i	$0.782421\pi$
$272$	1.71576			0.104033
$273$	6.55158	−	15.4455i	0.396520	−	0.934802i
$274$	12.2683			0.741155
$275$	−0.500000	−	0.866025i	−0.0301511	−	0.0522233i
$276$	5.30929	−	9.19597i	0.319582	−	0.553532i
$277$	9.18831	−	15.9146i	0.552072	−	0.956216i	−0.446053	−	0.895006i	$-0.647171\pi$
$277$	9.18831	−	15.9146i	0.552072	−	0.956216i	0.998125	−	0.0612099i	$-0.0194959\pi$
$278$	0.417501	+	0.723133i	0.0250400	+	0.0433706i
$279$	−2.10168			−0.125824
$280$	4.86229	+	6.44907i	0.290578	+	0.385405i
$281$	−2.89615			−0.172770			−0.0863849	−	0.996262i	$-0.527531\pi$
$281$	−2.89615			−0.172770			−0.0863849	+	0.996262i	$0.527531\pi$
$282$	1.72703	+	2.99130i	0.102843	+	0.178129i
$283$	−2.19606	+	3.80369i	−0.130542	+	0.226106i	−0.923886	−	0.382669i	$-0.875005\pi$
$283$	−2.19606	+	3.80369i	−0.130542	+	0.226106i	0.793344	+	0.608774i	$0.208338\pi$
$284$	3.53460	−	6.12211i	0.209740	−	0.363280i
$285$	13.0232	+	22.5569i	0.771430	+	1.33616i
$286$	2.19854			0.130002
$287$	−3.23641	+	0.398216i	−0.191039	+	0.0235060i
$288$	28.8996			1.70292
$289$	7.86909	+	13.6297i	0.462888	+	0.801745i
$290$	−2.14211	+	3.71024i	−0.125789	+	0.217873i
$291$	25.8683	−	44.8052i	1.51643	−	2.62653i
$292$	−5.59592	−	9.69242i	−0.327477	−	0.567206i
$293$	−21.0343			−1.22884			−0.614418	−	0.788981i	$-0.710609\pi$
$293$	−21.0343			−1.22884			−0.614418	+	0.788981i	$0.710609\pi$
$294$	22.2621	−	5.56260i	1.29835	−	0.324418i
$295$	−13.8692			−0.807497
$296$	8.25633	+	14.3004i	0.479890	+	0.831193i
$297$	−5.31201	+	9.20067i	−0.308234	+	0.533877i
$298$	−5.84950	+	10.1316i	−0.338852	+	0.586910i
$299$	−4.12379	−	7.14261i	−0.238485	−	0.413068i
$300$	−2.65514			−0.153295
$301$	31.7314	−	3.90432i	1.82897	−	0.225041i
$302$	−10.2624			−0.590535
$303$	−21.9132	−	37.9548i	−1.25888	−	2.18045i
$304$	6.46912	−	11.2049i	0.371030	−	0.642642i
$305$	0.819335	−	1.41913i	0.0469150	−	0.0812591i
$306$	3.86506	+	6.69447i	0.220950	+	0.382697i
$307$	24.8681			1.41930			0.709648	−	0.704556i	$-0.248854\pi$
$307$	24.8681			1.41930			0.709648	+	0.704556i	$0.248854\pi$
$308$	−1.37535	−	1.82419i	−0.0783679	−	0.103943i
$309$	−49.9926			−2.84398
$310$	−0.173549	−	0.300596i	−0.00985692	−	0.0170727i
$311$	12.1742	−	21.0864i	0.690336	−	1.19570i	−0.281391	−	0.959593i	$-0.590796\pi$
$311$	12.1742	−	21.0864i	0.690336	−	1.19570i	0.971728	−	0.236104i	$-0.0758708\pi$
$312$	9.67903	−	16.7646i	0.547967	−	0.949107i
$313$	−0.574509	−	0.995079i	−0.0324732	−	0.0562452i	0.849332	−	0.527859i	$-0.177005\pi$
$313$	−0.574509	−	0.995079i	−0.0324732	−	0.0562452i	−0.881805	+	0.471614i	$0.843672\pi$
$314$	−20.6307			−1.16426
$315$	−6.66911	+	15.7225i	−0.375762	+	0.885865i
$316$	−6.42419			−0.361389
$317$	−9.67734	−	16.7616i	−0.543533	−	0.941428i	−0.998698	−	0.0510201i	$-0.983753\pi$
$317$	−9.67734	−	16.7616i	−0.543533	−	0.941428i	0.455164	−	0.890408i	$-0.349581\pi$
$318$	1.44964	−	2.51084i	0.0812916	−	0.140801i
$319$	2.00934	−	3.48028i	0.112501	−	0.194858i
$320$	3.91385	+	6.77898i	0.218791	+	0.378956i
$321$	26.3837			1.47260
$322$	4.40487	−	10.3846i	0.245474	−	0.578710i
$323$	−9.51511			−0.529435
$324$	5.74335	+	9.94777i	0.319075	+	0.552654i
$325$	−1.03114	+	1.78598i	−0.0571973	+	0.0990685i
$326$	−8.59182	+	14.8815i	−0.475857	+	0.824208i
$327$	−6.36767	−	11.0291i	−0.352133	−	0.609912i
$328$	−3.76235			−0.207741
$329$	−1.67830	−	2.22600i	−0.0925274	−	0.122723i
$330$	−3.27808			−0.180452
$331$	1.62987	+	2.82301i	0.0895856	+	0.155167i	0.907336	−	0.420406i	$-0.138112\pi$
$331$	1.62987	+	2.82301i	0.0895856	+	0.155167i	−0.817750	+	0.575573i	$0.804779\pi$
$332$	1.81399	−	3.14192i	0.0995554	−	0.172435i
$333$	−17.4584	+	30.2389i	−0.956717	+	1.65708i
$334$	4.94260	+	8.56084i	0.270447	+	0.468428i
$335$	−10.7570			−0.587720
$336$	12.3332	−	1.51752i	0.672834	−	0.0827873i
$337$	−0.431489			−0.0235047			−0.0117523	−	0.999931i	$-0.503741\pi$
$337$	−0.431489			−0.0235047			−0.0117523	+	0.999931i	$0.503741\pi$
$338$	4.66248	+	8.07566i	0.253606	+	0.439258i
$339$	−4.54348	+	7.86955i	−0.246768	+	0.427415i
$340$	0.484978	−	0.840007i	0.0263017	−	0.0455558i
$341$	0.162793	+	0.281965i	0.00881571	+	0.0152693i
$342$	58.2915			3.15204
$343$	−17.2851	+	6.65026i	−0.933307	+	0.359080i
$344$	36.8881			1.98887
$345$	6.14868	+	10.6498i	0.331034	+	0.573367i
$346$	10.2564	−	17.7646i	0.551387	−	0.955030i
$347$	1.29750	−	2.24734i	0.0696535	−	0.120643i	−0.829095	−	0.559107i	$-0.811144\pi$
$347$	1.29750	−	2.24734i	0.0696535	−	0.120643i	0.898749	+	0.438464i	$0.144477\pi$
$348$	−5.33508	−	9.24063i	−0.285990	−	0.495350i
$349$	−11.7944			−0.631340			−0.315670	−	0.948869i	$-0.602229\pi$
$349$	−11.7944			−0.631340			−0.315670	+	0.948869i	$0.602229\pi$
$350$	−2.79946	+	0.344453i	−0.149637	+	0.0184118i
$351$	21.9097			1.16945
$352$	−2.23852	−	3.87722i	−0.119313	−	0.206657i
$353$	1.03652	−	1.79531i	0.0551685	−	0.0955546i	−0.837122	−	0.547016i	$-0.815764\pi$
$353$	1.03652	−	1.79531i	0.0551685	−	0.0955546i	0.892291	+	0.451461i	$0.149097\pi$
$354$	−22.7322	+	39.3734i	−1.20820	+	2.09267i
$355$	4.09341	+	7.09000i	0.217256	+	0.376298i
$356$	12.1679			0.644899
$357$	−5.50159	−	7.29700i	−0.291175	−	0.386198i
$358$	−8.89449			−0.470088
$359$	15.1378	+	26.2195i	0.798943	+	1.38381i	0.920305	+	0.391202i	$0.127941\pi$
$359$	15.1378	+	26.2195i	0.798943	+	1.38381i	−0.121362	+	0.992608i	$0.538726\pi$
$360$	−9.85266	+	17.0653i	−0.519281	+	0.899420i
$361$	−26.3759	+	45.6845i	−1.38821	+	2.40445i
$362$	10.0814	+	17.4615i	0.529868	+	0.917758i
$363$	3.07491			0.161391
$364$	−1.83979	+	4.33734i	−0.0964313	+	0.227339i
$365$	12.9612			0.678422
$366$	−2.68585	−	4.65202i	−0.140391	−	0.243165i
$367$	−4.01976	+	6.96242i	−0.209830	+	0.363435i	−0.951661	−	0.307151i	$-0.900624\pi$
$367$	−4.01976	+	6.96242i	−0.209830	+	0.363435i	0.741831	+	0.670587i	$0.233958\pi$
$368$	3.05427	−	5.29016i	0.159215	−	0.275769i
$369$	−3.97785	−	6.88983i	−0.207078	−	0.358670i
$370$	−5.76663			−0.299793
$371$	−0.913768	+	2.15423i	−0.0474405	+	0.111842i
$372$	0.864474			0.0448209
$373$	14.9828	+	25.9510i	0.775780	+	1.34369i	0.934355	+	0.356344i	$0.115977\pi$
$373$	14.9828	+	25.9510i	0.775780	+	1.34369i	−0.158575	+	0.987347i	$0.550690\pi$
$374$	0.598763	−	1.03709i	0.0309613	−	0.0536265i
$375$	1.53745	−	2.66295i	0.0793938	−	0.137514i
$376$	−1.60828	−	2.78563i	−0.0829408	−	0.143658i
$377$	−8.28763			−0.426835
$378$	18.0399	+	23.9271i	0.927874	+	1.23068i
$379$	19.3330			0.993068			0.496534	−	0.868017i	$-0.334606\pi$
$379$	19.3330			0.993068			0.496534	+	0.868017i	$0.334606\pi$
$380$	−3.65714	−	6.33436i	−0.187607	−	0.324946i
$381$	10.4370	−	18.0775i	0.534706	−	0.926137i
$382$	−0.636464	+	1.10239i	−0.0325643	+	0.0564031i
$383$	5.04615	+	8.74019i	0.257846	+	0.446603i	0.965665	−	0.259791i	$-0.0836538\pi$
$383$	5.04615	+	8.74019i	0.257846	+	0.446603i	−0.707818	+	0.706395i	$0.750320\pi$
$384$	−1.87312			−0.0955875
$385$	2.62595	−	0.323104i	0.133831	−	0.0164669i
$386$	−23.6764			−1.20510
$387$	39.0009	+	67.5515i	1.98253	+	3.43384i
$388$	−7.26424	+	12.5820i	−0.368786	+	0.638756i
$389$	−13.6428	+	23.6300i	−0.691717	+	1.19809i	0.279559	+	0.960129i	$0.409812\pi$
$389$	−13.6428	+	23.6300i	−0.691717	+	1.19809i	−0.971275	+	0.237960i	$0.923521\pi$
$390$	3.38016	+	5.85460i	0.171161	+	0.296459i
$391$	−4.49238			−0.227189
$392$	−20.7314	+	5.18013i	−1.04710	+	0.261636i
$393$	−12.6744			−0.639340
$394$	2.85221	+	4.94018i	0.143692	+	0.248883i
$395$	3.71992	−	6.44309i	0.187169	−	0.324187i
$396$	2.78693	−	4.82710i	0.140048	−	0.242571i
$397$	12.6298	+	21.8754i	0.633870	+	1.09789i	0.986753	+	0.162228i	$0.0518679\pi$
$397$	12.6298	+	21.8754i	0.633870	+	1.09789i	−0.352883	+	0.935667i	$0.614799\pi$
$398$	−11.7512			−0.589037
$399$	−68.3967	+	8.41572i	−3.42412	+	0.421313i
$400$	−1.52742			−0.0763711
$401$	−2.65566	−	4.59974i	−0.132617	−	0.229700i	0.792067	−	0.610434i	$-0.209005\pi$
$401$	−2.65566	−	4.59974i	−0.132617	−	0.229700i	−0.924685	+	0.380734i	$0.875671\pi$
$402$	−17.6312	+	30.5382i	−0.879366	+	1.52311i
$403$	0.335723	−	0.581490i	0.0167236	−	0.0289661i
$404$	6.15359	+	10.6583i	0.306153	+	0.530272i
$405$	−13.3027			−0.661017
$406$	−6.82385	−	9.05077i	−0.338662	−	0.449182i
$407$	5.40922			0.268125
$408$	−5.27208	−	9.13151i	−0.261007	−	0.452077i
$409$	15.0340	−	26.0397i	0.743384	−	1.28758i	−0.207562	−	0.978222i	$-0.566553\pi$
$409$	15.0340	−	26.0397i	0.743384	−	1.28758i	0.950946	−	0.309357i	$-0.100114\pi$
$410$	0.656953	−	1.13788i	0.0324446	−	0.0561957i
$411$	−17.6929	−	30.6450i	−0.872726	−	1.51161i
$412$	14.0387			0.691639
$413$	14.3291	−	33.7811i	0.705089	−	1.66226i
$414$	27.5212			1.35259
$415$	2.10077	+	3.63864i	0.103123	+	0.178614i
$416$	−4.61644	+	7.99591i	−0.226340	+	0.392032i
$417$	1.20421	−	2.08575i	0.0589704	−	0.102140i
$418$	−4.51517	−	7.82050i	−0.220844	−	0.382513i
$419$	12.9969			0.634938			0.317469	−	0.948269i	$-0.397167\pi$
$419$	12.9969			0.634938			0.317469	+	0.948269i	$0.397167\pi$
$420$	2.74318	−	6.46710i	0.133853	−	0.315562i
$421$	−2.56078			−0.124805			−0.0624024	−	0.998051i	$-0.519876\pi$
$421$	−2.56078			−0.124805			−0.0624024	+	0.998051i	$0.519876\pi$
$422$	−2.58145	−	4.47121i	−0.125663	−	0.217655i
$423$	3.40080	−	5.89035i	0.165352	−	0.286399i
$424$	−1.34996	+	2.33820i	−0.0655600	+	0.113553i
$425$	0.561652	+	0.972810i	0.0272441	+	0.0471882i
$426$	26.8371			1.30026
$427$	2.61006	+	3.46183i	0.126309	+	0.167530i
$428$	−7.40898			−0.358127
$429$	−3.17066	−	5.49174i	−0.153081	−	0.265144i
$430$	−6.44111	+	11.1563i	−0.310618	+	0.538006i
$431$	−0.494933	+	0.857249i	−0.0238401	+	0.0412922i	−0.877699	−	0.479212i	$-0.840923\pi$
$431$	−0.494933	+	0.857249i	−0.0238401	+	0.0412922i	0.853859	+	0.520504i	$0.174256\pi$
$432$	8.11368	+	14.0533i	0.390370	+	0.676140i
$433$	32.4815			1.56096			0.780482	−	0.625179i	$-0.214974\pi$
$433$	32.4815			1.56096			0.780482	+	0.625179i	$0.214974\pi$
$434$	0.911461	−	0.112149i	0.0437516	−	0.00538331i
$435$	12.3571			0.592477
$436$	1.78815	+	3.09716i	0.0856368	+	0.148327i
$437$	−16.9381	+	29.3377i	−0.810262	+	1.40341i
$438$	21.2440	−	36.7957i	1.01508	−	1.75817i
$439$	−1.22046	−	2.11390i	−0.0582495	−	0.100891i	0.835430	−	0.549597i	$-0.185219\pi$
$439$	−1.22046	−	2.11390i	−0.0582495	−	0.100891i	−0.893680	+	0.448705i	$0.851885\pi$
$440$	3.05269			0.145531
$441$	−31.4050	−	32.4877i	−1.49548	−	1.54704i
$442$	−2.46963			−0.117468
$443$	−14.8963	−	25.8012i	−0.707746	−	1.22585i	−0.965691	−	0.259692i	$-0.916379\pi$
$443$	−14.8963	−	25.8012i	−0.707746	−	1.22585i	0.257946	−	0.966159i	$-0.416954\pi$
$444$	7.18112	−	12.4381i	0.340801	−	0.590284i
$445$	−7.04583	+	12.2037i	−0.334004	+	0.578512i
$446$	5.73444	+	9.93234i	0.271534	+	0.470310i
$447$	33.7438			1.59603
$448$	−20.5551	+	2.52916i	−0.971138	+	0.119491i
$449$	32.6965			1.54304			0.771521	−	0.636203i	$-0.219496\pi$
$449$	32.6965			1.54304			0.771521	+	0.636203i	$0.219496\pi$
$450$	−3.44079	−	5.95963i	−0.162200	−	0.280939i
$451$	−0.616236	+	1.06735i	−0.0290174	+	0.0502596i
$452$	1.27589	−	2.20990i	0.0600126	−	0.103945i
$453$	14.8001	+	25.6345i	0.695368	+	1.20441i
$454$	4.93003			0.231378
$455$	−3.28477	−	4.35674i	−0.153993	−	0.204247i
$456$	−79.5118			−3.72348
$457$	−6.19525	−	10.7305i	−0.289801	−	0.501951i	0.683961	−	0.729519i	$-0.260256\pi$
$457$	−6.19525	−	10.7305i	−0.289801	−	0.501951i	−0.973762	+	0.227568i	$0.926923\pi$
$458$	0.881649	−	1.52706i	0.0411967	−	0.0713549i
$459$	5.96700	−	10.3352i	0.278516	−	0.482404i
$460$	−1.72665	−	2.99065i	−0.0805055	−	0.139440i
$461$	−36.7587			−1.71202			−0.856011	−	0.516957i	$-0.827065\pi$
$461$	−36.7587			−1.71202			−0.856011	+	0.516957i	$0.827065\pi$
$462$	3.38678	−	7.98439i	0.157567	−	0.371467i
$463$	18.1518			0.843585			0.421793	−	0.906692i	$-0.361401\pi$
$463$	18.1518			0.843585			0.421793	+	0.906692i	$0.361401\pi$
$464$	−3.06911	−	5.31585i	−0.142480	−	0.246782i
$465$	−0.500573	+	0.867017i	−0.0232135	+	0.0402070i
$466$	−1.11421	+	1.92986i	−0.0516146	+	0.0893992i
$467$	−16.8338	−	29.1571i	−0.778977	−	1.34923i	−0.932532	−	0.361088i	$-0.882405\pi$
$467$	−16.8338	−	29.1571i	−0.778977	−	1.34923i	0.153554	−	0.988140i	$-0.450928\pi$
$468$	−11.4948			−0.531349
$469$	11.1137	−	26.2008i	0.513184	−	1.20984i
$470$	1.12330			0.0518142
$471$	29.7529	+	51.5336i	1.37094	+	2.37454i
$472$	21.1692	−	36.6661i	0.974392	−	1.68770i
$473$	6.04190	−	10.4649i	0.277807	−	0.481176i
$474$	−12.1942	−	21.1210i	−0.560098	−	0.970118i
$475$	8.47065			0.388660
$476$	1.54494	+	2.04912i	0.0708121	+	0.0939211i
$477$	−5.70913			−0.261403
$478$	6.98596	+	12.1000i	0.319530	+	0.553443i
$479$	−10.9735	+	19.0067i	−0.501393	+	0.868439i	0.498605	+	0.866829i	$0.333846\pi$
$479$	−10.9735	+	19.0067i	−0.501393	+	0.868439i	−0.999999	+	0.00160973i	$0.999488\pi$
$480$	6.88323	−	11.9221i	0.314175	−	0.544167i
$481$	−5.57765	−	9.66078i	−0.254319	−	0.440494i
$482$	6.31801			0.287778
$483$	−32.2922	+	3.97332i	−1.46935	+	0.180792i
$484$	−0.863486			−0.0392493
$485$	−8.41270	−	14.5712i	−0.382001	−	0.661645i
$486$	−4.81468	+	8.33928i	−0.218398	+	0.378277i
$487$	−9.72600	+	16.8459i	−0.440727	+	0.763362i	−0.997744	−	0.0671397i	$-0.978613\pi$
$487$	−9.72600	+	16.8459i	−0.440727	+	0.763362i	0.557017	+	0.830501i	$0.311946\pi$
$488$	2.50117	+	4.33216i	0.113223	+	0.196108i
$489$	49.5633			2.24133
$490$	2.05330	−	7.17448i	0.0927587	−	0.324110i
$491$	6.22618			0.280984			0.140492	−	0.990082i	$-0.455132\pi$
$491$	6.22618			0.280984			0.140492	+	0.990082i	$0.455132\pi$
$492$	1.63619	+	2.83397i	0.0737653	+	0.127765i
$493$	−2.25710	+	3.90941i	−0.101655	+	0.176071i
$494$	−9.31153	+	16.1280i	−0.418945	+	0.725635i
$495$	3.22753	+	5.59025i	0.145067	+	0.251263i
$496$	0.497306			0.0223297
$497$	−21.4982	+	2.64519i	−0.964325	+	0.118653i
$498$	13.7730			0.617183
$499$	−5.18213	−	8.97571i	−0.231984	−	0.401808i	0.726408	−	0.687264i	$-0.241188\pi$
$499$	−5.18213	−	8.97571i	−0.231984	−	0.401808i	−0.958392	+	0.285456i	$0.907855\pi$
$500$	−0.431743	+	0.747801i	−0.0193081	+	0.0334427i
$501$	14.2561	−	24.6923i	0.636915	−	1.10317i
$502$	−4.32862	−	7.49738i	−0.193196	−	0.334625i
$503$	−4.68935			−0.209088			−0.104544	−	0.994520i	$-0.533338\pi$
$503$	−4.68935			−0.209088			−0.104544	+	0.994520i	$0.533338\pi$
$504$	−31.3864	−	41.6292i	−1.39806	−	1.85431i
$505$	−14.2529			−0.634246
$506$	−2.13175	−	3.69230i	−0.0947679	−	0.164143i
$507$	13.4481	−	23.2929i	0.597253	−	1.03447i
$508$	−2.93089	+	5.07646i	−0.130037	+	0.225231i
$509$	−15.1957	−	26.3196i	−0.673535	−	1.16660i	−0.976895	−	0.213721i	$-0.931442\pi$
$509$	−15.1957	−	26.3196i	−0.673535	−	1.16660i	0.303359	−	0.952876i	$-0.401892\pi$
$510$	3.68228			0.163054
$511$	−13.3910	+	31.5696i	−0.592383	+	1.39656i
$512$	−16.1638			−0.714346
$513$	−44.9962	−	77.9357i	−1.98663	−	3.44094i
$514$	−14.0624	+	24.3567i	−0.620264	+	1.07433i
$515$	−8.12911	+	14.0800i	−0.358212	+	0.620441i
$516$	−16.0421	−	27.7857i	−0.706214	−	1.22320i
$517$	−1.05368			−0.0463409
$518$	5.95784	−	14.0457i	0.261772	−	0.617134i
$519$	−59.1656			−2.59708
$520$	−3.14774	−	5.45205i	−0.138038	−	0.239088i
$521$	−10.1908	+	17.6509i	−0.446466	+	0.773301i	−0.998153	−	0.0607496i	$-0.980651\pi$
$521$	−10.1908	+	17.6509i	−0.446466	+	0.773301i	0.551687	+	0.834051i	$0.313984\pi$
$522$	13.8274	−	23.9498i	0.605211	−	1.04826i
$523$	−1.02964	−	1.78338i	−0.0450229	−	0.0779820i	0.842636	−	0.538484i	$-0.181003\pi$
$523$	−1.02964	−	1.78338i	−0.0450229	−	0.0779820i	−0.887659	+	0.460502i	$0.847669\pi$
$524$	3.55919			0.155484
$525$	4.89769	+	6.49601i	0.213753	+	0.283509i
$526$	−22.1413			−0.965408
$527$	−0.182866	−	0.316733i	−0.00796575	−	0.0137971i
$528$	2.34834	−	4.06745i	0.102198	−	0.177013i
$529$	3.50297	−	6.06733i	0.152303	−	0.263797i
$530$	−0.471440	−	0.816559i	−0.0204781	−	0.0354690i
$531$	89.5268			3.88513
$532$	19.2069	−	2.36327i	0.832726	−	0.102461i
$533$	2.54170			0.110093
$534$	23.0968	+	40.0048i	0.999496	+	1.73118i
$535$	4.29016	−	7.43078i	0.185480	−	0.321260i
$536$	16.4189	−	28.4385i	0.709191	−	1.22835i
$537$	12.8273	+	22.2176i	0.553540	+	0.958759i
$538$	−11.3777			−0.490529
$539$	−1.92604	+	6.72981i	−0.0829604	+	0.289874i
$540$	9.17369			0.394773
$541$	−1.30838	−	2.26618i	−0.0562516	−	0.0974305i	0.836528	−	0.547924i	$-0.184582\pi$
$541$	−1.30838	−	2.26618i	−0.0562516	−	0.0974305i	−0.892780	+	0.450493i	$0.851248\pi$
$542$	2.79504	−	4.84115i	0.120057	−	0.207945i
$543$	29.0781	−	50.3648i	1.24786	−	2.16136i
$544$	2.51453	+	4.35530i	0.107810	+	0.186732i
$545$	−4.14170			−0.177411
$546$	−17.7522	+	2.18428i	−0.759725	+	0.0934786i
$547$	44.6670			1.90982			0.954910	−	0.296894i	$-0.0959507\pi$
$547$	44.6670			1.90982			0.954910	+	0.296894i	$0.0959507\pi$
$548$	4.96846	+	8.60563i	0.212242	+	0.367614i
$549$	−5.28886	+	9.16058i	−0.225723	+	0.390964i
$550$	−0.533037	+	0.923247i	−0.0227288	+	0.0393674i
$551$	17.0204	+	29.4802i	0.725094	+	1.25590i
$552$	−37.5400			−1.59781
$553$	11.8501	+	15.7173i	0.503917	+	0.668367i
$554$	−19.5908			−0.832335
$555$	8.31643	+	14.4045i	0.353013	+	0.611436i
$556$	−0.338162	+	0.585714i	−0.0143413	+	0.0248398i
$557$	−13.8418	+	23.9747i	−0.586497	+	1.01584i	0.408190	+	0.912897i	$0.366160\pi$
$557$	−13.8418	+	23.9747i	−0.586497	+	1.01584i	−0.994687	+	0.102945i	$0.967173\pi$
$558$	1.12027	+	1.94037i	0.0474248	+	0.0821422i
$559$	−24.9201			−1.05401
$560$	1.57807	−	3.72032i	0.0666855	−	0.157212i
$561$	−3.45406			−0.145830
$562$	1.54376	+	2.67386i	0.0651194	+	0.112790i
$563$	8.93166	−	15.4701i	0.376425	−	0.651987i	−0.614114	−	0.789217i	$-0.710487\pi$
$563$	8.93166	−	15.4701i	0.376425	−	0.651987i	0.990539	+	0.137230i	$0.0438200\pi$
$564$	−1.39884	+	2.42286i	−0.0589017	+	0.102021i
$565$	1.47760	+	2.55928i	0.0621631	+	0.107670i
$566$	4.68232			0.196813
$567$	13.7438	−	32.4013i	0.577185	−	1.36073i
$568$	−24.9918			−1.04863
$569$	−13.5471	−	23.4643i	−0.567925	−	0.983675i	−0.996771	−	0.0802974i	$-0.974413\pi$
$569$	−13.5471	−	23.4643i	−0.567925	−	0.983675i	0.428846	−	0.903378i	$-0.358920\pi$
$570$	13.8837	−	24.0473i	0.581526	−	1.00723i
$571$	−16.8092	+	29.1144i	−0.703443	+	1.21840i	0.263808	+	0.964575i	$0.415022\pi$
$571$	−16.8092	+	29.1144i	−0.703443	+	1.21840i	−0.967251	+	0.253824i	$0.918312\pi$
$572$	0.890373	+	1.54217i	0.0372284	+	0.0644814i
$573$	3.67154			0.153381
$574$	2.09278	+	2.77574i	0.0873509	+	0.115857i
$575$	3.99926			0.166781
$576$	−25.2641	−	43.7588i	−1.05267	−	1.82328i
$577$	−0.255512	+	0.442560i	−0.0106371	+	0.0184240i	−0.871295	−	0.490760i	$-0.836719\pi$
$577$	−0.255512	+	0.442560i	−0.0106371	+	0.0184240i	0.860658	+	0.509184i	$0.170053\pi$
$578$	8.38904	−	14.5302i	0.348938	−	0.604378i
$579$	34.1453	+	59.1414i	1.41903	+	2.45783i
$580$	−3.47007			−0.144087
$581$	−11.0330	+	1.35753i	−0.457727	+	0.0563200i
$582$	−55.1550			−2.28625
$583$	0.442221	+	0.765949i	0.0183149	+	0.0317224i
$584$	−19.7833	+	34.2657i	−0.818639	+	1.41792i
$585$	6.65607	−	11.5286i	0.275195	−	0.476651i
$586$	11.2120	+	19.4198i	0.463165	+	0.802226i
$587$	24.8042			1.02378			0.511889	−	0.859052i	$-0.328946\pi$
$587$	24.8042			1.02378			0.511889	+	0.859052i	$0.328946\pi$
$588$	12.9177	+	13.3631i	0.532717	+	0.551084i
$589$	−2.75792			−0.113638
$590$	7.39281	+	12.8047i	0.304357	+	0.527162i
$591$	8.22673	−	14.2491i	0.338402	−	0.586130i
$592$	4.13108	−	7.15524i	0.169786	−	0.294078i
$593$	14.6406	+	25.3583i	0.601219	+	1.04134i	0.992637	+	0.121129i	$0.0386515\pi$
$593$	14.6406	+	25.3583i	0.601219	+	1.04134i	−0.391417	+	0.920213i	$0.628015\pi$
$594$	11.3260			0.464711
$595$	−2.94974	+	0.362944i	−0.120927	+	0.0148792i
$596$	−9.47581			−0.388144
$597$	16.9472	+	29.3535i	0.693604	+	1.20136i
$598$	−4.39626	+	7.61455i	−0.179777	+	0.311382i
$599$	7.91654	−	13.7119i	0.323461	−	0.560251i	−0.657739	−	0.753246i	$-0.728487\pi$
$599$	7.91654	−	13.7119i	0.323461	−	0.560251i	0.981200	+	0.192995i	$0.0618202\pi$
$600$	4.69337	+	8.12916i	0.191606	+	0.331871i
$601$	16.8302			0.686516			0.343258	−	0.939241i	$-0.388469\pi$
$601$	16.8302			0.686516			0.343258	+	0.939241i	$0.388469\pi$
$602$	−20.5187	−	27.2148i	−0.836279	−	1.10919i
$603$	69.4374			2.82771
$604$	−4.15611	−	7.19859i	−0.169110	−	0.292906i
$605$	0.500000	−	0.866025i	0.0203279	−	0.0352089i
$606$	−23.3611	+	40.4626i	−0.948980	+	1.64368i
$607$	−4.86376	−	8.42427i	−0.197414	−	0.341931i	0.750275	−	0.661126i	$-0.229921\pi$
$607$	−4.86376	−	8.42427i	−0.197414	−	0.341931i	−0.947689	+	0.319195i	$0.896588\pi$
$608$	37.9234			1.53800
$609$	−12.7668	+	30.0980i	−0.517338	+	1.21963i
$610$	−1.74694			−0.0707317
$611$	1.08649	+	1.88186i	0.0439548	+	0.0761319i
$612$	−3.13057	+	5.42231i	−0.126546	+	0.219184i
$613$	−5.37652	+	9.31241i	−0.217156	+	0.376125i	−0.953937	−	0.300006i	$-0.903011\pi$
$613$	−5.37652	+	9.31241i	−0.217156	+	0.376125i	0.736782	+	0.676131i	$0.236345\pi$
$614$	−13.2556	−	22.9594i	−0.534953	−	0.926566i
$615$	−3.78974			−0.152817
$616$	−3.15391	+	7.43540i	−0.127075	+	0.299581i
$617$	−18.5288			−0.745942			−0.372971	−	0.927843i	$-0.621661\pi$
$617$	−18.5288			−0.745942			−0.372971	+	0.927843i	$0.621661\pi$
$618$	26.6479	+	46.1555i	1.07194	+	1.85665i
$619$	12.2292	−	21.1817i	0.491535	−	0.851364i	−0.508417	−	0.861111i	$-0.669769\pi$
$619$	12.2292	−	21.1817i	0.491535	−	0.851364i	0.999952	+	0.00974711i	$0.00310265\pi$
$620$	0.140569	−	0.243473i	0.00564539	−	0.00977810i
$621$	−21.2441	−	36.7959i	−0.852496	−	1.47657i
$622$	−25.9572			−1.04079
$623$	−22.4450	−	29.7698i	−0.899242	−	1.19270i
$624$	−9.68586			−0.387745
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.612469	+	1.06083i	−0.0244792	+	0.0423992i
$627$	−13.0232	+	22.5569i	−0.520098	+	0.900836i
$628$	−8.35512	−	14.4715i	−0.333405	−	0.577475i
$629$	−6.07620			−0.242274
$630$	18.0707	−	2.22347i	0.719953	−	0.0885850i
$631$	−38.3589			−1.52704			−0.763522	−	0.645782i	$-0.776532\pi$
$631$	−38.3589			−1.52704			−0.763522	+	0.645782i	$0.776532\pi$
$632$	11.3557	+	19.6687i	0.451707	+	0.782380i
$633$	−7.44576	+	12.8964i	−0.295942	+	0.512587i
$634$	−10.3168	+	17.8692i	−0.409731	+	0.709675i
$635$	−3.39426	−	5.87903i	−0.134697	−	0.233302i
$636$	2.34832			0.0931168
$637$	14.0053	−	3.49949i	0.554912	−	0.138655i
$638$	−4.28421			−0.169614
$639$	−26.4233	−	45.7664i	−1.04529	−	1.81049i
$640$	−0.304582	+	0.527552i	−0.0120397	+	0.0208533i
$641$	16.0912	−	27.8707i	0.635563	−	1.10083i	−0.350832	−	0.936438i	$-0.614101\pi$
$641$	16.0912	−	27.8707i	0.635563	−	1.10083i	0.986396	−	0.164389i	$-0.0525654\pi$
$642$	−14.0635	−	24.3587i	−0.555042	−	0.961361i
$643$	−12.1417			−0.478821			−0.239410	−	0.970918i	$-0.576954\pi$
$643$	−12.1417			−0.478821			−0.239410	+	0.970918i	$0.576954\pi$
$644$	9.06819	−	1.11577i	0.357337	−	0.0439677i
$645$	37.1566			1.46304
$646$	5.07191	+	8.78480i	0.199552	+	0.345634i
$647$	−11.1058	+	19.2358i	−0.436615	+	0.756239i	−0.997426	−	0.0717050i	$-0.977156\pi$
$647$	−11.1058	+	19.2358i	−0.436615	+	0.756239i	0.560811	+	0.827944i	$0.310489\pi$
$648$	20.3045	−	35.1684i	0.797636	−	1.38155i
$649$	−6.93461	−	12.0111i	−0.272207	−	0.471477i
$650$	2.19854			0.0862338
$651$	−1.59461	−	2.11501i	−0.0624979	−	0.0828936i
$652$	−13.9182			−0.545079
$653$	−20.8939	−	36.1892i	−0.817640	−	1.41619i	−0.907417	−	0.420232i	$-0.861949\pi$
$653$	−20.8939	−	36.1892i	−0.817640	−	1.41619i	0.0897767	−	0.995962i	$-0.471385\pi$
$654$	−6.78841	+	11.7579i	−0.265448	+	0.459769i
$655$	−2.06094	+	3.56966i	−0.0805277	+	0.139478i
$656$	0.941252	+	1.63030i	0.0367497	+	0.0636524i
$657$	−83.6657			−3.26411
$658$	−1.16055	+	2.73602i	−0.0452430	+	0.106661i
$659$	−11.0308			−0.429700			−0.214850	−	0.976647i	$-0.568926\pi$
$659$	−11.0308			−0.429700			−0.214850	+	0.976647i	$0.568926\pi$
$660$	−1.32757	−	2.29942i	−0.0516756	−	0.0895048i
$661$	−20.3416	+	35.2327i	−0.791196	+	1.37039i	0.134030	+	0.990977i	$0.457208\pi$
$661$	−20.3416	+	35.2327i	−0.791196	+	1.37039i	−0.925227	+	0.379415i	$0.876125\pi$
$662$	1.73756	−	3.00954i	0.0675322	−	0.116969i
$663$	3.56161	+	6.16889i	0.138322	+	0.239580i
$664$	−12.8260			−0.497745
$665$	−8.75152	+	20.6319i	−0.339369	+	0.800070i
$666$	37.2240			1.44240
$667$	8.03587	+	13.9185i	0.311150	+	0.538928i
$668$	−4.00335	+	6.93400i	−0.154894	+	0.268285i
$669$	16.5400	−	28.6482i	0.639474	−	1.10760i
$670$	5.73390	+	9.93141i	0.221520	+	0.383684i
$671$	1.63867			0.0632601
$672$	21.9271	+	29.0828i	0.845856	+	1.12190i
$673$	−9.01027			−0.347320			−0.173660	−	0.984806i	$-0.555559\pi$
$673$	−9.01027			−0.347320			−0.173660	+	0.984806i	$0.555559\pi$
$674$	0.230000	+	0.398371i	0.00885925	+	0.0153447i
$675$	−5.31201	+	9.20067i	−0.204459	+	0.354134i
$676$	−3.77646	+	6.54102i	−0.145249	+	0.251578i
$677$	24.3179	+	42.1198i	0.934612	+	1.61880i	0.775325	+	0.631563i	$0.217586\pi$
$677$	24.3179	+	42.1198i	0.934612	+	1.61880i	0.159287	+	0.987232i	$0.449080\pi$
$678$	9.68738			0.372042
$679$	44.1826	−	5.43635i	1.69557	−	0.208628i
$680$	−3.42910			−0.131500
$681$	−7.10992	−	12.3147i	−0.272453	−	0.471902i
$682$	0.173549	−	0.300596i	0.00664554	−	0.0115104i
$683$	5.24405	−	9.08296i	0.200658	−	0.347550i	−0.748083	−	0.663606i	$-0.769025\pi$
$683$	5.24405	−	9.08296i	0.200658	−	0.347550i	0.948741	+	0.316056i	$0.102359\pi$
$684$	23.6071	+	40.8887i	0.902640	+	1.56342i
$685$	−11.5079			−0.439695
$686$	15.3534	+	12.4136i	0.586196	+	0.473952i
$687$	−5.08593			−0.194040
$688$	−9.22853	−	15.9843i	−0.351834	−	0.609395i
$689$	0.911982	−	1.57960i	0.0347437	−	0.0601779i
$690$	6.55495	−	11.3535i	0.249543	−	0.432220i
$691$	−11.2768	−	19.5320i	−0.428989	−	0.743031i	0.567795	−	0.823170i	$-0.307797\pi$
$691$	−11.2768	−	19.5320i	−0.428989	−	0.743031i	−0.996784	+	0.0801393i	$0.974463\pi$
$692$	16.6147			0.631595
$693$	−16.9507	+	2.08566i	−0.643903	+	0.0792276i
$694$	−2.76647			−0.105014
$695$	−0.391625	−	0.678314i	−0.0148552	−	0.0257299i
$696$	−18.8612	+	32.6685i	−0.714930	+	1.23830i
$697$	0.692220	−	1.19896i	0.0262197	−	0.0454139i
$698$	6.28686	+	10.8892i	0.237961	+	0.412161i
$699$	6.42748			0.243110
$700$	−1.37535	−	1.82419i	−0.0519834	−	0.0689478i
$701$	−25.9143			−0.978769			−0.489385	−	0.872068i	$-0.662779\pi$
$701$	−25.9143			−0.978769			−0.489385	+	0.872068i	$0.662779\pi$
$702$	−11.6787	−	20.2280i	−0.440783	−	0.763458i
$703$	−22.9098	+	39.6809i	−0.864060	+	1.49660i
$704$	−3.91385	+	6.77898i	−0.147509	+	0.255492i
$705$	−1.61999	−	2.80590i	−0.0610123	−	0.105676i
$706$	−2.21002			−0.0831751
$707$	14.7255	−	34.7157i	0.553810	−	1.30562i
$708$	−36.8247			−1.38396
$709$	26.0328	+	45.0901i	0.977682	+	1.69340i	0.670783	+	0.741653i	$0.265958\pi$
$709$	26.0328	+	45.0901i	0.977682	+	1.69340i	0.306899	+	0.951742i	$0.400709\pi$
$710$	4.36388	−	7.55846i	0.163774	−	0.283664i
$711$	−24.0123	+	41.5906i	−0.900532	+	1.55977i
$712$	−21.5087	−	37.2542i	−0.806073	−	1.39616i
$713$	−1.30210			−0.0487640
$714$	−3.80438	+	8.96890i	−0.142375	+	0.335653i
$715$	−2.06228			−0.0771248
$716$	−3.60212	−	6.23906i	−0.134618	−	0.233165i
$717$	20.1498	−	34.9005i	0.752509	−	1.30338i
$718$	16.1380	−	27.9519i	0.602266	−	1.04316i
$719$	−16.5697	−	28.6995i	−0.617944	−	1.07031i	−0.989860	−	0.142044i	$-0.954633\pi$
$719$	−16.5697	−	28.6995i	−0.617944	−	1.07031i	0.371917	−	0.928266i	$-0.378701\pi$
$720$	9.85961			0.367446
$721$	−25.8959	−	34.3469i	−0.964415	−	1.27915i
$722$	56.2374			2.09294
$723$	−9.11162	−	15.7818i	−0.338865	−	0.586931i
$724$	−8.16562	+	14.1433i	−0.303473	+	0.525631i
$725$	2.00934	−	3.48028i	0.0746250	−	0.129254i
$726$	−1.63904	−	2.83890i	−0.0608305	−	0.105362i
$727$	2.62195			0.0972428			0.0486214	−	0.998817i	$-0.484517\pi$
$727$	2.62195			0.0972428			0.0486214	+	0.998817i	$0.484517\pi$
$728$	16.5316	−	2.03410i	0.612703	−	0.0753886i
$729$	−12.1339			−0.449402
$730$	−6.90882	−	11.9664i	−0.255707	−	0.442897i
$731$	−6.78689	+	11.7552i	−0.251022	+	0.434783i
$732$	2.17545	−	3.76799i	0.0804069	−	0.139269i
$733$	6.86540	+	11.8912i	0.253579	+	0.439212i	0.964509	−	0.264051i	$-0.0850588\pi$
$733$	6.86540	+	11.8912i	0.253579	+	0.439212i	−0.710929	+	0.703263i	$0.751725\pi$
$734$	8.57072			0.316351
$735$	−20.8824	+	5.21784i	−0.770257	+	0.192463i
$736$	17.9048			0.659980
$737$	−5.37852	−	9.31587i	−0.198120	−	0.343155i
$738$	−4.24068	+	7.34507i	−0.156102	+	0.270376i
$739$	−2.27029	+	3.93225i	−0.0835138	+	0.144650i	−0.904757	−	0.425928i	$-0.859948\pi$
$739$	−2.27029	+	3.93225i	−0.0835138	+	0.144650i	0.821243	+	0.570578i	$0.193281\pi$
$740$	−2.33539	−	4.04502i	−0.0858507	−	0.148698i
$741$	53.7150			1.97327
$742$	2.47596	−	0.304648i	0.0908952	−	0.0111840i
$743$	23.7757			0.872245			0.436123	−	0.899887i	$-0.356351\pi$
$743$	23.7757			0.872245			0.436123	+	0.899887i	$0.356351\pi$
$744$	−1.52809	−	2.64673i	−0.0560226	−	0.0970339i
$745$	5.48695	−	9.50368i	0.201026	−	0.348188i
$746$	15.9728	−	27.6657i	0.584805	−	1.01291i
$747$	−13.5606	−	23.4877i	−0.496157	−	0.859370i
$748$	0.969957			0.0354651
$749$	13.6667	+	18.1267i	0.499369	+	0.662334i
$750$	−3.27808			−0.119699
$751$	−17.6055	−	30.4935i	−0.642432	−	1.11273i	−0.984888	−	0.173191i	$-0.944592\pi$
$751$	−17.6055	−	30.4935i	−0.642432	−	1.11273i	0.342456	−	0.939534i	$-0.388741\pi$
$752$	−0.804709	+	1.39380i	−0.0293447	+	0.0508265i
$753$	−12.4852	+	21.6249i	−0.454984	+	0.788056i
$754$	4.41761	+	7.65153i	0.160880	+	0.278652i
$755$	9.62635			0.350339
$756$	−9.47787	+	22.3443i	−0.344707	+	0.812653i
$757$	5.66097			0.205752			0.102876	−	0.994694i	$-0.467196\pi$
$757$	5.66097			0.205752			0.102876	+	0.994694i	$0.467196\pi$
$758$	−10.3052	−	17.8491i	−0.374301	−	0.648309i
$759$	−6.14868	+	10.6498i	−0.223183	+	0.386564i
$760$	−12.9291	+	22.3939i	−0.468989	+	0.812312i
$761$	7.78513	+	13.4842i	0.282211	+	0.488803i	0.971929	−	0.235274i	$-0.0755989\pi$
$761$	7.78513	+	13.4842i	0.282211	+	0.488803i	−0.689718	+	0.724078i	$0.742266\pi$
$762$	−22.2533			−0.806152
$763$	4.27903	−	10.0879i	0.154911	−	0.365206i
$764$	−1.03103			−0.0373014
$765$	−3.62550	−	6.27955i	−0.131080	−	0.227038i
$766$	5.37957	−	9.31770i	0.194372	−	0.336662i
$767$	−14.3011	+	24.7702i	−0.516382	+	0.894400i
$768$	25.0679	+	43.4189i	0.904559	+	1.56674i
$769$	−11.4329			−0.412281			−0.206140	−	0.978522i	$-0.566090\pi$
$769$	−11.4329			−0.412281			−0.206140	+	0.978522i	$0.566090\pi$
$770$	−1.69803	−	2.25217i	−0.0611928	−	0.0811627i
$771$	81.1209			2.92150
$772$	−9.58857	−	16.6079i	−0.345100	−	0.597731i
$773$	−4.16584	+	7.21545i	−0.149835	+	0.259522i	−0.931166	−	0.364595i	$-0.881208\pi$
$773$	−4.16584	+	7.21545i	−0.149835	+	0.259522i	0.781331	+	0.624116i	$0.214541\pi$
$774$	41.5778	−	72.0149i	1.49448	−	2.58852i
$775$	0.162793	+	0.281965i	0.00584768	+	0.0101285i
$776$	51.3627			1.84381
$777$	−43.6770	+	5.37414i	−1.56690	+	0.192796i
$778$	29.0884			1.04287
$779$	−5.21992	−	9.04116i	−0.187023	−	0.323933i
$780$	−2.73782	+	4.74204i	−0.0980296	+	0.169792i
$781$	−4.09341	+	7.09000i	−0.146474	+	0.253700i
$782$	2.39461	+	4.14758i	0.0856309	+	0.148317i
$783$	−42.6946			−1.52578
$784$	7.43116	+	7.68737i	0.265399	+	0.274549i
$785$	19.3521			0.690705
$786$	6.75594	+	11.7016i	0.240976	+	0.417384i
$787$	10.1759	−	17.6252i	0.362731	−	0.628269i	−0.625678	−	0.780082i	$-0.715178\pi$
$787$	10.1759	−	17.6252i	0.362731	−	0.628269i	0.988409	+	0.151812i	$0.0485109\pi$
$788$	−2.31020	+	4.00139i	−0.0822975	+	0.142543i
$789$	31.9315	+	55.3069i	1.13679	+	1.96898i
$790$	−7.93142			−0.282187
$791$	−7.76020	+	0.954836i	−0.275921	+	0.0339501i
$792$	−19.7053			−0.700198
$793$	−1.68969	−	2.92664i	−0.0600028	−	0.103928i
$794$	13.4643	−	23.3208i	0.477829	−	0.827624i
$795$	−1.35979	+	2.35522i	−0.0482268	+	0.0835312i
$796$	−4.75907	−	8.24294i	−0.168681	−	0.292163i
$797$	−11.4434			−0.405345			−0.202672	−	0.979247i	$-0.564963\pi$
$797$	−11.4434			−0.405345			−0.202672	+	0.979247i	$0.564963\pi$
$798$	44.2278	+	58.6612i	1.56565	+	2.07658i
$799$	1.18361			0.0418730
$800$	−2.23852	−	3.87722i	−0.0791435	−	0.137081i
$801$	45.4813	−	78.7759i	1.60700	−	2.78341i
$802$	−2.83113	+	4.90367i	−0.0999708	+	0.173154i
$803$	6.48062	+	11.2248i	0.228696	+	0.396113i
$804$	−28.5615			−1.00728
$805$	−4.13186	+	9.74095i	−0.145629	+	0.343323i
$806$	−0.715812			−0.0252134
$807$	16.4086	+	28.4205i	0.577609	+	1.00045i
$808$	21.7548	−	37.6805i	0.765333	−	1.32560i
$809$	20.6469	−	35.7616i	0.725908	−	1.25731i	−0.232691	−	0.972551i	$-0.574753\pi$
$809$	20.6469	−	35.7616i	0.725908	−	1.25731i	0.958599	−	0.284759i	$-0.0919134\pi$
$810$	7.09084	+	12.2817i	0.249147	+	0.431535i
$811$	−7.63142			−0.267976			−0.133988	−	0.990983i	$-0.542778\pi$
$811$	−7.63142			−0.267976			−0.133988	+	0.990983i	$0.542778\pi$
$812$	3.58513	−	8.45202i	0.125814	−	0.296608i
$813$	−16.1236			−0.565480
$814$	−2.88332	−	4.99405i	−0.101060	−	0.175041i
$815$	8.05931	−	13.9591i	0.282305	−	0.488967i
$816$	−2.63790	+	4.56898i	−0.0923450	+	0.159946i
$817$	51.1788	+	88.6443i	1.79052	+	3.10127i
$818$	−32.0547			−1.12077
$819$	21.2034	+	28.1230i	0.740908	+	0.982698i
$820$	1.06422			0.0371642
$821$	−27.7710	−	48.1008i	−0.969216	−	1.67873i	−0.697835	−	0.716259i	$-0.745853\pi$
$821$	−27.7710	−	48.1008i	−0.969216	−	1.67873i	−0.271381	−	0.962472i	$-0.587480\pi$
$822$	−18.8619	+	32.6698i	−0.657886	+	1.13949i
$823$	2.22654	−	3.85648i	0.0776122	−	0.134428i	−0.824607	−	0.565706i	$-0.808604\pi$
$823$	2.22654	−	3.85648i	0.0776122	−	0.134428i	0.902219	+	0.431278i	$0.141937\pi$
$824$	−24.8156	−	42.9820i	−0.864494	−	1.49735i
$825$	3.07491			0.107055
$826$	−38.8263	+	4.77729i	−1.35094	+	0.166223i
$827$	−3.60111			−0.125223			−0.0626114	−	0.998038i	$-0.519943\pi$
$827$	−3.60111			−0.125223			−0.0626114	+	0.998038i	$0.519943\pi$
$828$	11.1456	+	19.3048i	0.387338	+	0.670889i
$829$	8.04361	−	13.9319i	0.279366	−	0.483876i	−0.691861	−	0.722030i	$-0.743209\pi$
$829$	8.04361	−	13.9319i	0.279366	−	0.483876i	0.971227	+	0.238154i	$0.0765424\pi$
$830$	2.23958	−	3.87906i	0.0777369	−	0.134644i
$831$	28.2532	+	48.9360i	0.980093	+	1.69757i
$832$	16.1429			0.559653
$833$	2.16353	−	7.55963i	0.0749618	−	0.261926i
$834$	−2.56755			−0.0889071
$835$	−4.63626	−	8.03025i	−0.160445	−	0.277898i
$836$	3.65714	−	6.33436i	0.126485	−	0.219078i
$837$	1.72951	−	2.99560i	0.0597807	−	0.103543i
$838$	−6.92781	−	11.9993i	−0.239317	−	0.414509i
$839$	−14.6263			−0.504956			−0.252478	−	0.967603i	$-0.581246\pi$
$839$	−14.6263			−0.504956			−0.252478	+	0.967603i	$0.581246\pi$
$840$	−24.6491	+	3.03289i	−0.850475	+	0.104645i
$841$	−12.8502			−0.443110
$842$	1.36499	+	2.36423i	0.0470407	+	0.0814768i
$843$	4.45270	−	7.71230i	0.153359	−	0.265626i
$844$	2.09089	−	3.62153i	0.0719715	−	0.124658i
$845$	−4.37351	−	7.57514i	−0.150453	−	0.260593i
$846$	−7.25101			−0.249295
$847$	1.59279	+	2.11259i	0.0547289	+	0.0725893i
$848$	1.35092			0.0463906
$849$	−6.75268	−	11.6960i	−0.231751	−	0.401405i
$850$	0.598763	−	1.03709i	0.0205374	−	0.0355718i
$851$	−10.8164	+	18.7346i	−0.370782	+	0.642214i
$852$	10.8686	+	18.8249i	0.372351	+	0.644932i
$853$	−44.9908			−1.54046			−0.770228	−	0.637769i	$-0.779857\pi$
$853$	−44.9908			−1.54046			−0.770228	+	0.637769i	$0.779857\pi$
$854$	1.80487	−	4.25501i	0.0617613	−	0.145603i
$855$	−54.6786			−1.86997
$856$	13.0965	+	22.6838i	0.447630	+	0.775318i
$857$	19.4907	−	33.7588i	0.665789	−	1.15318i	−0.313282	−	0.949660i	$-0.601429\pi$
$857$	19.4907	−	33.7588i	0.665789	−	1.15318i	0.979071	−	0.203520i	$-0.0652380\pi$
$858$	−3.38016	+	5.85460i	−0.115397	+	0.199873i
$859$	−13.7589	−	23.8312i	−0.469449	−	0.813109i	0.529941	−	0.848034i	$-0.322214\pi$
$859$	−13.7589	−	23.8312i	−0.469449	−	0.813109i	−0.999390	+	0.0349252i	$0.988881\pi$
$860$	−10.4342			−0.355803
$861$	3.91540	−	9.23063i	0.133436	−	0.314579i
$862$	1.05527			0.0359427
$863$	10.8383	+	18.7725i	0.368941	+	0.639025i	0.989400	−	0.145214i	$-0.0463870\pi$
$863$	10.8383	+	18.7725i	0.368941	+	0.639025i	−0.620459	+	0.784239i	$0.713054\pi$
$864$	−23.7820	+	41.1917i	−0.809082	+	1.40137i
$865$	−9.62070	+	16.6635i	−0.327114	+	0.566578i
$866$	−17.3139	−	29.9885i	−0.588349	−	1.01905i
$867$	−48.3935			−1.64353
$868$	0.447794	+	0.593929i	0.0151991	+	0.0201592i
$869$	7.43983			0.252379
$870$	−6.58678	−	11.4086i	−0.223313	−	0.386789i
$871$	−11.0920	+	19.2119i	−0.375838	+	0.650970i
$872$	6.32165	−	10.9494i	0.214078	−	0.370794i
$873$	54.3045	+	94.0582i	1.83793	+	3.18339i
$874$	36.1146			1.22160
$875$	2.62595	−	0.323104i	0.0887733	−	0.0109229i
$876$	34.4139			1.16274
$877$	10.5589	+	18.2885i	0.356549	+	0.617560i	0.987382	−	0.158358i	$-0.0506201\pi$
$877$	10.5589	+	18.2885i	0.356549	+	0.617560i	−0.630833	+	0.775918i	$0.717287\pi$
$878$	−1.30110	+	2.25358i	−0.0439101	+	0.0760546i
$879$	32.3392	−	56.0132i	1.09078	−	1.88928i
$880$	−0.763711	−	1.32279i	−0.0257447	−	0.0445911i
$881$	12.4701			0.420128			0.210064	−	0.977688i	$-0.432633\pi$
$881$	12.4701			0.420128			0.210064	+	0.977688i	$0.432633\pi$
$882$	−13.2542	+	46.3118i	−0.446292	+	1.55940i
$883$	29.8363			1.00407			0.502035	−	0.864847i	$-0.332585\pi$
$883$	29.8363			1.00407			0.502035	+	0.864847i	$0.332585\pi$
$884$	−1.00016	−	1.73233i	−0.0336390	−	0.0582645i
$885$	21.3233	−	36.9330i	0.716775	−	1.24149i
$886$	−15.8806	+	27.5060i	−0.533519	+	0.924082i
$887$	−14.2285	−	24.6446i	−0.477748	−	0.827483i	0.521927	−	0.852990i	$-0.325213\pi$
$887$	−14.2285	−	24.6446i	−0.477748	−	0.827483i	−0.999675	+	0.0255070i	$0.991880\pi$
$888$	−50.7749			−1.70390
$889$	17.8263	−	2.19340i	0.597875	−	0.0735641i
$890$	15.0227			0.503564
$891$	−6.65135	−	11.5205i	−0.222829	−	0.385951i
$892$	−4.64471	+	8.04488i	−0.155516	+	0.269362i
$893$	4.46269	−	7.72960i	0.149338	−	0.258661i
$894$	−17.9867	−	31.1538i	−0.601565	−	1.04194i
$895$	8.34322			0.278883
$896$	−0.970271	−	1.28691i	−0.0324145	−	0.0429927i
$897$	25.3605			0.846764
$898$	−17.4284	−	30.1869i	−0.581595	−	1.00735i
$899$	−0.654212	+	1.13313i	−0.0218192	+	0.0377919i
$900$	2.78693	−	4.82710i	0.0928977	−	0.160903i
$901$	−0.496749	−	0.860394i	−0.0165491	−	0.0286639i
$902$	1.31391			0.0437483
$903$	−38.3886	+	90.5019i	−1.27749	+	3.01172i
$904$	−9.02130			−0.300044
$905$	−9.45658	−	16.3793i	−0.314347	−	0.544466i
$906$	15.7780	−	27.3283i	0.524188	−	0.907921i
$907$	5.46525	−	9.46609i	0.181471	−	0.314316i	−0.760911	−	0.648856i	$-0.775248\pi$
$907$	5.46525	−	9.46609i	0.181471	−	0.314316i	0.942382	+	0.334540i	$0.108581\pi$
$908$	1.99658	+	3.45818i	0.0662589	+	0.114764i
$909$	92.0035			3.05156
$910$	−2.27144	+	5.35496i	−0.0752975	+	0.177515i
$911$	4.19124			0.138862			0.0694310	−	0.997587i	$-0.477882\pi$
$911$	4.19124			0.138862			0.0694310	+	0.997587i	$0.477882\pi$
$912$	19.8920	+	34.4539i	0.658689	+	1.14088i
$913$	−2.10077	+	3.63864i	−0.0695254	+	0.120422i
$914$	−6.60459	+	11.4395i	−0.218461	+	0.378385i
$915$	2.51938	+	4.36369i	0.0832881	+	0.144259i
$916$	1.42821			0.0471895
$917$	−6.56530	−	8.70784i	−0.216805	−	0.287558i
$918$	−12.7225			−0.419906
$919$	−14.9232	−	25.8478i	−0.492272	−	0.852641i	0.507688	−	0.861541i	$-0.330500\pi$
$919$	−14.9232	−	25.8478i	−0.492272	−	0.852641i	−0.999960	+	0.00890030i	$0.997167\pi$
$920$	−6.10424	+	10.5729i	−0.201251	+	0.348577i
$921$	−38.2336	+	66.2225i	−1.25984	+	2.18210i
$922$	19.5937	+	33.9374i	0.645286	+	1.11767i
$923$	16.8835			0.555727
$924$	6.97226	−	0.857886i	0.229371	−	0.0282224i
$925$	5.40922			0.177854
$926$	−9.67558	−	16.7586i	−0.317959	−	0.550721i
$927$	52.4740	−	90.8876i	1.72347	−	2.98514i
$928$	8.99588	−	15.5813i	0.295304	−	0.511482i
$929$	8.32722	+	14.4232i	0.273207	+	0.473209i	0.969681	−	0.244373i	$-0.0785822\pi$
$929$	8.32722	+	14.4232i	0.273207	+	0.473209i	−0.696474	+	0.717582i	$0.745249\pi$
$930$	1.06730			0.0349980
$931$	−41.2111	−	42.6320i	−1.35064	−	1.39721i
$932$	−1.80494			−0.0591229
$933$	37.4346	+	64.8386i	1.22555	+	2.12272i
$934$	−17.9461	+	31.0836i	−0.587215	+	1.01709i
$935$	−0.561652	+	0.972810i	−0.0183680	+	0.0318143i
$936$	20.3189	+	35.1934i	0.664144	+	1.15033i
$937$	8.35998			0.273109			0.136554	−	0.990633i	$-0.456397\pi$
$937$	8.35998			0.273109			0.136554	+	0.990633i	$0.456397\pi$
$938$	−30.1139	+	3.70529i	−0.983253	+	0.120982i
$939$	3.53313			0.115299
$940$	0.454920	+	0.787944i	0.0148379	+	0.0256999i
$941$	−10.6580	+	18.4601i	−0.347440	+	0.601784i	−0.985794	−	0.167959i	$-0.946282\pi$
$941$	−10.6580	+	18.4601i	−0.347440	+	0.601784i	0.638354	+	0.769743i	$0.279616\pi$
$942$	31.7188	−	54.9386i	1.03346	−	1.79000i
$943$	−2.46449	−	4.26861i	−0.0802547	−	0.139005i
$944$	−21.1841			−0.689485
$945$	−16.9218	−	22.4442i	−0.550468	−	0.730109i
$946$	−12.8822			−0.418837
$947$	6.34435	+	10.9887i	0.206164	+	0.357086i	0.950503	−	0.310716i	$-0.100569\pi$
$947$	6.34435	+	10.9887i	0.206164	+	0.357086i	−0.744339	+	0.667802i	$0.767235\pi$
$948$	9.87690	−	17.1073i	0.320787	−	0.555619i
$949$	13.3648	−	23.1486i	0.433841	−	0.751434i
$950$	−4.51517	−	7.82050i	−0.146491	−	0.253731i
$951$	59.5139			1.92987
$952$	3.54280	−	8.35222i	0.114823	−	0.270697i
$953$	−38.6944			−1.25343			−0.626717	−	0.779247i	$-0.715602\pi$
$953$	−38.6944			−1.25343			−0.626717	+	0.779247i	$0.715602\pi$
$954$	3.04318	+	5.27094i	0.0985266	+	0.170653i
$955$	0.597017	−	1.03406i	0.0193190	−	0.0334615i
$956$	−5.65840	+	9.80064i	−0.183006	+	0.316975i
$957$	6.17854	+	10.7015i	0.199724	+	0.345932i
$958$	23.3972			0.755929
$959$	11.8895	−	28.0297i	0.383932	−	0.905127i
$960$	−24.0694			−0.776838
$961$	15.4470	+	26.7550i	0.498290	+	0.863064i
$962$	−5.94619	+	10.2991i	−0.191713	+	0.332057i
$963$	−27.6933	+	47.9662i	−0.892404	+	1.54569i
$964$	2.55869	+	4.43179i	0.0824100	+	0.142738i
$965$	22.2090			0.714933
$966$	20.8813	+	27.6958i	0.671845	+	0.891097i
$967$	−13.1619			−0.423259			−0.211630	−	0.977350i	$-0.567877\pi$
$967$	−13.1619			−0.423259			−0.211630	+	0.977350i	$0.567877\pi$
$968$	1.52634	+	2.64371i	0.0490586	+	0.0849719i
$969$	14.6291	−	25.3383i	0.469953	−	0.813983i
$970$	−8.96856	+	15.5340i	−0.287963	+	0.498767i
$971$	17.7976	+	30.8264i	0.571153	+	0.989266i	0.996448	+	0.0842114i	$0.0268371\pi$
$971$	17.7976	+	30.8264i	0.571153	+	0.989266i	−0.425295	+	0.905055i	$0.639830\pi$
$972$	−7.79948			−0.250168
$973$	2.05677	−	0.253071i	0.0659371	−	0.00811307i
$974$	20.7373			0.664465
$975$	−3.17066	−	5.49174i	−0.101542	−	0.175876i
$976$	1.25147	−	2.16761i	0.0400585	−	0.0693834i
$977$	9.60016	−	16.6280i	0.307136	−	0.531976i	−0.670598	−	0.741821i	$-0.733963\pi$
$977$	9.60016	−	16.6280i	0.307136	−	0.531976i	0.977735	+	0.209845i	$0.0672959\pi$
$978$	−26.4191	−	45.7592i	−0.844789	−	1.46322i
$979$	−14.0917			−0.450371
$980$	5.86411	−	1.46526i	0.187322	−	0.0468059i
$981$	26.7349			0.853581
$982$	−3.31879	−	5.74831i	−0.105907	−	0.183436i
$983$	16.4478	−	28.4884i	0.524603	−	0.908639i	−0.474987	−	0.879993i	$-0.657547\pi$
$983$	16.4478	−	28.4884i	0.524603	−	0.908639i	0.999590	−	0.0286461i	$-0.00911958\pi$
$984$	5.78445	−	10.0190i	0.184401	−	0.319393i
$985$	−2.67544	−	4.63399i	−0.0852465	−	0.147651i
$986$	4.81247			0.153260
$987$	8.50802	−	1.04685i	0.270813	−	0.0333216i
$988$	−15.0841			−0.479888
$989$	24.1631	+	41.8517i	0.768342	+	1.33081i
$990$	3.44079	−	5.95963i	0.109356	−	0.189409i
$991$	9.98802	−	17.2998i	0.317280	−	0.549545i	−0.662640	−	0.748939i	$-0.730564\pi$
$991$	9.98802	−	17.2998i	0.317280	−	0.549545i	0.979920	+	0.199393i	$0.0638972\pi$
$992$	0.728828	+	1.26237i	0.0231403	+	0.0400802i
$993$	−10.0234			−0.318083
$994$	13.9015	+	18.4381i	0.440929	+	0.584823i
$995$	11.0229			0.349450
$996$	5.57784	+	9.66111i	0.176741	+	0.306124i
$997$	2.02065	−	3.49986i	0.0639945	−	0.110842i	−0.832253	−	0.554396i	$-0.812949\pi$
$997$	2.02065	−	3.49986i	0.0639945	−	0.110842i	0.896248	+	0.443554i	$0.146283\pi$
$998$	−5.52454	+	9.56878i	−0.174876	+	0.302894i
$999$	−28.7338	−	49.7685i	−0.909099	−	1.57460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	385.2.i.d.221.5	✓	20
7.2	even	3	inner	385.2.i.d.331.5	yes	20
7.3	odd	6		2695.2.a.z.1.6		10
7.4	even	3		2695.2.a.y.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.i.d.221.5	✓	20	1.1	even	1	trivial
385.2.i.d.331.5	yes	20	7.2	even	3	inner
2695.2.a.y.1.6		10	7.4	even	3
2695.2.a.z.1.6		10	7.3	odd	6

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:	\( N \)	\(=\)	\( 385 = 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	385.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.533037 - 0.923247i) q^{2} +(-1.53745 + 2.66295i) q^{3} +(0.431743 - 0.747801i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.27808 q^{6} +(-2.62595 + 0.323104i) q^{7} -3.05269 q^{8} +(-3.22753 - 5.59025i) q^{9} +O(q^{10})\)	\(q+(-0.533037 - 0.923247i) q^{2} +(-1.53745 + 2.66295i) q^{3} +(0.431743 - 0.747801i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.27808 q^{6} +(-2.62595 + 0.323104i) q^{7} -3.05269 q^{8} +(-3.22753 - 5.59025i) q^{9} +(0.533037 - 0.923247i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.32757 + 2.29942i) q^{12} +2.06228 q^{13} +(1.69803 + 2.25217i) q^{14} -3.07491 q^{15} +(0.763711 + 1.32279i) q^{16} +(0.561652 - 0.972810i) q^{17} +(-3.44079 + 5.95963i) q^{18} +(-4.23532 - 7.33580i) q^{19} +0.863486 q^{20} +(3.17687 - 7.48953i) q^{21} +1.06607 q^{22} +(-1.99963 - 3.46346i) q^{23} +(4.69337 - 8.12916i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.09927 - 1.90399i) q^{26} +10.6240 q^{27} +(-0.892117 + 2.10318i) q^{28} -4.01868 q^{29} +(1.63904 + 2.83890i) q^{30} +(0.162793 - 0.281965i) q^{31} +(-2.23852 + 3.87722i) q^{32} +(-1.53745 - 2.66295i) q^{33} -1.19753 q^{34} +(-1.59279 - 2.11259i) q^{35} -5.57386 q^{36} +(-2.70461 - 4.68452i) q^{37} +(-4.51517 + 7.82050i) q^{38} +(-3.17066 + 5.49174i) q^{39} +(-1.52634 - 2.64371i) q^{40} +1.23247 q^{41} +(-8.60807 + 1.05916i) q^{42} -12.0838 q^{43} +(0.431743 + 0.747801i) q^{44} +(3.22753 - 5.59025i) q^{45} +(-2.13175 + 3.69230i) q^{46} +(0.526841 + 0.912516i) q^{47} -4.69668 q^{48} +(6.79121 - 1.69691i) q^{49} +1.06607 q^{50} +(1.72703 + 2.99130i) q^{51} +(0.890373 - 1.54217i) q^{52} +(0.442221 - 0.765949i) q^{53} +(-5.66300 - 9.80860i) q^{54} -1.00000 q^{55} +(8.01620 - 0.986335i) q^{56} +26.0465 q^{57} +(2.14211 + 3.71024i) q^{58} +(-6.93461 + 12.0111i) q^{59} +(-1.32757 + 2.29942i) q^{60} +(-0.819335 - 1.41913i) q^{61} -0.347098 q^{62} +(10.2816 + 13.6369i) q^{63} +7.82769 q^{64} +(1.03114 + 1.78598i) q^{65} +(-1.63904 + 2.83890i) q^{66} +(-5.37852 + 9.31587i) q^{67} +(-0.484978 - 0.840007i) q^{68} +12.2974 q^{69} +(-1.10142 + 2.59663i) q^{70} +8.18682 q^{71} +(9.85266 + 17.0653i) q^{72} +(6.48062 - 11.2248i) q^{73} +(-2.88332 + 4.99405i) q^{74} +(-1.53745 - 2.66295i) q^{75} -7.31428 q^{76} +(1.03316 - 2.43569i) q^{77} +6.76031 q^{78} +(-3.71992 - 6.44309i) q^{79} +(-0.763711 + 1.32279i) q^{80} +(-6.65135 + 11.5205i) q^{81} +(-0.656953 - 1.13788i) q^{82} +4.20154 q^{83} +(-4.22908 - 5.60921i) q^{84} +1.12330 q^{85} +(6.44111 + 11.1563i) q^{86} +(6.17854 - 10.7015i) q^{87} +(1.52634 - 2.64371i) q^{88} +(7.04583 + 12.2037i) q^{89} -6.88158 q^{90} +(-5.41543 + 0.666329i) q^{91} -3.45330 q^{92} +(0.500573 + 0.867017i) q^{93} +(0.561652 - 0.972810i) q^{94} +(4.23532 - 7.33580i) q^{95} +(-6.88323 - 11.9221i) q^{96} -16.8254 q^{97} +(-5.18663 - 5.36545i) q^{98} +6.45507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 3 q^{3} - 15 q^{4} + 10 q^{5} + 10 q^{6} - q^{7} + 18 q^{8} - 19 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 3 * q^3 - 15 * q^4 + 10 * q^5 + 10 * q^6 - q^7 + 18 * q^8 - 19 * q^9	\( 20 q - 3 q^{2} + 3 q^{3} - 15 q^{4} + 10 q^{5} + 10 q^{6} - q^{7} + 18 q^{8} - 19 q^{9} + 3 q^{10} - 10 q^{11} + 3 q^{12} - 12 q^{13} + 15 q^{14} + 6 q^{15} - 21 q^{16} + 5 q^{17} - q^{18} - q^{19} - 30 q^{20} + 24 q^{21} + 6 q^{22} - 18 q^{23} - 10 q^{24} - 10 q^{25} - 13 q^{26} - 30 q^{27} + 18 q^{28} + 28 q^{29} + 5 q^{30} - 10 q^{31} - 46 q^{32} + 3 q^{33} - 4 q^{34} + q^{35} + 52 q^{36} - 13 q^{37} - 9 q^{38} - 3 q^{39} + 9 q^{40} - 14 q^{41} + 76 q^{42} + 12 q^{43} - 15 q^{44} + 19 q^{45} - 10 q^{46} - q^{47} - 70 q^{48} + 11 q^{49} + 6 q^{50} - 9 q^{51} + 17 q^{52} - 16 q^{53} - 73 q^{54} - 20 q^{55} + 6 q^{56} + 24 q^{57} + 9 q^{58} - 13 q^{59} - 3 q^{60} - 18 q^{61} + 28 q^{62} + 17 q^{63} + 86 q^{64} - 6 q^{65} - 5 q^{66} - 29 q^{67} - 13 q^{68} + 3 q^{70} + 38 q^{71} + 48 q^{72} + 31 q^{73} + 8 q^{74} + 3 q^{75} - 16 q^{76} + 2 q^{77} + 6 q^{78} + 21 q^{80} - 42 q^{81} - q^{82} - 4 q^{83} - 12 q^{84} + 10 q^{85} - 10 q^{86} + 50 q^{87} - 9 q^{88} - 23 q^{89} - 2 q^{90} - 15 q^{91} + 28 q^{92} - 4 q^{93} + 5 q^{94} + q^{95} - 39 q^{96} - 86 q^{97} + 72 q^{98} + 38 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 3 * q^3 - 15 * q^4 + 10 * q^5 + 10 * q^6 - q^7 + 18 * q^8 - 19 * q^9 + 3 * q^10 - 10 * q^11 + 3 * q^12 - 12 * q^13 + 15 * q^14 + 6 * q^15 - 21 * q^16 + 5 * q^17 - q^18 - q^19 - 30 * q^20 + 24 * q^21 + 6 * q^22 - 18 * q^23 - 10 * q^24 - 10 * q^25 - 13 * q^26 - 30 * q^27 + 18 * q^28 + 28 * q^29 + 5 * q^30 - 10 * q^31 - 46 * q^32 + 3 * q^33 - 4 * q^34 + q^35 + 52 * q^36 - 13 * q^37 - 9 * q^38 - 3 * q^39 + 9 * q^40 - 14 * q^41 + 76 * q^42 + 12 * q^43 - 15 * q^44 + 19 * q^45 - 10 * q^46 - q^47 - 70 * q^48 + 11 * q^49 + 6 * q^50 - 9 * q^51 + 17 * q^52 - 16 * q^53 - 73 * q^54 - 20 * q^55 + 6 * q^56 + 24 * q^57 + 9 * q^58 - 13 * q^59 - 3 * q^60 - 18 * q^61 + 28 * q^62 + 17 * q^63 + 86 * q^64 - 6 * q^65 - 5 * q^66 - 29 * q^67 - 13 * q^68 + 3 * q^70 + 38 * q^71 + 48 * q^72 + 31 * q^73 + 8 * q^74 + 3 * q^75 - 16 * q^76 + 2 * q^77 + 6 * q^78 + 21 * q^80 - 42 * q^81 - q^82 - 4 * q^83 - 12 * q^84 + 10 * q^85 - 10 * q^86 + 50 * q^87 - 9 * q^88 - 23 * q^89 - 2 * q^90 - 15 * q^91 + 28 * q^92 - 4 * q^93 + 5 * q^94 + q^95 - 39 * q^96 - 86 * q^97 + 72 * q^98 + 38 * q^99

Introduction

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