LMFDB - Embedded newform 133.2.w.a.100.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [133,2,Mod(4,133)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(133, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([12, 2]))

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

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

chi := DirichletCharacter("133.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 133 = 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	133.w (of order $9$, degree $6$, 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:	$1.06201034688$
Analytic rank:	$0$
Dimension:	$66$
Relative dimension:	$11$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			100.8
Character	$\chi$	$=$	133.100
Dual form			133.2.w.a.4.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.150778 - 0.855105i) q^{2} +(-1.85257 + 0.674280i) q^{3} +(1.17091 + 0.426178i) q^{4} +(0.633253 - 0.230485i) q^{5} +(0.297254 + 1.68581i) q^{6} +(2.63508 + 0.237354i) q^{7} +(1.40927 - 2.44093i) q^{8} +(0.679226 - 0.569939i) q^{9} +O(q^{10})$	\(q+(0.150778 - 0.855105i) q^{2} +(-1.85257 + 0.674280i) q^{3} +(1.17091 + 0.426178i) q^{4} +(0.633253 - 0.230485i) q^{5} +(0.297254 + 1.68581i) q^{6} +(2.63508 + 0.237354i) q^{7} +(1.40927 - 2.44093i) q^{8} +(0.679226 - 0.569939i) q^{9} +(-0.101608 - 0.576250i) q^{10} +2.88403 q^{11} -2.45656 q^{12} +(-0.0914767 - 0.518790i) q^{13} +(0.600276 - 2.21749i) q^{14} +(-1.01773 + 0.853980i) q^{15} +(0.0343114 + 0.0287906i) q^{16} +(-3.33992 - 2.80252i) q^{17} +(-0.384945 - 0.666744i) q^{18} +(-2.19997 + 3.76299i) q^{19} +0.839713 q^{20} +(-5.04172 + 1.33707i) q^{21} +(0.434849 - 2.46615i) q^{22} +(0.216131 + 1.22574i) q^{23} +(-0.964903 + 5.47224i) q^{24} +(-3.48234 + 2.92203i) q^{25} -0.457413 q^{26} +(2.08318 - 3.60817i) q^{27} +(2.98430 + 1.40094i) q^{28} +(-7.70901 - 2.80585i) q^{29} +(0.576791 + 0.999031i) q^{30} +(-2.69106 + 4.66104i) q^{31} +(4.34805 - 3.64845i) q^{32} +(-5.34287 + 1.94464i) q^{33} +(-2.90004 + 2.43342i) q^{34} +(1.72338 - 0.457043i) q^{35} +(1.03821 - 0.377878i) q^{36} +(2.19191 - 3.79650i) q^{37} +(2.88605 + 2.44859i) q^{38} +(0.519277 + 0.899414i) q^{39} +(0.329827 - 1.87054i) q^{40} +(-0.375818 + 2.13137i) q^{41} +(0.383154 + 4.51280i) q^{42} +(-1.95385 - 1.63948i) q^{43} +(3.37695 + 1.22911i) q^{44} +(0.298760 - 0.517467i) q^{45} +1.08072 q^{46} +(2.94301 - 2.46948i) q^{47} +(-0.0829771 - 0.0302012i) q^{48} +(6.88733 + 1.25090i) q^{49} +(1.97358 + 3.41834i) q^{50} +(8.07711 + 2.93983i) q^{51} +(0.113986 - 0.646444i) q^{52} +(-11.6563 - 4.24256i) q^{53} +(-2.77127 - 2.32537i) q^{54} +(1.82632 - 0.664727i) q^{55} +(4.29291 - 6.09756i) q^{56} +(1.53829 - 8.45460i) q^{57} +(-3.56165 + 6.16896i) q^{58} +(-1.51982 - 1.27528i) q^{59} +(-1.55563 + 0.566202i) q^{60} +(-1.60149 - 9.08249i) q^{61} +(3.57993 + 3.00392i) q^{62} +(1.92510 - 1.34062i) q^{63} +(-2.41943 - 4.19057i) q^{64} +(-0.177501 - 0.307442i) q^{65} +(0.857288 + 4.86192i) q^{66} +(0.876820 + 4.97269i) q^{67} +(-2.71638 - 4.70491i) q^{68} +(-1.22689 - 2.12503i) q^{69} +(-0.130971 - 1.54258i) q^{70} +(0.299755 + 0.251524i) q^{71} +(-0.433966 - 2.46114i) q^{72} +(-9.01264 + 3.28033i) q^{73} +(-2.91591 - 2.44674i) q^{74} +(4.48100 - 7.76133i) q^{75} +(-4.17969 + 3.46856i) q^{76} +(7.59966 + 0.684537i) q^{77} +(0.847389 - 0.308424i) q^{78} +(9.96534 + 8.36191i) q^{79} +(0.0283636 + 0.0103235i) q^{80} +(-1.88822 + 10.7086i) q^{81} +(1.76588 + 0.642729i) q^{82} +(1.46419 + 2.53606i) q^{83} +(-6.47325 - 0.583075i) q^{84} +(-2.76095 - 1.00490i) q^{85} +(-1.69652 + 1.42355i) q^{86} +16.1734 q^{87} +(4.06438 - 7.03972i) q^{88} +(15.0598 + 5.48132i) q^{89} +(-0.397442 - 0.333494i) q^{90} +(-0.117912 - 1.38877i) q^{91} +(-0.269312 + 1.52735i) q^{92} +(1.84252 - 10.4494i) q^{93} +(-1.66792 - 2.88893i) q^{94} +(-0.525827 + 2.88999i) q^{95} +(-5.59499 + 9.69081i) q^{96} +(5.48454 - 1.99621i) q^{97} +(2.10811 - 5.70078i) q^{98} +(1.95891 - 1.64372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 66 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 - 9 * q^7 - 6 * q^8 - 3 * q^9	\( 66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9} + 15 q^{10} - 54 q^{12} - 12 q^{13} - 3 q^{14} - 9 q^{15} + 9 q^{16} - 18 q^{18} + 6 q^{19} + 18 q^{21} - 12 q^{22} - 3 q^{23} - 36 q^{24} - 3 q^{25} - 18 q^{26} + 30 q^{27} + 45 q^{28} + 6 q^{29} + 3 q^{30} + 39 q^{31} + 6 q^{32} - 39 q^{33} - 24 q^{34} - 27 q^{35} + 51 q^{36} + 6 q^{37} - 72 q^{38} - 24 q^{39} + 57 q^{40} - 30 q^{41} + 87 q^{42} + 12 q^{43} - 48 q^{44} - 3 q^{45} - 12 q^{46} - 21 q^{47} - 21 q^{48} - 21 q^{49} + 27 q^{50} - 3 q^{51} - 9 q^{52} - 9 q^{53} + 93 q^{54} - 27 q^{55} + 12 q^{56} + 6 q^{57} - 42 q^{58} + 6 q^{59} + 48 q^{60} + 18 q^{61} - 27 q^{62} - 87 q^{63} + 24 q^{64} + 21 q^{65} + 15 q^{66} - 18 q^{67} - 15 q^{68} + 42 q^{69} + 15 q^{70} + 30 q^{71} + 48 q^{72} - 78 q^{73} + 21 q^{74} + 57 q^{75} + 42 q^{76} + 18 q^{77} - 51 q^{78} - 81 q^{79} - 3 q^{80} + 48 q^{81} + 117 q^{82} - 18 q^{83} - 51 q^{84} - 24 q^{85} - 66 q^{86} + 18 q^{87} - 45 q^{88} - 3 q^{89} - 48 q^{90} + 78 q^{91} + 12 q^{92} + 33 q^{93} + 72 q^{94} + 93 q^{95} + 69 q^{96} + 3 q^{97} + 6 q^{98} - 156 q^{99}+O(q^{100}) \) 66 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 - 9 * q^7 - 6 * q^8 - 3 * q^9 + 15 * q^10 - 54 * q^12 - 12 * q^13 - 3 * q^14 - 9 * q^15 + 9 * q^16 - 18 * q^18 + 6 * q^19 + 18 * q^21 - 12 * q^22 - 3 * q^23 - 36 * q^24 - 3 * q^25 - 18 * q^26 + 30 * q^27 + 45 * q^28 + 6 * q^29 + 3 * q^30 + 39 * q^31 + 6 * q^32 - 39 * q^33 - 24 * q^34 - 27 * q^35 + 51 * q^36 + 6 * q^37 - 72 * q^38 - 24 * q^39 + 57 * q^40 - 30 * q^41 + 87 * q^42 + 12 * q^43 - 48 * q^44 - 3 * q^45 - 12 * q^46 - 21 * q^47 - 21 * q^48 - 21 * q^49 + 27 * q^50 - 3 * q^51 - 9 * q^52 - 9 * q^53 + 93 * q^54 - 27 * q^55 + 12 * q^56 + 6 * q^57 - 42 * q^58 + 6 * q^59 + 48 * q^60 + 18 * q^61 - 27 * q^62 - 87 * q^63 + 24 * q^64 + 21 * q^65 + 15 * q^66 - 18 * q^67 - 15 * q^68 + 42 * q^69 + 15 * q^70 + 30 * q^71 + 48 * q^72 - 78 * q^73 + 21 * q^74 + 57 * q^75 + 42 * q^76 + 18 * q^77 - 51 * q^78 - 81 * q^79 - 3 * q^80 + 48 * q^81 + 117 * q^82 - 18 * q^83 - 51 * q^84 - 24 * q^85 - 66 * q^86 + 18 * q^87 - 45 * q^88 - 3 * q^89 - 48 * q^90 + 78 * q^91 + 12 * q^92 + 33 * q^93 + 72 * q^94 + 93 * q^95 + 69 * q^96 + 3 * q^97 + 6 * q^98 - 156 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/133\mathbb{Z}\right)^\times$.

$n$	$78$	$115$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.150778	−	0.855105i	0.106616	−	0.604651i	−0.883946	−	0.467589i	$-0.845123\pi$
$2$	0.150778	−	0.855105i	0.106616	−	0.604651i	0.990562	−	0.137062i	$-0.0437660\pi$
$3$	−1.85257	+	0.674280i	−1.06958	+	0.389296i	−0.816020	−	0.578024i	$-0.803824\pi$
$3$	−1.85257	+	0.674280i	−1.06958	+	0.389296i	−0.253561	+	0.967319i	$0.581602\pi$
$4$	1.17091	+	0.426178i	0.585457	+	0.213089i
$5$	0.633253	−	0.230485i	0.283199	−	0.103076i	−0.196515	−	0.980501i	$-0.562962\pi$
$5$	0.633253	−	0.230485i	0.283199	−	0.103076i	0.479714	+	0.877425i	$0.340740\pi$
$6$	0.297254	+	1.68581i	0.121353	+	0.688228i
$7$	2.63508	+	0.237354i	0.995968	+	0.0897114i
$7$	2.63508	+	0.237354i	0.995968	+	0.0897114i
$8$	1.40927	−	2.44093i	0.498253	−	0.862999i
$9$	0.679226	−	0.569939i	0.226409	−	0.189980i
$10$	−0.101608	−	0.576250i	−0.0321314	−	0.182226i
$11$	2.88403			0.869568			0.434784	−	0.900535i	$-0.356825\pi$
$11$	2.88403			0.869568			0.434784	+	0.900535i	$0.356825\pi$
$12$	−2.45656			−0.709149
$13$	−0.0914767	−	0.518790i	−0.0253711	−	0.143887i	0.969491	−	0.245127i	$-0.0788298\pi$
$13$	−0.0914767	−	0.518790i	−0.0253711	−	0.143887i	−0.994862	+	0.101241i	$0.967719\pi$
$14$	0.600276	−	2.21749i	0.160430	−	0.592648i
$15$	−1.01773	+	0.853980i	−0.262778	+	0.220497i
$16$	0.0343114	+	0.0287906i	0.00857784	+	0.00719766i
$17$	−3.33992	−	2.80252i	−0.810049	−	0.679712i	0.140570	−	0.990071i	$-0.455106\pi$
$17$	−3.33992	−	2.80252i	−0.810049	−	0.679712i	−0.950619	+	0.310359i	$0.899551\pi$
$18$	−0.384945	−	0.666744i	−0.0907324	−	0.157153i
$19$	−2.19997	+	3.76299i	−0.504709	+	0.863290i
$19$	−2.19997	+	3.76299i	−0.504709	+	0.863290i
$20$	0.839713			0.187766
$21$	−5.04172	+	1.33707i	−1.10019	+	0.291772i
$22$	0.434849	−	2.46615i	0.0927100	−	0.525785i
$23$	0.216131	+	1.22574i	0.0450664	+	0.255584i	0.999014	−	0.0443878i	$-0.0141337\pi$
$23$	0.216131	+	1.22574i	0.0450664	+	0.255584i	−0.953948	+	0.299972i	$0.903023\pi$
$24$	−0.964903	+	5.47224i	−0.196960	+	1.11702i
$25$	−3.48234	+	2.92203i	−0.696467	+	0.584405i
$26$	−0.457413			−0.0897061
$27$	2.08318	−	3.60817i	0.400908	−	0.694393i
$28$	2.98430	+	1.40094i	0.563980	+	0.264752i
$29$	−7.70901	−	2.80585i	−1.43153	−	0.521034i	−0.494159	−	0.869372i	$-0.664524\pi$
$29$	−7.70901	−	2.80585i	−1.43153	−	0.521034i	−0.937369	+	0.348338i	$0.886746\pi$
$30$	0.576791	+	0.999031i	0.105307	+	0.182397i
$31$	−2.69106	+	4.66104i	−0.483328	+	0.837148i	−0.999817	−	0.0191455i	$-0.993905\pi$
$31$	−2.69106	+	4.66104i	−0.483328	+	0.837148i	0.516489	+	0.856294i	$0.327239\pi$
$32$	4.34805	−	3.64845i	0.768634	−	0.644961i
$33$	−5.34287	+	1.94464i	−0.930074	+	0.338519i
$34$	−2.90004	+	2.43342i	−0.497353	+	0.417328i
$35$	1.72338	−	0.457043i	0.291305	−	0.0772543i
$36$	1.03821	−	0.377878i	0.173035	−	0.0629797i
$37$	2.19191	−	3.79650i	0.360347	−	0.624140i	−0.627671	−	0.778479i	$-0.715991\pi$
$37$	2.19191	−	3.79650i	0.360347	−	0.624140i	0.988018	+	0.154339i	$0.0493248\pi$
$38$	2.88605	+	2.44859i	0.468179	+	0.397213i
$39$	0.519277	+	0.899414i	0.0831509	+	0.144022i
$40$	0.329827	−	1.87054i	0.0521503	−	0.295759i
$41$	−0.375818	+	2.13137i	−0.0586930	+	0.332864i	−0.999989	−	0.00471822i	$-0.998498\pi$
$41$	−0.375818	+	2.13137i	−0.0586930	+	0.332864i	0.941296	+	0.337583i	$0.109609\pi$
$42$	0.383154	+	4.51280i	0.0591220	+	0.696340i
$43$	−1.95385	−	1.63948i	−0.297960	−	0.250018i	0.481535	−	0.876427i	$-0.340080\pi$
$43$	−1.95385	−	1.63948i	−0.297960	−	0.250018i	−0.779495	+	0.626409i	$0.784524\pi$
$44$	3.37695	+	1.22911i	0.509095	+	0.185295i
$45$	0.298760	−	0.517467i	0.0445365	−	0.0771394i
$46$	1.08072			0.159344
$47$	2.94301	−	2.46948i	0.429283	−	0.360211i	−0.402398	−	0.915465i	$-0.631823\pi$
$47$	2.94301	−	2.46948i	0.429283	−	0.360211i	0.831681	+	0.555254i	$0.187379\pi$
$48$	−0.0829771	−	0.0302012i	−0.0119767	−	0.00435917i
$49$	6.88733	+	1.25090i	0.983904	+	0.178699i
$50$	1.97358	+	3.41834i	0.279106	+	0.483426i
$51$	8.07711	+	2.93983i	1.13102	+	0.411658i
$52$	0.113986	−	0.646444i	0.0158070	−	0.0896457i
$53$	−11.6563	−	4.24256i	−1.60112	−	0.582761i	−0.621465	−	0.783442i	$-0.713462\pi$
$53$	−11.6563	−	4.24256i	−1.60112	−	0.582761i	−0.979657	+	0.200681i	$0.935685\pi$
$54$	−2.77127	−	2.32537i	−0.377122	−	0.316443i
$55$	1.82632	−	0.664727i	0.246261	−	0.0896317i
$56$	4.29291	−	6.09756i	0.573665	−	0.814820i
$57$	1.53829	−	8.45460i	0.203752	−	1.11984i
$58$	−3.56165	+	6.16896i	−0.467667	+	0.810024i
$59$	−1.51982	−	1.27528i	−0.197864	−	0.166027i	0.538473	−	0.842643i	$-0.319002\pi$
$59$	−1.51982	−	1.27528i	−0.197864	−	0.166027i	−0.736337	+	0.676615i	$0.763446\pi$
$60$	−1.55563	+	0.566202i	−0.200831	+	0.0730963i
$61$	−1.60149	−	9.08249i	−0.205049	−	1.16289i	−0.897362	−	0.441295i	$-0.854519\pi$
$61$	−1.60149	−	9.08249i	−0.205049	−	1.16289i	0.692312	−	0.721598i	$-0.256592\pi$
$62$	3.57993	+	3.00392i	0.454652	+	0.381498i
$63$	1.92510	−	1.34062i	0.242539	−	0.168902i
$64$	−2.41943	−	4.19057i	−0.302428	−	0.523821i
$65$	−0.177501	−	0.307442i	−0.0220163	−	0.0381334i
$66$	0.857288	+	4.86192i	0.105525	+	0.598461i
$67$	0.876820	+	4.97269i	0.107121	+	0.607511i	0.990352	+	0.138574i	$0.0442519\pi$
$67$	0.876820	+	4.97269i	0.107121	+	0.607511i	−0.883231	+	0.468937i	$0.844637\pi$
$68$	−2.71638	−	4.70491i	−0.329410	−	0.570555i
$69$	−1.22689	−	2.12503i	−0.147700	−	0.255824i
$70$	−0.130971	−	1.54258i	−0.0156541	−	0.184374i
$71$	0.299755	+	0.251524i	0.0355743	+	0.0298504i	0.660401	−	0.750913i	$-0.270386\pi$
$71$	0.299755	+	0.251524i	0.0355743	+	0.0298504i	−0.624827	+	0.780763i	$0.714831\pi$
$72$	−0.433966	−	2.46114i	−0.0511434	−	0.290048i
$73$	−9.01264	+	3.28033i	−1.05485	+	0.383934i	−0.810491	−	0.585751i	$-0.800800\pi$
$73$	−9.01264	+	3.28033i	−1.05485	+	0.383934i	−0.244359	+	0.969685i	$0.578577\pi$
$74$	−2.91591	−	2.44674i	−0.338968	−	0.284428i
$75$	4.48100	−	7.76133i	0.517422	−	0.896201i
$76$	−4.17969	+	3.46856i	−0.479443	+	0.397871i
$77$	7.59966	+	0.684537i	0.866062	+	0.0780102i
$78$	0.847389	−	0.308424i	0.0959479	−	0.0349222i
$79$	9.96534	+	8.36191i	1.12119	+	0.940789i	0.998664	−	0.0516767i	$-0.0164565\pi$
$79$	9.96534	+	8.36191i	1.12119	+	0.940789i	0.122525	+	0.992465i	$0.460901\pi$
$80$	0.0283636	+	0.0103235i	0.00317115	+	0.00115420i
$81$	−1.88822	+	10.7086i	−0.209802	+	1.18985i
$82$	1.76588	+	0.642729i	0.195009	+	0.0709775i
$83$	1.46419	+	2.53606i	0.160716	+	0.278369i	0.935126	−	0.354316i	$-0.115286\pi$
$83$	1.46419	+	2.53606i	0.160716	+	0.278369i	−0.774410	+	0.632685i	$0.781953\pi$
$84$	−6.47325	−	0.583075i	−0.706289	−	0.0636188i
$85$	−2.76095	−	1.00490i	−0.299467	−	0.108997i
$86$	−1.69652	+	1.42355i	−0.182941	+	0.153506i
$87$	16.1734			1.73397
$88$	4.06438	−	7.03972i	0.433265	−	0.750436i
$89$	15.0598	+	5.48132i	1.59634	+	0.581018i	0.978673	−	0.205425i	$-0.0658576\pi$
$89$	15.0598	+	5.48132i	1.59634	+	0.581018i	0.617662	+	0.786443i	$0.288080\pi$
$90$	−0.397442	−	0.333494i	−0.0418941	−	0.0351533i
$91$	−0.117912	−	1.38877i	−0.0123605	−	0.145582i
$92$	−0.269312	+	1.52735i	−0.0280777	+	0.159237i
$93$	1.84252	−	10.4494i	0.191060	−	1.08356i
$94$	−1.66792	−	2.88893i	−0.172033	−	0.297970i
$95$	−0.525827	+	2.88999i	−0.0539487	+	0.296507i
$96$	−5.59499	+	9.69081i	−0.571036	+	0.989064i
$97$	5.48454	−	1.99621i	0.556871	−	0.202684i	−0.0482259	−	0.998836i	$-0.515357\pi$
$97$	5.48454	−	1.99621i	0.556871	−	0.202684i	0.605097	+	0.796152i	$0.293135\pi$
$98$	2.10811	−	5.70078i	0.212951	−	0.575866i
$99$	1.95891	−	1.64372i	0.196878	−	0.165200i
$100$	−5.32282	+	1.93735i	−0.532282	+	0.193735i
$101$	4.95492	−	4.15767i	0.493033	−	0.413704i	−0.362079	−	0.932148i	$-0.617933\pi$
$101$	4.95492	−	4.15767i	0.493033	−	0.413704i	0.855112	+	0.518444i	$0.173488\pi$
$102$	3.73172	−	6.46352i	0.369495	−	0.639984i
$103$	1.11105	+	1.92439i	0.109475	+	0.189616i	0.915558	−	0.402187i	$-0.131750\pi$
$103$	1.11105	+	1.92439i	0.109475	+	0.189616i	−0.806083	+	0.591803i	$0.798416\pi$
$104$	−1.39525	−	0.507828i	−0.136815	−	0.0497967i
$105$	−2.88451	+	2.00874i	−0.281499	+	0.196033i
$106$	−5.38536	+	9.32771i	−0.523072	+	0.905988i
$107$	−10.3061			−0.996326			−0.498163	−	0.867084i	$-0.665992\pi$
$107$	−10.3061			−0.996326			−0.498163	+	0.867084i	$0.665992\pi$
$108$	3.97695	−	3.33706i	0.382682	−	0.321108i
$109$	−2.97372	+	16.8648i	−0.284831	+	1.61536i	0.421058	+	0.907034i	$0.361659\pi$
$109$	−2.97372	+	16.8648i	−0.284831	+	1.61536i	−0.705889	+	0.708323i	$0.749452\pi$
$110$	−0.293042	−	1.66192i	−0.0279404	−	0.158458i
$111$	−1.50076	+	8.51123i	−0.142446	+	0.807850i
$112$	0.0835797	+	0.0840097i	0.00789754	+	0.00793817i
$113$	−2.35256			−0.221310			−0.110655	−	0.993859i	$-0.535295\pi$
$113$	−2.35256			−0.221310			−0.110655	+	0.993859i	$0.535295\pi$
$114$	−6.99763	−	2.59017i	−0.655388	−	0.242592i
$115$	0.419380	+	0.726388i	0.0391074	+	0.0677361i
$116$	−7.83080	−	6.57082i	−0.727072	−	0.610086i
$117$	−0.357812	−	0.300240i	−0.0330797	−	0.0277572i
$118$	−1.31966	+	1.10732i	−0.121484	+	0.101937i
$119$	−8.13577	−	8.17763i	−0.745805	−	0.749642i
$120$	0.650242	+	3.68771i	0.0593587	+	0.336640i
$121$	−2.68237			−0.243852
$122$	−8.00795			−0.725006
$123$	−0.740912	−	4.20192i	−0.0668058	−	0.378875i
$124$	−5.13743	+	4.31082i	−0.461355	+	0.387123i
$125$	−3.21645	+	5.57106i	−0.287688	+	0.498290i
$126$	−0.856107	−	1.84829i	−0.0762681	−	0.164659i
$127$	−1.43024	−	8.11127i	−0.126913	−	0.719759i	−0.980153	−	0.198241i	$-0.936477\pi$
$127$	−1.43024	−	8.11127i	−0.126913	−	0.719759i	0.853240	−	0.521518i	$-0.174634\pi$
$128$	6.71918	−	2.44558i	0.593897	−	0.216161i
$129$	4.72512	+	1.71980i	0.416023	+	0.151420i
$130$	−0.289658	+	0.105427i	−0.0254047	+	0.00924656i
$131$	−2.84638	+	16.1426i	−0.248690	+	1.41039i	0.563076	+	0.826405i	$0.309618\pi$
$131$	−2.84638	+	16.1426i	−0.248690	+	1.41039i	−0.811765	+	0.583984i	$0.801493\pi$
$132$	−7.08480			−0.616653
$133$	−6.69028	+	9.39362i	−0.580121	+	0.814531i
$134$	4.38438			0.378753
$135$	0.487549	−	2.76503i	0.0419615	−	0.237976i
$136$	−11.5476	+	4.20299i	−0.990200	+	0.360403i
$137$	16.6052	+	6.04380i	1.41868	+	0.516356i	0.933664	−	0.358150i	$-0.116593\pi$
$137$	16.6052	+	6.04380i	1.41868	+	0.516356i	0.485013	+	0.874507i	$0.338815\pi$
$138$	−2.00212	+	0.728711i	−0.170431	+	0.0620320i
$139$	−3.82105	−	21.6702i	−0.324097	−	1.83805i	−0.515946	−	0.856621i	$-0.672560\pi$
$139$	−3.82105	−	21.6702i	−0.324097	−	1.83805i	0.191849	−	0.981424i	$-0.438552\pi$
$140$	2.21271	+	0.199309i	0.187008	+	0.0168447i
$141$	−3.78701	+	6.55930i	−0.318924	+	0.552393i
$142$	0.260276	−	0.218397i	0.0218419	−	0.0183275i
$143$	−0.263822	−	1.49621i	−0.0220619	−	0.125119i
$144$	0.0397141			0.00330951
$145$	−5.52847			−0.459114
$146$	1.44612	+	8.20136i	0.119682	+	0.678749i
$147$	−13.6027	+	2.32662i	−1.12193	+	0.191896i
$148$	4.18452	−	3.51123i	0.343965	−	0.288621i
$149$	−17.9144	−	15.0320i	−1.46761	−	1.23147i	−0.918324	−	0.395829i	$-0.870457\pi$
$149$	−17.9144	−	15.0320i	−1.46761	−	1.23147i	−0.549281	−	0.835638i	$-0.685098\pi$
$150$	−5.96111	−	5.00197i	−0.486723	−	0.408409i
$151$	−5.35905	−	9.28214i	−0.436113	−	0.755370i	0.561273	−	0.827631i	$-0.310312\pi$
$151$	−5.35905	−	9.28214i	−0.436113	−	0.755370i	−0.997386	+	0.0722609i	$0.976979\pi$
$152$	6.08484	+	10.6731i	0.493546	+	0.865700i
$153$	−3.86583			−0.312534
$154$	1.73121	−	6.39530i	0.139505	−	0.515348i
$155$	−0.629817	+	3.57187i	−0.0505881	+	0.286899i
$156$	0.224718	+	1.27444i	0.0179919	+	0.102037i
$157$	4.08326	−	23.1573i	0.325880	−	1.84816i	−0.177540	−	0.984114i	$-0.556814\pi$
$157$	4.08326	−	23.1573i	0.325880	−	1.84816i	0.503420	−	0.864042i	$-0.332075\pi$
$158$	8.65287	−	7.26062i	0.688385	−	0.577624i
$159$	24.4549			1.93940
$160$	1.91250	−	3.31255i	0.151197	−	0.261880i
$161$	0.278589	+	3.28122i	0.0219559	+	0.258597i
$162$	8.87230	+	3.22925i	0.697074	+	0.253714i
$163$	5.83215	+	10.1016i	0.456809	+	0.791217i	0.998790	−	0.0491737i	$-0.0156588\pi$
$163$	5.83215	+	10.1016i	0.456809	+	0.791217i	−0.541981	+	0.840391i	$0.682325\pi$
$164$	−1.34840	+	2.33549i	−0.105292	+	0.182371i
$165$	−2.93517	+	2.46290i	−0.228503	+	0.191737i
$166$	2.38937	−	0.869658i	0.185451	−	0.0674986i
$167$	4.30254	−	3.61026i	0.332941	−	0.279370i	−0.460956	−	0.887423i	$-0.652493\pi$
$167$	4.30254	−	3.61026i	0.332941	−	0.279370i	0.793897	+	0.608053i	$0.208049\pi$
$168$	−3.84146	+	14.1908i	−0.296375	+	1.09484i
$169$	11.9552	−	4.35135i	0.919633	−	0.334719i
$170$	−1.27559	+	2.20939i	−0.0978334	+	0.169452i
$171$	0.650394	+	3.80977i	0.0497368	+	0.291341i
$172$	−1.58909	−	2.75238i	−0.121167	−	0.209867i
$173$	−0.936023	+	5.30845i	−0.0711645	+	0.403594i	0.928329	+	0.371760i	$0.121246\pi$
$173$	−0.936023	+	5.30845i	−0.0711645	+	0.403594i	−0.999493	+	0.0318335i	$0.989865\pi$
$174$	2.43860	−	13.8300i	0.184870	−	1.04845i
$175$	−9.86980	+	6.87324i	−0.746087	+	0.519568i
$176$	0.0989550	+	0.0830331i	0.00745901	+	0.00625885i
$177$	3.67547	+	1.33776i	0.276265	+	0.100552i
$178$	6.95779	−	12.0512i	0.521508	−	0.903279i
$179$	7.22995			0.540392			0.270196	−	0.962805i	$-0.412912\pi$
$179$	7.22995			0.540392			0.270196	+	0.962805i	$0.412912\pi$
$180$	0.570355	−	0.478585i	0.0425118	−	0.0356716i
$181$	22.3243	+	8.12539i	1.65935	+	0.603956i	0.990261	−	0.139223i	$-0.0444605\pi$
$181$	22.3243	+	8.12539i	1.65935	+	0.603956i	0.669093	+	0.743179i	$0.266683\pi$
$182$	−1.20532	−	0.108569i	−0.0893444	−	0.00804766i
$183$	9.09101	+	15.7461i	0.672027	+	1.16398i
$184$	3.29653	+	1.19984i	0.243024	+	0.0884533i
$185$	0.512996	−	2.90935i	0.0377162	−	0.213899i
$186$	−8.65755	−	3.15109i	−0.634803	−	0.231049i
$187$	−9.63242	−	8.08256i	−0.704393	−	0.591056i
$188$	4.49846	−	1.63730i	0.328084	−	0.119413i
$189$	6.34576	−	9.01338i	0.461586	−	0.655627i
$190$	2.39196	+	0.885384i	0.173531	+	0.0642325i
$191$	−1.54258	+	2.67182i	−0.111617	+	0.193326i	−0.916422	−	0.400213i	$-0.868936\pi$
$191$	−1.54258	+	2.67182i	−0.111617	+	0.193326i	0.804805	+	0.593539i	$0.202270\pi$
$192$	7.30777	+	6.13195i	0.527393	+	0.442535i
$193$	4.49973	−	1.63777i	0.323898	−	0.117889i	−0.174954	−	0.984577i	$-0.555978\pi$
$193$	4.49973	−	1.63777i	0.323898	−	0.117889i	0.498851	+	0.866687i	$0.333755\pi$
$194$	−0.880020	−	4.99084i	−0.0631818	−	0.358322i
$195$	0.536136	+	0.449871i	0.0383935	+	0.0322159i
$196$	7.53136	+	4.39992i	0.537955	+	0.314280i
$197$	2.11975	+	3.67152i	0.151026	+	0.261585i	0.931605	−	0.363472i	$-0.118409\pi$
$197$	2.11975	+	3.67152i	0.151026	+	0.261585i	−0.780579	+	0.625057i	$0.785076\pi$
$198$	−1.11019	−	1.92291i	−0.0788980	−	0.136655i
$199$	1.33551	+	7.57408i	0.0946721	+	0.536912i	0.994847	+	0.101384i	$0.0323272\pi$
$199$	1.33551	+	7.57408i	0.0946721	+	0.536912i	−0.900175	+	0.435528i	$0.856562\pi$
$200$	2.22491	+	12.6181i	0.157325	+	0.892232i
$201$	−4.97736	−	8.62104i	−0.351076	−	0.608081i
$202$	−2.80815	−	4.86386i	−0.197581	−	0.342220i
$203$	−19.6479	−	9.22342i	−1.37901	−	0.647357i
$204$	8.20472	+	6.88458i	0.574445	+	0.482017i
$205$	0.253262	+	1.43632i	0.0176886	+	0.100317i
$206$	1.81308	−	0.659907i	0.126323	−	0.0459779i
$207$	0.845398	+	0.709373i	0.0587592	+	0.0493048i
$208$	0.0117976	−	0.0204341i	0.000818018	−	0.00141685i
$209$	−6.34479	+	10.8526i	−0.438879	+	0.750689i
$210$	1.28277	+	2.76943i	0.0885194	+	0.191109i
$211$	7.39940	−	2.69316i	0.509395	−	0.185405i	−0.0745196	−	0.997220i	$-0.523742\pi$
$211$	7.39940	−	2.69316i	0.509395	−	0.185405i	0.583915	+	0.811815i	$0.301520\pi$
$212$	−11.8405	−	9.93535i	−0.813208	−	0.682363i
$213$	−0.724914	−	0.263847i	−0.0496703	−	0.0180785i
$214$	−1.55393	+	8.81278i	−0.106224	+	0.602429i
$215$	−1.61516	−	0.587870i	−0.110153	−	0.0400924i
$216$	−5.87153	−	10.1698i	−0.399507	−	0.691967i
$217$	−8.19747	+	11.6435i	−0.556481	+	0.790413i
$218$	13.9728	+	5.08569i	0.946359	+	0.344446i
$219$	14.4847	−	12.1541i	0.978784	−	0.821297i
$220$	2.42176			0.163275
$221$	−1.14840	+	1.98908i	−0.0772496	+	0.133800i
$222$	7.05172	+	2.56661i	0.473280	+	0.172260i
$223$	2.76817	+	2.32277i	0.185370	+	0.155544i	0.730750	−	0.682645i	$-0.239170\pi$
$223$	2.76817	+	2.32277i	0.185370	+	0.155544i	−0.545380	+	0.838189i	$0.683615\pi$
$224$	12.3235	−	8.58194i	0.823395	−	0.573405i
$225$	−0.699919	+	3.96944i	−0.0466612	+	0.264629i
$226$	−0.354714	+	2.01168i	−0.0235952	+	0.133815i
$227$	−7.40554	−	12.8268i	−0.491523	−	0.851343i	0.508429	−	0.861104i	$-0.330226\pi$
$227$	−7.40554	−	12.8268i	−0.491523	−	0.851343i	−0.999952	+	0.00976097i	$0.996893\pi$
$228$	5.40438	−	9.24403i	0.357914	−	0.612201i
$229$	8.46628	−	14.6640i	0.559467	−	0.969026i	−0.438074	−	0.898939i	$-0.644339\pi$
$229$	8.46628	−	14.6640i	0.559467	−	0.969026i	0.997541	−	0.0700867i	$-0.0223276\pi$
$230$	0.684372	−	0.249091i	0.0451261	−	0.0164246i
$231$	−14.5405	+	3.85615i	−0.956692	+	0.253716i
$232$	−17.7130	+	14.8630i	−1.16291	+	0.975801i
$233$	−11.7652	+	4.28218i	−0.770764	+	0.280535i	−0.697316	−	0.716764i	$-0.745623\pi$
$233$	−11.7652	+	4.28218i	−0.770764	+	0.280535i	−0.0734482	+	0.997299i	$0.523400\pi$
$234$	−0.310687	+	0.260697i	−0.0203102	+	0.0170423i
$235$	1.29449	−	2.24213i	0.0844434	−	0.146260i
$236$	−1.23608	−	2.14096i	−0.0804622	−	0.139365i
$237$	−24.0998	−	8.77159i	−1.56545	−	0.569776i
$238$	−8.21943	+	5.72393i	−0.532786	+	0.371027i
$239$	−9.14169	+	15.8339i	−0.591327	+	1.02421i	0.402727	+	0.915320i	$0.368062\pi$
$239$	−9.14169	+	15.8339i	−0.591327	+	1.02421i	−0.994054	+	0.108888i	$0.965271\pi$
$240$	−0.0595065			−0.00384113
$241$	7.83680	−	6.57586i	0.504813	−	0.423588i	−0.354487	−	0.935061i	$-0.615344\pi$
$241$	7.83680	−	6.57586i	0.504813	−	0.423588i	0.859299	+	0.511473i	$0.170900\pi$
$242$	−0.404443	+	2.29371i	−0.0259986	+	0.147445i
$243$	−1.55211	−	8.80247i	−0.0995681	−	0.564679i
$244$	1.99555	−	11.3173i	0.127752	−	0.724518i
$245$	4.64973	−	0.795294i	0.297061	−	0.0508095i
$246$	−3.70480			−0.236209
$247$	2.15345	+	0.797099i	0.137021	+	0.0507182i
$248$	7.58486	+	13.1374i	0.481639	+	0.834223i
$249$	−4.42254	−	3.71095i	−0.280267	−	0.235172i
$250$	4.27887	+	3.59040i	0.270619	+	0.227077i
$251$	5.98760	−	5.02419i	0.377934	−	0.317124i	−0.433957	−	0.900934i	$-0.642883\pi$
$251$	5.98760	−	5.02419i	0.377934	−	0.317124i	0.811891	+	0.583810i	$0.198439\pi$
$252$	2.82546	−	0.749316i	0.177987	−	0.0472025i
$253$	0.623328	+	3.53507i	0.0391883	+	0.222248i
$254$	−7.15164			−0.448734
$255$	5.79245			0.362737
$256$	−2.75864	−	15.6450i	−0.172415	−	0.977814i
$257$	−2.47699	+	2.07844i	−0.154510	+	0.129650i	−0.716766	−	0.697314i	$-0.754378\pi$
$257$	−2.47699	+	2.07844i	−0.154510	+	0.129650i	0.562255	+	0.826964i	$0.309934\pi$
$258$	2.18306	−	3.78116i	0.135911	−	0.235405i
$259$	6.67697	−	9.48382i	0.414887	−	0.589296i
$260$	−0.0768142	−	0.435635i	−0.00476381	−	0.0270169i
$261$	−6.83533	+	2.48786i	−0.423096	+	0.153994i
$262$	13.3745	+	4.86791i	0.826279	+	0.300741i
$263$	22.9307	−	8.34611i	1.41397	−	0.514643i	0.481678	−	0.876348i	$-0.340028\pi$
$263$	22.9307	−	8.34611i	1.41397	−	0.514643i	0.932292	+	0.361705i	$0.117805\pi$
$264$	−2.78281	+	15.7821i	−0.171270	+	0.971321i
$265$	−8.35926			−0.513506
$266$	7.02379	+	7.13724i	0.430656	+	0.437613i
$267$	−31.5953			−1.93360
$268$	−1.09257	+	6.19628i	−0.0667394	+	0.378498i
$269$	5.44403	−	1.98147i	0.331929	−	0.120812i	−0.170679	−	0.985327i	$-0.554596\pi$
$269$	5.44403	−	1.98147i	0.331929	−	0.120812i	0.502608	+	0.864515i	$0.332374\pi$
$270$	−2.29088	−	0.833812i	−0.139418	−	0.0507442i
$271$	21.8997	−	7.97083i	1.33031	−	0.484193i	0.423562	−	0.905867i	$-0.360779\pi$
$271$	21.8997	−	7.97083i	1.33031	−	0.484193i	0.906748	+	0.421674i	$0.138557\pi$
$272$	−0.0339106	−	0.192317i	−0.00205613	−	0.0116609i
$273$	1.15486	+	2.49328i	0.0698952	+	0.150900i
$274$	7.67178	−	13.2879i	0.463469	−	0.802752i
$275$	−10.0432	+	8.42721i	−0.605626	+	0.508180i
$276$	−0.530939	−	3.01111i	−0.0319588	−	0.181247i
$277$	19.2086			1.15413			0.577066	−	0.816698i	$-0.304198\pi$
$277$	19.2086			1.15413			0.577066	+	0.816698i	$0.304198\pi$
$278$	−19.1065			−1.14593
$279$	0.828673	+	4.69964i	0.0496114	+	0.281360i
$280$	1.31310	−	4.85075i	0.0784729	−	0.289888i
$281$	−13.9767	+	11.7279i	−0.833782	+	0.699626i	−0.956156	−	0.292858i	$-0.905394\pi$
$281$	−13.9767	+	11.7279i	−0.833782	+	0.699626i	0.122374	+	0.992484i	$0.460949\pi$
$282$	5.03789	+	4.22729i	0.300002	+	0.251732i
$283$	−8.56001	−	7.18270i	−0.508840	−	0.426967i	0.351881	−	0.936045i	$-0.385542\pi$
$283$	−8.56001	−	7.18270i	−0.508840	−	0.426967i	−0.860721	+	0.509077i	$0.829987\pi$
$284$	0.243793	+	0.422262i	0.0144665	+	0.0250566i
$285$	−0.974532	−	5.70846i	−0.0577263	−	0.338140i
$286$	−1.31919			−0.0780055
$287$	−1.49620	+	5.52714i	−0.0883181	+	0.326257i
$288$	0.873920	−	4.95624i	0.0514962	−	0.292050i
$289$	0.348892	+	1.97866i	0.0205230	+	0.116392i
$290$	−0.833572	+	4.72742i	−0.0489490	+	0.277604i
$291$	−8.81449	+	7.39623i	−0.516714	+	0.433575i
$292$	−11.9510			−0.699381
$293$	−9.88159	+	17.1154i	−0.577289	+	0.999894i	0.418500	+	0.908217i	$0.362556\pi$
$293$	−9.88159	+	17.1154i	−0.577289	+	0.999894i	−0.995789	+	0.0916768i	$0.970777\pi$
$294$	−0.0614887	+	11.9825i	−0.00358609	+	0.698836i
$295$	−1.25636	−	0.457279i	−0.0731484	−	0.0266238i
$296$	−6.17799	−	10.7006i	−0.359088	−	0.621959i
$297$	6.00795	−	10.4061i	0.348617	−	0.603822i
$298$	−15.5550	+	13.0522i	−0.901078	+	0.756094i
$299$	0.616131	−	0.224253i	0.0356318	−	0.0129689i
$300$	8.55458	−	7.17814i	0.493899	−	0.414430i
$301$	−4.75943	−	4.78392i	−0.274329	−	0.275740i
$302$	−8.74523	+	3.18301i	−0.503232	+	0.183161i
$303$	−6.37590	+	11.0434i	−0.366286	+	0.634426i
$304$	−0.183823	+	0.0657747i	−0.0105430	+	0.00377244i
$305$	−3.10753	−	5.38239i	−0.177936	−	0.308195i
$306$	−0.582882	+	3.30569i	−0.0333211	+	0.188974i
$307$	−2.44284	+	13.8541i	−0.139421	+	0.790693i	0.832258	+	0.554388i	$0.187048\pi$
$307$	−2.44284	+	13.8541i	−0.139421	+	0.790693i	−0.971679	+	0.236305i	$0.924064\pi$
$308$	8.60682	+	4.04034i	0.490419	+	0.230220i
$309$	−3.35587	−	2.81591i	−0.190909	−	0.160192i
$310$	2.95936	+	1.07712i	0.168080	+	0.0611763i
$311$	−15.6926	+	27.1804i	−0.889845	+	1.54126i	−0.0497875	+	0.998760i	$0.515854\pi$
$311$	−15.6926	+	27.1804i	−0.889845	+	1.54126i	−0.840058	+	0.542497i	$0.817479\pi$
$312$	2.92721			0.165721
$313$	−11.0438	+	9.26685i	−0.624233	+	0.523794i	−0.899131	−	0.437680i	$-0.855800\pi$
$313$	−11.0438	+	9.26685i	−0.624233	+	0.523794i	0.274898	+	0.961473i	$0.411356\pi$
$314$	−19.1863	−	6.98324i	−1.08274	−	0.394087i
$315$	0.910080	−	1.29266i	0.0512772	−	0.0728330i
$316$	8.10490	+	14.0381i	0.455936	+	0.789704i
$317$	−4.53697	−	1.65132i	−0.254822	−	0.0927475i	0.211451	−	0.977389i	$-0.432181\pi$
$317$	−4.53697	−	1.65132i	−0.254822	−	0.0927475i	−0.466273	+	0.884641i	$0.654403\pi$
$318$	3.68726	−	20.9115i	0.206771	−	1.17266i
$319$	−22.2330	−	8.09216i	−1.24481	−	0.453074i
$320$	−2.49797	−	2.09605i	−0.139641	−	0.117173i
$321$	19.0927	−	6.94918i	1.06565	−	0.387865i
$322$	2.84780	+	0.256514i	0.158702	+	0.0142950i
$323$	17.8936	−	6.40260i	0.995627	−	0.356250i
$324$	−6.77472	+	11.7342i	−0.376374	+	0.651898i
$325$	1.83447	+	1.53930i	0.101758	+	0.0853853i
$326$	9.51728	−	3.46401i	0.527113	−	0.191854i
$327$	−5.86258	−	33.2484i	−0.324202	−	1.83864i
$328$	4.67290	+	3.92103i	0.258018	+	0.216503i
$329$	8.34123	−	5.80875i	0.459867	−	0.320247i
$330$	1.66348	+	2.88124i	0.0915717	+	0.158607i
$331$	0.878621	+	1.52182i	0.0482934	+	0.0836466i	0.889162	−	0.457593i	$-0.151288\pi$
$331$	0.878621	+	1.52182i	0.0482934	+	0.0836466i	−0.840868	+	0.541240i	$0.817955\pi$
$332$	0.633634	+	3.59352i	0.0347752	+	0.197220i
$333$	−0.674968	−	3.82793i	−0.0369880	−	0.209769i
$334$	−2.43842	−	4.22347i	−0.133425	−	0.231098i
$335$	1.70138	+	2.94688i	0.0929564	+	0.161005i
$336$	−0.211483	−	0.0992776i	−0.0115374	−	0.00541604i
$337$	−12.0141	−	10.0810i	−0.654448	−	0.549147i	0.253969	−	0.967212i	$-0.418264\pi$
$337$	−12.0141	−	10.0810i	−0.654448	−	0.549147i	−0.908417	+	0.418065i	$0.862708\pi$
$338$	−1.91827	−	10.8791i	−0.104340	−	0.591743i
$339$	4.35828	−	1.58628i	0.236709	−	0.0861551i
$340$	−2.80457	−	2.35332i	−0.152099	−	0.127626i
$341$	−7.76109	+	13.4426i	−0.420286	+	0.727957i
$342$	3.35582	+	0.0182755i	0.181462	+	0.000988227i
$343$	17.8518	+	4.93095i	0.963905	+	0.266246i
$344$	−6.75536	+	2.45875i	−0.364225	+	0.132567i
$345$	−1.26672	−	1.06290i	−0.0681979	−	0.0572249i
$346$	4.39815	+	1.60080i	0.236446	+	0.0860593i
$347$	−4.67153	+	26.4936i	−0.250781	+	1.42225i	0.555894	+	0.831253i	$0.312376\pi$
$347$	−4.67153	+	26.4936i	−0.250781	+	1.42225i	−0.806675	+	0.590995i	$0.798735\pi$
$348$	18.9377	+	6.89275i	1.01517	+	0.369490i
$349$	−0.516292	−	0.894244i	−0.0276365	−	0.0478678i	0.851876	−	0.523743i	$-0.175465\pi$
$349$	−0.516292	−	0.894244i	−0.0276365	−	0.0478678i	−0.879513	+	0.475875i	$0.842131\pi$
$350$	4.38919	+	9.47605i	0.234612	+	0.506516i
$351$	−2.06245	−	0.750669i	−0.110085	−	0.0400678i
$352$	12.5399	−	10.5222i	0.668380	−	0.560837i
$353$	−15.5917			−0.829865			−0.414932	−	0.909852i	$-0.636195\pi$
$353$	−15.5917			−0.829865			−0.414932	+	0.909852i	$0.636195\pi$
$354$	1.69811	−	2.94121i	0.0902534	−	0.156323i
$355$	0.247793	+	0.0901893i	0.0131515	+	0.00478675i
$356$	15.2977	+	12.8363i	0.810777	+	0.680323i
$357$	20.5861	+	9.66383i	1.08953	+	0.511464i
$358$	1.09012	−	6.18237i	0.0576145	−	0.326748i
$359$	−1.96847	+	11.1638i	−0.103892	+	0.589201i	0.887765	+	0.460297i	$0.152257\pi$
$359$	−1.96847	+	11.1638i	−0.103892	+	0.589201i	−0.991657	+	0.128904i	$0.958854\pi$
$360$	−0.842067	−	1.45850i	−0.0443808	−	0.0768699i
$361$	−9.32022	−	16.5570i	−0.490538	−	0.871420i
$362$	10.3141	−	17.8645i	0.542096	−	0.938938i
$363$	4.96927	−	1.80867i	0.260819	−	0.0949305i
$364$	0.453798	−	1.67638i	0.0237855	−	0.0878662i
$365$	−4.95121	+	4.15456i	−0.259158	+	0.217460i
$366$	14.8353	−	5.39960i	0.775453	−	0.282242i
$367$	−24.3028	+	20.3925i	−1.26859	+	1.06448i	−0.273884	+	0.961763i	$0.588308\pi$
$367$	−24.3028	+	20.3925i	−1.26859	+	1.06448i	−0.994711	+	0.102715i	$0.967247\pi$
$368$	−0.0278741	+	0.0482793i	−0.00145304	+	0.00251673i
$369$	0.959485	+	1.66188i	0.0499488	+	0.0865139i
$370$	−2.41045	−	0.877331i	−0.125313	−	0.0456103i
$371$	−29.7084	−	13.9462i	−1.54239	−	0.724050i
$372$	6.61075	−	11.4502i	0.342751	−	0.593663i
$373$	38.1301			1.97430			0.987150	−	0.159798i	$-0.0510844\pi$
$373$	38.1301			1.97430			0.987150	+	0.159798i	$0.0510844\pi$
$374$	−8.36380	+	7.01806i	−0.432482	+	0.362895i
$375$	2.20225	−	12.4896i	0.113723	−	0.644958i
$376$	−1.88033	−	10.6639i	−0.0969704	−	0.549947i
$377$	−0.750453	+	4.25603i	−0.0386503	+	0.219197i
$378$	−6.75059	−	6.78532i	−0.347213	−	0.348999i
$379$	30.6787			1.57586			0.787930	−	0.615765i	$-0.211153\pi$
$379$	30.6787			1.57586			0.787930	+	0.615765i	$0.211153\pi$
$380$	−1.84735	+	3.15983i	−0.0947669	+	0.162096i
$381$	8.11888	+	14.0623i	0.415943	+	0.720434i
$382$	2.05210	+	1.72192i	0.104995	+	0.0881009i
$383$	20.4855	+	17.1894i	1.04676	+	0.878335i	0.992749	−	0.120205i	$-0.0383553\pi$
$383$	20.4855	+	17.1894i	1.04676	+	0.878335i	0.0540100	+	0.998540i	$0.482800\pi$
$384$	−10.7987	+	9.06121i	−0.551071	+	0.462403i
$385$	4.97028	−	1.31812i	0.253309	−	0.0671779i
$386$	−0.722003	−	4.09468i	−0.0367490	−	0.208414i
$387$	−2.26151			−0.114959
$388$	7.27267			0.369214
$389$	0.405495	+	2.29967i	0.0205594	+	0.116598i	0.993360	−	0.115045i	$-0.0367011\pi$
$389$	0.405495	+	2.29967i	0.0205594	+	0.116598i	−0.972801	+	0.231643i	$0.925590\pi$
$390$	0.465525	−	0.390622i	0.0235728	−	0.0197799i
$391$	2.71330	−	4.69958i	0.137218	−	0.237668i
$392$	12.7595	−	15.0486i	0.644450	−	0.760071i
$393$	−5.61154	−	31.8246i	−0.283065	−	1.60534i
$394$	3.45915	−	1.25903i	0.174270	−	0.0634289i
$395$	8.23788	+	2.99834i	0.414493	+	0.150863i
$396$	2.99423	−	1.08981i	0.150466	−	0.0547651i
$397$	−4.10502	+	23.2808i	−0.206025	+	1.16843i	0.689793	+	0.724007i	$0.257702\pi$
$397$	−4.10502	+	23.2808i	−0.206025	+	1.16843i	−0.895818	+	0.444421i	$0.853410\pi$
$398$	6.67800			0.334738
$399$	6.06027	−	21.9135i	0.303393	−	1.09705i
$400$	−0.203611			−0.0101805
$401$	4.62576	−	26.2340i	0.231000	−	1.31006i	−0.619878	−	0.784699i	$-0.712818\pi$
$401$	4.62576	−	26.2340i	0.231000	−	1.31006i	0.850877	−	0.525365i	$-0.176071\pi$
$402$	−8.12237	+	2.95630i	−0.405107	+	0.147447i
$403$	2.66427	+	0.969716i	0.132717	+	0.0483050i
$404$	7.57370	−	2.75660i	0.376805	−	0.137146i
$405$	1.27246	+	7.21648i	0.0632290	+	0.358590i
$406$	−10.8495	+	15.4103i	−0.538450	+	0.764802i
$407$	6.32153	−	10.9492i	0.313347	−	0.542732i
$408$	18.5588	−	15.5727i	0.918796	−	0.770961i
$409$	−4.39509	−	24.9258i	−0.217323	−	1.23250i	−0.876829	−	0.480802i	$-0.840346\pi$
$409$	−4.39509	−	24.9258i	−0.217323	−	1.23250i	0.659506	−	0.751699i	$-0.270766\pi$
$410$	1.26639			0.0625425
$411$	−34.8375			−1.71841
$412$	0.480809	+	2.72680i	0.0236877	+	0.134340i
$413$	−3.70216	−	3.72121i	−0.182171	−	0.183109i
$414$	0.734056	−	0.615946i	0.0360769	−	0.0302721i
$415$	1.51173	+	1.26849i	0.0742079	+	0.0622678i
$416$	−2.29053	−	1.92198i	−0.112302	−	0.0942328i
$417$	21.6906	+	37.5692i	1.06219	+	1.83977i
$418$	8.32344	+	7.06180i	0.407113	+	0.345404i
$419$	−11.8361			−0.578229			−0.289115	−	0.957295i	$-0.593361\pi$
$419$	−11.8361			−0.578229			−0.289115	+	0.957295i	$0.593361\pi$
$420$	−4.23360	+	1.12275i	−0.206578	+	0.0547848i
$421$	4.02598	−	22.8325i	0.196214	−	1.11279i	−0.714464	−	0.699672i	$-0.753330\pi$
$421$	4.02598	−	22.8325i	0.196214	−	1.11279i	0.910679	−	0.413115i	$-0.135559\pi$
$422$	−1.18727	−	6.73333i	−0.0577953	−	0.327773i
$423$	0.591519	−	3.35467i	0.0287607	−	0.163110i
$424$	−26.7828	+	22.4734i	−1.30069	+	1.09140i
$425$	19.8198			0.961400
$426$	−0.334918	+	0.580095i	−0.0162268	+	0.0281057i
$427$	−2.06429	−	24.3132i	−0.0998978	−	1.17660i
$428$	−12.0675	−	4.39222i	−0.583306	−	0.212306i
$429$	1.49761	+	2.59394i	0.0723053	+	0.125236i
$430$	−0.746222	+	1.29249i	−0.0359860	+	0.0623296i
$431$	11.9682	−	10.0425i	0.576486	−	0.483729i	−0.307305	−	0.951611i	$-0.599427\pi$
$431$	11.9682	−	10.0425i	0.576486	−	0.483729i	0.883791	+	0.467882i	$0.154983\pi$
$432$	0.175358	−	0.0638252i	0.00843693	−	0.00307079i
$433$	−18.5463	+	15.5622i	−0.891277	+	0.747870i	−0.968466	−	0.249146i	$-0.919850\pi$
$433$	−18.5463	+	15.5622i	−0.891277	+	0.747870i	0.0771887	+	0.997017i	$0.475406\pi$
$434$	8.72042	+	8.76529i	0.418594	+	0.420747i
$435$	10.2419	−	3.72773i	0.491060	−	0.178731i
$436$	−10.6694	+	18.4799i	−0.510971	+	0.885028i
$437$	−5.08793	−	1.88330i	−0.243389	−	0.0900903i
$438$	−8.20905	−	14.2185i	−0.392244	−	0.679386i
$439$	−1.93782	+	10.9899i	−0.0924872	+	0.524521i	0.903001	+	0.429638i	$0.141359\pi$
$439$	−1.93782	+	10.9899i	−0.0924872	+	0.524521i	−0.995488	+	0.0948830i	$0.969752\pi$
$440$	0.951232	−	5.39470i	0.0453482	−	0.257182i
$441$	5.39099	−	3.07571i	0.256714	−	0.146462i
$442$	1.52772	+	1.28191i	0.0726663	+	0.0609743i
$443$	−29.6124	−	10.7780i	−1.40693	−	0.512080i	−0.476702	−	0.879065i	$-0.658168\pi$
$443$	−29.6124	−	10.7780i	−1.40693	−	0.512080i	−0.930227	+	0.366985i	$0.880390\pi$
$444$	−5.38456	+	9.32633i	−0.255540	+	0.442608i
$445$	10.8000			0.511970
$446$	2.40359	−	2.01685i	0.113813	−	0.0955007i
$447$	43.3234	+	15.7684i	2.04913	+	0.745822i
$448$	−5.38074	−	11.6168i	−0.254216	−	0.548840i
$449$	14.6386	+	25.3549i	0.690840	+	1.19657i	0.971563	+	0.236781i	$0.0760924\pi$
$449$	14.6386	+	25.3549i	0.690840	+	1.19657i	−0.280723	+	0.959789i	$0.590574\pi$
$450$	3.28875	+	1.19701i	0.155033	+	0.0564275i
$451$	−1.08387	+	6.14694i	−0.0510375	+	0.289448i
$452$	−2.75464	−	1.00261i	−0.129568	−	0.0471587i
$453$	16.1868	+	13.5823i	0.760521	+	0.638153i
$454$	−12.0848	+	4.39852i	−0.567169	+	0.206433i
$455$	−0.394759	−	0.852265i	−0.0185066	−	0.0399548i
$456$	−18.4692	−	15.6697i	−0.864901	−	0.733801i
$457$	12.3829	−	21.4478i	0.579249	−	1.00329i	−0.416317	−	0.909219i	$-0.636679\pi$
$457$	12.3829	−	21.4478i	0.579249	−	1.00329i	0.995566	−	0.0940686i	$-0.0299873\pi$
$458$	−11.2628	−	9.45057i	−0.526274	−	0.441596i
$459$	−17.0696	+	6.21284i	−0.796742	+	0.289990i
$460$	0.181488	+	1.02927i	0.00846192	+	0.0479899i
$461$	0.823549	+	0.691040i	0.0383565	+	0.0321849i	0.661764	−	0.749712i	$-0.269808\pi$
$461$	0.823549	+	0.691040i	0.0383565	+	0.0321849i	−0.623408	+	0.781897i	$0.714252\pi$
$462$	1.10503	+	13.0151i	0.0514106	+	0.605515i
$463$	−5.81281	−	10.0681i	−0.270144	−	0.467903i	0.698754	−	0.715362i	$-0.253738\pi$
$463$	−5.81281	−	10.0681i	−0.270144	−	0.467903i	−0.968899	+	0.247458i	$0.920405\pi$
$464$	−0.183724	−	0.318220i	−0.00852919	−	0.0147730i
$465$	−1.24166	−	7.04181i	−0.0575807	−	0.326556i
$466$	1.88778	+	10.7061i	0.0874498	+	0.495953i
$467$	−12.4332	−	21.5350i	−0.575341	−	0.996520i	−0.996004	−	0.0893031i	$-0.971536\pi$
$467$	−12.4332	−	21.5350i	−0.575341	−	0.996520i	0.420663	−	0.907217i	$-0.361797\pi$
$468$	−0.291012	−	0.504047i	−0.0134520	−	0.0232996i
$469$	1.13020	+	13.3116i	0.0521880	+	0.614672i
$470$	−1.72207	−	1.44499i	−0.0794334	−	0.0666525i
$471$	8.05000	+	45.6538i	0.370924	+	2.10362i
$472$	−5.25471	+	1.91256i	−0.241868	+	0.0880327i
$473$	−5.63497	−	4.72831i	−0.259096	−	0.217408i
$474$	−11.1344	+	19.2853i	−0.511418	+	0.885801i
$475$	−3.33451	−	19.5324i	−0.152998	−	0.896208i
$476$	−6.04117	−	13.0426i	−0.276896	−	0.597806i
$477$	−10.3353	+	3.76174i	−0.473221	+	0.172238i
$478$	12.1613	+	10.2045i	0.556243	+	0.466743i
$479$	14.9577	+	5.44417i	0.683436	+	0.248751i	0.660322	−	0.750982i	$-0.270420\pi$
$479$	14.9577	+	5.44417i	0.683436	+	0.248751i	0.0231141	+	0.999733i	$0.492642\pi$
$480$	−1.30946	+	7.42630i	−0.0597683	+	0.338963i
$481$	−2.17009	−	0.789849i	−0.0989478	−	0.0360140i
$482$	−4.44143	−	7.69279i	−0.202302	−	0.350397i
$483$	−2.72857	−	5.89085i	−0.124154	−	0.268043i
$484$	−3.14082	−	1.14317i	−0.142765	−	0.0519621i
$485$	3.01300	−	2.52821i	0.136814	−	0.114800i
$486$	−7.76107			−0.352049
$487$	−9.03776	+	15.6539i	−0.409540	+	0.709344i	−0.994838	−	0.101474i	$-0.967644\pi$
$487$	−9.03776	+	15.6539i	−0.409540	+	0.709344i	0.585298	+	0.810818i	$0.300977\pi$
$488$	−24.4266	−	8.89057i	−1.10574	−	0.402457i
$489$	−17.6158	−	14.7814i	−0.796612	−	0.668437i
$490$	0.0210183	−	4.09592i	0.000949511	−	0.185035i
$491$	6.00249	−	34.0418i	0.270888	−	1.53628i	−0.480838	−	0.876810i	$-0.659667\pi$
$491$	6.00249	−	34.0418i	0.270888	−	1.53628i	0.751726	−	0.659475i	$-0.229221\pi$
$492$	0.923222	−	5.23585i	0.0416221	−	0.236050i
$493$	17.8840	+	30.9760i	0.805455	+	1.39509i
$494$	1.00630	−	1.72124i	0.0452754	−	0.0774423i
$495$	0.861632	−	1.49239i	0.0387275	−	0.0670780i
$496$	−0.226528	+	0.0824495i	−0.0101714	+	0.00370209i
$497$	0.730178	+	0.733935i	0.0327530	+	0.0329215i
$498$	−3.84007	+	3.22220i	−0.172078	+	0.144390i
$499$	−8.47250	+	3.08374i	−0.379281	+	0.138047i	−0.524623	−	0.851334i	$-0.675794\pi$
$499$	−8.47250	+	3.08374i	−0.379281	+	0.138047i	0.145342	+	0.989381i	$0.453572\pi$
$500$	−6.14045	+	5.15245i	−0.274609	+	0.230425i
$501$	−5.53643	+	9.58937i	−0.247349	+	0.428422i
$502$	−3.39341	−	5.87756i	−0.151455	−	0.262329i
$503$	26.2341	+	9.54842i	1.16972	+	0.425743i	0.852560	−	0.522629i	$-0.175049\pi$
$503$	26.2341	+	9.54842i	1.16972	+	0.425743i	0.317159	+	0.948372i	$0.397271\pi$
$504$	−0.559374	−	6.58832i	−0.0249165	−	0.293467i
$505$	2.17944	−	3.77490i	0.0969837	−	0.167981i
$506$	3.11684			0.138560
$507$	−19.2139	+	16.1223i	−0.853318	+	0.716019i
$508$	1.78216	−	10.1071i	0.0790706	−	0.448432i
$509$	4.38671	+	24.8783i	0.194437	+	1.10271i	0.913218	+	0.407472i	$0.133590\pi$
$509$	4.38671	+	24.8783i	0.194437	+	1.10271i	−0.718780	+	0.695237i	$0.755299\pi$
$510$	0.873374	−	4.95315i	0.0386737	−	0.219329i
$511$	−24.5277	+	6.50476i	−1.08504	+	0.287754i
$512$	0.506716			0.0223939
$513$	8.99458	+	15.7769i	0.397121	+	0.696566i
$514$	1.40381	+	2.43147i	0.0619194	+	0.107247i
$515$	1.14712	+	0.962546i	0.0505481	+	0.0424149i
$516$	4.79977	+	4.02748i	0.211298	+	0.177300i
$517$	8.48774	−	7.12206i	0.373290	−	0.313228i
$518$	−7.10292	−	7.13947i	−0.312085	−	0.313690i
$519$	−1.84533	−	10.4654i	−0.0810012	−	0.459381i
$520$	−1.00059			−0.0438788
$521$	2.58140			0.113093			0.0565465	−	0.998400i	$-0.481991\pi$
$521$	2.58140			0.113093			0.0565465	+	0.998400i	$0.481991\pi$
$522$	1.09676	+	6.22004i	0.0480039	+	0.272244i
$523$	−22.6138	+	18.9752i	−0.988831	+	0.829728i	−0.985398	−	0.170267i	$-0.945537\pi$
$523$	−22.6138	+	18.9752i	−0.988831	+	0.829728i	−0.00343276	+	0.999994i	$0.501093\pi$
$524$	−10.2125	+	17.6886i	−0.446136	+	0.772730i
$525$	13.6500	−	19.3882i	0.595735	−	0.846169i
$526$	−3.67935	−	20.8666i	−0.160427	−	0.909827i
$527$	22.0506	−	8.02576i	0.960539	−	0.349608i
$528$	−0.239309	−	0.0871012i	−0.0104146	−	0.00379059i
$529$	20.1572	−	7.33662i	0.876400	−	0.318984i
$530$	−1.26039	+	7.14805i	−0.0547480	+	0.310491i
$531$	−1.75913			−0.0763399
$532$	−11.8371	+	8.14788i	−0.513203	+	0.353255i
$533$	1.14011			0.0493838
$534$	−4.76387	+	27.0173i	−0.206153	+	1.16915i
$535$	−6.52635	+	2.37540i	−0.282159	+	0.102697i
$536$	13.3737	+	4.86762i	0.577655	+	0.210249i
$537$	−13.3940	+	4.87501i	−0.577993	+	0.210372i
$538$	−0.873521	−	4.95398i	−0.0376602	−	0.213581i
$539$	19.8633	+	3.60762i	0.855571	+	0.155391i
$540$	1.74927	−	3.02983i	0.0752767	−	0.130383i
$541$	−1.16669	+	0.978970i	−0.0501599	+	0.0420892i	−0.667523	−	0.744589i	$-0.732645\pi$
$541$	−1.16669	+	0.978970i	−0.0501599	+	0.0420892i	0.617363	+	0.786678i	$0.288201\pi$
$542$	−3.51391	−	19.9283i	−0.150935	−	0.855996i
$543$	−46.8362			−2.00993
$544$	−24.7470			−1.06102
$545$	2.00397	+	11.3651i	0.0858408	+	0.486827i
$546$	2.30615	−	0.611593i	0.0986940	−	0.0261738i
$547$	−17.7543	+	14.8976i	−0.759118	+	0.636976i	−0.937897	−	0.346913i	$-0.887230\pi$
$547$	−17.7543	+	14.8976i	−0.759118	+	0.636976i	0.178779	+	0.983889i	$0.442785\pi$
$548$	16.8675	+	14.1535i	0.720545	+	0.604609i
$549$	−6.26423	−	5.25631i	−0.267351	−	0.224334i
$550$	5.69187	+	9.85860i	0.242702	+	0.420372i
$551$	27.5180	−	22.8362i	1.17231	−	0.972853i
$552$	−6.91608			−0.294368
$553$	24.2748	+	24.3997i	1.03227	+	1.03758i
$554$	2.89623	−	16.4254i	0.123049	−	0.697847i
$555$	1.01135	+	5.73567i	0.0429295	+	0.243465i
$556$	4.76126	−	27.0024i	0.201922	−	1.14516i
$557$	18.0640	−	15.1575i	0.765395	−	0.642242i	−0.174130	−	0.984723i	$-0.555711\pi$
$557$	18.0640	−	15.1575i	0.765395	−	0.642242i	0.939525	+	0.342480i	$0.111267\pi$
$558$	4.14363			0.175414
$559$	−0.671813	+	1.16361i	−0.0284147	+	0.0492157i
$560$	0.0722901	+	0.0339355i	0.00305481	+	0.00143404i
$561$	23.2946	+	8.47856i	0.983501	+	0.357965i
$562$	7.92118	+	13.7199i	0.334135	+	0.578739i
$563$	13.3671	−	23.1525i	0.563357	−	0.975763i	−0.433843	−	0.900988i	$-0.642843\pi$
$563$	13.3671	−	23.1525i	0.563357	−	0.975763i	0.997200	−	0.0747748i	$-0.0238238\pi$
$564$	−7.22970	+	6.06644i	−0.304425	+	0.255443i
$565$	−1.48976	+	0.542230i	−0.0626749	+	0.0228118i
$566$	−7.43263	+	6.23672i	−0.312417	+	0.262149i
$567$	−7.51735	+	27.7699i	−0.315699	+	1.16623i
$568$	1.03639	−	0.377214i	0.0434859	−	0.0158276i
$569$	4.79467	−	8.30461i	0.201003	−	0.348147i	−0.747849	−	0.663869i	$-0.768913\pi$
$569$	4.79467	−	8.30461i	0.201003	−	0.348147i	0.948852	+	0.315722i	$0.102247\pi$
$570$	−5.02827	−	0.0273835i	−0.210611	−	0.00114697i
$571$	−14.6940	−	25.4508i	−0.614925	−	1.06508i	−0.990398	−	0.138248i	$-0.955853\pi$
$571$	−14.6940	−	25.4508i	−0.614925	−	1.06508i	0.375473	−	0.926833i	$-0.377480\pi$
$572$	0.328738	−	1.86437i	0.0137452	−	0.0779530i
$573$	1.05617	−	5.98986i	0.0441223	−	0.250230i
$574$	4.50069	+	2.11278i	0.187855	+	0.0881858i
$575$	−4.33428	−	3.63690i	−0.180752	−	0.151669i
$576$	−4.03170	−	1.46742i	−0.167988	−	0.0611425i
$577$	−15.6044	+	27.0276i	−0.649620	+	1.12517i	0.333594	+	0.942717i	$0.391739\pi$
$577$	−15.6044	+	27.0276i	−0.649620	+	1.12517i	−0.983214	+	0.182458i	$0.941595\pi$
$578$	1.74457			0.0725645
$579$	−7.23175	+	6.06816i	−0.300541	+	0.252184i
$580$	−6.47336	−	2.35611i	−0.268792	−	0.0978321i
$581$	3.25633	+	7.03026i	0.135095	+	0.291664i
$582$	4.99552	+	8.65250i	0.207071	+	0.358658i
$583$	−33.6172	−	12.2357i	−1.39228	−	0.506750i
$584$	−4.69420	+	26.6221i	−0.194247	+	1.10163i
$585$	−0.295786	−	0.107657i	−0.0122293	−	0.00445109i
$586$	13.1456	+	11.0304i	0.543038	+	0.455663i
$587$	19.0177	−	6.92189i	0.784946	−	0.285697i	0.0817124	−	0.996656i	$-0.473961\pi$
$587$	19.0177	−	6.92189i	0.784946	−	0.285697i	0.703233	+	0.710959i	$0.251739\pi$
$588$	−16.9192	−	3.07290i	−0.697734	−	0.126724i
$589$	−11.6192	−	20.3806i	−0.478762	−	0.839768i
$590$	−0.580454	+	1.00538i	−0.0238969	+	0.0413907i
$591$	−6.40263	−	5.37244i	−0.263369	−	0.220993i
$592$	0.184511	−	0.0671565i	0.00758335	−	0.00276011i
$593$	−5.70378	−	32.3478i	−0.234226	−	1.32836i	−0.844237	−	0.535970i	$-0.819946\pi$
$593$	−5.70378	−	32.3478i	−0.234226	−	1.32836i	0.610011	−	0.792393i	$-0.291165\pi$
$594$	−7.99242	−	6.70644i	−0.327933	−	0.275169i
$595$	−7.03682	−	3.30333i	−0.288482	−	0.135423i
$596$	−14.5699	−	25.2359i	−0.596808	−	1.03370i
$597$	−7.58118	−	13.1310i	−0.310277	−	0.537416i
$598$	−0.0988611	−	0.560669i	−0.00404273	−	0.0229275i
$599$	−6.71253	−	38.0686i	−0.274267	−	1.55544i	−0.741282	−	0.671194i	$-0.765782\pi$
$599$	−6.71253	−	38.0686i	−0.274267	−	1.55544i	0.467015	−	0.884249i	$-0.345329\pi$
$600$	−12.6299	−	21.8756i	−0.515614	−	0.893069i
$601$	−10.9461	−	18.9592i	−0.446500	−	0.773360i	0.551655	−	0.834072i	$-0.313996\pi$
$601$	−10.9461	−	18.9592i	−0.446500	−	0.773360i	−0.998155	+	0.0607116i	$0.980663\pi$
$602$	−4.80837	+	3.34850i	−0.195975	+	0.136475i
$603$	3.42969	+	2.87785i	0.139668	+	0.117195i
$604$	−2.31914	−	13.1525i	−0.0943645	−	0.535168i
$605$	−1.69862	+	0.618247i	−0.0690587	+	0.0251353i
$606$	8.48191	+	7.11716i	0.344554	+	0.289115i
$607$	−0.399113	+	0.691284i	−0.0161995	+	0.0280583i	−0.874012	−	0.485905i	$-0.838490\pi$
$607$	−0.399113	+	0.691284i	−0.0161995	+	0.0280583i	0.857812	+	0.513964i	$0.171823\pi$
$608$	4.16348	+	24.3882i	0.168851	+	0.989071i
$609$	42.6183	+	3.83883i	1.72698	+	0.155557i
$610$	−5.07106	+	1.84571i	−0.205321	+	0.0747308i
$611$	−1.55036	−	1.30091i	−0.0627209	−	0.0526291i
$612$	−4.52655	−	1.64753i	−0.182975	−	0.0665974i
$613$	−2.51979	+	14.2905i	−0.101773	+	0.577186i	0.890687	+	0.454618i	$0.150224\pi$
$613$	−2.51979	+	14.2905i	−0.101773	+	0.577186i	−0.992460	+	0.122568i	$0.960887\pi$
$614$	11.4784	+	4.17778i	0.463229	+	0.168601i
$615$	−1.43767	−	2.49011i	−0.0579723	−	0.100411i
$616$	12.3809	−	17.5855i	0.498840	−	0.708542i
$617$	1.86952	+	0.680448i	0.0752639	+	0.0273938i	0.379378	−	0.925242i	$-0.376138\pi$
$617$	1.86952	+	0.680448i	0.0752639	+	0.0273938i	−0.304114	+	0.952636i	$0.598360\pi$
$618$	−2.91389	+	2.44505i	−0.117214	+	0.0983541i
$619$	16.8225			0.676155			0.338077	−	0.941118i	$-0.390223\pi$
$619$	16.8225			0.676155			0.338077	+	0.941118i	$0.390223\pi$
$620$	−2.25971	+	3.91394i	−0.0907523	+	0.157188i
$621$	4.87292	+	1.77360i	0.195543	+	0.0711720i
$622$	20.8760	+	17.5170i	0.837050	+	0.702368i
$623$	38.3828	+	18.0182i	1.53777	+	0.721885i
$624$	−0.00807762	+	0.0458104i	−0.000323363	+	0.00183389i
$625$	3.19413	−	18.1148i	0.127765	−	0.724592i
$626$	6.25897	+	10.8409i	0.250159	+	0.433288i
$627$	4.43649	−	24.3833i	0.177176	−	0.973777i
$628$	14.6503	−	25.3750i	0.584610	−	1.01257i
$629$	−17.9606	+	6.53711i	−0.716134	+	0.260652i
$630$	−0.968137	−	0.973118i	−0.0385715	−	0.0387700i
$631$	−12.1936	+	10.2316i	−0.485418	+	0.407314i	−0.852381	−	0.522921i	$-0.824842\pi$
$631$	−12.1936	+	10.2316i	−0.485418	+	0.407314i	0.366963	+	0.930236i	$0.380398\pi$
$632$	34.4547	−	12.5405i	1.37054	−	0.498834i
$633$	−11.8920	+	9.97853i	−0.472663	+	0.396611i
$634$	−2.09613	+	3.63061i	−0.0832480	+	0.144190i
$635$	−2.77523	−	4.80684i	−0.110132	−	0.190754i
$636$	28.6345	+	10.4221i	1.13543	+	0.413264i
$637$	0.0189225	−	3.68751i	0.000749737	−	0.146104i
$638$	−10.2719	+	17.7915i	−0.406669	+	0.704371i
$639$	0.346954			0.0137253
$640$	3.69127	−	3.09734i	0.145910	−	0.122433i
$641$	−1.37836	+	7.81709i	−0.0544421	+	0.308756i	−0.999853	−	0.0171231i	$-0.994549\pi$
$641$	−1.37836	+	7.81709i	−0.0544421	+	0.308756i	0.945411	+	0.325880i	$0.105660\pi$
$642$	−3.06352	−	17.3741i	−0.120907	−	0.685700i
$643$	−1.03900	+	5.89249i	−0.0409743	+	0.232377i	−0.998417	−	0.0562469i	$-0.982087\pi$
$643$	−1.03900	+	5.89249i	−0.0409743	+	0.232377i	0.957443	+	0.288624i	$0.0931977\pi$
$644$	−1.07218	+	3.96076i	−0.0422499	+	0.156076i
$645$	3.38858			0.133425
$646$	−2.77693	−	16.2663i	−0.109257	−	0.639989i
$647$	−5.95979	−	10.3227i	−0.234304	−	0.405826i	0.724767	−	0.688995i	$-0.241948\pi$
$647$	−5.95979	−	10.3227i	−0.234304	−	0.405826i	−0.959070	+	0.283169i	$0.908614\pi$
$648$	23.4780	+	19.7004i	0.922303	+	0.773904i
$649$	−4.38321	−	3.67795i	−0.172056	−	0.144372i
$650$	1.59287	−	1.33657i	0.0624773	−	0.0524247i
$651$	7.33540	−	27.0978i	0.287497	−	1.06205i
$652$	2.52388	+	14.3136i	0.0988427	+	0.560565i
$653$	−14.4491			−0.565437			−0.282719	−	0.959203i	$-0.591236\pi$
$653$	−14.4491			−0.565437			−0.282719	+	0.959203i	$0.591236\pi$
$654$	−29.3148			−1.14630
$655$	1.91816	+	10.8784i	0.0749487	+	0.425055i
$656$	−0.0742584	+	0.0623102i	−0.00289930	+	0.00243281i
$657$	−4.25203	+	7.36474i	−0.165888	+	0.287326i
$658$	−3.70942	−	8.00846i	−0.144608	−	0.312202i
$659$	8.62249	+	48.9006i	0.335885	+	1.90490i	0.418320	+	0.908300i	$0.362619\pi$
$659$	8.62249	+	48.9006i	0.335885	+	1.90490i	−0.0824352	+	0.996596i	$0.526270\pi$
$660$	−4.48647	+	1.63294i	−0.174636	+	0.0635622i
$661$	26.9679	+	9.81550i	1.04893	+	0.381779i	0.808258	−	0.588828i	$-0.200411\pi$
$661$	26.9679	+	9.81550i	1.04893	+	0.381779i	0.240670	+	0.970607i	$0.422633\pi$
$662$	1.43379	−	0.521857i	0.0557258	−	0.0202825i
$663$	0.786287	−	4.45925i	0.0305369	−	0.173183i
$664$	8.25379			0.320309
$665$	−2.07155	+	7.49055i	−0.0803312	+	0.290471i
$666$	−3.37506			−0.130781
$667$	1.77309	−	10.0557i	0.0686542	−	0.389357i
$668$	6.57652	−	2.39366i	0.254453	−	0.0926134i
$669$	−6.69442	−	2.43657i	−0.258821	−	0.0942032i
$670$	2.77642	−	1.01054i	0.107263	−	0.0390404i
$671$	−4.61874	−	26.1942i	−0.178304	−	1.01121i
$672$	−17.0434	+	24.2081i	−0.657464	+	0.933847i
$673$	−10.6251	+	18.4032i	−0.409568	+	0.709393i	−0.994841	−	0.101443i	$-0.967654\pi$
$673$	−10.6251	+	18.4032i	−0.409568	+	0.709393i	0.585273	+	0.810836i	$0.300987\pi$
$674$	−10.4318	+	8.75330i	−0.401817	+	0.337165i
$675$	3.28885	+	18.6520i	0.126588	+	0.717915i
$676$	15.8530			0.609731
$677$	−14.7513			−0.566940			−0.283470	−	0.958981i	$-0.591486\pi$
$677$	−14.7513			−0.566940			−0.283470	+	0.958981i	$0.591486\pi$
$678$	−0.699306	−	3.96596i	−0.0268567	−	0.152312i
$679$	14.9260	−	3.95840i	0.572808	−	0.151909i
$680$	−6.34384	+	5.32311i	−0.243275	+	0.204132i
$681$	22.3681	+	18.7691i	0.857148	+	0.719233i
$682$	10.3246	+	8.66339i	0.395351	+	0.331738i
$683$	−13.0103	−	22.5345i	−0.497825	−	0.862259i	0.502171	−	0.864768i	$-0.332535\pi$
$683$	−13.0103	−	22.5345i	−0.497825	−	0.862259i	−0.999997	+	0.00250911i	$0.999201\pi$
$684$	−0.862086	+	4.73810i	−0.0329627	+	0.181166i
$685$	11.9083			0.454993
$686$	6.90814	−	14.5217i	0.263754	−	0.554440i
$687$	−5.79671	+	32.8748i	−0.221158	+	1.25425i
$688$	−0.0198377	−	0.112505i	−0.000756307	−	0.00428923i
$689$	−1.13472	+	6.43529i	−0.0432292	+	0.245165i
$690$	−1.09989	+	0.922916i	−0.0418721	+	0.0351348i
$691$	−11.8252			−0.449852			−0.224926	−	0.974376i	$-0.572214\pi$
$691$	−11.8252			−0.449852			−0.224926	+	0.974376i	$0.572214\pi$
$692$	−3.35835	+	5.81683i	−0.127665	+	0.221123i
$693$	5.55203	−	3.86638i	0.210904	−	0.146872i
$694$	21.9504	+	7.98930i	0.833226	+	0.303270i
$695$	−7.41436	−	12.8420i	−0.281243	−	0.487127i
$696$	22.7927	−	39.4782i	0.863956	−	1.49642i
$697$	7.22842	−	6.06537i	0.273796	−	0.229742i
$698$	−0.842519	+	0.306652i	−0.0318898	+	0.0116069i
$699$	18.9085	−	15.8661i	0.715184	−	0.600111i
$700$	−14.4859	+	3.84168i	−0.547516	+	0.145202i
$701$	22.5653	−	8.21311i	0.852281	−	0.310205i	0.121311	−	0.992615i	$-0.461290\pi$
$701$	22.5653	−	8.21311i	0.852281	−	0.310205i	0.730970	+	0.682409i	$0.239068\pi$
$702$	−0.952873	+	1.65042i	−0.0359639	+	0.0622913i
$703$	9.46404	+	16.6003i	0.356943	+	0.626093i
$704$	−6.97770	−	12.0857i	−0.262982	−	0.455498i
$705$	−0.886316	+	5.02655i	−0.0333806	+	0.189311i
$706$	−2.35089	+	13.3326i	−0.0884771	+	0.501778i
$707$	14.0435	−	9.77974i	0.528159	−	0.367805i
$708$	3.73354	+	3.13281i	0.140315	+	0.117738i
$709$	−16.0275	−	5.83352i	−0.601924	−	0.219082i	0.0230420	−	0.999734i	$-0.492665\pi$
$709$	−16.0275	−	5.83352i	−0.601924	−	0.219082i	−0.624966	+	0.780652i	$0.714887\pi$
$710$	0.114483	−	0.198291i	0.00429648	−	0.00744171i
$711$	11.5345			0.432577
$712$	34.6029	−	29.0352i	1.29680	−	1.08814i
$713$	−6.29485	−	2.29114i	−0.235744	−	0.0858037i
$714$	11.3675	−	16.1462i	0.425419	−	0.604255i
$715$	−0.511920	−	0.886671i	−0.0191447	−	0.0331596i
$716$	8.46565	+	3.08125i	0.316376	+	0.115152i
$717$	6.25915	−	35.4974i	0.233752	−	1.32567i
$718$	9.24938	+	3.36650i	0.345184	+	0.125637i
$719$	24.2133	+	20.3174i	0.903005	+	0.757711i	0.970775	−	0.239990i	$-0.0771441\pi$
$719$	24.2133	+	20.3174i	0.903005	+	0.757711i	−0.0677705	+	0.997701i	$0.521589\pi$
$720$	0.0251491	−	0.00915351i	0.000937250	−	0.000341131i
$721$	2.47094	+	5.33464i	0.0920226	+	0.198672i
$722$	−15.5632	+	5.47334i	−0.579204	+	0.203697i
$723$	−10.0842	+	17.4664i	−0.375037	+	0.649584i
$724$	22.6770	+	19.0283i	0.842785	+	0.707180i
$725$	35.0442	−	12.7550i	1.30151	−	0.473710i
$726$	−0.797344	−	4.52196i	−0.0295922	−	0.167826i
$727$	−27.4636	−	23.0447i	−1.01857	−	0.854679i	−0.0291203	−	0.999576i	$-0.509271\pi$
$727$	−27.4636	−	23.0447i	−1.01857	−	0.854679i	−0.989447	+	0.144897i	$0.953715\pi$
$728$	−3.55606	−	1.66934i	−0.131796	−	0.0618698i
$729$	−7.50000	−	12.9904i	−0.277778	−	0.481125i
$730$	2.80605	+	4.86023i	0.103857	+	0.179885i
$731$	1.93104	+	10.9514i	0.0714219	+	0.405054i
$732$	3.93416	+	22.3117i	0.145411	+	0.824664i
$733$	−9.58702	−	16.6052i	−0.354105	−	0.613327i	0.632860	−	0.774267i	$-0.281881\pi$
$733$	−9.58702	−	16.6052i	−0.354105	−	0.613327i	−0.986964	+	0.160939i	$0.948548\pi$
$734$	13.7734	+	23.8562i	0.508384	+	0.880547i
$735$	−8.07770	+	4.60856i	−0.297951	+	0.169989i
$736$	5.41180	+	4.54104i	0.199481	+	0.167385i
$737$	2.52878	+	14.3414i	0.0931486	+	0.528272i
$738$	1.56575	−	0.569886i	0.0576360	−	0.0209778i
$739$	−9.59550	−	8.05158i	−0.352976	−	0.296182i	0.449008	−	0.893528i	$-0.351778\pi$
$739$	−9.59550	−	8.05158i	−0.352976	−	0.296182i	−0.801984	+	0.597346i	$0.796222\pi$
$740$	1.84057	−	3.18797i	0.0676608	−	0.117192i
$741$	−4.52688	−	0.0246530i	−0.166299	−	0.000905651i
$742$	−16.4048	+	23.3011i	−0.602241	+	0.855409i
$743$	10.0643	−	3.66310i	0.369222	−	0.134386i	−0.150744	−	0.988573i	$-0.548167\pi$
$743$	10.0643	−	3.66310i	0.369222	−	0.134386i	0.519966	+	0.854187i	$0.325945\pi$
$744$	−22.9097	−	19.2235i	−0.839912	−	0.704770i
$745$	−14.8090	−	5.39004i	−0.542560	−	0.197476i
$746$	5.74918	−	32.6052i	0.210492	−	1.19376i
$747$	2.43992	+	0.888057i	0.0892719	+	0.0324923i
$748$	−7.83413	−	13.5691i	−0.286444	−	0.496136i
$749$	−27.1574	−	2.44619i	−0.992308	−	0.0893818i
$750$	−10.3478	−	3.76630i	−0.377849	−	0.137526i
$751$	−11.5159	+	9.66295i	−0.420220	+	0.352606i	−0.828247	−	0.560364i	$-0.810661\pi$
$751$	−11.5159	+	9.66295i	−0.420220	+	0.352606i	0.408027	+	0.912970i	$0.366217\pi$
$752$	0.172077			0.00627499
$753$	−7.70473	+	13.3450i	−0.280776	+	0.486318i
$754$	3.52620	+	1.28343i	0.128417	+	0.0467399i
$755$	−5.53303	−	4.64276i	−0.201368	−	0.168967i
$756$	11.2717	−	7.84947i	0.409946	−	0.285483i
$757$	−6.83931	+	38.7877i	−0.248579	+	1.40976i	0.563453	+	0.826148i	$0.309473\pi$
$757$	−6.83931	+	38.7877i	−0.248579	+	1.40976i	−0.812032	+	0.583613i	$0.801638\pi$
$758$	4.62568	−	26.2335i	0.168012	−	0.952845i
$759$	−3.53839	−	6.12866i	−0.128435	−	0.222456i
$760$	6.31323	+	5.35629i	0.229005	+	0.194293i
$761$	12.8284	−	22.2195i	0.465030	−	0.805456i	−0.534173	−	0.845375i	$-0.679377\pi$
$761$	12.8284	−	22.2195i	0.465030	−	0.805456i	0.999203	+	0.0399195i	$0.0127101\pi$
$762$	13.2489	−	4.82221i	0.479957	−	0.174690i
$763$	−11.8389	+	43.7344i	−0.428598	+	1.58329i
$764$	−2.94490	+	2.47106i	−0.106543	+	0.0893998i
$765$	−2.44805	+	0.891016i	−0.0885093	+	0.0322148i
$766$	17.7875	−	14.9255i	0.642687	−	0.539279i
$767$	−0.522575	+	0.905127i	−0.0188691	+	0.0326822i
$768$	15.6597	+	27.1234i	0.565071	+	0.978731i
$769$	−30.4273	−	11.0746i	−1.09724	−	0.399362i	−0.270940	−	0.962596i	$-0.587335\pi$
$769$	−30.4273	−	11.0746i	−1.09724	−	0.399362i	−0.826297	+	0.563234i	$0.809557\pi$
$770$	−0.377725	−	4.44886i	−0.0136123	−	0.160326i
$771$	3.18734	−	5.52064i	0.114789	−	0.198821i
$772$	5.96678			0.214749
$773$	−26.2546	+	22.0302i	−0.944311	+	0.792371i	−0.978330	−	0.207050i	$-0.933614\pi$
$773$	−26.2546	+	22.0302i	−0.944311	+	0.792371i	0.0340193	+	0.999421i	$0.489169\pi$
$774$	−0.340986	+	1.93383i	−0.0122565	+	0.0695101i
$775$	−4.24854	−	24.0947i	−0.152612	−	0.865506i
$776$	2.85660	−	16.2006i	0.102546	−	0.581567i
$777$	−5.97480	+	22.0716i	−0.214345	+	0.791814i
$778$	2.02760			0.0726931
$779$	−7.19355	−	6.10317i	−0.257736	−	0.218669i
$780$	0.436044	+	0.755250i	0.0156129	+	0.0270423i
$781$	0.864501	+	0.725403i	0.0309343	+	0.0259570i
$782$	−3.60953	−	3.02875i	−0.129076	−	0.108308i
$783$	−26.1833	+	21.9704i	−0.935713	+	0.785157i
$784$	0.200299	+	0.241210i	0.00715355	+	0.00861466i
$785$	−2.75168	−	15.6056i	−0.0982118	−	0.556987i
$786$	−28.0595			−1.00085
$787$	−20.1368			−0.717800			−0.358900	−	0.933376i	$-0.616848\pi$
$787$	−20.1368			−0.717800			−0.358900	+	0.933376i	$0.616848\pi$
$788$	0.917329	+	5.20243i	0.0326785	+	0.185329i
$789$	−36.8532	+	30.9235i	−1.31201	+	1.10091i
$790$	3.80599	−	6.59217i	0.135411	−	0.234539i
$791$	−6.19918	−	0.558389i	−0.220418	−	0.0198540i
$792$	−1.25157	−	7.09801i	−0.0444726	−	0.252217i
$793$	−4.56541	+	1.66167i	−0.162122	+	0.0590077i
$794$	19.2885	+	7.02046i	0.684525	+	0.249147i
$795$	15.4861	−	5.63649i	0.549236	−	0.199906i
$796$	−1.66413	+	9.43777i	−0.0589836	+	0.334513i
$797$	−30.9542			−1.09645			−0.548227	−	0.836330i	$-0.684697\pi$
$797$	−30.9542			−1.09645			−0.548227	+	0.836330i	$0.684697\pi$
$798$	−17.8246	−	8.48624i	−0.630983	−	0.300410i
$799$	−16.7502			−0.592580
$800$	−4.48051	+	25.4102i	−0.158410	+	0.898388i
$801$	13.3530	−	4.86010i	0.471806	−	0.171723i
$802$	−21.7354	−	7.91103i	−0.767502	−	0.279348i
$803$	−25.9927	+	9.46058i	−0.917263	+	0.333857i
$804$	−2.15396	−	12.2157i	−0.0759645	−	0.430816i
$805$	0.932691	+	2.01363i	0.0328730	+	0.0709713i
$806$	1.23092	−	2.13202i	0.0433574	−	0.0750973i
$807$	−8.74939	+	7.34161i	−0.307993	+	0.258437i
$808$	−3.16576	−	17.9539i	−0.111371	−	0.631616i
$809$	−55.4281			−1.94875			−0.974374	−	0.224934i	$-0.927783\pi$
$809$	−55.4281			−1.94875			−0.974374	+	0.224934i	$0.927783\pi$
$810$	6.36271			0.223563
$811$	0.718083	+	4.07245i	0.0252153	+	0.143003i	0.994816	−	0.101688i	$-0.0324245\pi$
$811$	0.718083	+	4.07245i	0.0252153	+	0.143003i	−0.969601	+	0.244691i	$0.921313\pi$
$812$	−19.0752	−	19.1733i	−0.669409	−	0.672852i
$813$	−35.1961	+	29.5330i	−1.23438	+	1.03577i
$814$	−8.40958	−	7.05647i	−0.294755	−	0.247329i
$815$	6.02150	+	5.05263i	0.210924	+	0.176986i
$816$	0.192497	+	0.333415i	0.00673875	+	0.0116719i
$817$	10.4678	−	3.74553i	0.366221	−	0.131039i
$818$	−21.9769			−0.768403
$819$	−0.871601	−	0.876085i	−0.0304562	−	0.0306129i
$820$	−0.315580	+	1.78974i	−0.0110205	+	0.0625005i
$821$	0.181002	+	1.02651i	0.00631700	+	0.0358255i	0.987803	−	0.155707i	$-0.0497655\pi$
$821$	0.181002	+	1.02651i	0.00631700	+	0.0358255i	−0.981486	+	0.191532i	$0.938654\pi$
$822$	−5.25273	+	29.7897i	−0.183210	+	1.03904i
$823$	19.4599	−	16.3288i	0.678331	−	0.569187i	−0.237187	−	0.971464i	$-0.576226\pi$
$823$	19.4599	−	16.3288i	0.678331	−	0.569187i	0.915518	+	0.402277i	$0.131781\pi$
$824$	6.26307			0.218184
$825$	12.9234	−	22.3839i	0.449933	−	0.779308i
$826$	−3.74023	+	2.60466i	−0.130139	+	0.0906277i
$827$	19.8682	+	7.23142i	0.690884	+	0.251461i	0.663513	−	0.748164i	$-0.269065\pi$
$827$	19.8682	+	7.23142i	0.690884	+	0.251461i	0.0273701	+	0.999625i	$0.491287\pi$
$828$	0.687569	+	1.19090i	0.0238947	+	0.0413868i
$829$	13.6782	−	23.6914i	0.475065	−	0.822836i	−0.524527	−	0.851394i	$-0.675758\pi$
$829$	13.6782	−	23.6914i	0.475065	−	0.822836i	0.999592	+	0.0285574i	$0.00909133\pi$
$830$	1.31263	−	1.10143i	0.0455621	−	0.0382311i
$831$	−35.5852	+	12.9520i	−1.23444	+	0.449299i
$832$	−1.95271	+	1.63851i	−0.0676979	+	0.0568053i
$833$	−19.4974	−	23.4798i	−0.675546	−	0.813526i
$834$	35.3960	−	12.8831i	1.22566	−	0.446105i
$835$	1.89249	−	3.27788i	0.0654921	−	0.113436i
$836$	−12.0543	+	10.0034i	−0.416908	+	0.345976i
$837$	11.2119	+	19.4196i	0.387540	+	0.671239i
$838$	−1.78462	+	10.1211i	−0.0616486	+	0.349627i
$839$	−0.733804	+	4.16161i	−0.0253337	+	0.143675i	−0.994851	−	0.101348i	$-0.967684\pi$
$839$	−0.733804	+	4.16161i	−0.0253337	+	0.143675i	0.969517	+	0.245023i	$0.0787955\pi$
$840$	0.838150	+	9.87175i	0.0289189	+	0.340608i
$841$	29.3408	+	24.6199i	1.01175	+	0.848961i
$842$	−18.9171	−	6.88528i	−0.651928	−	0.237282i
$843$	17.9850	−	31.1509i	0.619436	−	1.07290i
$844$	9.81183			0.337737
$845$	6.56776	−	5.51101i	0.225938	−	0.189584i
$846$	−2.77941	−	1.01162i	−0.0955581	−	0.0347803i
$847$	−7.06827	−	0.636671i	−0.242868	−	0.0218763i
$848$	−0.277799	−	0.481162i	−0.00953965	−	0.0165232i
$849$	20.7012	+	7.53461i	0.710462	+	0.258587i
$850$	2.98839	−	16.9480i	0.102501	−	0.581311i
$851$	5.12725	+	1.86617i	0.175760	+	0.0639714i
$852$	−0.736366	−	0.617885i	−0.0252275	−	0.0211684i
$853$	20.9548	−	7.62693i	0.717479	−	0.261141i	0.0426237	−	0.999091i	$-0.486428\pi$
$853$	20.9548	−	7.62693i	0.717479	−	0.261141i	0.674855	+	0.737950i	$0.264206\pi$
$854$	−21.1016	−	1.90072i	−0.722082	−	0.0650413i
$855$	1.28996	+	2.26265i	0.0441157	+	0.0773808i
$856$	−14.5241	+	25.1564i	−0.496422	+	0.859828i
$857$	−32.7223	−	27.4573i	−1.11777	−	0.937924i	−0.119284	−	0.992860i	$-0.538060\pi$
$857$	−32.7223	−	27.4573i	−1.11777	−	0.937924i	−0.998490	+	0.0549367i	$0.982504\pi$
$858$	2.44390	−	0.889506i	0.0834333	−	0.0303672i
$859$	3.97146	+	22.5233i	0.135505	+	0.768485i	0.974507	+	0.224357i	$0.0720282\pi$
$859$	3.97146	+	22.5233i	0.135505	+	0.768485i	−0.839002	+	0.544128i	$0.816861\pi$
$860$	−1.64068	−	1.37669i	−0.0559466	−	0.0469448i
$861$	−0.955022	−	11.2483i	−0.0325471	−	0.383340i
$862$	−6.78284	−	11.7482i	−0.231024	−	0.400146i
$863$	−1.31588	−	2.27917i	−0.0447930	−	0.0775837i	0.842760	−	0.538290i	$-0.180929\pi$
$863$	−1.31588	−	2.27917i	−0.0447930	−	0.0775837i	−0.887553	+	0.460706i	$0.847596\pi$
$864$	−4.10646	−	23.2889i	−0.139705	−	0.792304i
$865$	0.630780	+	3.57733i	0.0214472	+	0.121633i
$866$	10.5109	+	18.2055i	0.357176	+	0.618647i
$867$	−1.98052	−	3.43036i	−0.0672619	−	0.116501i
$868$	−14.5607	+	10.1400i	−0.494224	+	0.344173i
$869$	28.7403	+	24.1160i	0.974949	+	0.818080i
$870$	−1.64336	−	9.31993i	−0.0557150	−	0.315975i
$871$	2.49958	−	0.909772i	0.0846949	−	0.0308264i
$872$	36.9751	+	31.0258i	1.25213	+	1.05066i
$873$	2.58753	−	4.48173i	0.0875745	−	0.151684i
$874$	−2.37757	+	4.06676i	−0.0804223	+	0.137560i
$875$	−9.79793	+	13.9168i	−0.331230	+	0.470472i
$876$	22.1401	−	8.05834i	0.748045	−	0.272266i
$877$	−7.02509	−	5.89475i	−0.237221	−	0.199052i	0.516426	−	0.856332i	$-0.327262\pi$
$877$	−7.02509	−	5.89475i	−0.237221	−	0.199052i	−0.753646	+	0.657280i	$0.771707\pi$
$878$	9.10537	+	3.31408i	0.307291	+	0.111845i
$879$	6.76575	−	38.3705i	0.228203	−	1.29420i
$880$	0.0818015	+	0.0297733i	0.00275753	+	0.00100366i
$881$	−3.05637	−	5.29379i	−0.102972	−	0.178352i	0.809936	−	0.586518i	$-0.199502\pi$
$881$	−3.05637	−	5.29379i	−0.102972	−	0.178352i	−0.912908	+	0.408166i	$0.866168\pi$
$882$	−1.81721	−	5.07361i	−0.0611888	−	0.170837i
$883$	0.585600	+	0.213141i	0.0197070	+	0.00717276i	0.351855	−	0.936055i	$-0.385551\pi$
$883$	0.585600	+	0.213141i	0.0197070	+	0.00717276i	−0.332148	+	0.943227i	$0.607773\pi$
$884$	−2.19238	+	1.83962i	−0.0737377	+	0.0618732i
$885$	2.63584			0.0886027
$886$	−13.6813	+	23.6966i	−0.459631	+	0.796104i
$887$	21.8865	+	7.96602i	0.734875	+	0.267473i	0.682227	−	0.731140i	$-0.261012\pi$
$887$	21.8865	+	7.96602i	0.734875	+	0.267473i	0.0526482	+	0.998613i	$0.483234\pi$
$888$	18.6603	+	15.6579i	0.626200	+	0.525444i
$889$	−1.84355	−	21.7133i	−0.0618306	−	0.728242i
$890$	1.62841	−	9.23516i	0.0545843	−	0.309563i
$891$	−5.44568	+	30.8840i	−0.182437	+	1.03465i
$892$	2.25137	+	3.89949i	0.0753816	+	0.130565i
$893$	2.81808	+	16.5073i	0.0943036	+	0.552397i
$894$	20.0159	−	34.6686i	0.669432	−	1.15949i
$895$	4.57839	−	1.66640i	0.153039	−	0.0557015i
$896$	18.2861	−	4.84948i	0.610894	−	0.162010i
$897$	−0.990215	+	0.830889i	−0.0330623	+	0.0277426i
$898$	23.8883	−	8.69461i	0.797161	−	0.290143i
$899$	33.8236	−	28.3814i	1.12808	−	0.946571i
$900$	−2.51123	+	4.34958i	−0.0837077	+	0.144986i
$901$	27.0413	+	46.8370i	0.900878	+	1.56037i
$902$	5.09286	+	1.85365i	0.169574	+	0.0617198i
$903$	12.0429	+	5.65335i	0.400762	+	0.188132i
$904$	−3.31539	+	5.74243i	−0.110268	+	0.190990i
$905$	16.0097			0.532182
$906$	14.0549	−	11.7935i	0.466943	−	0.391812i
$907$	−0.923290	+	5.23624i	−0.0306573	+	0.173866i	−0.996292	−	0.0860371i	$-0.972580\pi$
$907$	−0.923290	+	5.23624i	−0.0306573	+	0.173866i	0.965635	+	0.259904i	$0.0836908\pi$
$908$	−3.20477	−	18.1751i	−0.106354	−	0.603163i
$909$	0.995895	−	5.64800i	0.0330317	−	0.187332i
$910$	−0.788297	+	0.209057i	−0.0261318	+	0.00693018i
$911$	−1.64311			−0.0544388			−0.0272194	−	0.999629i	$-0.508665\pi$
$911$	−1.64311			−0.0544388			−0.0272194	+	0.999629i	$0.508665\pi$
$912$	0.296194	−	0.245800i	0.00980798	−	0.00813926i
$913$	4.22278	+	7.31407i	0.139754	+	0.242061i
$914$	−16.4731	−	13.8226i	−0.544882	−	0.457210i
$915$	9.38615	+	7.87591i	0.310297	+	0.260370i
$916$	16.1628	−	13.5622i	0.534033	−	0.448107i
$917$	−11.3320	+	41.8616i	−0.374215	+	1.38239i
$918$	2.73890	+	15.5331i	0.0903973	+	0.512668i
$919$	14.7885			0.487827			0.243913	−	0.969797i	$-0.421569\pi$
$919$	14.7885			0.487827			0.243913	+	0.969797i	$0.421569\pi$
$920$	2.36408			0.0779415
$921$	−4.81598	−	27.3128i	−0.158692	−	0.899986i
$922$	0.715085	−	0.600027i	0.0235501	−	0.0197608i
$923$	0.103068	−	0.178518i	0.00339251	−	0.00587600i
$924$	−18.6690	−	1.68161i	−0.614167	−	0.0553208i
$925$	3.46050	+	19.6255i	0.113781	+	0.645282i
$926$	−9.48571	+	3.45252i	−0.311720	+	0.113457i
$927$	1.85144	+	0.673868i	0.0608092	+	0.0221327i
$928$	−43.7562	+	15.9260i	−1.43637	+	0.522795i
$929$	−6.70565	+	38.0296i	−0.220005	+	1.24771i	0.652002	+	0.758217i	$0.273929\pi$
$929$	−6.70565	+	38.0296i	−0.220005	+	1.24771i	−0.872007	+	0.489494i	$0.837182\pi$
$930$	−6.20870			−0.203591
$931$	−19.8591	+	23.1650i	−0.650854	+	0.759203i
$932$	−15.6010			−0.511028
$933$	10.7444	−	60.9347i	0.351757	−	1.99491i
$934$	−20.2893	+	7.38471i	−0.663887	+	0.241635i
$935$	−7.96267	−	2.89818i	−0.260407	−	0.0947805i
$936$	−1.23712	+	0.450275i	−0.0404365	+	0.0147177i
$937$	5.52899	+	31.3565i	0.180624	+	1.02437i	0.931450	+	0.363870i	$0.118545\pi$
$937$	5.52899	+	31.3565i	0.180624	+	1.02437i	−0.750825	+	0.660501i	$0.770344\pi$
$938$	11.5532	+	1.04065i	0.377226	+	0.0339785i
$939$	14.2110	−	24.6141i	0.463757	−	0.803251i
$940$	2.47129	−	2.07366i	0.0806045	−	0.0676352i
$941$	−5.81655	−	32.9873i	−0.189614	−	1.07535i	−0.919882	−	0.392194i	$-0.871716\pi$
$941$	−5.81655	−	32.9873i	−0.189614	−	1.07535i	0.730268	−	0.683160i	$-0.239395\pi$
$942$	40.2526			1.31150
$943$	−2.69373			−0.0877200
$944$	−0.0154309	−	0.0875132i	−0.000502235	−	0.00284831i
$945$	1.94102	−	7.17036i	0.0631415	−	0.233252i
$946$	−4.89283	+	4.10557i	−0.159080	+	0.133484i
$947$	−16.0845	−	13.4965i	−0.522675	−	0.438576i	0.342888	−	0.939376i	$-0.388595\pi$
$947$	−16.0845	−	13.4965i	−0.522675	−	0.438576i	−0.865563	+	0.500800i	$0.833039\pi$
$948$	−24.4805	−	20.5416i	−0.795089	−	0.667159i
$949$	2.52625	+	4.37560i	0.0820056	+	0.142038i
$950$	−17.2050	−	0.0936970i	−0.558205	−	0.00303993i
$951$	9.51851			0.308659
$952$	−31.4265	+	8.33435i	−1.01854	+	0.270118i
$953$	9.03137	−	51.2195i	0.292555	−	1.65916i	−0.384423	−	0.923157i	$-0.625599\pi$
$953$	9.03137	−	51.2195i	0.292555	−	1.65916i	0.676977	−	0.736004i	$-0.263289\pi$
$954$	1.65835	+	9.40495i	0.0536910	+	0.304497i
$955$	−0.361026	+	2.04748i	−0.0116825	+	0.0662549i
$956$	−17.4522	+	14.6441i	−0.564444	+	0.473625i
$957$	46.6446			1.50781
$958$	6.91064	−	11.9696i	0.223273	−	0.386719i
$959$	42.3215	+	19.8672i	1.36663	+	0.641546i
$960$	6.04099	+	2.19874i	0.194972	+	0.0709641i
$961$	1.01644	+	1.76053i	0.0327884	+	0.0567912i
$962$	−1.00261	+	1.73657i	−0.0323253	+	0.0559891i
$963$	−7.00015	+	5.87383i	−0.225577	+	0.189281i
$964$	11.9787	−	4.35989i	0.385808	−	0.140423i
$965$	2.47199	−	2.07424i	0.0795761	−	0.0667723i
$966$	−5.44870	+	1.44500i	−0.175309	+	0.0464922i
$967$	8.70130	−	3.16702i	0.279815	−	0.101844i	−0.198301	−	0.980141i	$-0.563542\pi$
$967$	8.70130	−	3.16702i	0.279815	−	0.101844i	0.478116	+	0.878297i	$0.341320\pi$
$968$	−3.78019	+	6.54748i	−0.121500	+	0.210444i
$969$	−28.8320	+	23.9266i	−0.926217	+	0.768632i
$970$	−1.70759	−	2.95764i	−0.0548275	−	0.0949639i
$971$	−1.75389	+	9.94678i	−0.0562849	+	0.319207i	−0.999931	−	0.0117488i	$-0.996260\pi$
$971$	−1.75389	+	9.94678i	−0.0562849	+	0.319207i	0.943646	+	0.330956i	$0.107371\pi$
$972$	1.93403	−	10.9684i	0.0620340	−	0.351812i
$973$	−4.92526	−	58.0098i	−0.157896	−	1.85971i
$974$	12.0230	+	10.0885i	0.385242	+	0.323256i
$975$	−4.43641	−	1.61472i	−0.142079	−	0.0517125i
$976$	0.206541	−	0.357740i	0.00661123	−	0.0114510i
$977$	−5.62028			−0.179809			−0.0899043	−	0.995950i	$-0.528656\pi$
$977$	−5.62028			−0.179809			−0.0899043	+	0.995950i	$0.528656\pi$
$978$	−15.2957	+	12.8346i	−0.489103	+	0.410406i
$979$	43.4329	+	15.8083i	1.38812	+	0.505235i
$980$	5.78338	+	1.05039i	0.184743	+	0.0335536i
$981$	7.59208	+	13.1499i	0.242396	+	0.419843i
$982$	−28.2043	−	10.2655i	−0.900035	−	0.327586i
$983$	−0.421506	+	2.39048i	−0.0134439	+	0.0762444i	−0.990792	−	0.135396i	$-0.956769\pi$
$983$	−0.421506	+	2.39048i	−0.0134439	+	0.0762444i	0.977348	+	0.211640i	$0.0678805\pi$
$984$	−11.3007	−	4.11314i	−0.360255	−	0.131122i
$985$	2.18857	+	1.83643i	0.0697337	+	0.0585136i
$986$	29.1843	−	10.6222i	0.929416	−	0.338280i
$987$	−11.5360	+	16.3854i	−0.367194	+	0.521554i
$988$	2.18180	+	1.85109i	0.0694123	+	0.0588910i
$989$	1.58728	−	2.74926i	0.0504727	−	0.0874213i
$990$	−1.14624	−	0.961806i	−0.0364298	−	0.0305682i
$991$	−5.41078	+	1.96936i	−0.171879	+	0.0625589i	−0.426526	−	0.904475i	$-0.640263\pi$
$991$	−5.41078	+	1.96936i	−0.171879	+	0.0625589i	0.254647	+	0.967034i	$0.418041\pi$
$992$	5.30473	+	30.0846i	0.168425	+	0.955188i
$993$	−2.65384	−	2.22683i	−0.0842170	−	0.0706664i
$994$	0.737686	−	0.513718i	0.0233980	−	0.0162941i
$995$	2.59143	+	4.48849i	0.0821539	+	0.142295i
$996$	−3.59689	−	6.22999i	−0.113972	−	0.197405i
$997$	−0.919209	−	5.21310i	−0.0291117	−	0.165100i	0.966786	−	0.255587i	$-0.0822688\pi$
$997$	−0.919209	−	5.21310i	−0.0291117	−	0.165100i	−0.995898	+	0.0904868i	$0.971158\pi$
$998$	1.35945	+	7.70984i	0.0430327	+	0.244051i
$999$	−9.13227	−	15.8176i	−0.288932	−	0.500445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	133.2.w.a.100.8	yes	66
7.2	even	3		931.2.w.f.442.4		66
7.3	odd	6		931.2.v.h.214.8		66
7.4	even	3		133.2.u.a.81.8	yes	66
7.5	odd	6		931.2.w.e.442.4		66
7.6	odd	2		931.2.x.h.765.8		66
19.4	even	9		133.2.u.a.23.8	✓	66
133.4	even	9	inner	133.2.w.a.4.8	yes	66
133.23	even	9		931.2.w.f.99.4		66
133.61	odd	18		931.2.w.e.99.4		66
133.80	odd	18		931.2.x.h.802.8		66
133.118	odd	18		931.2.v.h.422.8		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.u.a.23.8	✓	66	19.4	even	9
133.2.u.a.81.8	yes	66	7.4	even	3
133.2.w.a.4.8	yes	66	133.4	even	9	inner
133.2.w.a.100.8	yes	66	1.1	even	1	trivial
931.2.v.h.214.8		66	7.3	odd	6
931.2.v.h.422.8		66	133.118	odd	18
931.2.w.e.99.4		66	133.61	odd	18
931.2.w.e.442.4		66	7.5	odd	6
931.2.w.f.99.4		66	133.23	even	9
931.2.w.f.442.4		66	7.2	even	3
931.2.x.h.765.8		66	7.6	odd	2
931.2.x.h.802.8		66	133.80	odd	18

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:	\( N \)	\(=\)	\( 133 = 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	133.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.150778 - 0.855105i) q^{2} +(-1.85257 + 0.674280i) q^{3} +(1.17091 + 0.426178i) q^{4} +(0.633253 - 0.230485i) q^{5} +(0.297254 + 1.68581i) q^{6} +(2.63508 + 0.237354i) q^{7} +(1.40927 - 2.44093i) q^{8} +(0.679226 - 0.569939i) q^{9} +O(q^{10})\)	\(q+(0.150778 - 0.855105i) q^{2} +(-1.85257 + 0.674280i) q^{3} +(1.17091 + 0.426178i) q^{4} +(0.633253 - 0.230485i) q^{5} +(0.297254 + 1.68581i) q^{6} +(2.63508 + 0.237354i) q^{7} +(1.40927 - 2.44093i) q^{8} +(0.679226 - 0.569939i) q^{9} +(-0.101608 - 0.576250i) q^{10} +2.88403 q^{11} -2.45656 q^{12} +(-0.0914767 - 0.518790i) q^{13} +(0.600276 - 2.21749i) q^{14} +(-1.01773 + 0.853980i) q^{15} +(0.0343114 + 0.0287906i) q^{16} +(-3.33992 - 2.80252i) q^{17} +(-0.384945 - 0.666744i) q^{18} +(-2.19997 + 3.76299i) q^{19} +0.839713 q^{20} +(-5.04172 + 1.33707i) q^{21} +(0.434849 - 2.46615i) q^{22} +(0.216131 + 1.22574i) q^{23} +(-0.964903 + 5.47224i) q^{24} +(-3.48234 + 2.92203i) q^{25} -0.457413 q^{26} +(2.08318 - 3.60817i) q^{27} +(2.98430 + 1.40094i) q^{28} +(-7.70901 - 2.80585i) q^{29} +(0.576791 + 0.999031i) q^{30} +(-2.69106 + 4.66104i) q^{31} +(4.34805 - 3.64845i) q^{32} +(-5.34287 + 1.94464i) q^{33} +(-2.90004 + 2.43342i) q^{34} +(1.72338 - 0.457043i) q^{35} +(1.03821 - 0.377878i) q^{36} +(2.19191 - 3.79650i) q^{37} +(2.88605 + 2.44859i) q^{38} +(0.519277 + 0.899414i) q^{39} +(0.329827 - 1.87054i) q^{40} +(-0.375818 + 2.13137i) q^{41} +(0.383154 + 4.51280i) q^{42} +(-1.95385 - 1.63948i) q^{43} +(3.37695 + 1.22911i) q^{44} +(0.298760 - 0.517467i) q^{45} +1.08072 q^{46} +(2.94301 - 2.46948i) q^{47} +(-0.0829771 - 0.0302012i) q^{48} +(6.88733 + 1.25090i) q^{49} +(1.97358 + 3.41834i) q^{50} +(8.07711 + 2.93983i) q^{51} +(0.113986 - 0.646444i) q^{52} +(-11.6563 - 4.24256i) q^{53} +(-2.77127 - 2.32537i) q^{54} +(1.82632 - 0.664727i) q^{55} +(4.29291 - 6.09756i) q^{56} +(1.53829 - 8.45460i) q^{57} +(-3.56165 + 6.16896i) q^{58} +(-1.51982 - 1.27528i) q^{59} +(-1.55563 + 0.566202i) q^{60} +(-1.60149 - 9.08249i) q^{61} +(3.57993 + 3.00392i) q^{62} +(1.92510 - 1.34062i) q^{63} +(-2.41943 - 4.19057i) q^{64} +(-0.177501 - 0.307442i) q^{65} +(0.857288 + 4.86192i) q^{66} +(0.876820 + 4.97269i) q^{67} +(-2.71638 - 4.70491i) q^{68} +(-1.22689 - 2.12503i) q^{69} +(-0.130971 - 1.54258i) q^{70} +(0.299755 + 0.251524i) q^{71} +(-0.433966 - 2.46114i) q^{72} +(-9.01264 + 3.28033i) q^{73} +(-2.91591 - 2.44674i) q^{74} +(4.48100 - 7.76133i) q^{75} +(-4.17969 + 3.46856i) q^{76} +(7.59966 + 0.684537i) q^{77} +(0.847389 - 0.308424i) q^{78} +(9.96534 + 8.36191i) q^{79} +(0.0283636 + 0.0103235i) q^{80} +(-1.88822 + 10.7086i) q^{81} +(1.76588 + 0.642729i) q^{82} +(1.46419 + 2.53606i) q^{83} +(-6.47325 - 0.583075i) q^{84} +(-2.76095 - 1.00490i) q^{85} +(-1.69652 + 1.42355i) q^{86} +16.1734 q^{87} +(4.06438 - 7.03972i) q^{88} +(15.0598 + 5.48132i) q^{89} +(-0.397442 - 0.333494i) q^{90} +(-0.117912 - 1.38877i) q^{91} +(-0.269312 + 1.52735i) q^{92} +(1.84252 - 10.4494i) q^{93} +(-1.66792 - 2.88893i) q^{94} +(-0.525827 + 2.88999i) q^{95} +(-5.59499 + 9.69081i) q^{96} +(5.48454 - 1.99621i) q^{97} +(2.10811 - 5.70078i) q^{98} +(1.95891 - 1.64372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 66 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 - 9 * q^7 - 6 * q^8 - 3 * q^9	\( 66 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 12 q^{6} - 9 q^{7} - 6 q^{8} - 3 q^{9} + 15 q^{10} - 54 q^{12} - 12 q^{13} - 3 q^{14} - 9 q^{15} + 9 q^{16} - 18 q^{18} + 6 q^{19} + 18 q^{21} - 12 q^{22} - 3 q^{23} - 36 q^{24} - 3 q^{25} - 18 q^{26} + 30 q^{27} + 45 q^{28} + 6 q^{29} + 3 q^{30} + 39 q^{31} + 6 q^{32} - 39 q^{33} - 24 q^{34} - 27 q^{35} + 51 q^{36} + 6 q^{37} - 72 q^{38} - 24 q^{39} + 57 q^{40} - 30 q^{41} + 87 q^{42} + 12 q^{43} - 48 q^{44} - 3 q^{45} - 12 q^{46} - 21 q^{47} - 21 q^{48} - 21 q^{49} + 27 q^{50} - 3 q^{51} - 9 q^{52} - 9 q^{53} + 93 q^{54} - 27 q^{55} + 12 q^{56} + 6 q^{57} - 42 q^{58} + 6 q^{59} + 48 q^{60} + 18 q^{61} - 27 q^{62} - 87 q^{63} + 24 q^{64} + 21 q^{65} + 15 q^{66} - 18 q^{67} - 15 q^{68} + 42 q^{69} + 15 q^{70} + 30 q^{71} + 48 q^{72} - 78 q^{73} + 21 q^{74} + 57 q^{75} + 42 q^{76} + 18 q^{77} - 51 q^{78} - 81 q^{79} - 3 q^{80} + 48 q^{81} + 117 q^{82} - 18 q^{83} - 51 q^{84} - 24 q^{85} - 66 q^{86} + 18 q^{87} - 45 q^{88} - 3 q^{89} - 48 q^{90} + 78 q^{91} + 12 q^{92} + 33 q^{93} + 72 q^{94} + 93 q^{95} + 69 q^{96} + 3 q^{97} + 6 q^{98} - 156 q^{99}+O(q^{100}) \) 66 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 12 * q^6 - 9 * q^7 - 6 * q^8 - 3 * q^9 + 15 * q^10 - 54 * q^12 - 12 * q^13 - 3 * q^14 - 9 * q^15 + 9 * q^16 - 18 * q^18 + 6 * q^19 + 18 * q^21 - 12 * q^22 - 3 * q^23 - 36 * q^24 - 3 * q^25 - 18 * q^26 + 30 * q^27 + 45 * q^28 + 6 * q^29 + 3 * q^30 + 39 * q^31 + 6 * q^32 - 39 * q^33 - 24 * q^34 - 27 * q^35 + 51 * q^36 + 6 * q^37 - 72 * q^38 - 24 * q^39 + 57 * q^40 - 30 * q^41 + 87 * q^42 + 12 * q^43 - 48 * q^44 - 3 * q^45 - 12 * q^46 - 21 * q^47 - 21 * q^48 - 21 * q^49 + 27 * q^50 - 3 * q^51 - 9 * q^52 - 9 * q^53 + 93 * q^54 - 27 * q^55 + 12 * q^56 + 6 * q^57 - 42 * q^58 + 6 * q^59 + 48 * q^60 + 18 * q^61 - 27 * q^62 - 87 * q^63 + 24 * q^64 + 21 * q^65 + 15 * q^66 - 18 * q^67 - 15 * q^68 + 42 * q^69 + 15 * q^70 + 30 * q^71 + 48 * q^72 - 78 * q^73 + 21 * q^74 + 57 * q^75 + 42 * q^76 + 18 * q^77 - 51 * q^78 - 81 * q^79 - 3 * q^80 + 48 * q^81 + 117 * q^82 - 18 * q^83 - 51 * q^84 - 24 * q^85 - 66 * q^86 + 18 * q^87 - 45 * q^88 - 3 * q^89 - 48 * q^90 + 78 * q^91 + 12 * q^92 + 33 * q^93 + 72 * q^94 + 93 * q^95 + 69 * q^96 + 3 * q^97 + 6 * q^98 - 156 * q^99

Introduction

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