LMFDB - Embedded newform 138.2.e.d.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (of order $11$, degree $10$, 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:	$1.10193554789$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			49.1
Root			$0.142315 + 0.989821i$ of defining polynomial
Character	$\chi$	$=$	138.49
Dual form			138.2.e.d.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.81440 + 2.09393i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.163423 - 0.105026i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.81440 + 2.09393i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.163423 - 0.105026i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.33083 - 1.49793i) q^{10} +(-0.413293 + 2.87451i) q^{11} +(0.142315 - 0.989821i) q^{12} +(0.910738 + 0.585296i) q^{13} +(0.127214 + 0.146813i) q^{14} +(-1.15098 - 2.52028i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.45384 + 1.30777i) q^{17} +(0.654861 - 0.755750i) q^{18} +(4.24593 - 1.24672i) q^{19} +(1.15098 - 2.52028i) q^{20} +(0.0276463 + 0.192284i) q^{21} -2.90407 q^{22} +(-4.73556 + 0.757939i) q^{23} +1.00000 q^{24} +(-0.380916 - 2.64933i) q^{25} +(-0.449727 + 0.984764i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-0.127214 + 0.146813i) q^{28} +(8.83766 + 2.59497i) q^{29} +(2.33083 - 1.49793i) q^{30} +(-2.85525 - 6.25212i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-2.44306 - 1.57006i) q^{33} +(-0.660607 + 4.59462i) q^{34} +(-0.0765987 + 0.532755i) q^{35} +(0.841254 + 0.540641i) q^{36} +(3.17329 + 3.66217i) q^{37} +(1.83829 + 4.02529i) q^{38} +(-0.910738 + 0.585296i) q^{39} +(2.65843 + 0.780586i) q^{40} +(3.76214 - 4.34174i) q^{41} +(-0.186393 + 0.0547299i) q^{42} +(3.14342 - 6.88313i) q^{43} +(-0.413293 - 2.87451i) q^{44} +2.77066 q^{45} +(-1.42416 - 4.57949i) q^{46} -5.61457 q^{47} +(0.142315 + 0.989821i) q^{48} +(-2.89223 + 6.33310i) q^{49} +(2.56815 - 0.754078i) q^{50} +(-3.03978 + 3.50809i) q^{51} +(-1.03874 - 0.305003i) q^{52} +(-3.48496 + 2.23965i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-5.26914 - 6.08092i) q^{55} +(-0.163423 - 0.105026i) q^{56} +(-0.629769 + 4.38014i) q^{57} +(-1.31083 + 9.11701i) q^{58} +(-9.01685 - 5.79478i) q^{59} +(1.81440 + 2.09393i) q^{60} +(-1.19623 - 2.61939i) q^{61} +(5.78214 - 3.71596i) q^{62} +(-0.186393 - 0.0547299i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-2.87801 + 0.845060i) q^{65} +(1.20640 - 2.64164i) q^{66} +(2.08311 + 14.4884i) q^{67} -4.64187 q^{68} +(1.27778 - 4.62248i) q^{69} -0.538234 q^{70} +(-1.81195 - 12.6024i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(-2.86708 + 0.841852i) q^{73} +(-3.17329 + 3.66217i) q^{74} +(2.56815 + 0.754078i) q^{75} +(-3.72270 + 2.39243i) q^{76} +(0.234356 + 0.513169i) q^{77} +(-0.708950 - 0.818172i) q^{78} +(2.15275 + 1.38349i) q^{79} +(-0.394306 + 2.74246i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(4.83295 + 3.10595i) q^{82} +(0.531462 + 0.613340i) q^{83} +(-0.0806993 - 0.176707i) q^{84} +(-10.8194 + 6.95322i) q^{85} +(7.26043 + 2.13185i) q^{86} +(-6.03176 + 6.96103i) q^{87} +(2.78644 - 0.818172i) q^{88} +(2.81645 - 6.16716i) q^{89} +(0.394306 + 2.74246i) q^{90} +0.210307 q^{91} +(4.33020 - 2.06140i) q^{92} +6.87324 q^{93} +(-0.799036 - 5.55742i) q^{94} +(-5.09327 + 11.1527i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(8.09928 - 9.34707i) q^{97} +(-6.68024 - 1.96150i) q^{98} +(2.44306 - 1.57006i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$2$	0.142315	+	0.989821i	0.100632	+	0.699909i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−1.81440	+	2.09393i	−0.811424	+	0.936433i	−0.998949	−	0.0458269i	$-0.985408\pi$
$5$	−1.81440	+	2.09393i	−0.811424	+	0.936433i	0.187526	+	0.982260i	$0.439953\pi$
$6$	−0.959493	−	0.281733i	−0.391711	−	0.115017i
$7$	0.163423	−	0.105026i	0.0617682	−	0.0396960i	−0.509392	−	0.860534i	$-0.670130\pi$
$7$	0.163423	−	0.105026i	0.0617682	−	0.0396960i	0.571160	+	0.820838i	$0.306493\pi$
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−2.33083	−	1.49793i	−0.737073	−	0.473688i
$11$	−0.413293	+	2.87451i	−0.124612	+	0.866698i	0.827612	+	0.561300i	$0.189699\pi$
$11$	−0.413293	+	2.87451i	−0.124612	+	0.866698i	−0.952225	+	0.305398i	$0.901210\pi$
$12$	0.142315	−	0.989821i	0.0410828	−	0.285737i
$13$	0.910738	+	0.585296i	0.252593	+	0.162332i	0.660810	−	0.750553i	$-0.270213\pi$
$13$	0.910738	+	0.585296i	0.252593	+	0.162332i	−0.408217	+	0.912885i	$0.633849\pi$
$14$	0.127214	+	0.146813i	0.0339995	+	0.0392375i
$15$	−1.15098	−	2.52028i	−0.297180	−	0.650734i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	4.45384	+	1.30777i	1.08022	+	0.317180i	0.772965	−	0.634449i	$-0.218773\pi$
$17$	4.45384	+	1.30777i	1.08022	+	0.317180i	0.307251	+	0.951629i	$0.400591\pi$
$18$	0.654861	−	0.755750i	0.154352	−	0.178132i
$19$	4.24593	−	1.24672i	0.974083	−	0.286017i	0.244303	−	0.969699i	$-0.421441\pi$
$19$	4.24593	−	1.24672i	0.974083	−	0.286017i	0.729780	+	0.683682i	$0.239623\pi$
$20$	1.15098	−	2.52028i	0.257366	−	0.563553i
$21$	0.0276463	+	0.192284i	0.00603292	+	0.0419599i
$22$	−2.90407			−0.619150
$23$	−4.73556	+	0.757939i	−0.987433	+	0.158041i
$23$	−4.73556	+	0.757939i	−0.987433	+	0.158041i
$24$	1.00000			0.204124
$25$	−0.380916	−	2.64933i	−0.0761832	−	0.529866i
$26$	−0.449727	+	0.984764i	−0.0881987	+	0.193128i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	−0.127214	+	0.146813i	−0.0240413	+	0.0277451i
$29$	8.83766	+	2.59497i	1.64111	+	0.481874i	0.966579	−	0.256371i	$-0.0825268\pi$
$29$	8.83766	+	2.59497i	1.64111	+	0.481874i	0.674533	+	0.738245i	$0.264345\pi$
$30$	2.33083	−	1.49793i	0.425549	−	0.273484i
$31$	−2.85525	−	6.25212i	−0.512818	−	1.12291i	−0.972088	−	0.234617i	$-0.924616\pi$
$31$	−2.85525	−	6.25212i	−0.512818	−	1.12291i	0.459270	−	0.888297i	$-0.348111\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	−2.44306	−	1.57006i	−0.425282	−	0.273312i
$34$	−0.660607	+	4.59462i	−0.113293	+	0.787972i
$35$	−0.0765987	+	0.532755i	−0.0129475	+	0.0900521i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	3.17329	+	3.66217i	0.521685	+	0.602057i	0.954052	−	0.299641i	$-0.0968669\pi$
$37$	3.17329	+	3.66217i	0.521685	+	0.602057i	−0.432367	+	0.901698i	$0.642321\pi$
$38$	1.83829	+	4.02529i	0.298209	+	0.652988i
$39$	−0.910738	+	0.585296i	−0.145835	+	0.0937223i
$40$	2.65843	+	0.780586i	0.420335	+	0.123421i
$41$	3.76214	−	4.34174i	0.587547	−	0.678065i	−0.381663	−	0.924302i	$-0.624648\pi$
$41$	3.76214	−	4.34174i	0.587547	−	0.678065i	0.969210	+	0.246236i	$0.0791939\pi$
$42$	−0.186393	+	0.0547299i	−0.0287610	+	0.00844500i
$43$	3.14342	−	6.88313i	0.479367	−	1.04967i	−0.503270	−	0.864129i	$-0.667870\pi$
$43$	3.14342	−	6.88313i	0.479367	−	1.04967i	0.982637	−	0.185538i	$-0.0594029\pi$
$44$	−0.413293	−	2.87451i	−0.0623062	−	0.433349i
$45$	2.77066			0.413026
$46$	−1.42416	−	4.57949i	−0.209982	−	0.675209i
$47$	−5.61457			−0.818969			−0.409484	−	0.912317i	$-0.634291\pi$
$47$	−5.61457			−0.818969			−0.409484	+	0.912317i	$0.634291\pi$
$48$	0.142315	+	0.989821i	0.0205414	+	0.142868i
$49$	−2.89223	+	6.33310i	−0.413175	+	0.904728i
$50$	2.56815	−	0.754078i	0.363192	−	0.106643i
$51$	−3.03978	+	3.50809i	−0.425654	+	0.491231i
$52$	−1.03874	−	0.305003i	−0.144048	−	0.0422963i
$53$	−3.48496	+	2.23965i	−0.478697	+	0.307640i	−0.757645	−	0.652666i	$-0.773650\pi$
$53$	−3.48496	+	2.23965i	−0.478697	+	0.307640i	0.278949	+	0.960306i	$0.410014\pi$
$54$	0.415415	+	0.909632i	0.0565308	+	0.123785i
$55$	−5.26914	−	6.08092i	−0.710491	−	0.819951i
$56$	−0.163423	−	0.105026i	−0.0218384	−	0.0140347i
$57$	−0.629769	+	4.38014i	−0.0834149	+	0.580164i
$58$	−1.31083	+	9.11701i	−0.172120	+	1.19712i
$59$	−9.01685	−	5.79478i	−1.17389	−	0.754416i	−0.199640	−	0.979869i	$-0.563977\pi$
$59$	−9.01685	−	5.79478i	−1.17389	−	0.754416i	−0.974254	+	0.225453i	$0.927614\pi$
$60$	1.81440	+	2.09393i	0.234238	+	0.270325i
$61$	−1.19623	−	2.61939i	−0.153162	−	0.335378i	0.817461	−	0.575984i	$-0.195381\pi$
$61$	−1.19623	−	2.61939i	−0.153162	−	0.335378i	−0.970623	+	0.240606i	$0.922654\pi$
$62$	5.78214	−	3.71596i	0.734332	−	0.471927i
$63$	−0.186393	−	0.0547299i	−0.0234833	−	0.00689531i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−2.87801	+	0.845060i	−0.356973	+	0.104817i
$66$	1.20640	−	2.64164i	0.148497	−	0.325163i
$67$	2.08311	+	14.4884i	0.254493	+	1.77003i	0.570519	+	0.821284i	$0.306742\pi$
$67$	2.08311	+	14.4884i	0.254493	+	1.77003i	−0.316027	+	0.948750i	$0.602349\pi$
$68$	−4.64187			−0.562910
$69$	1.27778	−	4.62248i	0.153826	−	0.556481i
$70$	−0.538234			−0.0643313
$71$	−1.81195	−	12.6024i	−0.215038	−	1.49563i	−0.755997	−	0.654576i	$-0.772847\pi$
$71$	−1.81195	−	12.6024i	−0.215038	−	1.49563i	0.540958	−	0.841050i	$-0.318062\pi$
$72$	−0.415415	+	0.909632i	−0.0489571	+	0.107201i
$73$	−2.86708	+	0.841852i	−0.335567	+	0.0985313i	−0.445175	−	0.895444i	$-0.646859\pi$
$73$	−2.86708	+	0.841852i	−0.335567	+	0.0985313i	0.109608	+	0.993975i	$0.465040\pi$
$74$	−3.17329	+	3.66217i	−0.368887	+	0.425718i
$75$	2.56815	+	0.754078i	0.296545	+	0.0870734i
$76$	−3.72270	+	2.39243i	−0.427023	+	0.274431i
$77$	0.234356	+	0.513169i	0.0267074	+	0.0584811i
$78$	−0.708950	−	0.818172i	−0.0802728	−	0.0926397i
$79$	2.15275	+	1.38349i	0.242203	+	0.155654i	0.656111	−	0.754664i	$-0.272200\pi$
$79$	2.15275	+	1.38349i	0.242203	+	0.155654i	−0.413908	+	0.910319i	$0.635837\pi$
$80$	−0.394306	+	2.74246i	−0.0440848	+	0.306617i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	4.83295	+	3.10595i	0.533710	+	0.342995i
$83$	0.531462	+	0.613340i	0.0583356	+	0.0673228i	0.784167	−	0.620549i	$-0.213090\pi$
$83$	0.531462	+	0.613340i	0.0583356	+	0.0673228i	−0.725832	+	0.687872i	$0.758545\pi$
$84$	−0.0806993	−	0.176707i	−0.00880501	−	0.0192803i
$85$	−10.8194	+	6.95322i	−1.17353	+	0.754182i
$86$	7.26043	+	2.13185i	0.782912	+	0.229884i
$87$	−6.03176	+	6.96103i	−0.646673	+	0.746300i
$88$	2.78644	−	0.818172i	0.297035	−	0.0872174i
$89$	2.81645	−	6.16716i	0.298543	−	0.653717i	−0.699607	−	0.714528i	$-0.746641\pi$
$89$	2.81645	−	6.16716i	0.298543	−	0.653717i	0.998149	+	0.0608109i	$0.0193687\pi$
$90$	0.394306	+	2.74246i	0.0415635	+	0.289081i
$91$	0.210307			0.0220462
$92$	4.33020	−	2.06140i	0.451455	−	0.214916i
$93$	6.87324			0.712722
$94$	−0.799036	−	5.55742i	−0.0824143	−	0.573204i
$95$	−5.09327	+	11.1527i	−0.522559	+	1.14424i
$96$	−0.959493	+	0.281733i	−0.0979278	+	0.0287542i
$97$	8.09928	−	9.34707i	0.822357	−	0.949051i	−0.177024	−	0.984206i	$-0.556647\pi$
$97$	8.09928	−	9.34707i	0.822357	−	0.949051i	0.999382	+	0.0351554i	$0.0111926\pi$
$98$	−6.68024	−	1.96150i	−0.674806	−	0.198141i
$99$	2.44306	−	1.57006i	0.245537	−	0.157797i
$100$	1.11189	+	2.43470i	0.111189	+	0.243470i
$101$	−10.2791	−	11.8628i	−1.02281	−	1.18039i	−0.983453	−	0.181163i	$-0.942014\pi$
$101$	−10.2791	−	11.8628i	−1.02281	−	1.18039i	−0.0393592	−	0.999225i	$-0.512532\pi$
$102$	−3.90499	−	2.50959i	−0.386652	−	0.248486i
$103$	−1.34415	+	9.34877i	−0.132443	+	0.921162i	0.809913	+	0.586550i	$0.199514\pi$
$103$	−1.34415	+	9.34877i	−0.132443	+	0.921162i	−0.942356	+	0.334612i	$0.891395\pi$
$104$	0.154070	−	1.07158i	0.0151078	−	0.105077i
$105$	−0.452791	−	0.290991i	−0.0441879	−	0.0283978i
$106$	−2.71282	−	3.13076i	−0.263492	−	0.304086i
$107$	3.95144	+	8.65244i	0.382000	+	0.836463i	0.998783	+	0.0493295i	$0.0157084\pi$
$107$	3.95144	+	8.65244i	0.382000	+	0.836463i	−0.616783	+	0.787133i	$0.711564\pi$
$108$	−0.841254	+	0.540641i	−0.0809497	+	0.0520232i
$109$	19.4026	+	5.69711i	1.85843	+	0.545684i	0.999432	+	0.0337045i	$0.0107305\pi$
$109$	19.4026	+	5.69711i	1.85843	+	0.545684i	0.858998	+	0.511980i	$0.171088\pi$
$110$	5.26914	−	6.08092i	0.502393	−	0.579793i
$111$	−4.64946	+	1.36520i	−0.441307	+	0.129579i
$112$	0.0806993	−	0.176707i	0.00762536	−	0.0166972i
$113$	−0.187381	−	1.30327i	−0.0176274	−	0.122601i	0.979108	−	0.203342i	$-0.0651804\pi$
$113$	−0.187381	−	1.30327i	−0.0176274	−	0.122601i	−0.996735	+	0.0807412i	$0.974271\pi$
$114$	−4.42518			−0.414456
$115$	7.00512	−	11.2911i	0.653231	−	1.05290i
$116$	−9.21076			−0.855197
$117$	−0.154070	−	1.07158i	−0.0142437	−	0.0990673i
$118$	4.45257	−	9.74976i	0.409892	−	0.897538i
$119$	0.865212	−	0.254049i	0.0793138	−	0.0232886i
$120$	−1.81440	+	2.09393i	−0.165631	+	0.191149i
$121$	2.46241	+	0.723028i	0.223855	+	0.0657298i
$122$	2.42248	−	1.55683i	0.219321	−	0.140949i
$123$	2.38653	+	5.22578i	0.215187	+	0.471193i
$124$	4.50102	+	5.19445i	0.404203	+	0.466475i
$125$	−5.41551	−	3.48034i	−0.484378	−	0.311291i
$126$	0.0276463	−	0.192284i	0.00246293	−	0.0171301i
$127$	0.685740	−	4.76943i	0.0608496	−	0.423218i	−0.936513	−	0.350634i	$-0.885966\pi$
$127$	0.685740	−	4.76943i	0.0608496	−	0.423218i	0.997362	−	0.0725845i	$-0.0231247\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	4.95529	+	5.71871i	0.436289	+	0.503505i
$130$	−1.24604	−	2.72845i	−0.109285	−	0.239301i
$131$	13.4413	−	8.63823i	1.17438	−	0.754725i	0.200032	−	0.979789i	$-0.435896\pi$
$131$	13.4413	−	8.63823i	1.17438	−	0.754725i	0.974344	+	0.225064i	$0.0722592\pi$
$132$	2.78644	+	0.818172i	0.242528	+	0.0712127i
$133$	0.562947	−	0.649675i	0.0488137	−	0.0563340i
$134$	−14.0444	+	4.12382i	−1.21325	+	0.356243i
$135$	−1.15098	+	2.52028i	−0.0990602	+	0.216911i
$136$	−0.660607	−	4.59462i	−0.0566466	−	0.393986i
$137$	18.7720			1.60380			0.801898	−	0.597460i	$-0.203824\pi$
$137$	18.7720			1.60380			0.801898	+	0.597460i	$0.203824\pi$
$138$	4.75727	+	0.606924i	0.404966	+	0.0516648i
$139$	17.7540			1.50588			0.752938	−	0.658092i	$-0.228636\pi$
$139$	17.7540			1.50588			0.752938	+	0.658092i	$0.228636\pi$
$140$	−0.0765987	−	0.532755i	−0.00647377	−	0.0450261i
$141$	2.33238	−	5.10719i	0.196421	−	0.430103i
$142$	12.2162	−	3.58701i	1.02516	−	0.301015i
$143$	−2.05884	+	2.37603i	−0.172169	+	0.198694i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−21.4687	+	13.7971i	−1.78288	+	1.14579i
$146$	−1.24131	−	2.71809i	−0.102732	−	0.224951i
$147$	−4.55931	−	5.26173i	−0.376046	−	0.433980i
$148$	−4.07650	−	2.61981i	−0.335086	−	0.215347i
$149$	1.35418	−	9.41852i	0.110939	−	0.771595i	−0.856072	−	0.516857i	$-0.827102\pi$
$149$	1.35418	−	9.41852i	0.110939	−	0.771595i	0.967010	−	0.254738i	$-0.0819891\pi$
$150$	−0.380916	+	2.64933i	−0.0311017	+	0.216317i
$151$	−7.30101	−	4.69207i	−0.594148	−	0.381835i	0.208735	−	0.977972i	$-0.433065\pi$
$151$	−7.30101	−	4.69207i	−0.594148	−	0.381835i	−0.802883	+	0.596137i	$0.796702\pi$
$152$	−2.89788	−	3.34433i	−0.235049	−	0.271261i
$153$	−1.92830	−	4.22240i	−0.155894	−	0.341360i
$154$	−0.474593	+	0.305003i	−0.0382438	+	0.0245778i
$155$	18.2720	+	5.36516i	1.46765	+	0.430940i
$156$	0.708950	−	0.818172i	0.0567614	−	0.0655062i
$157$	−19.0136	+	5.58290i	−1.51745	+	0.445564i	−0.931183	−	0.364552i	$-0.881222\pi$
$157$	−19.0136	+	5.58290i	−1.51745	+	0.445564i	−0.586270	+	0.810116i	$0.699404\pi$
$158$	−1.06304	+	2.32772i	−0.0845706	+	0.185184i
$159$	−0.589551	−	4.10042i	−0.0467545	−	0.325184i
$160$	−2.77066			−0.219040
$161$	−0.694298	+	0.621221i	−0.0547184	+	0.0489591i
$162$	−1.00000			−0.0785674
$163$	−2.06377	−	14.3538i	−0.161647	−	1.12428i	−0.895530	−	0.445001i	$-0.853203\pi$
$163$	−2.06377	−	14.3538i	−0.161647	−	1.12428i	0.733883	−	0.679276i	$-0.237706\pi$
$164$	−2.38653	+	5.22578i	−0.186357	+	0.408065i
$165$	7.72028	−	2.26688i	0.601023	−	0.176476i
$166$	−0.531462	+	0.613340i	−0.0412495	+	0.0476044i
$167$	9.49053	+	2.78667i	0.734399	+	0.215639i	0.627484	−	0.778629i	$-0.284085\pi$
$167$	9.49053	+	2.78667i	0.734399	+	0.215639i	0.106915	+	0.994268i	$0.465903\pi$
$168$	0.163423	−	0.105026i	0.0126084	−	0.00810292i
$169$	−4.91352	−	10.7591i	−0.377963	−	0.827624i
$170$	−8.42221	−	9.71974i	−0.645954	−	0.745470i
$171$	−3.72270	−	2.39243i	−0.284682	−	0.182954i
$172$	−1.07689	+	7.48992i	−0.0821119	+	0.571101i
$173$	−1.88474	+	13.1086i	−0.143294	+	0.996631i	0.783589	+	0.621280i	$0.213387\pi$
$173$	−1.88474	+	13.1086i	−0.143294	+	0.996631i	−0.926883	+	0.375351i	$0.877522\pi$
$174$	−7.74858	−	4.97971i	−0.587419	−	0.377511i
$175$	−0.340499	−	0.392956i	−0.0257393	−	0.0297047i
$176$	1.20640	+	2.64164i	0.0909355	+	0.199121i
$177$	9.01685	−	5.79478i	0.677748	−	0.435562i
$178$	6.50521	+	1.91010i	0.487586	+	0.143168i
$179$	−3.43495	+	3.96414i	−0.256740	+	0.296294i	−0.869457	−	0.494009i	$-0.835531\pi$
$179$	−3.43495	+	3.96414i	−0.256740	+	0.296294i	0.612717	+	0.790302i	$0.290077\pi$
$180$	−2.65843	+	0.780586i	−0.198148	+	0.0581814i
$181$	−6.75269	+	14.7863i	−0.501924	+	1.09906i	0.473916	+	0.880570i	$0.342840\pi$
$181$	−6.75269	+	14.7863i	−0.501924	+	1.09906i	−0.975839	+	0.218489i	$0.929887\pi$
$182$	0.0299298	+	0.208166i	0.00221855	+	0.0154303i
$183$	2.87961			0.212867
$184$	2.65667	+	3.99276i	0.195852	+	0.294350i
$185$	−13.4259			−0.987093
$186$	0.978164	+	6.80328i	0.0717225	+	0.498841i
$187$	−5.59993	+	12.2621i	−0.409508	+	0.896697i
$188$	5.38714	−	1.58181i	0.392897	−	0.115365i
$189$	0.127214	−	0.146813i	0.00925349	−	0.0106791i
$190$	−11.7640	−	3.45423i	−0.853453	−	0.250596i
$191$	−6.47147	+	4.15896i	−0.468259	+	0.300932i	−0.753410	−	0.657551i	$-0.771593\pi$
$191$	−6.47147	+	4.15896i	−0.468259	+	0.300932i	0.285151	+	0.958483i	$0.407956\pi$
$192$	−0.415415	−	0.909632i	−0.0299800	−	0.0656470i
$193$	0.934780	+	1.07879i	0.0672869	+	0.0776533i	0.788395	−	0.615169i	$-0.210912\pi$
$193$	0.934780	+	1.07879i	0.0672869	+	0.0776533i	−0.721108	+	0.692823i	$0.756367\pi$
$194$	10.4046	+	6.68662i	0.747005	+	0.480071i
$195$	0.426875	−	2.96898i	0.0305691	−	0.212613i
$196$	0.990833	−	6.89140i	0.0707738	−	0.492243i
$197$	5.26265	+	3.38210i	0.374948	+	0.240965i	0.714519	−	0.699616i	$-0.246646\pi$
$197$	5.26265	+	3.38210i	0.374948	+	0.240965i	−0.339571	+	0.940580i	$0.610282\pi$
$198$	1.90176	+	2.19475i	0.135152	+	0.155974i
$199$	0.358560	+	0.785136i	0.0254176	+	0.0556568i	0.921915	−	0.387392i	$-0.126624\pi$
$199$	0.358560	+	0.785136i	0.0254176	+	0.0556568i	−0.896497	+	0.443049i	$0.853897\pi$
$200$	−2.25168	+	1.44706i	−0.159218	+	0.102323i
$201$	−14.0444	−	4.12382i	−0.990617	−	0.290872i
$202$	10.2791	−	11.8628i	0.723237	−	0.834661i
$203$	1.71682	−	0.504104i	0.120497	−	0.0353811i
$204$	1.92830	−	4.22240i	0.135008	−	0.295627i
$205$	2.26527	+	15.7553i	0.158213	+	1.10040i
$206$	−9.44491			−0.658058
$207$	3.67394	+	3.08255i	0.255357	+	0.214252i
$208$	1.08260			0.0750646
$209$	1.82889	+	12.7202i	0.126507	+	0.879878i
$210$	0.223590	−	0.489595i	0.0154292	−	0.0337852i
$211$	−18.2924	+	5.37114i	−1.25930	+	0.369764i	−0.842234	−	0.539112i	$-0.818760\pi$
$211$	−18.2924	+	5.37114i	−1.25930	+	0.369764i	−0.417067	+	0.908876i	$0.636942\pi$
$212$	2.71282	−	3.13076i	0.186317	−	0.215021i
$213$	12.2162	+	3.58701i	0.837042	+	0.245778i
$214$	−8.00202	+	5.14259i	−0.547007	+	0.351540i
$215$	8.70936	+	19.0708i	0.593973	+	1.30062i
$216$	−0.654861	−	0.755750i	−0.0445576	−	0.0514222i
$217$	−1.12325	−	0.721868i	−0.0762511	−	0.0490036i
$218$	−2.87785	+	20.0159i	−0.194912	+	1.35565i
$219$	0.425254	−	2.95771i	0.0287360	−	0.199863i
$220$	6.76890	+	4.35011i	0.456359	+	0.293284i
$221$	3.29085	+	3.79785i	0.221367	+	0.255471i
$222$	−2.01299	−	4.40784i	−0.135103	−	0.295835i
$223$	5.39879	−	3.46959i	0.361529	−	0.232341i	−0.347248	−	0.937774i	$-0.612884\pi$
$223$	5.39879	−	3.46959i	0.361529	−	0.232341i	0.708777	+	0.705433i	$0.249247\pi$
$224$	0.186393	+	0.0547299i	0.0124539	+	0.00365679i
$225$	−1.75278	+	2.02282i	−0.116852	+	0.134855i
$226$	1.26333	−	0.370948i	0.0840357	−	0.0246751i
$227$	−0.497189	+	1.08869i	−0.0329996	+	0.0722590i	−0.925414	−	0.378958i	$-0.876283\pi$
$227$	−0.497189	+	1.08869i	−0.0329996	+	0.0722590i	0.892414	+	0.451217i	$0.149010\pi$
$228$	−0.629769	−	4.38014i	−0.0417075	−	0.290082i
$229$	−28.0856			−1.85595			−0.927974	−	0.372646i	$-0.878451\pi$
$229$	−28.0856			−1.85595			−0.927974	+	0.372646i	$0.878451\pi$
$230$	12.1731	+	5.32693i	0.802672	+	0.351247i
$231$	−0.564150			−0.0371184
$232$	−1.31083	−	9.11701i	−0.0860600	−	0.598561i
$233$	−6.81811	+	14.9296i	−0.446669	+	0.978070i	0.543656	+	0.839308i	$0.317039\pi$
$233$	−6.81811	+	14.9296i	−0.446669	+	0.978070i	−0.990326	+	0.138762i	$0.955688\pi$
$234$	1.03874	−	0.305003i	0.0679048	−	0.0199386i
$235$	10.1871	−	11.7565i	0.664531	−	0.766909i
$236$	10.2842	+	3.01971i	0.669444	+	0.196566i
$237$	−2.15275	+	1.38349i	−0.139836	+	0.0898671i
$238$	0.374596	+	0.820250i	0.0242814	+	0.0531689i
$239$	−6.76847	−	7.81123i	−0.437816	−	0.505266i	0.493366	−	0.869822i	$-0.335766\pi$
$239$	−6.76847	−	7.81123i	−0.437816	−	0.505266i	−0.931182	+	0.364556i	$0.881221\pi$
$240$	−2.33083	−	1.49793i	−0.150454	−	0.0966912i
$241$	3.12210	−	21.7147i	0.201112	−	1.39877i	−0.599879	−	0.800091i	$-0.704785\pi$
$241$	3.12210	−	21.7147i	0.201112	−	1.39877i	0.800991	−	0.598676i	$-0.204306\pi$
$242$	−0.365231	+	2.54024i	−0.0234780	+	0.163293i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	1.88574	+	2.17626i	0.120722	+	0.139321i
$245$	−8.01339	−	17.5469i	−0.511957	−	1.12103i
$246$	−4.83295	+	3.10595i	−0.308138	+	0.198028i
$247$	4.59663	+	1.34969i	0.292476	+	0.0858788i
$248$	−4.50102	+	5.19445i	−0.285815	+	0.329848i
$249$	−0.778691	+	0.228644i	−0.0493476	+	0.0144897i
$250$	2.67421	−	5.85569i	0.169132	−	0.370347i
$251$	−0.0385613	−	0.268200i	−0.00243397	−	0.0169286i	0.988568	−	0.150774i	$-0.0481766\pi$
$251$	−0.0385613	−	0.268200i	−0.00243397	−	0.0169286i	−0.991002	+	0.133845i	$0.957267\pi$
$252$	0.194262			0.0122373
$253$	−0.221534	−	13.9257i	−0.0139277	−	0.875500i
$254$	4.81847			0.302338
$255$	−1.83032	−	12.7302i	−0.114619	−	0.797193i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−14.0118	+	4.11424i	−0.874033	+	0.256639i	−0.687830	−	0.725872i	$-0.741436\pi$
$257$	−14.0118	+	4.11424i	−0.874033	+	0.256639i	−0.186203	+	0.982511i	$0.559618\pi$
$258$	−4.95529	+	5.71871i	−0.308503	+	0.356031i
$259$	0.903212	+	0.265207i	0.0561228	+	0.0164792i
$260$	2.52335	−	1.62166i	0.156491	−	0.100571i
$261$	−3.82629	−	8.37840i	−0.236841	−	0.518610i
$262$	10.4632	+	12.0752i	0.646419	+	0.746007i
$263$	−14.3594	−	9.22820i	−0.885436	−	0.569035i	0.0170015	−	0.999855i	$-0.494588\pi$
$263$	−14.3594	−	9.22820i	−0.885436	−	0.569035i	−0.902438	+	0.430820i	$0.858224\pi$
$264$	−0.413293	+	2.87451i	−0.0254364	+	0.176914i
$265$	1.63345	−	11.3609i	0.100342	−	0.697893i
$266$	0.723178	+	0.464758i	0.0443409	+	0.0284962i
$267$	4.43985	+	5.12386i	0.271714	+	0.313575i
$268$	−6.08057	−	13.3146i	−0.371430	−	0.813318i
$269$	27.1087	−	17.4217i	1.65284	−	1.06222i	0.725349	−	0.688381i	$-0.241678\pi$
$269$	27.1087	−	17.4217i	1.65284	−	1.06222i	0.927494	−	0.373837i	$-0.121958\pi$
$270$	−2.65843	−	0.780586i	−0.161787	−	0.0475049i
$271$	−2.00662	+	2.31576i	−0.121893	+	0.140672i	−0.813416	−	0.581682i	$-0.802395\pi$
$271$	−2.00662	+	2.31576i	−0.121893	+	0.140672i	0.691523	+	0.722355i	$0.256940\pi$
$272$	4.45384	−	1.30777i	0.270054	−	0.0792950i
$273$	−0.0873647	+	0.191302i	−0.00528755	+	0.0115781i
$274$	2.67153	+	18.5809i	0.161393	+	1.12251i
$275$	7.77296			0.468727
$276$	0.0762839	+	4.79522i	0.00459175	+	0.288639i
$277$	−5.05736			−0.303867			−0.151934	−	0.988391i	$-0.548550\pi$
$277$	−5.05736			−0.303867			−0.151934	+	0.988391i	$0.548550\pi$
$278$	2.52666	+	17.5733i	0.151539	+	1.05398i
$279$	−2.85525	+	6.25212i	−0.170939	+	0.374305i
$280$	0.516432	−	0.151638i	0.0308627	−	0.00906210i
$281$	5.50042	−	6.34782i	0.328127	−	0.378679i	−0.567584	−	0.823316i	$-0.692122\pi$
$281$	5.50042	−	6.34782i	0.328127	−	0.378679i	0.895711	+	0.444636i	$0.146667\pi$
$282$	5.38714	+	1.58181i	0.320799	+	0.0941952i
$283$	12.8122	−	8.23389i	0.761605	−	0.489454i	−0.101278	−	0.994858i	$-0.532293\pi$
$283$	12.8122	−	8.23389i	0.761605	−	0.489454i	0.862883	+	0.505404i	$0.168657\pi$
$284$	5.28905	+	11.5814i	0.313847	+	0.687229i
$285$	−8.02904	−	9.26601i	−0.475599	−	0.548871i
$286$	−2.64485	−	1.69974i	−0.156393	−	0.100508i
$287$	0.158827	−	1.10466i	0.00937524	−	0.0652062i
$288$	0.142315	−	0.989821i	0.00838598	−	0.0583258i
$289$	3.82516	+	2.45828i	0.225010	+	0.144605i
$290$	−16.7120	−	19.2867i	−0.981361	−	1.13255i
$291$	5.13783	+	11.2503i	0.301185	+	0.659503i
$292$	2.51377	−	1.61550i	0.147107	−	0.0945401i
$293$	−27.7542	−	8.14937i	−1.62142	−	0.476091i	−0.660018	−	0.751249i	$-0.729452\pi$
$293$	−27.7542	−	8.14937i	−1.62142	−	0.476091i	−0.961399	+	0.275158i	$0.911270\pi$
$294$	4.55931	−	5.26173i	0.265904	−	0.306870i
$295$	28.4940	−	8.36660i	1.65899	−	0.487122i
$296$	2.01299	−	4.40784i	0.117003	−	0.256201i
$297$	0.413293	+	2.87451i	0.0239817	+	0.166796i
$298$	9.51537			0.551211
$299$	−4.75647	−	2.08142i	−0.275074	−	0.120372i
$300$	−2.67657			−0.154532
$301$	−0.209198	−	1.45501i	−0.0120580	−	0.0838651i
$302$	3.60527	−	7.89445i	0.207460	−	0.454274i
$303$	15.0608	−	4.42226i	0.865223	−	0.254052i
$304$	2.89788	−	3.34433i	0.166205	−	0.191810i
$305$	7.65525	+	2.24778i	0.438338	+	0.128708i
$306$	3.90499	−	2.50959i	0.223234	−	0.143463i
$307$	−8.96612	−	19.6331i	−0.511724	−	1.12052i	−0.972479	−	0.232991i	$-0.925149\pi$
$307$	−8.96612	−	19.6331i	−0.511724	−	1.12052i	0.460755	−	0.887527i	$-0.347579\pi$
$308$	−0.369440	−	0.426356i	−0.0210508	−	0.0242939i
$309$	−7.94556	−	5.10630i	−0.452007	−	0.290487i
$310$	−2.71016	+	18.8496i	−0.153927	+	1.07059i
$311$	−0.125077	+	0.869929i	−0.00709246	+	0.0493291i	−0.993060	−	0.117606i	$-0.962478\pi$
$311$	−0.125077	+	0.869929i	−0.00709246	+	0.0493291i	0.985968	+	0.166935i	$0.0533871\pi$
$312$	0.910738	+	0.585296i	0.0515604	+	0.0331359i
$313$	3.57263	+	4.12304i	0.201937	+	0.233048i	0.847681	−	0.530506i	$-0.177998\pi$
$313$	3.57263	+	4.12304i	0.201937	+	0.233048i	−0.645744	+	0.763554i	$0.723453\pi$
$314$	−8.23200	−	18.0256i	−0.464559	−	1.01724i
$315$	0.452791	−	0.290991i	0.0255119	−	0.0163955i
$316$	−2.45532	−	0.720946i	−0.138122	−	0.0405564i
$317$	3.33115	−	3.84435i	0.187096	−	0.215920i	−0.654451	−	0.756105i	$-0.727100\pi$
$317$	3.33115	−	3.84435i	0.187096	−	0.215920i	0.841547	+	0.540184i	$0.181645\pi$
$318$	3.97478	−	1.16710i	0.222895	−	0.0654478i
$319$	−11.1118	+	24.3315i	−0.622142	+	1.36230i
$320$	−0.394306	−	2.74246i	−0.0220424	−	0.153308i
$321$	−9.51202			−0.530909
$322$	−0.713707	−	0.598822i	−0.0397733	−	0.0333711i
$323$	20.5411			1.14294
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	1.20373	−	2.63579i	0.0667708	−	0.146208i
$326$	13.9140	−	4.08552i	0.770625	−	0.226276i
$327$	−13.2424	+	15.2825i	−0.732306	+	0.845126i
$328$	−5.51223	−	1.61854i	−0.304362	−	0.0893688i
$329$	−0.917552	+	0.589675i	−0.0505863	+	0.0325098i
$330$	3.34251	+	7.31909i	0.183999	+	0.402902i
$331$	23.3216	+	26.9146i	1.28187	+	1.47936i	0.795954	+	0.605356i	$0.206969\pi$
$331$	23.3216	+	26.9146i	1.28187	+	1.47936i	0.485919	+	0.874004i	$0.338485\pi$
$332$	−0.682732	−	0.438765i	−0.0374698	−	0.0240804i
$333$	0.689621	−	4.79642i	0.0377910	−	0.262842i
$334$	−1.40766	+	9.79051i	−0.0770239	+	0.535713i
$335$	−34.1172	−	21.9258i	−1.86402	−	1.19793i
$336$	0.127214	+	0.146813i	0.00694011	+	0.00800932i
$337$	4.77911	+	10.4648i	0.260335	+	0.570053i	0.993990	−	0.109468i	$-0.0349147\pi$
$337$	4.77911	+	10.4648i	0.260335	+	0.570053i	−0.733656	+	0.679521i	$0.762187\pi$
$338$	9.95033	−	6.39469i	0.541227	−	0.347825i
$339$	1.26333	+	0.370948i	0.0686149	+	0.0201471i
$340$	8.42221	−	9.71974i	0.456758	−	0.527127i
$341$	19.1519	−	5.62349i	1.03713	−	0.304529i
$342$	1.83829	−	4.02529i	0.0994032	−	0.217663i
$343$	0.386005	+	2.68473i	0.0208423	+	0.144962i
$344$	−7.56694			−0.407982
$345$	7.36073	+	11.0626i	0.396289	+	0.595590i
$346$	−13.2434			−0.711972
$347$	2.24907	+	15.6426i	0.120736	+	0.839740i	0.956725	+	0.290993i	$0.0939858\pi$
$347$	2.24907	+	15.6426i	0.120736	+	0.839740i	−0.835989	+	0.548747i	$0.815105\pi$
$348$	3.82629	−	8.37840i	0.205111	−	0.449129i
$349$	−11.7351	+	3.44574i	−0.628167	+	0.184446i	−0.580294	−	0.814407i	$-0.697062\pi$
$349$	−11.7351	+	3.44574i	−0.628167	+	0.184446i	−0.0478727	+	0.998853i	$0.515244\pi$
$350$	0.340499	−	0.392956i	0.0182004	−	0.0210044i
$351$	1.03874	+	0.305003i	0.0554440	+	0.0162798i
$352$	−2.44306	+	1.57006i	−0.130216	+	0.0836845i
$353$	1.51906	+	3.32628i	0.0808514	+	0.177040i	0.945740	−	0.324923i	$-0.105339\pi$
$353$	1.51906	+	3.32628i	0.0808514	+	0.177040i	−0.864889	+	0.501963i	$0.832611\pi$
$354$	7.01903	+	8.10039i	0.373057	+	0.430531i
$355$	29.6760	+	19.0716i	1.57504	+	1.01222i
$356$	−0.964871	+	6.71083i	−0.0511381	+	0.355673i
$357$	−0.128331	+	0.892560i	−0.00679198	+	0.0472393i
$358$	−4.41264	−	2.83583i	−0.233215	−	0.149878i
$359$	8.61646	+	9.94392i	0.454759	+	0.524820i	0.936110	−	0.351708i	$-0.114399\pi$
$359$	8.61646	+	9.94392i	0.454759	+	0.524820i	−0.481351	+	0.876528i	$0.659854\pi$
$360$	−1.15098	−	2.52028i	−0.0606617	−	0.132831i
$361$	0.489802	−	0.314776i	0.0257790	−	0.0165672i
$362$	−15.5968	−	4.57965i	−0.819752	−	0.240701i
$363$	−1.68061	+	1.93953i	−0.0882091	+	0.101799i
$364$	−0.201788	+	0.0592504i	−0.0105766	+	0.00310556i
$365$	3.43926	−	7.53092i	0.180019	−	0.394186i
$366$	0.409811	+	2.85030i	0.0214212	+	0.148988i
$367$	−12.3385			−0.644064			−0.322032	−	0.946729i	$-0.604366\pi$
$367$	−12.3385			−0.644064			−0.322032	+	0.946729i	$0.604366\pi$
$368$	−3.57403	+	3.19786i	−0.186309	+	0.166700i
$369$	−5.74494			−0.299070
$370$	−1.91071	−	13.2893i	−0.0993330	−	0.690876i
$371$	−0.334303	+	0.732022i	−0.0173562	+	0.0380047i
$372$	−6.59483	+	1.93642i	−0.341926	+	0.100398i
$373$	12.1475	−	14.0189i	0.628973	−	0.725873i	−0.348412	−	0.937341i	$-0.613279\pi$
$373$	12.1475	−	14.0189i	0.628973	−	0.725873i	0.977385	+	0.211468i	$0.0678244\pi$
$374$	−12.9343	−	3.79785i	−0.668816	−	0.196382i
$375$	5.41551	−	3.48034i	0.279656	−	0.179724i
$376$	2.33238	+	5.10719i	0.120283	+	0.263383i
$377$	6.52997	+	7.53598i	0.336310	+	0.388123i
$378$	0.163423	+	0.105026i	0.00840559	+	0.00540195i
$379$	−0.406982	+	2.83062i	−0.0209053	+	0.145399i	−0.997601	−	0.0692308i	$-0.977946\pi$
$379$	−0.406982	+	2.83062i	−0.0209053	+	0.145399i	0.976695	+	0.214630i	$0.0688546\pi$
$380$	1.74488	−	12.1359i	0.0895103	−	0.622558i
$381$	4.05356	+	2.60506i	0.207670	+	0.133461i
$382$	−5.03762	−	5.81372i	−0.257747	−	0.297456i
$383$	−0.0334270	−	0.0731949i	−0.00170804	−	0.00374009i	0.908776	−	0.417284i	$-0.137018\pi$
$383$	−0.0334270	−	0.0731949i	−0.00170804	−	0.00374009i	−0.910484	+	0.413544i	$0.864291\pi$
$384$	0.841254	−	0.540641i	0.0429300	−	0.0275895i
$385$	−1.49975	−	0.440368i	−0.0764346	−	0.0224432i
$386$	−0.934780	+	1.07879i	−0.0475791	+	0.0549092i
$387$	−7.26043	+	2.13185i	−0.369068	+	0.108368i
$388$	−5.13783	+	11.2503i	−0.260834	+	0.571146i
$389$	1.95719	+	13.6126i	0.0992337	+	0.690185i	0.977333	+	0.211707i	$0.0679023\pi$
$389$	1.95719	+	13.6126i	0.0992337	+	0.690185i	−0.878099	+	0.478478i	$0.841189\pi$
$390$	2.99951			0.151886
$391$	−22.0827	−	2.81726i	−1.11677	−	0.142475i
$392$	6.96226			0.351647
$393$	2.27387	+	15.8151i	0.114702	+	0.797767i
$394$	−2.59872	+	5.69041i	−0.130922	+	0.286678i
$395$	−6.80286	+	1.99750i	−0.342289	+	0.100505i
$396$	−1.90176	+	2.19475i	−0.0955672	+	0.110290i
$397$	6.36046	+	1.86760i	0.319222	+	0.0937321i	0.437418	−	0.899258i	$-0.355893\pi$
$397$	6.36046	+	1.86760i	0.319222	+	0.0937321i	−0.118196	+	0.992990i	$0.537711\pi$
$398$	−0.726117	+	0.466647i	−0.0363969	+	0.0233909i
$399$	0.357109	+	0.781959i	0.0178778	+	0.0391469i
$400$	−1.75278	−	2.02282i	−0.0876391	−	0.101141i
$401$	−29.6875	−	19.0790i	−1.48252	−	0.952759i	−0.996907	−	0.0785860i	$-0.974959\pi$
$401$	−29.6875	−	19.0790i	−1.48252	−	0.952759i	−0.485615	−	0.874173i	$-0.661404\pi$
$402$	2.08311	−	14.4884i	0.103896	−	0.722613i
$403$	1.05896	−	7.36521i	0.0527504	−	0.366887i
$404$	13.2049	+	8.48626i	0.656967	+	0.422207i
$405$	−1.81440	−	2.09393i	−0.0901582	−	0.104048i
$406$	0.743301	+	1.62760i	0.0368894	+	0.0807766i
$407$	−11.8384	+	7.60811i	−0.586810	+	0.377120i
$408$	4.45384	+	1.30777i	0.220498	+	0.0647441i
$409$	19.1568	−	22.1082i	0.947244	−	1.09318i	−0.0482952	−	0.998833i	$-0.515379\pi$
$409$	19.1568	−	22.1082i	0.947244	−	1.09318i	0.995540	−	0.0943452i	$-0.0300757\pi$
$410$	−15.2725	+	4.48442i	−0.754257	+	0.221470i
$411$	−7.79815	+	17.0756i	−0.384655	+	0.842276i
$412$	−1.34415	−	9.34877i	−0.0662215	−	0.460581i
$413$	−2.08217			−0.102457
$414$	−2.52832	+	4.07524i	−0.124260	+	0.200287i
$415$	−2.24857			−0.110378
$416$	0.154070	+	1.07158i	0.00755388	+	0.0525384i
$417$	−7.37528	+	16.1496i	−0.361169	+	0.790850i
$418$	−12.3305	+	3.62056i	−0.603104	+	0.177087i
$419$	−0.476760	+	0.550210i	−0.0232912	+	0.0268795i	−0.767276	−	0.641317i	$-0.778388\pi$
$419$	−0.476760	+	0.550210i	−0.0232912	+	0.0268795i	0.743984	+	0.668197i	$0.232934\pi$
$420$	0.516432	+	0.151638i	0.0251993	+	0.00739918i
$421$	−28.4791	+	18.3024i	−1.38798	+	0.892004i	−0.999565	−	0.0294793i	$-0.990615\pi$
$421$	−28.4791	+	18.3024i	−1.38798	+	0.892004i	−0.388419	+	0.921483i	$0.626979\pi$
$422$	−7.91975	−	17.3418i	−0.385527	−	0.844187i
$423$	3.67676	+	4.24321i	0.178770	+	0.206312i
$424$	3.48496	+	2.23965i	0.169245	+	0.108767i
$425$	1.76816	−	12.2979i	0.0857685	−	0.596533i
$426$	−1.81195	+	12.6024i	−0.0877891	+	0.610586i
$427$	−0.470596	−	0.302434i	−0.0227737	−	0.0146358i
$428$	−6.22905	−	7.18871i	−0.301092	−	0.347479i
$429$	−1.30604	−	2.85983i	−0.0630562	−	0.138074i
$430$	−17.6373	+	11.3348i	−0.850544	+	0.546611i
$431$	−1.42384	−	0.418077i	−0.0685839	−	0.0201381i	0.247261	−	0.968949i	$-0.420470\pi$
$431$	−1.42384	−	0.418077i	−0.0685839	−	0.0201381i	−0.315845	+	0.948811i	$0.602288\pi$
$432$	0.654861	−	0.755750i	0.0315070	−	0.0363610i
$433$	6.69224	−	1.96502i	0.321608	−	0.0944327i	−0.116944	−	0.993139i	$-0.537310\pi$
$433$	6.69224	−	1.96502i	0.321608	−	0.0944327i	0.438552	+	0.898706i	$0.355492\pi$
$434$	0.554666	−	1.21455i	0.0266248	−	0.0583002i
$435$	−3.63186	−	25.2601i	−0.174134	−	1.21113i
$436$	−20.2217			−0.968443
$437$	−19.1619	+	9.12206i	−0.916639	+	0.436367i
$438$	2.98812			0.142778
$439$	−1.32651	−	9.22605i	−0.0633106	−	0.440335i	−0.996680	−	0.0814180i	$-0.974055\pi$
$439$	−1.32651	−	9.22605i	−0.0633106	−	0.440335i	0.933369	−	0.358917i	$-0.116854\pi$
$440$	−3.34251	+	7.31909i	−0.159348	+	0.348924i
$441$	6.68024	−	1.96150i	0.318107	−	0.0934046i
$442$	−3.29085	+	3.79785i	−0.156530	+	0.180645i
$443$	−30.3672	−	8.91661i	−1.44279	−	0.423641i	−0.535638	−	0.844448i	$-0.679929\pi$
$443$	−30.3672	−	8.91661i	−1.44279	−	0.423641i	−0.907150	+	0.420807i	$0.861747\pi$
$444$	4.07650	−	2.61981i	0.193462	−	0.124331i
$445$	7.80342	+	17.0871i	0.369918	+	0.810007i
$446$	4.20260	+	4.85006i	0.198999	+	0.229657i
$447$	8.00484	+	5.14440i	0.378616	+	0.243322i
$448$	−0.0276463	+	0.192284i	−0.00130617	+	0.00908459i
$449$	1.36062	−	9.46329i	0.0642115	−	0.446600i	−0.932199	−	0.361946i	$-0.882112\pi$
$449$	1.36062	−	9.46329i	0.0642115	−	0.446600i	0.996410	−	0.0846542i	$-0.0269785\pi$
$450$	−2.25168	−	1.44706i	−0.106145	−	0.0682153i
$451$	10.9255	+	12.6087i	0.514463	+	0.593721i
$452$	0.546964	+	1.19768i	0.0257270	+	0.0563343i
$453$	7.30101	−	4.69207i	0.343031	−	0.220453i
$454$	−1.14837	−	0.337191i	−0.0538955	−	0.0158252i
$455$	−0.381581	+	0.440368i	−0.0178888	+	0.0206448i
$456$	4.24593	−	1.24672i	0.198834	−	0.0583829i
$457$	−5.34240	+	11.6982i	−0.249907	+	0.547220i	−0.992460	−	0.122567i	$-0.960887\pi$
$457$	−5.34240	+	11.6982i	−0.249907	+	0.547220i	0.742553	+	0.669787i	$0.233615\pi$
$458$	−3.99700	−	27.7997i	−0.186767	−	1.29900i
$459$	4.64187			0.216664
$460$	−3.54029	+	12.8073i	−0.165067	+	0.597145i
$461$	18.4038			0.857151			0.428575	−	0.903506i	$-0.359016\pi$
$461$	18.4038			0.857151			0.428575	+	0.903506i	$0.359016\pi$
$462$	−0.0802870	−	0.558408i	−0.00373529	−	0.0259795i
$463$	11.4891	−	25.1576i	0.533944	−	1.16917i	−0.429941	−	0.902857i	$-0.641466\pi$
$463$	11.4891	−	25.1576i	0.533944	−	1.16917i	0.963885	−	0.266318i	$-0.0858070\pi$
$464$	8.83766	−	2.59497i	0.410278	−	0.120468i
$465$	−12.4708	+	14.3921i	−0.578319	+	0.667416i
$466$	−15.7479	−	4.62401i	−0.729509	−	0.214203i
$467$	20.4802	−	13.1618i	0.947711	−	0.609057i	0.0271399	−	0.999632i	$-0.491360\pi$
$467$	20.4802	−	13.1618i	0.947711	−	0.609057i	0.920571	+	0.390575i	$0.127724\pi$
$468$	0.449727	+	0.984764i	0.0207886	+	0.0455207i
$469$	1.86208	+	2.14896i	0.0859829	+	0.0992296i
$470$	13.0866	+	8.41025i	0.603640	+	0.387936i
$471$	2.82016	−	19.6146i	0.129946	−	0.903794i
$472$	−1.52538	+	10.6093i	−0.0702114	+	0.488331i
$473$	18.4865	+	11.8806i	0.850010	+	0.546268i
$474$	−1.67577	−	1.93394i	−0.0769708	−	0.0888290i
$475$	−4.92031	−	10.7740i	−0.225759	−	0.494344i
$476$	−0.758591	+	0.487517i	−0.0347699	+	0.0223453i
$477$	3.97478	+	1.16710i	0.181993	+	0.0534379i
$478$	6.76847	−	7.81123i	0.309582	−	0.357277i
$479$	6.99671	−	2.05442i	0.319688	−	0.0938689i	−0.117952	−	0.993019i	$-0.537633\pi$
$479$	6.99671	−	2.05442i	0.319688	−	0.0938689i	0.437640	+	0.899150i	$0.355815\pi$
$480$	1.15098	−	2.52028i	0.0525346	−	0.115035i
$481$	0.746581	+	5.19259i	0.0340412	+	0.236762i
$482$	21.9380			0.999248
$483$	−0.276661	−	0.889620i	−0.0125885	−	0.0404791i
$484$	−2.56636			−0.116653
$485$	4.87676	+	33.9186i	0.221442	+	1.54016i
$486$	0.415415	−	0.909632i	0.0188436	−	0.0412617i
$487$	−21.5014	+	6.31339i	−0.974323	+	0.286087i	−0.729879	−	0.683576i	$-0.760424\pi$
$487$	−21.5014	+	6.31339i	−0.974323	+	0.286087i	−0.244444	+	0.969663i	$0.578605\pi$
$488$	−1.88574	+	2.17626i	−0.0853636	+	0.0985149i
$489$	13.9140	+	4.08552i	0.629213	+	0.184754i
$490$	16.2279	−	10.4290i	0.733100	−	0.471134i
$491$	8.18375	+	17.9199i	0.369328	+	0.808715i	0.999480	+	0.0322432i	$0.0102651\pi$
$491$	8.18375	+	17.9199i	0.369328	+	0.808715i	−0.630152	+	0.776471i	$0.717008\pi$
$492$	−3.76214	−	4.34174i	−0.169610	−	0.195741i
$493$	35.9679	+	23.1152i	1.61991	+	1.04106i
$494$	−0.681786	+	4.74192i	−0.0306750	+	0.213349i
$495$	−1.14509	+	7.96431i	−0.0514682	+	0.357969i
$496$	−5.78214	−	3.71596i	−0.259626	−	0.166851i
$497$	−1.61969	−	1.86922i	−0.0726529	−	0.0838460i
$498$	−0.337136	−	0.738226i	−0.0151074	−	0.0330807i
$499$	−14.5484	+	9.34971i	−0.651277	+	0.418550i	−0.824133	−	0.566397i	$-0.808337\pi$
$499$	−14.5484	+	9.34971i	−0.651277	+	0.418550i	0.172855	+	0.984947i	$0.444701\pi$
$500$	6.17667	+	1.81363i	0.276229	+	0.0811082i
$501$	−6.47735	+	7.47526i	−0.289387	+	0.333970i
$502$	0.259982	−	0.0763376i	0.0116036	−	0.00340711i
$503$	6.82524	−	14.9452i	0.304323	−	0.666373i	−0.694253	−	0.719731i	$-0.744265\pi$
$503$	6.82524	−	14.9452i	0.304323	−	0.666373i	0.998575	+	0.0533577i	$0.0169923\pi$
$504$	0.0276463	+	0.192284i	0.00123147	+	0.00856503i
$505$	43.4902			1.93529
$506$	13.7524	−	2.20111i	0.611369	−	0.0978513i
$507$	11.8280			0.525299
$508$	0.685740	+	4.76943i	0.0304248	+	0.211609i
$509$	11.2142	−	24.5556i	0.497059	−	1.08841i	−0.480354	−	0.877074i	$-0.659492\pi$
$509$	11.2142	−	24.5556i	0.497059	−	1.08841i	0.977414	−	0.211334i	$-0.0677807\pi$
$510$	12.3401	−	3.62338i	0.546429	−	0.160446i
$511$	−0.380132	+	0.438696i	−0.0168161	+	0.0194068i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	3.72270	−	2.39243i	0.164361	−	0.105629i
$514$	−6.06645	−	13.2837i	−0.267580	−	0.585918i
$515$	−17.1368	−	19.7770i	−0.755139	−	0.871477i
$516$	−6.36572	−	4.09100i	−0.280235	−	0.180096i
$517$	2.32046	−	16.1392i	0.102054	−	0.709799i
$518$	−0.133967	+	0.931761i	−0.00588617	+	0.0409392i
$519$	−11.1411	−	7.15994i	−0.489040	−	0.314287i
$520$	1.96426	+	2.26688i	0.0861386	+	0.0994092i
$521$	9.75660	+	21.3640i	0.427444	+	0.935973i	0.993734	+	0.111767i	$0.0356509\pi$
$521$	9.75660	+	21.3640i	0.427444	+	0.935973i	−0.566290	+	0.824206i	$0.691622\pi$
$522$	7.74858	−	4.97971i	0.339146	−	0.217956i
$523$	−28.1477	−	8.26490i	−1.23081	−	0.361399i	−0.399255	−	0.916840i	$-0.630731\pi$
$523$	−28.1477	−	8.26490i	−1.23081	−	0.361399i	−0.831556	+	0.555441i	$0.812550\pi$
$524$	−10.4632	+	12.0752i	−0.457087	+	0.527507i
$525$	0.498894	−	0.146488i	0.0217735	−	0.00639328i
$526$	7.09072	−	15.5265i	0.309170	−	0.676988i
$527$	−4.54051	−	31.5800i	−0.197788	−	1.37565i
$528$	−2.90407			−0.126384
$529$	21.8511	−	7.17853i	0.950046	−	0.312110i
$530$	11.4777			0.498560
$531$	1.52538	+	10.6093i	0.0661959	+	0.460403i
$532$	−0.357109	+	0.781959i	−0.0154826	+	0.0339022i
$533$	5.96752	−	1.75222i	0.258482	−	0.0758972i
$534$	−4.43985	+	5.12386i	−0.192131	+	0.221731i
$535$	−25.2871	−	7.42495i	−1.09326	−	0.321009i
$536$	12.3137	−	7.91354i	0.531872	−	0.341813i
$537$	−2.17898	−	4.77130i	−0.0940299	−	0.205897i
$538$	21.1023	+	24.3534i	0.909785	+	1.04995i
$539$	−17.0092	−	10.9312i	−0.732640	−	0.470839i
$540$	0.394306	−	2.74246i	0.0169682	−	0.118017i
$541$	0.682956	−	4.75006i	0.0293626	−	0.204221i	−0.969859	−	0.243666i	$-0.921650\pi$
$541$	0.682956	−	4.75006i	0.0293626	−	0.204221i	0.999222	+	0.0394449i	$0.0125590\pi$
$542$	−2.57776	−	1.65662i	−0.110724	−	0.0711581i
$543$	−10.6450	−	12.2849i	−0.456819	−	0.527197i
$544$	1.92830	+	4.22240i	0.0826753	+	0.181034i
$545$	−47.1333	+	30.2908i	−2.01897	+	1.29751i
$546$	−0.201788	−	0.0592504i	−0.00863574	−	0.00253568i
$547$	−18.0000	+	20.7731i	−0.769622	+	0.888192i	−0.996315	−	0.0857749i	$-0.972663\pi$
$547$	−18.0000	+	20.7731i	−0.769622	+	0.888192i	0.226692	+	0.973966i	$0.427209\pi$
$548$	−18.0116	+	5.28867i	−0.769416	+	0.225921i
$549$	−1.19623	+	2.61939i	−0.0510540	+	0.111793i
$550$	1.10621	+	7.69385i	0.0471689	+	0.328067i
$551$	40.7593			1.73640
$552$	−4.73556	+	0.757939i	−0.201559	+	0.0322600i
$553$	0.497111			0.0211393
$554$	−0.719737	−	5.00588i	−0.0305787	−	0.212679i
$555$	5.57733	−	12.2126i	0.236744	−	0.518398i
$556$	−17.0348	+	5.00188i	−0.722438	+	0.212127i
$557$	7.86165	−	9.07283i	0.333109	−	0.384428i	−0.564343	−	0.825540i	$-0.690870\pi$
$557$	7.86165	−	9.07283i	0.333109	−	0.384428i	0.897452	+	0.441112i	$0.145416\pi$
$558$	−6.59483	−	1.93642i	−0.279181	−	0.0819750i
$559$	6.89150	−	4.42890i	0.291479	−	0.187322i
$560$	0.223590	+	0.489595i	0.00944842	+	0.0206892i
$561$	−8.82774	−	10.1878i	−0.372708	−	0.430127i
$562$	7.06600	+	4.54104i	0.298061	+	0.191552i
$563$	0.869255	−	6.04580i	0.0366347	−	0.254800i	−0.963271	−	0.268531i	$-0.913462\pi$
$563$	0.869255	−	6.04580i	0.0366347	−	0.254800i	0.999906	+	0.0137310i	$0.00437086\pi$
$564$	−0.799036	+	5.55742i	−0.0336455	+	0.234010i
$565$	3.06893	+	1.97228i	0.129111	+	0.0829745i
$566$	9.97344	+	11.5100i	0.419215	+	0.483800i
$567$	0.0806993	+	0.176707i	0.00338905	+	0.00742098i
$568$	−10.7108	+	6.88341i	−0.449415	+	0.288822i
$569$	−23.9950	−	7.04556i	−1.00592	−	0.295365i	−0.263038	−	0.964786i	$-0.584724\pi$
$569$	−23.9950	−	7.04556i	−1.00592	−	0.295365i	−0.742884	+	0.669420i	$0.766543\pi$
$570$	8.02904	−	9.26601i	0.336300	−	0.388110i
$571$	22.4009	−	6.57751i	0.937450	−	0.275260i	0.222898	−	0.974842i	$-0.428448\pi$
$571$	22.4009	−	6.57751i	0.937450	−	0.275260i	0.714553	+	0.699582i	$0.246630\pi$
$572$	1.30604	−	2.85983i	0.0546082	−	0.119575i
$573$	−1.09478	−	7.61436i	−0.0457350	−	0.318094i
$574$	1.11602			0.0465819
$575$	3.81188	+	12.2573i	0.158966	+	0.511167i
$576$	1.00000			0.0416667
$577$	−5.23379	−	36.4018i	−0.217886	−	1.51543i	−0.745823	−	0.666145i	$-0.767943\pi$
$577$	−5.23379	−	36.4018i	−0.217886	−	1.51543i	0.527937	−	0.849284i	$-0.322966\pi$
$578$	−1.88888	+	4.13608i	−0.0785672	+	0.172038i
$579$	−1.36963	+	0.402159i	−0.0569198	+	0.0167131i
$580$	16.7120	−	19.2867i	0.693927	−	0.800835i
$581$	0.151270	+	0.0444169i	0.00627573	+	0.00184272i
$582$	−10.4046	+	6.68662i	−0.431284	+	0.277169i
$583$	−4.99759	−	10.9432i	−0.206979	−	0.453221i
$584$	1.95680	+	2.25827i	0.0809731	+	0.0934480i
$585$	2.52335	+	1.62166i	0.104328	+	0.0670473i
$586$	4.11658	−	28.6315i	0.170055	−	1.18276i
$587$	−3.37092	+	23.4453i	−0.139133	+	0.967690i	0.793938	+	0.607998i	$0.208027\pi$
$587$	−3.37092	+	23.4453i	−0.139133	+	0.967690i	−0.933071	+	0.359692i	$0.882882\pi$
$588$	5.85703	+	3.76408i	0.241540	+	0.155228i
$589$	−19.9178	−	22.9864i	−0.820699	−	0.947137i
$590$	12.3366	+	27.0133i	0.507888	+	1.11212i
$591$	−5.26265	+	3.38210i	−0.216476	+	0.139121i
$592$	4.64946	+	1.36520i	0.191091	+	0.0561095i
$593$	−17.0796	+	19.7109i	−0.701376	+	0.809431i	−0.988938	−	0.148331i	$-0.952610\pi$
$593$	−17.0796	+	19.7109i	−0.701376	+	0.809431i	0.287562	+	0.957762i	$0.407155\pi$
$594$	−2.78644	+	0.818172i	−0.114329	+	0.0335700i
$595$	−1.03788	+	2.27264i	−0.0425489	+	0.0931690i
$596$	1.35418	+	9.41852i	0.0554693	+	0.385797i
$597$	−0.863136			−0.0353258
$598$	1.38332	−	5.00428i	0.0565680	−	0.204640i
$599$	11.2311			0.458891			0.229445	−	0.973322i	$-0.426309\pi$
$599$	11.2311			0.458891			0.229445	+	0.973322i	$0.426309\pi$
$600$	−0.380916	−	2.64933i	−0.0155508	−	0.108158i
$601$	9.43741	−	20.6650i	0.384960	−	0.842945i	−0.613616	−	0.789604i	$-0.710286\pi$
$601$	9.43741	−	20.6650i	0.384960	−	0.842945i	0.998576	−	0.0533404i	$-0.0169868\pi$
$602$	1.41042	−	0.414138i	0.0574846	−	0.0168790i
$603$	9.58542	−	11.0622i	0.390348	−	0.450486i
$604$	8.32718	+	2.44508i	0.338828	+	0.0994889i
$605$	−5.98175	+	3.84424i	−0.243193	+	0.156291i
$606$	6.52063	+	14.2782i	0.264883	+	0.580012i
$607$	−10.5182	−	12.1387i	−0.426922	−	0.492694i	0.501011	−	0.865441i	$-0.332962\pi$
$607$	−10.5182	−	12.1387i	−0.426922	−	0.492694i	−0.927933	+	0.372747i	$0.878416\pi$
$608$	3.72270	+	2.39243i	0.150975	+	0.0970260i
$609$	−0.254644	+	1.77109i	−0.0103187	+	0.0717680i
$610$	−1.13545	+	7.89722i	−0.0459730	+	0.319749i
$611$	−5.11340	−	3.28618i	−0.206866	−	0.132945i
$612$	3.03978	+	3.50809i	0.122876	+	0.141806i
$613$	2.61584	+	5.72789i	0.105653	+	0.231347i	0.955074	−	0.296369i	$-0.0957757\pi$
$613$	2.61584	+	5.72789i	0.105653	+	0.231347i	−0.849421	+	0.527716i	$0.823048\pi$
$614$	18.1572	−	11.6689i	0.732766	−	0.470920i
$615$	−15.2725	−	4.48442i	−0.615848	−	0.180829i
$616$	0.369440	−	0.426356i	0.0148852	−	0.0171784i
$617$	9.23760	−	2.71240i	0.371892	−	0.109197i	−0.0904455	−	0.995901i	$-0.528829\pi$
$617$	9.23760	−	2.71240i	0.371892	−	0.109197i	0.462337	+	0.886704i	$0.347011\pi$
$618$	3.92356	−	8.59139i	0.157829	−	0.345596i
$619$	−3.51921	−	24.4767i	−0.141449	−	0.983800i	−0.929666	−	0.368403i	$-0.879905\pi$
$619$	−3.51921	−	24.4767i	−0.141449	−	0.983800i	0.788217	−	0.615397i	$-0.211004\pi$
$620$	−19.0434			−0.764803
$621$	−4.33020	+	2.06140i	−0.173765	+	0.0827211i
$622$	−0.878874			−0.0352396
$623$	−0.187438	−	1.30366i	−0.00750953	−	0.0522299i
$624$	−0.449727	+	0.984764i	−0.0180035	+	0.0394221i
$625$	29.9542	−	8.79536i	1.19817	−	0.351814i
$626$	−3.57263	+	4.12304i	−0.142791	+	0.164790i
$627$	−12.3305	−	3.62056i	−0.492432	−	0.144591i
$628$	16.6706	−	10.7135i	0.665228	−	0.427516i
$629$	9.34406	+	20.4606i	0.372572	+	0.815819i
$630$	0.352468	+	0.406770i	0.0140427	+	0.0162061i
$631$	30.1416	+	19.3708i	1.19992	+	0.771141i	0.978942	−	0.204138i	$-0.0654391\pi$
$631$	30.1416	+	19.3708i	1.19992	+	0.771141i	0.220977	+	0.975279i	$0.429076\pi$
$632$	0.364180	−	2.53293i	0.0144863	−	0.100754i
$633$	2.71318	−	18.8706i	0.107839	−	0.750039i
$634$	4.27930	+	2.75014i	0.169953	+	0.109222i
$635$	8.74263	+	10.0895i	0.346941	+	0.400391i
$636$	1.72089	+	3.76823i	0.0682378	+	0.149420i
$637$	−6.34080	+	4.07498i	−0.251232	+	0.161457i
$638$	−25.6652	−	7.53598i	−1.01609	−	0.298352i
$639$	−8.33766	+	9.62217i	−0.329833	+	0.380647i
$640$	2.65843	−	0.780586i	0.105084	−	0.0308554i
$641$	−5.26851	+	11.5364i	−0.208094	+	0.455662i	−0.984685	−	0.174343i	$-0.944220\pi$
$641$	−5.26851	+	11.5364i	−0.208094	+	0.455662i	0.776591	+	0.630005i	$0.216947\pi$
$642$	−1.35370	−	9.41520i	−0.0534264	−	0.371588i
$643$	−27.3350			−1.07799			−0.538993	−	0.842310i	$-0.681195\pi$
$643$	−27.3350			−1.07799			−0.538993	+	0.842310i	$0.681195\pi$
$644$	0.491156	−	0.791664i	0.0193543	−	0.0311959i
$645$	−20.9654			−0.825514
$646$	2.92331	+	20.3320i	0.115016	+	0.799954i
$647$	−1.94623	+	4.26166i	−0.0765143	+	0.167543i	−0.944024	−	0.329878i	$-0.892992\pi$
$647$	−1.94623	+	4.26166i	−0.0765143	+	0.167543i	0.867509	+	0.497421i	$0.165720\pi$
$648$	0.959493	−	0.281733i	0.0376924	−	0.0110675i
$649$	20.3838	−	23.5241i	0.800133	−	0.923403i
$650$	2.78027	+	0.816362i	0.109051	+	0.0320204i
$651$	1.12325	−	0.721868i	0.0440236	−	0.0282922i
$652$	6.02410	+	13.1909i	0.235922	+	0.516597i
$653$	18.8217	+	21.7214i	0.736550	+	0.850024i	0.993193	−	0.116482i	$-0.0371618\pi$
$653$	18.8217	+	21.7214i	0.736550	+	0.850024i	−0.256643	+	0.966506i	$0.582616\pi$
$654$	−17.0116	−	10.9327i	−0.665205	−	0.427501i
$655$	−6.30013	+	43.8184i	−0.246167	+	1.71213i
$656$	0.817590	−	5.68647i	0.0319215	−	0.222019i
$657$	2.51377	+	1.61550i	0.0980715	+	0.0630267i
$658$	−0.714254	−	0.824293i	−0.0278445	−	0.0321343i
$659$	1.50370	+	3.29264i	0.0585758	+	0.128263i	0.936656	−	0.350250i	$-0.113903\pi$
$659$	1.50370	+	3.29264i	0.0585758	+	0.128263i	−0.878081	+	0.478513i	$0.841176\pi$
$660$	−6.76890	+	4.35011i	−0.263479	+	0.169328i
$661$	16.3839	+	4.81074i	0.637259	+	0.187116i	0.584374	−	0.811485i	$-0.301340\pi$
$661$	16.3839	+	4.81074i	0.637259	+	0.187116i	0.0528849	+	0.998601i	$0.483158\pi$
$662$	−23.3216	+	26.9146i	−0.906421	+	1.04607i
$663$	−4.82172	+	1.41578i	−0.187260	+	0.0549845i
$664$	0.337136	−	0.738226i	0.0130834	−	0.0286487i
$665$	0.338963	+	2.35754i	0.0131444	+	0.0914215i
$666$	4.84574			0.187769
$667$	−43.8181	−	5.59023i	−1.69664	−	0.216455i
$668$	−9.89119			−0.382702
$669$	0.913312	+	6.35223i	0.0353107	+	0.245591i
$670$	16.8472	−	36.8903i	0.650865	−	1.42519i
$671$	8.02385	−	2.35602i	0.309757	−	0.0909530i
$672$	−0.127214	+	0.146813i	−0.00490740	+	0.00566344i
$673$	−42.8696	−	12.5877i	−1.65250	−	0.485219i	−0.683025	−	0.730395i	$-0.739336\pi$
$673$	−42.8696	−	12.5877i	−1.65250	−	0.485219i	−0.969478	+	0.245177i	$0.921154\pi$
$674$	−9.67814	+	6.21976i	−0.372788	+	0.239576i
$675$	−1.11189	−	2.43470i	−0.0427966	−	0.0937115i
$676$	7.74568	+	8.93899i	0.297911	+	0.343807i
$677$	17.0221	+	10.9395i	0.654214	+	0.420438i	0.825204	−	0.564835i	$-0.191060\pi$
$677$	17.0221	+	10.9395i	0.654214	+	0.420438i	−0.170990	+	0.985273i	$0.554697\pi$
$678$	−0.187381	+	1.30327i	−0.00719634	+	0.0500517i
$679$	0.341928	−	2.37816i	0.0131220	−	0.0912655i
$680$	10.8194	+	6.95322i	0.414906	+	0.266644i
$681$	−0.783769	−	0.904517i	−0.0300341	−	0.0346612i
$682$	8.29185	+	18.1566i	0.317511	+	0.695253i
$683$	−34.6818	+	22.2886i	−1.32706	+	0.852850i	−0.995877	−	0.0907163i	$-0.971084\pi$
$683$	−34.6818	+	22.2886i	−1.32706	+	0.852850i	−0.331184	+	0.943566i	$0.607448\pi$
$684$	4.24593	+	1.24672i	0.162347	+	0.0476694i
$685$	−34.0598	+	39.3071i	−1.30136	+	1.50185i
$686$	−2.60247	+	0.764153i	−0.0993626	+	0.0291755i
$687$	11.6672	−	25.5475i	0.445130	−	0.974700i
$688$	−1.07689	−	7.48992i	−0.0410560	−	0.285551i
$689$	−4.48475			−0.170855
$690$	−9.90244	+	8.86018i	−0.376980	+	0.337301i
$691$	−39.4196			−1.49959			−0.749795	−	0.661670i	$-0.769848\pi$
$691$	−39.4196			−1.49959			−0.749795	+	0.661670i	$0.769848\pi$
$692$	−1.88474	−	13.1086i	−0.0716470	−	0.498316i
$693$	0.234356	−	0.513169i	0.00890247	−	0.0194937i
$694$	−15.1633	+	4.45236i	−0.575592	+	0.169009i
$695$	−32.2128	+	37.1756i	−1.22190	+	1.41015i
$696$	8.83766	+	2.59497i	0.334991	+	0.0983621i
$697$	22.4339	−	14.4174i	0.849746	−	0.546099i
$698$	−5.08075	−	11.1253i	−0.192309	−	0.421099i
$699$	−10.7481	−	12.4039i	−0.406530	−	0.469160i
$700$	0.437415	+	0.281109i	0.0165327	+	0.0106249i
$701$	6.43057	−	44.7256i	0.242879	−	1.68926i	−0.394645	−	0.918834i	$-0.629132\pi$
$701$	6.43057	−	44.7256i	0.242879	−	1.68926i	0.637525	−	0.770430i	$-0.279958\pi$
$702$	−0.154070	+	1.07158i	−0.00581498	+	0.0404441i
$703$	18.0392	+	11.5931i	0.680363	+	0.437243i
$704$	−1.90176	−	2.19475i	−0.0716754	−	0.0827178i
$705$	6.46223	+	14.1503i	0.243382	+	0.532931i
$706$	−3.07624	+	1.97698i	−0.115776	+	0.0744045i
$707$	−2.92575	−	0.859077i	−0.110034	−	0.0323089i
$708$	−7.01903	+	8.10039i	−0.263791	+	0.304431i
$709$	−30.6067	+	8.98694i	−1.14946	+	0.337511i	−0.800328	−	0.599563i	$-0.795341\pi$
$709$	−30.6067	+	8.98694i	−1.14946	+	0.337511i	−0.349131	+	0.937074i	$0.613523\pi$
$710$	−14.6542	+	32.0881i	−0.549961	+	1.20425i
$711$	−0.364180	−	2.53293i	−0.0136578	−	0.0949922i
$712$	−6.77984			−0.254085
$713$	18.2599	+	27.4432i	0.683840	+	1.02776i
$714$	−0.901738			−0.0337467
$715$	−1.23968	−	8.62213i	−0.0463612	−	0.322449i
$716$	2.17898	−	4.77130i	0.0814323	−	0.178312i
$717$	9.91706	−	2.91191i	0.370360	−	0.108747i
$718$	−8.61646	+	9.94392i	−0.321563	+	0.371104i
$719$	24.1545	+	7.09239i	0.900809	+	0.264502i	0.699168	−	0.714958i	$-0.253554\pi$
$719$	24.1545	+	7.09239i	0.900809	+	0.264502i	0.201642	+	0.979459i	$0.435372\pi$
$720$	2.33083	−	1.49793i	0.0868649	−	0.0558247i
$721$	0.762197	+	1.66898i	0.0283857	+	0.0621560i
$722$	0.381279	+	0.440019i	0.0141897	+	0.0163758i
$723$	18.4554	+	11.8606i	0.686364	+	0.441100i
$724$	2.31337	−	16.0898i	0.0859757	−	0.597974i
$725$	3.50853	−	24.4023i	0.130303	−	0.906280i
$726$	−2.15896	−	1.38748i	−0.0801266	−	0.0514942i
$727$	−1.54963	−	1.78836i	−0.0574725	−	0.0663268i	0.726285	−	0.687393i	$-0.241245\pi$
$727$	−1.54963	−	1.78836i	−0.0574725	−	0.0663268i	−0.783758	+	0.621067i	$0.786700\pi$
$728$	−0.0873647	−	0.191302i	−0.00323795	−	0.00709013i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	7.94372	+	2.33249i	0.294010	+	0.0863292i
$731$	23.0018	−	26.5455i	0.850754	−	0.981822i
$732$	−2.76297	+	0.811280i	−0.102122	+	0.0299858i
$733$	−0.181280	+	0.396947i	−0.00669571	+	0.0146616i	−0.912950	−	0.408071i	$-0.866202\pi$
$733$	−0.181280	+	0.396947i	−0.00669571	+	0.0146616i	0.906255	+	0.422732i	$0.138929\pi$
$734$	−1.75595	−	12.2129i	−0.0648133	−	0.450786i
$735$	19.2901			0.711525
$736$	−3.67394	−	3.08255i	−0.135423	−	0.113624i
$737$	−42.5079			−1.56580
$738$	−0.817590	−	5.68647i	−0.0300959	−	0.209322i
$739$	−14.5747	+	31.9141i	−0.536138	+	1.17398i	0.426822	+	0.904336i	$0.359633\pi$
$739$	−14.5747	+	31.9141i	−0.536138	+	1.17398i	−0.962960	+	0.269643i	$0.913094\pi$
$740$	12.8821	−	3.78252i	0.473555	−	0.139048i
$741$	−3.13723	+	3.62056i	−0.115249	+	0.133005i
$742$	−0.772148	−	0.226723i	−0.0283464	−	0.00832327i
$743$	28.2800	−	18.1745i	1.03749	−	0.666756i	0.0931277	−	0.995654i	$-0.470314\pi$
$743$	28.2800	−	18.1745i	1.03749	−	0.666756i	0.944366	+	0.328898i	$0.106677\pi$
$744$	−2.85525	−	6.25212i	−0.104678	−	0.229214i
$745$	17.2647	+	19.9245i	0.632529	+	0.729977i
$746$	15.6050	+	10.0287i	0.571340	+	0.367178i
$747$	0.115498	−	0.803305i	0.00422584	−	0.0293914i
$748$	1.91845	−	13.3431i	0.0701455	−	0.487873i
$749$	1.55449	+	0.999008i	0.0567997	+	0.0365030i
$750$	4.21562	+	4.86509i	0.153933	+	0.177648i
$751$	16.5189	+	36.1713i	0.602782	+	1.31991i	0.927403	+	0.374064i	$0.122036\pi$
$751$	16.5189	+	36.1713i	0.602782	+	1.31991i	−0.324621	+	0.945844i	$0.605237\pi$
$752$	−4.72328	+	3.03546i	−0.172240	+	0.110692i
$753$	0.259982	+	0.0763376i	0.00947426	+	0.00278190i
$754$	−6.52997	+	7.53598i	−0.237807	+	0.274444i
$755$	23.0718	−	6.77449i	0.839669	−	0.246549i
$756$	−0.0806993	+	0.176707i	−0.00293500	+	0.00642676i
$757$	3.53539	+	24.5892i	0.128496	+	0.893709i	0.947462	+	0.319868i	$0.103638\pi$
$757$	3.53539	+	24.5892i	0.128496	+	0.893709i	−0.818966	+	0.573842i	$0.805452\pi$
$758$	−2.85973			−0.103870
$759$	12.7593	+	5.58342i	0.463132	+	0.202665i
$760$	12.2607			0.444742
$761$	3.46327	+	24.0876i	0.125543	+	0.873174i	0.951106	+	0.308864i	$0.0999487\pi$
$761$	3.46327	+	24.0876i	0.125543	+	0.873174i	−0.825563	+	0.564310i	$0.809142\pi$
$762$	−2.00167	+	4.38304i	−0.0725127	+	0.158781i
$763$	3.76918	−	1.10673i	0.136453	−	0.0400663i
$764$	5.03762	−	5.81372i	0.182255	−	0.210333i
$765$	12.3401	+	3.62338i	0.446157	+	0.131004i
$766$	0.0676928	−	0.0435035i	0.00244584	−	0.00157185i
$767$	−4.82033	−	10.5551i	−0.174052	−	0.381121i
$768$	0.654861	+	0.755750i	0.0236303	+	0.0272708i
$769$	−22.2445	−	14.2957i	−0.802159	−	0.515516i	0.0741608	−	0.997246i	$-0.476372\pi$
$769$	−22.2445	−	14.2957i	−0.802159	−	0.515516i	−0.876320	+	0.481730i	$0.840009\pi$
$770$	0.222448	−	1.54716i	0.00801647	−	0.0557558i
$771$	2.07827	−	14.4547i	0.0748472	−	0.520574i
$772$	−1.20085	−	0.771737i	−0.0432194	−	0.0277754i
$773$	−14.4872	−	16.7191i	−0.521067	−	0.601343i	0.432831	−	0.901475i	$-0.357515\pi$
$773$	−14.4872	−	16.7191i	−0.521067	−	0.601343i	−0.953898	+	0.300132i	$0.902969\pi$
$774$	−3.14342	−	6.88313i	−0.112988	−	0.247409i
$775$	−15.4763	+	9.94603i	−0.555926	+	0.357272i
$776$	−11.8670	−	3.48445i	−0.425999	−	0.125085i
$777$	−0.616448	+	0.711419i	−0.0221150	+	0.0255220i
$778$	−13.1955	+	3.87455i	−0.473081	+	0.138909i
$779$	10.5608	−	23.1250i	0.378382	−	0.828540i
$780$	0.426875	+	2.96898i	0.0152846	+	0.106307i
$781$	36.9745			1.32305
$782$	−0.354100	−	22.2588i	−0.0126626	−	0.795974i
$783$	9.21076			0.329166
$784$	0.990833	+	6.89140i	0.0353869	+	0.246121i
$785$	22.8081	−	49.9428i	0.814056	−	1.78253i
$786$	−15.3305	+	4.50145i	−0.546822	+	0.160562i
$787$	−2.95813	+	3.41387i	−0.105446	+	0.121691i	−0.806019	−	0.591889i	$-0.798382\pi$
$787$	−2.95813	+	3.41387i	−0.105446	+	0.121691i	0.700573	+	0.713581i	$0.252928\pi$
$788$	−6.00232	−	1.76244i	−0.213824	−	0.0627844i
$789$	14.3594	−	9.22820i	0.511207	−	0.328533i
$790$	−2.94532	−	6.44934i	−0.104790	−	0.229457i
$791$	−0.167499	−	0.193304i	−0.00595559	−	0.00687311i
$792$	−2.44306	−	1.57006i	−0.0868104	−	0.0557897i
$793$	0.443660	−	3.08572i	0.0157548	−	0.109577i
$794$	−0.943402	+	6.56150i	−0.0334801	+	0.232859i
$795$	9.65566	+	6.20532i	0.342451	+	0.220080i
$796$	−0.565234	−	0.652315i	−0.0200342	−	0.0231207i
$797$	−12.5900	−	27.5683i	−0.445961	−	0.976518i	−0.990466	−	0.137760i	$-0.956010\pi$
$797$	−12.5900	−	27.5683i	−0.445961	−	0.976518i	0.544505	−	0.838758i	$-0.316718\pi$
$798$	−0.723178	+	0.464758i	−0.0256002	+	0.0164523i
$799$	−25.0064	−	7.34255i	−0.884663	−	0.259761i
$800$	1.75278	−	2.02282i	0.0619702	−	0.0715175i
$801$	−6.50521	+	1.91010i	−0.229850	+	0.0674901i
$802$	14.6598	−	32.1005i	0.517656	−	1.13351i
$803$	−1.23497	−	8.58940i	−0.0435811	−	0.303113i
$804$	14.6373			0.516219
$805$	−0.0410586	−	2.58095i	−0.00144712	−	0.0909666i
$806$	7.44095			0.262096
$807$	4.58597	+	31.8961i	0.161434	+	1.12280i
$808$	−6.52063	+	14.2782i	−0.229395	+	0.502305i
$809$	−27.2132	+	7.99050i	−0.956764	+	0.280931i	−0.722600	−	0.691266i	$-0.757053\pi$
$809$	−27.2132	+	7.99050i	−0.956764	+	0.280931i	−0.234163	+	0.972197i	$0.575235\pi$
$810$	1.81440	−	2.09393i	0.0637515	−	0.0735731i
$811$	10.1871	+	2.99120i	0.357718	+	0.105035i	0.455653	−	0.890157i	$-0.349406\pi$
$811$	10.1871	+	2.99120i	0.357718	+	0.105035i	−0.0979355	+	0.995193i	$0.531224\pi$
$812$	−1.50525	+	0.967368i	−0.0528240	+	0.0339479i
$813$	−1.27291	−	2.78728i	−0.0446429	−	0.0977543i
$814$	−9.21546	−	10.6352i	−0.323002	−	0.372764i
$815$	33.8003	+	21.7221i	1.18397	+	0.760894i
$816$	−0.660607	+	4.59462i	−0.0231259	+	0.160844i
$817$	4.76542	−	33.1443i	0.166721	−	1.15957i
$818$	24.6094	+	15.8155i	0.860449	+	0.552977i
$819$	−0.137722	−	0.158939i	−0.00481239	−	0.00555380i
$820$	−6.61228	−	14.4789i	−0.230911	−	0.505625i
$821$	13.0634	−	8.39532i	0.455915	−	0.292999i	−0.292456	−	0.956279i	$-0.594473\pi$
$821$	13.0634	−	8.39532i	0.455915	−	0.292999i	0.748371	+	0.663280i	$0.230836\pi$
$822$	−18.0116	−	5.28867i	−0.628225	−	0.184464i
$823$	32.8520	−	37.9133i	1.14515	−	1.32157i	0.205808	−	0.978592i	$-0.434018\pi$
$823$	32.8520	−	37.9133i	1.14515	−	1.32157i	0.939342	−	0.342981i	$-0.111437\pi$
$824$	9.06232	−	2.66094i	0.315701	−	0.0926982i
$825$	−3.22901	+	7.07054i	−0.112420	+	0.246164i
$826$	−0.296323	−	2.06097i	−0.0103104	−	0.0717104i
$827$	−33.0620			−1.14968			−0.574839	−	0.818267i	$-0.694935\pi$
$827$	−33.0620			−1.14968			−0.574839	+	0.818267i	$0.694935\pi$
$828$	−4.39358	−	1.92262i	−0.152687	−	0.0668156i
$829$	−11.7345			−0.407556			−0.203778	−	0.979017i	$-0.565322\pi$
$829$	−11.7345			−0.407556			−0.203778	+	0.979017i	$0.565322\pi$
$830$	−0.320005	−	2.22569i	−0.0111076	−	0.0772547i
$831$	2.10090	−	4.60033i	0.0728795	−	0.159584i
$832$	−1.03874	+	0.305003i	−0.0360120	+	0.0105741i
$833$	−21.1637	+	24.4243i	−0.733280	+	0.846251i
$834$	−17.0348	−	5.00188i	−0.589869	−	0.173201i
$835$	−23.0547	+	14.8163i	−0.797840	+	0.512741i
$836$	−5.33852	−	11.6897i	−0.184637	−	0.404298i
$837$	−4.50102	−	5.19445i	−0.155578	−	0.179546i
$838$	−0.612459	−	0.393604i	−0.0211571	−	0.0135968i
$839$	1.09621	−	7.62430i	0.0378453	−	0.263220i	−0.962110	−	0.272661i	$-0.912096\pi$
$839$	1.09621	−	7.62430i	0.0378453	−	0.263220i	0.999955	+	0.00944127i	$0.00300529\pi$
$840$	−0.0765987	+	0.532755i	−0.00264291	+	0.0183818i
$841$	46.9740	+	30.1883i	1.61979	+	1.04098i
$842$	−22.1691	−	25.5845i	−0.763997	−	0.881700i
$843$	3.48922	+	7.64034i	0.120175	+	0.263147i
$844$	16.0382	−	10.3071i	0.552058	−	0.354786i
$845$	31.4439	+	9.23276i	1.08170	+	0.317617i
$846$	−3.67676	+	4.24321i	−0.126410	+	0.145884i
$847$	0.478351	−	0.140457i	0.0164364	−	0.00482615i
$848$	−1.72089	+	3.76823i	−0.0590957	+	0.129401i
$849$	2.16744	+	15.0748i	0.0743862	+	0.517367i
$850$	12.4243			0.426150
$851$	−17.8030	−	14.9373i	−0.610279	−	0.512043i
$852$	−12.7320			−0.436190
$853$	6.01254	+	41.8181i	0.205865	+	1.43183i	0.786464	+	0.617636i	$0.211909\pi$
$853$	6.01254	+	41.8181i	0.205865	+	1.43183i	−0.580599	+	0.814190i	$0.697181\pi$
$854$	0.232382	−	0.508847i	0.00795196	−	0.0174124i
$855$	11.7640	−	3.45423i	0.402322	−	0.118132i
$856$	6.22905	−	7.18871i	0.212905	−	0.245705i
$857$	18.5488	+	5.44641i	0.633613	+	0.186046i	0.582739	−	0.812659i	$-0.301981\pi$
$857$	18.5488	+	5.44641i	0.633613	+	0.186046i	0.0508744	+	0.998705i	$0.483799\pi$
$858$	2.64485	−	1.69974i	0.0902937	−	0.0580282i
$859$	−8.34241	−	18.2673i	−0.284639	−	0.623273i	0.712264	−	0.701912i	$-0.247670\pi$
$859$	−8.34241	−	18.2673i	−0.284639	−	0.623273i	−0.996903	+	0.0786387i	$0.974943\pi$
$860$	−13.7294	−	15.8446i	−0.468170	−	0.540297i
$861$	0.938858	+	0.603367i	0.0319962	+	0.0205627i
$862$	0.211188	−	1.46885i	0.00719309	−	0.0500291i
$863$	−0.826096	+	5.74562i	−0.0281206	+	0.195583i	−0.999039	−	0.0438270i	$-0.986045\pi$
$863$	−0.826096	+	5.74562i	−0.0281206	+	0.195583i	0.970919	+	0.239410i	$0.0769541\pi$
$864$	0.841254	+	0.540641i	0.0286200	+	0.0183930i
$865$	−24.0289	−	27.7308i	−0.817006	−	0.942875i
$866$	2.89742	+	6.34447i	0.0984584	+	0.215594i
$867$	−3.82516	+	2.45828i	−0.129909	+	0.0834876i
$868$	1.28112	+	0.376172i	0.0434841	+	0.0127681i
$869$	−4.86656	+	5.61631i	−0.165087	+	0.190520i
$870$	24.4862	−	7.18979i	0.830159	−	0.243757i
$871$	−6.58281	+	14.4143i	−0.223050	+	0.488411i
$872$	−2.87785	−	20.0159i	−0.0974562	−	0.677823i
$873$	−12.3679			−0.418591
$874$	−11.7562	−	17.6687i	−0.397661	−	0.597652i
$875$	−1.25055			−0.0422762
$876$	0.425254	+	2.95771i	0.0143680	+	0.0999317i
$877$	14.9519	−	32.7400i	0.504889	−	1.10555i	−0.469960	−	0.882688i	$-0.655732\pi$
$877$	14.9519	−	32.7400i	0.504889	−	1.10555i	0.974849	−	0.222865i	$-0.0715410\pi$
$878$	8.94336	−	2.62601i	0.301824	−	0.0886234i
$879$	18.9424	−	21.8607i	0.638912	−	0.737344i
$880$	−7.72028	−	2.26688i	−0.260251	−	0.0764165i
$881$	31.4703	−	20.2247i	1.06026	−	0.681388i	0.110344	−	0.993893i	$-0.464805\pi$
$881$	31.4703	−	20.2247i	1.06026	−	0.681388i	0.949916	+	0.312506i	$0.101168\pi$
$882$	2.89223	+	6.33310i	0.0973864	+	0.213246i
$883$	32.9735	+	38.0535i	1.10965	+	1.28060i	0.956287	+	0.292431i	$0.0944643\pi$
$883$	32.9735	+	38.0535i	1.10965	+	1.28060i	0.153361	+	0.988170i	$0.450990\pi$
$884$	−4.22753	−	2.71687i	−0.142187	−	0.0913782i
$885$	−4.22632	+	29.3947i	−0.142066	+	0.988091i
$886$	4.50415	−	31.3270i	0.151320	−	1.05245i
$887$	25.8216	+	16.5945i	0.867004	+	0.557190i	0.896835	−	0.442365i	$-0.145860\pi$
$887$	25.8216	+	16.5945i	0.867004	+	0.557190i	−0.0298308	+	0.999555i	$0.509497\pi$
$888$	3.17329	+	3.66217i	0.106489	+	0.122894i
$889$	−0.388847	−	0.851456i	−0.0130415	−	0.0285569i
$890$	−15.8026	+	10.1557i	−0.529706	+	0.340421i
$891$	−2.78644	−	0.818172i	−0.0933492	−	0.0274098i
$892$	−4.20260	+	4.85006i	−0.140713	+	0.162392i
$893$	−23.8391	+	6.99978i	−0.797744	+	0.234239i
$894$	−3.95283	+	8.65548i	−0.132202	+	0.289483i
$895$	−2.06826	−	14.3851i	−0.0691343	−	0.480840i
$896$	−0.194262			−0.00648983
$897$	3.86924	−	3.46199i	0.129190	−	0.115592i
$898$	9.56061			0.319042
$899$	−9.00963	−	62.6634i	−0.300488	−	2.08994i
$900$	1.11189	−	2.43470i	0.0370630	−	0.0811566i
$901$	−18.4504	+	5.41753i	−0.614673	+	0.180484i
$902$	−10.9255	+	12.6087i	−0.363780	+	0.419824i
$903$	1.41042	+	0.414138i	0.0469359	+	0.0137816i
$904$	−1.10765	+	0.711845i	−0.0368400	+	0.0236756i
$905$	−18.7094	−	40.9680i	−0.621923	−	1.36182i
$906$	5.68336	+	6.55894i	0.188817	+	0.217906i
$907$	−4.54974	−	2.92394i	−0.151071	−	0.0970877i	0.462921	−	0.886399i	$-0.346801\pi$
$907$	−4.54974	−	2.92394i	−0.151071	−	0.0970877i	−0.613993	+	0.789312i	$0.710438\pi$
$908$	0.170329	−	1.18467i	0.00565257	−	0.0393145i
$909$	−2.23387	+	15.5369i	−0.0740928	+	0.515327i
$910$	−0.490190	−	0.315026i	−0.0162496	−	0.0104430i
$911$	29.6277	+	34.1922i	0.981610	+	1.13284i	0.991132	+	0.132883i	$0.0424235\pi$
$911$	29.6277	+	34.1922i	0.981610	+	1.13284i	−0.00952202	+	0.999955i	$0.503031\pi$
$912$	1.83829	+	4.02529i	0.0608718	+	0.133291i
$913$	−1.98270	+	1.27421i	−0.0656179	+	0.0421701i
$914$	−12.3395	−	3.62319i	−0.408153	−	0.119845i
$915$	−5.22476	+	6.02970i	−0.172725	+	0.199336i
$916$	26.9479	−	7.91262i	0.890384	−	0.261440i
$917$	1.28939	−	2.82338i	0.0425795	−	0.0932361i
$918$	0.660607	+	4.59462i	0.0218033	+	0.151645i
$919$	10.7793			0.355576			0.177788	−	0.984069i	$-0.443106\pi$
$919$	10.7793			0.355576			0.177788	+	0.984069i	$0.443106\pi$
$920$	−13.1808	−	1.68158i	−0.434558	−	0.0554401i
$921$	21.5835			0.711201
$922$	2.61914	+	18.2165i	0.0862566	+	0.599928i
$923$	5.72590	−	12.5380i	0.188470	−	0.412692i
$924$	0.541298	−	0.158939i	0.0178074	−	0.00522873i
$925$	8.49354	−	9.80206i	0.279266	−	0.322290i
$926$	26.5366	+	7.79186i	0.872048	+	0.256056i
$927$	7.94556	−	5.10630i	0.260967	−	0.167713i
$928$	3.82629	+	8.37840i	0.125604	+	0.275034i
$929$	20.5270	+	23.6894i	0.673470	+	0.777226i	0.984915	−	0.173038i	$-0.0553585\pi$
$929$	20.5270	+	23.6894i	0.673470	+	0.777226i	−0.311445	+	0.950264i	$0.600813\pi$
$930$	−16.0204	−	10.2957i	−0.525328	−	0.337608i
$931$	−4.38462	+	30.4957i	−0.143700	+	0.999455i
$932$	2.33578	−	16.2457i	0.0765111	−	0.532146i
$933$	−0.739356	−	0.475155i	−0.0242054	−	0.0155559i
$934$	15.9425	+	18.3986i	0.521655	+	0.602022i
$935$	−15.5155	−	33.9743i	−0.507412	−	1.11108i
$936$	−0.910738	+	0.585296i	−0.0297684	+	0.0191310i
$937$	−15.5397	−	4.56287i	−0.507661	−	0.149063i	0.0178650	−	0.999840i	$-0.494313\pi$
$937$	−15.5397	−	4.56287i	−0.507661	−	0.149063i	−0.525526	+	0.850778i	$0.676131\pi$
$938$	−1.86208	+	2.14896i	−0.0607991	+	0.0701659i
$939$	−5.23457	+	1.53701i	−0.170824	+	0.0501584i
$940$	−6.46223	+	14.1503i	−0.210775	+	0.461532i
$941$	3.42607	+	23.8289i	0.111687	+	0.776798i	0.966279	+	0.257498i	$0.0828982\pi$
$941$	3.42607	+	23.8289i	0.111687	+	0.776798i	−0.854592	+	0.519300i	$0.826193\pi$
$942$	19.8163			0.645651
$943$	−14.5251	+	23.4120i	−0.473001	+	0.762400i
$944$	−10.7184			−0.348853
$945$	0.0765987	+	0.532755i	0.00249175	+	0.0173305i
$946$	−9.12872	+	19.9891i	−0.296800	+	0.649902i
$947$	−4.75553	+	1.39635i	−0.154534	+	0.0453753i	−0.358085	−	0.933689i	$-0.616570\pi$
$947$	−4.75553	+	1.39635i	−0.154534	+	0.0453753i	0.203551	+	0.979064i	$0.434752\pi$
$948$	1.67577	−	1.93394i	0.0544265	−	0.0628116i
$949$	−3.10389	−	0.911386i	−0.100757	−	0.0295848i
$950$	9.96408	−	6.40352i	0.323277	−	0.207758i
$951$	2.11314	+	4.62712i	0.0685231	+	0.150045i
$952$	−0.590513	−	0.681488i	−0.0191386	−	0.0220872i
$953$	−32.4534	−	20.8566i	−1.05127	−	0.675610i	−0.103521	−	0.994627i	$-0.533011\pi$
$953$	−32.4534	−	20.8566i	−1.05127	−	0.675610i	−0.947749	+	0.319017i	$0.896647\pi$
$954$	−0.589551	+	4.10042i	−0.0190874	+	0.132756i
$955$	3.03326	−	21.0968i	0.0981541	−	0.682677i
$956$	8.69497	+	5.58792i	0.281215	+	0.180726i
$957$	−17.5167	−	20.2153i	−0.566234	−	0.653469i
$958$	3.02925	+	6.63312i	0.0978705	+	0.214306i
$959$	3.06778	−	1.97154i	0.0990637	−	0.0636644i
$960$	2.65843	+	0.780586i	0.0858005	+	0.0251933i
$961$	−10.6359	+	12.2745i	−0.343093	+	0.395951i
$962$	−5.03349	+	1.47796i	−0.162286	+	0.0476515i
$963$	3.95144	−	8.65244i	0.127333	−	0.278821i
$964$	3.12210	+	21.7147i	0.100556	+	0.699383i
$965$	−3.95498			−0.127315
$966$	0.841192	−	0.400451i	0.0270649	−	0.0128843i
$967$	47.2484			1.51940			0.759702	−	0.650271i	$-0.225345\pi$
$967$	47.2484			1.51940			0.759702	+	0.650271i	$0.225345\pi$
$968$	−0.365231	−	2.54024i	−0.0117390	−	0.0816464i
$969$	−8.53309	+	18.6849i	−0.274122	+	0.600244i
$970$	−32.8793	+	9.65424i	−1.05569	+	0.309979i
$971$	−11.2136	+	12.9412i	−0.359863	+	0.415304i	−0.906594	−	0.422005i	$-0.861327\pi$
$971$	−11.2136	+	12.9412i	−0.359863	+	0.415304i	0.546731	+	0.837308i	$0.315872\pi$
$972$	0.959493	+	0.281733i	0.0307758	+	0.00903658i
$973$	2.90142	−	1.86463i	0.0930153	−	0.0597773i
$974$	−9.30911	−	20.3841i	−0.298283	−	0.653149i
$975$	1.89756	+	2.18990i	0.0607704	+	0.0701328i
$976$	−2.42248	−	1.55683i	−0.0775418	−	0.0498331i
$977$	3.35123	−	23.3083i	0.107215	−	0.745699i	−0.863306	−	0.504682i	$-0.831610\pi$
$977$	3.35123	−	23.3083i	0.107215	−	0.745699i	0.970521	−	0.241017i	$-0.0774810\pi$
$978$	−2.06377	+	14.3538i	−0.0659920	+	0.458984i
$979$	16.5636	+	10.6448i	0.529374	+	0.340208i
$980$	12.6323	+	14.5785i	0.403525	+	0.465692i
$981$	−8.40040	−	18.3943i	−0.268204	−	0.587285i
$982$	−16.5729	+	10.6507i	−0.528861	+	0.339878i
$983$	7.70621	+	2.26275i	0.245790	+	0.0721704i	0.402307	−	0.915505i	$-0.368208\pi$
$983$	7.70621	+	2.26275i	0.245790	+	0.0721704i	−0.156517	+	0.987675i	$0.550027\pi$
$984$	3.76214	−	4.34174i	0.119933	−	0.138410i
$985$	−16.6304	+	4.88313i	−0.529889	+	0.155589i
$986$	−17.7611	+	38.8915i	−0.565630	+	1.23856i
$987$	−0.155222	−	1.07959i	−0.00494078	−	0.0343639i
$988$	−4.79069			−0.152412
$989$	−9.66886	+	34.9780i	−0.307452	+	1.11224i
$990$	−8.04621			−0.255725
$991$	7.56451	+	52.6123i	0.240294	+	1.67128i	0.650664	+	0.759365i	$0.274490\pi$
$991$	7.56451	+	52.6123i	0.240294	+	1.67128i	−0.410370	+	0.911919i	$0.634600\pi$
$992$	2.85525	−	6.25212i	0.0906542	−	0.198505i
$993$	−34.1705	+	10.0334i	−1.08437	+	0.318400i
$994$	1.61969	−	1.86922i	0.0513734	−	0.0592880i
$995$	−2.29459	−	0.673752i	−0.0727434	−	0.0213594i
$996$	0.682732	−	0.438765i	0.0216332	−	0.0139028i
$997$	−5.98347	−	13.1020i	−0.189498	−	0.414944i	0.790906	−	0.611937i	$-0.209610\pi$
$997$	−5.98347	−	13.1020i	−0.189498	−	0.414944i	−0.980405	+	0.196993i	$0.936882\pi$
$998$	−11.3250	−	13.0697i	−0.358487	−	0.413716i
$999$	4.07650	+	2.61981i	0.128975	+	0.0828870i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.d.49.1	yes	10
3.2	odd	2		414.2.i.a.325.1		10
23.8	even	11	inner	138.2.e.d.31.1	✓	10
23.10	odd	22		3174.2.a.w.1.2		5
23.13	even	11		3174.2.a.x.1.4		5
69.8	odd	22		414.2.i.a.307.1		10
69.56	even	22		9522.2.a.by.1.4		5
69.59	odd	22		9522.2.a.bx.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.31.1	✓	10	23.8	even	11	inner
138.2.e.d.49.1	yes	10	1.1	even	1	trivial
414.2.i.a.307.1		10	69.8	odd	22
414.2.i.a.325.1		10	3.2	odd	2
3174.2.a.w.1.2		5	23.10	odd	22
3174.2.a.x.1.4		5	23.13	even	11
9522.2.a.bx.1.2		5	69.59	odd	22
9522.2.a.by.1.4		5	69.56	even	22

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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.81440 + 2.09393i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.163423 - 0.105026i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-1.81440 + 2.09393i) q^{5} +(-0.959493 - 0.281733i) q^{6} +(0.163423 - 0.105026i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.33083 - 1.49793i) q^{10} +(-0.413293 + 2.87451i) q^{11} +(0.142315 - 0.989821i) q^{12} +(0.910738 + 0.585296i) q^{13} +(0.127214 + 0.146813i) q^{14} +(-1.15098 - 2.52028i) q^{15} +(0.841254 - 0.540641i) q^{16} +(4.45384 + 1.30777i) q^{17} +(0.654861 - 0.755750i) q^{18} +(4.24593 - 1.24672i) q^{19} +(1.15098 - 2.52028i) q^{20} +(0.0276463 + 0.192284i) q^{21} -2.90407 q^{22} +(-4.73556 + 0.757939i) q^{23} +1.00000 q^{24} +(-0.380916 - 2.64933i) q^{25} +(-0.449727 + 0.984764i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-0.127214 + 0.146813i) q^{28} +(8.83766 + 2.59497i) q^{29} +(2.33083 - 1.49793i) q^{30} +(-2.85525 - 6.25212i) q^{31} +(0.654861 + 0.755750i) q^{32} +(-2.44306 - 1.57006i) q^{33} +(-0.660607 + 4.59462i) q^{34} +(-0.0765987 + 0.532755i) q^{35} +(0.841254 + 0.540641i) q^{36} +(3.17329 + 3.66217i) q^{37} +(1.83829 + 4.02529i) q^{38} +(-0.910738 + 0.585296i) q^{39} +(2.65843 + 0.780586i) q^{40} +(3.76214 - 4.34174i) q^{41} +(-0.186393 + 0.0547299i) q^{42} +(3.14342 - 6.88313i) q^{43} +(-0.413293 - 2.87451i) q^{44} +2.77066 q^{45} +(-1.42416 - 4.57949i) q^{46} -5.61457 q^{47} +(0.142315 + 0.989821i) q^{48} +(-2.89223 + 6.33310i) q^{49} +(2.56815 - 0.754078i) q^{50} +(-3.03978 + 3.50809i) q^{51} +(-1.03874 - 0.305003i) q^{52} +(-3.48496 + 2.23965i) q^{53} +(0.415415 + 0.909632i) q^{54} +(-5.26914 - 6.08092i) q^{55} +(-0.163423 - 0.105026i) q^{56} +(-0.629769 + 4.38014i) q^{57} +(-1.31083 + 9.11701i) q^{58} +(-9.01685 - 5.79478i) q^{59} +(1.81440 + 2.09393i) q^{60} +(-1.19623 - 2.61939i) q^{61} +(5.78214 - 3.71596i) q^{62} +(-0.186393 - 0.0547299i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-2.87801 + 0.845060i) q^{65} +(1.20640 - 2.64164i) q^{66} +(2.08311 + 14.4884i) q^{67} -4.64187 q^{68} +(1.27778 - 4.62248i) q^{69} -0.538234 q^{70} +(-1.81195 - 12.6024i) q^{71} +(-0.415415 + 0.909632i) q^{72} +(-2.86708 + 0.841852i) q^{73} +(-3.17329 + 3.66217i) q^{74} +(2.56815 + 0.754078i) q^{75} +(-3.72270 + 2.39243i) q^{76} +(0.234356 + 0.513169i) q^{77} +(-0.708950 - 0.818172i) q^{78} +(2.15275 + 1.38349i) q^{79} +(-0.394306 + 2.74246i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(4.83295 + 3.10595i) q^{82} +(0.531462 + 0.613340i) q^{83} +(-0.0806993 - 0.176707i) q^{84} +(-10.8194 + 6.95322i) q^{85} +(7.26043 + 2.13185i) q^{86} +(-6.03176 + 6.96103i) q^{87} +(2.78644 - 0.818172i) q^{88} +(2.81645 - 6.16716i) q^{89} +(0.394306 + 2.74246i) q^{90} +0.210307 q^{91} +(4.33020 - 2.06140i) q^{92} +6.87324 q^{93} +(-0.799036 - 5.55742i) q^{94} +(-5.09327 + 11.1527i) q^{95} +(-0.959493 + 0.281733i) q^{96} +(8.09928 - 9.34707i) q^{97} +(-6.68024 - 1.96150i) q^{98} +(2.44306 - 1.57006i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Introduction

L-functions

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