LMFDB - Embedded newform 605.2.g.o.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 6 x^{10} - 12 x^{9} + 43 x^{8} + 72 x^{7} + 155 x^{6} + 162 x^{5} + 541 x^{4} + \cdots + 1 $ x^12 - x^11 + 6x^10 - 12x^9 + 43x^8 + 72x^7 + 155x^6 + 162x^5 + 541x^4 + 114x^3 + 24x^2 + 5x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.3
Root			$0.0651271 + 0.200441i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.o.366.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.22061 + 1.61337i) q^{2} +(-0.0651271 + 0.200441i) q^{3} +(1.71012 + 5.26321i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.468007 + 0.340027i) q^{6} +(-0.717944 - 2.20960i) q^{7} +(-2.99759 + 9.22564i) q^{8} +(2.39112 + 1.73725i) q^{9} +O(q^{10})$	\(q+(2.22061 + 1.61337i) q^{2} +(-0.0651271 + 0.200441i) q^{3} +(1.71012 + 5.26321i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.468007 + 0.340027i) q^{6} +(-0.717944 - 2.20960i) q^{7} +(-2.99759 + 9.22564i) q^{8} +(2.39112 + 1.73725i) q^{9} +2.74483 q^{10} -1.16634 q^{12} +(0.432072 + 0.313919i) q^{13} +(1.97063 - 6.06498i) q^{14} +(0.0651271 + 0.200441i) q^{15} +(-12.5865 + 9.14464i) q^{16} +(-1.95904 + 1.42333i) q^{17} +(2.50692 + 7.71550i) q^{18} +(1.53136 - 4.71304i) q^{19} +(4.47716 + 3.25284i) q^{20} +0.489652 q^{21} -4.53407 q^{23} +(-1.65397 - 1.20168i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.452997 + 1.39418i) q^{26} +(-1.01546 + 0.737773i) q^{27} +(10.4018 - 7.55738i) q^{28} +(-1.69640 - 5.22097i) q^{29} +(-0.178763 + 0.550175i) q^{30} +(-0.844952 - 0.613894i) q^{31} -23.3026 q^{32} -6.64663 q^{34} +(-1.87960 - 1.36561i) q^{35} +(-5.05440 + 15.5559i) q^{36} +(2.31443 + 7.12308i) q^{37} +(11.0044 - 7.99518i) q^{38} +(-0.0910617 + 0.0661602i) q^{39} +(2.99759 + 9.22564i) q^{40} +(3.27626 - 10.0833i) q^{41} +(1.08733 + 0.789989i) q^{42} +4.32331 q^{43} +2.95558 q^{45} +(-10.0684 - 7.31513i) q^{46} +(2.09160 - 6.43727i) q^{47} +(-1.01323 - 3.11842i) q^{48} +(1.29622 - 0.941756i) q^{49} +(2.22061 - 1.61337i) q^{50} +(-0.157706 - 0.485370i) q^{51} +(-0.913325 + 2.81093i) q^{52} +(3.66814 + 2.66506i) q^{53} -3.44523 q^{54} +22.5371 q^{56} +(0.844952 + 0.613894i) q^{57} +(4.65631 - 14.3307i) q^{58} +(-1.99169 - 6.12978i) q^{59} +(-0.943587 + 0.685556i) q^{60} +(-5.50019 + 3.99612i) q^{61} +(-0.885873 - 2.72644i) q^{62} +(2.12194 - 6.53066i) q^{63} +(-26.5730 - 19.3064i) q^{64} +0.534070 q^{65} +0.721104 q^{67} +(-10.8415 - 7.87680i) q^{68} +(0.295291 - 0.908812i) q^{69} +(-1.97063 - 6.06498i) q^{70} +(-3.66814 + 2.66506i) q^{71} +(-23.1948 + 16.8520i) q^{72} +(0.330074 + 1.01586i) q^{73} +(-6.35271 + 19.5516i) q^{74} +(0.170505 + 0.123879i) q^{75} +27.4245 q^{76} -0.308953 q^{78} +(-3.75920 - 2.73122i) q^{79} +(-4.80762 + 14.7963i) q^{80} +(2.65823 + 8.18119i) q^{81} +(23.5434 - 17.1053i) q^{82} +(-11.0044 + 7.99518i) q^{83} +(0.837365 + 2.57714i) q^{84} +(-0.748288 + 2.30299i) q^{85} +(9.60040 + 6.97510i) q^{86} +1.15698 q^{87} +12.7148 q^{89} +(6.56320 + 4.76844i) q^{90} +(0.383432 - 1.18008i) q^{91} +(-7.75381 - 23.8638i) q^{92} +(0.178079 - 0.129382i) q^{93} +(15.0303 - 10.9202i) q^{94} +(-1.53136 - 4.71304i) q^{95} +(1.51763 - 4.67079i) q^{96} +(-3.85026 - 2.79738i) q^{97} +4.39779 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{2} - q^{3} - 9 q^{4} + 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 12 * q - q^2 - q^3 - 9 * q^4 + 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 - 2 * q^9	$ 12 q - q^{2} - q^{3} - 9 q^{4} + 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} - 2 q^{9} - 4 q^{10} + 36 q^{12} - 6 q^{13} - 5 q^{14} + q^{15} - 13 q^{16} - 4 q^{17} - 20 q^{18} - 4 q^{19} + 9 q^{20} - 68 q^{21} - 24 q^{23} - 17 q^{24} - 3 q^{25} - 12 q^{26} - 13 q^{27} + 25 q^{28} - 2 q^{29} + 5 q^{30} - 14 q^{31} - 108 q^{32} - 32 q^{34} - q^{35} - 2 q^{36} - 4 q^{37} + 18 q^{38} + 4 q^{39} - 9 q^{40} - 9 q^{41} + 35 q^{42} + 28 q^{43} - 8 q^{45} - 8 q^{46} + 15 q^{47} - 7 q^{48} - 18 q^{49} - q^{50} + 20 q^{51} - 2 q^{52} + 6 q^{53} + 76 q^{54} - 12 q^{56} + 14 q^{57} - 30 q^{58} - 10 q^{59} + 9 q^{60} - 3 q^{61} - 24 q^{62} + 12 q^{63} - 29 q^{64} - 24 q^{65} + 76 q^{67} + 8 q^{69} + 5 q^{70} - 6 q^{71} - 48 q^{72} + 12 q^{73} + 28 q^{74} - q^{75} + 64 q^{76} - 8 q^{78} - 2 q^{79} + 13 q^{80} - 3 q^{81} + 27 q^{82} - 18 q^{83} + 31 q^{84} + 4 q^{85} + 3 q^{86} + 40 q^{87} + 44 q^{89} + 20 q^{90} - 20 q^{91} + 34 q^{92} - 20 q^{93} + 59 q^{94} + 4 q^{95} + 7 q^{96} + 2 q^{97} + 144 q^{98}+O(q^{100}) $ 12 * q - q^2 - q^3 - 9 * q^4 + 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 - 2 * q^9 - 4 * q^10 + 36 * q^12 - 6 * q^13 - 5 * q^14 + q^15 - 13 * q^16 - 4 * q^17 - 20 * q^18 - 4 * q^19 + 9 * q^20 - 68 * q^21 - 24 * q^23 - 17 * q^24 - 3 * q^25 - 12 * q^26 - 13 * q^27 + 25 * q^28 - 2 * q^29 + 5 * q^30 - 14 * q^31 - 108 * q^32 - 32 * q^34 - q^35 - 2 * q^36 - 4 * q^37 + 18 * q^38 + 4 * q^39 - 9 * q^40 - 9 * q^41 + 35 * q^42 + 28 * q^43 - 8 * q^45 - 8 * q^46 + 15 * q^47 - 7 * q^48 - 18 * q^49 - q^50 + 20 * q^51 - 2 * q^52 + 6 * q^53 + 76 * q^54 - 12 * q^56 + 14 * q^57 - 30 * q^58 - 10 * q^59 + 9 * q^60 - 3 * q^61 - 24 * q^62 + 12 * q^63 - 29 * q^64 - 24 * q^65 + 76 * q^67 + 8 * q^69 + 5 * q^70 - 6 * q^71 - 48 * q^72 + 12 * q^73 + 28 * q^74 - q^75 + 64 * q^76 - 8 * q^78 - 2 * q^79 + 13 * q^80 - 3 * q^81 + 27 * q^82 - 18 * q^83 + 31 * q^84 + 4 * q^85 + 3 * q^86 + 40 * q^87 + 44 * q^89 + 20 * q^90 - 20 * q^91 + 34 * q^92 - 20 * q^93 + 59 * q^94 + 4 * q^95 + 7 * q^96 + 2 * q^97 + 144 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	2.22061	+	1.61337i	1.57021	+	1.14082i	0.926956	+	0.375170i	$0.122416\pi$
$2$	2.22061	+	1.61337i	1.57021	+	1.14082i	0.643253	+	0.765654i	$0.277584\pi$
$3$	−0.0651271	+	0.200441i	−0.0376012	+	0.115725i	−0.968095	−	0.250582i	$-0.919378\pi$
$3$	−0.0651271	+	0.200441i	−0.0376012	+	0.115725i	0.930494	+	0.366307i	$0.119378\pi$
$4$	1.71012	+	5.26321i	0.855061	+	2.63161i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$5$	0.809017	−	0.587785i	0.361803	−	0.262866i
$6$	−0.468007	+	0.340027i	−0.191063	+	0.138815i
$7$	−0.717944	−	2.20960i	−0.271357	−	0.835152i	−0.990160	−	0.139938i	$-0.955310\pi$
$7$	−0.717944	−	2.20960i	−0.271357	−	0.835152i	0.718803	−	0.695214i	$-0.244690\pi$
$8$	−2.99759	+	9.22564i	−1.05981	+	3.26175i
$9$	2.39112	+	1.73725i	0.797039	+	0.579082i
$10$	2.74483			0.867990
$11$		0			0
$11$		0			0
$12$	−1.16634			−0.336693
$13$	0.432072	+	0.313919i	0.119835	+	0.0870654i	0.646089	−	0.763262i	$-0.276404\pi$
$13$	0.432072	+	0.313919i	0.119835	+	0.0870654i	−0.526253	+	0.850328i	$0.676404\pi$
$14$	1.97063	−	6.06498i	0.526673	−	1.62093i
$15$	0.0651271	+	0.200441i	0.0168158	+	0.0517536i
$16$	−12.5865	+	9.14464i	−3.14663	+	2.28616i
$17$	−1.95904	+	1.42333i	−0.475138	+	0.345208i	−0.799440	−	0.600746i	$-0.794870\pi$
$17$	−1.95904	+	1.42333i	−0.475138	+	0.345208i	0.324302	+	0.945953i	$0.394870\pi$
$18$	2.50692	+	7.71550i	0.590886	+	1.81856i
$19$	1.53136	−	4.71304i	0.351318	−	1.08125i	−0.606796	−	0.794858i	$-0.707546\pi$
$19$	1.53136	−	4.71304i	0.351318	−	1.08125i	0.958114	−	0.286388i	$-0.0924545\pi$
$20$	4.47716	+	3.25284i	1.00112	+	0.727358i
$21$	0.489652			0.106851
$22$		0			0
$23$	−4.53407			−0.945419			−0.472709	−	0.881218i	$-0.656724\pi$
$23$	−4.53407			−0.945419			−0.472709	+	0.881218i	$0.656724\pi$
$24$	−1.65397	−	1.20168i	−0.337615	−	0.245292i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	0.452997	+	1.39418i	0.0888401	+	0.273422i
$27$	−1.01546	+	0.737773i	−0.195425	+	0.141984i
$28$	10.4018	−	7.55738i	1.96576	−	1.42821i
$29$	−1.69640	−	5.22097i	−0.315013	−	0.969510i	−0.975749	−	0.218892i	$-0.929756\pi$
$29$	−1.69640	−	5.22097i	−0.315013	−	0.969510i	0.660736	−	0.750618i	$-0.270244\pi$
$30$	−0.178763	+	0.550175i	−0.0326375	+	0.100448i
$31$	−0.844952	−	0.613894i	−0.151758	−	0.110259i	0.509315	−	0.860580i	$-0.329899\pi$
$31$	−0.844952	−	0.613894i	−0.151758	−	0.110259i	−0.661073	+	0.750321i	$0.729899\pi$
$32$	−23.3026			−4.11936
$33$		0			0
$34$	−6.64663			−1.13989
$35$	−1.87960	−	1.36561i	−0.317711	−	0.230830i
$36$	−5.05440	+	15.5559i	−0.842401	+	2.59264i
$37$	2.31443	+	7.12308i	0.380490	+	1.17103i	0.939700	+	0.342001i	$0.111105\pi$
$37$	2.31443	+	7.12308i	0.380490	+	1.17103i	−0.559210	+	0.829026i	$0.688895\pi$
$38$	11.0044	−	7.99518i	1.78515	−	1.29699i
$39$	−0.0910617	+	0.0661602i	−0.0145815	+	0.0105941i
$40$	2.99759	+	9.22564i	0.473961	+	1.45870i
$41$	3.27626	−	10.0833i	0.511666	−	1.57475i	−0.277600	−	0.960697i	$-0.589539\pi$
$41$	3.27626	−	10.0833i	0.511666	−	1.57475i	0.789267	−	0.614050i	$-0.210461\pi$
$42$	1.08733	+	0.789989i	0.167778	+	0.121898i
$43$	4.32331			0.659299			0.329650	−	0.944103i	$-0.393069\pi$
$43$	4.32331			0.659299			0.329650	+	0.944103i	$0.393069\pi$
$44$		0			0
$45$	2.95558			0.440592
$46$	−10.0684	−	7.31513i	−1.48451	−	1.07856i
$47$	2.09160	−	6.43727i	0.305091	−	0.938973i	−0.674553	−	0.738227i	$-0.735663\pi$
$47$	2.09160	−	6.43727i	0.305091	−	0.938973i	0.979643	−	0.200746i	$-0.0643366\pi$
$48$	−1.01323	−	3.11842i	−0.146248	−	0.450105i
$49$	1.29622	−	0.941756i	0.185174	−	0.134537i
$50$	2.22061	−	1.61337i	0.314042	−	0.228165i
$51$	−0.157706	−	0.485370i	−0.0220833	−	0.0679653i
$52$	−0.913325	+	2.81093i	−0.126655	+	0.389805i
$53$	3.66814	+	2.66506i	0.503858	+	0.366074i	0.810489	−	0.585754i	$-0.199202\pi$
$53$	3.66814	+	2.66506i	0.503858	+	0.366074i	−0.306631	+	0.951829i	$0.599202\pi$
$54$	−3.44523			−0.468837
$55$		0			0
$56$	22.5371			3.01165
$57$	0.844952	+	0.613894i	0.111917	+	0.0813122i
$58$	4.65631	−	14.3307i	0.611404	−	1.88171i
$59$	−1.99169	−	6.12978i	−0.259296	−	0.798030i	−0.992953	−	0.118510i	$-0.962188\pi$
$59$	−1.99169	−	6.12978i	−0.259296	−	0.798030i	0.733657	−	0.679520i	$-0.237812\pi$
$60$	−0.943587	+	0.685556i	−0.121817	+	0.0885049i
$61$	−5.50019	+	3.99612i	−0.704227	+	0.511651i	−0.881306	−	0.472546i	$-0.843335\pi$
$61$	−5.50019	+	3.99612i	−0.704227	+	0.511651i	0.177079	+	0.984197i	$0.443335\pi$
$62$	−0.885873	−	2.72644i	−0.112506	−	0.346258i
$63$	2.12194	−	6.53066i	0.267339	−	0.822786i
$64$	−26.5730	−	19.3064i	−3.32163	−	2.41330i
$65$	0.534070			0.0662433
$66$		0			0
$67$	0.721104			0.0880968			0.0440484	−	0.999029i	$-0.485974\pi$
$67$	0.721104			0.0880968			0.0440484	+	0.999029i	$0.485974\pi$
$68$	−10.8415	−	7.87680i	−1.31472	−	0.955203i
$69$	0.295291	−	0.908812i	0.0355489	−	0.109408i
$70$	−1.97063	−	6.06498i	−0.235535	−	0.724903i
$71$	−3.66814	+	2.66506i	−0.435328	+	0.316284i	−0.783776	−	0.621044i	$-0.786709\pi$
$71$	−3.66814	+	2.66506i	−0.435328	+	0.316284i	0.348448	+	0.937328i	$0.386709\pi$
$72$	−23.1948	+	16.8520i	−2.73353	+	1.98603i
$73$	0.330074	+	1.01586i	0.0386322	+	0.118898i	0.968513	−	0.248964i	$-0.0800900\pi$
$73$	0.330074	+	1.01586i	0.0386322	+	0.118898i	−0.929881	+	0.367862i	$0.880090\pi$
$74$	−6.35271	+	19.5516i	−0.738487	+	2.27283i
$75$	0.170505	+	0.123879i	0.0196882	+	0.0143043i
$76$	27.4245			3.14581
$77$		0			0
$78$	−0.308953			−0.0349821
$79$	−3.75920	−	2.73122i	−0.422943	−	0.307286i	0.355878	−	0.934533i	$-0.384182\pi$
$79$	−3.75920	−	2.73122i	−0.422943	−	0.307286i	−0.778821	+	0.627246i	$0.784182\pi$
$80$	−4.80762	+	14.7963i	−0.537509	+	1.65428i
$81$	2.65823	+	8.18119i	0.295359	+	0.909021i
$82$	23.5434	−	17.1053i	2.59993	−	1.88896i
$83$	−11.0044	+	7.99518i	−1.20789	+	0.877585i	−0.995038	−	0.0994991i	$-0.968276\pi$
$83$	−11.0044	+	7.99518i	−1.20789	+	0.877585i	−0.212854	+	0.977084i	$0.568276\pi$
$84$	0.837365	+	2.57714i	0.0913640	+	0.281189i
$85$	−0.748288	+	2.30299i	−0.0811633	+	0.249795i
$86$	9.60040	+	6.97510i	1.03524	+	0.752144i
$87$	1.15698			0.124041
$88$		0			0
$89$	12.7148			1.34776			0.673881	−	0.738840i	$-0.264626\pi$
$89$	12.7148			1.34776			0.673881	+	0.738840i	$0.264626\pi$
$90$	6.56320	+	4.76844i	0.691822	+	0.502638i
$91$	0.383432	−	1.18008i	0.0401946	−	0.123706i
$92$	−7.75381	−	23.8638i	−0.808391	−	2.48797i
$93$	0.178079	−	0.129382i	0.0184659	−	0.0134163i
$94$	15.0303	−	10.9202i	1.55026	−	1.12633i
$95$	−1.53136	−	4.71304i	−0.157114	−	0.483548i
$96$	1.51763	−	4.67079i	0.154893	−	0.476711i
$97$	−3.85026	−	2.79738i	−0.390935	−	0.284031i	0.374904	−	0.927064i	$-0.377676\pi$
$97$	−3.85026	−	2.79738i	−0.390935	−	0.284031i	−0.765839	+	0.643033i	$0.777676\pi$
$98$	4.39779			0.444244
$99$		0			0
$100$	5.53407			0.553407
$101$	5.32211	+	3.86674i	0.529570	+	0.384755i	0.820197	−	0.572082i	$-0.193864\pi$
$101$	5.32211	+	3.86674i	0.529570	+	0.384755i	−0.290627	+	0.956836i	$0.593864\pi$
$102$	0.432876	−	1.33226i	0.0428611	−	0.131913i
$103$	5.05440	+	15.5559i	0.498025	+	1.53276i	0.812188	+	0.583395i	$0.198276\pi$
$103$	5.05440	+	15.5559i	0.498025	+	1.53276i	−0.314163	+	0.949369i	$0.601724\pi$
$104$	−4.19127	+	3.04514i	−0.410988	+	0.298600i
$105$	0.396137	−	0.287810i	0.0386590	−	0.0280874i
$106$	3.84579	+	11.8361i	0.373536	+	1.14963i
$107$	3.15530	−	9.71101i	0.305034	−	0.938798i	−0.674630	−	0.738156i	$-0.735697\pi$
$107$	3.15530	−	9.71101i	0.305034	−	0.938798i	0.979664	−	0.200643i	$-0.0643030\pi$
$108$	−5.61961	−	4.08289i	−0.540747	−	0.392876i
$109$	−12.0919			−1.15819			−0.579095	−	0.815260i	$-0.696594\pi$
$109$	−12.0919			−1.15819			−0.579095	+	0.815260i	$0.696594\pi$
$110$		0			0
$111$	−1.57849			−0.149823
$112$	29.2424	+	21.2459i	2.76315	+	2.00755i
$113$	−3.35068	+	10.3123i	−0.315205	+	0.970102i	0.660465	+	0.750857i	$0.270359\pi$
$113$	−3.35068	+	10.3123i	−0.315205	+	0.970102i	−0.975670	+	0.219245i	$0.929641\pi$
$114$	0.885873	+	2.72644i	0.0829696	+	0.255354i
$115$	−3.66814	+	2.66506i	−0.342056	+	0.248518i
$116$	24.5780	−	17.8570i	2.28201	−	1.65798i
$117$	0.487780	+	1.50123i	0.0450952	+	0.138789i
$118$	5.46683	−	16.8252i	0.503263	−	1.54888i
$119$	4.55148	+	3.30684i	0.417233	+	0.303138i
$120$	−2.04442			−0.186629
$121$		0			0
$122$	−18.6610			−1.68949
$123$	1.80773	+	1.31339i	0.162998	+	0.118425i
$124$	1.78608	−	5.49700i	0.160395	−	0.493645i
$125$	−0.309017	−	0.951057i	−0.0276393	−	0.0850651i
$126$	15.2484	−	11.0786i	1.35843	−	0.986959i
$127$	6.57077	−	4.77394i	0.583062	−	0.423619i	−0.256765	−	0.966474i	$-0.582657\pi$
$127$	6.57077	−	4.77394i	0.583062	−	0.423619i	0.839827	+	0.542855i	$0.182657\pi$
$128$	−13.4581	−	41.4199i	−1.18954	−	3.66104i
$129$	−0.281565	+	0.866568i	−0.0247904	+	0.0762971i
$130$	1.18596	+	0.861652i	0.104016	+	0.0755719i
$131$	5.79861			0.506627			0.253313	−	0.967384i	$-0.418480\pi$
$131$	5.79861			0.506627			0.253313	+	0.967384i	$0.418480\pi$
$132$		0			0
$133$	−11.5134			−0.998336
$134$	1.60129	+	1.16341i	0.138330	+	0.100503i
$135$	−0.387870	+	1.19374i	−0.0333825	+	0.102741i
$136$	−7.25870	−	22.3400i	−0.622429	−	1.91564i
$137$	−7.17335	+	5.21174i	−0.612860	+	0.445269i	−0.850420	−	0.526104i	$-0.823652\pi$
$137$	−7.17335	+	5.21174i	−0.612860	+	0.445269i	0.237560	+	0.971373i	$0.423652\pi$
$138$	2.12198	−	1.54171i	0.180635	−	0.131239i
$139$	−5.21211	−	16.0412i	−0.442085	−	1.36060i	−0.885649	−	0.464356i	$-0.846286\pi$
$139$	−5.21211	−	16.0412i	−0.442085	−	1.36060i	0.443563	−	0.896243i	$-0.353714\pi$
$140$	3.97315	−	12.2281i	0.335792	−	1.03346i
$141$	1.15407	+	0.838482i	0.0971904	+	0.0706130i
$142$	−12.4452			−1.04438
$143$		0			0
$144$	−45.9823			−3.83186
$145$	−4.44122	−	3.22674i	−0.368823	−	0.267966i
$146$	−0.905994	+	2.78836i	−0.0749806	+	0.230767i
$147$	0.104347	+	0.321148i	0.00860643	+	0.0264879i
$148$	−33.5323	+	24.3627i	−2.75634	+	2.00260i
$149$	−3.61301	+	2.62501i	−0.295990	+	0.215049i	−0.725862	−	0.687841i	$-0.758559\pi$
$149$	−3.61301	+	2.62501i	−0.295990	+	0.215049i	0.429872	+	0.902890i	$0.358559\pi$
$150$	0.178763	+	0.550175i	0.0145959	+	0.0449216i
$151$	−3.55783	+	10.9499i	−0.289532	+	0.891088i	0.695472	+	0.718554i	$0.255196\pi$
$151$	−3.55783	+	10.9499i	−0.289532	+	0.891088i	−0.985004	+	0.172534i	$0.944804\pi$
$152$	38.8904	+	28.2555i	3.15443	+	2.29183i
$153$	−7.15698			−0.578607
$154$		0			0
$155$	−1.04442			−0.0838897
$156$	−0.503942	−	0.366135i	−0.0403476	−	0.0293143i
$157$	−1.82665	+	5.62185i	−0.145783	+	0.448673i	−0.997111	−	0.0759609i	$-0.975798\pi$
$157$	−1.82665	+	5.62185i	−0.145783	+	0.448673i	0.851328	+	0.524633i	$0.175798\pi$
$158$	−3.94126	−	12.1300i	−0.313550	−	0.965007i
$159$	−0.773082	+	0.561677i	−0.0613094	+	0.0445439i
$160$	−18.8522	+	13.6969i	−1.49040	+	1.08284i
$161$	3.25521	+	10.0185i	0.256546	+	0.789568i
$162$	−7.29638	+	22.4559i	−0.573258	+	1.76431i
$163$	−19.0111	−	13.8124i	−1.48906	−	1.08187i	−0.974492	−	0.224422i	$-0.927951\pi$
$163$	−19.0111	−	13.8124i	−1.48906	−	1.08187i	−0.514572	−	0.857447i	$-0.672049\pi$
$164$	58.6734			4.58162
$165$		0			0
$166$	−37.3357			−2.89781
$167$	−11.5159	−	8.36682i	−0.891130	−	0.647444i	0.0450426	−	0.998985i	$-0.485658\pi$
$167$	−11.5159	−	8.36682i	−0.891130	−	0.647444i	−0.936172	+	0.351541i	$0.885658\pi$
$168$	−1.46778	+	4.51735i	−0.113241	+	0.348521i
$169$	−3.92908	−	12.0925i	−0.302237	−	0.930190i
$170$	−5.37724	+	3.90679i	−0.412415	+	0.299637i
$171$	11.8494	−	8.60907i	0.906144	−	0.658352i
$172$	7.39339	+	22.7545i	0.563741	+	1.73502i
$173$	−1.99169	+	6.12978i	−0.151425	+	0.466039i	−0.997781	−	0.0665789i	$-0.978792\pi$
$173$	−1.99169	+	6.12978i	−0.151425	+	0.466039i	0.846356	+	0.532618i	$0.178792\pi$
$174$	2.56919	+	1.86663i	0.194770	+	0.141509i
$175$	−2.32331			−0.175626
$176$		0			0
$177$	1.35837			0.102101
$178$	28.2346	+	20.5136i	2.11627	+	1.53756i
$179$	5.24689	−	16.1483i	0.392171	−	1.20698i	−0.538971	−	0.842324i	$-0.681187\pi$
$179$	5.24689	−	16.1483i	0.392171	−	1.20698i	0.931143	−	0.364655i	$-0.118813\pi$
$180$	5.05440	+	15.5559i	0.376733	+	1.15947i
$181$	−3.63220	+	2.63895i	−0.269980	+	0.196152i	−0.714535	−	0.699600i	$-0.753362\pi$
$181$	−3.63220	+	2.63895i	−0.269980	+	0.196152i	0.444555	+	0.895751i	$0.353362\pi$
$182$	2.75536	−	2.00189i	0.204241	−	0.148390i
$183$	−0.442774	−	1.36272i	−0.0327308	−	0.100735i
$184$	13.5913	−	41.8297i	1.00196	−	3.08373i
$185$	6.05926	+	4.40231i	0.445485	+	0.323664i
$186$	0.604184			0.0443009
$187$		0			0
$188$	37.4576			2.73188
$189$	2.35923	+	1.71408i	0.171608	+	0.124681i
$190$	4.20331	−	12.9365i	0.304940	−	0.938510i
$191$	−0.852636	−	2.62414i	−0.0616946	−	0.189876i	0.915459	−	0.402412i	$-0.131828\pi$
$191$	−0.852636	−	2.62414i	−0.0616946	−	0.189876i	−0.977153	+	0.212535i	$0.931828\pi$
$192$	5.60042	−	4.06894i	0.404175	−	0.293651i
$193$	−9.54932	+	6.93799i	−0.687375	+	0.499407i	−0.875796	−	0.482681i	$-0.839663\pi$
$193$	−9.54932	+	6.93799i	−0.687375	+	0.499407i	0.188421	+	0.982088i	$0.439663\pi$
$194$	−4.03673	−	12.4238i	−0.289821	−	0.891976i
$195$	−0.0347825	+	0.107049i	−0.00249082	+	0.00766597i
$196$	7.17335	+	5.21174i	0.512382	+	0.372267i
$197$	−6.51035			−0.463843			−0.231922	−	0.972734i	$-0.574501\pi$
$197$	−6.51035			−0.463843			−0.231922	+	0.972734i	$0.574501\pi$
$198$		0			0
$199$	23.9586			1.69838			0.849190	−	0.528087i	$-0.177090\pi$
$199$	23.9586			1.69838			0.849190	+	0.528087i	$0.177090\pi$
$200$	7.84779	+	5.70176i	0.554923	+	0.403175i
$201$	−0.0469634	+	0.144539i	−0.00331254	+	0.0101950i
$202$	5.57986	+	17.1730i	0.392598	+	1.20829i
$203$	−10.3184	+	7.49672i	−0.724207	+	0.526167i
$204$	2.28491	−	1.66008i	0.159976	−	0.116229i
$205$	−3.27626	−	10.0833i	−0.228824	−	0.704248i
$206$	−13.8735	+	42.6981i	−0.966610	+	2.97492i
$207$	−10.8415	−	7.87680i	−0.753536	−	0.547476i
$208$	−8.30895			−0.576122
$209$		0			0
$210$	1.34401			0.0927455
$211$	13.6455	+	9.91402i	0.939394	+	0.682510i	0.948275	−	0.317451i	$-0.102827\pi$
$211$	13.6455	+	9.91402i	0.939394	+	0.682510i	−0.00888082	+	0.999961i	$0.502827\pi$
$212$	−7.75381	+	23.8638i	−0.532534	+	1.63897i
$213$	−0.295291	−	0.908812i	−0.0202330	−	0.0622708i
$214$	22.6741	−	16.4737i	1.54997	−	1.12612i
$215$	3.49763	−	2.54118i	0.238537	−	0.173307i
$216$	−3.76250	−	11.5798i	−0.256006	−	0.787904i
$217$	−0.749833	+	2.30775i	−0.0509020	+	0.156660i
$218$	−26.8513	−	19.5086i	−1.81860	−	1.32129i
$219$	−0.225117			−0.0152120
$220$		0			0
$221$	−1.29326			−0.0869939
$222$	−3.50521	−	2.54668i	−0.235254	−	0.170922i
$223$	−7.73080	+	23.7929i	−0.517693	+	1.59329i	0.260636	+	0.965437i	$0.416068\pi$
$223$	−7.73080	+	23.7929i	−0.517693	+	1.59329i	−0.778329	+	0.627857i	$0.783932\pi$
$224$	16.7300	+	51.4895i	1.11782	+	3.44029i
$225$	2.39112	−	1.73725i	0.159408	−	0.115816i
$226$	−24.0781	+	17.4938i	−1.60165	+	1.16367i
$227$	1.23896	+	3.81313i	0.0822327	+	0.253086i	0.983717	−	0.179726i	$-0.0575212\pi$
$227$	1.23896	+	3.81313i	0.0822327	+	0.253086i	−0.901484	+	0.432813i	$0.857521\pi$
$228$	−1.78608	+	5.49700i	−0.118286	+	0.364047i
$229$	14.0224	+	10.1879i	0.926628	+	0.673235i	0.945165	−	0.326593i	$-0.105901\pi$
$229$	14.0224	+	10.1879i	0.926628	+	0.673235i	−0.0185367	+	0.999828i	$0.505901\pi$
$230$	−12.4452			−0.820614
$231$		0			0
$232$	53.2519			3.49616
$233$	−1.70910	−	1.24173i	−0.111967	−	0.0813485i	0.530393	−	0.847752i	$-0.322044\pi$
$233$	−1.70910	−	1.24173i	−0.111967	−	0.0813485i	−0.642360	+	0.766403i	$0.722044\pi$
$234$	−1.33887	+	4.12062i	−0.0875247	+	0.269373i
$235$	−2.09160	−	6.43727i	−0.136441	−	0.419921i
$236$	28.8563	−	20.9653i	1.87839	−	1.36473i
$237$	0.792274	−	0.575621i	0.0514637	−	0.0373906i
$238$	4.77190	+	14.6864i	0.309317	+	0.951979i
$239$	−7.39629	+	22.7634i	−0.478426	+	1.47244i	0.362855	+	0.931846i	$0.381802\pi$
$239$	−7.39629	+	22.7634i	−0.478426	+	1.47244i	−0.841281	+	0.540598i	$0.818198\pi$
$240$	−2.65268	−	1.92729i	−0.171230	−	0.124406i
$241$	−14.5134			−0.934889			−0.467444	−	0.884023i	$-0.654825\pi$
$241$	−14.5134			−0.934889			−0.467444	+	0.884023i	$0.654825\pi$
$242$		0			0
$243$	−5.57849			−0.357860
$244$	−30.4384	−	22.1148i	−1.94862	−	1.41576i
$245$	0.495110	−	1.52379i	0.0316314	−	0.0973516i
$246$	1.89528	+	5.83307i	0.120839	+	0.371903i
$247$	2.14117	−	1.55565i	0.136239	−	0.0989836i
$248$	8.19638	−	5.95502i	0.520471	−	0.378144i
$249$	−0.885873	−	2.72644i	−0.0561399	−	0.172781i
$250$	0.848198	−	2.61048i	0.0536447	−	0.165102i
$251$	−23.3051	−	16.9321i	−1.47100	−	1.06875i	−0.980322	−	0.197406i	$-0.936748\pi$
$251$	−23.3051	−	16.9321i	−1.47100	−	1.06875i	−0.490680	−	0.871340i	$-0.663252\pi$
$252$	38.0011			2.39384
$253$		0			0
$254$	22.2933			1.39880
$255$	−0.412880	−	0.299975i	−0.0258556	−	0.0187852i
$256$	16.6403	−	51.2135i	1.04002	−	3.20084i
$257$	−8.54421	−	26.2964i	−0.532973	−	1.64032i	−0.747988	−	0.663713i	$-0.768980\pi$
$257$	−8.54421	−	26.2964i	−0.532973	−	1.64032i	0.215014	−	0.976611i	$-0.431020\pi$
$258$	−2.02334	+	1.47004i	−0.125968	+	0.0915209i
$259$	14.0776	−	10.2279i	0.874737	−	0.635533i
$260$	0.913325	+	2.81093i	0.0566420	+	0.174326i
$261$	5.01384	−	15.4310i	0.310349	−	0.955155i
$262$	12.8764	+	9.35529i	0.795510	+	0.577972i
$263$	3.13325			0.193205			0.0966024	−	0.995323i	$-0.469202\pi$
$263$	3.13325			0.193205			0.0966024	+	0.995323i	$0.469202\pi$
$264$		0			0
$265$	4.53407			0.278526
$266$	−25.5667	−	18.5753i	−1.56760	−	1.13893i
$267$	−0.828077	+	2.54856i	−0.0506775	+	0.155969i
$268$	1.23318	+	3.79532i	0.0753282	+	0.231836i
$269$	−14.5648	+	10.5819i	−0.888029	+	0.645191i	−0.935363	−	0.353688i	$-0.884927\pi$
$269$	−14.5648	+	10.5819i	−0.888029	+	0.645191i	0.0473345	+	0.998879i	$0.484927\pi$
$270$	−2.78725	+	2.02506i	−0.169627	+	0.123241i
$271$	6.28314	+	19.3375i	0.381674	+	1.17467i	0.938865	+	0.344286i	$0.111879\pi$
$271$	6.28314	+	19.3375i	0.381674	+	1.17467i	−0.557191	+	0.830384i	$0.688121\pi$
$272$	11.6417	−	35.8295i	0.705883	−	2.17248i
$273$	0.211565	+	0.153711i	0.0128045	+	0.00930301i
$274$	−24.3377			−1.47029
$275$		0			0
$276$	5.28826			0.318316
$277$	20.6216	+	14.9824i	1.23903	+	0.900208i	0.997533	−	0.0701941i	$-0.0223619\pi$
$277$	20.6216	+	14.9824i	1.23903	+	0.900208i	0.241496	+	0.970402i	$0.422362\pi$
$278$	14.3063	−	44.0304i	0.858037	−	2.64077i
$279$	−0.953893	−	2.93578i	−0.0571081	−	0.175761i
$280$	18.2329	−	13.2470i	1.08962	−	0.791658i
$281$	−14.7828	+	10.7403i	−0.881869	+	0.640715i	−0.933745	−	0.357938i	$-0.883480\pi$
$281$	−14.7828	+	10.7403i	−0.881869	+	0.640715i	0.0518765	+	0.998654i	$0.483480\pi$
$282$	1.20996	+	3.72389i	0.0720523	+	0.221754i
$283$	−3.41581	+	10.5128i	−0.203049	+	0.624919i	0.796739	+	0.604323i	$0.206556\pi$
$283$	−3.41581	+	10.5128i	−0.203049	+	0.624919i	−0.999788	+	0.0205961i	$0.993444\pi$
$284$	−20.2997	−	14.7486i	−1.20457	−	0.875170i
$285$	1.04442			0.0618660
$286$		0			0
$287$	−24.6323			−1.45400
$288$	−55.7193	−	40.4824i	−3.28329	−	2.38545i
$289$	−3.44130	+	10.5912i	−0.202429	+	0.623014i
$290$	−4.65631	−	14.3307i	−0.273428	−	0.841525i
$291$	0.811466	−	0.589564i	0.0475690	−	0.0345609i
$292$	−4.78223	+	3.47449i	−0.279859	+	0.203329i
$293$	8.38651	+	25.8110i	0.489945	+	1.50790i	0.824689	+	0.565586i	$0.191350\pi$
$293$	8.38651	+	25.8110i	0.489945	+	1.50790i	−0.334744	+	0.942309i	$0.608650\pi$
$294$	−0.286415	+	0.881496i	−0.0167041	+	0.0514099i
$295$	−5.21430	−	3.78841i	−0.303589	−	0.220570i
$296$	−72.6527			−4.22285
$297$		0			0
$298$	−12.2582			−0.710098
$299$	−1.95904	−	1.42333i	−0.113294	−	0.0823132i
$300$	−0.360418	+	1.10925i	−0.0208088	+	0.0640428i
$301$	−3.10390	−	9.55281i	−0.178906	−	0.550615i
$302$	−25.5667	+	18.5753i	−1.47120	+	1.06889i
$303$	−1.12167	+	0.814938i	−0.0644380	+	0.0468170i
$304$	23.8246	+	73.3245i	1.36643	+	4.20545i
$305$	−2.10088	+	6.46586i	−0.120296	+	0.370234i
$306$	−15.8929	−	11.5468i	−0.908534	−	0.660089i
$307$	11.7385			0.669951			0.334976	−	0.942227i	$-0.391272\pi$
$307$	11.7385			0.669951			0.334976	+	0.942227i	$0.391272\pi$
$308$		0			0
$309$	−3.44721			−0.196105
$310$	−2.31925	−	1.68503i	−0.131724	−	0.0957033i
$311$	3.28844	−	10.1208i	0.186471	−	0.573897i	−0.813500	−	0.581565i	$-0.802441\pi$
$311$	3.28844	−	10.1208i	0.186471	−	0.573897i	0.999971	+	0.00766747i	$0.00244066\pi$
$312$	−0.337404	−	1.03842i	−0.0191017	−	0.0587891i
$313$	21.9896	−	15.9764i	1.24293	−	0.903040i	0.245138	−	0.969488i	$-0.421167\pi$
$313$	21.9896	−	15.9764i	1.24293	−	0.903040i	0.997790	+	0.0664478i	$0.0211666\pi$
$314$	−13.1264	+	9.53688i	−0.740765	+	0.538198i
$315$	−2.12194	−	6.53066i	−0.119558	−	0.367961i
$316$	7.94630	−	24.4562i	0.447014	−	1.37577i
$317$	−4.02834	−	2.92676i	−0.226254	−	0.164383i	0.468883	−	0.883260i	$-0.344657\pi$
$317$	−4.02834	−	2.92676i	−0.226254	−	0.164383i	−0.695137	+	0.718877i	$0.744657\pi$
$318$	−2.62291			−0.147085
$319$		0			0
$320$	−32.8461			−1.83615
$321$	1.74099	+	1.26490i	0.0971724	+	0.0705998i
$322$	−8.93498	+	27.4990i	−0.497927	+	1.53246i
$323$	3.70820	+	11.4127i	0.206330	+	0.635018i
$324$	−38.5134	+	27.9817i	−2.13964	+	1.55454i
$325$	0.432072	−	0.313919i	0.0239670	−	0.0174131i
$326$	−19.9318	−	61.3438i	−1.10392	−	3.39752i
$327$	0.787509	−	2.42370i	0.0435493	−	0.134031i
$328$	83.2040	+	60.4512i	4.59417	+	3.33786i
$329$	−15.7255			−0.866973
$330$		0			0
$331$	7.55477			0.415247			0.207624	−	0.978209i	$-0.433427\pi$
$331$	7.55477			0.415247			0.207624	+	0.978209i	$0.433427\pi$
$332$	−60.8992	−	44.2459i	−3.34228	−	2.42831i
$333$	−6.84049	+	21.0529i	−0.374856	+	1.15369i
$334$	−12.0737	−	37.1589i	−0.660641	−	2.03324i
$335$	0.583385	−	0.423854i	0.0318737	−	0.0231576i
$336$	−6.16302	+	4.47769i	−0.336220	+	0.244278i
$337$	1.14060	+	3.51039i	0.0621322	+	0.191223i	0.977304	−	0.211840i	$-0.0679455\pi$
$337$	1.14060	+	3.51039i	0.0621322	+	0.191223i	−0.915172	+	0.403063i	$0.867946\pi$
$338$	10.7846	−	33.1917i	0.586607	−	1.80539i
$339$	−1.84879	−	1.34323i	−0.100413	−	0.0729540i
$340$	−13.4008			−0.726761
$341$		0			0
$342$	40.2024			2.17390
$343$	−16.1687	−	11.7473i	−0.873029	−	0.634293i
$344$	−12.9595	+	39.8853i	−0.698731	+	2.15047i
$345$	−0.295291	−	0.908812i	−0.0158979	−	0.0489288i
$346$	−14.3124	+	10.3985i	−0.769437	+	0.559029i
$347$	12.7546	−	9.26674i	0.684701	−	0.497465i	−0.190213	−	0.981743i	$-0.560918\pi$
$347$	12.7546	−	9.26674i	0.684701	−	0.497465i	0.874914	+	0.484278i	$0.160918\pi$
$348$	1.97857	+	6.08941i	0.106063	+	0.326427i
$349$	−3.26254	+	10.0411i	−0.174640	+	0.537485i	−0.999617	−	0.0276805i	$-0.991188\pi$
$349$	−3.26254	+	10.0411i	−0.174640	+	0.537485i	0.824977	+	0.565166i	$0.191188\pi$
$350$	−5.15918	−	3.74836i	−0.275770	−	0.200358i
$351$	−0.670351			−0.0357807
$352$		0			0
$353$	−24.5528			−1.30681			−0.653407	−	0.757007i	$-0.726661\pi$
$353$	−24.5528			−1.30681			−0.653407	+	0.757007i	$0.726661\pi$
$354$	3.01641	+	2.19155i	0.160321	+	0.116480i
$355$	−1.40110	+	4.31216i	−0.0743629	+	0.228866i
$356$	21.7438	+	66.9205i	1.15242	+	3.54678i
$357$	−0.959250	+	0.696936i	−0.0507689	+	0.0368858i
$358$	37.7044	−	27.3939i	1.99274	−	1.44781i
$359$	−5.15142	−	15.8544i	−0.271882	−	0.836766i	−0.990028	−	0.140873i	$-0.955009\pi$
$359$	−5.15142	−	15.8544i	−0.271882	−	0.836766i	0.718146	−	0.695892i	$-0.244991\pi$
$360$	−8.85963	+	27.2671i	−0.466943	+	1.43710i
$361$	−4.49635	−	3.26679i	−0.236650	−	0.171936i
$362$	−12.3233			−0.647699
$363$		0			0
$364$	6.86675			0.359915
$365$	0.864144	+	0.627837i	0.0452314	+	0.0328625i
$366$	1.21534	−	3.74042i	0.0635267	−	0.195515i
$367$	4.72144	+	14.5311i	0.246457	+	0.758517i	0.995393	+	0.0958749i	$0.0305649\pi$
$367$	4.72144	+	14.5311i	0.246457	+	0.758517i	−0.748936	+	0.662642i	$0.769435\pi$
$368$	57.0682	−	41.4624i	2.97488	−	2.16138i
$369$	25.3511	−	18.4187i	1.31973	−	0.958837i
$370$	6.35271	+	19.5516i	0.330262	+	1.01644i
$371$	3.25521	−	10.0185i	0.169002	−	0.520134i
$372$	0.985499	+	0.716007i	0.0510958	+	0.0371232i
$373$	17.8461			0.924033			0.462017	−	0.886871i	$-0.347126\pi$
$373$	17.8461			0.924033			0.462017	+	0.886871i	$0.347126\pi$
$374$		0			0
$375$	0.210756			0.0108834
$376$	53.1182	+	38.5926i	2.73936	+	1.99026i
$377$	0.905994	−	2.78836i	0.0466611	−	0.143608i
$378$	2.47348	+	7.61260i	0.127222	+	0.391550i
$379$	−1.53102	+	1.11235i	−0.0786431	+	0.0571375i	−0.626412	−	0.779492i	$-0.715477\pi$
$379$	−1.53102	+	1.11235i	−0.0786431	+	0.0571375i	0.547769	+	0.836630i	$0.315477\pi$
$380$	22.1869	−	16.1197i	1.13816	−	0.826925i
$381$	0.528957	+	1.62796i	0.0270993	+	0.0834031i
$382$	2.34034	−	7.20282i	0.119742	−	0.368528i
$383$	−4.30153	−	3.12524i	−0.219798	−	0.159692i	0.472438	−	0.881364i	$-0.343374\pi$
$383$	−4.30153	−	3.12524i	−0.219798	−	0.159692i	−0.692236	+	0.721672i	$0.743374\pi$
$384$	9.17873			0.468400
$385$		0			0
$386$	−32.3988			−1.64906
$387$	10.3375	+	7.51067i	0.525487	+	0.381789i
$388$	8.13879	−	25.0486i	0.413184	−	1.27165i
$389$	−8.29010	−	25.5143i	−0.420325	−	1.29363i	−0.907401	−	0.420267i	$-0.861936\pi$
$389$	−8.29010	−	25.5143i	−0.420325	−	1.29363i	0.487076	−	0.873360i	$-0.338064\pi$
$390$	−0.249948	+	0.181598i	−0.0126566	+	0.00919558i
$391$	8.88244	−	6.45347i	0.449204	−	0.326366i
$392$	4.80277	+	14.7814i	0.242577	+	0.746574i
$393$	−0.377647	+	1.16228i	−0.0190498	+	0.0586291i
$394$	−14.4569	−	10.5036i	−0.728331	−	0.529163i
$395$	−4.64663			−0.233797
$396$		0			0
$397$	31.5972			1.58582			0.792909	−	0.609340i	$-0.208565\pi$
$397$	31.5972			1.58582			0.792909	+	0.609340i	$0.208565\pi$
$398$	53.2027	+	38.6541i	2.66681	+	1.93755i
$399$	0.749833	−	2.30775i	0.0375386	−	0.115532i
$400$	4.80762	+	14.7963i	0.240381	+	0.739817i
$401$	2.53730	−	1.84346i	0.126707	−	0.0920580i	−0.522627	−	0.852562i	$-0.675048\pi$
$401$	2.53730	−	1.84346i	0.126707	−	0.0920580i	0.649334	+	0.760504i	$0.275048\pi$
$402$	−0.337481	+	0.245195i	−0.0168320	+	0.0122292i
$403$	−0.172367	−	0.530492i	−0.00858623	−	0.0264257i
$404$	−11.2500	+	34.6240i	−0.559709	+	1.72261i
$405$	6.95933	+	5.05625i	0.345812	+	0.251247i
$406$	−35.0080			−1.73742
$407$		0			0
$408$	4.95058			0.245090
$409$	−0.343459	−	0.249537i	−0.0169829	−	0.0123388i	0.579261	−	0.815142i	$-0.303341\pi$
$409$	−0.343459	−	0.249537i	−0.0169829	−	0.0123388i	−0.596244	+	0.802803i	$0.703341\pi$
$410$	8.99277	−	27.6769i	0.444121	−	1.36687i
$411$	−0.577466	−	1.77726i	−0.0284843	−	0.0876656i
$412$	−73.2302	+	53.2048i	−3.60779	+	2.62121i
$413$	−12.1145	+	8.80168i	−0.596114	+	0.433102i
$414$	−11.3665	−	34.9826i	−0.558635	−	1.71930i
$415$	−4.20331	+	12.9365i	−0.206333	+	0.635026i
$416$	−10.0684	−	7.31513i	−0.493644	−	0.358654i
$417$	3.55477			0.174078
$418$		0			0
$419$	6.71174			0.327890			0.163945	−	0.986469i	$-0.447578\pi$
$419$	6.71174			0.327890			0.163945	+	0.986469i	$0.447578\pi$
$420$	2.19225	+	1.59276i	0.106971	+	0.0777189i
$421$	0.859031	−	2.64383i	0.0418666	−	0.128852i	−0.927939	−	0.372733i	$-0.878421\pi$
$421$	0.859031	−	2.64383i	0.0418666	−	0.128852i	0.969805	+	0.243881i	$0.0784207\pi$
$422$	14.3063	+	44.0304i	0.696422	+	2.14337i
$423$	16.1844	−	11.7586i	0.786912	−	0.571725i
$424$	−35.5825	+	25.8522i	−1.72804	+	1.25549i
$425$	0.748288	+	2.30299i	0.0362973	+	0.111712i
$426$	0.810523	−	2.49453i	0.0392699	−	0.120860i
$427$	12.7787	+	9.28424i	0.618403	+	0.449296i
$428$	56.5070			2.73137
$429$		0			0
$430$	11.8667			0.572265
$431$	−13.1032	−	9.52000i	−0.631157	−	0.458562i	0.225644	−	0.974210i	$-0.427551\pi$
$431$	−13.1032	−	9.52000i	−0.631157	−	0.458562i	−0.856801	+	0.515647i	$0.827551\pi$
$432$	6.03440	−	18.5720i	0.290330	−	0.893545i
$433$	2.41878	+	7.44423i	0.116239	+	0.357747i	0.992203	−	0.124629i	$-0.0397740\pi$
$433$	2.41878	+	7.44423i	0.116239	+	0.357747i	−0.875964	+	0.482376i	$0.839774\pi$
$434$	−5.38834	+	3.91486i	−0.258648	+	0.187919i
$435$	0.936014	−	0.680054i	0.0448784	−	0.0326061i
$436$	−20.6786	−	63.6421i	−0.990323	−	3.04790i
$437$	−6.94329	+	21.3692i	−0.332143	+	1.02223i
$438$	−0.499897	−	0.363196i	−0.0238860	−	0.0173542i
$439$	20.7355			0.989650			0.494825	−	0.868993i	$-0.335232\pi$
$439$	20.7355			0.989650			0.494825	+	0.868993i	$0.335232\pi$
$440$		0			0
$441$	4.73546			0.225498
$442$	−2.87182	−	2.08650i	−0.136599	−	0.0992447i
$443$	1.63860	−	5.04309i	0.0778522	−	0.239604i	−0.904555	−	0.426358i	$-0.859796\pi$
$443$	1.63860	−	5.04309i	0.0778522	−	0.239604i	0.982407	+	0.186753i	$0.0597965\pi$
$444$	−2.69941	−	8.30792i	−0.128108	−	0.394276i
$445$	10.2865	−	7.47355i	0.487625	−	0.354280i
$446$	−55.5539	+	40.3623i	−2.63055	+	1.91121i
$447$	−0.290853	−	0.895154i	−0.0137569	−	0.0423393i
$448$	−23.5816	+	72.5767i	−1.11413	+	3.42893i
$449$	24.2730	+	17.6353i	1.14551	+	0.832263i	0.987878	−	0.155235i	$-0.0496133\pi$
$449$	24.2730	+	17.6353i	1.14551	+	0.832263i	0.157634	+	0.987498i	$0.449613\pi$
$450$	8.11256			0.382430
$451$		0			0
$452$	−60.0061			−2.82245
$453$	−1.96309	−	1.42627i	−0.0922340	−	0.0670119i
$454$	−3.40073	+	10.4664i	−0.159604	+	0.491211i
$455$	−0.383432	−	1.18008i	−0.0179756	−	0.0553232i
$456$	−8.19638	+	5.95502i	−0.383831	+	0.278869i
$457$	−30.3490	+	22.0498i	−1.41966	+	1.03145i	−0.427837	+	0.903856i	$0.640724\pi$
$457$	−30.3490	+	22.0498i	−1.41966	+	1.03145i	−0.991827	+	0.127591i	$0.959276\pi$
$458$	14.7015	+	45.2467i	0.686958	+	2.11424i
$459$	0.939232	−	2.89066i	0.0438396	−	0.134924i
$460$	−20.2997	−	14.7486i	−0.946480	−	0.687658i
$461$	15.7829			0.735083			0.367542	−	0.930007i	$-0.380200\pi$
$461$	15.7829			0.735083			0.367542	+	0.930007i	$0.380200\pi$
$462$		0			0
$463$	−16.5672			−0.769941			−0.384970	−	0.922929i	$-0.625788\pi$
$463$	−16.5672			−0.769941			−0.384970	+	0.922929i	$0.625788\pi$
$464$	69.0956	+	50.2009i	3.20768	+	2.33052i
$465$	0.0680200	−	0.209344i	0.00315435	−	0.00970809i
$466$	−1.79187	−	5.51480i	−0.0830067	−	0.255468i
$467$	−2.99369	+	2.17505i	−0.138532	+	0.100649i	−0.654893	−	0.755722i	$-0.727286\pi$
$467$	−2.99369	+	2.17505i	−0.138532	+	0.100649i	0.516361	+	0.856371i	$0.327286\pi$
$468$	−7.06714	+	5.13458i	−0.326679	+	0.237346i
$469$	−0.517712	−	1.59335i	−0.0239057	−	0.0735742i
$470$	5.74107	−	17.6692i	0.264816	−	0.815019i
$471$	−1.00788	−	0.732270i	−0.0464408	−	0.0337412i
$472$	62.5214			2.87778
$473$		0			0
$474$	2.68802			0.123465
$475$	−4.00915	−	2.91282i	−0.183952	−	0.133649i
$476$	−9.62103	+	29.6105i	−0.440979	+	1.35719i
$477$	4.14108	+	12.7449i	0.189607	+	0.583550i
$478$	−53.1501	+	38.6158i	−2.43103	+	1.76624i
$479$	−1.02303	+	0.743275i	−0.0467435	+	0.0339611i	−0.610912	−	0.791699i	$-0.709197\pi$
$479$	−1.02303	+	0.743275i	−0.0467435	+	0.0339611i	0.564168	+	0.825660i	$0.309197\pi$
$480$	−1.51763	−	4.67079i	−0.0692702	−	0.213192i
$481$	−1.23607	+	3.80423i	−0.0563598	+	0.173458i
$482$	−32.2286	−	23.4154i	−1.46797	−	1.06654i
$483$	−2.22012			−0.101019
$484$		0			0
$485$	−4.75919			−0.216104
$486$	−12.3877	−	9.00016i	−0.561915	−	0.408255i
$487$	6.67545	−	20.5449i	0.302494	−	0.930979i	−0.678107	−	0.734963i	$-0.737199\pi$
$487$	6.67545	−	20.5449i	0.302494	−	0.930979i	0.980601	−	0.196016i	$-0.0628005\pi$
$488$	−20.3794	−	62.7215i	−0.922534	−	2.83927i
$489$	4.00670	−	2.91104i	0.181189	−	0.131642i
$490$	3.55789	−	2.58496i	0.160729	−	0.116776i
$491$	7.89140	+	24.2872i	0.356134	+	1.09607i	0.955349	+	0.295479i	$0.0954793\pi$
$491$	7.89140	+	24.2872i	0.356134	+	1.09607i	−0.599215	+	0.800588i	$0.704521\pi$
$492$	−3.82123	+	11.7605i	−0.172274	+	0.530206i
$493$	10.7545	+	7.81358i	0.484357	+	0.351906i
$494$	7.26454			0.326847
$495$		0			0
$496$	16.2488			0.729594
$497$	8.52224	+	6.19177i	0.382275	+	0.277739i
$498$	2.43157	−	7.48360i	0.108961	−	0.335348i
$499$	7.52809	+	23.1691i	0.337003	+	1.03719i	0.965727	+	0.259561i	$0.0835778\pi$
$499$	7.52809	+	23.1691i	0.337003	+	1.03719i	−0.628723	+	0.777629i	$0.716422\pi$
$500$	4.47716	−	3.25284i	0.200225	−	0.145472i
$501$	2.42705	−	1.76336i	0.108433	−	0.0787809i
$502$	−24.4337	−	75.1993i	−1.09053	−	3.35631i
$503$	−3.86147	+	11.8844i	−0.172175	+	0.529899i	−0.999493	−	0.0318342i	$-0.989865\pi$
$503$	−3.86147	+	11.8844i	−0.172175	+	0.529899i	0.827319	+	0.561733i	$0.189865\pi$
$504$	53.8888	+	39.1525i	2.40040	+	1.74399i
$505$	6.57849			0.292739
$506$		0			0
$507$	2.67971			0.119010
$508$	36.3631	+	26.4193i	1.61335	+	1.17217i
$509$	7.55493	−	23.2517i	0.334866	−	1.03061i	−0.631922	−	0.775032i	$-0.717734\pi$
$509$	7.55493	−	23.2517i	0.334866	−	1.03061i	0.966788	−	0.255580i	$-0.0822665\pi$
$510$	−0.432876	−	1.33226i	−0.0191681	−	0.0589933i
$511$	2.00768	−	1.45866i	0.0888144	−	0.0645275i
$512$	49.1101	−	35.6806i	2.17038	−	1.57687i
$513$	1.92212	+	5.91568i	0.0848638	+	0.261184i
$514$	23.4524	−	72.1790i	1.03444	−	3.18368i
$515$	13.2326	+	9.61405i	0.583098	+	0.423646i
$516$	−5.04245			−0.221981
$517$		0			0
$518$	47.7622			2.09855
$519$	−1.09895	−	0.798430i	−0.0482383	−	0.0350472i
$520$	−1.60092	+	4.92714i	−0.0702052	+	0.216069i
$521$	−0.0121810	−	0.0374891i	−0.000533658	−	0.00164243i	0.950789	−	0.309838i	$-0.100275\pi$
$521$	−0.0121810	−	0.0374891i	−0.000533658	−	0.00164243i	−0.951323	+	0.308196i	$0.900275\pi$
$522$	36.0297	−	26.1771i	1.57698	−	1.14574i
$523$	17.0637	−	12.3975i	0.746142	−	0.542104i	−0.148486	−	0.988914i	$-0.547440\pi$
$523$	17.0637	−	12.3975i	0.746142	−	0.542104i	0.894629	+	0.446810i	$0.147440\pi$
$524$	9.91632	+	30.5193i	0.433197	+	1.33324i
$525$	0.151311	−	0.465687i	0.00660375	−	0.0203242i
$526$	6.95774	+	5.05509i	0.303372	+	0.220413i
$527$	2.52907			0.110168
$528$		0			0
$529$	−2.44221			−0.106183
$530$	10.0684	+	7.31513i	0.437344	+	0.317749i
$531$	5.88659	−	18.1171i	0.255456	−	0.786214i
$532$	−19.6893	−	60.5973i	−0.853638	−	2.62723i
$533$	4.58092	−	3.32823i	0.198422	−	0.144162i
$534$	−5.95060	+	4.32336i	−0.257508	+	0.187090i
$535$	−3.15530	−	9.71101i	−0.136415	−	0.419843i
$536$	−2.16157	+	6.65264i	−0.0933658	+	0.287350i
$537$	2.89506	+	2.10338i	0.124931	+	0.0907677i
$538$	−49.4152			−2.13044
$539$		0			0
$540$	−6.94622			−0.298918
$541$	27.0537	+	19.6557i	1.16313	+	0.845064i	0.990171	−	0.139865i	$-0.0446670\pi$
$541$	27.0537	+	19.6557i	1.16313	+	0.845064i	0.172960	+	0.984929i	$0.444667\pi$
$542$	−17.2461	+	53.0781i	−0.740785	+	2.27990i
$543$	−0.292398	−	0.899909i	−0.0125480	−	0.0386188i
$544$	45.6509	−	33.1673i	1.95726	−	1.42204i
$545$	−9.78252	+	7.10742i	−0.419037	+	0.304448i
$546$	0.221811	+	0.682664i	0.00949264	+	0.0292153i
$547$	10.1378	−	31.2010i	0.433461	−	1.33406i	−0.461194	−	0.887299i	$-0.652579\pi$
$547$	10.1378	−	31.2010i	0.433461	−	1.33406i	0.894655	−	0.446757i	$-0.147421\pi$
$548$	−39.6978	−	28.8421i	−1.69581	−	1.23208i
$549$	−20.0938			−0.857584
$550$		0			0
$551$	−27.2044			−1.15895
$552$	7.49921	+	5.44850i	0.319188	+	0.231903i
$553$	−3.33602	+	10.2672i	−0.141862	+	0.436606i
$554$	21.6203	+	66.5403i	0.918557	+	2.82703i
$555$	−1.27702	+	0.927812i	−0.0542066	+	0.0393834i
$556$	75.5151	−	54.8649i	3.20255	−	2.32679i
$557$	8.75528	+	26.9460i	0.370973	+	1.14174i	0.946155	+	0.323712i	$0.104931\pi$
$557$	8.75528	+	26.9460i	0.370973	+	1.14174i	−0.575182	+	0.818025i	$0.695069\pi$
$558$	2.61827	−	8.05821i	0.110840	−	0.341131i
$559$	1.86798	+	1.35717i	0.0790072	+	0.0574021i
$560$	36.1456			1.52743
$561$		0			0
$562$	−50.1550			−2.11566
$563$	−23.4907	−	17.0670i	−0.990015	−	0.719288i	−0.0300908	−	0.999547i	$-0.509580\pi$
$563$	−23.4907	−	17.0670i	−0.990015	−	0.719288i	−0.959924	+	0.280259i	$0.909580\pi$
$564$	−2.43951	+	7.50803i	−0.102722	+	0.316145i
$565$	3.35068	+	10.3123i	0.140964	+	0.433843i
$566$	−24.5461	+	17.8338i	−1.03175	+	0.749611i
$567$	16.1687	−	11.7473i	0.679022	−	0.493339i
$568$	−13.5913	−	41.8297i	−0.570278	−	1.75513i
$569$	8.87181	−	27.3046i	0.371925	−	1.14467i	−0.573604	−	0.819133i	$-0.694455\pi$
$569$	8.87181	−	27.3046i	0.371925	−	1.14467i	0.945530	−	0.325536i	$-0.105545\pi$
$570$	2.31925	+	1.68503i	0.0971425	+	0.0705782i
$571$	0.824301			0.0344959			0.0172480	−	0.999851i	$-0.494510\pi$
$571$	0.824301			0.0344959			0.0172480	+	0.999851i	$0.494510\pi$
$572$		0			0
$573$	0.581515			0.0242931
$574$	−54.6987	−	39.7409i	−2.28308	−	1.65875i
$575$	−1.40110	+	4.31216i	−0.0584301	+	0.179829i
$576$	−29.9991	−	92.3278i	−1.24996	−	3.84699i
$577$	25.5181	−	18.5400i	1.06233	−	0.771829i	0.0878137	−	0.996137i	$-0.472012\pi$
$577$	25.5181	−	18.5400i	1.06233	−	0.771829i	0.974518	+	0.224307i	$0.0720120\pi$
$578$	−24.7293	+	17.9669i	−1.02861	+	0.747325i
$579$	−0.768735	−	2.36592i	−0.0319475	−	0.0983244i
$580$	9.38797	−	28.8932i	0.389814	−	1.19973i
$581$	25.5667	+	18.5753i	1.06069	+	0.770634i
$582$	2.75313			0.114121
$583$		0			0
$584$	−10.3614			−0.428758
$585$	1.27702	+	0.927812i	0.0527984	+	0.0383603i
$586$	−23.0195	+	70.8467i	−0.950927	+	2.92665i
$587$	−8.27348	−	25.4632i	−0.341483	−	1.05098i	−0.963440	−	0.267925i	$-0.913662\pi$
$587$	−8.27348	−	25.4632i	−0.341483	−	1.05098i	0.621957	−	0.783052i	$-0.286338\pi$
$588$	−1.51183	+	1.09841i	−0.0623466	+	0.0452975i
$589$	−4.18723	+	3.04220i	−0.172532	+	0.125352i
$590$	−5.46683	−	16.8252i	−0.225066	−	0.692682i
$591$	0.424000	−	1.30494i	0.0174410	−	0.0536780i
$592$	−94.2686	−	68.4902i	−3.87442	−	2.81493i
$593$	−11.0731			−0.454719			−0.227360	−	0.973811i	$-0.573009\pi$
$593$	−11.0731			−0.454719			−0.227360	+	0.973811i	$0.573009\pi$
$594$		0			0
$595$	5.62593			0.230641
$596$	−19.9947	−	14.5270i	−0.819014	−	0.595048i
$597$	−1.56036	+	4.80228i	−0.0638611	+	0.196544i
$598$	−2.05392	−	6.32132i	−0.0839911	−	0.258498i
$599$	9.65553	−	7.01515i	0.394514	−	0.286631i	−0.372789	−	0.927916i	$-0.621598\pi$
$599$	9.65553	−	7.01515i	0.394514	−	0.286631i	0.767303	+	0.641285i	$0.221598\pi$
$600$	−1.65397	+	1.20168i	−0.0675230	+	0.0490583i
$601$	1.62683	+	5.00687i	0.0663598	+	0.204235i	0.978738	−	0.205113i	$-0.0657563\pi$
$601$	1.62683	+	5.00687i	0.0663598	+	0.204235i	−0.912378	+	0.409348i	$0.865756\pi$
$602$	8.51965	−	26.2208i	0.347235	−	1.06868i
$603$	1.72424	+	1.25274i	0.0702166	+	0.0510153i
$604$	−63.7158			−2.59256
$605$		0			0
$606$	−3.80558			−0.154591
$607$	−29.0001	−	21.0698i	−1.17708	−	0.855196i	−0.185237	−	0.982694i	$-0.559305\pi$
$607$	−29.0001	−	21.0698i	−1.17708	−	0.855196i	−0.991839	+	0.127498i	$0.959305\pi$
$608$	−35.6847	+	109.826i	−1.44720	+	4.45404i
$609$	−0.830644	−	2.55646i	−0.0336594	−	0.103593i
$610$	−15.0971	+	10.9687i	−0.611262	+	0.444108i
$611$	2.92450	−	2.12477i	0.118313	−	0.0859591i
$612$	−12.2393	−	37.6687i	−0.494744	−	1.52267i
$613$	2.02647	−	6.23683i	0.0818483	−	0.251903i	−0.901755	−	0.432247i	$-0.857721\pi$
$613$	2.02647	−	6.23683i	0.0818483	−	0.251903i	0.983604	+	0.180344i	$0.0577209\pi$
$614$	26.0666	+	18.9385i	1.05196	+	0.764296i
$615$	2.23448			0.0901029
$616$		0			0
$617$	17.7986			0.716545			0.358272	−	0.933617i	$-0.383366\pi$
$617$	17.7986			0.716545			0.358272	+	0.933617i	$0.383366\pi$
$618$	−7.65491	−	5.56161i	−0.307925	−	0.223721i
$619$	13.8719	−	42.6934i	0.557559	−	1.71599i	−0.131527	−	0.991313i	$-0.541988\pi$
$619$	13.8719	−	42.6934i	0.557559	−	1.71599i	0.689087	−	0.724679i	$-0.258012\pi$
$620$	−1.78608	−	5.49700i	−0.0717308	−	0.220765i
$621$	4.60415	−	3.34511i	0.184758	−	0.134235i
$622$	23.6309	−	17.1689i	0.947513	−	0.688409i
$623$	−9.12849	−	28.0946i	−0.365725	−	1.12559i
$624$	0.541138	−	1.66545i	0.0216629	−	0.0666715i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	74.6063			2.98187
$627$		0			0
$628$	−32.7128			−1.30538
$629$	−14.6726	−	10.6602i	−0.585033	−	0.425052i
$630$	5.82436	−	17.9255i	0.232048	−	0.714170i
$631$	6.77092	+	20.8388i	0.269546	+	0.829578i	0.990611	+	0.136710i	$0.0436529\pi$
$631$	6.77092	+	20.8388i	0.269546	+	0.829578i	−0.721065	+	0.692867i	$0.756347\pi$
$632$	36.4658	−	26.4939i	1.45053	−	1.05387i
$633$	−2.87587	+	2.08944i	−0.114305	+	0.0830477i
$634$	−4.22344	−	12.9984i	−0.167734	−	0.516232i
$635$	2.50981	−	7.72440i	0.0995988	−	0.306534i
$636$	−4.27829	−	3.10836i	−0.169645	−	0.123254i
$637$	0.855693			0.0339038
$638$		0			0
$639$	−13.4008			−0.530128
$640$	−35.2339	−	25.5989i	−1.39274	−	1.01189i
$641$	11.0423	−	33.9846i	0.436143	−	1.34231i	−0.455768	−	0.890099i	$-0.650635\pi$
$641$	11.0423	−	33.9846i	0.436143	−	1.34231i	0.891911	−	0.452211i	$-0.149365\pi$
$642$	1.82530	+	5.61770i	0.0720389	+	0.221713i
$643$	−0.333437	+	0.242256i	−0.0131495	+	0.00955364i	−0.594341	−	0.804213i	$-0.702587\pi$
$643$	−0.333437	+	0.242256i	−0.0131495	+	0.00955364i	0.581191	+	0.813767i	$0.302587\pi$
$644$	−47.1627	+	34.2657i	−1.85847	+	1.35026i
$645$	0.281565	+	0.866568i	0.0110866	+	0.0341211i
$646$	−10.1784	+	31.3258i	−0.400463	+	1.23250i
$647$	13.3880	+	9.72692i	0.526335	+	0.382405i	0.818985	−	0.573815i	$-0.194537\pi$
$647$	13.3880	+	9.72692i	0.526335	+	0.382405i	−0.292650	+	0.956220i	$0.594537\pi$
$648$	−83.4450			−3.27803
$649$		0			0
$650$	1.46593			0.0574985
$651$	−0.413733	−	0.300594i	−0.0162155	−	0.0117812i
$652$	40.1862	−	123.680i	1.57381	−	4.84370i
$653$	3.40167	+	10.4693i	0.133118	+	0.409694i	0.995292	−	0.0969171i	$-0.0308982\pi$
$653$	3.40167	+	10.4693i	0.133118	+	0.409694i	−0.862175	+	0.506611i	$0.830898\pi$
$654$	5.65907	−	4.11156i	0.221287	−	0.160775i
$655$	4.69117	−	3.40833i	0.183299	−	0.133175i
$656$	50.9714	+	156.874i	1.99010	+	6.12490i
$657$	−0.975559	+	3.00246i	−0.0380602	+	0.117137i
$658$	−34.9201	−	25.3710i	−1.36133	−	0.989063i
$659$	42.9980			1.67497			0.837483	−	0.546464i	$-0.184026\pi$
$659$	42.9980			1.67497			0.837483	+	0.546464i	$0.184026\pi$
$660$		0			0
$661$	19.4927			0.758177			0.379089	−	0.925360i	$-0.376238\pi$
$661$	19.4927			0.758177			0.379089	+	0.925360i	$0.376238\pi$
$662$	16.7762	+	12.1886i	0.652025	+	0.473724i
$663$	0.0842262	−	0.259221i	0.00327107	−	0.0100673i
$664$	−40.7739	−	125.489i	−1.58233	−	4.86992i
$665$	−9.31452	+	6.76739i	−0.361201	+	0.262428i
$666$	−49.1561	+	35.7140i	−1.90476	+	1.38389i
$667$	7.69158	+	23.6722i	0.297819	+	0.916593i
$668$	24.3427	−	74.9191i	0.941847	−	2.89871i
$669$	−4.26559	−	3.09913i	−0.164917	−	0.119819i
$670$	1.97930			0.0764672
$671$		0			0
$672$	−11.4102			−0.440157
$673$	5.50668	+	4.00084i	0.212267	+	0.154221i	0.688839	−	0.724915i	$-0.258121\pi$
$673$	5.50668	+	4.00084i	0.212267	+	0.154221i	−0.476572	+	0.879136i	$0.658121\pi$
$674$	−3.13074	+	9.63542i	−0.120592	+	0.371143i
$675$	0.387870	+	1.19374i	0.0149291	+	0.0459471i
$676$	56.9260	−	41.3592i	2.18946	−	1.59074i
$677$	0.825760	−	0.599950i	0.0317365	−	0.0230579i	−0.571804	−	0.820390i	$-0.693756\pi$
$677$	0.825760	−	0.599950i	0.0317365	−	0.0230579i	0.603540	+	0.797332i	$0.293756\pi$
$678$	−1.93833	−	5.96556i	−0.0744410	−	0.229106i
$679$	−3.41683	+	10.5159i	−0.131126	+	0.403564i
$680$	−19.0035	−	13.8069i	−0.728752	−	0.529469i
$681$	−0.844996			−0.0323803
$682$		0			0
$683$	2.09820			0.0802853			0.0401426	−	0.999194i	$-0.487219\pi$
$683$	2.09820			0.0802853			0.0401426	+	0.999194i	$0.487219\pi$
$684$	65.5753	+	47.6432i	2.50733	+	1.82168i
$685$	−2.73998	+	8.43278i	−0.104689	+	0.322200i
$686$	−16.9518	−	52.1722i	−0.647222	−	1.99194i
$687$	−2.95531	+	2.14716i	−0.112752	+	0.0819192i
$688$	−54.4155	+	39.5352i	−2.07457	+	1.50726i
$689$	0.748288	+	2.30299i	0.0285075	+	0.0877371i
$690$	0.810523	−	2.49453i	0.0308561	−	0.0949652i
$691$	−9.70416	−	7.05048i	−0.369164	−	0.268213i	0.387700	−	0.921785i	$-0.373270\pi$
$691$	−9.70416	−	7.05048i	−0.369164	−	0.268213i	−0.756864	+	0.653572i	$0.773270\pi$
$692$	−35.6684			−1.35591
$693$		0			0
$694$	43.2736			1.64264
$695$	−13.6455	−	9.91402i	−0.517603	−	0.376060i
$696$	−3.46814	+	10.6738i	−0.131460	+	0.404591i
$697$	7.93351	+	24.4168i	0.300503	+	0.924854i
$698$	−23.4447	+	17.0336i	−0.887397	+	0.644732i
$699$	0.360202	−	0.261702i	0.0136241	−	0.00989848i
$700$	−3.97315	−	12.2281i	−0.150171	−	0.462179i
$701$	9.07256	−	27.9225i	0.342666	−	1.05462i	−0.620156	−	0.784479i	$-0.712931\pi$
$701$	9.07256	−	27.9225i	0.342666	−	1.05462i	0.962822	−	0.270138i	$-0.0870695\pi$
$702$	−1.48859	−	1.08152i	−0.0561832	−	0.0408195i
$703$	37.1156			1.39984
$704$		0			0
$705$	1.42651			0.0537255
$706$	−54.5222	−	39.6127i	−2.05197	−	1.49084i
$707$	4.72298	−	14.5358i	0.177626	−	0.546677i
$708$	2.32298	+	7.14940i	0.0873029	+	0.268691i
$709$	30.3746	−	22.0685i	1.14074	−	0.828799i	0.153521	−	0.988145i	$-0.450939\pi$
$709$	30.3746	−	22.0685i	1.14074	−	0.828799i	0.987223	+	0.159347i	$0.0509387\pi$
$710$	−10.0684	+	7.31513i	−0.377861	+	0.274532i
$711$	−4.24388	−	13.0613i	−0.159158	−	0.489838i
$712$	−38.1137	+	117.302i	−1.42837	+	4.39607i
$713$	3.83107	+	2.78344i	0.143475	+	0.104241i
$714$	−3.25454			−0.121798
$715$		0			0
$716$	93.9647			3.51162
$717$	−4.08102	−	2.96503i	−0.152408	−	0.110731i
$718$	14.1398	−	43.5177i	0.527691	−	1.62407i
$719$	−1.23452	−	3.79947i	−0.0460399	−	0.141696i	0.925394	−	0.379007i	$-0.123734\pi$
$719$	−1.23452	−	3.79947i	−0.0460399	−	0.141696i	−0.971434	+	0.237310i	$0.923734\pi$
$720$	−37.2005	+	27.0277i	−1.38638	+	1.00726i
$721$	30.7435	−	22.3365i	1.14495	−	0.831853i
$722$	−4.71411	−	14.5085i	−0.175441	−	0.539952i
$723$	0.945215	−	2.90907i	0.0351529	−	0.108190i
$724$	−20.1009	−	14.6041i	−0.747043	−	0.542759i
$725$	−5.48965			−0.203881
$726$		0			0
$727$	−25.4990			−0.945706			−0.472853	−	0.881141i	$-0.656776\pi$
$727$	−25.4990			−0.945706			−0.472853	+	0.881141i	$0.656776\pi$
$728$	9.73765	+	7.07481i	0.360901	+	0.262210i
$729$	−7.61138	+	23.4254i	−0.281903	+	0.867608i
$730$	0.905994	+	2.78836i	0.0335324	+	0.103202i
$731$	−8.46956	+	6.15350i	−0.313258	+	0.227595i
$732$	6.41508	−	4.66083i	0.237108	−	0.172269i
$733$	−11.1872	−	34.4306i	−0.413208	−	1.27172i	−0.913844	−	0.406065i	$-0.866901\pi$
$733$	−11.1872	−	34.4306i	−0.413208	−	1.27172i	0.500637	−	0.865658i	$-0.333099\pi$
$734$	−12.9595	+	39.8853i	−0.478345	+	1.47219i
$735$	0.273185	+	0.198481i	0.0100766	+	0.00732107i
$736$	105.656			3.89452
$737$		0			0
$738$	86.0111			3.16611
$739$	4.90274	+	3.56205i	0.180350	+	0.131032i	0.674298	−	0.738460i	$-0.264447\pi$
$739$	4.90274	+	3.56205i	0.180350	+	0.131032i	−0.493948	+	0.869492i	$0.664447\pi$
$740$	−12.8082	+	39.4196i	−0.470839	+	1.44909i
$741$	0.172367	+	0.530492i	0.00633207	+	0.0194881i
$742$	23.3921	−	16.9953i	0.858750	−	0.623918i
$743$	−29.3567	+	21.3289i	−1.07699	+	0.782482i	−0.977156	−	0.212522i	$-0.931832\pi$
$743$	−29.3567	+	21.3289i	−1.07699	+	0.782482i	−0.0998379	+	0.995004i	$0.531832\pi$
$744$	0.659821	+	2.03072i	0.0241902	+	0.0744499i
$745$	−1.38005	+	4.24735i	−0.0505611	+	0.155611i
$746$	39.6291	+	28.7923i	1.45093	+	1.05416i
$747$	−40.2024			−1.47093
$748$		0			0
$749$	−23.7228			−0.866812
$750$	0.468007	+	0.340027i	0.0170892	+	0.0124160i
$751$	−4.86192	+	14.9634i	−0.177414	+	0.546024i	−0.999735	−	0.0229993i	$-0.992678\pi$
$751$	−4.86192	+	14.9634i	−0.177414	+	0.546024i	0.822322	+	0.569023i	$0.192678\pi$
$752$	32.5406	+	100.150i	1.18663	+	3.65209i
$753$	4.91168	−	3.56854i	0.178991	−	0.130045i
$754$	6.51052	−	4.73017i	0.237099	−	0.172263i
$755$	3.55783	+	10.9499i	0.129483	+	0.398507i
$756$	−4.98699	+	15.3484i	−0.181375	+	0.558216i
$757$	20.3381	+	14.7765i	0.739202	+	0.537062i	0.892461	−	0.451124i	$-0.148977\pi$
$757$	20.3381	+	14.7765i	0.739202	+	0.537062i	−0.153259	+	0.988186i	$0.548977\pi$
$758$	−5.19442			−0.188670
$759$		0			0
$760$	48.0712			1.74372
$761$	12.5162	+	9.09358i	0.453714	+	0.329642i	0.791060	−	0.611738i	$-0.209529\pi$
$761$	12.5162	+	9.09358i	0.453714	+	0.329642i	−0.337347	+	0.941380i	$0.609529\pi$
$762$	−1.45190	+	4.46848i	−0.0525967	+	0.161876i
$763$	8.68128	+	26.7182i	0.314283	+	0.967264i
$764$	12.3533	−	8.97521i	0.446927	−	0.324712i
$765$	−5.79012	+	4.20677i	−0.209342	+	0.152096i
$766$	−4.50985	−	13.8799i	−0.162948	−	0.501501i
$767$	1.06370	−	3.27373i	0.0384080	−	0.118208i
$768$	9.18154	+	6.67078i	0.331310	+	0.240711i
$769$	17.3220			0.624647			0.312323	−	0.949976i	$-0.398893\pi$
$769$	17.3220			0.624647			0.312323	+	0.949976i	$0.398893\pi$
$770$		0			0
$771$	5.82733			0.209866
$772$	−52.8466	−	38.3953i	−1.90199	−	1.38188i
$773$	−7.01440	+	21.5881i	−0.252290	+	0.776470i	0.742061	+	0.670332i	$0.233848\pi$
$773$	−7.01440	+	21.5881i	−0.252290	+	0.776470i	−0.994351	+	0.106138i	$0.966152\pi$
$774$	10.8382	+	33.3565i	0.389571	+	1.19898i
$775$	−0.844952	+	0.613894i	−0.0303516	+	0.0220517i
$776$	37.3491	−	27.1357i	1.34076	−	0.974116i
$777$	1.13327	+	3.48783i	0.0406557	+	0.125125i
$778$	22.7549	−	70.0323i	0.815802	−	2.51078i
$779$	−42.5059	−	30.8823i	−1.52293	−	1.10647i
$780$	−0.622906			−0.0223036
$781$		0			0
$782$	30.1363			1.07767
$783$	5.57451	+	4.05012i	0.199217	+	0.144739i
$784$	−7.70282	+	23.7069i	−0.275101	+	0.846673i
$785$	1.82665	+	5.62185i	0.0651959	+	0.200652i
$786$	−2.71379	+	1.97168i	−0.0967976	+	0.0703276i
$787$	−2.50894	+	1.82285i	−0.0894342	+	0.0649777i	−0.631604	−	0.775291i	$-0.717603\pi$
$787$	−2.50894	+	1.82285i	−0.0894342	+	0.0649777i	0.542170	+	0.840269i	$0.317603\pi$
$788$	−11.1335	−	34.2654i	−0.396614	−	1.22065i
$789$	−0.204060	+	0.628032i	−0.00726473	+	0.0223585i
$790$	−10.3184	−	7.49672i	−0.367111	−	0.266721i
$791$	25.1918			0.895716
$792$		0			0
$793$	−3.63093			−0.128938
$794$	70.1651	+	50.9779i	2.49007	+	1.80914i
$795$	−0.295291	+	0.908812i	−0.0104729	+	0.0322323i
$796$	40.9721	+	126.099i	1.45222	+	4.46947i
$797$	15.4456	−	11.2219i	0.547113	−	0.397501i	−0.279607	−	0.960115i	$-0.590204\pi$
$797$	15.4456	−	11.2219i	0.547113	−	0.397501i	0.826720	+	0.562614i	$0.190204\pi$
$798$	5.38834	−	3.91486i	0.190745	−	0.138584i
$799$	5.06483	+	15.5879i	0.179181	+	0.551461i
$800$	−7.20091	+	22.1621i	−0.254590	+	0.783549i
$801$	30.4025	+	22.0887i	1.07422	+	0.780466i
$802$	8.60855			0.303978
$803$		0			0
$804$	−0.841051			−0.0296616
$805$	8.52224	+	6.19177i	0.300370	+	0.218231i
$806$	0.473118	−	1.45611i	0.0166649	−	0.0512892i
$807$	−1.17249	−	3.60854i	−0.0412735	−	0.127027i
$808$	−51.6266	+	37.5089i	−1.81622	+	1.31956i
$809$	−3.61546	+	2.62679i	−0.127113	+	0.0923529i	−0.649525	−	0.760340i	$-0.725032\pi$
$809$	−3.61546	+	2.62679i	−0.127113	+	0.0923529i	0.522412	+	0.852693i	$0.325032\pi$
$810$	7.29638	+	22.4559i	0.256369	+	0.789021i
$811$	−1.50391	+	4.62855i	−0.0528093	+	0.162530i	−0.973983	−	0.226622i	$-0.927232\pi$
$811$	−1.50391	+	4.62855i	−0.0528093	+	0.162530i	0.921174	+	0.389152i	$0.127232\pi$
$812$	−57.1025	−	41.4874i	−2.00390	−	1.45592i
$813$	−4.28523			−0.150290
$814$		0			0
$815$	−23.4990			−0.823135
$816$	6.42350	+	4.66695i	0.224868	+	0.163376i
$817$	6.62055	−	20.3759i	0.231624	−	0.712864i
$818$	−0.360093	−	1.10825i	−0.0125903	−	0.0387491i
$819$	2.96693	−	2.15560i	0.103673	−	0.0753227i
$820$	47.4678	−	34.4873i	1.65765	−	1.20435i
$821$	5.25483	+	16.1727i	0.183395	+	0.564432i	0.999917	−	0.0128826i	$-0.00410077\pi$
$821$	5.25483	+	16.1727i	0.183395	+	0.564432i	−0.816522	+	0.577314i	$0.804101\pi$
$822$	1.58504	−	4.87826i	0.0552847	−	0.170149i
$823$	17.5944	+	12.7831i	0.613302	+	0.445590i	0.850575	−	0.525853i	$-0.176254\pi$
$823$	17.5944	+	12.7831i	0.613302	+	0.445590i	−0.237274	+	0.971443i	$0.576254\pi$
$824$	−158.664			−5.52731
$825$		0			0
$826$	−41.1019			−1.43012
$827$	16.7535	+	12.1721i	0.582575	+	0.423266i	0.839652	−	0.543125i	$-0.182759\pi$
$827$	16.7535	+	12.1721i	0.582575	+	0.423266i	−0.257076	+	0.966391i	$0.582759\pi$
$828$	22.9170	−	70.5314i	0.796422	−	2.45113i
$829$	3.49466	+	10.7555i	0.121375	+	0.373552i	0.993223	−	0.116223i	$-0.0370788\pi$
$829$	3.49466	+	10.7555i	0.121375	+	0.373552i	−0.871849	+	0.489775i	$0.837079\pi$
$830$	−30.2052	+	21.9454i	−1.04844	+	0.761735i
$831$	−4.34612	+	3.15764i	−0.150765	+	0.109537i
$832$	−5.42081	−	16.6835i	−0.187933	−	0.578397i
$833$	−1.19892	+	3.68988i	−0.0415400	+	0.127847i
$834$	7.89375	+	5.73515i	0.273338	+	0.198592i
$835$	−14.2345			−0.492604
$836$		0			0
$837$	1.31093			0.0453122
$838$	14.9042	+	10.8285i	0.514856	+	0.374065i
$839$	−13.4448	+	41.3789i	−0.464167	+	1.42856i	0.395860	+	0.918311i	$0.370446\pi$
$839$	−13.4448	+	41.3789i	−0.464167	+	1.42856i	−0.860027	+	0.510248i	$0.829554\pi$
$840$	1.46778	+	4.51735i	0.0506431	+	0.155863i
$841$	−0.919270	+	0.667889i	−0.0316990	+	0.0230307i
$842$	6.17304	−	4.48497i	0.212737	−	0.154562i
$843$	−1.19004	−	3.66257i	−0.0409871	−	0.126145i
$844$	−28.8442	+	88.7733i	−0.992858	+	3.05570i
$845$	−10.2865	−	7.47355i	−0.353865	−	0.257098i
$846$	54.9102			1.88785
$847$		0			0
$848$	−70.5401			−2.42236
$849$	−1.88473	−	1.36933i	−0.0646836	−	0.0469954i
$850$	−2.05392	+	6.32132i	−0.0704489	+	0.216819i
$851$	−10.4938	−	32.2966i	−0.359722	−	1.10711i
$852$	4.27829	−	3.10836i	0.146572	−	0.106491i
$853$	0.902527	−	0.655724i	0.0309019	−	0.0224516i	−0.572227	−	0.820095i	$-0.693920\pi$
$853$	0.902527	−	0.655724i	0.0309019	−	0.0224516i	0.603129	+	0.797644i	$0.293920\pi$
$854$	13.3975	+	41.2334i	0.458454	+	1.41098i
$855$	4.52606	−	13.9298i	0.154788	−	0.476388i
$856$	80.1319	+	58.2192i	2.73885	+	1.98989i
$857$	7.80361			0.266566			0.133283	−	0.991078i	$-0.457448\pi$
$857$	7.80361			0.266566			0.133283	+	0.991078i	$0.457448\pi$
$858$		0			0
$859$	30.5341			1.04181			0.520905	−	0.853615i	$-0.325595\pi$
$859$	30.5341			1.04181			0.520905	+	0.853615i	$0.325595\pi$
$860$	19.3562	+	14.0631i	0.660039	+	0.479547i
$861$	1.60423	−	4.93731i	0.0546720	−	0.168263i
$862$	−13.7377	−	42.2804i	−0.467910	−	1.44008i
$863$	3.47035	−	2.52136i	0.118132	−	0.0858281i	−0.527150	−	0.849772i	$-0.676740\pi$
$863$	3.47035	−	2.52136i	0.118132	−	0.0858281i	0.645283	+	0.763944i	$0.276740\pi$
$864$	23.6628	−	17.1920i	0.805025	−	0.584885i
$865$	1.99169	+	6.12978i	0.0677194	+	0.208419i
$866$	−6.63912	+	20.4331i	−0.225607	+	0.694346i
$867$	−1.89879	−	1.37955i	−0.0644864	−	0.0468521i
$868$	−13.4285			−0.455792
$869$		0			0
$870$	3.17570			0.107666
$871$	0.311569	+	0.226368i	0.0105571	+	0.00767018i
$872$	36.2465	−	111.555i	1.22746	−	3.77773i
$873$	−4.34668	−	13.3777i	−0.147113	−	0.452767i
$874$	−49.8948	+	36.2507i	−1.68772	+	1.22620i
$875$	−1.87960	+	1.36561i	−0.0635421	+	0.0461660i
$876$	−0.384977	−	1.18484i	−0.0130072	−	0.0400320i
$877$	3.51180	−	10.8082i	0.118585	−	0.364967i	−0.874093	−	0.485759i	$-0.838543\pi$
$877$	3.51180	−	10.8082i	0.118585	−	0.364967i	0.992678	+	0.120792i	$0.0385433\pi$
$878$	46.0454	+	33.4539i	1.55396	+	1.12902i
$879$	−5.71977			−0.192923
$880$		0			0
$881$	−11.3277			−0.381639			−0.190820	−	0.981625i	$-0.561115\pi$
$881$	−11.3277			−0.381639			−0.190820	+	0.981625i	$0.561115\pi$
$882$	10.5156	+	7.64005i	0.354080	+	0.257254i
$883$	9.66860	−	29.7569i	0.325374	−	1.00140i	−0.645897	−	0.763425i	$-0.723516\pi$
$883$	9.66860	−	29.7569i	0.325374	−	1.00140i	0.971271	−	0.237975i	$-0.0764836\pi$
$884$	−2.21163	−	6.80669i	−0.0743851	−	0.228934i
$885$	1.09895	−	0.798430i	0.0369406	−	0.0268389i
$886$	11.7751	−	8.55508i	0.395591	−	0.287413i
$887$	−8.73959	−	26.8977i	−0.293447	−	0.903137i	−0.983739	−	0.179606i	$-0.942518\pi$
$887$	−8.73959	−	26.8977i	−0.293447	−	0.903137i	0.690292	−	0.723531i	$-0.257482\pi$
$888$	4.73166	−	14.5626i	0.158784	−	0.488687i
$889$	−15.2660	−	11.0914i	−0.512004	−	0.371993i
$890$	34.8998			1.16984
$891$		0			0
$892$	−138.448			−4.63558
$893$	−27.1361	−	19.7155i	−0.908076	−	0.659756i
$894$	0.798342	−	2.45704i	0.0267005	−	0.0821758i
$895$	−5.24689	−	16.1483i	−0.175384	−	0.539777i
$896$	−81.8594	+	59.4743i	−2.73473	+	1.98690i
$897$	0.412880	−	0.299975i	0.0137857	−	0.0100159i
$898$	25.4485	+	78.3224i	0.849228	+	2.61365i
$899$	−1.77175	+	5.45287i	−0.0590911	+	0.181864i
$900$	13.2326	+	9.61405i	0.441087	+	0.320468i
$901$	−10.9793			−0.365774
$902$		0			0
$903$	2.11692			0.0704467
$904$	−85.0938	−	61.8243i	−2.83018	−	2.05625i
$905$	−1.38738	+	4.26991i	−0.0461180	+	0.141937i
$906$	−2.05816	−	6.33437i	−0.0683778	−	0.210445i
$907$	−27.1964	+	19.7593i	−0.903041	+	0.656098i	−0.939245	−	0.343247i	$-0.888473\pi$
$907$	−27.1964	+	19.7593i	−0.903041	+	0.656098i	0.0362044	+	0.999344i	$0.488473\pi$
$908$	−17.9505	+	13.0418i	−0.595710	+	0.432808i
$909$	6.00830	+	18.4916i	0.199283	+	0.613329i
$910$	1.05245	−	3.23912i	0.0348885	−	0.107376i
$911$	−6.09274	−	4.42664i	−0.201862	−	0.146661i	0.482262	−	0.876027i	$-0.339815\pi$
$911$	−6.09274	−	4.42664i	−0.201862	−	0.146661i	−0.684124	+	0.729366i	$0.739815\pi$
$912$	−16.2488			−0.538053
$913$		0			0
$914$	−102.968			−3.40587
$915$	−1.15920	−	0.842206i	−0.0383219	−	0.0278425i
$916$	−29.6410	+	91.2256i	−0.979366	+	3.01418i
$917$	−4.16307	−	12.8126i	−0.137477	−	0.423110i
$918$	6.74937	−	4.90370i	0.222762	−	0.161846i
$919$	−32.3950	+	23.5364i	−1.06861	+	0.776393i	−0.975662	−	0.219278i	$-0.929630\pi$
$919$	−32.3950	+	23.5364i	−1.06861	+	0.776393i	−0.0929506	+	0.995671i	$0.529630\pi$
$920$	−13.5913	−	41.8297i	−0.448091	−	1.37908i
$921$	−0.764494	+	2.35287i	−0.0251909	+	0.0775298i
$922$	35.0477	+	25.4636i	1.15423	+	0.838601i
$923$	−2.42151			−0.0797050
$924$		0			0
$925$	7.48965			0.246258
$926$	−36.7892	−	26.7289i	−1.20897	−	0.878367i
$927$	−14.9387	+	45.9766i	−0.490652	+	1.51007i
$928$	39.5305	+	121.662i	1.29765	+	3.99376i
$929$	−41.5355	+	30.1773i	−1.36274	+	0.990085i	−0.364470	+	0.931215i	$0.618750\pi$
$929$	−41.5355	+	30.1773i	−1.36274	+	0.990085i	−0.998266	+	0.0588702i	$0.981250\pi$
$930$	0.488795	−	0.355130i	0.0160282	−	0.0116452i
$931$	−2.45356	−	7.55128i	−0.0804122	−	0.247483i
$932$	3.61273	−	11.1188i	0.118339	−	0.364210i
$933$	1.81445	+	1.31828i	0.0594025	+	0.0431584i
$934$	−10.1570			−0.332346
$935$		0			0
$936$	−15.3120			−0.500488
$937$	29.0041	+	21.0727i	0.947523	+	0.688416i	0.950220	−	0.311581i	$-0.100858\pi$
$937$	29.0041	+	21.0727i	0.947523	+	0.688416i	−0.00269678	+	0.999996i	$0.500858\pi$
$938$	1.42103	−	4.37348i	0.0463982	−	0.142799i
$939$	1.77020	+	5.44812i	0.0577683	+	0.177793i
$940$	30.3039	−	22.0170i	0.988403	−	0.718117i
$941$	0.491243	−	0.356909i	0.0160141	−	0.0116349i	−0.579749	−	0.814795i	$-0.696850\pi$
$941$	0.491243	−	0.356909i	0.0160141	−	0.0116349i	0.595764	+	0.803160i	$0.296850\pi$
$942$	−1.05670	−	3.25217i	−0.0344290	−	0.105962i
$943$	−14.8548	+	45.7184i	−0.483739	+	1.48880i
$944$	81.1231	+	58.9394i	2.64033	+	1.91831i
$945$	2.91616			0.0948628
$946$		0			0
$947$	−26.3851			−0.857401			−0.428701	−	0.903447i	$-0.641028\pi$
$947$	−26.3851			−0.857401			−0.428701	+	0.903447i	$0.641028\pi$
$948$	4.38450	+	3.18552i	0.142402	+	0.103461i
$949$	−0.176282	+	0.542542i	−0.00572237	+	0.0176116i
$950$	−4.20331	−	12.9365i	−0.136374	−	0.419715i
$951$	0.848997	−	0.616832i	0.0275306	−	0.0200022i
$952$	−44.1512	+	32.0777i	−1.43095	+	1.03964i
$953$	−10.9267	−	33.6288i	−0.353949	−	1.08934i	−0.956616	−	0.291351i	$-0.905895\pi$
$953$	−10.9267	−	33.6288i	−0.353949	−	1.08934i	0.602667	−	0.797993i	$-0.294105\pi$
$954$	−11.3665	+	34.9826i	−0.368005	+	1.13260i
$955$	−2.23223	−	1.62181i	−0.0722332	−	0.0524805i
$956$	−132.457			−4.28398
$957$		0			0
$958$	−3.47093			−0.112141
$959$	16.6659	+	12.1085i	0.538171	+	0.391004i
$960$	2.13917	−	6.58369i	0.0690414	−	0.212488i
$961$	−9.24245	−	28.4453i	−0.298143	−	0.917591i
$962$	−8.88244	+	6.45347i	−0.286381	+	0.208068i
$963$	24.4151	−	17.7386i	0.786766	−	0.571619i
$964$	−24.8196	−	76.3870i	−0.799387	−	2.46026i
$965$	−3.64751	+	11.2259i	−0.117418	+	0.361374i
$966$	−4.93002	−	3.58187i	−0.158621	−	0.115245i
$967$	−3.86872			−0.124410			−0.0622048	−	0.998063i	$-0.519813\pi$
$967$	−3.86872			−0.124410			−0.0622048	+	0.998063i	$0.519813\pi$
$968$		0			0
$969$	−2.52907			−0.0812455
$970$	−10.5683	−	7.67832i	−0.339328	−	0.246536i
$971$	7.44965	−	22.9277i	0.239070	−	0.735783i	−0.757485	−	0.652853i	$-0.773572\pi$
$971$	7.44965	−	22.9277i	0.239070	−	0.735783i	0.996555	−	0.0829306i	$-0.0264280\pi$
$972$	−9.53989	−	29.3608i	−0.305992	−	0.941747i
$973$	−31.7027	+	23.0334i	−1.01634	+	0.738417i
$974$	47.9701	−	34.8523i	1.53706	−	1.11674i
$975$	0.0347825	+	0.107049i	0.00111393	+	0.00342833i
$976$	32.6851	−	100.594i	1.04623	−	3.21995i
$977$	−8.74895	−	6.35649i	−0.279904	−	0.203362i	0.438972	−	0.898501i	$-0.355343\pi$
$977$	−8.74895	−	6.35649i	−0.279904	−	0.203362i	−0.718875	+	0.695139i	$0.755343\pi$
$978$	13.5939			0.434685
$979$		0			0
$980$	8.86675			0.283238
$981$	−28.9130	−	21.0066i	−0.923123	−	0.670688i
$982$	−21.6605	+	66.6642i	−0.691215	+	2.12734i
$983$	−11.9616	−	36.8139i	−0.381515	−	1.17418i	−0.938977	−	0.343979i	$-0.888225\pi$
$983$	−11.9616	−	36.8139i	−0.381515	−	1.17418i	0.557463	−	0.830202i	$-0.311775\pi$
$984$	−17.5357	+	12.7405i	−0.559019	+	0.406151i
$985$	−5.26698	+	3.82669i	−0.167820	+	0.121928i
$986$	11.2753	+	34.7018i	0.359079	+	1.10513i
$987$	1.02415	−	3.15202i	0.0325992	−	0.100330i
$988$	11.8494	+	8.60907i	0.376979	+	0.273891i
$989$	−19.6022			−0.623314
$990$		0			0
$991$	61.4533			1.95213			0.976064	−	0.217485i	$-0.0697854\pi$
$991$	61.4533			1.95213			0.976064	+	0.217485i	$0.0697854\pi$
$992$	19.6896	+	14.3053i	0.625145	+	0.454195i
$993$	−0.492020	+	1.51428i	−0.0156138	+	0.0480543i
$994$	8.93498	+	27.4990i	0.283400	+	0.872216i
$995$	19.3829	−	14.0825i	0.614480	−	0.446446i
$996$	12.8349	−	9.32508i	0.406688	−	0.295476i
$997$	−11.8470	−	36.4613i	−0.375198	−	1.15474i	−0.943345	−	0.331814i	$-0.892339\pi$
$997$	−11.8470	−	36.4613i	−0.375198	−	1.15474i	0.568147	−	0.822927i	$-0.307661\pi$
$998$	−20.6633	+	63.5951i	−0.654085	+	2.01307i
$999$	−7.60542	−	5.52566i	−0.240625	−	0.174824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.o.81.3		12
11.2	odd	10		605.2.g.p.511.3		12
11.3	even	5	inner	605.2.g.o.366.3		12
11.4	even	5	inner	605.2.g.o.251.1		12
11.5	even	5		605.2.a.h.1.1	yes	3
11.6	odd	10		605.2.a.g.1.3	✓	3
11.7	odd	10		605.2.g.p.251.3		12
11.8	odd	10		605.2.g.p.366.1		12
11.9	even	5	inner	605.2.g.o.511.1		12
11.10	odd	2		605.2.g.p.81.1		12
33.5	odd	10		5445.2.a.bb.1.3		3
33.17	even	10		5445.2.a.bd.1.1		3
44.27	odd	10		9680.2.a.cb.1.2		3
44.39	even	10		9680.2.a.bz.1.2		3
55.39	odd	10		3025.2.a.u.1.1		3
55.49	even	10		3025.2.a.p.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.g.1.3	✓	3	11.6	odd	10
605.2.a.h.1.1	yes	3	11.5	even	5
605.2.g.o.81.3		12	1.1	even	1	trivial
605.2.g.o.251.1		12	11.4	even	5	inner
605.2.g.o.366.3		12	11.3	even	5	inner
605.2.g.o.511.1		12	11.9	even	5	inner
605.2.g.p.81.1		12	11.10	odd	2
605.2.g.p.251.3		12	11.7	odd	10
605.2.g.p.366.1		12	11.8	odd	10
605.2.g.p.511.3		12	11.2	odd	10
3025.2.a.p.1.3		3	55.49	even	10
3025.2.a.u.1.1		3	55.39	odd	10
5445.2.a.bb.1.3		3	33.5	odd	10
5445.2.a.bd.1.1		3	33.17	even	10
9680.2.a.bz.1.2		3	44.39	even	10
9680.2.a.cb.1.2		3	44.27	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.22061 + 1.61337i) q^{2} +(-0.0651271 + 0.200441i) q^{3} +(1.71012 + 5.26321i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.468007 + 0.340027i) q^{6} +(-0.717944 - 2.20960i) q^{7} +(-2.99759 + 9.22564i) q^{8} +(2.39112 + 1.73725i) q^{9} +O(q^{10})\)	\(q+(2.22061 + 1.61337i) q^{2} +(-0.0651271 + 0.200441i) q^{3} +(1.71012 + 5.26321i) q^{4} +(0.809017 - 0.587785i) q^{5} +(-0.468007 + 0.340027i) q^{6} +(-0.717944 - 2.20960i) q^{7} +(-2.99759 + 9.22564i) q^{8} +(2.39112 + 1.73725i) q^{9} +2.74483 q^{10} -1.16634 q^{12} +(0.432072 + 0.313919i) q^{13} +(1.97063 - 6.06498i) q^{14} +(0.0651271 + 0.200441i) q^{15} +(-12.5865 + 9.14464i) q^{16} +(-1.95904 + 1.42333i) q^{17} +(2.50692 + 7.71550i) q^{18} +(1.53136 - 4.71304i) q^{19} +(4.47716 + 3.25284i) q^{20} +0.489652 q^{21} -4.53407 q^{23} +(-1.65397 - 1.20168i) q^{24} +(0.309017 - 0.951057i) q^{25} +(0.452997 + 1.39418i) q^{26} +(-1.01546 + 0.737773i) q^{27} +(10.4018 - 7.55738i) q^{28} +(-1.69640 - 5.22097i) q^{29} +(-0.178763 + 0.550175i) q^{30} +(-0.844952 - 0.613894i) q^{31} -23.3026 q^{32} -6.64663 q^{34} +(-1.87960 - 1.36561i) q^{35} +(-5.05440 + 15.5559i) q^{36} +(2.31443 + 7.12308i) q^{37} +(11.0044 - 7.99518i) q^{38} +(-0.0910617 + 0.0661602i) q^{39} +(2.99759 + 9.22564i) q^{40} +(3.27626 - 10.0833i) q^{41} +(1.08733 + 0.789989i) q^{42} +4.32331 q^{43} +2.95558 q^{45} +(-10.0684 - 7.31513i) q^{46} +(2.09160 - 6.43727i) q^{47} +(-1.01323 - 3.11842i) q^{48} +(1.29622 - 0.941756i) q^{49} +(2.22061 - 1.61337i) q^{50} +(-0.157706 - 0.485370i) q^{51} +(-0.913325 + 2.81093i) q^{52} +(3.66814 + 2.66506i) q^{53} -3.44523 q^{54} +22.5371 q^{56} +(0.844952 + 0.613894i) q^{57} +(4.65631 - 14.3307i) q^{58} +(-1.99169 - 6.12978i) q^{59} +(-0.943587 + 0.685556i) q^{60} +(-5.50019 + 3.99612i) q^{61} +(-0.885873 - 2.72644i) q^{62} +(2.12194 - 6.53066i) q^{63} +(-26.5730 - 19.3064i) q^{64} +0.534070 q^{65} +0.721104 q^{67} +(-10.8415 - 7.87680i) q^{68} +(0.295291 - 0.908812i) q^{69} +(-1.97063 - 6.06498i) q^{70} +(-3.66814 + 2.66506i) q^{71} +(-23.1948 + 16.8520i) q^{72} +(0.330074 + 1.01586i) q^{73} +(-6.35271 + 19.5516i) q^{74} +(0.170505 + 0.123879i) q^{75} +27.4245 q^{76} -0.308953 q^{78} +(-3.75920 - 2.73122i) q^{79} +(-4.80762 + 14.7963i) q^{80} +(2.65823 + 8.18119i) q^{81} +(23.5434 - 17.1053i) q^{82} +(-11.0044 + 7.99518i) q^{83} +(0.837365 + 2.57714i) q^{84} +(-0.748288 + 2.30299i) q^{85} +(9.60040 + 6.97510i) q^{86} +1.15698 q^{87} +12.7148 q^{89} +(6.56320 + 4.76844i) q^{90} +(0.383432 - 1.18008i) q^{91} +(-7.75381 - 23.8638i) q^{92} +(0.178079 - 0.129382i) q^{93} +(15.0303 - 10.9202i) q^{94} +(-1.53136 - 4.71304i) q^{95} +(1.51763 - 4.67079i) q^{96} +(-3.85026 - 2.79738i) q^{97} +4.39779 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{2} - q^{3} - 9 q^{4} + 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 12 * q - q^2 - q^3 - 9 * q^4 + 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 - 2 * q^9	\( 12 q - q^{2} - q^{3} - 9 q^{4} + 3 q^{5} - 5 q^{6} + q^{7} + 9 q^{8} - 2 q^{9} - 4 q^{10} + 36 q^{12} - 6 q^{13} - 5 q^{14} + q^{15} - 13 q^{16} - 4 q^{17} - 20 q^{18} - 4 q^{19} + 9 q^{20} - 68 q^{21} - 24 q^{23} - 17 q^{24} - 3 q^{25} - 12 q^{26} - 13 q^{27} + 25 q^{28} - 2 q^{29} + 5 q^{30} - 14 q^{31} - 108 q^{32} - 32 q^{34} - q^{35} - 2 q^{36} - 4 q^{37} + 18 q^{38} + 4 q^{39} - 9 q^{40} - 9 q^{41} + 35 q^{42} + 28 q^{43} - 8 q^{45} - 8 q^{46} + 15 q^{47} - 7 q^{48} - 18 q^{49} - q^{50} + 20 q^{51} - 2 q^{52} + 6 q^{53} + 76 q^{54} - 12 q^{56} + 14 q^{57} - 30 q^{58} - 10 q^{59} + 9 q^{60} - 3 q^{61} - 24 q^{62} + 12 q^{63} - 29 q^{64} - 24 q^{65} + 76 q^{67} + 8 q^{69} + 5 q^{70} - 6 q^{71} - 48 q^{72} + 12 q^{73} + 28 q^{74} - q^{75} + 64 q^{76} - 8 q^{78} - 2 q^{79} + 13 q^{80} - 3 q^{81} + 27 q^{82} - 18 q^{83} + 31 q^{84} + 4 q^{85} + 3 q^{86} + 40 q^{87} + 44 q^{89} + 20 q^{90} - 20 q^{91} + 34 q^{92} - 20 q^{93} + 59 q^{94} + 4 q^{95} + 7 q^{96} + 2 q^{97} + 144 q^{98}+O(q^{100}) \) 12 * q - q^2 - q^3 - 9 * q^4 + 3 * q^5 - 5 * q^6 + q^7 + 9 * q^8 - 2 * q^9 - 4 * q^10 + 36 * q^12 - 6 * q^13 - 5 * q^14 + q^15 - 13 * q^16 - 4 * q^17 - 20 * q^18 - 4 * q^19 + 9 * q^20 - 68 * q^21 - 24 * q^23 - 17 * q^24 - 3 * q^25 - 12 * q^26 - 13 * q^27 + 25 * q^28 - 2 * q^29 + 5 * q^30 - 14 * q^31 - 108 * q^32 - 32 * q^34 - q^35 - 2 * q^36 - 4 * q^37 + 18 * q^38 + 4 * q^39 - 9 * q^40 - 9 * q^41 + 35 * q^42 + 28 * q^43 - 8 * q^45 - 8 * q^46 + 15 * q^47 - 7 * q^48 - 18 * q^49 - q^50 + 20 * q^51 - 2 * q^52 + 6 * q^53 + 76 * q^54 - 12 * q^56 + 14 * q^57 - 30 * q^58 - 10 * q^59 + 9 * q^60 - 3 * q^61 - 24 * q^62 + 12 * q^63 - 29 * q^64 - 24 * q^65 + 76 * q^67 + 8 * q^69 + 5 * q^70 - 6 * q^71 - 48 * q^72 + 12 * q^73 + 28 * q^74 - q^75 + 64 * q^76 - 8 * q^78 - 2 * q^79 + 13 * q^80 - 3 * q^81 + 27 * q^82 - 18 * q^83 + 31 * q^84 + 4 * q^85 + 3 * q^86 + 40 * q^87 + 44 * q^89 + 20 * q^90 - 20 * q^91 + 34 * q^92 - 20 * q^93 + 59 * q^94 + 4 * q^95 + 7 * q^96 + 2 * q^97 + 144 * q^98

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