LMFDB - Embedded newform 418.2.v.b.13.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	418.13
Dual form			418.2.v.b.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.374607 - 0.927184i) q^{2} +(-0.873028 - 3.04461i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.51211 - 1.33571i) q^{5} +(-2.49587 + 1.94999i) q^{6} +(-1.97806 - 4.44279i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-5.96333 + 3.72630i) q^{9} +O(q^{10})$	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.873028 - 3.04461i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.51211 - 1.33571i) q^{5} +(-2.49587 + 1.94999i) q^{6} +(-1.97806 - 4.44279i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-5.96333 + 3.72630i) q^{9} +(-2.17951 - 1.82882i) q^{10} +(2.97950 + 1.45690i) q^{11} +(2.74297 + 1.58365i) q^{12} +(-0.0313349 - 0.897314i) q^{13} +(-3.37829 + 3.49832i) q^{14} +(-6.25987 - 6.48229i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(1.55186 - 2.48350i) q^{17} +(5.68887 + 4.13320i) q^{18} +(4.33137 - 0.489118i) q^{19} +(-0.879197 + 2.70589i) q^{20} +(-11.7997 + 9.90108i) q^{21} +(0.234671 - 3.30831i) q^{22} +(-0.313757 + 1.77940i) q^{23} +(0.440804 - 3.13648i) q^{24} +(1.73061 - 2.56574i) q^{25} +(-0.820236 + 0.365193i) q^{26} +(9.48998 + 8.54482i) q^{27} +(4.50911 + 1.82180i) q^{28} +(1.94266 + 7.79159i) q^{29} +(-3.66528 + 8.23236i) q^{30} +(1.65824 - 1.49309i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(1.83450 - 10.3433i) q^{33} +(-2.88400 - 0.508527i) q^{34} +(-10.9034 - 8.51866i) q^{35} +(1.70115 - 6.82295i) q^{36} +(-5.15392 + 7.09376i) q^{37} +(-2.07606 - 3.83275i) q^{38} +(-2.70461 + 0.878782i) q^{39} +(2.83821 - 0.198467i) q^{40} +(0.471148 - 0.135099i) q^{41} +(13.6004 + 7.23143i) q^{42} +(5.63289 - 0.993231i) q^{43} +(-3.15532 + 1.02173i) q^{44} +(-10.0033 + 17.3262i) q^{45} +(1.76737 - 0.375666i) q^{46} +(4.38285 + 0.306478i) q^{47} +(-3.07322 + 0.766241i) q^{48} +(-11.1417 + 12.3741i) q^{49} +(-3.02721 - 0.643453i) q^{50} +(-8.91611 - 2.55665i) q^{51} +(0.645867 + 0.623706i) q^{52} +(-0.808299 + 1.52019i) q^{53} +(4.36761 - 11.9999i) q^{54} +(9.43085 - 0.319873i) q^{55} -4.86323i q^{56} +(-5.27058 - 12.7603i) q^{57} +(6.49651 - 4.71999i) q^{58} +(0.0838253 + 1.19876i) q^{59} +(9.00595 + 0.314495i) q^{60} +(-1.01086 - 7.19265i) q^{61} +(-2.00555 - 0.978174i) q^{62} +(28.3509 + 19.1230i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-1.27727 - 2.21230i) q^{65} +(-10.2774 + 2.17377i) q^{66} +(-2.02733 + 2.41607i) q^{67} +(0.608867 + 2.86449i) q^{68} +(5.69150 - 0.598201i) q^{69} +(-3.81388 + 13.3006i) q^{70} +(-7.60405 - 14.3011i) q^{71} +(-6.96339 + 0.978641i) q^{72} +(5.96418 - 4.02289i) q^{73} +(8.50792 + 2.12126i) q^{74} +(-9.32254 - 3.02908i) q^{75} +(-2.77596 + 3.36066i) q^{76} +(0.579062 - 16.1191i) q^{77} +(1.82796 + 2.17848i) q^{78} +(-2.16962 + 2.77699i) q^{79} +(-1.24723 - 2.55720i) q^{80} +(8.48296 - 17.3927i) q^{81} +(-0.301757 - 0.386231i) q^{82} +(3.71177 - 17.4625i) q^{83} +(1.61009 - 15.3190i) q^{84} +(0.581209 - 8.31167i) q^{85} +(-3.03103 - 4.85066i) q^{86} +(22.0264 - 12.7169i) q^{87} +(2.12934 + 2.54282i) q^{88} +(-0.737370 - 2.02591i) q^{89} +(19.8118 + 2.78437i) q^{90} +(-3.92459 + 1.91415i) q^{91} +(-1.01038 - 1.49795i) q^{92} +(-5.99356 - 3.74519i) q^{93} +(-1.35768 - 4.17851i) q^{94} +(10.2276 - 7.01419i) q^{95} +(1.86170 + 2.56240i) q^{96} +(-1.26703 + 0.511914i) q^{97} +(15.6469 + 5.69499i) q^{98} +(-23.1966 + 2.41457i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$2$	−0.374607	−	0.927184i	−0.264887	−	0.655618i
$3$	−0.873028	−	3.04461i	−0.504043	−	1.75781i	−0.641320	−	0.767274i	$-0.721613\pi$
$3$	−0.873028	−	3.04461i	−0.504043	−	1.75781i	0.137277	−	0.990533i	$-0.456165\pi$
$4$	−0.719340	+	0.694658i	−0.359670	+	0.347329i
$5$	2.51211	−	1.33571i	1.12345	−	0.597349i	0.199514	−	0.979895i	$-0.436064\pi$
$5$	2.51211	−	1.33571i	1.12345	−	0.597349i	0.923937	+	0.382546i	$0.124953\pi$
$6$	−2.49587	+	1.94999i	−1.01894	+	0.796079i
$7$	−1.97806	−	4.44279i	−0.747635	−	1.67922i	−0.733851	−	0.679310i	$-0.762279\pi$
$7$	−1.97806	−	4.44279i	−0.747635	−	1.67922i	−0.0137833	−	0.999905i	$-0.504388\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	−5.96333	+	3.72630i	−1.98778	+	1.24210i
$10$	−2.17951	−	1.82882i	−0.689220	−	0.578324i
$11$	2.97950	+	1.45690i	0.898354	+	0.439271i
$11$	2.97950	+	1.45690i	0.898354	+	0.439271i
$12$	2.74297	+	1.58365i	0.791826	+	0.457161i
$13$	−0.0313349	−	0.897314i	−0.00869073	−	0.248870i	−0.995959	−	0.0898071i	$-0.971375\pi$
$13$	−0.0313349	−	0.897314i	−0.00869073	−	0.248870i	0.987268	−	0.159063i	$-0.0508473\pi$
$14$	−3.37829	+	3.49832i	−0.902885	+	0.934965i
$15$	−6.25987	−	6.48229i	−1.61629	−	1.67372i
$16$	0.0348995	−	0.999391i	0.00872487	−	0.249848i
$17$	1.55186	−	2.48350i	0.376382	−	0.602337i	−0.604578	−	0.796546i	$-0.706658\pi$
$17$	1.55186	−	2.48350i	0.376382	−	0.602337i	0.980960	+	0.194209i	$0.0622139\pi$
$18$	5.68887	+	4.13320i	1.34088	+	0.974205i
$19$	4.33137	−	0.489118i	0.993684	−	0.112211i
$19$	4.33137	−	0.489118i	0.993684	−	0.112211i
$20$	−0.879197	+	2.70589i	−0.196595	+	0.605056i
$21$	−11.7997	+	9.90108i	−2.57489	+	2.16059i
$22$	0.234671	−	3.30831i	0.0500320	−	0.705335i
$23$	−0.313757	+	1.77940i	−0.0654228	+	0.371031i	0.934465	+	0.356055i	$0.115878\pi$
$23$	−0.313757	+	1.77940i	−0.0654228	+	0.371031i	−0.999888	+	0.0149761i	$0.995233\pi$
$24$	0.440804	−	3.13648i	0.0899787	−	0.640232i
$25$	1.73061	−	2.56574i	0.346122	−	0.513147i
$26$	−0.820236	+	0.365193i	−0.160862	+	0.0716202i
$27$	9.48998	+	8.54482i	1.82635	+	1.64445i
$28$	4.50911	+	1.82180i	0.852142	+	0.344288i
$29$	1.94266	+	7.79159i	0.360743	+	1.44686i	0.826994	+	0.562210i	$0.190049\pi$
$29$	1.94266	+	7.79159i	0.360743	+	1.44686i	−0.466251	+	0.884652i	$0.654396\pi$
$30$	−3.66528	+	8.23236i	−0.669186	+	1.50302i
$31$	1.65824	−	1.49309i	0.297829	−	0.268166i	−0.506644	−	0.862155i	$-0.669114\pi$
$31$	1.65824	−	1.49309i	0.297829	−	0.268166i	0.804473	+	0.593989i	$0.202448\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	1.83450	−	10.3433i	0.319345	−	1.80054i
$34$	−2.88400	−	0.508527i	−0.494602	−	0.0872116i
$35$	−10.9034	−	8.51866i	−1.84301	−	1.43992i
$36$	1.70115	−	6.82295i	0.283525	−	1.13716i
$37$	−5.15392	+	7.09376i	−0.847299	+	1.16621i	0.137152	+	0.990550i	$0.456205\pi$
$37$	−5.15392	+	7.09376i	−0.847299	+	1.16621i	−0.984451	+	0.175658i	$0.943795\pi$
$38$	−2.07606	−	3.83275i	−0.336782	−	0.621754i
$39$	−2.70461	+	0.878782i	−0.433085	+	0.140718i
$40$	2.83821	−	0.198467i	0.448761	−	0.0313804i
$41$	0.471148	−	0.135099i	0.0735809	−	0.0210990i	−0.238645	−	0.971107i	$-0.576703\pi$
$41$	0.471148	−	0.135099i	0.0735809	−	0.0210990i	0.312226	+	0.950008i	$0.398925\pi$
$42$	13.6004	+	7.23143i	2.09858	+	1.11583i
$43$	5.63289	−	0.993231i	0.859008	−	0.151466i	0.273241	−	0.961946i	$-0.411904\pi$
$43$	5.63289	−	0.993231i	0.859008	−	0.151466i	0.585767	+	0.810479i	$0.300793\pi$
$44$	−3.15532	+	1.02173i	−0.475683	+	0.154032i
$45$	−10.0033	+	17.3262i	−1.49120	+	2.58283i
$46$	1.76737	−	0.375666i	0.260584	−	0.0553889i
$47$	4.38285	+	0.306478i	0.639304	+	0.0447045i	0.385730	−	0.922612i	$-0.373950\pi$
$47$	4.38285	+	0.306478i	0.639304	+	0.0447045i	0.253574	+	0.967316i	$0.418394\pi$
$48$	−3.07322	+	0.766241i	−0.443582	+	0.110597i
$49$	−11.1417	+	12.3741i	−1.59167	+	1.76773i
$50$	−3.02721	−	0.643453i	−0.428112	−	0.0909980i
$51$	−8.91611	−	2.55665i	−1.24850	−	0.358003i
$52$	0.645867	+	0.623706i	0.0895656	+	0.0864925i
$53$	−0.808299	+	1.52019i	−0.111028	+	0.208814i	−0.932267	−	0.361771i	$-0.882172\pi$
$53$	−0.808299	+	1.52019i	−0.111028	+	0.208814i	0.821239	+	0.570585i	$0.193283\pi$
$54$	4.36761	−	11.9999i	0.594356	−	1.63298i
$55$	9.43085	−	0.319873i	1.27166	−	0.0431316i
$56$		−	4.86323i		−	0.649877i
$57$	−5.27058	−	12.7603i	−0.698105	−	1.69015i
$58$	6.49651	−	4.71999i	0.853033	−	0.619765i
$59$	0.0838253	+	1.19876i	0.0109131	+	0.156065i	0.999964	+	0.00848977i	$0.00270241\pi$
$59$	0.0838253	+	1.19876i	0.0109131	+	0.156065i	−0.989051	+	0.147575i	$0.952853\pi$
$60$	9.00595	+	0.314495i	1.16266	+	0.0406011i
$61$	−1.01086	−	7.19265i	−0.129427	−	0.920924i	−0.941415	−	0.337250i	$-0.890503\pi$
$61$	−1.01086	−	7.19265i	−0.129427	−	0.920924i	0.811988	−	0.583674i	$-0.198386\pi$
$62$	−2.00555	−	0.978174i	−0.254706	−	0.124228i
$63$	28.3509	+	19.1230i	3.57188	+	2.40927i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	−1.27727	−	2.21230i	−0.158426	−	0.274402i
$66$	−10.2774	+	2.17377i	−1.26506	+	0.267572i
$67$	−2.02733	+	2.41607i	−0.247677	+	0.295170i	−0.875532	−	0.483160i	$-0.839489\pi$
$67$	−2.02733	+	2.41607i	−0.247677	+	0.295170i	0.627855	+	0.778331i	$0.283933\pi$
$68$	0.608867	+	2.86449i	0.0738360	+	0.347371i
$69$	5.69150	−	0.598201i	0.685176	−	0.0720149i
$70$	−3.81388	+	13.3006i	−0.455846	+	1.58972i
$71$	−7.60405	−	14.3011i	−0.902435	−	1.69723i	−0.695033	−	0.718978i	$-0.744610\pi$
$71$	−7.60405	−	14.3011i	−0.902435	−	1.69723i	−0.207402	−	0.978256i	$-0.566501\pi$
$72$	−6.96339	+	0.978641i	−0.820644	+	0.115334i
$73$	5.96418	−	4.02289i	0.698055	−	0.470844i	−0.158194	−	0.987408i	$-0.550567\pi$
$73$	5.96418	−	4.02289i	0.698055	−	0.470844i	0.856248	+	0.516564i	$0.172789\pi$
$74$	8.50792	+	2.12126i	0.989025	+	0.246592i
$75$	−9.32254	−	3.02908i	−1.07647	−	0.349768i
$76$	−2.77596	+	3.36066i	−0.318424	+	0.385495i
$77$	0.579062	−	16.1191i	0.0659902	−	1.83694i
$78$	1.82796	+	2.17848i	0.206976	+	0.246664i
$79$	−2.16962	+	2.77699i	−0.244101	+	0.312435i	−0.894422	−	0.447225i	$-0.852412\pi$
$79$	−2.16962	+	2.77699i	−0.244101	+	0.312435i	0.650320	+	0.759660i	$0.274635\pi$
$80$	−1.24723	−	2.55720i	−0.139444	−	0.285903i
$81$	8.48296	−	17.3927i	0.942552	−	1.93252i
$82$	−0.301757	−	0.386231i	−0.0333235	−	0.0426521i
$83$	3.71177	−	17.4625i	0.407419	−	1.91676i	0.00804976	−	0.999968i	$-0.497438\pi$
$83$	3.71177	−	17.4625i	0.407419	−	1.91676i	0.399370	−	0.916790i	$-0.369229\pi$
$84$	1.61009	−	15.3190i	0.175675	−	1.67144i
$85$	0.581209	−	8.31167i	0.0630409	−	0.901528i
$86$	−3.03103	−	4.85066i	−0.326844	−	0.523060i
$87$	22.0264	−	12.7169i	2.36147	−	1.36340i
$88$	2.12934	+	2.54282i	0.226988	+	0.271065i
$89$	−0.737370	−	2.02591i	−0.0781611	−	0.214746i	0.894458	−	0.447153i	$-0.147562\pi$
$89$	−0.737370	−	2.02591i	−0.0781611	−	0.214746i	−0.972619	+	0.232407i	$0.925340\pi$
$90$	19.8118	+	2.78437i	2.08835	+	0.293499i
$91$	−3.92459	+	1.91415i	−0.411409	+	0.200657i
$92$	−1.01038	−	1.49795i	−0.105339	−	0.156172i
$93$	−5.99356	−	3.74519i	−0.621503	−	0.388358i
$94$	−1.35768	−	4.17851i	−0.140034	−	0.430981i
$95$	10.2276	−	7.01419i	1.04933	−	0.719641i
$96$	1.86170	+	2.56240i	0.190009	+	0.261524i
$97$	−1.26703	+	0.511914i	−0.128647	+	0.0519770i	−0.438028	−	0.898961i	$-0.644323\pi$
$97$	−1.26703	+	0.511914i	−0.128647	+	0.0519770i	0.309380	+	0.950938i	$0.399878\pi$
$98$	15.6469	+	5.69499i	1.58057	+	0.575281i
$99$	−23.1966	+	2.41457i	−2.33135	+	0.242673i
$100$	0.537413	+	3.04782i	0.0537413	+	0.304782i
$101$	8.40738	−	0.293592i	0.836565	−	0.0292135i	0.386587	−	0.922253i	$-0.373654\pi$
$101$	8.40738	−	0.293592i	0.836565	−	0.0292135i	0.449978	+	0.893039i	$0.351432\pi$
$102$	0.969545	+	9.22461i	0.0959993	+	0.913372i
$103$	−15.5968	−	1.63929i	−1.53680	−	0.161524i	−0.702040	−	0.712138i	$-0.747727\pi$
$103$	−15.5968	−	1.63929i	−1.53680	−	0.161524i	−0.834760	+	0.550614i	$0.814394\pi$
$104$	0.336344	−	0.832482i	0.0329813	−	0.0816316i
$105$	−16.4170	+	40.6336i	−1.60214	+	3.96543i
$106$	1.71229	+	0.179969i	0.166312	+	0.0174801i
$107$	−0.264587	−	2.51738i	−0.0255786	−	0.243364i	−0.999839	−	0.0179391i	$-0.994290\pi$
$107$	−0.264587	−	2.51738i	−0.0255786	−	0.243364i	0.974260	−	0.225425i	$-0.0723772\pi$
$108$	−12.7622	+	0.445668i	−1.22805	+	0.0428844i
$109$	0.713783	+	4.04806i	0.0683680	+	0.387734i	0.999721	+	0.0236169i	$0.00751819\pi$
$109$	0.713783	+	4.04806i	0.0683680	+	0.387734i	−0.931353	+	0.364117i	$0.881371\pi$
$110$	−3.82944	−	8.62430i	−0.365123	−	0.822295i
$111$	26.0973	+	9.49863i	2.47704	+	0.901570i
$112$	−4.50911	+	1.82180i	−0.426071	+	0.172144i
$113$	2.16063	+	2.97385i	0.203255	+	0.279756i	0.898460	−	0.439055i	$-0.144687\pi$
$113$	2.16063	+	2.97385i	0.203255	+	0.279756i	−0.695205	+	0.718811i	$0.744687\pi$
$114$	−9.85677	+	9.66689i	−0.923171	+	0.905388i
$115$	1.58858	+	4.88914i	0.148136	+	0.455915i
$116$	−6.80993	−	4.25532i	−0.632286	−	0.395096i
$117$	3.53052	+	5.23421i	0.326397	+	0.483903i
$118$	1.08007	−	0.526784i	0.0994283	−	0.0484944i
$119$	−14.1033	−	1.98209i	−1.29285	−	0.181698i
$120$	−3.08209	−	8.46798i	−0.281355	−	0.773017i
$121$	6.75489	+	8.68167i	0.614081	+	0.789243i
$122$	−6.29023	+	3.63167i	−0.569491	+	0.328796i
$123$	−0.822650	−	1.31652i	−0.0741759	−	0.118706i
$124$	−0.155653	+	2.22595i	−0.0139781	+	0.199896i
$125$	−0.566592	+	5.39077i	−0.0506776	+	0.482165i
$126$	7.11004	−	33.4501i	0.633413	−	2.97997i
$127$	10.1794	+	13.0290i	0.903273	+	1.15614i	0.987172	+	0.159662i	$0.0510405\pi$
$127$	10.1794	+	13.0290i	0.903273	+	1.15614i	−0.0838987	+	0.996474i	$0.526737\pi$
$128$	0.438371	−	0.898794i	0.0387469	−	0.0794429i
$129$	−7.94167	−	16.2828i	−0.699225	−	1.43362i
$130$	−1.57273	+	2.01301i	−0.137938	+	0.176552i
$131$	−9.82203	−	11.7054i	−0.858155	−	1.02271i	−0.999464	−	0.0327437i	$-0.989575\pi$
$131$	−9.82203	−	11.7054i	−0.858155	−	1.02271i	0.141309	−	0.989966i	$-0.454869\pi$
$132$	5.86546	+	8.71473i	0.510523	+	0.758520i
$133$	−10.7407	−	18.2758i	−0.931340	−	1.58472i
$134$	2.99959	+	0.974627i	0.259125	+	0.0841950i
$135$	35.2533	+	8.78964i	3.03412	+	0.756492i
$136$	2.42783	−	1.63759i	0.208184	−	0.140422i
$137$	−4.40937	+	0.619696i	−0.376718	+	0.0529442i	−0.324991	−	0.945717i	$-0.605361\pi$
$137$	−4.40937	+	0.619696i	−0.376718	+	0.0529442i	−0.0517266	+	0.998661i	$0.516472\pi$
$138$	−2.68672	−	5.05298i	−0.228708	−	0.430138i
$139$	−2.48487	+	8.66576i	−0.210764	+	0.735020i	0.782853	+	0.622207i	$0.213764\pi$
$139$	−2.48487	+	8.66576i	−0.210764	+	0.735020i	−0.993616	+	0.112813i	$0.964014\pi$
$140$	13.7608	−	1.44632i	1.16300	−	0.122236i
$141$	−2.89324	−	13.6116i	−0.243655	−	1.14631i
$142$	−10.4113	+	12.4077i	−0.873694	+	1.04123i
$143$	1.21393	−	2.71920i	0.101514	−	0.227391i
$144$	3.51591	+	6.08974i	0.292993	+	0.507478i
$145$	15.2875	+	16.9785i	1.26956	+	1.40999i
$146$	−5.96418	−	4.02289i	−0.493599	−	0.332937i
$147$	47.4015	+	23.1192i	3.90961	+	1.90684i
$148$	−1.22032	−	8.68304i	−0.100310	−	0.713742i
$149$	−3.64821	−	0.127398i	−0.298873	−	0.0104369i	−0.114929	−	0.993374i	$-0.536664\pi$
$149$	−3.64821	−	0.127398i	−0.298873	−	0.0104369i	−0.183944	+	0.982937i	$0.558886\pi$
$150$	0.683774	+	9.77842i	0.0558299	+	0.798405i
$151$	−4.66514	+	3.38942i	−0.379643	+	0.275827i	−0.761198	−	0.648519i	$-0.775389\pi$
$151$	−4.66514	+	3.38942i	−0.379643	+	0.275827i	0.381555	+	0.924346i	$0.375389\pi$
$152$	4.15585	+	1.31490i	0.337084	+	0.106652i
$153$			20.5926i			1.66482i
$154$	−15.1623	+	5.50143i	−1.22181	+	0.443318i
$155$	2.17135	−	5.96574i	0.174407	−	0.479180i
$156$	1.33508	−	2.51093i	0.106892	−	0.201035i
$157$	14.2214	+	13.7334i	1.13499	+	1.09605i	0.994368	+	0.105982i	$0.0337987\pi$
$157$	14.2214	+	13.7334i	1.13499	+	1.09605i	0.140621	+	0.990064i	$0.455090\pi$
$158$	3.38753	+	0.971359i	0.269497	+	0.0772771i
$159$	5.33405	+	1.13379i	0.423018	+	0.0899152i
$160$	−1.90377	+	2.11435i	−0.150506	+	0.167154i
$161$	8.52613	−	2.12580i	0.671953	−	0.167537i
$162$	−19.3040	−	1.34986i	−1.51666	−	0.106055i
$163$	−11.2716	+	2.39585i	−0.882859	+	0.187658i	−0.626965	−	0.779047i	$-0.715703\pi$
$163$	−11.2716	+	2.39585i	−0.882859	+	0.187658i	−0.255894	+	0.966705i	$0.582370\pi$
$164$	−0.245067	+	0.424469i	−0.0191365	+	0.0331455i
$165$	−9.20728	−	28.4340i	−0.716786	−	2.21358i
$166$	−17.5814	+	3.10007i	−1.36458	+	0.240612i
$167$	−9.63842	−	5.12484i	−0.745843	−	0.396572i	0.0526208	−	0.998615i	$-0.483243\pi$
$167$	−9.63842	−	5.12484i	−0.745843	−	0.396572i	−0.798464	+	0.602043i	$0.794354\pi$
$168$	−14.8067	+	4.24574i	−1.14236	+	0.327566i
$169$	12.1641	−	0.850600i	0.935703	−	0.0654307i
$170$	−7.92417	+	2.57472i	−0.607756	+	0.197472i
$171$	−24.0068	+	19.0568i	−1.83584	+	1.45731i
$172$	−3.36201	+	4.62741i	−0.256351	+	0.352836i
$173$	1.22264	−	4.90372i	0.0929553	−	0.372823i	−0.905743	−	0.423827i	$-0.860686\pi$
$173$	1.22264	−	4.90372i	0.0929553	−	0.372823i	0.998698	+	0.0510037i	$0.0162420\pi$
$174$	−20.0422	−	15.6586i	−1.51939	−	1.18708i
$175$	−14.8223	−	2.61356i	−1.12046	−	0.197567i
$176$	1.55999	−	2.92684i	0.117589	−	0.220619i
$177$	3.57657	−	1.30176i	0.268831	−	0.0978466i
$178$	−1.60217	+	1.44260i	−0.120087	+	0.108127i
$179$	−5.61119	+	12.6029i	−0.419400	+	0.941988i	0.573071	+	0.819506i	$0.305752\pi$
$179$	−5.61119	+	12.6029i	−0.419400	+	0.941988i	−0.992471	+	0.122482i	$0.960915\pi$
$180$	−4.84002	−	19.4123i	−0.360754	−	1.44691i
$181$	4.74801	+	1.91832i	0.352917	+	0.142588i	0.544218	−	0.838944i	$-0.316826\pi$
$181$	4.74801	+	1.91832i	0.352917	+	0.142588i	−0.191301	+	0.981531i	$0.561271\pi$
$182$	3.24495	+	2.92176i	0.240531	+	0.216575i
$183$	−21.0163	+	9.35706i	−1.55357	+	0.691693i
$184$	−1.01038	+	1.49795i	−0.0744861	+	0.110430i
$185$	−3.47199	+	24.7045i	−0.255266	+	1.81631i
$186$	−1.22725	+	6.96010i	−0.0899866	+	0.510340i
$187$	8.24199	−	5.13869i	0.602714	−	0.375778i
$188$	−3.36565	+	2.82412i	−0.245466	+	0.205970i
$189$	19.1911	−	59.0641i	1.39595	−	4.29628i
$190$	−10.3348	−	6.85527i	−0.749762	−	0.497334i
$191$	4.66077	+	3.38624i	0.337241	+	0.245020i	0.743497	−	0.668739i	$-0.233166\pi$
$191$	4.66077	+	3.38624i	0.337241	+	0.245020i	−0.406256	+	0.913759i	$0.633166\pi$
$192$	1.67842	−	2.68603i	0.121129	−	0.193847i
$193$	0.392800	−	11.2483i	0.0282743	−	0.809671i	−0.899586	−	0.436744i	$-0.856132\pi$
$193$	0.392800	−	11.2483i	0.0282743	−	0.809671i	0.927860	−	0.372928i	$-0.121646\pi$
$194$	0.949276	+	0.983004i	0.0681541	+	0.0705756i
$195$	−5.62049	+	5.82019i	−0.402492	+	0.416792i
$196$	−0.581113	−	16.6409i	−0.0415081	−	1.18864i
$197$	13.9040	+	8.02747i	0.990618	+	0.571934i	0.905459	−	0.424434i	$-0.139527\pi$
$197$	13.9040	+	8.02747i	0.990618	+	0.571934i	0.0851593	+	0.996367i	$0.472860\pi$
$198$	10.9283	+	20.6030i	0.776644	+	1.46419i
$199$	−6.39052	−	5.36229i	−0.453012	−	0.380122i	0.387540	−	0.921853i	$-0.373325\pi$
$199$	−6.39052	−	5.36229i	−0.453012	−	0.380122i	−0.840552	+	0.541731i	$0.817769\pi$
$200$	2.62457	−	1.64001i	0.185585	−	0.115967i
$201$	9.12591	+	4.06312i	0.643692	+	0.286590i
$202$	−3.42167	−	7.68520i	−0.240748	−	0.540729i
$203$	30.7737	−	24.0430i	2.15989	−	1.68749i
$204$	8.18971	−	4.35455i	0.573394	−	0.304879i
$205$	1.00312	−	0.968703i	0.0700610	−	0.0676572i
$206$	4.32274	+	15.0752i	0.301180	+	1.05034i
$207$	−4.75955	−	11.7803i	−0.330812	−	0.818788i
$208$	−0.897861			−0.0622554
$209$	13.6179	+	4.85304i	0.941972	+	0.335692i
$210$	43.8247			3.02419
$211$	1.43958	+	3.56308i	0.0991045	+	0.245292i	0.968589	−	0.248669i	$-0.0799930\pi$
$211$	1.43958	+	3.56308i	0.0991045	+	0.245292i	−0.869484	+	0.493961i	$0.835549\pi$
$212$	−0.474571	−	1.65502i	−0.0325936	−	0.113668i
$213$	−36.9029	+	35.6367i	−2.52854	+	2.44178i
$214$	−2.23496	+	1.18835i	−0.152779	+	0.0812338i
$215$	12.8238	−	10.0190i	0.874575	−	0.683293i
$216$	5.19404	+	11.6660i	0.353410	+	0.793771i
$217$	−9.91356	−	4.41380i	−0.672976	−	0.299628i
$218$	3.48591	−	2.17824i	0.236096	−	0.147529i
$219$	−17.4550	−	14.6465i	−1.17950	−	0.989719i
$220$	−6.56178	+	6.78131i	−0.442395	+	0.457196i
$221$	−2.27711	−	1.31469i	−0.153175	−	0.0884354i
$222$	−0.969233	−	27.7552i	−0.0650507	−	1.86281i
$223$	−10.2251	+	10.5884i	−0.684726	+	0.709055i	−0.968270	−	0.249905i	$-0.919601\pi$
$223$	−10.2251	+	10.5884i	−0.684726	+	0.709055i	0.283544	+	0.958959i	$0.408490\pi$
$224$	3.37829	+	3.49832i	0.225721	+	0.233741i
$225$	−0.759495	+	21.7491i	−0.0506330	+	1.44994i
$226$	1.94792	−	3.11733i	0.129574	−	0.207361i
$227$	−16.6079	−	12.0663i	−1.10230	−	0.800871i	−0.120870	−	0.992668i	$-0.538568\pi$
$227$	−16.6079	−	12.0663i	−1.10230	−	0.800871i	−0.981435	+	0.191797i	$0.938568\pi$
$228$	12.6554	+	5.51775i	0.838124	+	0.365422i
$229$	3.65738	−	11.2562i	0.241686	−	0.743833i	−0.754478	−	0.656326i	$-0.772110\pi$
$229$	3.65738	−	11.2562i	0.241686	−	0.743833i	0.996164	−	0.0875078i	$-0.0278903\pi$
$230$	3.93804	−	3.30441i	0.259667	−	0.217886i
$231$	−49.5820	+	12.3094i	−3.26225	+	0.809901i
$232$	−1.39442	+	7.90813i	−0.0915479	+	0.519194i
$233$	1.08494	−	7.71972i	0.0710765	−	0.505736i	−0.921900	−	0.387427i	$-0.873364\pi$
$233$	1.08494	−	7.71972i	0.0710765	−	0.505736i	0.992977	−	0.118309i	$-0.0377472\pi$
$234$	3.53052	−	5.23421i	0.230797	−	0.342171i
$235$	11.4196	−	5.08432i	0.744930	−	0.331664i
$236$	−0.893026	−	0.804084i	−0.0581311	−	0.0523414i
$237$	10.3490	+	4.18126i	0.672238	+	0.271602i
$238$	3.44543	+	13.8189i	0.223334	+	0.895745i
$239$	−4.25952	+	9.56704i	−0.275525	+	0.618840i	−0.997312	−	0.0732757i	$-0.976655\pi$
$239$	−4.25952	+	9.56704i	−0.275525	+	0.618840i	0.721786	+	0.692116i	$0.243321\pi$
$240$	−6.69680	+	6.02983i	−0.432277	+	0.389224i
$241$	14.3860	−	5.23608i	0.926685	−	0.337286i	0.165790	−	0.986161i	$-0.446983\pi$
$241$	14.3860	−	5.23608i	0.926685	−	0.337286i	0.760895	+	0.648875i	$0.224760\pi$
$242$	5.51908	−	9.51524i	0.354780	−	0.611663i
$243$	−22.6316	−	3.99057i	−1.45182	−	0.255995i
$244$	5.72358	+	4.47175i	0.366415	+	0.286275i
$245$	−11.4610	+	45.9674i	−0.732213	+	2.93675i
$246$	−0.912482	+	1.25592i	−0.0581777	+	0.0800747i
$247$	−0.574615	−	3.87127i	−0.0365619	−	0.246323i
$248$	2.12217	−	0.689536i	0.134758	−	0.0437856i
$249$	−56.4070	+	3.94436i	−3.57465	+	0.249964i
$250$	5.21048	−	1.49408i	0.329540	−	0.0944940i
$251$	23.8431	+	12.6776i	1.50496	+	0.800202i	0.998087	−	0.0618184i	$-0.0196900\pi$
$251$	23.8431	+	12.6776i	1.50496	+	0.800202i	0.506874	+	0.862020i	$0.330801\pi$
$252$	−33.6779	+	5.93832i	−2.12151	+	0.374079i
$253$	−3.52725	+	4.84462i	−0.221756	+	0.304579i
$254$	8.26702	−	14.3189i	0.518719	−	0.898447i
$255$	−25.8132	+	5.48677i	−1.61649	+	0.343595i
$256$	−0.997564	−	0.0697565i	−0.0623478	−	0.00435978i
$257$	4.18274	−	1.04288i	0.260912	−	0.0650528i	−0.109269	−	0.994012i	$-0.534851\pi$
$257$	4.18274	−	1.04288i	0.260912	−	0.0650528i	0.370182	+	0.928959i	$0.379295\pi$
$258$	−12.1222	+	13.4630i	−0.754694	+	0.838173i
$259$	41.7108	+	8.86591i	2.59178	+	0.550901i
$260$	2.45558	+	0.704127i	0.152289	+	0.0436681i
$261$	−40.6186	−	39.2249i	−2.51423	−	2.42796i
$262$	−7.17370	+	13.4918i	−0.443193	+	0.833524i
$263$	−8.71422	+	23.9421i	−0.537342	+	1.47633i	0.312820	+	0.949812i	$0.398726\pi$
$263$	−8.71422	+	23.9421i	−0.537342	+	1.47633i	−0.850162	+	0.526521i	$0.823496\pi$
$264$	5.88291	−	8.70296i	0.362068	−	0.535630i
$265$			4.89854i			0.300915i
$266$	−12.9215	+	16.8049i	−0.792269	+	1.03037i
$267$	−5.52435	+	4.01368i	−0.338085	+	0.245633i
$268$	−0.220009	−	3.14628i	−0.0134392	−	0.192189i
$269$	22.7179	+	0.793325i	1.38513	+	0.0483699i	0.717727	−	0.696325i	$-0.245183\pi$
$269$	22.7179	+	0.793325i	1.38513	+	0.0483699i	0.667406	+	0.744694i	$0.267405\pi$
$270$	−5.05651	−	35.9790i	−0.307730	−	2.18961i
$271$	−1.28078	−	0.624676i	−0.0778016	−	0.0379464i	0.399060	−	0.916925i	$-0.369337\pi$
$271$	−1.28078	−	0.624676i	−0.0778016	−	0.0379464i	−0.476861	+	0.878979i	$0.658226\pi$
$272$	−2.42783	−	1.63759i	−0.147209	−	0.0992935i
$273$	9.25412	+	10.2777i	0.560085	+	0.622037i
$274$	2.22635	+	3.85615i	0.134499	+	0.232959i
$275$	8.89438	−	5.12330i	0.536351	−	0.308947i
$276$	−3.67858	+	4.38396i	−0.221424	+	0.263883i
$277$	−4.90017	−	23.0535i	−0.294423	−	1.38515i	−0.837944	−	0.545756i	$-0.816243\pi$
$277$	−4.90017	−	23.0535i	−0.294423	−	1.38515i	0.543521	−	0.839395i	$-0.317091\pi$
$278$	8.96560	−	0.942322i	0.537721	−	0.0565167i
$279$	−4.32494	+	15.0829i	−0.258928	+	0.902988i
$280$	−6.49589	−	12.2170i	−0.388204	−	0.730105i
$281$	−3.29639	+	0.463277i	−0.196646	+	0.0276368i	−0.236808	−	0.971556i	$-0.576101\pi$
$281$	−3.29639	+	0.463277i	−0.196646	+	0.0276368i	0.0401623	+	0.999193i	$0.487212\pi$
$282$	−11.5366	+	7.78157i	−0.686997	+	0.463386i
$283$	6.79573	+	1.69437i	0.403964	+	0.100720i	0.438604	−	0.898680i	$-0.355473\pi$
$283$	6.79573	+	1.69437i	0.403964	+	0.100720i	−0.0346402	+	0.999400i	$0.511029\pi$
$284$	15.4043	+	5.00516i	0.914077	+	0.297002i
$285$	−30.2844	−	25.0154i	−1.79389	−	1.48178i
$286$	−2.97595	−	0.106908i	−0.175971	−	0.00632158i
$287$	−1.53217	−	1.82597i	−0.0904414	−	0.107784i
$288$	4.32922	−	5.54115i	0.255102	−	0.326516i
$289$	3.69282	+	7.57140i	0.217225	+	0.445376i
$290$	10.0154	−	20.5346i	0.588124	−	1.20583i
$291$	2.66473	+	3.41070i	0.156209	+	0.199939i
$292$	−1.49574	+	7.03689i	−0.0875315	+	0.411803i
$293$	−0.393650	+	3.74533i	−0.0229973	+	0.218804i	0.976988	+	0.213296i	$0.0684199\pi$
$293$	−0.393650	+	3.74533i	−0.0229973	+	0.218804i	−0.999985	+	0.00550807i	$0.998247\pi$
$294$	3.67888	−	52.6105i	0.214557	−	3.06831i
$295$	1.81178	+	2.89945i	0.105486	+	0.168812i
$296$	−7.59364	+	4.38419i	−0.441371	+	0.254826i
$297$	15.8265	+	39.2853i	0.918347	+	2.27956i
$298$	1.24852	+	3.43029i	0.0723250	+	0.198711i
$299$	1.60651	+	0.225781i	0.0929070	+	0.0130572i
$300$	8.81025	−	4.29704i	0.508660	−	0.248090i
$301$	−15.5549	−	23.0611i	−0.896569	−	1.32922i
$302$	4.89021	+	3.05574i	0.281400	+	0.175838i
$303$	−8.23375	−	25.3409i	−0.473016	−	1.45579i
$304$	−0.337657	−	4.34580i	−0.0193660	−	0.249249i
$305$	−12.1467	−	16.7185i	−0.695519	−	0.957299i
$306$	19.0932	−	7.71413i	1.09148	−	0.440988i
$307$	24.8635	+	9.04958i	1.41904	+	0.516487i	0.933768	−	0.357879i	$-0.116500\pi$
$307$	24.8635	+	9.04958i	1.41904	+	0.516487i	0.485268	+	0.874366i	$0.338722\pi$
$308$	10.7807	+	11.9974i	0.614290	+	0.683614i
$309$	8.62545	+	48.9174i	0.490685	+	2.78281i
$310$	−6.34474	+	0.221563i	−0.360357	+	0.0125839i
$311$	−0.552766	−	5.25921i	−0.0313445	−	0.298223i	−0.998952	−	0.0457644i	$-0.985428\pi$
$311$	−0.552766	−	5.25921i	−0.0313445	−	0.298223i	0.967608	−	0.252458i	$-0.0812390\pi$
$312$	−2.82822	−	0.297258i	−0.160116	−	0.0168289i
$313$	−0.305342	+	0.755749i	−0.0172590	+	0.0427174i	−0.935567	−	0.353148i	$-0.885111\pi$
$313$	−0.305342	+	0.755749i	−0.0172590	+	0.0427174i	0.918308	+	0.395866i	$0.129555\pi$
$314$	7.40598	−	18.3305i	0.417944	−	1.03445i
$315$	96.7635	+	10.1703i	5.45201	+	0.573029i
$316$	−0.368363	−	3.50474i	−0.0207220	−	0.197157i
$317$	−23.8449	+	0.832684i	−1.33927	+	0.0467682i	−0.695540	−	0.718488i	$-0.744835\pi$
$317$	−23.8449	+	0.832684i	−1.33927	+	0.0467682i	−0.643726	+	0.765256i	$0.722612\pi$
$318$	−0.946941	−	5.37037i	−0.0531018	−	0.301155i
$319$	−5.56339	+	26.0454i	−0.311490	+	1.45826i
$320$	2.67356	+	0.973096i	0.149457	+	0.0543977i
$321$	−7.43345	+	3.00331i	−0.414895	+	0.167628i
$322$	−5.16495	−	7.10895i	−0.287832	−	0.396166i
$323$	5.50697	−	11.5160i	0.306416	−	0.640767i
$324$	5.97982	+	18.4040i	0.332212	+	1.02244i
$325$	−2.35650	−	1.47250i	−0.130715	−	0.0816798i
$326$	6.44381	+	9.55334i	0.356889	+	0.529110i
$327$	11.7016	−	5.70726i	0.647101	−	0.315612i
$328$	0.485365	+	0.0682136i	0.0267998	+	0.00376646i
$329$	−7.30789	−	20.0783i	−0.402897	−	1.10695i
$330$	−22.9144	+	19.1884i	−1.26140	+	1.05629i
$331$	12.2245	−	7.05780i	0.671918	−	0.387932i	−0.124885	−	0.992171i	$-0.539856\pi$
$331$	12.2245	−	7.05780i	0.671918	−	0.387932i	0.796803	+	0.604239i	$0.206523\pi$
$332$	9.46044	+	15.1399i	0.519209	+	0.830909i
$333$	4.30102	−	61.5075i	0.235695	−	3.37059i
$334$	−1.14105	+	10.8564i	−0.0624356	+	0.594035i
$335$	−1.86569	+	8.77737i	−0.101933	+	0.479559i
$336$	9.48325	+	12.1380i	0.517354	+	0.662182i
$337$	−4.77231	+	9.78468i	−0.259964	+	0.533005i	−0.988357	−	0.152155i	$-0.951379\pi$
$337$	−4.77231	+	9.78468i	−0.259964	+	0.533005i	0.728393	+	0.685160i	$0.240268\pi$
$338$	−5.34543	−	10.9598i	−0.290753	−	0.596132i
$339$	7.16793	−	9.17453i	0.389308	−	0.498292i
$340$	5.35569	+	6.38266i	0.290453	+	0.346148i
$341$	7.11601	−	2.03277i	0.385354	−	0.110081i
$342$	26.6622	+	15.1199i	1.44173	+	0.817591i
$343$	44.6381	+	14.5038i	2.41023	+	0.783132i
$344$	5.54989	+	1.38374i	0.299230	+	0.0746064i
$345$	13.4987	−	9.10496i	0.726744	−	0.490195i
$346$	−5.00466	+	0.703359i	−0.269052	+	0.0378128i
$347$	−3.78815	−	7.12448i	−0.203359	−	0.382462i	0.760311	−	0.649559i	$-0.225047\pi$
$347$	−3.78815	−	7.12448i	−0.203359	−	0.382462i	−0.963670	+	0.267097i	$0.913936\pi$
$348$	−7.01052	+	24.4486i	−0.375803	+	1.31058i
$349$	−20.7667	+	2.18267i	−1.11162	+	0.116836i	−0.642489	−	0.766295i	$-0.722098\pi$
$349$	−20.7667	+	2.18267i	−1.11162	+	0.116836i	−0.469128	+	0.883130i	$0.655432\pi$
$350$	3.12926	+	14.7220i	0.167266	+	0.786925i
$351$	7.37001	−	8.78324i	0.393382	−	0.468815i
$352$	−3.29811	−	0.349986i	−0.175790	−	0.0186543i
$353$	−1.64122	−	2.84268i	−0.0873534	−	0.151301i	0.819038	−	0.573739i	$-0.194508\pi$
$353$	−1.64122	−	2.84268i	−0.0873534	−	0.151301i	−0.906392	+	0.422438i	$0.861174\pi$
$354$	−2.54678	−	2.82849i	−0.135360	−	0.150332i
$355$	−38.2045	−	25.7692i	−2.02768	−	1.36769i
$356$	1.93773	+	0.945096i	0.102700	+	0.0500900i
$357$	6.27790	+	44.6695i	0.332261	+	2.36416i
$358$	13.7872	+	0.481461i	0.728678	+	0.0254460i
$359$	1.11111	+	15.8896i	0.0586422	+	0.838622i	0.934480	+	0.356016i	$0.115865\pi$
$359$	1.11111	+	15.8896i	0.0586422	+	0.838622i	−0.875838	+	0.482606i	$0.839690\pi$
$360$	−16.1856	+	11.7596i	−0.853058	+	0.619783i
$361$	18.5215	−	4.23710i	0.974817	−	0.223005i
$362$		−	5.12090i		−	0.269148i
$363$	20.5351	−	28.1454i	1.07781	−	1.47725i
$364$	1.49343	−	4.10317i	0.0782772	−	0.215065i
$365$	9.60926	−	18.0724i	0.502972	−	0.945952i
$366$	16.5486	+	15.9808i	0.865007	+	0.835327i
$367$	24.4499	+	7.01090i	1.27627	+	0.365966i	0.844276	−	0.535909i	$-0.180031\pi$
$367$	24.4499	+	7.01090i	1.27627	+	0.365966i	0.431998	+	0.901874i	$0.357809\pi$
$368$	1.76737	+	0.375666i	0.0921304	+	0.0195829i
$369$	−2.30619	+	2.56128i	−0.120055	+	0.133335i
$370$	24.2062	−	6.03529i	1.25842	−	0.313760i
$371$	8.35274	+	0.584080i	0.433652	+	0.0303239i
$372$	6.91303	−	1.46941i	0.358424	−	0.0761854i
$373$	6.79916	−	11.7765i	0.352047	−	0.609763i	−0.634561	−	0.772873i	$-0.718819\pi$
$373$	6.79916	−	11.7765i	0.352047	−	0.609763i	0.986608	+	0.163110i	$0.0521524\pi$
$374$	−7.85202	−	5.71685i	−0.406018	−	0.295611i
$375$	16.9074	−	2.98124i	0.873096	−	0.153950i
$376$	3.87927	+	2.06265i	0.200058	+	0.106373i
$377$	6.93063	−	1.98733i	0.356946	−	0.102353i
$378$	−61.9523	+	4.33213i	−3.18648	+	0.222821i
$379$	10.1892	−	3.31069i	0.523387	−	0.170059i	−0.0353951	−	0.999373i	$-0.511269\pi$
$379$	10.1892	−	3.31069i	0.523387	−	0.170059i	0.558782	+	0.829315i	$0.311269\pi$
$380$	−2.48463	+	12.1502i	−0.127459	+	0.623295i
$381$	30.7813	−	42.3669i	1.57698	−	2.17052i
$382$	1.39372	−	5.58990i	0.0713088	−	0.286004i
$383$	−29.4539	−	23.0119i	−1.50502	−	1.17585i	−0.935217	−	0.354075i	$-0.884796\pi$
$383$	−29.4539	−	23.0119i	−1.50502	−	1.17585i	−0.569807	−	0.821779i	$-0.692982\pi$
$384$	−3.11919	−	0.549997i	−0.159175	−	0.0280669i
$385$	−20.0759	−	41.2665i	−1.02316	−	2.10314i
$386$	−10.5764	+	3.84949i	−0.538325	+	0.195934i
$387$	−29.8897	+	26.9128i	−1.51938	+	1.36805i
$388$	0.555821	−	1.24839i	0.0282175	−	0.0633776i
$389$	−2.84517	−	11.4114i	−0.144256	−	0.578579i	−0.998295	−	0.0583703i	$-0.981410\pi$
$389$	−2.84517	−	11.4114i	−0.144256	−	0.578579i	0.854039	−	0.520209i	$-0.174146\pi$
$390$	7.50186	+	3.03095i	0.379871	+	0.153478i
$391$	3.93224	+	3.54060i	0.198862	+	0.179056i
$392$	−15.2115	+	6.77259i	−0.768296	+	0.342067i
$393$	−27.0636	+	40.1234i	−1.36518	+	2.02396i
$394$	2.23442	−	15.8987i	0.112568	−	0.800965i
$395$	−1.74107	+	9.87409i	−0.0876027	+	0.496819i
$396$	15.0089	−	17.8506i	0.754228	−	0.897027i
$397$	−27.2299	+	22.8486i	−1.36663	+	1.14674i	−0.392755	+	0.919643i	$0.628478\pi$
$397$	−27.2299	+	22.8486i	−1.36663	+	1.14674i	−0.973873	+	0.227094i	$0.927078\pi$
$398$	−2.57789	+	7.93394i	−0.129218	+	0.397692i
$399$	−46.2659	+	48.6567i	−2.31619	+	2.43588i
$400$	−2.50378	−	1.81910i	−0.125189	−	0.0909550i
$401$	9.29179	−	14.8700i	0.464010	−	0.742571i	−0.530447	−	0.847718i	$-0.677976\pi$
$401$	9.29179	−	14.8700i	0.464010	−	0.742571i	0.994457	+	0.105147i	$0.0335314\pi$
$402$	0.348630	−	9.98347i	0.0173881	−	0.497930i
$403$	−1.39173	−	1.44118i	−0.0693269	−	0.0717901i
$404$	−5.84381	+	6.05145i	−0.290741	+	0.301071i
$405$	−1.92145	−	55.0231i	−0.0954776	−	2.73412i
$406$	−33.8203	−	19.5262i	−1.67848	−	0.969068i
$407$	−25.6910	+	13.6272i	−1.27346	+	0.675473i
$408$	−7.10538	−	5.96213i	−0.351769	−	0.295169i
$409$	9.15629	−	5.72149i	0.452749	−	0.282909i	−0.284316	−	0.958731i	$-0.591766\pi$
$409$	9.15629	−	5.72149i	0.452749	−	0.282909i	0.737065	+	0.675821i	$0.236211\pi$
$410$	−1.27394	−	0.567196i	−0.0629155	−	0.0280118i
$411$	5.73624	+	12.8838i	0.282948	+	0.635511i
$412$	12.3582	−	9.65525i	0.608843	−	0.475680i
$413$	5.16001	−	2.74363i	0.253908	−	0.135005i
$414$	−9.13955	+	8.82596i	−0.449184	+	0.433772i
$415$	−14.0005	−	48.8256i	−0.687258	−	2.39675i
$416$	0.336344	+	0.832482i	0.0164906	+	0.0408158i
$417$	28.5532			1.39826
$418$	−0.601709	−	14.4443i	−0.0294305	−	0.706494i
$419$	−3.65857			−0.178733			−0.0893664	−	0.995999i	$-0.528484\pi$
$419$	−3.65857			−0.178733			−0.0893664	+	0.995999i	$0.528484\pi$
$420$	−16.4170	−	40.6336i	−0.801069	−	1.98272i
$421$	6.40783	+	22.3468i	0.312298	+	1.08911i	0.948287	+	0.317415i	$0.102815\pi$
$421$	6.40783	+	22.3468i	0.312298	+	1.08911i	−0.635988	+	0.771699i	$0.719407\pi$
$422$	2.76435	−	2.66950i	0.134567	−	0.129949i
$423$	−27.2784	+	14.5042i	−1.32632	+	0.705217i
$424$	−1.35673	+	1.06000i	−0.0658889	+	0.0514780i
$425$	−3.68633	−	8.27964i	−0.178813	−	0.401622i
$426$	46.8658	+	20.8660i	2.27066	+	1.01096i
$427$	−29.9558	+	18.7185i	−1.44966	+	0.905851i
$428$	1.93905	+	1.62705i	0.0937274	+	0.0786466i
$429$	−9.33870	−	1.32201i	−0.450877	−	0.0638273i
$430$	−14.0934	−	8.13681i	−0.679642	−	0.392392i
$431$	0.0224575	+	0.643099i	0.00108174	+	0.0309770i	0.999812	−	0.0194068i	$-0.00617777\pi$
$431$	0.0224575	+	0.643099i	0.00108174	+	0.0309770i	−0.998730	+	0.0503838i	$0.983956\pi$
$432$	8.87081	−	9.18599i	0.426797	−	0.441961i
$433$	26.9359	+	27.8929i	1.29445	+	1.34045i	0.908475	+	0.417939i	$0.137248\pi$
$433$	26.9359	+	27.8929i	1.29445	+	1.34045i	0.385979	+	0.922507i	$0.373864\pi$
$434$	−0.378720	+	10.8451i	−0.0181792	+	0.520583i
$435$	38.3465	−	61.3673i	1.83857	−	2.94234i
$436$	−3.32547	−	2.41610i	−0.159261	−	0.115710i
$437$	−0.488659	+	7.86071i	−0.0233757	+	0.376029i
$438$	−7.04124	+	21.6707i	−0.336443	+	1.03547i
$439$	−19.0241	+	15.9631i	−0.907969	+	0.761876i	−0.971731	−	0.236089i	$-0.924134\pi$
$439$	−19.0241	+	15.9631i	−0.907969	+	0.761876i	0.0637628	+	0.997965i	$0.479690\pi$
$440$	8.74561	+	3.54365i	0.416931	+	0.168937i
$441$	20.3320	−	115.308i	0.968190	−	5.49088i
$442$	−0.365938	+	2.60379i	−0.0174059	+	0.123849i
$443$	13.7253	−	20.3486i	0.652109	−	0.966791i	−0.347468	−	0.937692i	$-0.612958\pi$
$443$	13.7253	−	20.3486i	0.652109	−	0.966791i	0.999577	−	0.0290989i	$-0.00926376\pi$
$444$	−25.3711	+	11.2959i	−1.20406	+	0.536082i
$445$	−4.55839	−	4.10439i	−0.216088	−	0.194567i
$446$	13.6478	+	5.51408i	0.646244	+	0.261099i
$447$	2.79711	+	11.2186i	0.132299	+	0.530622i
$448$	1.97806	−	4.44279i	0.0934543	−	0.209902i
$449$	−8.03371	+	7.23358i	−0.379134	+	0.341374i	−0.836561	−	0.547873i	$-0.815438\pi$
$449$	−8.03371	+	7.23358i	−0.379134	+	0.341374i	0.457427	+	0.889247i	$0.348771\pi$
$450$	20.4499	−	7.44317i	0.964019	−	0.350874i
$451$	1.60061	+	0.283885i	0.0753699	+	0.0133676i
$452$	−3.62004	−	0.638310i	−0.170272	−	0.0300236i
$453$	14.3923	+	11.2445i	0.676207	+	0.528311i
$454$	−4.96629	+	19.9187i	−0.233080	+	0.934831i
$455$	−7.30225	+	10.0507i	−0.342335	+	0.471184i
$456$	0.375175	−	13.8009i	0.0175692	−	0.646285i
$457$	−13.1223	+	4.26371i	−0.613838	+	0.199448i	−0.599402	−	0.800448i	$-0.704595\pi$
$457$	−13.1223	+	4.26371i	−0.613838	+	0.199448i	−0.0144352	+	0.999896i	$0.504595\pi$
$458$	−11.8067	+	0.825604i	−0.551690	+	0.0385779i
$459$	35.9482	−	10.3080i	1.67792	−	0.481135i
$460$	−4.53901	−	2.41344i	−0.211633	−	0.112527i
$461$	−16.6581	+	2.93728i	−0.775846	+	0.136803i	−0.547532	−	0.836785i	$-0.684433\pi$
$461$	−16.6581	+	2.93728i	−0.775846	+	0.136803i	−0.228314	+	0.973587i	$0.573321\pi$
$462$	29.9868	+	41.3604i	1.39511	+	1.92426i
$463$	−5.03910	+	8.72798i	−0.234187	+	0.405623i	−0.959036	−	0.283284i	$-0.908576\pi$
$463$	−5.03910	+	8.72798i	−0.234187	+	0.405623i	0.724849	+	0.688908i	$0.241909\pi$
$464$	7.85465	−	1.66956i	0.364643	−	0.0775072i
$465$	−20.0590	−	1.40266i	−0.930214	−	0.0650469i
$466$	−7.56403	+	1.88592i	−0.350397	+	0.0873637i
$467$	7.55773	−	8.39371i	0.349730	−	0.388414i	−0.542455	−	0.840085i	$-0.682505\pi$
$467$	7.55773	−	8.39371i	0.349730	−	0.388414i	0.892185	+	0.451670i	$0.149172\pi$
$468$	−6.17563	−	1.31267i	−0.285469	−	0.0606782i
$469$	14.7443	+	4.22785i	0.680827	+	0.195224i
$470$	−8.99194	−	8.68342i	−0.414767	−	0.400536i
$471$	29.3972	−	55.2882i	1.35455	−	2.54754i
$472$	−0.411001	+	1.12921i	−0.0189178	+	0.0519763i
$473$	18.2303	+	5.24722i	0.838228	+	0.241267i
$474$		−	11.1617i		−	0.512675i
$475$	6.24097	−	11.9596i	0.286355	−	0.548745i
$476$	11.5220	−	8.37119i	0.528108	−	0.383693i
$477$	−0.844531	−	12.0774i	−0.0386684	−	0.552984i
$478$	10.4660	+	0.365482i	0.478706	+	0.0167168i
$479$	1.89986	+	13.5182i	0.0868070	+	0.617664i	0.984283	+	0.176600i	$0.0565099\pi$
$479$	1.89986	+	13.5182i	0.0868070	+	0.617664i	−0.897476	+	0.441064i	$0.854601\pi$
$480$	8.09943	+	3.95035i	0.369687	+	0.180308i
$481$	6.52683	+	4.40240i	0.297598	+	0.200732i
$482$	−10.2439	−	11.3770i	−0.466597	−	0.518209i
$483$	−13.9158	−	24.1028i	−0.633190	−	1.09672i
$484$	−10.8899	−	1.55273i	−0.494994	−	0.0705785i
$485$	−2.49915	+	2.97837i	−0.113481	+	0.135241i
$486$	4.77797	+	22.4786i	0.216733	+	1.01965i
$487$	9.91187	−	1.04178i	0.449150	−	0.0472075i	0.122746	−	0.992438i	$-0.460830\pi$
$487$	9.91187	−	1.04178i	0.449150	−	0.0472075i	0.326403	+	0.945231i	$0.394163\pi$
$488$	2.00205	−	6.98196i	0.0906283	−	0.316059i
$489$	17.1348	+	32.2260i	0.774865	+	1.45731i
$490$	46.9136	−	6.59327i	2.11934	−	0.297854i
$491$	20.9064	−	14.1015i	0.943492	−	0.636393i	0.0119115	−	0.999929i	$-0.496208\pi$
$491$	20.9064	−	14.1015i	0.943492	−	0.636393i	0.931580	+	0.363536i	$0.118431\pi$
$492$	1.50629	+	0.375561i	0.0679089	+	0.0169316i
$493$	22.3652	+	7.26688i	1.00728	+	0.327284i
$494$	−3.37412	+	1.98298i	−0.151809	+	0.0892184i
$495$	−55.0473	+	37.0497i	−2.47419	+	1.66526i
$496$	−1.43431	−	1.70934i	−0.0644022	−	0.0767516i
$497$	−48.4957	+	62.0716i	−2.17533	+	2.78429i
$498$	24.7876	+	50.8220i	1.11076	+	2.27739i
$499$	−7.94198	+	16.2835i	−0.355532	+	0.728948i	−0.999343	−	0.0362359i	$-0.988463\pi$
$499$	−7.94198	+	16.2835i	−0.355532	+	0.728948i	0.643811	+	0.765184i	$0.277352\pi$
$500$	−3.33717	−	4.27138i	−0.149243	−	0.191022i
$501$	−7.18852	+	33.8193i	−0.321160	+	1.51094i
$502$	2.82268	−	26.8560i	0.125982	−	1.19864i
$503$	−1.63096	+	23.3239i	−0.0727210	+	1.03996i	0.814965	+	0.579510i	$0.196756\pi$
$503$	−1.63096	+	23.3239i	−0.0727210	+	1.03996i	−0.887686	+	0.460449i	$0.847688\pi$
$504$	18.1219	+	29.0011i	0.807212	+	1.29181i
$505$	20.7281	−	11.9674i	0.922389	−	0.532542i
$506$	5.81319	+	1.45558i	0.258428	+	0.0647083i
$507$	−13.2094	−	36.2925i	−0.586649	−	1.61181i
$508$	−16.3731	−	2.30109i	−0.726440	−	0.102094i
$509$	7.70753	−	3.75921i	0.341630	−	0.166624i	−0.259567	−	0.965725i	$-0.583580\pi$
$509$	7.70753	−	3.75921i	0.341630	−	0.166624i	0.601197	+	0.799101i	$0.294691\pi$
$510$	14.7570	+	21.8782i	0.653453	+	0.968784i
$511$	−29.6703	−	18.5401i	−1.31254	−	0.820165i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	45.2840	+	32.3690i	1.99934	+	1.42913i
$514$	−2.53382	−	3.48751i	−0.111762	−	0.153827i
$515$	−41.3706	+	16.7148i	−1.82300	+	0.736542i
$516$	17.0238	+	6.19615i	0.749430	+	0.272770i
$517$	12.6122	+	7.29852i	0.554684	+	0.320988i
$518$	−7.40482	−	41.9948i	−0.325349	−	1.84515i
$519$	−15.9973	+	0.558639i	−0.702205	+	0.0245215i
$520$	−0.267022	−	2.54055i	−0.0117097	−	0.111410i
$521$	19.0033	+	1.99733i	0.832551	+	0.0875047i	0.511207	−	0.859458i	$-0.329199\pi$
$521$	19.0033	+	1.99733i	0.832551	+	0.0875047i	0.321345	+	0.946962i	$0.395865\pi$
$522$	−21.1527	+	52.3548i	−0.925828	+	2.29151i
$523$	−13.3657	+	33.0812i	−0.584440	+	1.44654i	0.287910	+	0.957657i	$0.407039\pi$
$523$	−13.3657	+	33.0812i	−0.584440	+	1.44654i	−0.872350	+	0.488882i	$0.837405\pi$
$524$	15.1967	+	1.59723i	0.663869	+	0.0697755i
$525$	4.98296	+	47.4097i	0.217474	+	2.06913i
$526$	25.4631	−	0.889192i	1.11025	−	0.0387706i
$527$	−1.13472	−	6.43531i	−0.0494291	−	0.280326i
$528$	−10.2730	−	2.19436i	−0.447076	−	0.0954971i
$529$	18.5451	+	6.74987i	0.806309	+	0.293472i
$530$	4.54185	−	1.83503i	0.197285	−	0.0797084i
$531$	−4.96681	−	6.83623i	−0.215541	−	0.296667i
$532$	20.4217	+	5.68540i	0.885393	+	0.246493i
$533$	−0.135990	−	0.418534i	−0.00589038	−	0.0181287i
$534$	5.79088	+	3.61854i	0.250596	+	0.156590i
$535$	−4.02717	−	5.97053i	−0.174110	−	0.258128i
$536$	−2.83476	+	1.38260i	−0.122443	+	0.0597194i
$537$	43.2698	+	6.08117i	1.86723	+	0.262422i
$538$	−7.77470	−	21.3608i	−0.335191	−	0.920930i
$539$	−51.2247	+	20.6364i	−2.20640	+	0.888874i
$540$	−31.4649	+	18.1663i	−1.35403	+	0.781752i
$541$	0.602231	+	0.963772i	0.0258920	+	0.0414358i	0.860741	−	0.509043i	$-0.170001\pi$
$541$	0.602231	+	0.963772i	0.0258920	+	0.0414358i	−0.834849	+	0.550479i	$0.814445\pi$
$542$	−0.0994025	+	1.42152i	−0.00426970	+	0.0610596i
$543$	1.69539	−	16.1306i	0.0727563	−	0.692230i
$544$	−0.608867	+	2.86449i	−0.0261050	+	0.122814i
$545$	7.20016	+	9.21578i	0.308421	+	0.394761i
$546$	6.06270	−	12.4304i	0.259460	−	0.531971i
$547$	4.93889	+	10.1262i	0.211172	+	0.432966i	0.977919	−	0.208982i	$-0.0670151\pi$
$547$	4.93889	+	10.1262i	0.211172	+	0.432966i	−0.766748	+	0.641949i	$0.778126\pi$
$548$	2.74136	−	3.50878i	0.117105	−	0.149888i
$549$	32.8300	+	39.1253i	1.40115	+	1.66983i
$550$	−8.08213	−	6.32751i	−0.344623	−	0.269806i
$551$	12.2254	+	32.7981i	0.520819	+	1.39725i
$552$	5.44276	+	1.76846i	0.231659	+	0.0752706i
$553$	16.6292	+	4.14612i	0.707145	+	0.176311i
$554$	−19.5392	+	13.1794i	−0.830141	+	0.559937i
$555$	78.2467	−	10.9969i	3.32139	−	0.466790i
$556$	−4.23228	−	7.95976i	−0.179489	−	0.337569i
$557$	12.3027	−	42.9046i	0.521281	−	1.81792i	−0.0521083	−	0.998641i	$-0.516594\pi$
$557$	12.3027	−	42.9046i	0.521281	−	1.81792i	0.573390	−	0.819283i	$-0.305628\pi$
$558$	15.6047	−	1.64013i	0.660602	−	0.0694320i
$559$	−1.06775	−	5.02335i	−0.0451608	−	0.212465i
$560$	−8.89399	+	10.5994i	−0.375840	+	0.447908i
$561$	−22.8408	−	20.6074i	−0.964339	−	0.870046i
$562$	1.66439	+	2.88281i	0.0702082	+	0.121604i
$563$	−23.4167	−	26.0069i	−0.986896	−	1.09606i	−0.995372	−	0.0960947i	$-0.969365\pi$
$563$	−23.4167	−	26.0069i	−0.986896	−	1.09606i	0.00847644	−	0.999964i	$-0.497302\pi$
$564$	11.5366	+	7.78157i	0.485781	+	0.327663i
$565$	9.39996	+	4.58467i	0.395459	+	0.192878i
$566$	−0.974737	−	6.93561i	−0.0409712	−	0.291525i
$567$	−94.0516	−	3.28435i	−3.94980	−	0.137930i
$568$	−1.12985	−	16.1576i	−0.0474074	−	0.677957i
$569$	19.9665	−	14.5065i	0.837038	−	0.608144i	−0.0845034	−	0.996423i	$-0.526930\pi$
$569$	19.9665	−	14.5065i	0.837038	−	0.608144i	0.921542	+	0.388279i	$0.126930\pi$
$570$	−11.8491	+	37.4501i	−0.496304	+	1.56861i
$571$			6.21379i			0.260039i	0.991511	+	0.130020i	$0.0415040\pi$
$571$			6.21379i			0.260039i	−0.991511	+	0.130020i	$0.958496\pi$
$572$	1.01569	+	2.79930i	0.0424680	+	0.117045i
$573$	6.24081	−	17.1465i	0.260714	−	0.716305i
$574$	−1.11905	+	2.10463i	−0.0467083	+	0.0878455i
$575$	4.02249	+	3.88447i	0.167749	+	0.161994i
$576$	−6.75943	−	1.93823i	−0.281643	−	0.0807598i
$577$	−36.9246	−	7.84856i	−1.53719	−	0.326740i	−0.639996	−	0.768378i	$-0.721064\pi$
$577$	−36.9246	−	7.84856i	−1.53719	−	0.326740i	−0.897193	+	0.441638i	$0.854398\pi$
$578$	5.63672	−	6.26022i	0.234457	−	0.260391i
$579$	−34.5897	+	8.62417i	−1.43750	+	0.358408i
$580$	−22.7912	−	1.59372i	−0.946353	−	0.0661754i
$581$	−84.9242	+	18.0512i	−3.52325	+	0.748890i
$582$	2.16412	−	3.74837i	0.0897056	−	0.155375i
$583$	−4.62309	+	3.35180i	−0.191469	+	0.138817i
$584$	7.08481	−	1.24924i	0.293171	−	0.0516940i
$585$	15.8605	+	8.43316i	0.655750	+	0.348668i
$586$	3.62007	−	1.03804i	0.149544	−	0.0428810i
$587$	−26.4690	+	1.85090i	−1.09249	+	0.0763946i	−0.604616	−	0.796517i	$-0.706673\pi$
$587$	−26.4690	+	1.85090i	−1.09249	+	0.0763946i	−0.487878	+	0.872912i	$0.662229\pi$
$588$	−50.1577	+	16.2972i	−2.06847	+	0.672087i
$589$	6.45216	−	7.27819i	0.265857	−	0.299893i
$590$	2.00962	−	2.76600i	0.0827347	−	0.113874i
$591$	12.3020	−	49.3404i	0.506035	−	2.02959i
$592$	6.90957	+	5.39835i	0.283982	+	0.221871i
$593$	−36.6879	−	6.46907i	−1.50659	−	0.265653i	−0.641445	−	0.767169i	$-0.721665\pi$
$593$	−36.6879	−	6.46907i	−1.50659	−	0.265653i	−0.865148	+	0.501516i	$0.832776\pi$
$594$	30.4959	−	29.3906i	1.25126	−	1.20591i
$595$	−38.0766	+	13.8588i	−1.56099	+	0.568154i
$596$	2.71280	−	2.44262i	0.111121	−	0.100054i
$597$	−10.7470	+	24.1381i	−0.439844	+	0.987906i
$598$	−0.392470	−	1.57411i	−0.0160493	−	0.0643702i
$599$	5.95076	+	2.40426i	0.243142	+	0.0982356i	0.492943	−	0.870061i	$-0.335921\pi$
$599$	5.95076	+	2.40426i	0.243142	+	0.0982356i	−0.249802	+	0.968297i	$0.580365\pi$
$600$	−7.28453	−	6.55902i	−0.297390	−	0.267771i
$601$	−5.02782	+	2.23853i	−0.205089	+	0.0913115i	−0.506711	−	0.862116i	$-0.669139\pi$
$601$	−5.02782	+	2.23853i	−0.205089	+	0.0913115i	0.301622	+	0.953428i	$0.402472\pi$
$602$	−15.5549	+	23.0611i	−0.633970	+	0.939899i
$603$	3.08659	−	21.9623i	0.125696	−	0.894372i
$604$	1.00133	−	5.67882i	0.0407435	−	0.231068i
$605$	28.5653	+	12.7867i	1.16134	+	0.519854i
$606$	−20.4112	+	17.1271i	−0.829149	+	0.695739i
$607$	8.95625	−	27.5645i	0.363523	−	1.11881i	−0.587378	−	0.809313i	$-0.699840\pi$
$607$	8.95625	−	27.5645i	0.363523	−	1.11881i	0.950901	−	0.309496i	$-0.100160\pi$
$608$	−3.90287	+	1.94104i	−0.158282	+	0.0787194i
$609$	−100.068	−	72.7036i	−4.05496	−	2.94610i
$610$	−10.9509	+	17.5251i	−0.443389	+	0.709570i
$611$	0.137671	−	3.94239i	0.00556959	−	0.159492i
$612$	−14.3048	−	14.8131i	−0.578239	−	0.598784i
$613$	9.86291	−	10.2133i	0.398359	−	0.412513i	−0.489956	−	0.871747i	$-0.662987\pi$
$613$	9.86291	−	10.2133i	0.398359	−	0.412513i	0.888315	+	0.459234i	$0.151876\pi$
$614$	−0.923413	−	26.4431i	−0.0372659	−	1.06716i
$615$	−3.82508	−	2.20841i	−0.154242	−	0.0890516i
$616$	7.08524	−	14.4900i	0.285472	−	0.583820i
$617$	20.1425	+	16.9015i	0.810905	+	0.680430i	0.950824	−	0.309733i	$-0.100240\pi$
$617$	20.1425	+	16.9015i	0.810905	+	0.680430i	−0.139918	+	0.990163i	$0.544684\pi$
$618$	42.1242	−	26.3221i	1.69449	−	1.05883i
$619$	−31.4050	−	13.9824i	−1.26227	−	0.562000i	−0.337072	−	0.941479i	$-0.609437\pi$
$619$	−31.4050	−	13.9824i	−1.26227	−	0.562000i	−0.925200	+	0.379479i	$0.876103\pi$
$620$	2.58221	+	5.79974i	0.103704	+	0.232923i
$621$	−18.1822	+	14.2055i	−0.729627	+	0.570047i
$622$	−4.66919	+	2.48265i	−0.187217	+	0.0995452i
$623$	−7.54211	+	7.28334i	−0.302168	+	0.291801i
$624$	0.783857	+	2.73364i	0.0313794	+	0.109433i
$625$	11.5739	+	28.6464i	0.462956	+	1.14586i
$626$	0.815101			0.0325780
$627$	2.88677	−	45.6981i	0.115287	−	1.82501i
$628$	−19.7700			−0.788910
$629$	9.61918	+	23.8083i	0.383542	+	0.949299i
$630$	−26.8186	−	93.5274i	−1.06848	−	3.72622i
$631$	34.7598	−	33.5671i	1.38377	−	1.33629i	0.501792	−	0.864988i	$-0.332674\pi$
$631$	34.7598	−	33.5671i	1.38377	−	1.33629i	0.881974	−	0.471298i	$-0.156215\pi$
$632$	−3.11155	+	1.65444i	−0.123771	+	0.0658101i
$633$	9.59139	−	7.49361i	0.381223	−	0.297844i
$634$	9.70453	+	21.7967i	0.385416	+	0.865658i
$635$	42.9747	+	19.1336i	1.70540	+	0.759293i
$636$	−4.62459	+	2.88976i	−0.183377	+	0.114587i
$637$	11.4526	+	9.60988i	0.453769	+	0.380757i
$638$	26.2329	−	4.59848i	1.03857	−	0.182055i
$639$	98.6358	+	56.9474i	3.90197	+	2.25280i
$640$	−0.0992941	−	2.84341i	−0.00392494	−	0.112396i
$641$	−17.3183	+	17.9337i	−0.684033	+	0.708337i	−0.968127	−	0.250459i	$-0.919418\pi$
$641$	−17.3183	+	17.9337i	−0.684033	+	0.708337i	0.284094	+	0.958797i	$0.408307\pi$
$642$	5.56924	+	5.76711i	0.219800	+	0.227610i
$643$	1.13241	−	32.4280i	0.0446580	−	1.27884i	−0.745737	−	0.666240i	$-0.767903\pi$
$643$	1.13241	−	32.4280i	0.0446580	−	1.27884i	0.790395	−	0.612597i	$-0.209875\pi$
$644$	−4.65648	+	7.45192i	−0.183491	+	0.293647i
$645$	−41.6996	−	30.2965i	−1.64192	−	1.19292i
$646$	−12.7404	−	0.792003i	−0.501264	−	0.0311609i
$647$	4.69718	−	14.4564i	0.184665	−	0.568341i	−0.815277	−	0.579071i	$-0.803415\pi$
$647$	4.69718	−	14.4564i	0.184665	−	0.568341i	0.999942	+	0.0107297i	$0.00341545\pi$
$648$	14.8238	−	12.4386i	0.582334	−	0.488636i
$649$	−1.49671	+	3.69383i	−0.0587510	+	0.144996i
$650$	−0.482522	+	2.73652i	−0.0189261	+	0.107335i
$651$	−4.78349	+	34.0363i	−0.187480	+	1.33399i
$652$	6.44381	−	9.55334i	0.252359	−	0.374138i
$653$	30.9141	−	13.7638i	1.20976	−	0.538620i	0.300074	−	0.953916i	$-0.402989\pi$
$653$	30.9141	−	13.7638i	1.20976	−	0.538620i	0.909686	+	0.415296i	$0.136322\pi$
$654$	−9.67519	−	8.71158i	−0.378330	−	0.340650i
$655$	−40.3092	−	16.2860i	−1.57501	−	0.636345i
$656$	−0.118574	−	0.475576i	−0.00462955	−	0.0185681i
$657$	−20.5759	+	46.2141i	−0.802741	+	1.80299i
$658$	−15.8787	+	14.2972i	−0.619015	+	0.557364i
$659$	−1.38321	+	0.503448i	−0.0538823	+	0.0196116i	−0.368821	−	0.929501i	$-0.620238\pi$
$659$	−1.38321	+	0.503448i	−0.0538823	+	0.0196116i	0.314938	+	0.949112i	$0.398016\pi$
$660$	26.3751	+	14.0578i	1.02665	+	0.547199i
$661$	−26.1814	−	4.61648i	−1.01834	−	0.179560i	−0.360531	−	0.932747i	$-0.617404\pi$
$661$	−26.1814	−	4.61648i	−1.01834	−	0.179560i	−0.657807	+	0.753187i	$0.728516\pi$
$662$	−11.1233	−	8.69044i	−0.432317	−	0.337763i
$663$	−2.01473	+	8.08066i	−0.0782458	+	0.313827i
$664$	10.4935	−	14.4431i	0.407227	−	0.560500i
$665$	−51.3932	−	31.5644i	−1.99294	−	1.22402i
$666$	−58.6399	+	19.0533i	−2.27225	+	0.738299i
$667$	−14.4739	+	1.01211i	−0.560432	+	0.0391892i
$668$	10.4933	−	3.00891i	0.405998	−	0.116418i
$669$	41.1645	+	21.8876i	1.59151	+	0.846222i
$670$	8.83714	−	1.55823i	0.341408	−	0.0601995i
$671$	7.46709	−	22.9032i	0.288264	−	0.884170i
$672$	7.70167	−	13.3397i	0.297099	−	0.514590i
$673$	25.8434	−	5.49318i	0.996189	−	0.211746i	0.319158	−	0.947701i	$-0.396600\pi$
$673$	25.8434	−	5.49318i	0.996189	−	0.211746i	0.677031	+	0.735955i	$0.263266\pi$
$674$	10.8599	+	0.759400i	0.418309	+	0.0292510i
$675$	38.3472	−	9.56103i	1.47598	−	0.368004i
$676$	−8.15928	+	9.06179i	−0.313818	+	0.348531i
$677$	−11.9199	−	2.53365i	−0.458118	−	0.0973760i	−0.0269285	−	0.999637i	$-0.508573\pi$
$677$	−11.9199	−	2.53365i	−0.458118	−	0.0973760i	−0.431190	+	0.902261i	$0.641906\pi$
$678$	−11.1916	−	3.20915i	−0.429812	−	0.123247i
$679$	4.78058	+	4.61655i	0.183462	+	0.177167i
$680$	3.91162	−	7.35669i	0.150004	−	0.282116i
$681$	−22.2382	+	61.0988i	−0.852168	+	2.34131i
$682$	−4.55046	−	5.83636i	−0.174246	−	0.223486i
$683$			32.8872i			1.25839i	0.777247	+	0.629196i	$0.216616\pi$
$683$			32.8872i			1.25839i	−0.777247	+	0.629196i	$0.783384\pi$
$684$	4.03109	−	30.3848i	0.154133	−	1.16179i
$685$	−10.2491	+	7.44640i	−0.391598	+	0.284512i
$686$	−3.27404	−	46.8210i	−0.125003	−	1.78763i
$687$	−37.4639	−	1.30827i	−1.42934	−	0.0499135i
$688$	−0.796041	−	5.66412i	−0.0303488	−	0.215943i
$689$	1.38941	+	0.677663i	0.0529325	+	0.0258169i
$690$	−13.4987	−	9.10496i	−0.513885	−	0.346620i
$691$	−24.7913	−	27.5335i	−0.943104	−	1.04742i	−0.998800	−	0.0489752i	$-0.984404\pi$
$691$	−24.7913	−	27.5335i	−0.943104	−	1.04742i	0.0556961	−	0.998448i	$-0.482262\pi$
$692$	2.52692	+	4.37676i	0.0960592	+	0.166379i
$693$	56.6116	+	98.2814i	2.15050	+	3.73340i
$694$	−5.18664	+	6.18119i	−0.196882	+	0.234635i
$695$	5.33271	+	25.0884i	0.202281	+	0.951658i
$696$	25.2945	−	2.65856i	0.958787	−	0.100773i
$697$	0.395637	−	1.37975i	0.0149858	−	0.0522618i
$698$	9.80309	+	18.4369i	0.371052	+	0.697848i
$699$	−24.4507	+	3.43633i	−0.924811	+	0.129974i
$700$	12.4778	−	8.41637i	0.471616	−	0.318109i
$701$	−11.5750	−	2.88597i	−0.437181	−	0.109001i	0.0171126	−	0.999854i	$-0.494553\pi$
$701$	−11.5750	−	2.88597i	−0.437181	−	0.109001i	−0.454293	+	0.890852i	$0.650108\pi$
$702$	−10.9045	−	3.54310i	−0.411565	−	0.133726i
$703$	−18.8539	+	33.2466i	−0.711087	+	1.25392i
$704$	0.910991	+	3.18906i	0.0343343	+	0.120192i
$705$	−25.4494	−	30.3294i	−0.958479	−	1.14227i
$706$	−2.02087	+	2.58660i	−0.0760566	+	0.0973480i
$707$	−17.9346	−	36.7714i	−0.674501	−	1.38293i
$708$	−1.66849	+	3.42090i	−0.0627056	+	0.128565i
$709$	−11.1490	−	14.2700i	−0.418708	−	0.535922i	0.531698	−	0.846934i	$-0.321554\pi$
$709$	−11.1490	−	14.2700i	−0.418708	−	0.535922i	−0.950406	+	0.311012i	$0.899332\pi$
$710$	−9.58118	+	45.0759i	−0.359575	+	1.69167i
$711$	2.59027	−	24.6447i	0.0971425	−	0.924250i
$712$	0.150390	−	2.15067i	0.00563610	−	0.0805999i
$713$	2.13652	+	3.41914i	0.0800132	+	0.128048i
$714$	39.0651	−	22.5543i	1.46198	−	0.844072i
$715$	−0.582541	−	8.45240i	−0.0217858	−	0.316102i
$716$	−4.71839	−	12.9637i	−0.176334	−	0.484475i
$717$	32.8466	+	4.61629i	1.22668	+	0.172398i
$718$	14.3164	−	6.98256i	0.534282	−	0.260587i
$719$	−2.27977	−	3.37990i	−0.0850212	−	0.126049i	0.784128	−	0.620599i	$-0.213111\pi$
$719$	−2.27977	−	3.37990i	−0.0850212	−	0.126049i	−0.869149	+	0.494550i	$0.835333\pi$
$720$	16.9665	+	10.6019i	0.632305	+	0.395108i
$721$	23.5683	+	72.5359i	0.877731	+	2.70138i
$722$	−10.8669	−	15.5856i	−0.404423	−	0.580037i
$723$	−28.5012	−	39.2286i	−1.05997	−	1.45893i
$724$	−4.74801	+	1.91832i	−0.176459	+	0.0712939i
$725$	23.3532	+	8.49986i	0.867315	+	0.315677i
$726$	−33.7885	−	8.49637i	−1.25401	−	0.315330i
$727$	−7.61338	−	43.1777i	−0.282365	−	1.60137i	−0.714549	−	0.699585i	$-0.753368\pi$
$727$	−7.61338	−	43.1777i	−0.282365	−	1.60137i	0.432184	−	0.901785i	$-0.357743\pi$
$728$	−4.36385	+	0.152389i	−0.161735	+	0.00564791i
$729$	1.54011	+	14.6531i	0.0570410	+	0.542709i
$730$	−20.3561	−	2.13951i	−0.753414	−	0.0791870i
$731$	6.27479	−	15.5306i	0.232081	−	0.574422i
$732$	8.61790	−	21.3300i	0.318527	−	0.788381i
$733$	−5.03901	−	0.529621i	−0.186120	−	0.0195620i	0.0110098	−	0.999939i	$-0.496495\pi$
$733$	−5.03901	−	0.529621i	−0.186120	−	0.0195620i	−0.197130	+	0.980377i	$0.563162\pi$
$734$	−2.65870	−	25.2959i	−0.0981346	−	0.933688i
$735$	149.958	−	5.23666i	5.53130	−	0.193157i
$736$	−0.313757	−	1.77940i	−0.0115652	−	0.0655896i
$737$	−9.56040	+	4.24509i	−0.352162	+	0.156370i
$738$	3.23869	+	1.17879i	0.119218	+	0.0433917i
$739$	−5.70449	+	2.30476i	−0.209843	+	0.0847820i	−0.477122	−	0.878837i	$-0.658320\pi$
$739$	−5.70449	+	2.30476i	−0.209843	+	0.0847820i	0.267279	+	0.963619i	$0.413875\pi$
$740$	−14.6636	−	20.1828i	−0.539046	−	0.741933i
$741$	−11.2849	+	5.12921i	−0.414559	+	0.188426i
$742$	−2.58744	−	7.96332i	−0.0949879	−	0.292343i
$743$	−20.9148	−	13.0690i	−0.767290	−	0.479456i	0.0889489	−	0.996036i	$-0.471649\pi$
$743$	−20.9148	−	13.0690i	−0.767290	−	0.479456i	−0.856239	+	0.516580i	$0.827205\pi$
$744$	−3.95208	−	5.85920i	−0.144890	−	0.214809i
$745$	−9.33489	+	4.55293i	−0.342004	+	0.166806i
$746$	−13.4660	−	1.89252i	−0.493024	−	0.0692900i
$747$	42.9360	+	117.966i	1.57095	+	4.31614i
$748$	−2.35916	+	9.42183i	−0.0862593	+	0.344496i
$749$	−10.6608	+	6.15502i	−0.389538	+	0.224900i
$750$	−9.09779	−	14.5595i	−0.332204	−	0.531638i
$751$	0.722419	−	10.3311i	0.0263614	−	0.376986i	−0.966413	−	0.256993i	$-0.917268\pi$
$751$	0.722419	−	10.3311i	0.0263614	−	0.376986i	0.992775	−	0.119993i	$-0.0382873\pi$
$752$	0.459251	−	4.36948i	0.0167472	−	0.159339i
$753$	17.7826	−	83.6607i	0.648035	−	3.04877i
$754$	−4.43888	−	5.68150i	−0.161654	−	0.206908i
$755$	−7.19205	+	14.7459i	−0.261746	+	0.536658i
$756$	27.2244	+	55.8184i	0.990143	+	2.03009i
$757$	−18.5468	+	23.7388i	−0.674095	+	0.862802i	−0.996482	−	0.0838061i	$-0.973292\pi$
$757$	−18.5468	+	23.7388i	−0.674095	+	0.862802i	0.322388	+	0.946608i	$0.395515\pi$
$758$	−6.88658	−	8.20710i	−0.250132	−	0.298095i
$759$	17.8294	+	6.50960i	0.647165	+	0.236283i
$760$	12.1963	−	2.24785i	0.442405	−	0.0815383i
$761$	−12.7566	−	4.14488i	−0.462428	−	0.150252i	0.0685320	−	0.997649i	$-0.478168\pi$
$761$	−12.7566	−	4.14488i	−0.462428	−	0.150252i	−0.530960	+	0.847397i	$0.678168\pi$
$762$	−50.8128	−	12.6691i	−1.84075	−	0.458951i
$763$	16.5728	−	11.1785i	0.599975	−	0.404688i
$764$	−5.70496	+	0.801779i	−0.206398	+	0.0290074i
$765$	27.5059	+	51.7310i	0.994476	+	1.87034i
$766$	−10.3026	+	35.9296i	−0.372250	+	1.29819i
$767$	1.07304	−	0.112781i	0.0387451	−	0.00407227i
$768$	0.658520	+	3.09809i	0.0237623	+	0.111793i
$769$	0.618087	−	0.736607i	0.0222888	−	0.0265627i	−0.754785	−	0.655972i	$-0.772259\pi$
$769$	0.618087	−	0.736607i	0.0222888	−	0.0265627i	0.777074	+	0.629410i	$0.216703\pi$
$770$	−30.7411	+	34.0727i	−1.10783	+	1.22790i
$771$	−6.82680	−	11.8244i	−0.245861	−	0.425844i
$772$	7.53118	+	8.36422i	0.271053	+	0.301035i
$773$	−8.49370	−	5.72907i	−0.305497	−	0.206060i	0.396871	−	0.917874i	$-0.370096\pi$
$773$	−8.49370	−	5.72907i	−0.305497	−	0.206060i	−0.702368	+	0.711814i	$0.747874\pi$
$774$	36.1500	+	17.6315i	1.29938	+	0.633752i
$775$	−0.961098	−	6.83856i	−0.0345236	−	0.245648i
$776$	−1.36570	−	0.0476914i	−0.0490259	−	0.00171202i
$777$	−9.42147	−	134.733i	−0.337993	−	4.83353i
$778$	−9.51462	+	6.91277i	−0.341116	+	0.247835i
$779$	1.97464	−	0.815612i	0.0707486	−	0.0292223i
$780$		−	8.09101i		−	0.289705i
$781$	−1.82100	−	53.6887i	−0.0651604	−	1.92113i
$782$	1.80975	−	4.97224i	0.0647164	−	0.177807i
$783$	−48.1419	+	90.5418i	−1.72045	+	3.23570i
$784$	11.9778	+	11.5668i	0.427777	+	0.413100i
$785$	54.0696	+	15.5042i	1.92983	+	0.553369i
$786$	47.3400	+	10.0624i	1.68856	+	0.358915i
$787$	6.50675	−	7.22648i	0.231941	−	0.257596i	−0.615928	−	0.787802i	$-0.711219\pi$
$787$	6.50675	−	7.22648i	0.231941	−	0.257596i	0.847869	+	0.530206i	$0.177886\pi$
$788$	−15.5780	+	3.88404i	−0.554945	+	0.138363i
$789$	80.5021	+	5.62926i	2.86595	+	0.200407i
$790$	9.80731	−	2.08461i	0.348929	−	0.0741670i
$791$	8.93834	−	15.4817i	0.317811	−	0.550464i
$792$	−22.1732	−	7.22909i	−0.787892	−	0.256875i
$793$	−6.42238	+	1.13244i	−0.228066	+	0.0402141i
$794$	31.3853	+	16.6879i	1.11382	+	0.592230i
$795$	14.9141	−	4.27656i	0.528950	−	0.151674i
$796$	8.32191	−	0.581925i	0.294962	−	0.0206258i
$797$	15.6334	−	5.07962i	0.553765	−	0.179929i	−0.0187487	−	0.999824i	$-0.505968\pi$
$797$	15.6334	−	5.07962i	0.553765	−	0.179929i	0.572514	+	0.819895i	$0.305968\pi$
$798$	62.4452	+	24.6698i	2.21054	+	0.873303i
$799$	7.56271	−	10.4092i	0.267550	−	0.368250i
$800$	−0.748709	+	3.00291i	−0.0264709	+	0.106169i
$801$	11.9463	+	9.33349i	0.422102	+	0.329783i
$802$	−17.2680	−	3.04481i	−0.609753	−	0.107516i
$803$	23.6313	−	3.29702i	0.833929	−	0.116349i
$804$	−9.38711	+	3.41663i	−0.331058	+	0.120495i
$805$	18.5791	−	16.7287i	0.654828	−	0.589610i
$806$	−0.814885	+	1.83026i	−0.0287031	+	0.0644682i
$807$	−17.4180	−	69.8596i	−0.613141	−	2.45918i
$808$	7.79994	+	3.15138i	0.274401	+	0.110865i
$809$	33.5491	+	30.2078i	1.17952	+	1.06205i	0.996885	+	0.0788688i	$0.0251308\pi$
$809$	33.5491	+	30.2078i	1.17952	+	1.06205i	0.182640	+	0.983180i	$0.441536\pi$
$810$	−50.2968	+	22.3936i	−1.76725	+	0.786829i
$811$	−19.8513	+	29.4308i	−0.697075	+	1.03346i	0.299765	+	0.954013i	$0.403092\pi$
$811$	−19.8513	+	29.4308i	−0.697075	+	1.03346i	−0.996839	+	0.0794427i	$0.974686\pi$
$812$	−5.43504	+	38.6723i	−0.190732	+	1.35713i
$813$	−0.783742	+	4.44482i	−0.0274870	+	0.155887i
$814$	22.2589	+	18.7155i	0.780174	+	0.655977i
$815$	−25.1153	+	21.0743i	−0.879752	+	0.738199i
$816$	−2.86626	+	8.82145i	−0.100339	+	0.308812i
$817$	23.9123	−	7.05720i	0.836587	−	0.246900i
$818$	−8.73488	−	6.34626i	−0.305408	−	0.221892i
$819$	16.2709	−	26.0389i	0.568552	−	0.909873i
$820$	−0.0486675	+	1.39365i	−0.00169954	+	0.0486685i
$821$	−7.28772	−	7.54665i	−0.254343	−	0.263380i	0.580011	−	0.814608i	$-0.303048\pi$
$821$	−7.28772	−	7.54665i	−0.254343	−	0.263380i	−0.834354	+	0.551228i	$0.814159\pi$
$822$	9.79682	−	10.1449i	0.341703	−	0.353844i
$823$	0.727086	+	20.8210i	0.0253446	+	0.725775i	0.943852	+	0.330370i	$0.107173\pi$
$823$	0.727086	+	20.8210i	0.0253446	+	0.725775i	−0.918507	+	0.395405i	$0.870604\pi$
$824$	−13.5816	−	7.84136i	−0.473139	−	0.273167i
$825$	−23.3635	−	22.6071i	−0.813412	−	0.787080i
$826$	−4.47682	−	3.75650i	−0.155769	−	0.130705i
$827$	15.1759	−	9.48294i	0.527717	−	0.329754i	−0.239758	−	0.970833i	$-0.577068\pi$
$827$	15.1759	−	9.48294i	0.527717	−	0.329754i	0.767475	+	0.641078i	$0.221513\pi$
$828$	11.6070	+	5.16778i	0.403372	+	0.179593i
$829$	8.04764	+	18.0753i	0.279506	+	0.627781i	0.997680	−	0.0680831i	$-0.0216883\pi$
$829$	8.04764	+	18.0753i	0.279506	+	0.627781i	−0.718174	+	0.695864i	$0.755022\pi$
$830$	−40.0256	+	31.2714i	−1.38931	+	1.08545i
$831$	−65.9109	+	35.0455i	−2.28643	+	1.21571i
$832$	0.645867	−	0.623706i	0.0223914	−	0.0216231i
$833$	13.4407	+	46.8734i	0.465694	+	1.62407i
$834$	−10.6962	−	26.4741i	−0.370380	−	0.916722i
$835$	−31.0581			−1.07481
$836$	−13.1671	+	5.96883i	−0.455394	+	0.206436i
$837$	28.4948			0.984926
$838$	1.37052	+	3.39217i	0.0473440	+	0.117180i
$839$	−6.83726	−	23.8444i	−0.236049	−	0.823199i	−0.986707	−	0.162509i	$-0.948041\pi$
$839$	−6.83726	−	23.8444i	−0.236049	−	0.823199i	0.750659	−	0.660690i	$-0.229736\pi$
$840$	−31.5249	+	30.4432i	−1.08771	+	1.05039i
$841$	−31.3295	+	16.6582i	−1.08033	+	0.574421i
$842$	18.3191	−	14.3125i	0.631319	−	0.493240i
$843$	4.28834	+	9.63177i	0.147698	+	0.331736i
$844$	−3.51067	−	1.56305i	−0.120842	−	0.0538024i
$845$	29.4215	−	18.3846i	1.01213	−	0.632450i
$846$	23.6667	+	19.8587i	0.813678	+	0.682757i
$847$	25.2092	−	47.1834i	0.866200	−	1.62124i
$848$	1.49105	+	0.860860i	0.0512030	+	0.0295621i
$849$	−0.774179	−	22.1696i	−0.0265697	−	0.760858i
$850$	−6.29583	+	6.51952i	−0.215945	+	0.223618i
$851$	−11.0056	−	11.3966i	−0.377266	−	0.390671i
$852$	1.79038	−	51.2698i	0.0613374	−	1.75647i
$853$	−9.08613	+	14.5408i	−0.311103	+	0.497869i	−0.966241	−	0.257640i	$-0.917055\pi$
$853$	−9.08613	+	14.5408i	−0.311103	+	0.497869i	0.655138	+	0.755509i	$0.272611\pi$
$854$	28.5771	+	20.7625i	0.977889	+	0.710478i
$855$	−34.8533	+	79.9389i	−1.19196	+	2.73385i
$856$	0.782198	−	2.40736i	0.0267350	−	0.0822818i
$857$	−5.47595	+	4.59487i	−0.187055	+	0.156958i	−0.731506	−	0.681835i	$-0.761182\pi$
$857$	−5.47595	+	4.59487i	−0.187055	+	0.156958i	0.544451	+	0.838792i	$0.316738\pi$
$858$	2.27259	+	9.15393i	0.0775850	+	0.312510i
$859$	−1.04524	+	5.92785i	−0.0356631	+	0.202256i	−0.997433	−	0.0716024i	$-0.977189\pi$
$859$	−1.04524	+	5.92785i	−0.0356631	+	0.202256i	0.961770	+	0.273858i	$0.0882998\pi$
$860$	−2.26485	+	16.1152i	−0.0772307	+	0.549525i
$861$	−4.22175	+	6.25900i	−0.143877	+	0.213306i
$862$	0.587858	−	0.261731i	0.0200225	−	0.00891460i
$863$	26.7857	+	24.1180i	0.911797	+	0.820985i	0.984322	−	0.176381i	$-0.0564391\pi$
$863$	26.7857	+	24.1180i	0.911797	+	0.820985i	−0.0725253	+	0.997367i	$0.523106\pi$
$864$	−11.8402	−	4.78374i	−0.402811	−	0.162746i
$865$	−3.47857	−	13.9518i	−0.118275	−	0.474375i
$866$	15.7715	−	35.4233i	0.535937	−	1.20373i
$867$	19.8280	−	17.8532i	0.673395	−	0.606327i
$868$	10.1973	−	3.71151i	0.346119	−	0.125977i
$869$	−10.5102	+	5.11313i	−0.356533	+	0.173451i
$870$	−71.2636	−	12.5657i	−2.41606	−	0.426017i
$871$	2.23150	+	1.74344i	0.0756115	+	0.0590742i
$872$	−0.994423	+	3.98841i	−0.0336754	+	0.135065i
$873$	5.64817	−	7.77405i	0.191162	−	0.263112i
$874$	7.47138	−	2.49160i	0.252723	−	0.0842795i
$875$	25.0708	−	8.14599i	0.847547	−	0.275385i
$876$	22.7304	−	1.58947i	0.767990	−	0.0537031i
$877$	−25.2671	+	7.24523i	−0.853210	+	0.244654i	−0.673611	−	0.739086i	$-0.735258\pi$
$877$	−25.2671	+	7.24523i	−0.853210	+	0.244654i	−0.179599	+	0.983740i	$0.557480\pi$
$878$	21.9272	+	11.6589i	0.740009	+	0.393470i
$879$	11.7467	−	2.07126i	0.396207	−	0.0698620i
$880$	0.00945389	−	9.43627i	0.000318691	−	0.318096i
$881$	11.1521	−	19.3160i	0.375725	−	0.650774i	−0.614711	−	0.788753i	$-0.710727\pi$
$881$	11.1521	−	19.3160i	0.375725	−	0.650774i	0.990435	+	0.137979i	$0.0440605\pi$
$882$	−114.529	+	24.3438i	−3.85638	+	0.819699i
$883$	−5.13457	−	0.359044i	−0.172792	−	0.0120828i	−0.0169017	−	0.999857i	$-0.505380\pi$
$883$	−5.13457	−	0.359044i	−0.172792	−	0.0120828i	−0.155890	+	0.987774i	$0.549825\pi$
$884$	2.55127	−	0.636103i	0.0858085	−	0.0213945i
$885$	7.24596	−	8.04745i	0.243570	−	0.270512i
$886$	−24.0085	−	5.10316i	−0.806580	−	0.171444i
$887$	−13.7795	−	3.95121i	−0.462671	−	0.132669i	0.0362011	−	0.999345i	$-0.488474\pi$
$887$	−13.7795	−	3.95121i	−0.462671	−	0.132669i	−0.498872	+	0.866676i	$0.666252\pi$
$888$	19.9776	+	19.2921i	0.670404	+	0.647402i
$889$	37.7497	−	70.9968i	1.26608	−	2.38116i
$890$	−2.09792	+	5.76400i	−0.0703226	+	0.193210i
$891$	50.6144	−	39.4627i	1.69564	−	1.32205i
$892$		−	14.7197i		−	0.492851i
$893$	19.1336	−	0.816256i	0.640283	−	0.0273150i
$894$	9.35389	−	6.79600i	0.312841	−	0.227292i
$895$	2.73798	+	39.1549i	0.0915206	+	1.30881i
$896$	−4.86027	−	0.169724i	−0.162370	−	0.00567009i
$897$	−0.715116	−	5.08832i	−0.0238770	−	0.169894i
$898$	9.71634	+	4.73898i	0.324239	+	0.158142i
$899$	14.8549	+	10.0198i	0.495440	+	0.334178i
$900$	−14.5619	−	16.1726i	−0.485395	−	0.539086i
$901$	2.52102	+	4.36654i	0.0839874	+	0.145470i
$902$	−0.336387	−	1.59041i	−0.0112004	−	0.0529548i
$903$	−56.6321	+	67.4915i	−1.88460	+	2.24598i
$904$	0.764259	+	3.59556i	0.0254189	+	0.119586i
$905$	14.4899	−	1.52295i	0.481660	−	0.0506245i
$906$	5.03425	−	17.5565i	0.167252	−	0.583276i
$907$	−9.02896	−	16.9810i	−0.299802	−	0.563845i	0.686829	−	0.726819i	$-0.259002\pi$
$907$	−9.02896	−	16.9810i	−0.299802	−	0.563845i	−0.986630	+	0.162975i	$0.947891\pi$
$908$	20.3287	−	2.85701i	0.674632	−	0.0948133i
$909$	−49.0419	+	33.0792i	−1.62662	+	1.09717i
$910$	12.0543	+	3.00548i	0.399596	+	0.0996306i
$911$	17.3443	+	5.63550i	0.574642	+	0.186712i	0.581899	−	0.813261i	$-0.302310\pi$
$911$	17.3443	+	5.63550i	0.574642	+	0.186712i	−0.00725705	+	0.999974i	$0.502310\pi$
$912$	−12.9365	+	4.82204i	−0.428370	+	0.159674i
$913$	36.5003	−	46.6219i	1.20798	−	1.54296i
$914$	8.86896	+	10.5696i	0.293359	+	0.349612i
$915$	−40.2969	+	51.5777i	−1.33218	+	1.70511i
$916$	5.18835	+	10.6377i	0.171428	+	0.351479i
$917$	−32.5762	+	66.7912i	−1.07576	+	2.20564i
$918$	−23.0238	−	29.4691i	−0.759899	−	0.972627i
$919$	−5.42723	+	25.5331i	−0.179028	+	0.842260i	0.793335	+	0.608785i	$0.208343\pi$
$919$	−5.42723	+	25.5331i	−0.179028	+	0.842260i	−0.972363	+	0.233474i	$0.924990\pi$
$920$	−0.537355	+	5.11259i	−0.0177161	+	0.168557i
$921$	5.84590	−	83.6002i	0.192629	−	2.75472i
$922$	8.96364	+	14.3448i	0.295202	+	0.472422i
$923$	−12.5943	+	7.27134i	−0.414548	+	0.239339i
$924$	27.1154	−	43.2972i	0.892033	−	1.42437i
$925$	9.28130	+	25.5002i	0.305167	+	0.838440i
$926$	9.98012	+	1.40261i	0.327967	+	0.0460928i
$927$	99.1174	−	48.3428i	3.25544	−	1.58779i
$928$	−4.49039	−	6.65727i	−0.147404	−	0.218536i
$929$	24.5871	+	15.3637i	0.806677	+	0.504068i	0.869486	−	0.493958i	$-0.164450\pi$
$929$	24.5871	+	15.3637i	0.806677	+	0.504068i	−0.0628085	+	0.998026i	$0.520006\pi$
$930$	6.21371	+	19.1238i	0.203755	+	0.627095i
$931$	−42.2065	+	59.0466i	−1.38326	+	1.93517i
$932$	4.58213	+	6.30676i	0.150093	+	0.206585i
$933$	−15.5297	+	6.27439i	−0.508419	+	0.205414i
$934$	−10.6137	−	3.86307i	−0.347290	−	0.126403i
$935$	13.8410	−	23.9179i	0.452648	−	0.782199i
$936$	1.09635	+	6.21768i	0.0358352	+	0.203231i
$937$	−10.0700	+	0.351652i	−0.328973	+	0.0114880i	−0.198910	−	0.980018i	$-0.563740\pi$
$937$	−10.0700	+	0.351652i	−0.328973	+	0.0114880i	−0.130063	+	0.991506i	$0.541518\pi$
$938$	−1.60330	−	15.2544i	−0.0523497	−	0.498074i
$939$	2.56753	+	0.269858i	0.0837882	+	0.00880650i
$940$	−4.68268	+	11.5901i	−0.152732	+	0.378026i
$941$	15.0575	−	37.2685i	0.490859	−	1.21492i	−0.455044	−	0.890469i	$-0.650376\pi$
$941$	15.0575	−	37.2685i	0.490859	−	1.21492i	0.945903	−	0.324450i	$-0.105179\pi$
$942$	−62.2747	−	6.54533i	−2.02902	−	0.213259i
$943$	0.0925705	+	0.880749i	0.00301451	+	0.0286811i
$944$	1.20095	−	0.0419382i	0.0390877	−	0.00136497i
$945$	−30.6825	−	174.009i	−0.998103	−	5.66052i
$946$	−1.96404	−	18.8684i	−0.0638566	−	0.613466i
$947$	18.5548	+	6.75338i	0.602949	+	0.219455i	0.625415	−	0.780292i	$-0.284930\pi$
$947$	18.5548	+	6.75338i	0.602949	+	0.219455i	−0.0224665	+	0.999748i	$0.507152\pi$
$948$	−10.3490	+	4.18126i	−0.336119	+	0.135801i
$949$	−3.79668	−	5.22568i	−0.123246	−	0.169633i
$950$	−13.4267	−	1.30637i	−0.435619	−	0.0423843i
$951$	23.3525	+	71.8716i	0.757257	+	2.33060i
$952$	−12.0778	−	7.54707i	−0.391445	−	0.244602i
$953$	33.2575	+	49.3063i	1.07732	+	1.59719i	0.761259	+	0.648448i	$0.224582\pi$
$953$	33.2575	+	49.3063i	1.07732	+	1.59719i	0.316058	+	0.948740i	$0.397641\pi$
$954$	−10.8816	+	5.30729i	−0.352303	+	0.171830i
$955$	16.2314	+	2.28118i	0.525236	+	0.0738172i
$956$	−3.58178	−	9.84086i	−0.115843	−	0.318276i
$957$	84.1549	−	5.79997i	2.72034	−	0.187486i
$958$	11.8222	−	6.82554i	0.381958	−	0.220523i
$959$	11.4752	+	18.3641i	0.370552	+	0.593007i
$960$	0.628606	−	8.98949i	0.0202882	−	0.290134i
$961$	−2.71993	+	25.8784i	−0.0877396	+	0.834786i
$962$	1.63684	−	7.70074i	0.0527739	−	0.248282i
$963$	10.9583	+	14.0260i	0.353127	+	0.451983i
$964$	−6.71114	+	13.7599i	−0.216151	+	0.443176i
$965$	−14.0378	−	28.7817i	−0.451892	−	0.926515i
$966$	−17.1348	+	21.9316i	−0.551304	+	0.705637i
$967$	37.6097	+	44.8215i	1.20945	+	1.44136i	0.864422	+	0.502767i	$0.167685\pi$
$967$	37.6097	+	44.8215i	1.20945	+	1.44136i	0.345023	+	0.938594i	$0.387871\pi$
$968$	2.63975	+	10.6786i	0.0848448	+	0.343222i
$969$	−39.8695	−	6.71278i	−1.28079	−	0.215646i
$970$	3.69770	+	1.20146i	0.118726	+	0.0385764i
$971$	35.0457	+	8.73788i	1.12467	+	0.280412i	0.759486	−	0.650523i	$-0.225450\pi$
$971$	35.0457	+	8.73788i	1.12467	+	0.280412i	0.365185	+	0.930935i	$0.381006\pi$
$972$	19.0519	−	12.8507i	0.611091	−	0.412186i
$973$	43.4153	−	6.10162i	1.39183	−	0.195609i
$974$	−4.67897	−	8.79987i	−0.149924	−	0.281966i
$975$	−2.42591	+	8.46016i	−0.0776913	+	0.270942i
$976$	−7.22354	+	0.759225i	−0.231220	+	0.0243022i
$977$	5.70477	+	26.8388i	0.182512	+	0.858650i	0.970149	+	0.242511i	$0.0779710\pi$
$977$	5.70477	+	26.8388i	0.182512	+	0.858650i	−0.787637	+	0.616140i	$0.788696\pi$
$978$	23.4606	−	27.9592i	0.750186	−	0.894037i
$979$	0.754544	−	7.11047i	0.0241153	−	0.227252i
$980$	−23.6873	−	41.0276i	−0.756663	−	1.31058i
$981$	−19.3408	−	21.4802i	−0.617505	−	0.685809i
$982$	−20.9064	−	14.1015i	−0.667149	−	0.449998i
$983$	−52.6752	−	25.6914i	−1.68008	−	0.819429i	−0.995934	−	0.0900812i	$-0.971287\pi$
$983$	−52.6752	−	25.6914i	−1.68008	−	0.819429i	−0.684143	−	0.729347i	$-0.739824\pi$
$984$	−0.216053	−	1.53730i	−0.00688752	−	0.0490073i
$985$	45.6508	+	1.59416i	1.45456	+	0.0507942i
$986$	−1.64040	−	23.4588i	−0.0522410	−	0.747082i
$987$	−54.7505	+	39.7786i	−1.74273	+	1.26617i
$988$	3.10255	+	2.38560i	0.0987054	+	0.0758960i
$989$			10.3348i			0.328628i
$990$	54.9729	+	37.1599i	1.74715	+	1.18102i
$991$	−3.00266	+	8.24975i	−0.0953828	+	0.262062i	−0.978204	−	0.207648i	$-0.933419\pi$
$991$	−3.00266	+	8.24975i	−0.0953828	+	0.262062i	0.882821	+	0.469710i	$0.155641\pi$
$992$	−1.04757	+	1.97020i	−0.0332604	+	0.0625538i
$993$	−32.1606	−	31.0571i	−1.02058	−	0.985567i
$994$	75.7186	+	21.7120i	2.40165	+	0.688662i
$995$	−23.2162	−	4.93475i	−0.736003	−	0.156442i
$996$	37.8358	−	42.0209i	1.19887	−	1.33148i
$997$	4.55219	−	1.13499i	0.144169	−	0.0359455i	−0.169169	−	0.985587i	$-0.554108\pi$
$997$	4.55219	−	1.13499i	0.144169	−	0.0359455i	0.313338	+	0.949642i	$0.398553\pi$
$998$	18.0729	+	1.26378i	0.572087	+	0.0400042i
$999$	−109.526	+	23.2804i	−3.46523	+	0.736558i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.13.1	yes	240
11.6	odd	10		418.2.v.a.127.10	yes	240
19.3	odd	18		418.2.v.a.79.10	✓	240
209.193	even	90	inner	418.2.v.b.193.1	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.79.10	✓	240	19.3	odd	18
418.2.v.a.127.10	yes	240	11.6	odd	10
418.2.v.b.13.1	yes	240	1.1	even	1	trivial
418.2.v.b.193.1	yes	240	209.193	even	90	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.873028 - 3.04461i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.51211 - 1.33571i) q^{5} +(-2.49587 + 1.94999i) q^{6} +(-1.97806 - 4.44279i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-5.96333 + 3.72630i) q^{9} +O(q^{10})\)	\(q+(-0.374607 - 0.927184i) q^{2} +(-0.873028 - 3.04461i) q^{3} +(-0.719340 + 0.694658i) q^{4} +(2.51211 - 1.33571i) q^{5} +(-2.49587 + 1.94999i) q^{6} +(-1.97806 - 4.44279i) q^{7} +(0.913545 + 0.406737i) q^{8} +(-5.96333 + 3.72630i) q^{9} +(-2.17951 - 1.82882i) q^{10} +(2.97950 + 1.45690i) q^{11} +(2.74297 + 1.58365i) q^{12} +(-0.0313349 - 0.897314i) q^{13} +(-3.37829 + 3.49832i) q^{14} +(-6.25987 - 6.48229i) q^{15} +(0.0348995 - 0.999391i) q^{16} +(1.55186 - 2.48350i) q^{17} +(5.68887 + 4.13320i) q^{18} +(4.33137 - 0.489118i) q^{19} +(-0.879197 + 2.70589i) q^{20} +(-11.7997 + 9.90108i) q^{21} +(0.234671 - 3.30831i) q^{22} +(-0.313757 + 1.77940i) q^{23} +(0.440804 - 3.13648i) q^{24} +(1.73061 - 2.56574i) q^{25} +(-0.820236 + 0.365193i) q^{26} +(9.48998 + 8.54482i) q^{27} +(4.50911 + 1.82180i) q^{28} +(1.94266 + 7.79159i) q^{29} +(-3.66528 + 8.23236i) q^{30} +(1.65824 - 1.49309i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(1.83450 - 10.3433i) q^{33} +(-2.88400 - 0.508527i) q^{34} +(-10.9034 - 8.51866i) q^{35} +(1.70115 - 6.82295i) q^{36} +(-5.15392 + 7.09376i) q^{37} +(-2.07606 - 3.83275i) q^{38} +(-2.70461 + 0.878782i) q^{39} +(2.83821 - 0.198467i) q^{40} +(0.471148 - 0.135099i) q^{41} +(13.6004 + 7.23143i) q^{42} +(5.63289 - 0.993231i) q^{43} +(-3.15532 + 1.02173i) q^{44} +(-10.0033 + 17.3262i) q^{45} +(1.76737 - 0.375666i) q^{46} +(4.38285 + 0.306478i) q^{47} +(-3.07322 + 0.766241i) q^{48} +(-11.1417 + 12.3741i) q^{49} +(-3.02721 - 0.643453i) q^{50} +(-8.91611 - 2.55665i) q^{51} +(0.645867 + 0.623706i) q^{52} +(-0.808299 + 1.52019i) q^{53} +(4.36761 - 11.9999i) q^{54} +(9.43085 - 0.319873i) q^{55} -4.86323i q^{56} +(-5.27058 - 12.7603i) q^{57} +(6.49651 - 4.71999i) q^{58} +(0.0838253 + 1.19876i) q^{59} +(9.00595 + 0.314495i) q^{60} +(-1.01086 - 7.19265i) q^{61} +(-2.00555 - 0.978174i) q^{62} +(28.3509 + 19.1230i) q^{63} +(0.669131 + 0.743145i) q^{64} +(-1.27727 - 2.21230i) q^{65} +(-10.2774 + 2.17377i) q^{66} +(-2.02733 + 2.41607i) q^{67} +(0.608867 + 2.86449i) q^{68} +(5.69150 - 0.598201i) q^{69} +(-3.81388 + 13.3006i) q^{70} +(-7.60405 - 14.3011i) q^{71} +(-6.96339 + 0.978641i) q^{72} +(5.96418 - 4.02289i) q^{73} +(8.50792 + 2.12126i) q^{74} +(-9.32254 - 3.02908i) q^{75} +(-2.77596 + 3.36066i) q^{76} +(0.579062 - 16.1191i) q^{77} +(1.82796 + 2.17848i) q^{78} +(-2.16962 + 2.77699i) q^{79} +(-1.24723 - 2.55720i) q^{80} +(8.48296 - 17.3927i) q^{81} +(-0.301757 - 0.386231i) q^{82} +(3.71177 - 17.4625i) q^{83} +(1.61009 - 15.3190i) q^{84} +(0.581209 - 8.31167i) q^{85} +(-3.03103 - 4.85066i) q^{86} +(22.0264 - 12.7169i) q^{87} +(2.12934 + 2.54282i) q^{88} +(-0.737370 - 2.02591i) q^{89} +(19.8118 + 2.78437i) q^{90} +(-3.92459 + 1.91415i) q^{91} +(-1.01038 - 1.49795i) q^{92} +(-5.99356 - 3.74519i) q^{93} +(-1.35768 - 4.17851i) q^{94} +(10.2276 - 7.01419i) q^{95} +(1.86170 + 2.56240i) q^{96} +(-1.26703 + 0.511914i) q^{97} +(15.6469 + 5.69499i) q^{98} +(-23.1966 + 2.41457i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

Varieties

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