LMFDB - Embedded newform 171.2.x.a.14.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,2,Mod(14,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([15, 7]))

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

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

chi := DirichletCharacter("171.14");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.x (of order $18$, 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			14.12
Character	$\chi$	$=$	171.14
Dual form			171.2.x.a.110.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.469442 + 0.393909i) q^{2} +(1.72885 + 0.105209i) q^{3} +(-0.282084 - 1.59978i) q^{4} +(-0.821139 - 2.25606i) q^{5} +(0.770154 + 0.730400i) q^{6} +(-0.676894 + 1.17241i) q^{7} +(1.11056 - 1.92354i) q^{8} +(2.97786 + 0.363781i) q^{9} +O(q^{10})$	\(q+(0.469442 + 0.393909i) q^{2} +(1.72885 + 0.105209i) q^{3} +(-0.282084 - 1.59978i) q^{4} +(-0.821139 - 2.25606i) q^{5} +(0.770154 + 0.730400i) q^{6} +(-0.676894 + 1.17241i) q^{7} +(1.11056 - 1.92354i) q^{8} +(2.97786 + 0.363781i) q^{9} +(0.503205 - 1.38254i) q^{10} -0.212949i q^{11} +(-0.319372 - 2.79546i) q^{12} +(-2.01801 + 5.54444i) q^{13} +(-0.779587 + 0.283747i) q^{14} +(-1.18227 - 3.98679i) q^{15} +(-1.77394 + 0.645662i) q^{16} +(0.897444 + 2.46571i) q^{17} +(1.25464 + 1.34378i) q^{18} +(-0.154798 + 4.35615i) q^{19} +(-3.37757 + 1.95004i) q^{20} +(-1.29360 + 1.95572i) q^{21} +(0.0838824 - 0.0999672i) q^{22} +(1.61574 - 0.284898i) q^{23} +(2.12237 - 3.20868i) q^{24} +(-0.585319 + 0.491141i) q^{25} +(-3.13134 + 1.80788i) q^{26} +(5.11001 + 0.942220i) q^{27} +(2.06655 + 0.752162i) q^{28} +(-0.914202 - 5.18470i) q^{29} +(1.01542 - 2.33727i) q^{30} +3.57339i q^{31} +(-5.26143 - 1.91500i) q^{32} +(0.0224041 - 0.368157i) q^{33} +(-0.549965 + 1.51102i) q^{34} +(3.20086 + 0.564398i) q^{35} +(-0.258040 - 4.86654i) q^{36} -8.01979i q^{37} +(-1.78859 + 1.98398i) q^{38} +(-4.07217 + 9.37321i) q^{39} +(-5.25156 - 0.925991i) q^{40} +(-6.91883 - 5.80559i) q^{41} +(-1.37764 + 0.408537i) q^{42} +(-0.233045 + 1.32166i) q^{43} +(-0.340671 + 0.0600696i) q^{44} +(-1.62453 - 7.01695i) q^{45} +(0.870720 + 0.502711i) q^{46} +(2.80328 - 0.494293i) q^{47} +(-3.13481 + 0.929620i) q^{48} +(2.58363 + 4.47498i) q^{49} -0.468238 q^{50} +(1.29213 + 4.35726i) q^{51} +(9.43914 + 1.66438i) q^{52} +(-7.65410 + 6.42256i) q^{53} +(2.02771 + 2.45520i) q^{54} +(-0.480426 + 0.174861i) q^{55} +(1.50346 + 2.60407i) q^{56} +(-0.725928 + 7.51485i) q^{57} +(1.61313 - 2.79403i) q^{58} +(1.30385 - 7.39448i) q^{59} +(-6.04448 + 3.01599i) q^{60} +(-4.70028 - 1.71076i) q^{61} +(-1.40759 + 1.67750i) q^{62} +(-2.44220 + 3.24505i) q^{63} +(0.172188 + 0.298239i) q^{64} +14.1657 q^{65} +(0.155538 - 0.164003i) q^{66} +(-6.37567 - 7.59823i) q^{67} +(3.69143 - 2.13125i) q^{68} +(2.82335 - 0.322558i) q^{69} +(1.28030 + 1.52580i) q^{70} +(-7.93377 - 6.65722i) q^{71} +(4.00684 - 5.32405i) q^{72} +(-1.33247 + 7.55679i) q^{73} +(3.15906 - 3.76483i) q^{74} +(-1.06360 + 0.787530i) q^{75} +(7.01255 - 0.981159i) q^{76} +(0.249664 + 0.144144i) q^{77} +(-5.60384 + 2.79612i) q^{78} +(-1.92202 - 5.28069i) q^{79} +(2.91331 + 3.47194i) q^{80} +(8.73533 + 2.16658i) q^{81} +(-0.961119 - 5.45078i) q^{82} +(14.1234 + 8.15413i) q^{83} +(3.49362 + 1.51780i) q^{84} +(4.82586 - 4.04937i) q^{85} +(-0.630016 + 0.528646i) q^{86} +(-1.03505 - 9.05976i) q^{87} +(-0.409617 - 0.236492i) q^{88} +(-0.680140 - 3.85727i) q^{89} +(2.00142 - 3.93397i) q^{90} +(-5.13440 - 6.11895i) q^{91} +(-0.911550 - 2.50446i) q^{92} +(-0.375951 + 6.17786i) q^{93} +(1.51068 + 0.872193i) q^{94} +(9.95485 - 3.22777i) q^{95} +(-8.89476 - 3.86431i) q^{96} +(4.16363 - 4.96202i) q^{97} +(-0.549868 + 3.11846i) q^{98} +(0.0774666 - 0.634132i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) $ 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{18}\right)$

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 $

$2$	0.469442	+	0.393909i	0.331946	+	0.278536i	0.793492	−	0.608580i	$-0.208261\pi$
$2$	0.469442	+	0.393909i	0.331946	+	0.278536i	−0.461546	+	0.887116i	$0.652705\pi$
$3$	1.72885	+	0.105209i	0.998153	+	0.0607422i
$3$	1.72885	+	0.105209i	0.998153	+	0.0607422i
$4$	−0.282084	−	1.59978i	−0.141042	−	0.799890i
$5$	−0.821139	−	2.25606i	−0.367225	−	1.00894i	−0.976412	−	0.215915i	$-0.930727\pi$
$5$	−0.821139	−	2.25606i	−0.367225	−	1.00894i	0.609188	−	0.793026i	$-0.291496\pi$
$6$	0.770154	+	0.730400i	0.314414	+	0.298184i
$7$	−0.676894	+	1.17241i	−0.255842	+	0.443131i	−0.965124	−	0.261794i	$-0.915686\pi$
$7$	−0.676894	+	1.17241i	−0.255842	+	0.443131i	0.709282	+	0.704925i	$0.249019\pi$
$8$	1.11056	−	1.92354i	0.392642	−	0.680076i
$9$	2.97786	+	0.363781i	0.992621	+	0.121260i
$10$	0.503205	−	1.38254i	0.159127	−	0.437199i
$11$		−	0.212949i		−	0.0642065i	−0.999485	−	0.0321032i	$-0.989779\pi$
$11$		−	0.212949i		−	0.0642065i	0.999485	−	0.0321032i	$-0.0102205\pi$
$12$	−0.319372	−	2.79546i	−0.0921947	−	0.806980i
$13$	−2.01801	+	5.54444i	−0.559696	+	1.53775i	0.260386	+	0.965505i	$0.416150\pi$
$13$	−2.01801	+	5.54444i	−0.559696	+	1.53775i	−0.820081	+	0.572247i	$0.806072\pi$
$14$	−0.779587	+	0.283747i	−0.208353	+	0.0758344i
$15$	−1.18227	−	3.98679i	−0.305261	−	1.02938i
$16$	−1.77394	+	0.645662i	−0.443485	+	0.161415i
$17$	0.897444	+	2.46571i	0.217662	+	0.598022i	0.999682	−	0.0252323i	$-0.00803255\pi$
$17$	0.897444	+	2.46571i	0.217662	+	0.598022i	−0.782020	+	0.623254i	$0.785810\pi$
$18$	1.25464	+	1.34378i	0.295721	+	0.316732i
$19$	−0.154798	+	4.35615i	−0.0355132	+	0.999369i
$19$	−0.154798	+	4.35615i	−0.0355132	+	0.999369i
$20$	−3.37757	+	1.95004i	−0.755248	+	0.436043i
$21$	−1.29360	+	1.95572i	−0.282286	+	0.426772i
$22$	0.0838824	−	0.0999672i	0.0178838	−	0.0213131i
$23$	1.61574	−	0.284898i	0.336905	−	0.0594054i	−0.00263654	−	0.999997i	$-0.500839\pi$
$23$	1.61574	−	0.284898i	0.336905	−	0.0594054i	0.339541	+	0.940591i	$0.389728\pi$
$24$	2.12237	−	3.20868i	0.433226	−	0.654970i
$25$	−0.585319	+	0.491141i	−0.117064	+	0.0982282i
$26$	−3.13134	+	1.80788i	−0.614107	+	0.354555i
$27$	5.11001	+	0.942220i	0.983422	+	0.181330i
$28$	2.06655	+	0.752162i	0.390541	+	0.142145i
$29$	−0.914202	−	5.18470i	−0.169763	−	0.962774i	−0.944016	−	0.329899i	$-0.892985\pi$
$29$	−0.914202	−	5.18470i	−0.169763	−	0.962774i	0.774253	−	0.632876i	$-0.218126\pi$
$30$	1.01542	−	2.33727i	0.185390	−	0.426726i
$31$			3.57339i			0.641800i	0.947113	+	0.320900i	$0.103985\pi$
$31$			3.57339i			0.641800i	−0.947113	+	0.320900i	$0.896015\pi$
$32$	−5.26143	−	1.91500i	−0.930098	−	0.338528i
$33$	0.0224041	−	0.368157i	0.00390005	−	0.0640879i
$34$	−0.549965	+	1.51102i	−0.0943183	+	0.259137i
$35$	3.20086	+	0.564398i	0.541045	+	0.0954008i
$36$	−0.258040	−	4.86654i	−0.0430066	−	0.811091i
$37$		−	8.01979i		−	1.31844i	−0.751948	−	0.659222i	$-0.770886\pi$
$37$		−	8.01979i		−	1.31844i	0.751948	−	0.659222i	$-0.229114\pi$
$38$	−1.78859	+	1.98398i	−0.290148	+	0.321845i
$39$	−4.07217	+	9.37321i	−0.652069	+	1.50091i
$40$	−5.25156	−	0.925991i	−0.830344	−	0.146412i
$41$	−6.91883	−	5.80559i	−1.08054	−	0.906681i	−0.0845746	−	0.996417i	$-0.526953\pi$
$41$	−6.91883	−	5.80559i	−1.08054	−	0.906681i	−0.995966	+	0.0897363i	$0.971398\pi$
$42$	−1.37764	+	0.408537i	−0.212575	+	0.0630386i
$43$	−0.233045	+	1.32166i	−0.0355390	+	0.201552i	−0.997407	−	0.0719608i	$-0.977074\pi$
$43$	−0.233045	+	1.32166i	−0.0355390	+	0.201552i	0.961868	+	0.273512i	$0.0881855\pi$
$44$	−0.340671	+	0.0600696i	−0.0513582	+	0.00905583i
$45$	−1.62453	−	7.01695i	−0.242170	−	1.04603i
$46$	0.870720	+	0.502711i	0.128381	+	0.0741206i
$47$	2.80328	−	0.494293i	0.408900	−	0.0721000i	0.0345849	−	0.999402i	$-0.488989\pi$
$47$	2.80328	−	0.494293i	0.408900	−	0.0721000i	0.374315	+	0.927302i	$0.377878\pi$
$48$	−3.13481	+	0.929620i	−0.452471	+	0.134179i
$49$	2.58363	+	4.47498i	0.369090	+	0.639282i
$50$	−0.468238			−0.0662189
$51$	1.29213	+	4.35726i	0.180935	+	0.610139i
$52$	9.43914	+	1.66438i	1.30897	+	0.230807i
$53$	−7.65410	+	6.42256i	−1.05137	+	0.882206i	−0.993237	−	0.116103i	$-0.962960\pi$
$53$	−7.65410	+	6.42256i	−1.05137	+	0.882206i	−0.0581349	+	0.998309i	$0.518515\pi$
$54$	2.02771	+	2.45520i	0.275936	+	0.334110i
$55$	−0.480426	+	0.174861i	−0.0647806	+	0.0235782i
$56$	1.50346	+	2.60407i	0.200908	+	0.347984i
$57$	−0.725928	+	7.51485i	−0.0961515	+	0.995367i
$58$	1.61313	−	2.79403i	0.211815	−	0.366874i
$59$	1.30385	−	7.39448i	0.169746	−	0.962679i	−0.774288	−	0.632833i	$-0.781892\pi$
$59$	1.30385	−	7.39448i	0.169746	−	0.962679i	0.944035	−	0.329846i	$-0.106997\pi$
$60$	−6.04448	+	3.01599i	−0.780340	+	0.389362i
$61$	−4.70028	−	1.71076i	−0.601810	−	0.219041i	0.0231061	−	0.999733i	$-0.492644\pi$
$61$	−4.70028	−	1.71076i	−0.601810	−	0.219041i	−0.624916	+	0.780692i	$0.714867\pi$
$62$	−1.40759	+	1.67750i	−0.178764	+	0.213043i
$63$	−2.44220	+	3.24505i	−0.307688	+	0.408838i
$64$	0.172188	+	0.298239i	0.0215235	+	0.0372798i
$65$	14.1657			1.75703
$66$	0.155538	−	0.164003i	0.0191454	−	0.0201874i
$67$	−6.37567	−	7.59823i	−0.778912	−	0.928271i	0.219972	−	0.975506i	$-0.429403\pi$
$67$	−6.37567	−	7.59823i	−0.778912	−	0.928271i	−0.998884	+	0.0472352i	$0.984959\pi$
$68$	3.69143	−	2.13125i	0.447652	−	0.258452i
$69$	2.82335	−	0.322558i	0.339891	−	0.0388314i
$70$	1.28030	+	1.52580i	0.153025	+	0.182368i
$71$	−7.93377	−	6.65722i	−0.941565	−	0.790067i	0.0362918	−	0.999341i	$-0.488445\pi$
$71$	−7.93377	−	6.65722i	−0.941565	−	0.790067i	−0.977857	+	0.209274i	$0.932890\pi$
$72$	4.00684	−	5.32405i	0.472210	−	0.627445i
$73$	−1.33247	+	7.55679i	−0.155953	+	0.884455i	0.801956	+	0.597383i	$0.203793\pi$
$73$	−1.33247	+	7.55679i	−0.155953	+	0.884455i	−0.957909	+	0.287072i	$0.907318\pi$
$74$	3.15906	−	3.76483i	0.367234	−	0.437652i
$75$	−1.06360	+	0.787530i	−0.122814	+	0.0909361i
$76$	7.01255	−	0.981159i	0.804395	−	0.112547i
$77$	0.249664	+	0.144144i	0.0284519	+	0.0164267i
$78$	−5.60384	+	2.79612i	−0.634510	+	0.316598i
$79$	−1.92202	−	5.28069i	−0.216244	−	0.594125i	0.783380	−	0.621543i	$-0.213494\pi$
$79$	−1.92202	−	5.28069i	−0.216244	−	0.594125i	−0.999624	+	0.0274180i	$0.991271\pi$
$80$	2.91331	+	3.47194i	0.325717	+	0.388175i
$81$	8.73533	+	2.16658i	0.970592	+	0.240731i
$82$	−0.961119	−	5.45078i	−0.106138	−	0.601938i
$83$	14.1234	+	8.15413i	1.55024	+	0.895032i	0.998121	+	0.0612667i	$0.0195140\pi$
$83$	14.1234	+	8.15413i	1.55024	+	0.895032i	0.552119	+	0.833765i	$0.313819\pi$
$84$	3.49362	+	1.51780i	0.381185	+	0.165605i
$85$	4.82586	−	4.04937i	0.523438	−	0.439216i
$86$	−0.630016	+	0.528646i	−0.0679363	+	0.0570054i
$87$	−1.03505	−	9.05976i	−0.110969	−	0.971308i
$88$	−0.409617	−	0.236492i	−0.0436653	−	0.0252102i
$89$	−0.680140	−	3.85727i	−0.0720947	−	0.408869i	−0.999402	−	0.0345692i	$-0.988994\pi$
$89$	−0.680140	−	3.85727i	−0.0720947	−	0.408869i	0.927308	−	0.374300i	$-0.122117\pi$
$90$	2.00142	−	3.93397i	0.210968	−	0.414677i
$91$	−5.13440	−	6.11895i	−0.538232	−	0.641440i
$92$	−0.911550	−	2.50446i	−0.0950356	−	0.261108i
$93$	−0.375951	+	6.17786i	−0.0389844	+	0.640615i
$94$	1.51068	+	0.872193i	0.155815	+	0.0899598i
$95$	9.95485	−	3.22777i	1.02135	−	0.331162i
$96$	−8.89476	−	3.86431i	−0.907818	−	0.394399i
$97$	4.16363	−	4.96202i	0.422753	−	0.503817i	−0.512064	−	0.858947i	$-0.671119\pi$
$97$	4.16363	−	4.96202i	0.422753	−	0.503817i	0.934817	+	0.355130i	$0.115563\pi$
$98$	−0.549868	+	3.11846i	−0.0555451	+	0.315012i
$99$	0.0774666	−	0.634132i	0.00778569	−	0.0637327i
$100$	0.950827	+	0.797839i	0.0950827	+	0.0797839i
$101$	0.214724	+	0.255898i	0.0213659	+	0.0254628i	0.776622	−	0.629967i	$-0.216932\pi$
$101$	0.214724	+	0.255898i	0.0213659	+	0.0254628i	−0.755256	+	0.655430i	$0.772487\pi$
$102$	−1.10978	+	2.55447i	−0.109885	+	0.252930i
$103$	10.2900	−	5.94094i	1.01390	−	0.585378i	0.101572	−	0.994828i	$-0.467613\pi$
$103$	10.2900	−	5.94094i	1.01390	−	0.585378i	0.912333	+	0.409450i	$0.134279\pi$
$104$	8.42386	+	10.0392i	0.826027	+	0.984421i
$105$	5.47444	+	1.31252i	0.534251	+	0.128089i
$106$	−6.12306			−0.594724
$107$	9.58046	+	16.5938i	0.926178	+	1.60419i	0.789656	+	0.613550i	$0.210259\pi$
$107$	9.58046	+	16.5938i	0.926178	+	1.60419i	0.136522	+	0.990637i	$0.456408\pi$
$108$	0.0658898	−	8.44068i	0.00634025	−	0.812205i
$109$	−8.42729	+	10.0433i	−0.807188	+	0.961970i	−0.999814	−	0.0193028i	$-0.993855\pi$
$109$	−8.42729	+	10.0433i	−0.807188	+	0.961970i	0.192625	+	0.981272i	$0.438300\pi$
$110$	−0.294411	−	0.107157i	−0.0280710	−	0.0102170i
$111$	0.843751	−	13.8650i	0.0800853	−	1.31601i
$112$	0.443787	−	2.51684i	0.0419339	−	0.237819i
$113$	−8.50021	+	14.7228i	−0.799632	+	1.38500i	0.120223	+	0.992747i	$0.461639\pi$
$113$	−8.50021	+	14.7228i	−0.799632	+	1.38500i	−0.919856	+	0.392257i	$0.871694\pi$
$114$	−3.30095	+	3.24184i	−0.309162	+	0.303626i
$115$	−1.96949	−	3.41126i	−0.183656	−	0.318102i
$116$	−8.03650	+	2.92505i	−0.746170	+	0.271584i
$117$	−8.02632	+	15.7765i	−0.742034	+	1.45854i
$118$	3.52483	−	2.95769i	0.324487	−	0.272277i
$119$	−3.49830	−	0.616845i	−0.320689	−	0.0565461i
$120$	−8.98174	−	2.15341i	−0.819917	−	0.196579i
$121$	10.9547			0.995878
$122$	−1.53263	−	2.65459i	−0.138758	−	0.240335i
$123$	−11.3508	−	10.7649i	−1.02347	−	0.970641i
$124$	5.71664	−	1.00800i	0.513369	−	0.0905209i
$125$	−8.80731	−	5.08490i	−0.787750	−	0.454808i
$126$	−2.42472	+	0.561359i	−0.216012	+	0.0500099i
$127$	3.40423	−	0.600258i	0.302077	−	0.0532643i	−0.0205553	−	0.999789i	$-0.506543\pi$
$127$	3.40423	−	0.600258i	0.302077	−	0.0532643i	0.322632	+	0.946524i	$0.395432\pi$
$128$	−1.98119	+	11.2359i	−0.175114	+	0.993123i
$129$	−0.541950	+	2.26044i	−0.0477161	+	0.199021i
$130$	6.64996	+	5.57998i	0.583240	+	0.489397i
$131$	9.62379	+	1.69693i	0.840835	+	0.148262i	0.577447	−	0.816428i	$-0.304049\pi$
$131$	9.62379	+	1.69693i	0.840835	+	0.148262i	0.263388	+	0.964690i	$0.415160\pi$
$132$	−0.595291	+	0.0680098i	−0.0518134	+	0.00591950i
$133$	−5.00243	−	3.13014i	−0.433766	−	0.271417i
$134$		−	6.07836i		−	0.525090i
$135$	−2.07032	−	12.3022i	−0.178185	−	1.05880i
$136$	5.73956	+	1.01204i	0.492163	+	0.0867816i
$137$	5.77948	−	15.8790i	0.493774	−	1.35663i	−0.403427	−	0.915012i	$-0.632181\pi$
$137$	5.77948	−	15.8790i	0.493774	−	1.35663i	0.897201	−	0.441622i	$-0.145597\pi$
$138$	1.45246	+	0.960720i	0.123641	+	0.0817819i
$139$	−19.5422	−	7.11276i	−1.65754	−	0.603297i	−0.667570	−	0.744547i	$-0.732666\pi$
$139$	−19.5422	−	7.11276i	−1.65754	−	0.603297i	−0.989974	+	0.141250i	$0.954888\pi$
$140$		−	5.27989i		−	0.446232i
$141$	4.89845	−	0.559631i	0.412524	−	0.0471294i
$142$	−1.10211	−	6.25036i	−0.0924868	−	0.524519i
$143$	1.18068	+	0.429733i	0.0987336	+	0.0359361i
$144$	−5.51743	+	1.27737i	−0.459786	+	0.106447i
$145$	−10.9463	+	6.31985i	−0.909042	+	0.524835i
$146$	−3.60220	+	3.02261i	−0.298120	+	0.250153i
$147$	3.99591	+	8.00840i	0.329577	+	0.660521i
$148$	−12.8299	+	2.26226i	−1.05461	+	0.185956i
$149$	−7.27209	+	8.66654i	−0.595753	+	0.709991i	−0.976701	−	0.214606i	$-0.931153\pi$
$149$	−7.27209	+	8.66654i	−0.595753	+	0.709991i	0.380948	+	0.924597i	$0.375598\pi$
$150$	−0.809515	−	0.0492627i	−0.0660966	−	0.00402229i
$151$	10.6353	−	6.14027i	0.865485	−	0.499688i	−0.000360371	−	1.00000i	$-0.500115\pi$
$151$	10.6353	−	6.14027i	0.865485	−	0.499688i	0.865845	+	0.500312i	$0.166781\pi$
$152$	8.20733	+	5.13552i	0.665703	+	0.416546i
$153$	1.77549	+	7.66901i	0.143540	+	0.620002i
$154$	0.0604235	+	0.166012i	0.00486906	+	0.0133776i
$155$	8.06178	−	2.93425i	0.647538	−	0.235685i
$156$	16.1438	+	3.87054i	1.29254	+	0.309891i
$157$	−4.54760	+	1.65519i	−0.362938	+	0.132098i	−0.517051	−	0.855955i	$-0.672970\pi$
$157$	−4.54760	+	1.65519i	−0.362938	+	0.132098i	0.154113	+	0.988053i	$0.450748\pi$
$158$	1.17784	−	3.23608i	0.0937037	−	0.257449i
$159$	−13.9085	+	10.2984i	−1.10302	+	0.816714i
$160$			13.4426i			1.06273i
$161$	−0.759665	+	2.08716i	−0.0598700	+	0.164491i
$162$	3.24730	+	4.45801i	0.255132	+	0.350254i
$163$	5.44633	−	9.43332i	0.426589	−	0.738874i	−0.569978	−	0.821660i	$-0.693048\pi$
$163$	5.44633	−	9.43332i	0.426589	−	0.738874i	0.996567	+	0.0827855i	$0.0263816\pi$
$164$	−7.33597	+	12.7063i	−0.572843	+	0.992194i
$165$	−0.848982	+	0.251763i	−0.0660931	+	0.0195997i
$166$	3.41812	+	9.39121i	0.265298	+	0.728899i
$167$	−3.48347	−	19.7558i	−0.269559	−	1.52875i	−0.755730	−	0.654883i	$-0.772718\pi$
$167$	−3.48347	−	19.7558i	−0.269559	−	1.52875i	0.486171	−	0.873864i	$-0.338393\pi$
$168$	2.32529	+	4.66023i	0.179400	+	0.359545i
$169$	−16.7099	−	14.0213i	−1.28538	−	1.07856i
$170$	3.86055			0.296090
$171$	−2.04565	+	12.9157i	−0.156435	+	0.987688i
$172$	2.18011			0.166232
$173$	−5.47511	−	4.59417i	−0.416265	−	0.349288i	0.410475	−	0.911872i	$-0.365363\pi$
$173$	−5.47511	−	4.59417i	−0.416265	−	0.349288i	−0.826740	+	0.562584i	$0.809807\pi$
$174$	3.08283	−	4.66075i	0.233708	−	0.353330i
$175$	−0.179622	−	1.01869i	−0.0135781	−	0.0770055i
$176$	0.137493	+	0.377759i	0.0103639	+	0.0284746i
$177$	3.03212	−	12.6468i	0.227908	−	0.950591i
$178$	1.20012	−	2.07868i	0.0899531	−	0.155803i
$179$	0.552620	−	0.957166i	0.0413048	−	0.0715419i	−0.844634	−	0.535344i	$-0.820182\pi$
$179$	0.552620	−	0.957166i	0.0413048	−	0.0715419i	0.885939	+	0.463802i	$0.153515\pi$
$180$	−10.7673	+	4.57826i	−0.802549	+	0.341243i
$181$	−1.96608	+	5.40177i	−0.146138	+	0.401510i	−0.991066	−	0.133369i	$-0.957421\pi$
$181$	−1.96608	+	5.40177i	−0.146138	+	0.401510i	0.844929	+	0.534879i	$0.179643\pi$
$182$		−	4.89498i		−	0.362840i
$183$	−7.94611	−	3.45217i	−0.587393	−	0.255192i
$184$	1.24636	−	3.42434i	0.0918828	−	0.252446i
$185$	−18.0931	+	6.58536i	−1.33023	+	0.484165i
$186$	−2.61000	+	2.75206i	−0.191375	+	0.201791i
$187$	0.525069	−	0.191110i	0.0383969	−	0.0139753i
$188$	−1.58152	−	4.34519i	−0.115344	−	0.316906i
$189$	−4.56361	+	5.35327i	−0.331954	+	0.389393i
$190$	5.94467	+	2.40605i	0.431272	+	0.174553i
$191$	−6.92801	+	3.99989i	−0.501293	+	0.289422i	−0.729247	−	0.684250i	$-0.760130\pi$
$191$	−6.92801	+	3.99989i	−0.501293	+	0.289422i	0.227954	+	0.973672i	$0.426796\pi$
$192$	0.266311	+	0.533726i	0.0192193	+	0.0385184i
$193$	−5.85776	+	6.98100i	−0.421651	+	0.502504i	−0.934494	−	0.355978i	$-0.884148\pi$
$193$	−5.85776	+	6.98100i	−0.421651	+	0.502504i	0.512844	+	0.858482i	$0.328592\pi$
$194$	3.90917	−	0.689292i	0.280662	−	0.0494883i
$195$	24.4903	+	1.49035i	1.75379	+	0.106726i
$196$	6.43018	−	5.39556i	0.459299	−	0.385397i
$197$	−2.20914	+	1.27545i	−0.157394	+	0.0908717i	−0.576629	−	0.817006i	$-0.695632\pi$
$197$	−2.20914	+	1.27545i	−0.157394	+	0.0908717i	0.419234	+	0.907878i	$0.362299\pi$
$198$	0.286156	−	0.267174i	0.0203363	−	0.0189872i
$199$	2.04453	+	0.744147i	0.144933	+	0.0527512i	0.413468	−	0.910519i	$-0.364317\pi$
$199$	2.04453	+	0.744147i	0.144933	+	0.0527512i	−0.268535	+	0.963270i	$0.586540\pi$
$200$	0.294700	+	1.67133i	0.0208385	+	0.118181i
$201$	−10.2232	−	13.8070i	−0.721088	−	0.973870i
$202$			0.204711i			0.0144034i
$203$	6.69744	+	2.43767i	0.470068	+	0.171091i
$204$	6.60617	−	3.29625i	0.462524	−	0.230783i
$205$	−7.41644	+	20.3765i	−0.517987	+	1.42316i
$206$	7.17075	+	1.26440i	0.499610	+	0.0880947i
$207$	4.91509	−	0.260614i	0.341622	−	0.0181139i
$208$		−	11.1385i		−	0.772314i
$209$	0.927637	+	0.0329641i	0.0641660	+	0.00228018i
$210$	2.05292	+	2.77258i	0.141665	+	0.191326i
$211$	5.67921	+	1.00140i	0.390973	+	0.0689391i	0.365679	−	0.930741i	$-0.380837\pi$
$211$	5.67921	+	1.00140i	0.390973	+	0.0689391i	0.0252939	+	0.999680i	$0.491948\pi$
$212$	12.4338	+	10.4332i	0.853956	+	0.716554i
$213$	−13.0159	−	12.3441i	−0.891836	−	0.845801i
$214$	−2.03899	+	11.5637i	−0.139382	+	0.790477i
$215$	3.17311	−	0.559505i	0.216405	−	0.0381580i
$216$	7.48737	−	8.78294i	0.509451	−	0.597604i
$217$	−4.18949	−	2.41881i	−0.284401	−	0.164199i
$218$	−7.91226	+	1.39514i	−0.535886	+	0.0944911i
$219$	−3.09868	+	12.9244i	−0.209389	+	0.873349i
$220$	0.415259	+	0.719250i	0.0279968	+	0.0484918i
$221$	−15.4820			−1.04143
$222$	5.85765	−	6.17647i	0.393140	−	0.414538i
$223$	20.6749	+	3.64555i	1.38449	+	0.244124i	0.815757	−	0.578395i	$-0.196321\pi$
$223$	20.6749	+	3.64555i	1.38449	+	0.244124i	0.568738	+	0.822519i	$0.307432\pi$
$224$	5.80661	−	4.87232i	0.387970	−	0.325546i
$225$	−1.92167	+	1.24962i	−0.128111	+	0.0833082i
$226$	−9.78980	+	3.56319i	−0.651208	+	0.237020i
$227$	−8.24758	−	14.2852i	−0.547411	−	0.948144i	−0.998451	−	0.0556402i	$-0.982280\pi$
$227$	−8.24758	−	14.2852i	−0.547411	−	0.948144i	0.451040	−	0.892504i	$-0.351053\pi$
$228$	12.2269	−	0.958498i	0.809746	−	0.0634781i
$229$	−2.42135	+	4.19390i	−0.160007	+	0.277140i	−0.934871	−	0.354988i	$-0.884485\pi$
$229$	−2.42135	+	4.19390i	−0.160007	+	0.277140i	0.774864	+	0.632128i	$0.217818\pi$
$230$	0.419163	−	2.37719i	0.0276388	−	0.156747i
$231$	0.416468	+	0.275470i	0.0274016	+	0.0181246i
$232$	−10.9883	−	3.99940i	−0.721415	−	0.262574i
$233$	10.7581	−	12.8210i	0.704786	−	0.839932i	−0.288273	−	0.957548i	$-0.593081\pi$
$233$	10.7581	−	12.8210i	0.704786	−	0.839932i	0.993059	+	0.117617i	$0.0375254\pi$
$234$	−9.98239	+	4.24450i	−0.652569	+	0.277472i
$235$	−3.41703	−	5.91848i	−0.222903	−	0.386079i
$236$	−12.1973			−0.793979
$237$	−2.76731	−	9.33175i	−0.179756	−	0.606163i
$238$	−1.39927	−	1.66759i	−0.0907013	−	0.108094i
$239$	−1.63304	+	0.942835i	−0.105632	+	0.0609870i	−0.551886	−	0.833920i	$-0.686091\pi$
$239$	−1.63304	+	0.942835i	−0.105632	+	0.0609870i	0.446253	+	0.894907i	$0.352758\pi$
$240$	4.67140	+	6.30898i	0.301537	+	0.407243i
$241$	13.8818	+	16.5437i	0.894206	+	1.06567i	0.997475	+	0.0710202i	$0.0226255\pi$
$241$	13.8818	+	16.5437i	0.894206	+	1.06567i	−0.103268	+	0.994654i	$0.532930\pi$
$242$	5.14258	+	4.31513i	0.330577	+	0.277387i
$243$	14.8742	+	4.66472i	0.954177	+	0.299242i
$244$	−1.41097	+	8.00200i	−0.0903280	+	0.512276i
$245$	7.97430	−	9.50340i	0.509459	−	0.607150i
$246$	−1.08816	−	9.52471i	−0.0693788	−	0.607273i
$247$	−23.8400	−	9.64903i	−1.51690	−	0.613953i
$248$	6.87357	+	3.96846i	0.436472	+	0.251997i
$249$	23.5593	+	15.5832i	1.49301	+	0.987544i
$250$	−2.13154	−	5.85635i	−0.134810	−	0.370388i
$251$	−2.14692	−	2.55860i	−0.135512	−	0.161497i	0.694020	−	0.719955i	$-0.255838\pi$
$251$	−2.14692	−	2.55860i	−0.135512	−	0.161497i	−0.829533	+	0.558458i	$0.811393\pi$
$252$	5.88027	+	2.99160i	0.370422	+	0.188453i
$253$	−0.0606688	−	0.344070i	−0.00381421	−	0.0216315i
$254$	1.83454	+	1.05917i	0.115109	+	0.0664583i
$255$	8.76922	−	6.49305i	0.549150	−	0.406611i
$256$	−4.82836	+	4.05148i	−0.301773	+	0.253217i
$257$	5.04333	−	4.23186i	0.314594	−	0.263976i	−0.471793	−	0.881709i	$-0.656393\pi$
$257$	5.04333	−	4.23186i	0.314594	−	0.263976i	0.786388	+	0.617733i	$0.211949\pi$
$258$	−1.14482	+	0.847668i	−0.0712735	+	0.0527735i
$259$	9.40252	+	5.42855i	0.584244	+	0.337313i
$260$	−3.99591	−	22.6620i	−0.247816	−	1.40543i
$261$	−0.836276	−	15.7719i	−0.0517642	−	0.976255i
$262$	3.84938	+	4.58751i	0.237815	+	0.283417i
$263$	−1.92918	−	5.30037i	−0.118958	−	0.326835i	0.865895	−	0.500226i	$-0.166750\pi$
$263$	−1.92918	−	5.30037i	−0.118958	−	0.326835i	−0.984853	+	0.173391i	$0.944528\pi$
$264$	−0.683286	−	0.451955i	−0.0420533	−	0.0278159i
$265$	20.7748	+	11.9943i	1.27618	+	0.736805i
$266$	−1.11536	−	3.43992i	−0.0683873	−	0.210915i
$267$	−0.770044	−	6.74020i	−0.0471259	−	0.412494i
$268$	−10.3570	+	12.3430i	−0.632655	+	0.753969i
$269$	0.178129	−	1.01022i	0.0108607	−	0.0615942i	−0.978896	−	0.204360i	$-0.934489\pi$
$269$	0.178129	−	1.01022i	0.0108607	−	0.0615942i	0.989756	+	0.142766i	$0.0455997\pi$
$270$	3.87404	−	6.59069i	0.235767	−	0.401097i
$271$	21.3831	+	17.9426i	1.29893	+	1.08993i	0.990328	+	0.138743i	$0.0443062\pi$
$271$	21.3831	+	17.9426i	1.29893	+	1.08993i	0.308604	+	0.951191i	$0.400138\pi$
$272$	−3.18402	−	3.79457i	−0.193060	−	0.230080i
$273$	−8.23286	−	11.1189i	−0.498276	−	0.672949i
$274$	8.96801	−	5.17768i	0.541777	−	0.312795i
$275$	0.104588	+	0.124643i	0.00630689	+	0.00751626i
$276$	−1.31244	−	4.42575i	−0.0789999	−	0.266399i
$277$	24.0100			1.44262			0.721312	−	0.692610i	$-0.243539\pi$
$277$	24.0100			1.44262			0.721312	+	0.692610i	$0.243539\pi$
$278$	−6.37213	−	11.0369i	−0.382175	−	0.661947i
$279$	−1.29993	+	10.6411i	−0.0778247	+	0.637064i
$280$	4.64039	−	5.53020i	0.277316	−	0.330493i
$281$	−9.92863	−	3.61372i	−0.592292	−	0.215577i	0.0284451	−	0.999595i	$-0.490944\pi$
$281$	−9.92863	−	3.61372i	−0.592292	−	0.215577i	−0.620737	+	0.784019i	$0.713167\pi$
$282$	2.51998	+	1.66683i	0.150063	+	0.0992583i
$283$	4.38438	−	24.8650i	0.260624	−	1.47807i	−0.520588	−	0.853808i	$-0.674287\pi$
$283$	4.38438	−	24.8650i	0.260624	−	1.47807i	0.781212	−	0.624266i	$-0.214602\pi$
$284$	−8.41210	+	14.5702i	−0.499166	+	0.864582i
$285$	17.5501	−	4.53300i	1.03958	−	0.268512i
$286$	0.384987	+	0.666816i	0.0227647	+	0.0394297i
$287$	11.4899	−	4.18197i	0.678226	−	0.246854i
$288$	−14.9712	−	7.61662i	−0.882185	−	0.448814i
$289$	7.74845	−	6.50173i	0.455791	−	0.382454i
$290$	−7.62811	−	1.34504i	−0.447938	−	0.0789835i
$291$	7.72035	−	8.14056i	0.452575	−	0.477208i
$292$	12.4651			0.729463
$293$	−4.14145	−	7.17321i	−0.241946	−	0.419063i	0.719322	−	0.694676i	$-0.244452\pi$
$293$	−4.14145	−	7.17321i	−0.241946	−	0.419063i	−0.961269	+	0.275613i	$0.911119\pi$
$294$	−1.27873	+	5.33350i	−0.0745770	+	0.311056i
$295$	−17.7530	+	3.13034i	−1.03362	+	0.182255i
$296$	−15.4264	−	8.90644i	−0.896642	−	0.517677i
$297$	0.200645	−	1.08817i	0.0116426	−	0.0631421i
$298$	−6.82766	+	1.20390i	−0.395516	+	0.0697401i
$299$	−1.68098	+	9.53330i	−0.0972135	+	0.551325i
$300$	1.55990	+	1.47938i	0.0900609	+	0.0854121i
$301$	−1.39179	−	1.16785i	−0.0802214	−	0.0673138i
$302$	7.41134	+	1.30682i	0.426475	+	0.0751990i
$303$	0.344304	+	0.465001i	0.0197797	+	0.0267136i
$304$	−2.53800	−	7.82750i	−0.145564	−	0.448938i
$305$			12.0089i			0.687628i
$306$	−2.18740	+	4.29954i	−0.125045	+	0.245788i
$307$	2.56320	+	0.451961i	0.146290	+	0.0257948i	0.246313	−	0.969190i	$-0.420781\pi$
$307$	2.56320	+	0.451961i	0.146290	+	0.0257948i	−0.100024	+	0.994985i	$0.531892\pi$
$308$	0.160172	−	0.440069i	0.00912665	−	0.0250753i
$309$	18.4149	−	9.18841i	1.04759	−	0.522710i
$310$	4.94037	+	1.79815i	0.280594	+	0.102128i
$311$			14.3781i			0.815309i	0.913136	+	0.407655i	$0.133653\pi$
$311$			14.3781i			0.815309i	−0.913136	+	0.407655i	$0.866347\pi$
$312$	13.5074	+	18.2425i	0.764706	+	1.03278i
$313$	3.18914	+	18.0865i	0.180261	+	1.02231i	0.931895	+	0.362729i	$0.118155\pi$
$313$	3.18914	+	18.0865i	0.180261	+	1.02231i	−0.751634	+	0.659580i	$0.770734\pi$
$314$	−2.78683	−	1.01432i	−0.157270	−	0.0572415i
$315$	9.32641	+	2.84511i	0.525484	+	0.160304i
$316$	−7.90578	+	4.56440i	−0.444735	+	0.256768i
$317$	−20.0836	+	16.8521i	−1.12801	+	0.946510i	−0.998981	−	0.0451313i	$-0.985629\pi$
$317$	−20.0836	+	16.8521i	−1.12801	+	0.946510i	−0.129026	+	0.991641i	$0.541185\pi$
$318$	−10.5859	−	0.644199i	−0.593626	−	0.0361249i
$319$	−1.10408	+	0.194678i	−0.0618164	+	0.0108999i
$320$	0.531454	−	0.633363i	0.0297092	−	0.0354060i
$321$	14.8174	+	29.6962i	0.827026	+	1.65748i
$322$	−1.17877	+	0.680563i	−0.0656903	+	0.0379263i
$323$	−10.8799	+	3.52771i	−0.605374	+	0.196287i
$324$	1.00195	−	14.5858i	0.0556637	−	0.810320i
$325$	−1.54192	−	4.23640i	−0.0855305	−	0.234993i
$326$	6.27260	−	2.28304i	0.347407	−	0.126446i
$327$	−15.6262	+	16.4767i	−0.864130	+	0.911163i
$328$	−18.8511	+	6.86123i	−1.04088	+	0.378848i
$329$	−1.31800	+	3.62118i	−0.0726639	+	0.199642i
$330$	−0.497720	−	0.216233i	−0.0273986	−	0.0119032i
$331$			3.89688i			0.214192i	0.994249	+	0.107096i	$0.0341552\pi$
$331$			3.89688i			0.214192i	−0.994249	+	0.107096i	$0.965845\pi$
$332$	9.06083	−	24.8944i	0.497278	−	1.36626i
$333$	2.91744	−	23.8818i	0.159875	−	1.30872i
$334$	6.14668	−	10.6464i	0.336331	−	0.582543i
$335$	−11.9067	+	20.6231i	−0.650535	+	1.12676i
$336$	1.03204	−	4.30455i	0.0563021	−	0.234833i
$337$	−2.57105	−	7.06390i	−0.140054	−	0.384795i	0.849758	−	0.527172i	$-0.176748\pi$
$337$	−2.57105	−	7.06390i	−0.140054	−	0.384795i	−0.989813	+	0.142377i	$0.954526\pi$
$338$	−2.32123	−	13.1643i	−0.126258	−	0.716046i
$339$	−16.2446	+	24.5592i	−0.882284	+	1.33388i
$340$	−7.83941	−	6.57805i	−0.425152	−	0.356745i
$341$	0.760949			0.0412077
$342$	−6.04792	+	5.25738i	−0.327034	+	0.284286i
$343$	−16.4719			−0.889398
$344$	2.28347	+	1.91606i	0.123116	+	0.103307i
$345$	−3.04607	−	6.10478i	−0.163995	−	0.328670i
$346$	−0.760567	−	4.31339i	−0.0408884	−	0.231889i
$347$	−12.3808	−	34.0160i	−0.664636	−	1.82607i	−0.554548	−	0.832152i	$-0.687109\pi$
$347$	−12.3808	−	34.0160i	−0.664636	−	1.82607i	−0.110089	−	0.993922i	$-0.535113\pi$
$348$	−14.2017	+	4.21146i	−0.761289	+	0.225758i
$349$	−4.15719	+	7.20046i	−0.222529	+	0.385432i	−0.955575	−	0.294747i	$-0.904765\pi$
$349$	−4.15719	+	7.20046i	−0.222529	+	0.385432i	0.733046	+	0.680179i	$0.238098\pi$
$350$	0.316948	−	0.548970i	0.0169416	−	0.0293437i
$351$	−15.5361	+	26.4308i	−0.829258	+	1.41077i
$352$	−0.407798	+	1.12042i	−0.0217357	+	0.0597183i
$353$			21.4379i			1.14102i	0.821290	+	0.570512i	$0.193255\pi$
$353$			21.4379i			1.14102i	−0.821290	+	0.570512i	$0.806745\pi$
$354$	6.40509	−	4.74256i	0.340427	−	0.252064i
$355$	−8.50437	+	23.3656i	−0.451365	+	1.24012i
$356$	−5.97892	+	2.17615i	−0.316882	+	0.115336i
$357$	−5.98315	−	1.43449i	−0.316662	−	0.0759211i
$358$	0.636459	−	0.231652i	0.0336379	−	0.0122432i
$359$	11.3838	+	31.2766i	0.600812	+	1.65072i	0.749634	+	0.661853i	$0.230230\pi$
$359$	11.3838	+	31.2766i	0.600812	+	1.65072i	−0.148822	+	0.988864i	$0.547548\pi$
$360$	−15.3016	−	4.66789i	−0.806463	−	0.246019i
$361$	−18.9521	−	1.34865i	−0.997478	−	0.0709816i
$362$	−3.05077	+	1.76136i	−0.160345	+	0.0925751i
$363$	18.9390	+	1.15252i	0.994039	+	0.0604918i
$364$	−8.34063	+	9.93998i	−0.437168	+	0.520997i
$365$	18.1427	−	3.19905i	0.949633	−	0.167446i
$366$	−2.37040	−	4.75064i	−0.123903	−	0.248320i
$367$	6.22477	−	5.22321i	0.324931	−	0.272649i	−0.465700	−	0.884943i	$-0.654197\pi$
$367$	6.22477	−	5.22321i	0.324931	−	0.272649i	0.790631	+	0.612294i	$0.209753\pi$
$368$	−2.68228	+	1.54861i	−0.139823	+	0.0807271i
$369$	−18.4914	−	19.8052i	−0.962622	−	1.03102i
$370$	−11.0877	−	4.03560i	−0.576423	−	0.209801i
$371$	−2.34888	−	13.3212i	−0.121948	−	0.691601i
$372$	9.98928	−	1.14124i	0.517920	−	0.0591705i
$373$			12.8929i			0.667571i	0.942649	+	0.333786i	$0.108326\pi$
$373$			12.8929i			0.667571i	−0.942649	+	0.333786i	$0.891674\pi$
$374$	0.321769	+	0.117115i	0.0166383	+	0.00605585i
$375$	−14.6916	−	9.71765i	−0.758669	−	0.501818i
$376$	2.16241	−	5.94116i	0.111518	−	0.306392i
$377$	30.5911	+	5.39404i	1.57552	+	0.277807i
$378$	−4.25105	+	0.715406i	−0.218650	+	0.0367965i
$379$			8.14641i			0.418453i	0.977867	+	0.209226i	$0.0670946\pi$
$379$			8.14641i			0.418453i	−0.977867	+	0.209226i	$0.932905\pi$
$380$	−7.97183	−	15.0151i	−0.408946	−	0.770257i
$381$	5.94857	−	0.679603i	0.304755	−	0.0348171i
$382$	−4.82789	−	0.851288i	−0.247016	−	0.0435557i
$383$	12.3997	+	10.4046i	0.633593	+	0.531648i	0.902043	−	0.431646i	$-0.142067\pi$
$383$	12.3997	+	10.4046i	0.633593	+	0.531648i	−0.268450	+	0.963294i	$0.586511\pi$
$384$	−4.60730	+	19.2168i	−0.235115	+	0.980652i
$385$	0.120188	−	0.681620i	0.00612535	−	0.0347386i
$386$	−5.49976	+	0.969756i	−0.279930	+	0.0493593i
$387$	−1.17477	+	3.85095i	−0.0597169	+	0.195755i
$388$	−9.11264	−	5.26119i	−0.462624	−	0.267096i
$389$	3.70389	−	0.653095i	0.187794	−	0.0331132i	−0.0789598	−	0.996878i	$-0.525160\pi$
$389$	3.70389	−	0.653095i	0.187794	−	0.0331132i	0.266754	+	0.963765i	$0.414049\pi$
$390$	10.9097	+	10.3466i	0.552436	+	0.523920i
$391$	2.15251	+	3.72826i	0.108857	+	0.188546i
$392$	11.4771			0.579680
$393$	16.4596	+	3.94626i	0.830276	+	0.199062i
$394$	−1.53947	−	0.271450i	−0.0775575	−	0.0136755i
$395$	−10.3353	+	8.67237i	−0.520027	+	0.436354i
$396$	−1.03632	+	0.0549493i	−0.0520773	+	0.00276130i
$397$	17.7014	−	6.44279i	0.888408	−	0.323354i	0.142810	−	0.989750i	$-0.454386\pi$
$397$	17.7014	−	6.44279i	0.888408	−	0.323354i	0.745598	+	0.666396i	$0.232164\pi$
$398$	0.666661	+	1.15469i	0.0334167	+	0.0578794i
$399$	−8.31915	−	5.93785i	−0.416478	−	0.297264i
$400$	0.721211	−	1.24917i	0.0360605	−	0.0624587i
$401$	−4.99660	+	28.3371i	−0.249518	+	1.41509i	0.560242	+	0.828329i	$0.310708\pi$
$401$	−4.99660	+	28.3371i	−0.249518	+	1.41509i	−0.809761	+	0.586760i	$0.800403\pi$
$402$	0.639496	−	10.5086i	0.0318952	−	0.524121i
$403$	−19.8124	−	7.21114i	−0.986928	−	0.359213i
$404$	0.348811	−	0.415697i	0.0173540	−	0.0206817i
$405$	−2.28499	−	21.4865i	−0.113542	−	1.06767i
$406$	2.18384	+	3.78252i	0.108382	+	0.187723i
$407$	−1.70780			−0.0846527
$408$	9.81637	+	2.35352i	0.485983	+	0.116516i
$409$	−8.01624	−	9.55338i	−0.396377	−	0.472384i	0.530534	−	0.847663i	$-0.321991\pi$
$409$	−8.01624	−	9.55338i	−0.396377	−	0.472384i	−0.926912	+	0.375279i	$0.877547\pi$
$410$	−11.5081	+	6.64419i	−0.568343	+	0.328133i
$411$	11.6625	−	26.8444i	0.575268	−	1.32414i
$412$	−12.4069	−	14.7859i	−0.611242	−	0.728449i
$413$	7.78683	+	6.53393i	0.383165	+	0.321514i
$414$	2.41001	+	1.81375i	0.118445	+	0.0891411i
$415$	6.79896	−	38.5588i	0.333748	−	1.89278i
$416$	21.2353	−	25.3072i	1.04114	−	1.24079i
$417$	−33.0372	−	14.3529i	−1.61784	−	0.702866i
$418$	0.422487	+	0.380879i	0.0206645	+	0.0186294i
$419$	21.1781	+	12.2272i	1.03462	+	0.597336i	0.918304	−	0.395877i	$-0.129559\pi$
$419$	21.1781	+	12.2272i	1.03462	+	0.597336i	0.116312	+	0.993213i	$0.462893\pi$
$420$	0.555490	−	9.12814i	0.0271051	−	0.445408i
$421$	−12.2078	−	33.5405i	−0.594969	−	1.63466i	−0.761155	−	0.648570i	$-0.775367\pi$
$421$	−12.2078	−	33.5405i	−0.594969	−	1.63466i	0.166185	−	0.986095i	$-0.446855\pi$
$422$	2.27160	+	2.70719i	0.110580	+	0.131784i
$423$	8.52758	−	0.452160i	0.414625	−	0.0219848i
$424$	3.85374	+	21.8556i	0.187154	+	1.06140i
$425$	−1.73630	−	1.00245i	−0.0842229	−	0.0486261i
$426$	−1.24779	−	10.9219i	−0.0604556	−	0.529168i
$427$	5.18732	−	4.35268i	0.251032	−	0.210641i
$428$	23.8440	−	20.0075i	1.15254	−	0.967099i
$429$	1.99601	+	0.867164i	0.0963685	+	0.0418670i
$430$	1.70999	+	0.987262i	0.0824629	+	0.0476100i
$431$	−2.41299	−	13.6847i	−0.116230	−	0.659170i	−0.986134	−	0.165950i	$-0.946931\pi$
$431$	−2.41299	−	13.6847i	−0.116230	−	0.659170i	0.869905	−	0.493220i	$-0.164180\pi$
$432$	−9.67322	+	1.62790i	−0.465403	+	0.0783222i
$433$	22.9078	+	27.3004i	1.10088	+	1.31197i	0.946046	+	0.324032i	$0.105039\pi$
$433$	22.9078	+	27.3004i	1.10088	+	1.31197i	0.154830	+	0.987941i	$0.450517\pi$
$434$	−1.01394	−	2.78577i	−0.0486705	−	0.133721i
$435$	−19.5895	+	9.77445i	−0.939243	+	0.468649i
$436$	18.4442	+	10.6488i	0.883318	+	0.509984i
$437$	0.990946	+	7.08250i	0.0474034	+	0.338802i
$438$	−6.54568	+	4.84666i	−0.312765	+	0.231582i
$439$	1.12626	−	1.34223i	0.0537536	−	0.0640610i	−0.738498	−	0.674256i	$-0.764464\pi$
$439$	1.12626	−	1.34223i	0.0537536	−	0.0640610i	0.792251	+	0.610195i	$0.208909\pi$
$440$	−0.197189	+	1.11831i	−0.00940060	+	0.0533135i
$441$	6.06578	+	14.2657i	0.288847	+	0.679321i
$442$	−7.26791	−	6.09850i	−0.345699	−	0.290076i
$443$	16.4881	+	19.6498i	0.783375	+	0.933590i	0.999081	−	0.0428681i	$-0.0136495\pi$
$443$	16.4881	+	19.6498i	0.783375	+	0.933590i	−0.215705	+	0.976458i	$0.569205\pi$
$444$	−22.4190	+	2.56129i	−1.06396	+	0.121554i
$445$	−8.14374	+	4.70179i	−0.386050	+	0.222886i
$446$	8.26967	+	9.85540i	0.391580	+	0.466667i
$447$	−13.4842	+	14.2181i	−0.637780	+	0.672493i
$448$	−0.466213			−0.0220265
$449$	−17.1648	−	29.7304i	−0.810059	−	1.40306i	−0.912822	−	0.408358i	$-0.866102\pi$
$449$	−17.1648	−	29.7304i	−0.810059	−	1.40306i	0.102763	−	0.994706i	$-0.467232\pi$
$450$	−1.39435	−	0.170336i	−0.0657303	−	0.00802972i
$451$	−1.23629	+	1.47336i	−0.0582148	+	0.0693777i
$452$	25.9510	+	9.44540i	1.22063	+	0.444274i
$453$	19.0328	−	9.49670i	0.894239	−	0.446194i
$454$	1.75532	−	9.95489i	0.0823810	−	0.467206i
$455$	−9.58865	+	16.6080i	−0.449523	+	0.778597i
$456$	13.6490	+	9.74204i	0.639171	+	0.456213i
$457$	−5.00753	−	8.67330i	−0.234242	−	0.405720i	0.724810	−	0.688949i	$-0.241928\pi$
$457$	−5.00753	−	8.67330i	−0.234242	−	0.405720i	−0.959052	+	0.283229i	$0.908594\pi$
$458$	−2.78870	+	1.01500i	−0.130307	+	0.0474279i
$459$	2.26271	+	13.4454i	0.105614	+	0.627576i
$460$	−4.90171	+	4.11302i	−0.228543	+	0.191771i
$461$	−30.0961	−	5.30675i	−1.40171	−	0.247160i	−0.578866	−	0.815423i	$-0.696505\pi$
$461$	−30.0961	−	5.30675i	−1.40171	−	0.247160i	−0.822847	+	0.568263i	$0.807616\pi$
$462$	0.0869974	+	0.293368i	0.00404749	+	0.0136487i
$463$	8.47540			0.393885			0.196943	−	0.980415i	$-0.436899\pi$
$463$	8.47540			0.393885			0.196943	+	0.980415i	$0.436899\pi$
$464$	4.96930	+	8.60709i	0.230694	+	0.399574i
$465$	14.2463	−	4.22471i	0.660658	−	0.195916i
$466$	10.1006	−	1.78101i	0.467902	−	0.0825037i
$467$	16.4095	+	9.47405i	0.759343	+	0.438407i	0.829060	−	0.559160i	$-0.188876\pi$
$467$	16.4095	+	9.47405i	0.759343	+	0.438407i	−0.0697170	+	0.997567i	$0.522210\pi$
$468$	27.5030	+	8.39005i	1.27133	+	0.387830i
$469$	13.2239	−	2.33173i	0.610624	−	0.107669i
$470$	0.727240	−	4.12438i	0.0335451	−	0.190244i
$471$	−8.03626	+	2.38313i	−0.370291	+	0.109809i
$472$	−12.7756	−	10.7200i	−0.588045	−	0.493429i
$473$	0.281447	+	0.0496266i	0.0129409	+	0.00228183i
$474$	2.37677	−	5.47079i	0.109169	−	0.251282i
$475$	−2.04888	−	2.62577i	−0.0940089	−	0.120478i
$476$			5.77052i			0.264491i
$477$	−25.1293	+	16.3411i	−1.15059	+	0.748206i
$478$	−1.13801	−	0.200662i	−0.0520513	−	0.00917805i
$479$	−5.21255	+	14.3213i	−0.238167	+	0.654359i	0.761811	+	0.647799i	$0.224310\pi$
$479$	−5.21255	+	14.3213i	−0.238167	+	0.654359i	−0.999978	+	0.00656008i	$0.997912\pi$
$480$	−1.41428	+	23.2403i	−0.0645526	+	1.06077i
$481$	44.4652	+	16.1840i	2.02744	+	0.737928i
$482$			13.2345i			0.602814i
$483$	−1.53294	+	3.52847i	−0.0697510	+	0.160551i
$484$	−3.09014	−	17.5250i	−0.140461	−	0.796593i
$485$	−14.6135	−	5.31890i	−0.663567	−	0.241519i
$486$	5.14508	+	8.04888i	0.233386	+	0.365105i
$487$	27.1431	−	15.6711i	1.22997	−	0.710124i	0.262947	−	0.964810i	$-0.415305\pi$
$487$	27.1431	−	15.6711i	1.22997	−	0.710124i	0.967024	+	0.254686i	$0.0819721\pi$
$488$	−8.51067	+	7.14130i	−0.385260	+	0.323271i
$489$	10.4084	−	15.7358i	0.470683	−	0.711598i
$490$	7.48695	−	1.32015i	0.338226	−	0.0596383i
$491$	−8.20427	+	9.77747i	−0.370253	+	0.441251i	−0.918713	−	0.394926i	$-0.870770\pi$
$491$	−8.20427	+	9.77747i	−0.370253	+	0.441251i	0.548459	+	0.836177i	$0.315215\pi$
$492$	−14.0196	+	21.1955i	−0.632054	+	0.955566i
$493$	11.9635	−	6.90713i	0.538809	−	0.311081i
$494$	−7.39068	−	13.9205i	−0.332522	−	0.626311i
$495$	−1.49425	+	0.345941i	−0.0671616	+	0.0155489i
$496$	−2.30720	−	6.33898i	−0.103596	−	0.284629i
$497$	13.1753	−	4.79543i	0.590995	−	0.215105i
$498$	4.92139	+	16.5956i	0.220533	+	0.743668i
$499$	−14.6783	+	5.34245i	−0.657089	+	0.239161i	−0.648979	−	0.760806i	$-0.724804\pi$
$499$	−14.6783	+	5.34245i	−0.657089	+	0.239161i	−0.00810997	+	0.999967i	$0.502582\pi$
$500$	−5.65032	+	15.5241i	−0.252690	+	0.694261i
$501$	−3.94394	−	34.5213i	−0.176202	−	1.54230i
$502$		−	2.04681i		−	0.0913534i
$503$	5.95501	−	16.3613i	0.265521	−	0.729513i	−0.733250	−	0.679959i	$-0.761998\pi$
$503$	5.95501	−	16.3613i	0.265521	−	0.729513i	0.998771	−	0.0495542i	$-0.0157801\pi$
$504$	3.52979	+	8.30149i	0.157229	+	0.369778i
$505$	0.401004	−	0.694559i	0.0178444	−	0.0309075i
$506$	0.107052	−	0.185419i	0.00475903	−	0.00824287i
$507$	−27.4138	−	25.9987i	−1.21749	−	1.15464i
$508$	−1.92056	−	5.27670i	−0.0852112	−	0.234116i
$509$	−6.02951	−	34.1951i	−0.267253	−	1.51567i	−0.762541	−	0.646940i	$-0.776048\pi$
$509$	−6.02951	−	34.1951i	−0.267253	−	1.51567i	0.495288	−	0.868729i	$-0.335063\pi$
$510$	6.67431	+	0.406163i	0.295544	+	0.0179852i
$511$	−7.95775	−	6.67735i	−0.352030	−	0.295388i
$512$	18.9559			0.837741
$513$	−4.89547	+	22.1141i	−0.216140	+	0.976362i
$514$	4.03452			0.177955
$515$	−21.8526	−	18.3365i	−0.962943	−	0.808005i
$516$	3.76909	+	0.229366i	0.165925	+	0.0100973i
$517$	−0.105259	−	0.596954i	−0.00462929	−	0.0262540i
$518$	2.27559	+	6.25212i	0.0999835	+	0.274703i
$519$	−8.98232	−	8.51867i	−0.394280	−	0.373928i
$520$	15.7318	−	27.2483i	0.689885	−	1.19492i
$521$	−11.4232	+	19.7856i	−0.500460	+	0.866823i	0.499540	+	0.866291i	$0.333503\pi$
$521$	−11.4232	+	19.7856i	−0.500460	+	0.866823i	−1.00000		0.000531511i	$0.999831\pi$
$522$	5.82010	−	7.73341i	0.254739	−	0.338482i
$523$	−4.04599	+	11.1163i	−0.176919	+	0.486080i	−0.996178	−	0.0873428i	$-0.972162\pi$
$523$	−4.04599	+	11.1163i	−0.176919	+	0.486080i	0.819260	+	0.573423i	$0.194385\pi$
$524$		−	15.8746i		−	0.693487i
$525$	−0.203365	−	1.78006i	−0.00887559	−	0.0776881i
$526$	1.18223	−	3.24814i	0.0515475	−	0.141626i
$527$	−8.81093	+	3.20692i	−0.383810	+	0.139695i
$528$	0.197962	+	0.667555i	0.00861517	+	0.0290516i
$529$	−19.0835	+	6.94582i	−0.829717	+	0.301992i
$530$	5.02788	+	13.8140i	0.218397	+	0.600042i
$531$	6.57264	−	21.5454i	0.285228	−	0.934992i
$532$	−3.59643	+	8.88576i	−0.155925	+	0.385246i
$533$	46.1510	−	26.6453i	1.99902	−	1.15414i
$534$	2.29353	−	3.46746i	0.0992509	−	0.150052i
$535$	29.5698	−	35.2399i	1.27841	−	1.52356i
$536$	−21.6961	+	3.82560i	−0.937128	+	0.165241i
$537$	1.05610	−	1.59666i	0.0455741	−	0.0689009i
$538$	0.481556	−	0.404073i	0.0207614	−	0.0174208i
$539$	0.952941	−	0.550181i	0.0410461	−	0.0236980i
$540$	−19.0968	+	6.78232i	−0.821795	+	0.291865i
$541$	29.2199	+	10.6352i	1.25626	+	0.457242i	0.882513	−	0.470287i	$-0.155850\pi$
$541$	29.2199	+	10.6352i	1.25626	+	0.457242i	0.373750	+	0.927530i	$0.378072\pi$
$542$	2.97041	+	16.8460i	0.127590	+	0.723598i
$543$	−3.96738	+	9.13201i	−0.170257	+	0.391892i
$544$		−	14.6917i		−	0.629904i
$545$	29.5782	+	10.7656i	1.26699	+	0.461147i
$546$	0.514994	−	8.46270i	0.0220397	−	0.362170i
$547$	−2.95216	+	8.11099i	−0.126225	+	0.346801i	−0.986668	−	0.162746i	$-0.947965\pi$
$547$	−2.95216	+	8.11099i	−0.126225	+	0.346801i	0.860443	+	0.509547i	$0.170187\pi$
$548$	−27.0332	−	4.76668i	−1.15480	−	0.203623i
$549$	−13.3745	−	6.80429i	−0.570808	−	0.290400i
$550$			0.0997108i			0.00425168i
$551$	22.7268	−	3.17982i	0.968196	−	0.135465i
$552$	2.51504	−	5.78905i	0.107047	−	0.246399i
$553$	7.49216	+	1.32107i	0.318599	+	0.0561776i
$554$	11.2713	+	9.45777i	0.478873	+	0.401822i
$555$	−31.9732	+	9.48156i	−1.35719	+	0.402470i
$556$	−5.86632	+	33.2696i	−0.248787	+	1.41094i
$557$	−13.9869	+	2.46627i	−0.592644	+	0.104499i	−0.461923	−	0.886920i	$-0.652840\pi$
$557$	−13.9869	+	2.46627i	−0.592644	+	0.104499i	−0.130721	+	0.991419i	$0.541729\pi$
$558$	−4.80185	+	4.48331i	−0.203279	+	0.189794i
$559$	−6.85759	−	3.95923i	−0.290045	−	0.167458i
$560$	−6.04255	+	1.06547i	−0.255345	+	0.0450241i
$561$	0.927874	−	0.275158i	0.0391749	−	0.0116172i
$562$	−3.23744	−	5.60741i	−0.136563	−	0.236534i
$563$	1.37069			0.0577678			0.0288839	−	0.999583i	$-0.490805\pi$
$563$	1.37069			0.0577678			0.0288839	+	0.999583i	$0.490805\pi$
$564$	−2.27706	−	7.67859i	−0.0958817	−	0.323327i
$565$	40.1954	+	7.08753i	1.69103	+	0.298175i
$566$	11.8528	−	9.94566i	0.498209	−	0.418047i
$567$	−8.45302	+	8.77488i	−0.354993	+	0.368510i
$568$	−21.6164	+	7.86772i	−0.907003	+	0.330122i
$569$	4.06382	+	7.03874i	0.170364	+	0.295079i	0.938547	−	0.345151i	$-0.112172\pi$
$569$	4.06382	+	7.03874i	0.170364	+	0.295079i	−0.768183	+	0.640230i	$0.778839\pi$
$570$	10.0243	+	4.78514i	0.419873	+	0.200427i
$571$	4.97865	−	8.62328i	0.208350	−	0.360873i	−0.742845	−	0.669464i	$-0.766524\pi$
$571$	4.97865	−	8.62328i	0.208350	−	0.360873i	0.951195	+	0.308591i	$0.0998573\pi$
$572$	0.354427	−	2.01005i	0.0148193	−	0.0840446i
$573$	−12.3983	+	6.18633i	−0.517948	+	0.258438i
$574$	7.04115	+	2.56277i	0.293892	+	0.106968i
$575$	−0.805798	+	0.960312i	−0.0336041	+	0.0400478i
$576$	0.404259	+	0.950753i	0.0168441	+	0.0396147i
$577$	−16.9104	−	29.2897i	−0.703989	−	1.21934i	−0.967055	−	0.254567i	$-0.918067\pi$
$577$	−16.9104	−	29.2897i	−0.703989	−	1.21934i	0.263066	−	0.964778i	$-0.415266\pi$
$578$	6.19854			0.257825
$579$	−10.8617	+	11.4528i	−0.451395	+	0.475964i
$580$	13.1982	+	15.7290i	0.548024	+	0.653110i
$581$	−19.1200	+	11.0390i	−0.793233	+	0.457973i
$582$	6.83090	−	0.780406i	0.283150	−	0.0323489i
$583$	1.36768	+	1.62993i	0.0566434	+	0.0675049i
$584$	13.0560	+	10.9553i	0.540263	+	0.453334i
$585$	42.1834	+	5.15319i	1.74407	+	0.213058i
$586$	0.881416	−	4.99876i	0.0364110	−	0.206497i
$587$	−5.32697	+	6.34844i	−0.219868	+	0.262028i	−0.864692	−	0.502303i	$-0.832486\pi$
$587$	−5.32697	+	6.34844i	−0.219868	+	0.262028i	0.644824	+	0.764331i	$0.276931\pi$
$588$	11.6845	−	8.65162i	0.481860	−	0.356787i
$589$	−15.5662	−	0.553155i	−0.641395	−	0.0227924i
$590$	−9.56710	−	5.52356i	−0.393871	−	0.227402i
$591$	−3.95346	+	1.97264i	−0.162624	+	0.0811435i
$592$	5.17807	+	14.2266i	0.212817	+	0.584711i
$593$	11.1484	+	13.2861i	0.457810	+	0.545597i	0.944730	−	0.327850i	$-0.106324\pi$
$593$	11.1484	+	13.2861i	0.457810	+	0.545597i	−0.486920	+	0.873447i	$0.661880\pi$
$594$	0.522831	−	0.431798i	0.0214520	−	0.0177169i
$595$	1.48095	+	8.39890i	0.0607132	+	0.344321i
$596$	15.9159	+	9.18906i	0.651941	+	0.376398i
$597$	3.45639	+	1.50162i	0.141461	+	0.0614573i
$598$	−4.54437	+	3.81318i	−0.185833	+	0.155933i
$599$	10.7279	−	9.00179i	0.438331	−	0.367803i	−0.396753	−	0.917925i	$-0.629863\pi$
$599$	10.7279	−	9.00179i	0.438331	−	0.367803i	0.835084	+	0.550122i	$0.185419\pi$
$600$	0.333655	+	2.92049i	0.0136214	+	0.119228i
$601$	6.29360	+	3.63361i	0.256721	+	0.148218i	0.622838	−	0.782351i	$-0.285980\pi$
$601$	6.29360	+	3.63361i	0.256721	+	0.148218i	−0.366117	+	0.930569i	$0.619313\pi$
$602$	−0.193338	−	1.09648i	−0.00787989	−	0.0446891i
$603$	−16.2218	−	24.9458i	−0.660602	−	1.01587i
$604$	−12.8231	−	15.2820i	−0.521765	−	0.621816i
$605$	−8.99529	−	24.7144i	−0.365711	−	1.00478i
$606$	−0.0215374	+	0.353916i	−0.000874897	+	0.0143768i
$607$	6.15466	+	3.55340i	0.249810	+	0.144228i	0.619677	−	0.784857i	$-0.287263\pi$
$607$	6.15466	+	3.55340i	0.249810	+	0.144228i	−0.369867	+	0.929085i	$0.620597\pi$
$608$	9.15650	−	22.6231i	0.371345	−	0.917489i
$609$	11.3224	+	4.91900i	0.458807	+	0.199328i
$610$	−4.73041	+	5.63748i	−0.191529	+	0.228255i
$611$	−2.91646	+	16.5401i	−0.117987	+	0.669140i
$612$	11.7679	−	5.00370i	0.475689	−	0.202262i
$613$	−20.3676	−	17.0904i	−0.822640	−	0.690277i	0.130949	−	0.991389i	$-0.458198\pi$
$613$	−20.3676	−	17.0904i	−0.822640	−	0.690277i	−0.953589	+	0.301112i	$0.902642\pi$
$614$	1.02524	+	1.22184i	0.0413755	+	0.0493093i
$615$	−14.9657	+	34.4477i	−0.603476	+	1.38907i
$616$	0.554534	−	0.320160i	0.0223428	−	0.0128996i
$617$	−4.45163	−	5.30524i	−0.179216	−	0.213581i	0.668956	−	0.743302i	$-0.266741\pi$
$617$	−4.45163	−	5.30524i	−0.179216	−	0.213581i	−0.848172	+	0.529721i	$0.822297\pi$
$618$	12.2641	+	2.94038i	0.493336	+	0.118280i
$619$	6.66725			0.267979			0.133990	−	0.990983i	$-0.457221\pi$
$619$	6.66725			0.267979			0.133990	+	0.990983i	$0.457221\pi$
$620$	−6.96826	−	12.0694i	−0.279852	−	0.484718i
$621$	8.52488	+	0.0665471i	0.342092	+	0.00267044i
$622$	−5.66367	+	6.74970i	−0.227093	+	0.270638i
$623$	4.98270	+	1.81355i	0.199628	+	0.0726585i
$624$	1.17186	−	19.2568i	0.0469121	−	0.770888i
$625$	−4.90323	+	27.8076i	−0.196129	+	1.11230i
$626$	−5.62732	+	9.74680i	−0.224913	+	0.389560i
$627$	1.60028	+	0.154586i	0.0639090	+	0.00617355i
$628$	3.93075	+	6.80825i	0.156854	+	0.271679i
$629$	19.7744	−	7.19731i	0.788458	−	0.286975i
$630$	3.25750	+	5.00937i	0.129782	+	0.199578i
$631$	−28.4771	+	23.8951i	−1.13365	+	0.951248i	−0.999213	−	0.0396733i	$-0.987368\pi$
$631$	−28.4771	+	23.8951i	−1.13365	+	0.951248i	−0.134441	+	0.990922i	$0.542924\pi$
$632$	−12.2922	−	2.16744i	−0.488956	−	0.0862161i
$633$	9.71317	+	2.32877i	0.386064	+	0.0925604i
$634$	−16.0663			−0.638074
$635$	−4.14957	−	7.18727i	−0.164671	−	0.285218i
$636$	20.3985	+	19.3456i	0.808854	+	0.767102i
$637$	−30.0250	+	5.29423i	−1.18964	+	0.209765i
$638$	−0.594985	−	0.343515i	−0.0235557	−	0.0135999i
$639$	−21.2039	−	22.7104i	−0.838814	−	0.898411i
$640$	26.9757	−	4.75655i	1.06631	−	0.188019i
$641$	5.77012	−	32.7240i	0.227906	−	1.29252i	−0.629145	−	0.777288i	$-0.716595\pi$
$641$	5.77012	−	32.7240i	0.227906	−	1.29252i	0.857051	−	0.515232i	$-0.172294\pi$
$642$	−4.74171	+	19.7774i	−0.187140	+	0.780551i
$643$	−13.9016	−	11.6648i	−0.548224	−	0.460015i	0.326115	−	0.945330i	$-0.394260\pi$
$643$	−13.9016	−	11.6648i	−0.548224	−	0.460015i	−0.874339	+	0.485316i	$0.838705\pi$
$644$	3.55329	+	0.626541i	0.140019	+	0.0246892i
$645$	5.54471	−	0.633463i	0.218323	−	0.0249426i
$646$	−6.49708	−	2.62963i	−0.255624	−	0.103462i
$647$			4.03472i			0.158621i	0.996850	+	0.0793107i	$0.0252719\pi$
$647$			4.03472i			0.158621i	−0.996850	+	0.0793107i	$0.974728\pi$
$648$	13.8686	−	14.3967i	0.544810	−	0.565555i
$649$	−1.57465	−	0.277653i	−0.0618103	−	0.0108988i
$650$	0.944911	−	2.59612i	0.0370624	−	0.101828i
$651$	−6.98854	−	4.62253i	−0.273902	−	0.181171i
$652$	−16.6276	−	6.05194i	−0.651186	−	0.237012i
$653$		−	23.1593i		−	0.906294i	−0.891436	−	0.453147i	$-0.850301\pi$
$653$		−	23.1593i		−	0.906294i	0.891436	−	0.453147i	$-0.149699\pi$
$654$	−13.8259	+	1.57956i	−0.540636	+	0.0617657i
$655$	−4.07409	−	23.1053i	−0.159188	−	0.902798i
$656$	16.0221	+	5.83155i	0.625556	+	0.227684i
$657$	−6.71691	+	22.0183i	−0.262052	+	0.859018i
$658$	−2.04514	+	1.18076i	−0.0797280	+	0.0460310i
$659$	−26.1518	+	21.9440i	−1.01873	+	0.854816i	−0.989467	−	0.144756i	$-0.953760\pi$
$659$	−26.1518	+	21.9440i	−1.01873	+	0.854816i	−0.0292625	+	0.999572i	$0.509316\pi$
$660$	0.642251	+	1.28717i	0.0249996	+	0.0501029i
$661$	−28.8821	+	5.09269i	−1.12338	+	0.198083i	−0.704325	−	0.709877i	$-0.748750\pi$
$661$	−28.8821	+	5.09269i	−1.12338	+	0.198083i	−0.419057	+	0.907960i	$0.637639\pi$
$662$	−1.53502	+	1.82936i	−0.0596601	+	0.0711001i
$663$	−26.7661	−	1.62884i	−1.03951	−	0.0632590i
$664$	31.3697	−	18.1113i	1.21738	−	0.702854i
$665$	−2.95409	+	13.8561i	−0.114555	+	0.537315i
$666$	10.7768	−	10.0619i	0.417594	−	0.389892i
$667$	−2.95422	−	8.11667i	−0.114388	−	0.314279i
$668$	−30.6223	+	11.1456i	−1.18481	+	0.431236i
$669$	35.3603	+	8.47779i	1.36711	+	0.327770i
$670$	−13.7132	+	4.99118i	−0.529785	+	0.192826i
$671$	−0.364305	+	1.00092i	−0.0140638	+	0.0386401i
$672$	10.5514	−	7.81262i	0.407028	−	0.301378i
$673$			15.3248i			0.590728i	0.955385	+	0.295364i	$0.0954410\pi$
$673$			15.3248i			0.590728i	−0.955385	+	0.295364i	$0.904559\pi$
$674$	1.57557	−	4.32885i	0.0606889	−	0.166741i
$675$	−3.45375	+	1.95824i	−0.132935	+	0.0753726i
$676$	−17.7173	+	30.6873i	−0.681436	+	1.18028i
$677$	3.60132	−	6.23768i	0.138410	−	0.239733i	−0.788485	−	0.615054i	$-0.789134\pi$
$677$	3.60132	−	6.23768i	0.138410	−	0.239733i	0.926895	+	0.375321i	$0.122467\pi$
$678$	−17.3000	+	5.13027i	−0.664402	+	0.197027i
$679$	2.99921	+	8.24027i	0.115099	+	0.316232i
$680$	−2.42975	−	13.7798i	−0.0931768	−	0.528432i
$681$	−12.7559	−	25.5648i	−0.488808	−	0.979644i
$682$	0.357222	+	0.299745i	0.0136787	+	0.0114778i
$683$	−26.7216			−1.02247			−0.511236	−	0.859440i	$-0.670812\pi$
$683$	−26.7216			−1.02247			−0.511236	+	0.859440i	$0.670812\pi$
$684$	21.2393	−	0.370727i	0.812106	−	0.0141751i
$685$	−40.5697			−1.55009
$686$	−7.73260	−	6.48842i	−0.295232	−	0.247729i
$687$	−4.62739	+	6.99588i	−0.176546	+	0.266909i
$688$	−0.439939	−	2.49502i	−0.0167725	−	0.0951217i
$689$	−20.1634	−	55.3985i	−0.768165	−	2.11052i
$690$	0.974773	−	4.06572i	0.0371090	−	0.154779i
$691$	−14.8317	+	25.6893i	−0.564224	+	0.977265i	0.432897	+	0.901443i	$0.357491\pi$
$691$	−14.8317	+	25.6893i	−0.564224	+	0.977265i	−0.997121	+	0.0758219i	$0.975842\pi$
$692$	−5.80521	+	10.0549i	−0.220681	+	0.382231i
$693$	0.691029	+	0.520063i	0.0262500	+	0.0197556i
$694$	7.58712	−	20.8454i	0.288003	−	0.791282i
$695$			49.9289i			1.89391i
$696$	−18.5763	−	8.07044i	−0.704134	−	0.305909i
$697$	8.10562	−	22.2700i	0.307022	−	0.843536i
$698$	−4.78789	+	1.74265i	−0.181224	+	0.0659602i
$699$	19.9480	−	21.0338i	0.754504	−	0.795570i
$700$	−1.57901	+	0.574712i	−0.0596809	+	0.0217221i
$701$	−3.28213	−	9.01757i	−0.123964	−	0.340589i	0.862151	−	0.506651i	$-0.169117\pi$
$701$	−3.28213	−	9.01757i	−0.123964	−	0.340589i	−0.986115	+	0.166062i	$0.946895\pi$
$702$	−17.7046	+	6.28789i	−0.668218	+	0.237321i
$703$	34.9354	+	1.24145i	1.31761	+	0.0468222i
$704$	0.0635096	−	0.0366673i	0.00239361	−	0.00138195i
$705$	−5.28487	−	10.5917i	−0.199040	−	0.398906i
$706$	−8.44457	+	10.0638i	−0.317816	+	0.378758i
$707$	−0.445365	+	0.0785298i	−0.0167497	+	0.00295342i
$708$	−21.0874	−	1.28327i	−0.792513	−	0.0482281i
$709$	18.4100	−	15.4478i	0.691402	−	0.580155i	−0.227911	−	0.973682i	$-0.573190\pi$
$709$	18.4100	−	15.4478i	0.691402	−	0.580155i	0.919313	+	0.393527i	$0.128745\pi$
$710$	−13.1962	+	7.61884i	−0.495245	+	0.285930i
$711$	−3.80248	−	16.4244i	−0.142604	−	0.615962i
$712$	−8.17496	−	2.97544i	−0.306369	−	0.111509i
$713$	1.01805	+	5.77366i	0.0381264	+	0.216225i
$714$	−2.24369	−	3.03023i	−0.0839679	−	0.113403i
$715$		−	3.01656i		−	0.112813i
$716$	−1.68714	−	0.614069i	−0.0630514	−	0.0229488i
$717$	−2.92248	+	1.45821i	−0.109142	+	0.0544580i
$718$	−6.97612	+	19.1667i	−0.260346	+	0.715296i
$719$	21.3021	+	3.75613i	0.794434	+	0.140080i	0.556113	−	0.831107i	$-0.312292\pi$
$719$	21.3021	+	3.75613i	0.794434	+	0.140080i	0.238320	+	0.971187i	$0.423403\pi$
$720$	7.41240	+	11.3988i	0.276244	+	0.424807i
$721$			16.0855i			0.599057i
$722$	−8.36566	−	8.09850i	−0.311338	−	0.301395i
$723$	22.2591	+	30.0621i	0.827824	+	1.11802i
$724$	9.19625	+	1.62155i	0.341776	+	0.0602643i
$725$	3.08152	+	2.58570i	0.114445	+	0.0960305i
$726$	8.43677	+	8.00128i	0.313118	+	0.296955i
$727$	−8.01126	+	45.4341i	−0.297121	+	1.68506i	0.361332	+	0.932437i	$0.382322\pi$
$727$	−8.01126	+	45.4341i	−0.297121	+	1.68506i	−0.658453	+	0.752622i	$0.728789\pi$
$728$	−17.4721	+	3.08081i	−0.647560	+	0.114182i
$729$	25.2244	+	9.62951i	0.934239	+	0.356648i
$730$	9.77709	+	5.64481i	0.361866	+	0.208924i
$731$	−3.46798	+	0.611498i	−0.128268	+	0.0226171i
$732$	−3.28124	+	13.6858i	−0.121278	+	0.505843i
$733$	1.24814	+	2.16184i	0.0461010	+	0.0798493i	0.888155	−	0.459544i	$-0.151987\pi$
$733$	1.24814	+	2.16184i	0.0461010	+	0.0798493i	−0.842054	+	0.539393i	$0.818654\pi$
$734$	4.97964			0.183802
$735$	14.7862	−	15.5910i	0.545398	−	0.575083i
$736$	−9.04668	−	1.59517i	−0.333465	−	0.0587989i
$737$	−1.61803	+	1.35769i	−0.0596010	+	0.0500112i
$738$	−0.879194	−	16.5813i	−0.0323636	−	0.610366i
$739$	21.6651	−	7.88546i	0.796965	−	0.290071i	0.0887366	−	0.996055i	$-0.471717\pi$
$739$	21.6651	−	7.88546i	0.796965	−	0.290071i	0.708228	+	0.705984i	$0.249495\pi$
$740$	15.6389	+	27.0874i	0.574898	+	0.995753i
$741$	−40.2007	−	19.1899i	−1.47681	−	0.704960i
$742$	4.14466	−	7.17877i	0.152155	−	0.263541i
$743$	−0.425244	+	2.41168i	−0.0156007	+	0.0884760i	−0.991614	−	0.129235i	$-0.958748\pi$
$743$	−0.425244	+	2.41168i	−0.0156007	+	0.0884760i	0.976013	+	0.217711i	$0.0698590\pi$
$744$	11.4659	+	7.58404i	0.420359	+	0.278044i
$745$	25.5237	+	9.28985i	0.935114	+	0.340354i
$746$	−5.07864	+	6.05249i	−0.185942	+	0.221597i
$747$	39.0911	+	29.4197i	1.43027	+	1.07641i
$748$	−0.453847	−	0.786087i	−0.0165943	−	0.0287422i
$749$	−25.9398			−0.947820
$750$	−3.06897	−	10.3490i	−0.112063	−	0.377893i
$751$	12.5354	+	14.9392i	0.457425	+	0.545138i	0.944625	−	0.328153i	$-0.106426\pi$
$751$	12.5354	+	14.9392i	0.457425	+	0.545138i	−0.487200	+	0.873291i	$0.661982\pi$
$752$	−4.65370	+	2.68681i	−0.169703	+	0.0979781i
$753$	−3.44252	−	4.64932i	−0.125452	−	0.169431i
$754$	12.2360	+	14.5823i	0.445609	+	0.531056i
$755$	−22.5858	−	18.9518i	−0.821983	−	0.689726i
$756$	9.85138	+	5.79070i	0.358291	+	0.210606i
$757$	−6.48157	+	36.7588i	−0.235577	+	1.33602i	0.605819	+	0.795603i	$0.292846\pi$
$757$	−6.48157	+	36.7588i	−0.235577	+	1.33602i	−0.841396	+	0.540420i	$0.818266\pi$
$758$	−3.20894	+	3.82427i	−0.116554	+	0.138904i
$759$	−0.0686883	−	0.601229i	−0.00249323	−	0.0218232i
$760$	4.84669	−	22.7332i	0.175808	−	0.824621i
$761$	−45.1859	−	26.0881i	−1.63799	−	0.945694i	−0.981524	−	0.191337i	$-0.938718\pi$
$761$	−45.1859	−	26.0881i	−1.63799	−	0.945694i	−0.656465	−	0.754357i	$-0.727949\pi$
$762$	3.06021	+	2.02416i	0.110860	+	0.0733276i
$763$	−6.07048	−	16.6785i	−0.219766	−	0.603802i
$764$	8.35323	+	9.95499i	0.302209	+	0.360159i
$765$	15.8438	−	10.3029i	0.572835	−	0.372503i
$766$	1.72248	+	9.76867i	0.0622358	+	0.352957i
$767$	38.3671	+	22.1512i	1.38536	+	0.799835i
$768$	−8.77377	+	6.49642i	−0.316596	+	0.234419i
$769$	1.32416	−	1.11110i	0.0477503	−	0.0400672i	−0.618600	−	0.785706i	$-0.712300\pi$
$769$	1.32416	−	1.11110i	0.0477503	−	0.0400672i	0.666350	+	0.745639i	$0.267855\pi$
$770$	0.324918	−	0.272638i	0.0117092	−	0.00982520i
$771$	9.16441	−	6.78566i	0.330048	−	0.244379i
$772$	12.8205	+	7.40189i	0.461418	+	0.266400i
$773$	0.754896	+	4.28123i	0.0271517	+	0.153985i	0.995369	−	0.0961242i	$-0.0306446\pi$
$773$	0.754896	+	4.28123i	0.0271517	+	0.153985i	−0.968218	+	0.250109i	$0.919533\pi$
$774$	−2.06841	+	1.34505i	−0.0743475	+	0.0483467i
$775$	−1.75504	−	2.09157i	−0.0630428	−	0.0751315i
$776$	−4.92071	−	13.5195i	−0.176643	−	0.485323i
$777$	15.6844	+	10.3744i	0.562676	+	0.372179i
$778$	1.99602	+	1.15240i	0.0715608	+	0.0413157i
$779$	26.3610	−	29.2408i	0.944482	−	1.04766i
$780$	−4.52411	−	39.5996i	−0.161989	−	1.41789i
$781$	−1.41765	+	1.68949i	−0.0507274	+	0.0604546i
$782$	−0.458114	+	2.59809i	−0.0163821	+	0.0929077i
$783$	0.213541	−	27.3553i	0.00763133	−	0.977597i
$784$	−7.47253	−	6.27020i	−0.266876	−	0.223936i
$785$	7.46842	+	8.90051i	0.266559	+	0.317673i
$786$	6.17236	+	8.33612i	0.220161	+	0.297339i
$787$	−33.1048	+	19.1130i	−1.18006	+	0.681307i	−0.956028	−	0.293276i	$-0.905255\pi$
$787$	−33.1048	+	19.1130i	−1.18006	+	0.681307i	−0.224030	+	0.974582i	$0.571921\pi$
$788$	2.66360	+	3.17435i	0.0948867	+	0.113082i
$789$	−2.77762	−	9.36653i	−0.0988859	−	0.333457i
$790$	−8.26796			−0.294161
$791$	−11.5075	−	19.9315i	−0.409159	−	0.708684i
$792$	−1.13375	−	0.853252i	−0.0402861	−	0.0303190i
$793$	18.9705	−	22.6081i	0.673660	−	0.802837i
$794$	10.8477	+	3.94823i	0.384969	+	0.140117i
$795$	34.6546	+	22.9221i	1.22907	+	0.812963i
$796$	0.613743	−	3.48071i	0.0217535	−	0.123370i
$797$	−12.9113	+	22.3631i	−0.457343	+	0.792140i	−0.998820	−	0.0485751i	$-0.984532\pi$
$797$	−12.9113	+	22.3631i	−0.457343	+	0.792140i	0.541477	+	0.840716i	$0.317865\pi$
$798$	−1.56639	−	6.06446i	−0.0554496	−	0.214680i
$799$	3.73456	+	6.46845i	0.132119	+	0.228837i
$800$	4.02015	−	1.46322i	0.142134	−	0.0517325i
$801$	−0.622165	−	11.7338i	−0.0219831	−	0.414594i
$802$	−13.5079	+	11.3344i	−0.476979	+	0.400233i
$803$	1.60921	+	0.283747i	0.0567878	+	0.0100132i
$804$	−19.2043	+	20.2496i	−0.677285	+	0.714148i
$805$	5.33256			0.187948
$806$	−6.46027	−	11.1895i	−0.227553	−	0.394134i
$807$	0.414243	−	1.72778i	0.0145820	−	0.0608208i
$808$	0.730696	−	0.128841i	0.0257058	−	0.00453262i
$809$	15.4313	+	8.90926i	0.542535	+	0.313233i	0.746106	−	0.665827i	$-0.231921\pi$
$809$	15.4313	+	8.90926i	0.542535	+	0.313233i	−0.203571	+	0.979060i	$0.565255\pi$
$810$	7.39105	−	10.9867i	0.259695	−	0.386035i
$811$	−6.39075	+	1.12686i	−0.224410	+	0.0395695i	−0.284722	−	0.958610i	$-0.591901\pi$
$811$	−6.39075	+	1.12686i	−0.224410	+	0.0395695i	0.0603125	+	0.998180i	$0.480790\pi$
$812$	2.01049	−	11.4021i	0.0705544	−	0.400134i
$813$	35.0806	+	33.2698i	1.23033	+	1.16682i
$814$	−0.801716	−	0.672719i	−0.0281001	−	0.0235788i
$815$	−25.7543	−	4.54118i	−0.902135	−	0.159071i
$816$	−5.10549	−	6.89524i	−0.178728	−	0.241382i
$817$	−5.72128	−	1.21977i	−0.200162	−	0.0426743i
$818$		−	7.64243i		−	0.267211i
$819$	−13.0636	−	20.0892i	−0.456479	−	0.701973i
$820$	34.6900	+	6.11678i	1.21143	+	0.213607i
$821$	14.1538	−	38.8874i	0.493973	−	1.35718i	−0.403043	−	0.915181i	$-0.632048\pi$
$821$	14.1538	−	38.8874i	0.493973	−	1.35718i	0.897016	−	0.441998i	$-0.145730\pi$
$822$	16.0491	−	8.00794i	0.559777	−	0.279309i
$823$	16.6469	+	6.05899i	0.580276	+	0.211203i	0.615447	−	0.788178i	$-0.288975\pi$
$823$	16.6469	+	6.05899i	0.580276	+	0.211203i	−0.0351713	+	0.999381i	$0.511198\pi$
$824$		−	26.3910i		−	0.919376i
$825$	0.167704	+	0.226493i	0.00583869	+	0.00788547i
$826$	1.08170	+	6.13460i	0.0376370	+	0.213450i
$827$	−8.30461	−	3.02263i	−0.288780	−	0.105107i	0.193569	−	0.981087i	$-0.437994\pi$
$827$	−8.30461	−	3.02263i	−0.288780	−	0.105107i	−0.482348	+	0.875980i	$0.660216\pi$
$828$	−1.80340	−	7.78955i	−0.0626723	−	0.270706i
$829$	35.6777	−	20.5985i	1.23914	−	0.715416i	0.270219	−	0.962799i	$-0.412904\pi$
$829$	35.6777	−	20.5985i	1.23914	−	0.715416i	0.968918	+	0.247383i	$0.0795706\pi$
$830$	18.3804	−	15.4230i	0.637993	−	0.535339i
$831$	41.5098	+	2.52606i	1.43996	+	0.0876282i
$832$	−2.00105	+	0.352838i	−0.0693738	+	0.0122325i
$833$	−8.71532	+	10.3865i	−0.301968	+	0.359871i
$834$	−9.85531	−	19.7515i	−0.341261	−	0.683939i
$835$	−41.7098	+	24.0812i	−1.44343	+	0.833363i
$836$	−0.208937	−	1.49331i	−0.00722622	−	0.0516474i
$837$	−3.36692	+	18.2601i	−0.116378	+	0.631160i
$838$	5.12549	+	14.0822i	0.177057	+	0.486460i
$839$	12.1875	−	4.43588i	0.420758	−	0.153144i	−0.122959	−	0.992412i	$-0.539238\pi$
$839$	12.1875	−	4.43588i	0.420758	−	0.153144i	0.543718	+	0.839268i	$0.317016\pi$
$840$	8.60438	−	9.07270i	0.296879	−	0.313038i
$841$	1.20575	−	0.438857i	0.0415775	−	0.0151330i
$842$	7.48107	−	20.5541i	0.257815	−	0.708340i
$843$	−16.7849	−	7.29217i	−0.578104	−	0.251156i
$844$		−	9.36797i		−	0.322459i
$845$	−17.9117	+	49.2119i	−0.616180	+	1.69294i
$846$	4.18132	+	3.14683i	0.143757	+	0.108190i
$847$	−7.41514	+	12.8434i	−0.254787	+	0.441304i
$848$	9.43113	−	16.3352i	0.323866	−	0.560953i
$849$	10.1960	−	42.5267i	0.349925	−	1.45951i
$850$	−0.420218	−	1.15454i	−0.0144133	−	0.0396003i
$851$	−2.28482	−	12.9579i	−0.0783228	−	0.444191i
$852$	−16.0762	+	24.3047i	−0.550761	+	0.832665i
$853$	−27.1392	−	22.7725i	−0.929228	−	0.779715i	0.0464505	−	0.998921i	$-0.485209\pi$
$853$	−27.1392	−	22.7725i	−0.929228	−	0.779715i	−0.975679	+	0.219206i	$0.929653\pi$
$854$	4.14970			0.142000
$855$	30.8184	−	5.99047i	1.05397	−	0.204870i
$856$	42.5586			1.45462
$857$	21.0222	+	17.6398i	0.718106	+	0.602562i	0.926861	−	0.375406i	$-0.122497\pi$
$857$	21.0222	+	17.6398i	0.718106	+	0.602562i	−0.208755	+	0.977968i	$0.566941\pi$
$858$	0.595430	+	1.19333i	0.0203276	+	0.0407396i
$859$	−3.20675	−	18.1864i	−0.109413	−	0.620511i	−0.989366	−	0.145450i	$-0.953537\pi$
$859$	−3.20675	−	18.1864i	−0.109413	−	0.620511i	0.879953	−	0.475061i	$-0.157574\pi$
$860$	−1.79017	−	4.91846i	−0.0610444	−	0.167718i
$861$	20.3043	−	6.02118i	0.691968	−	0.205201i
$862$	4.25778	−	7.37469i	0.145021	−	0.251183i
$863$	14.5665	−	25.2300i	0.495850	−	0.858838i	−0.504138	−	0.863623i	$-0.668190\pi$
$863$	14.5665	−	25.2300i	0.495850	−	0.858838i	0.999989	+	0.00478491i	$0.00152309\pi$
$864$	−25.0816	−	14.7431i	−0.853294	−	0.501571i
$865$	−5.86889	+	16.1246i	−0.199548	+	0.548254i
$866$			21.8395i			0.742137i
$867$	14.0800	−	10.4253i	0.478181	−	0.354062i
$868$	−2.68777	+	7.38458i	−0.0912288	+	0.250649i
$869$	−1.12452	+	0.409291i	−0.0381467	+	0.0138842i
$870$	−13.0464	−	3.12792i	−0.442313	−	0.106046i
$871$	54.9941	−	20.0162i	1.86340	−	0.678224i
$872$	9.95964	+	27.3639i	0.337276	+	0.926658i
$873$	14.2038	−	13.2616i	0.480726	−	0.448836i
$874$	−2.32467	+	3.71517i	−0.0786331	+	0.125667i
$875$	11.9232	−	6.88388i	0.403079	−	0.232718i
$876$	21.5503	+	1.31143i	0.728116	+	0.0443092i
$877$	11.4240	−	13.6146i	0.385762	−	0.459734i	−0.537862	−	0.843033i	$-0.680768\pi$
$877$	11.4240	−	13.6146i	0.385762	−	0.459734i	0.923624	+	0.383299i	$0.125212\pi$
$878$	1.05743	−	0.186454i	0.0356866	−	0.00629250i
$879$	−6.40528	−	12.8371i	−0.216045	−	0.432986i
$880$	0.739346	−	0.620385i	0.0249233	−	0.0209132i
$881$	−48.0148	+	27.7214i	−1.61766	+	0.933957i	−0.630138	+	0.776483i	$0.717002\pi$
$881$	−48.0148	+	27.7214i	−1.61766	+	0.933957i	−0.987523	+	0.157474i	$0.949665\pi$
$882$	−2.77187	+	9.08631i	−0.0933336	+	0.305952i
$883$	−41.9764	−	15.2781i	−1.41262	−	0.514150i	−0.480720	−	0.876874i	$-0.659625\pi$
$883$	−41.9764	−	15.2781i	−1.41262	−	0.514150i	−0.931897	+	0.362724i	$0.881847\pi$
$884$	4.36724	+	24.7678i	0.146886	+	0.833032i
$885$	−31.0217	+	3.54412i	−1.04278	+	0.119134i
$886$			15.7193i			0.528099i
$887$	−2.41742	−	0.879868i	−0.0811690	−	0.0295431i	0.301117	−	0.953587i	$-0.402641\pi$
$887$	−2.41742	−	0.879868i	−0.0811690	−	0.0295431i	−0.382285	+	0.924044i	$0.624863\pi$
$888$	−25.7330	−	17.0209i	−0.863542	−	0.571185i
$889$	−1.60055	+	4.39749i	−0.0536809	+	0.147487i
$890$	−5.67509	−	1.00067i	−0.190229	−	0.0335426i
$891$	0.461370	−	1.86018i	0.0154565	−	0.0623183i
$892$		−	34.1037i		−	1.14188i
$893$	1.71927	+	12.2880i	0.0575332	+	0.411202i
$894$	−11.9307	+	1.36304i	−0.399021	+	0.0455868i
$895$	−2.61320	−	0.460778i	−0.0873497	−	0.0154021i
$896$	−11.8321	−	9.92829i	−0.395282	−	0.331681i
$897$	−3.90915	+	16.3048i	−0.130523	+	0.544402i
$898$	3.65316	−	20.7181i	0.121907	−	0.691372i
$899$	18.5269	−	3.26680i	0.617908	−	0.108954i
$900$	2.54119	+	2.72175i	0.0847065	+	0.0907249i
$901$	−22.7053	−	13.1089i	−0.756422	−	0.436720i
$902$	−1.16074	+	0.204669i	−0.0386483	+	0.00681474i
$903$	−2.28333	−	2.16547i	−0.0759845	−	0.0720623i
$904$	18.8800	+	32.7011i	0.627938	+	1.08762i
$905$	13.8011			0.458766
$906$	12.6756	+	3.03904i	0.421120	+	0.100965i
$907$	−33.3558	−	5.88153i	−1.10756	−	0.195293i	−0.410188	−	0.912001i	$-0.634537\pi$
$907$	−33.3558	−	5.88153i	−1.10756	−	0.195293i	−0.697373	+	0.716708i	$0.745648\pi$
$908$	−20.5267	+	17.2240i	−0.681203	+	0.571597i
$909$	0.546328	+	0.840143i	0.0181206	+	0.0278658i
$910$	−11.0434	+	4.01946i	−0.366084	+	0.133244i
$911$	−17.2638	−	29.9017i	−0.571974	−	0.990689i	−0.996363	−	0.0852086i	$-0.972844\pi$
$911$	−17.2638	−	29.9017i	−0.571974	−	0.990689i	0.424389	−	0.905480i	$-0.360489\pi$
$912$	−3.56430	−	13.7996i	−0.118026	−	0.456951i
$913$	1.73641	−	3.00755i	0.0574669	−	0.0995355i
$914$	1.06574	−	6.04412i	0.0352516	−	0.199922i
$915$	−1.26344	+	20.7616i	−0.0417680	+	0.686358i
$916$	7.39234	+	2.69059i	0.244250	+	0.0888996i
$917$	−8.50380	+	10.1344i	−0.280820	+	0.334668i
$918$	−4.23404	+	7.20313i	−0.139744	+	0.237739i
$919$	1.00426	+	1.73944i	0.0331276	+	0.0573787i	0.882114	−	0.471036i	$-0.156120\pi$
$919$	1.00426	+	1.73944i	0.0331276	+	0.0573787i	−0.848986	+	0.528415i	$0.822787\pi$
$920$	−8.74896			−0.288445
$921$	4.38385	+	1.05105i	0.144453	+	0.0346331i
$922$	−12.0380	−	14.3463i	−0.396450	−	0.472471i
$923$	52.9210	−	30.5540i	1.74192	−	1.00570i
$924$	0.323213	−	0.743963i	0.0106329	−	0.0244746i
$925$	3.93885	+	4.69413i	0.129508	+	0.154342i
$926$	3.97871	+	3.33853i	0.130748	+	0.109711i
$927$	32.8034	−	13.9480i	1.07741	−	0.458112i
$928$	−5.11871	+	29.0296i	−0.168030	+	0.952944i
$929$	10.4762	−	12.4850i	0.343712	−	0.409620i	−0.566302	−	0.824198i	$-0.691626\pi$
$929$	10.4762	−	12.4850i	0.343712	−	0.409620i	0.910014	+	0.414578i	$0.136071\pi$
$930$	8.35199	+	3.62850i	0.273872	+	0.118983i
$931$	−19.8936	+	10.5620i	−0.651987	+	0.346154i
$932$	−23.5455	−	13.5940i	−0.771258	−	0.445286i
$933$	−1.51270	+	24.8577i	−0.0495237	+	0.813804i
$934$	3.97142	+	10.9114i	0.129949	+	0.357031i
$935$	−0.862310	−	1.02766i	−0.0282005	−	0.0336081i
$936$	21.4330	+	32.9597i	0.700561	+	1.07732i
$937$	1.47493	+	8.36474i	0.0481839	+	0.273264i	0.999375	−	0.0353367i	$-0.0112504\pi$
$937$	1.47493	+	8.36474i	0.0481839	+	0.273264i	−0.951192	+	0.308601i	$0.900139\pi$
$938$	7.12636	+	4.11441i	0.232684	+	0.134340i
$939$	3.61069	+	31.6044i	0.117830	+	1.03137i
$940$	−8.50437	+	7.13601i	−0.277382	+	0.232751i
$941$	−24.8610	+	20.8609i	−0.810446	+	0.680045i	−0.950714	−	0.310068i	$-0.899648\pi$
$941$	−24.8610	+	20.8609i	−0.810446	+	0.680045i	0.140268	+	0.990114i	$0.455204\pi$
$942$	−4.71130	−	2.04681i	−0.153502	−	0.0666887i
$943$	−12.8330	−	7.40915i	−0.417901	−	0.241275i
$944$	2.46139	+	13.9592i	0.0801113	+	0.454334i
$945$	15.8247	+	5.90000i	0.514776	+	0.191927i
$946$	0.112575	+	0.134161i	0.00366011	+	0.00436195i
$947$	−8.19676	−	22.5204i	−0.266359	−	0.731815i	−0.998705	−	0.0508819i	$-0.983797\pi$
$947$	−8.19676	−	22.5204i	−0.266359	−	0.731815i	0.732346	−	0.680933i	$-0.238425\pi$
$948$	−14.1481	+	7.05943i	−0.459510	+	0.229280i
$949$	−39.2092	−	22.6375i	−1.27279	−	0.734843i
$950$	0.0724826	−	2.03972i	0.00235164	−	0.0661771i
$951$	−36.4946	+	27.0219i	−1.18342	+	0.876245i
$952$	−5.07160	+	6.04410i	−0.164372	+	0.195890i
$953$	8.66744	−	49.1555i	0.280766	−	1.59230i	−0.439263	−	0.898359i	$-0.644760\pi$
$953$	8.66744	−	49.1555i	0.280766	−	1.59230i	0.720029	−	0.693944i	$-0.244129\pi$
$954$	−18.2336	−	2.22745i	−0.590336	−	0.0721164i
$955$	14.7128	+	12.3455i	0.476097	+	0.399492i
$956$	1.96898	+	2.34654i	0.0636815	+	0.0758927i
$957$	−1.92927	+	0.220412i	−0.0623643	+	0.00712490i
$958$	−8.08830	+	4.66978i	−0.261321	+	0.150874i
$959$	14.7047	+	17.5243i	0.474839	+	0.565891i
$960$	0.985441	−	1.03908i	0.0318050	−	0.0335361i
$961$	18.2309			0.588093
$962$	14.4988	+	25.1127i	0.467461	+	0.809666i
$963$	22.4928	+	52.8993i	0.724819	+	1.70466i
$964$	22.5505	−	26.8746i	0.726301	−	0.865572i
$965$	20.5596	+	7.48308i	0.661837	+	0.240889i
$966$	−2.10952	+	1.05258i	−0.0678727	+	0.0338661i
$967$	−3.14701	+	17.8476i	−0.101201	+	0.573939i	0.891469	+	0.453082i	$0.149676\pi$
$967$	−3.14701	+	17.8476i	−0.101201	+	0.573939i	−0.992670	+	0.120857i	$0.961436\pi$
$968$	12.1658	−	21.0718i	0.391023	−	0.677272i
$969$	−19.1809	+	4.95423i	−0.616179	+	0.159153i
$970$	−4.76506	−	8.25332i	−0.152997	−	0.264998i
$971$	39.2188	−	14.2745i	1.25859	−	0.458090i	0.375296	−	0.926905i	$-0.377541\pi$
$971$	39.2188	−	14.2745i	1.25859	−	0.458090i	0.883296	+	0.468815i	$0.155319\pi$
$972$	3.26677	−	25.1112i	0.104782	−	0.805443i
$973$	21.5671	−	18.0969i	0.691409	−	0.580161i
$974$	18.9151	+	3.33524i	0.606079	+	0.106868i
$975$	−2.22005	−	7.48633i	−0.0710985	−	0.239754i
$976$	9.44260			0.302250
$977$	14.0995	+	24.4211i	0.451084	+	0.781300i	0.998454	−	0.0555909i	$-0.0177043\pi$
$977$	14.0995	+	24.4211i	0.451084	+	0.781300i	−0.547370	+	0.836891i	$0.684371\pi$
$978$	11.0846	−	3.28711i	0.354446	−	0.105110i
$979$	−0.821400	+	0.144835i	−0.0262521	+	0.00462895i
$980$	−17.4528	−	10.0764i	−0.557509	−	0.321878i
$981$	−28.7489	+	26.8418i	−0.917880	+	0.856991i
$982$	−7.70286	+	1.35822i	−0.245808	+	0.0433426i
$983$	−9.72698	+	55.1645i	−0.310243	+	1.75947i	0.287496	+	0.957782i	$0.407177\pi$
$983$	−9.72698	+	55.1645i	−0.310243	+	1.75947i	−0.597739	+	0.801691i	$0.703934\pi$
$984$	−33.3126	+	9.87876i	−1.06197	+	0.314923i
$985$	4.69149	+	3.93663i	0.149483	+	0.125431i
$986$	8.33695	+	1.47003i	0.265503	+	0.0468153i
$987$	−2.65961	+	6.12183i	−0.0846564	+	0.194860i
$988$	−8.71143	+	40.8607i	−0.277148	+	1.29995i
$989$			2.20186i			0.0700149i
$990$	−0.837734	−	0.426200i	−0.0266249	−	0.0135455i
$991$	−52.6592	−	9.28524i	−1.67277	−	0.294955i	−0.744714	−	0.667384i	$-0.767414\pi$
$991$	−52.6592	−	9.28524i	−1.67277	−	0.294955i	−0.928061	+	0.372429i	$0.878525\pi$
$992$	6.84305	−	18.8011i	0.217267	−	0.596937i
$993$	−0.409985	+	6.73713i	−0.0130105	+	0.213796i
$994$	8.07403	+	2.93871i	0.256093	+	0.0932101i
$995$		−	5.22363i		−	0.165600i
$996$	18.2840	−	42.0855i	0.579349	−	1.33353i
$997$	−1.57180	−	8.91410i	−0.0497793	−	0.282312i	0.949749	−	0.313011i	$-0.101338\pi$
$997$	−1.57180	−	8.91410i	−0.0497793	−	0.282312i	−0.999529	+	0.0306989i	$0.990227\pi$
$998$	−8.99503	−	3.27392i	−0.284733	−	0.103634i
$999$	7.55640	−	40.9812i	0.239074	−	1.29659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.x.a.14.12	✓	108
3.2	odd	2		513.2.bo.a.71.7		108
9.2	odd	6		171.2.bd.a.128.7	yes	108
9.7	even	3		513.2.cd.a.413.12		108
19.15	odd	18		171.2.bd.a.167.7	yes	108
57.53	even	18		513.2.cd.a.395.12		108
171.34	odd	18		513.2.bo.a.224.7		108
171.110	even	18	inner	171.2.x.a.110.12	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.x.a.14.12	✓	108	1.1	even	1	trivial
171.2.x.a.110.12	yes	108	171.110	even	18	inner
171.2.bd.a.128.7	yes	108	9.2	odd	6
171.2.bd.a.167.7	yes	108	19.15	odd	18
513.2.bo.a.71.7		108	3.2	odd	2
513.2.bo.a.224.7		108	171.34	odd	18
513.2.cd.a.395.12		108	57.53	even	18
513.2.cd.a.413.12		108	9.7	even	3

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.x (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.469442 + 0.393909i) q^{2} +(1.72885 + 0.105209i) q^{3} +(-0.282084 - 1.59978i) q^{4} +(-0.821139 - 2.25606i) q^{5} +(0.770154 + 0.730400i) q^{6} +(-0.676894 + 1.17241i) q^{7} +(1.11056 - 1.92354i) q^{8} +(2.97786 + 0.363781i) q^{9} +O(q^{10})\)	\(q+(0.469442 + 0.393909i) q^{2} +(1.72885 + 0.105209i) q^{3} +(-0.282084 - 1.59978i) q^{4} +(-0.821139 - 2.25606i) q^{5} +(0.770154 + 0.730400i) q^{6} +(-0.676894 + 1.17241i) q^{7} +(1.11056 - 1.92354i) q^{8} +(2.97786 + 0.363781i) q^{9} +(0.503205 - 1.38254i) q^{10} -0.212949i q^{11} +(-0.319372 - 2.79546i) q^{12} +(-2.01801 + 5.54444i) q^{13} +(-0.779587 + 0.283747i) q^{14} +(-1.18227 - 3.98679i) q^{15} +(-1.77394 + 0.645662i) q^{16} +(0.897444 + 2.46571i) q^{17} +(1.25464 + 1.34378i) q^{18} +(-0.154798 + 4.35615i) q^{19} +(-3.37757 + 1.95004i) q^{20} +(-1.29360 + 1.95572i) q^{21} +(0.0838824 - 0.0999672i) q^{22} +(1.61574 - 0.284898i) q^{23} +(2.12237 - 3.20868i) q^{24} +(-0.585319 + 0.491141i) q^{25} +(-3.13134 + 1.80788i) q^{26} +(5.11001 + 0.942220i) q^{27} +(2.06655 + 0.752162i) q^{28} +(-0.914202 - 5.18470i) q^{29} +(1.01542 - 2.33727i) q^{30} +3.57339i q^{31} +(-5.26143 - 1.91500i) q^{32} +(0.0224041 - 0.368157i) q^{33} +(-0.549965 + 1.51102i) q^{34} +(3.20086 + 0.564398i) q^{35} +(-0.258040 - 4.86654i) q^{36} -8.01979i q^{37} +(-1.78859 + 1.98398i) q^{38} +(-4.07217 + 9.37321i) q^{39} +(-5.25156 - 0.925991i) q^{40} +(-6.91883 - 5.80559i) q^{41} +(-1.37764 + 0.408537i) q^{42} +(-0.233045 + 1.32166i) q^{43} +(-0.340671 + 0.0600696i) q^{44} +(-1.62453 - 7.01695i) q^{45} +(0.870720 + 0.502711i) q^{46} +(2.80328 - 0.494293i) q^{47} +(-3.13481 + 0.929620i) q^{48} +(2.58363 + 4.47498i) q^{49} -0.468238 q^{50} +(1.29213 + 4.35726i) q^{51} +(9.43914 + 1.66438i) q^{52} +(-7.65410 + 6.42256i) q^{53} +(2.02771 + 2.45520i) q^{54} +(-0.480426 + 0.174861i) q^{55} +(1.50346 + 2.60407i) q^{56} +(-0.725928 + 7.51485i) q^{57} +(1.61313 - 2.79403i) q^{58} +(1.30385 - 7.39448i) q^{59} +(-6.04448 + 3.01599i) q^{60} +(-4.70028 - 1.71076i) q^{61} +(-1.40759 + 1.67750i) q^{62} +(-2.44220 + 3.24505i) q^{63} +(0.172188 + 0.298239i) q^{64} +14.1657 q^{65} +(0.155538 - 0.164003i) q^{66} +(-6.37567 - 7.59823i) q^{67} +(3.69143 - 2.13125i) q^{68} +(2.82335 - 0.322558i) q^{69} +(1.28030 + 1.52580i) q^{70} +(-7.93377 - 6.65722i) q^{71} +(4.00684 - 5.32405i) q^{72} +(-1.33247 + 7.55679i) q^{73} +(3.15906 - 3.76483i) q^{74} +(-1.06360 + 0.787530i) q^{75} +(7.01255 - 0.981159i) q^{76} +(0.249664 + 0.144144i) q^{77} +(-5.60384 + 2.79612i) q^{78} +(-1.92202 - 5.28069i) q^{79} +(2.91331 + 3.47194i) q^{80} +(8.73533 + 2.16658i) q^{81} +(-0.961119 - 5.45078i) q^{82} +(14.1234 + 8.15413i) q^{83} +(3.49362 + 1.51780i) q^{84} +(4.82586 - 4.04937i) q^{85} +(-0.630016 + 0.528646i) q^{86} +(-1.03505 - 9.05976i) q^{87} +(-0.409617 - 0.236492i) q^{88} +(-0.680140 - 3.85727i) q^{89} +(2.00142 - 3.93397i) q^{90} +(-5.13440 - 6.11895i) q^{91} +(-0.911550 - 2.50446i) q^{92} +(-0.375951 + 6.17786i) q^{93} +(1.51068 + 0.872193i) q^{94} +(9.95485 - 3.22777i) q^{95} +(-8.89476 - 3.86431i) q^{96} +(4.16363 - 4.96202i) q^{97} +(-0.549868 + 3.11846i) q^{98} +(0.0774666 - 0.634132i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9}+O(q^{10}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9	\( 108 q - 9 q^{2} - 3 q^{4} - 9 q^{5} + 3 q^{7} - 24 q^{9} - 12 q^{10} - 9 q^{12} - 6 q^{13} - 9 q^{14} - 36 q^{15} - 9 q^{16} + 27 q^{17} + 36 q^{18} - 15 q^{19} - 18 q^{20} + 3 q^{21} + 30 q^{22} - 45 q^{23} - 21 q^{24} - 3 q^{25} - 72 q^{26} - 36 q^{28} - 9 q^{29} - 21 q^{30} - 9 q^{32} - 6 q^{33} + 33 q^{34} + 45 q^{35} + 18 q^{36} - 9 q^{38} - 18 q^{39} + 15 q^{40} - 9 q^{41} + 15 q^{42} + 9 q^{43} - 63 q^{44} + 33 q^{45} - 18 q^{46} - 9 q^{47} + 3 q^{48} - 15 q^{49} + 126 q^{50} + 39 q^{51} - 39 q^{52} - 51 q^{54} + 3 q^{55} + 63 q^{56} - 78 q^{57} - 6 q^{58} + 36 q^{59} - 75 q^{60} - 24 q^{61} + 18 q^{62} - 9 q^{63} - 18 q^{65} + 159 q^{66} - 63 q^{67} + 54 q^{68} - 9 q^{69} + 39 q^{70} + 141 q^{72} - 45 q^{73} - 117 q^{74} - 3 q^{76} - 18 q^{77} + 27 q^{78} + 3 q^{79} + 126 q^{80} - 60 q^{81} - 3 q^{82} + 27 q^{83} - 117 q^{84} - 3 q^{85} - 171 q^{86} + 15 q^{87} - 9 q^{88} + 54 q^{89} - 21 q^{90} - 9 q^{91} - 27 q^{92} + 42 q^{93} + 99 q^{95} + 207 q^{96} - 57 q^{97} - 27 q^{98} + 39 q^{99}+O(q^{100}) \) 108 * q - 9 * q^2 - 3 * q^4 - 9 * q^5 + 3 * q^7 - 24 * q^9 - 12 * q^10 - 9 * q^12 - 6 * q^13 - 9 * q^14 - 36 * q^15 - 9 * q^16 + 27 * q^17 + 36 * q^18 - 15 * q^19 - 18 * q^20 + 3 * q^21 + 30 * q^22 - 45 * q^23 - 21 * q^24 - 3 * q^25 - 72 * q^26 - 36 * q^28 - 9 * q^29 - 21 * q^30 - 9 * q^32 - 6 * q^33 + 33 * q^34 + 45 * q^35 + 18 * q^36 - 9 * q^38 - 18 * q^39 + 15 * q^40 - 9 * q^41 + 15 * q^42 + 9 * q^43 - 63 * q^44 + 33 * q^45 - 18 * q^46 - 9 * q^47 + 3 * q^48 - 15 * q^49 + 126 * q^50 + 39 * q^51 - 39 * q^52 - 51 * q^54 + 3 * q^55 + 63 * q^56 - 78 * q^57 - 6 * q^58 + 36 * q^59 - 75 * q^60 - 24 * q^61 + 18 * q^62 - 9 * q^63 - 18 * q^65 + 159 * q^66 - 63 * q^67 + 54 * q^68 - 9 * q^69 + 39 * q^70 + 141 * q^72 - 45 * q^73 - 117 * q^74 - 3 * q^76 - 18 * q^77 + 27 * q^78 + 3 * q^79 + 126 * q^80 - 60 * q^81 - 3 * q^82 + 27 * q^83 - 117 * q^84 - 3 * q^85 - 171 * q^86 + 15 * q^87 - 9 * q^88 + 54 * q^89 - 21 * q^90 - 9 * q^91 - 27 * q^92 + 42 * q^93 + 99 * q^95 + 207 * q^96 - 57 * q^97 - 27 * q^98 + 39 * q^99

Introduction

L-functions

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