LMFDB - Embedded newform 418.2.n.c.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			201.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	418.201
Dual form			418.2.n.c.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.104528 - 0.994522i) q^{2} +(-1.95630 - 0.415823i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.348943 + 0.155360i) q^{5} +(-0.209057 + 1.98904i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})$	\(q+(-0.104528 - 0.994522i) q^{2} +(-1.95630 - 0.415823i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.348943 + 0.155360i) q^{5} +(-0.209057 + 1.98904i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.190983 + 0.330792i) q^{10} +(-2.54508 + 2.12663i) q^{11} +2.00000 q^{12} +(-1.69381 - 0.754131i) q^{13} +(-4.14350 - 0.880728i) q^{14} +(0.747238 - 0.158830i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-4.91667 + 2.18904i) q^{17} +(0.309017 - 0.951057i) q^{18} +(4.30146 + 0.705295i) q^{19} +(0.309017 - 0.224514i) q^{20} +(-4.23607 + 7.33708i) q^{21} +(2.38101 + 2.30885i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.209057 - 1.98904i) q^{24} +(-3.24803 + 3.60730i) q^{25} +(-0.572949 + 1.76336i) q^{26} +(3.23607 + 2.35114i) q^{27} +(-0.442790 + 4.21286i) q^{28} +(-2.18720 + 0.464905i) q^{29} +(-0.236068 - 0.726543i) q^{30} +(-7.97214 + 5.79210i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.86324 - 3.10200i) q^{33} +(2.69098 + 4.66092i) q^{34} +(0.169131 + 1.60917i) q^{35} +(-0.978148 - 0.207912i) q^{36} +(-1.04508 + 3.21644i) q^{37} +(0.251807 - 4.35162i) q^{38} +(3.00000 + 2.17963i) q^{39} +(-0.255585 - 0.283856i) q^{40} +(-9.72697 - 2.06753i) q^{41} +(7.73968 + 3.44593i) q^{42} +(5.35410 - 9.27358i) q^{43} +(2.04732 - 2.60931i) q^{44} -0.381966 q^{45} +(0.809017 - 0.587785i) q^{46} +(0.669131 - 0.743145i) q^{47} +(-1.95630 + 0.415823i) q^{48} +(-8.85410 - 6.43288i) q^{49} +(3.92705 + 2.85317i) q^{50} +(10.5287 - 2.23795i) q^{51} +(1.81359 + 0.385489i) q^{52} +(6.17916 + 2.75114i) q^{53} +(2.00000 - 3.46410i) q^{54} +(0.557699 - 1.13748i) q^{55} +4.23607 q^{56} +(-8.12165 - 3.16841i) q^{57} +(0.690983 + 2.12663i) q^{58} +(5.82693 + 6.47146i) q^{59} +(-0.697887 + 0.310719i) q^{60} +(0.746950 - 7.10675i) q^{61} +(6.59368 + 7.32302i) q^{62} +(2.83448 - 3.14801i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.708204 q^{65} +(-3.69789 - 5.50687i) q^{66} +(-6.16312 - 10.6748i) q^{67} +(4.35410 - 3.16344i) q^{68} +(-0.618034 - 1.90211i) q^{69} +(1.58268 - 0.336408i) q^{70} +(-5.77931 + 2.57311i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-7.51840 - 8.35003i) q^{73} +(3.30806 + 0.703150i) q^{74} +(7.85410 - 5.70634i) q^{75} +(-4.35410 + 0.204441i) q^{76} +(5.23607 + 13.0373i) q^{77} +(1.85410 - 3.21140i) q^{78} +(-0.387613 - 3.68789i) q^{79} +(-0.255585 + 0.283856i) q^{80} +(-7.36044 - 8.17459i) q^{81} +(-1.03946 + 9.88980i) q^{82} +(-9.28115 - 6.74315i) q^{83} +(2.61803 - 8.05748i) q^{84} +(1.37555 - 1.52770i) q^{85} +(-9.78243 - 4.35542i) q^{86} +4.47214 q^{87} +(-2.80902 - 1.76336i) q^{88} +(-7.35410 - 12.7377i) q^{89} +(0.0399263 + 0.379874i) q^{90} +(-5.25542 + 5.83674i) q^{91} +(-0.669131 - 0.743145i) q^{92} +(18.0043 - 8.01605i) q^{93} +(-0.809017 - 0.587785i) q^{94} +(-1.61054 + 0.422165i) q^{95} +(0.618034 + 1.90211i) q^{96} +(1.69131 + 16.0917i) q^{97} +(-5.47214 + 9.47802i) q^{98} +(-3.19003 + 0.907591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9} + 6 q^{10} + 2 q^{11} + 16 q^{12} - 6 q^{13} - 3 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} - 18 q^{26} + 8 q^{27} + 7 q^{28} - 5 q^{29} + 16 q^{30} - 28 q^{31} - 4 q^{32} + 18 q^{33} + 26 q^{34} - 3 q^{35} + q^{36} + 14 q^{37} - 13 q^{38} + 24 q^{39} - 4 q^{40} - 19 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} - 12 q^{45} + 2 q^{46} + q^{47} + 2 q^{48} - 44 q^{49} + 18 q^{50} - 18 q^{51} + 9 q^{52} + 4 q^{53} + 16 q^{54} + 14 q^{55} + 16 q^{56} - 26 q^{57} + 10 q^{58} - 13 q^{59} + 2 q^{60} - 3 q^{61} - q^{62} - 3 q^{63} - 2 q^{64} - 48 q^{65} - 22 q^{66} - 18 q^{67} + 8 q^{68} + 4 q^{69} + 2 q^{70} - 16 q^{71} + q^{72} - 4 q^{73} - 7 q^{74} + 36 q^{75} - 8 q^{76} + 24 q^{77} - 12 q^{78} + 12 q^{79} - 4 q^{80} - 11 q^{81} + 21 q^{82} - 34 q^{83} + 12 q^{84} + 31 q^{85} - 19 q^{86} - 18 q^{88} - 32 q^{89} + q^{90} + 3 q^{91} - q^{92} + 28 q^{93} - 2 q^{94} - 38 q^{95} - 4 q^{96} - 30 q^{97} - 8 q^{98} - q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9 + 6 * q^10 + 2 * q^11 + 16 * q^12 - 6 * q^13 - 3 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 2 * q^18 - 4 * q^19 - 2 * q^20 - 16 * q^21 - q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 - 18 * q^26 + 8 * q^27 + 7 * q^28 - 5 * q^29 + 16 * q^30 - 28 * q^31 - 4 * q^32 + 18 * q^33 + 26 * q^34 - 3 * q^35 + q^36 + 14 * q^37 - 13 * q^38 + 24 * q^39 - 4 * q^40 - 19 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 - 12 * q^45 + 2 * q^46 + q^47 + 2 * q^48 - 44 * q^49 + 18 * q^50 - 18 * q^51 + 9 * q^52 + 4 * q^53 + 16 * q^54 + 14 * q^55 + 16 * q^56 - 26 * q^57 + 10 * q^58 - 13 * q^59 + 2 * q^60 - 3 * q^61 - q^62 - 3 * q^63 - 2 * q^64 - 48 * q^65 - 22 * q^66 - 18 * q^67 + 8 * q^68 + 4 * q^69 + 2 * q^70 - 16 * q^71 + q^72 - 4 * q^73 - 7 * q^74 + 36 * q^75 - 8 * q^76 + 24 * q^77 - 12 * q^78 + 12 * q^79 - 4 * q^80 - 11 * q^81 + 21 * q^82 - 34 * q^83 + 12 * q^84 + 31 * q^85 - 19 * q^86 - 18 * q^88 - 32 * q^89 + q^90 + 3 * q^91 - q^92 + 28 * q^93 - 2 * q^94 - 38 * q^95 - 4 * q^96 - 30 * q^97 - 8 * q^98 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$2$	−0.104528	−	0.994522i	−0.0739128	−	0.703233i
$3$	−1.95630	−	0.415823i	−1.12947	−	0.240076i	−0.394975	−	0.918692i	$-0.629247\pi$
$3$	−1.95630	−	0.415823i	−1.12947	−	0.240076i	−0.734493	+	0.678616i	$0.762580\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	−0.348943	+	0.155360i	−0.156052	+	0.0694789i	−0.483276	−	0.875468i	$-0.660553\pi$
$5$	−0.348943	+	0.155360i	−0.156052	+	0.0694789i	0.327224	+	0.944947i	$0.393887\pi$
$6$	−0.209057	+	1.98904i	−0.0853471	+	0.812024i
$7$	1.30902	−	4.02874i	0.494762	−	1.52272i	−0.322566	−	0.946547i	$-0.604545\pi$
$7$	1.30902	−	4.02874i	0.494762	−	1.52272i	0.817327	−	0.576173i	$-0.195455\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	0.913545	+	0.406737i	0.304515	+	0.135579i
$10$	0.190983	+	0.330792i	0.0603941	+	0.104606i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$11$	−2.54508	+	2.12663i	−0.767372	+	0.641202i
$12$	2.00000			0.577350
$13$	−1.69381	−	0.754131i	−0.469777	−	0.209158i	0.158174	−	0.987411i	$-0.449439\pi$
$13$	−1.69381	−	0.754131i	−0.469777	−	0.209158i	−0.627951	+	0.778253i	$0.716106\pi$
$14$	−4.14350	−	0.880728i	−1.10740	−	0.235384i
$15$	0.747238	−	0.158830i	0.192936	−	0.0410098i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	−4.91667	+	2.18904i	−1.19247	+	0.530921i	−0.904399	−	0.426689i	$-0.859680\pi$
$17$	−4.91667	+	2.18904i	−1.19247	+	0.530921i	−0.288069	+	0.957610i	$0.593013\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	4.30146	+	0.705295i	0.986823	+	0.161806i
$19$	4.30146	+	0.705295i	0.986823	+	0.161806i
$20$	0.309017	−	0.224514i	0.0690983	−	0.0502029i
$21$	−4.23607	+	7.33708i	−0.924386	+	1.60108i
$22$	2.38101	+	2.30885i	0.507633	+	0.492248i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$	−0.209057	−	1.98904i	−0.0426736	−	0.406012i
$25$	−3.24803	+	3.60730i	−0.649606	+	0.721460i
$26$	−0.572949	+	1.76336i	−0.112365	+	0.345823i
$27$	3.23607	+	2.35114i	0.622782	+	0.452477i
$28$	−0.442790	+	4.21286i	−0.0836794	+	0.796156i
$29$	−2.18720	+	0.464905i	−0.406154	+	0.0863306i	−0.406458	−	0.913669i	$-0.633236\pi$
$29$	−2.18720	+	0.464905i	−0.406154	+	0.0863306i	0.000304639		1.00000i	$0.499903\pi$
$30$	−0.236068	−	0.726543i	−0.0430999	−	0.132648i
$31$	−7.97214	+	5.79210i	−1.43184	+	1.04029i	−0.442167	+	0.896933i	$0.645790\pi$
$31$	−7.97214	+	5.79210i	−1.43184	+	1.04029i	−0.989671	+	0.143358i	$0.954210\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	5.86324	−	3.10200i	1.02066	−	0.539990i
$34$	2.69098	+	4.66092i	0.461500	+	0.799341i
$35$	0.169131	+	1.60917i	0.0285883	+	0.271999i
$36$	−0.978148	−	0.207912i	−0.163025	−	0.0346519i
$37$	−1.04508	+	3.21644i	−0.171811	+	0.528780i	−0.999473	−	0.0324464i	$-0.989670\pi$
$37$	−1.04508	+	3.21644i	−0.171811	+	0.528780i	0.827663	+	0.561226i	$0.189670\pi$
$38$	0.251807	−	4.35162i	0.0408484	−	0.705926i
$39$	3.00000	+	2.17963i	0.480384	+	0.349020i
$40$	−0.255585	−	0.283856i	−0.0404116	−	0.0448816i
$41$	−9.72697	−	2.06753i	−1.51910	−	0.322894i	−0.628544	−	0.777774i	$-0.716349\pi$
$41$	−9.72697	−	2.06753i	−1.51910	−	0.322894i	−0.890553	+	0.454880i	$0.849682\pi$
$42$	7.73968	+	3.44593i	1.19426	+	0.531718i
$43$	5.35410	−	9.27358i	0.816493	−	1.41421i	−0.0917581	−	0.995781i	$-0.529249\pi$
$43$	5.35410	−	9.27358i	0.816493	−	1.41421i	0.908251	−	0.418426i	$-0.137418\pi$
$44$	2.04732	−	2.60931i	0.308645	−	0.393368i
$45$	−0.381966			−0.0569401
$46$	0.809017	−	0.587785i	0.119283	−	0.0866642i
$47$	0.669131	−	0.743145i	0.0976027	−	0.108399i	−0.692364	−	0.721548i	$-0.743431\pi$
$47$	0.669131	−	0.743145i	0.0976027	−	0.108399i	0.789967	+	0.613149i	$0.210098\pi$
$48$	−1.95630	+	0.415823i	−0.282367	+	0.0600189i
$49$	−8.85410	−	6.43288i	−1.26487	−	0.918983i
$50$	3.92705	+	2.85317i	0.555369	+	0.403499i
$51$	10.5287	−	2.23795i	1.47431	−	0.313375i
$52$	1.81359	+	0.385489i	0.251499	+	0.0534578i
$53$	6.17916	+	2.75114i	0.848773	+	0.377898i	0.784571	−	0.620039i	$-0.212883\pi$
$53$	6.17916	+	2.75114i	0.848773	+	0.377898i	0.0642018	+	0.997937i	$0.479550\pi$
$54$	2.00000	−	3.46410i	0.272166	−	0.471405i
$55$	0.557699	−	1.13748i	0.0752001	−	0.153377i
$56$	4.23607			0.566068
$57$	−8.12165	−	3.16841i	−1.07574	−	0.419667i
$58$	0.690983	+	2.12663i	0.0907305	+	0.279240i
$59$	5.82693	+	6.47146i	0.758601	+	0.842512i	0.991516	−	0.129985i	$-0.0414930\pi$
$59$	5.82693	+	6.47146i	0.758601	+	0.842512i	−0.232915	+	0.972497i	$0.574826\pi$
$60$	−0.697887	+	0.310719i	−0.0900968	+	0.0401137i
$61$	0.746950	−	7.10675i	0.0956371	−	0.909926i	−0.836536	−	0.547913i	$-0.815423\pi$
$61$	0.746950	−	7.10675i	0.0956371	−	0.909926i	0.932173	−	0.362014i	$-0.117911\pi$
$62$	6.59368	+	7.32302i	0.837398	+	0.930025i
$63$	2.83448	−	3.14801i	0.357111	−	0.396612i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.708204			0.0878419
$66$	−3.69789	−	5.50687i	−0.455178	−	0.677849i
$67$	−6.16312	−	10.6748i	−0.752945	−	1.30414i	−0.946390	−	0.323028i	$-0.895299\pi$
$67$	−6.16312	−	10.6748i	−0.752945	−	1.30414i	0.193445	−	0.981111i	$-0.438034\pi$
$68$	4.35410	−	3.16344i	0.528012	−	0.383623i
$69$	−0.618034	−	1.90211i	−0.0744025	−	0.228988i
$70$	1.58268	−	0.336408i	0.189166	−	0.0402085i
$71$	−5.77931	+	2.57311i	−0.685877	+	0.305372i	−0.719929	−	0.694048i	$-0.755826\pi$
$71$	−5.77931	+	2.57311i	−0.685877	+	0.305372i	0.0340515	+	0.999420i	$0.489159\pi$
$72$	−0.104528	+	0.994522i	−0.0123188	+	0.117206i
$73$	−7.51840	−	8.35003i	−0.879962	−	0.977297i	0.119918	−	0.992784i	$-0.461737\pi$
$73$	−7.51840	−	8.35003i	−0.879962	−	0.977297i	−0.999880	+	0.0154872i	$0.995070\pi$
$74$	3.30806	+	0.703150i	0.384554	+	0.0817396i
$75$	7.85410	−	5.70634i	0.906914	−	0.658911i
$76$	−4.35410	+	0.204441i	−0.499450	+	0.0234510i
$77$	5.23607	+	13.0373i	0.596705	+	1.48574i
$78$	1.85410	−	3.21140i	0.209936	−	0.363619i
$79$	−0.387613	−	3.68789i	−0.0436099	−	0.414920i	−0.994448	−	0.105231i	$-0.966442\pi$
$79$	−0.387613	−	3.68789i	−0.0436099	−	0.414920i	0.950838	−	0.309689i	$-0.100225\pi$
$80$	−0.255585	+	0.283856i	−0.0285753	+	0.0317361i
$81$	−7.36044	−	8.17459i	−0.817826	−	0.908288i
$82$	−1.03946	+	9.88980i	−0.114789	+	1.09215i
$83$	−9.28115	−	6.74315i	−1.01874	−	0.740157i	−0.0527149	−	0.998610i	$-0.516787\pi$
$83$	−9.28115	−	6.74315i	−1.01874	−	0.740157i	−0.966024	+	0.258452i	$0.916787\pi$
$84$	2.61803	−	8.05748i	0.285651	−	0.879143i
$85$	1.37555	−	1.52770i	0.149199	−	0.165703i
$86$	−9.78243	−	4.35542i	−1.05487	−	0.469657i
$87$	4.47214			0.479463
$88$	−2.80902	−	1.76336i	−0.299442	−	0.187974i
$89$	−7.35410	−	12.7377i	−0.779533	−	1.35019i	−0.932211	−	0.361915i	$-0.882123\pi$
$89$	−7.35410	−	12.7377i	−0.779533	−	1.35019i	0.152678	−	0.988276i	$-0.451210\pi$
$90$	0.0399263	+	0.379874i	0.00420860	+	0.0400422i
$91$	−5.25542	+	5.83674i	−0.550918	+	0.611856i
$92$	−0.669131	−	0.743145i	−0.0697617	−	0.0774782i
$93$	18.0043	−	8.01605i	1.86696	−	0.831226i
$94$	−0.809017	−	0.587785i	−0.0834437	−	0.0606254i
$95$	−1.61054	+	0.422165i	−0.165238	+	0.0433132i
$96$	0.618034	+	1.90211i	0.0630778	+	0.194134i
$97$	1.69131	+	16.0917i	0.171726	+	1.63386i	0.653045	+	0.757319i	$0.273491\pi$
$97$	1.69131	+	16.0917i	0.171726	+	1.63386i	−0.481319	+	0.876546i	$0.659842\pi$
$98$	−5.47214	+	9.47802i	−0.552769	+	0.957424i
$99$	−3.19003	+	0.907591i	−0.320610	+	0.0912163i
$100$	2.42705	−	4.20378i	0.242705	−	0.420378i
$101$	2.52498	+	1.12419i	0.251245	+	0.111861i	0.528495	−	0.848936i	$-0.322756\pi$
$101$	2.52498	+	1.12419i	0.251245	+	0.111861i	−0.277250	+	0.960798i	$0.589423\pi$
$102$	−3.32624	−	10.2371i	−0.329347	−	1.01362i
$103$	2.76393	−	8.50651i	0.272338	−	0.838171i	−0.717573	−	0.696483i	$-0.754747\pi$
$103$	2.76393	−	8.50651i	0.272338	−	0.838171i	0.989911	−	0.141688i	$-0.0452529\pi$
$104$	0.193806	−	1.84395i	0.0190043	−	0.180814i
$105$	0.338261	−	3.21834i	0.0330109	−	0.314078i
$106$	2.09017	−	6.43288i	0.203015	−	0.624817i
$107$	1.88197	+	5.79210i	0.181937	+	0.559943i	0.999882	−	0.0153525i	$-0.00488705\pi$
$107$	1.88197	+	5.79210i	0.181937	+	0.559943i	−0.817946	+	0.575296i	$0.804887\pi$
$108$	−3.65418	−	1.62695i	−0.351624	−	0.156553i
$109$	−3.95492	+	6.85011i	−0.378812	+	0.656122i	−0.990890	−	0.134676i	$-0.957001\pi$
$109$	−3.95492	+	6.85011i	−0.378812	+	0.656122i	0.612078	+	0.790798i	$0.290334\pi$
$110$	−1.18954	−	0.435745i	−0.113418	−	0.0415466i
$111$	3.38197	−	5.85774i	0.321002	−	0.555992i
$112$	−0.442790	−	4.21286i	−0.0418397	−	0.398078i
$113$	3.40983	+	10.4944i	0.320770	+	0.987228i	0.973314	+	0.229477i	$0.0737017\pi$
$113$	3.40983	+	10.4944i	0.320770	+	0.987228i	−0.652544	+	0.757751i	$0.726298\pi$
$114$	−2.30211	+	8.40835i	−0.215613	+	0.787514i
$115$	−0.309017	−	0.224514i	−0.0288160	−	0.0209360i
$116$	2.04275	−	0.909491i	0.189665	−	0.0844441i
$117$	−1.24064	−	1.37787i	−0.114697	−	0.127384i
$118$	5.82693	−	6.47146i	0.536412	−	0.595746i
$119$	2.38308	+	22.6735i	0.218456	+	2.07847i
$120$	0.381966	+	0.661585i	0.0348686	+	0.0603941i
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	−7.14590			−0.646959
$123$	18.1691	+	8.08940i	1.63825	+	0.729397i
$124$	6.59368	−	7.32302i	0.592130	−	0.657627i
$125$	1.16312	−	3.57971i	0.104033	−	0.320179i
$126$	−3.42705	−	2.48990i	−0.305306	−	0.221818i
$127$	0.0587770	−	0.559226i	0.00521561	−	0.0496232i	−0.991605	−	0.129308i	$-0.958725\pi$
$127$	0.0587770	−	0.559226i	0.00521561	−	0.0496232i	0.996820	+	0.0796843i	$0.0253912\pi$
$128$	0.669131	+	0.743145i	0.0591433	+	0.0656853i
$129$	−14.3304	+	15.9155i	−1.26172	+	1.40128i
$130$	−0.0740275	−	0.704324i	−0.00649264	−	0.0617733i
$131$	−1.73607	+	3.00696i	−0.151681	+	0.262719i	−0.931846	−	0.362855i	$-0.881802\pi$
$131$	−1.73607	+	3.00696i	−0.151681	+	0.262719i	0.780165	+	0.625574i	$0.215135\pi$
$132$	−5.09017	+	4.25325i	−0.443042	+	0.370198i
$133$	8.47214	−	16.4062i	0.734627	−	1.42260i
$134$	−9.97214	+	7.24518i	−0.861461	+	0.625888i
$135$	−1.49448	−	0.317661i	−0.128624	−	0.0273399i
$136$	−3.60124	−	3.99958i	−0.308804	−	0.342961i
$137$	1.15341	−	10.9740i	0.0985427	−	0.937572i	−0.827834	−	0.560973i	$-0.810427\pi$
$137$	1.15341	−	10.9740i	0.0985427	−	0.937572i	0.926377	−	0.376598i	$-0.122906\pi$
$138$	−1.82709	+	0.813473i	−0.155532	+	0.0692474i
$139$	10.1888	−	2.16569i	0.864201	−	0.183692i	0.245576	−	0.969377i	$-0.421023\pi$
$139$	10.1888	−	2.16569i	0.864201	−	0.183692i	0.618626	+	0.785686i	$0.287690\pi$
$140$	−0.500000	−	1.53884i	−0.0422577	−	0.130056i
$141$	−1.61803	+	1.17557i	−0.136263	+	0.0990009i
$142$	3.16312	+	5.47868i	0.265443	+	0.459761i
$143$	5.91464	−	1.68277i	0.494607	−	0.140720i
$144$	1.00000			0.0833333
$145$	0.690983	−	0.502029i	0.0573830	−	0.0416912i
$146$	−7.51840	+	8.35003i	−0.622227	+	0.691053i
$147$	14.6463	+	16.2664i	1.20801	+	1.34163i
$148$	0.353512	−	3.36344i	0.0290585	−	0.276473i
$149$	−8.30428	+	3.69731i	−0.680313	+	0.302895i	−0.717646	−	0.696408i	$-0.754780\pi$
$149$	−8.30428	+	3.69731i	−0.680313	+	0.302895i	0.0373328	+	0.999303i	$0.488114\pi$
$150$	−6.49606	−	7.21460i	−0.530401	−	0.589070i
$151$	2.39919	+	7.38394i	0.195243	+	0.600896i	0.999974	+	0.00725620i	$0.00230974\pi$
$151$	2.39919	+	7.38394i	0.195243	+	0.600896i	−0.804731	+	0.593640i	$0.797690\pi$
$152$	0.658449	+	4.30888i	0.0534072	+	0.349496i
$153$	−5.38197			−0.435106
$154$	12.4185	−	6.57015i	1.00071	−	0.529438i
$155$	1.88197	−	3.25966i	0.151163	−	0.261822i
$156$	−3.38761	−	1.50826i	−0.271226	−	0.120758i
$157$	−8.42971	−	1.79179i	−0.672764	−	0.143000i	−0.141151	−	0.989988i	$-0.545080\pi$
$157$	−8.42971	−	1.79179i	−0.672764	−	0.143000i	−0.531613	+	0.846988i	$0.678414\pi$
$158$	−3.62717	+	0.770979i	−0.288562	+	0.0613358i
$159$	−10.9443	−	7.95148i	−0.867937	−	0.630593i
$160$	0.309017	+	0.224514i	0.0244299	+	0.0177494i
$161$	4.14350	−	0.880728i	0.326554	−	0.0694111i
$162$	−7.36044	+	8.17459i	−0.578291	+	0.642257i
$163$	4.00000	−	2.90617i	0.313304	−	0.227629i	−0.420009	−	0.907520i	$-0.637973\pi$
$163$	4.00000	−	2.90617i	0.313304	−	0.227629i	0.733313	+	0.679891i	$0.237973\pi$
$164$	9.94427			0.776517
$165$	−1.56401	+	1.99333i	−0.121758	+	0.155181i
$166$	−5.73607	+	9.93516i	−0.445205	+	0.771118i
$167$	15.5303	+	6.91452i	1.20177	+	0.535062i	0.907253	−	0.420585i	$-0.138175\pi$
$167$	15.5303	+	6.91452i	1.20177	+	0.535062i	0.294515	+	0.955647i	$0.404842\pi$
$168$	−8.28700	−	1.76146i	−0.639356	−	0.135899i
$169$	−6.39843	−	7.10618i	−0.492187	−	0.546629i
$170$	−1.66312	−	1.20833i	−0.127555	−	0.0926744i
$171$	3.64271	+	2.39388i	0.278565	+	0.183065i
$172$	−3.30902	+	10.1841i	−0.252310	+	0.776531i
$173$	−20.6630	−	4.39205i	−1.57098	−	0.333922i	−0.661588	−	0.749867i	$-0.730117\pi$
$173$	−20.6630	−	4.39205i	−1.57098	−	0.333922i	−0.909390	+	0.415946i	$0.863451\pi$
$174$	−0.467465	−	4.44764i	−0.0354385	−	0.337175i
$175$	10.2812	+	17.8075i	0.777182	+	1.34612i
$176$	−1.46007	+	2.97795i	−0.110057	+	0.224471i
$177$	−8.70820	−	15.0831i	−0.654549	−	1.13371i
$178$	−11.8992	+	8.64527i	−0.891882	+	0.647990i
$179$	−0.527864	−	1.62460i	−0.0394544	−	0.121428i	0.929389	−	0.369101i	$-0.120334\pi$
$179$	−0.527864	−	1.62460i	−0.0394544	−	0.121428i	−0.968844	+	0.247673i	$0.920334\pi$
$180$	0.373619	−	0.0794152i	0.0278479	−	0.00591926i
$181$	−1.12514	+	10.7050i	−0.0836308	+	0.795694i	0.869662	+	0.493647i	$0.164337\pi$
$181$	−1.12514	+	10.7050i	−0.0836308	+	0.795694i	−0.953293	+	0.302047i	$0.902330\pi$
$182$	6.35410	+	4.61653i	0.470997	+	0.342200i
$183$	−4.41641	+	13.5923i	−0.326470	+	1.00477i
$184$	−0.669131	+	0.743145i	−0.0493290	+	0.0547854i
$185$	−0.135029	−	1.28472i	−0.00992756	−	0.0944545i
$186$	−9.85410	−	17.0678i	−0.722538	−	1.25147i
$187$	7.85807	−	16.0272i	0.574639	−	1.17203i
$188$	−0.500000	+	0.866025i	−0.0364662	+	0.0631614i
$189$	13.7082	−	9.95959i	0.997125	−	0.724454i
$190$	0.588200	+	1.55759i	0.0426725	+	0.112999i
$191$	−0.0901699	+	0.277515i	−0.00652447	+	0.0200802i	−0.954266	−	0.298960i	$-0.903360\pi$
$191$	−0.0901699	+	0.277515i	−0.00652447	+	0.0200802i	0.947741	+	0.319040i	$0.103360\pi$
$192$	1.82709	−	0.813473i	0.131859	−	0.0587074i
$193$	7.68877	−	3.42326i	0.553450	−	0.246412i	−0.110902	−	0.993831i	$-0.535374\pi$
$193$	7.68877	−	3.42326i	0.553450	−	0.246412i	0.664352	+	0.747420i	$0.268707\pi$
$194$	15.8268	−	3.36408i	1.13630	−	0.241527i
$195$	−1.38546	−	0.294488i	−0.0992146	−	0.0210887i
$196$	9.99809	+	4.45144i	0.714149	+	0.317960i
$197$	25.5623			1.82124			0.910619	−	0.413246i	$-0.135605\pi$
$197$	25.5623			1.82124			0.910619	+	0.413246i	$0.135605\pi$
$198$	1.23607	+	3.07768i	0.0878435	+	0.218721i
$199$	−10.4271	−	18.0602i	−0.739154	−	1.28025i	−0.952877	−	0.303358i	$-0.901892\pi$
$199$	−10.4271	−	18.0602i	−0.739154	−	1.28025i	0.213723	−	0.976894i	$-0.431441\pi$
$200$	−4.43444	−	1.97434i	−0.313562	−	0.139607i
$201$	7.61803	+	23.4459i	0.537335	+	1.65375i
$202$	0.854102	−	2.62866i	0.0600944	−	0.184952i
$203$	−0.990108	+	9.42025i	−0.0694919	+	0.661172i
$204$	−9.83334	+	4.37809i	−0.688472	+	0.306527i
$205$	3.71537	−	0.789726i	0.259493	−	0.0551569i
$206$	−8.74882	−	1.85962i	−0.609559	−	0.129566i
$207$	0.104528	+	0.994522i	0.00726523	+	0.0691241i
$208$	−1.85410			−0.128559
$209$	−12.4475	+	7.35256i	−0.861010	+	0.508588i
$210$	−3.23607			−0.223310
$211$	−0.931331	−	8.86102i	−0.0641155	−	0.610018i	−0.978653	−	0.205518i	$-0.934112\pi$
$211$	−0.931331	−	8.86102i	−0.0641155	−	0.610018i	0.914538	−	0.404500i	$-0.132554\pi$
$212$	−6.61612	−	1.40630i	−0.454397	−	0.0965851i
$213$	12.3760	−	2.63060i	0.847989	−	0.180246i
$214$	5.56365	−	2.47710i	0.380323	−	0.169331i
$215$	−0.427539	+	4.06776i	−0.0291579	+	0.277419i
$216$	−1.23607	+	3.80423i	−0.0841038	+	0.258845i
$217$	12.8992	+	39.6996i	0.875654	+	2.69499i
$218$	7.22599	+	3.21722i	0.489406	+	0.217897i
$219$	11.2361	+	19.4614i	0.759263	+	1.31508i
$220$	−0.309017	+	1.22857i	−0.0208339	+	0.0828302i
$221$	9.97871			0.671241
$222$	−6.17916	−	2.75114i	−0.414718	−	0.184644i
$223$	−20.0248	−	4.25640i	−1.34096	−	0.285029i	−0.519096	−	0.854716i	$-0.673731\pi$
$223$	−20.0248	−	4.25640i	−1.34096	−	0.285029i	−0.821862	+	0.569687i	$0.807065\pi$
$224$	−4.14350	+	0.880728i	−0.276849	+	0.0588461i
$225$	−4.43444	+	1.97434i	−0.295630	+	0.131623i
$226$	10.0805	−	4.48811i	0.670543	−	0.298545i
$227$	2.16312	−	6.65740i	0.143571	−	0.441867i	−0.853253	−	0.521497i	$-0.825374\pi$
$227$	2.16312	−	6.65740i	0.143571	−	0.441867i	0.996824	+	0.0796299i	$0.0253739\pi$
$228$	8.60292	+	1.41059i	0.569742	+	0.0934187i
$229$	−15.1353	+	10.9964i	−1.00017	+	0.726663i	−0.962124	−	0.272613i	$-0.912112\pi$
$229$	−15.1353	+	10.9964i	−1.00017	+	0.726663i	−0.0380421	+	0.999276i	$0.512112\pi$
$230$	−0.190983	+	0.330792i	−0.0125930	+	0.0218118i
$231$	−4.82209	−	27.6820i	−0.317270	−	1.82134i
$232$	−1.11803	−	1.93649i	−0.0734025	−	0.127137i
$233$	1.06054	+	10.0903i	0.0694780	+	0.661039i	0.972732	+	0.231932i	$0.0745048\pi$
$233$	1.06054	+	10.0903i	0.0694780	+	0.661039i	−0.903254	+	0.429106i	$0.858829\pi$
$234$	−1.24064	+	1.37787i	−0.0811029	+	0.0900739i
$235$	−0.118034	+	0.363271i	−0.00769969	+	0.0236972i
$236$	−7.04508	−	5.11855i	−0.458596	−	0.333189i
$237$	−0.775226	+	7.37578i	−0.0503563	+	0.479108i
$238$	22.3002	−	4.74005i	1.44551	−	0.307252i
$239$	−7.82624	−	24.0867i	−0.506237	−	1.55804i	−0.798681	−	0.601755i	$-0.794468\pi$
$239$	−7.82624	−	24.0867i	−0.506237	−	1.55804i	0.292443	−	0.956283i	$-0.405532\pi$
$240$	0.618034	−	0.449028i	0.0398939	−	0.0289846i
$241$	2.66312	+	4.61266i	0.171547	+	0.297127i	0.938961	−	0.344024i	$-0.111790\pi$
$241$	2.66312	+	4.61266i	0.171547	+	0.297127i	−0.767414	+	0.641152i	$0.778457\pi$
$242$	−10.9699	−	0.812696i	−0.705174	−	0.0522421i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	0.746950	+	7.10675i	0.0478186	+	0.454963i
$245$	4.08899	+	0.869142i	0.261236	+	0.0555274i
$246$	6.14590	−	18.9151i	0.391848	−	1.20598i
$247$	−6.75396	−	4.43850i	−0.429744	−	0.282415i
$248$	−7.97214	−	5.79210i	−0.506231	−	0.367798i
$249$	15.3527	+	17.0509i	0.972939	+	1.08056i
$250$	−3.68168	−	0.782565i	−0.232850	−	0.0494938i
$251$	−19.0512	−	8.48213i	−1.20250	−	0.535387i	−0.295023	−	0.955490i	$-0.595327\pi$
$251$	−19.0512	−	8.48213i	−1.20250	−	0.535387i	−0.907476	+	0.420103i	$0.861994\pi$
$252$	−2.11803	+	3.66854i	−0.133424	+	0.231096i
$253$	−3.11426	−	1.14079i	−0.195792	−	0.0717212i
$254$	−0.562306			−0.0352822
$255$	−3.32624	+	2.41665i	−0.208297	+	0.151337i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−13.6941	+	2.91076i	−0.854212	+	0.181568i	−0.614150	−	0.789189i	$-0.710501\pi$
$257$	−13.6941	+	2.91076i	−0.854212	+	0.181568i	−0.240062	+	0.970758i	$0.577168\pi$
$258$	17.3262	+	12.5882i	1.07868	+	0.783710i
$259$	11.5902	+	8.42075i	0.720178	+	0.523240i
$260$	−0.692728	+	0.147244i	−0.0429612	+	0.00913168i
$261$	−2.18720	−	0.464905i	−0.135385	−	0.0287769i
$262$	3.17195	+	1.41224i	0.195964	+	0.0872488i
$263$	−8.39919	+	14.5478i	−0.517916	+	0.897057i	0.481867	+	0.876244i	$0.339959\pi$
$263$	−8.39919	+	14.5478i	−0.517916	+	0.897057i	−0.999783	+	0.0208127i	$0.993375\pi$
$264$	4.76202	+	4.61770i	0.293082	+	0.284200i
$265$	−2.58359			−0.158709
$266$	−17.2019	−	6.71081i	−1.05472	−	0.411466i
$267$	9.09017	+	27.9767i	0.556309	+	1.71214i
$268$	8.24786	+	9.16018i	0.503818	+	0.559547i
$269$	−14.0012	+	6.23374i	−0.853669	+	0.380078i	−0.786445	−	0.617660i	$-0.788081\pi$
$269$	−14.0012	+	6.23374i	−0.853669	+	0.380078i	−0.0672238	+	0.997738i	$0.521414\pi$
$270$	−0.159705	+	1.51949i	−0.00971935	+	0.0924735i
$271$	1.75181	+	1.94558i	0.106415	+	0.118185i	0.793999	−	0.607919i	$-0.207995\pi$
$271$	1.75181	+	1.94558i	0.106415	+	0.118185i	−0.687584	+	0.726105i	$0.741329\pi$
$272$	−3.60124	+	3.99958i	−0.218357	+	0.242510i
$273$	12.7082	−	9.23305i	0.769135	−	0.558810i
$274$	−11.0344			−0.666615
$275$	0.595124	−	16.0882i	0.0358874	−	0.970157i
$276$	1.00000	+	1.73205i	0.0601929	+	0.104257i
$277$	10.0451	−	7.29818i	0.603551	−	0.438505i	−0.243587	−	0.969879i	$-0.578324\pi$
$277$	10.0451	−	7.29818i	0.603551	−	0.438505i	0.847137	+	0.531374i	$0.178324\pi$
$278$	−3.21885	−	9.90659i	−0.193054	−	0.594158i
$279$	−9.63877	+	2.04878i	−0.577058	+	0.122657i
$280$	−1.47815	+	0.658114i	−0.0883362	+	0.0393298i
$281$	0.372362	−	3.54279i	0.0222133	−	0.211345i	−0.977785	−	0.209609i	$-0.932781\pi$
$281$	0.372362	−	3.54279i	0.0222133	−	0.211345i	0.999998	−	0.00173588i	$-0.000552548\pi$
$282$	1.33826	+	1.48629i	0.0796923	+	0.0885073i
$283$	−15.4195	−	3.27751i	−0.916591	−	0.194827i	−0.274617	−	0.961554i	$-0.588551\pi$
$283$	−15.4195	−	3.27751i	−0.916591	−	0.194827i	−0.641974	+	0.766726i	$0.721884\pi$
$284$	5.11803	−	3.71847i	0.303699	−	0.220651i
$285$	3.32624	−	0.156179i	0.197029	−	0.00925124i
$286$	−2.29180	−	5.70634i	−0.135517	−	0.337423i
$287$	−21.0623	+	36.4810i	−1.24327	+	2.15340i
$288$	−0.104528	−	0.994522i	−0.00615940	−	0.0586028i
$289$	8.00652	−	8.89214i	0.470972	−	0.523067i
$290$	−0.571506	−	0.634721i	−0.0335600	−	0.0372721i
$291$	3.38261	−	32.1834i	0.198292	−	1.88662i
$292$	9.09017	+	6.60440i	0.531962	+	0.386493i
$293$	−5.69098	+	17.5150i	−0.332471	+	1.02324i	0.635484	+	0.772114i	$0.280801\pi$
$293$	−5.69098	+	17.5150i	−0.332471	+	1.02324i	−0.967955	+	0.251126i	$0.919199\pi$
$294$	14.6463	−	16.2664i	0.854189	−	0.948673i
$295$	−3.03867	−	1.35290i	−0.176918	−	0.0787690i
$296$	−3.38197			−0.196573
$297$	−13.2361	+	0.898056i	−0.768035	+	0.0521105i
$298$	4.54508	+	7.87232i	0.263290	+	0.456031i
$299$	−0.193806	−	1.84395i	−0.0112081	−	0.106638i
$300$	−6.49606	+	7.21460i	−0.375050	+	0.416535i
$301$	−30.3522	−	33.7096i	−1.74947	−	1.94299i
$302$	7.09270	−	3.15788i	0.408139	−	0.181715i
$303$	−4.47214	−	3.24920i	−0.256917	−	0.186661i
$304$	4.21645	−	1.10524i	0.241830	−	0.0633900i
$305$	0.843459	+	2.59590i	0.0482963	+	0.148641i
$306$	0.562569	+	5.35248i	0.0321599	+	0.305981i
$307$	−4.13525	+	7.16247i	−0.236011	+	0.408784i	−0.959566	−	0.281483i	$-0.909174\pi$
$307$	−4.13525	+	7.16247i	−0.236011	+	0.408784i	0.723555	+	0.690267i	$0.242507\pi$
$308$	−7.83225	−	11.6637i	−0.446284	−	0.664603i
$309$	−8.94427	+	15.4919i	−0.508822	+	0.881305i
$310$	−3.43852	−	1.53093i	−0.195295	−	0.0869509i
$311$	−4.80902	−	14.8006i	−0.272694	−	0.839267i	−0.989820	−	0.142323i	$-0.954543\pi$
$311$	−4.80902	−	14.8006i	−0.272694	−	0.839267i	0.717126	−	0.696944i	$-0.245457\pi$
$312$	−1.14590	+	3.52671i	−0.0648737	+	0.199661i
$313$	0.528467	−	5.02803i	0.0298707	−	0.284201i	−0.969382	−	0.245557i	$-0.921029\pi$
$313$	0.528467	−	5.02803i	0.0298707	−	0.284201i	0.999253	−	0.0386446i	$-0.0123040\pi$
$314$	−0.900830	+	8.57082i	−0.0508368	+	0.483680i
$315$	−0.500000	+	1.53884i	−0.0281718	+	0.0867039i
$316$	1.14590	+	3.52671i	0.0644618	+	0.198393i
$317$	−1.18011	−	0.525421i	−0.0662818	−	0.0295106i	0.373328	−	0.927699i	$-0.378217\pi$
$317$	−1.18011	−	0.525421i	−0.0662818	−	0.0295106i	−0.439610	+	0.898189i	$0.644883\pi$
$318$	−6.76393	+	11.7155i	−0.379302	+	0.656971i
$319$	4.57794	−	5.83459i	0.256316	−	0.326674i
$320$	0.190983	−	0.330792i	0.0106763	−	0.0184919i
$321$	−1.27319	−	12.1136i	−0.0710627	−	0.676116i
$322$	−1.30902	−	4.02874i	−0.0729487	−	0.224513i
$323$	−22.6928	+	5.94838i	−1.26266	+	0.330976i
$324$	8.89919	+	6.46564i	0.494399	+	0.359202i
$325$	8.22191	−	3.66063i	0.456069	−	0.203055i
$326$	−3.30836	−	3.67431i	−0.183233	−	0.203501i
$327$	10.5854	−	11.7563i	0.585375	−	0.650125i
$328$	−1.03946	−	9.88980i	−0.0573945	−	0.546073i
$329$	−2.11803	−	3.66854i	−0.116771	−	0.202253i
$330$	2.14590	+	1.34708i	0.118128	+	0.0741545i
$331$	12.0344			0.661473			0.330736	−	0.943723i	$-0.392703\pi$
$331$	12.0344			0.661473			0.330736	+	0.943723i	$0.392703\pi$
$332$	10.4803	+	4.66614i	0.575182	+	0.256088i
$333$	−2.26298	+	2.51329i	−0.124010	+	0.137727i
$334$	5.25329	−	16.1680i	0.287447	−	0.884671i
$335$	3.80902	+	2.76741i	0.208109	+	0.151200i
$336$	−0.885579	+	8.42572i	−0.0483123	+	0.459661i
$337$	15.3900	+	17.0923i	0.838347	+	0.931079i	0.998429	−	0.0560251i	$-0.0178427\pi$
$337$	15.3900	+	17.0923i	0.838347	+	0.931079i	−0.160082	+	0.987104i	$0.551176\pi$
$338$	−6.39843	+	7.10618i	−0.348029	+	0.386525i
$339$	−2.30683	−	21.9480i	−0.125290	−	1.19205i
$340$	−1.02786	+	1.78031i	−0.0557438	+	0.0965510i
$341$	7.97214	−	31.6951i	0.431715	−	1.71639i
$342$	2.00000	−	3.87298i	0.108148	−	0.209427i
$343$	−13.5172	+	9.82084i	−0.729861	+	0.530275i
$344$	10.4742	+	2.22636i	0.564731	+	0.120037i
$345$	0.511170	+	0.567712i	0.0275205	+	0.0305646i
$346$	−2.20812	+	21.0089i	−0.118709	+	1.12944i
$347$	4.78339	−	2.12970i	0.256786	−	0.114328i	−0.274307	−	0.961642i	$-0.588448\pi$
$347$	4.78339	−	2.12970i	0.256786	−	0.114328i	0.531092	+	0.847314i	$0.321782\pi$
$348$	−4.37441	+	0.929809i	−0.234493	+	0.0498430i
$349$	5.34346	+	16.4455i	0.286029	+	0.880306i	0.986088	+	0.166222i	$0.0531567\pi$
$349$	5.34346	+	16.4455i	0.286029	+	0.880306i	−0.700060	+	0.714084i	$0.746843\pi$
$350$	16.6353	−	12.0862i	0.889192	−	0.646036i
$351$	−3.70820	−	6.42280i	−0.197929	−	0.342824i
$352$	3.11426	+	1.14079i	0.165990	+	0.0608046i
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$	−14.0902	+	10.2371i	−0.748884	+	0.544096i
$355$	1.61689	−	1.79574i	0.0858157	−	0.0953080i
$356$	9.84171	+	10.9303i	0.521610	+	0.579306i
$357$	4.76616	−	45.3470i	0.252252	−	2.40002i
$358$	−1.56052	+	0.694789i	−0.0824761	+	0.0367207i
$359$	15.5107	+	17.2263i	0.818622	+	0.909172i	0.997202	−	0.0747534i	$-0.0238170\pi$
$359$	15.5107	+	17.2263i	0.818622	+	0.909172i	−0.178580	+	0.983925i	$0.557150\pi$
$360$	−0.118034	−	0.363271i	−0.00622094	−	0.0191461i
$361$	18.0051	+	6.06760i	0.947638	+	0.319347i
$362$	10.7639			0.565740
$363$	−8.32563	+	20.3638i	−0.436982	+	1.06882i
$364$	3.92705	−	6.80185i	0.205833	−	0.356514i
$365$	3.92075	+	1.74563i	0.205221	+	0.0913705i
$366$	13.9795	+	2.97143i	0.730719	+	0.155319i
$367$	26.6201	−	5.65827i	1.38956	−	0.295359i	0.548429	−	0.836197i	$-0.315226\pi$
$367$	26.6201	−	5.65827i	1.38956	−	0.295359i	0.841127	+	0.540837i	$0.181893\pi$
$368$	0.809017	+	0.587785i	0.0421729	+	0.0306404i
$369$	−8.04508	−	5.84510i	−0.418810	−	0.304284i
$370$	−1.26357	+	0.268580i	−0.0656897	+	0.0139628i
$371$	19.1722	−	21.2929i	0.995374	−	1.10547i
$372$	−15.9443	+	11.5842i	−0.826672	+	0.600612i
$373$	−15.3607			−0.795346			−0.397673	−	0.917527i	$-0.630182\pi$
$373$	−15.3607			−0.795346			−0.397673	+	0.917527i	$0.630182\pi$
$374$	−16.7608	−	6.13972i	−0.866681	−	0.317477i
$375$	−3.76393	+	6.51932i	−0.194369	+	0.336656i
$376$	0.913545	+	0.406737i	0.0471125	+	0.0209758i
$377$	4.05530	+	0.861981i	0.208859	+	0.0443943i
$378$	−11.3379	−	12.5920i	−0.583160	−	0.647665i
$379$	13.2082	+	9.59632i	0.678460	+	0.492930i	0.872846	−	0.487995i	$-0.162272\pi$
$379$	13.2082	+	9.59632i	0.678460	+	0.492930i	−0.194387	+	0.980925i	$0.562272\pi$
$380$	1.48757	−	0.747790i	0.0763109	−	0.0383608i
$381$	−0.347524	+	1.06957i	−0.0178042	+	0.0547957i
$382$	0.285420	+	0.0606678i	0.0146033	+	0.00310404i
$383$	−2.63789	−	25.0978i	−0.134790	−	1.28244i	−0.827600	−	0.561319i	$-0.810294\pi$
$383$	−2.63789	−	25.0978i	−0.134790	−	1.28244i	0.692810	−	0.721120i	$-0.256372\pi$
$384$	−1.00000	−	1.73205i	−0.0510310	−	0.0883883i
$385$	−3.85256	−	3.73580i	−0.196344	−	0.190394i
$386$	−4.20820	−	7.28882i	−0.214192	−	0.370991i
$387$	8.66312	−	6.29412i	0.440371	−	0.319948i
$388$	−5.00000	−	15.3884i	−0.253837	−	0.781229i
$389$	13.4968	−	2.86884i	0.684317	−	0.145456i	0.147382	−	0.989080i	$-0.452915\pi$
$389$	13.4968	−	2.86884i	0.684317	−	0.145456i	0.536935	+	0.843624i	$0.319582\pi$
$390$	−0.148055	+	1.40865i	−0.00749705	+	0.0713297i
$391$	−4.35410	−	3.16344i	−0.220196	−	0.159982i
$392$	3.38197	−	10.4086i	0.170815	−	0.525715i
$393$	4.64662	−	5.16060i	0.234391	−	0.260318i
$394$	−2.67199	−	25.4223i	−0.134613	−	1.28076i
$395$	0.708204	+	1.22665i	0.0356336	+	0.0617192i
$396$	2.93162	−	1.55100i	0.147319	−	0.0779408i
$397$	0.527864	−	0.914287i	0.0264927	−	0.0458868i	−0.852475	−	0.522768i	$-0.824899\pi$
$397$	0.527864	−	0.914287i	0.0264927	−	0.0458868i	0.878968	+	0.476881i	$0.158233\pi$
$398$	−16.8713	+	12.2577i	−0.845683	+	0.614425i
$399$	−23.3961	+	28.5725i	−1.17127	+	1.43041i
$400$	−1.50000	+	4.61653i	−0.0750000	+	0.230826i
$401$	17.3065	−	7.70533i	0.864243	−	0.384786i	0.0737646	−	0.997276i	$-0.476499\pi$
$401$	17.3065	−	7.70533i	0.864243	−	0.384786i	0.790478	+	0.612490i	$0.209832\pi$
$402$	22.5212	−	10.0271i	1.12325	−	0.500105i
$403$	17.8713	−	3.79865i	0.890231	−	0.189224i
$404$	−2.70353	−	0.574654i	−0.134506	−	0.0285901i
$405$	3.83838	+	1.70896i	0.190730	+	0.0849187i
$406$	9.47214			0.470094
$407$	−4.18034	−	10.4086i	−0.207212	−	0.515936i
$408$	5.38197	+	9.32184i	0.266447	+	0.461500i
$409$	−20.6117	−	9.17692i	−1.01918	−	0.453769i	−0.172015	−	0.985094i	$-0.555028\pi$
$409$	−20.6117	−	9.17692i	−1.01918	−	0.453769i	−0.847168	+	0.531325i	$0.821694\pi$
$410$	−1.17376	−	3.61247i	−0.0579680	−	0.178407i
$411$	−6.81966	+	20.9888i	−0.336389	+	1.03530i
$412$	−0.934931	+	8.89527i	−0.0460607	+	0.438239i
$413$	33.6994	−	15.0039i	1.65824	−	0.738295i
$414$	0.978148	−	0.207912i	0.0480733	−	0.0102183i
$415$	4.28621	+	0.911062i	0.210402	+	0.0447223i
$416$	0.193806	+	1.84395i	0.00950214	+	0.0904068i
$417$	−20.8328			−1.02019
$418$	8.61340	+	11.6107i	0.421295	+	0.567900i
$419$	−33.6525			−1.64403			−0.822016	−	0.569465i	$-0.807150\pi$
$419$	−33.6525			−1.64403			−0.822016	+	0.569465i	$0.807150\pi$
$420$	0.338261	+	3.21834i	0.0165055	+	0.157039i
$421$	−2.47262	−	0.525572i	−0.120508	−	0.0256148i	0.147263	−	0.989097i	$-0.452954\pi$
$421$	−2.47262	−	0.525572i	−0.120508	−	0.0256148i	−0.267771	+	0.963483i	$0.586287\pi$
$422$	−8.71513	+	1.85246i	−0.424246	+	0.0901762i
$423$	0.913545	−	0.406737i	0.0444181	−	0.0197762i
$424$	−0.707023	+	6.72688i	−0.0343361	+	0.326686i
$425$	8.07295	−	24.8460i	0.391596	−	1.20521i
$426$	−3.90983	−	12.0332i	−0.189432	−	0.583011i
$427$	−27.6535	−	12.3121i	−1.33825	−	0.595826i
$428$	−3.04508	−	5.27424i	−0.147190	−	0.254940i
$429$	−12.2705	+	0.832544i	−0.592426	+	0.0401956i
$430$	4.09017			0.197246
$431$	−19.6158	−	8.73350i	−0.944859	−	0.420678i	−0.124303	−	0.992244i	$-0.539669\pi$
$431$	−19.6158	−	8.73350i	−0.944859	−	0.420678i	−0.820556	+	0.571566i	$0.806336\pi$
$432$	3.91259	+	0.831647i	0.188245	+	0.0400126i
$433$	2.61533	−	0.555906i	0.125685	−	0.0267152i	−0.144640	−	0.989484i	$-0.546202\pi$
$433$	2.61533	−	0.555906i	0.125685	−	0.0267152i	0.270325	+	0.962769i	$0.412869\pi$
$434$	38.1338	−	16.9783i	1.83048	−	0.814983i
$435$	−1.56052	+	0.694789i	−0.0748213	+	0.0333126i
$436$	2.44427	−	7.52270i	0.117059	−	0.360272i
$437$	1.53993	+	4.07782i	0.0736647	+	0.195069i
$438$	18.1803	−	13.2088i	0.868690	−	0.631140i
$439$	17.9164	−	31.0321i	0.855103	−	1.48108i	−0.0214455	−	0.999770i	$-0.506827\pi$
$439$	17.9164	−	31.0321i	0.855103	−	1.48108i	0.876549	−	0.481313i	$-0.159840\pi$
$440$	1.25414	+	0.178904i	0.0597889	+	0.00852889i
$441$	−5.47214	−	9.47802i	−0.260578	−	0.451334i
$442$	−1.04306	−	9.92405i	−0.0496133	−	0.472039i
$443$	8.17328	−	9.07735i	0.388324	−	0.431278i	−0.517009	−	0.855980i	$-0.672955\pi$
$443$	8.17328	−	9.07735i	0.388324	−	0.431278i	0.905333	+	0.424702i	$0.139621\pi$
$444$	−2.09017	+	6.43288i	−0.0991951	+	0.305291i
$445$	4.54508	+	3.30220i	0.215458	+	0.156539i
$446$	−2.13992	+	20.3600i	−0.101328	+	0.964073i
$447$	17.7831	−	3.77991i	0.841110	−	0.178783i
$448$	1.30902	+	4.02874i	0.0618452	+	0.190340i
$449$	−4.11803	+	2.99193i	−0.194342	+	0.141198i	−0.680701	−	0.732561i	$-0.738325\pi$
$449$	−4.11803	+	2.99193i	−0.194342	+	0.141198i	0.486359	+	0.873759i	$0.338325\pi$
$450$	2.42705	+	4.20378i	0.114412	+	0.198168i
$451$	29.1528	−	15.4236i	1.37275	−	0.726268i
$452$	−5.51722	−	9.55611i	−0.259508	−	0.449481i
$453$	−1.62310	−	15.4428i	−0.0762601	−	0.725566i
$454$	−6.84703	−	1.45538i	−0.321347	−	0.0683045i
$455$	0.927051	−	2.85317i	0.0434608	−	0.133759i
$456$	0.503613	−	8.70324i	0.0235839	−	0.407567i
$457$	−8.80902	−	6.40013i	−0.412068	−	0.299385i	0.362370	−	0.932034i	$-0.381968\pi$
$457$	−8.80902	−	6.40013i	−0.412068	−	0.299385i	−0.774439	+	0.632649i	$0.781968\pi$
$458$	12.5182	+	13.9029i	0.584939	+	0.649640i
$459$	−21.0574	−	4.47589i	−0.982877	−	0.208917i
$460$	0.348943	+	0.155360i	0.0162696	+	0.00724368i
$461$	−1.82624	+	3.16314i	−0.0850564	+	0.147322i	−0.905415	−	0.424527i	$-0.860440\pi$
$461$	−1.82624	+	3.16314i	−0.0850564	+	0.147322i	0.820359	+	0.571849i	$0.193774\pi$
$462$	−27.0264	+	7.68924i	−1.25738	+	0.357736i
$463$	10.7082			0.497652			0.248826	−	0.968548i	$-0.419955\pi$
$463$	10.7082			0.497652			0.248826	+	0.968548i	$0.419955\pi$
$464$	−1.80902	+	1.31433i	−0.0839815	+	0.0610161i
$465$	−5.03712	+	5.59429i	−0.233591	+	0.259429i
$466$	9.92419	−	2.10945i	0.459729	−	0.0977184i
$467$	14.8541	+	10.7921i	0.687366	+	0.499401i	0.875793	−	0.482687i	$-0.160339\pi$
$467$	14.8541	+	10.7921i	0.687366	+	0.499401i	−0.188427	+	0.982087i	$0.560339\pi$
$468$	1.50000	+	1.08981i	0.0693375	+	0.0503767i
$469$	−51.0738	+	10.8561i	−2.35837	+	0.501286i
$470$	0.373619	+	0.0794152i	0.0172338	+	0.00366315i
$471$	15.7459	+	7.01054i	0.725534	+	0.323029i
$472$	−4.35410	+	7.54153i	−0.200414	+	0.347127i
$473$	6.09479	+	34.9882i	0.280239	+	1.60876i
$474$	7.41641			0.340647
$475$	−16.5155	+	13.2258i	−0.757782	+	0.606843i
$476$	−7.04508	−	21.6825i	−0.322911	−	0.993818i
$477$	4.52595	+	5.02658i	0.207229	+	0.230151i
$478$	−23.1367	+	10.3011i	−1.05825	+	0.471162i
$479$	−3.32744	+	31.6584i	−0.152034	+	1.44651i	0.606607	+	0.795002i	$0.292530\pi$
$479$	−3.32744	+	31.6584i	−0.152034	+	1.44651i	−0.758641	+	0.651509i	$0.774136\pi$
$480$	−0.511170	−	0.567712i	−0.0233316	−	0.0259124i
$481$	4.19579	−	4.65990i	0.191312	−	0.212473i
$482$	4.30902	−	3.13068i	0.196270	−	0.142599i
$483$	−8.47214			−0.385496
$484$	0.338426	+	10.9948i	0.0153830	+	0.499763i
$485$	−3.09017	−	5.35233i	−0.140317	−	0.243037i
$486$	8.09017	−	5.87785i	0.366978	−	0.266625i
$487$	4.34346	+	13.3678i	0.196821	+	0.605752i	0.999951	+	0.00994811i	$0.00316663\pi$
$487$	4.34346	+	13.3678i	0.196821	+	0.605752i	−0.803130	+	0.595804i	$0.796833\pi$
$488$	6.98974	−	1.48572i	0.316411	−	0.0672552i
$489$	−9.03363	+	4.02203i	−0.408515	+	0.181883i
$490$	0.436965	−	4.15744i	0.0197400	−	0.187814i
$491$	7.44382	+	8.26720i	0.335935	+	0.373093i	0.887318	−	0.461159i	$-0.152566\pi$
$491$	7.44382	+	8.26720i	0.335935	+	0.373093i	−0.551383	+	0.834252i	$0.685900\pi$
$492$	−19.4539	−	4.13506i	−0.877051	−	0.186423i
$493$	9.73607	−	7.07367i	0.438490	−	0.318582i
$494$	−3.70820	+	7.18091i	−0.166840	+	0.323084i
$495$	0.972136	−	0.812299i	0.0436943	−	0.0365101i
$496$	−4.92705	+	8.53390i	−0.221231	+	0.383184i
$497$	2.80119	+	26.6516i	0.125651	+	1.19549i
$498$	15.3527	−	17.0509i	0.687972	−	0.764070i
$499$	28.2099	+	31.3303i	1.26285	+	1.40254i	0.877366	+	0.479821i	$0.159298\pi$
$499$	28.2099	+	31.3303i	1.26285	+	1.40254i	0.385483	+	0.922715i	$0.374035\pi$
$500$	−0.393438	+	3.74331i	−0.0175951	+	0.167406i
$501$	−27.5066	−	19.9847i	−1.22890	−	0.892850i
$502$	−6.44427	+	19.8334i	−0.287622	+	0.885209i
$503$	−12.0301	+	13.3608i	−0.536396	+	0.595728i	−0.949037	−	0.315166i	$-0.897940\pi$
$503$	−12.0301	+	13.3608i	−0.536396	+	0.595728i	0.412641	+	0.910894i	$0.364607\pi$
$504$	3.86984	+	1.72296i	0.172376	+	0.0767469i
$505$	−1.05573			−0.0469793
$506$	−0.809017	+	3.21644i	−0.0359652	+	0.142988i
$507$	9.56231	+	16.5624i	0.424677	+	0.735562i
$508$	0.0587770	+	0.559226i	0.00260781	+	0.0248116i
$509$	16.6537	−	18.4958i	0.738162	−	0.819812i	−0.250791	−	0.968041i	$-0.580691\pi$
$509$	16.6537	−	18.4958i	0.738162	−	0.819812i	0.988953	+	0.148230i	$0.0473575\pi$
$510$	2.75110	+	3.05541i	0.121821	+	0.135296i
$511$	−43.4818	+	19.3593i	−1.92352	+	0.856407i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	12.2616	+	12.3957i	0.541361	+	0.547285i
$514$	4.32624	+	13.3148i	0.190822	+	0.587290i
$515$	0.357112	+	3.39769i	0.0157362	+	0.149720i
$516$	10.7082	−	18.5472i	0.471402	−	0.816493i
$517$	−0.122602	+	3.31436i	−0.00539205	+	0.145765i
$518$	7.16312	−	12.4069i	0.314729	−	0.545127i
$519$	38.5966	+	17.1843i	1.69420	+	0.754307i
$520$	0.218847	+	0.673542i	0.00959708	+	0.0295368i
$521$	−7.07295	+	21.7683i	−0.309872	+	0.953686i	0.667943	+	0.744213i	$0.267175\pi$
$521$	−7.07295	+	21.7683i	−0.309872	+	0.953686i	−0.977814	+	0.209474i	$0.932825\pi$
$522$	−0.233733	+	2.22382i	−0.0102302	+	0.0973339i
$523$	2.06367	−	19.6345i	0.0902379	−	0.858556i	−0.851984	−	0.523568i	$-0.824601\pi$
$523$	2.06367	−	19.6345i	0.0902379	−	0.858556i	0.942222	−	0.334989i	$-0.108733\pi$
$524$	1.07295	−	3.30220i	0.0468720	−	0.144257i
$525$	−12.7082	−	39.1118i	−0.554631	−	1.70698i
$526$	15.3461	+	6.83251i	0.669121	+	0.297912i
$527$	26.5172	−	45.9292i	1.15511	−	2.00071i
$528$	4.09464	−	5.21862i	0.178196	−	0.227111i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	0.270059	+	2.56944i	0.0117306	+	0.111609i
$531$	2.69098	+	8.28199i	0.116779	+	0.359408i
$532$	−4.87595	+	17.8092i	−0.211399	+	0.772125i
$533$	14.9164	+	10.8374i	0.646101	+	0.469420i
$534$	26.8732	−	11.9647i	1.16292	−	0.517765i
$535$	−1.55656	−	1.72873i	−0.0672958	−	0.0747396i
$536$	8.24786	−	9.16018i	0.356253	−	0.395660i
$537$	0.357112	+	3.39769i	0.0154105	+	0.146621i
$538$	7.66312	+	13.2729i	0.330381	+	0.572236i
$539$	36.2148	−	2.45714i	1.55988	−	0.105837i
$540$	1.52786			0.0657488
$541$	26.4734	+	11.7867i	1.13818	+	0.506750i	0.887265	−	0.461259i	$-0.152602\pi$
$541$	26.4734	+	11.7867i	1.13818	+	0.506750i	0.250914	+	0.968009i	$0.419269\pi$
$542$	1.75181	−	1.94558i	0.0752465	−	0.0835697i
$543$	6.65248	−	20.4742i	0.285485	−	0.878633i
$544$	4.35410	+	3.16344i	0.186681	+	0.135631i
$545$	0.315810	−	3.00474i	0.0135278	−	0.128709i
$546$	−10.5108	−	11.6735i	−0.449822	−	0.499578i
$547$	5.19508	−	5.76973i	0.222126	−	0.246696i	−0.621774	−	0.783197i	$-0.713588\pi$
$547$	5.19508	−	5.76973i	0.222126	−	0.246696i	0.843900	+	0.536501i	$0.180254\pi$
$548$	1.15341	+	10.9740i	0.0492714	+	0.468786i
$549$	3.57295	−	6.18853i	0.152490	−	0.264120i
$550$	−16.0623	+	1.08981i	−0.684899	+	0.0464698i
$551$	−9.73607	+	0.457144i	−0.414770	+	0.0194750i
$552$	1.61803	−	1.17557i	0.0688681	−	0.0500356i
$553$	−15.3649	−	3.26592i	−0.653384	−	0.138881i
$554$	−8.30820	−	9.22719i	−0.352982	−	0.392026i
$555$	−0.270059	+	2.56944i	−0.0114634	+	0.109067i
$556$	−9.51586	+	4.23673i	−0.403562	+	0.179678i
$557$	26.0155	−	5.52977i	1.10231	−	0.234304i	0.379394	−	0.925235i	$-0.376133\pi$
$557$	26.0155	−	5.52977i	1.10231	−	0.234304i	0.722920	+	0.690931i	$0.242799\pi$
$558$	3.04508	+	9.37181i	0.128909	+	0.396740i
$559$	−16.0623	+	11.6699i	−0.679363	+	0.493586i
$560$	0.809017	+	1.40126i	0.0341872	+	0.0592140i
$561$	−22.0372	+	28.0864i	−0.930411	+	1.18581i
$562$	−3.56231			−0.150267
$563$	10.6180	−	7.71445i	0.447497	−	0.325125i	−0.341110	−	0.940023i	$-0.610803\pi$
$563$	10.6180	−	7.71445i	0.447497	−	0.325125i	0.788607	+	0.614898i	$0.210803\pi$
$564$	1.33826	−	1.48629i	0.0563510	−	0.0625841i
$565$	−2.82024	−	3.13219i	−0.118648	−	0.131772i
$566$	−1.64778	+	15.6776i	−0.0692613	+	0.658978i
$567$	−42.5682	+	18.9526i	−1.78770	+	0.795935i
$568$	−4.23308	−	4.70131i	−0.177616	−	0.197263i
$569$	6.96556	+	21.4378i	0.292011	+	0.898719i	0.984209	+	0.177011i	$0.0566427\pi$
$569$	6.96556	+	21.4378i	0.292011	+	0.898719i	−0.692198	+	0.721708i	$0.743357\pi$
$570$	−0.503010	−	3.29169i	−0.0210688	−	0.137874i
$571$	1.03444			0.0432900			0.0216450	−	0.999766i	$-0.493110\pi$
$571$	1.03444			0.0432900			0.0216450	+	0.999766i	$0.493110\pi$
$572$	−5.43552	+	2.87572i	−0.227271	+	0.120240i
$573$	0.291796	−	0.505406i	0.0121900	−	0.0211136i
$574$	38.4827	+	17.1336i	1.60624	+	0.715144i
$575$	−4.74803	−	1.00922i	−0.198006	−	0.0420876i
$576$	−0.978148	+	0.207912i	−0.0407562	+	0.00866299i
$577$	−27.9615	−	20.3152i	−1.16405	−	0.845733i	−0.173767	−	0.984787i	$-0.555594\pi$
$577$	−27.9615	−	20.3152i	−1.16405	−	0.845733i	−0.990285	+	0.139053i	$0.955594\pi$
$578$	−9.68034	−	7.03318i	−0.402649	−	0.292542i
$579$	−16.4650	+	3.49974i	−0.684261	+	0.145444i
$580$	−0.571506	+	0.634721i	−0.0237305	+	0.0263554i
$581$	−39.3156	+	28.5645i	−1.63109	+	1.18505i
$582$	−32.3607			−1.34139
$583$	−21.5771	+	6.13888i	−0.893634	+	0.254247i
$584$	5.61803	−	9.73072i	0.232476	−	0.402660i
$585$	0.646976	+	0.288052i	0.0267492	+	0.0119095i
$586$	18.0140	+	3.82899i	0.744150	+	0.158174i
$587$	−13.2619	−	14.7289i	−0.547379	−	0.607926i	0.404448	−	0.914561i	$-0.367464\pi$
$587$	−13.2619	−	14.7289i	−0.547379	−	0.607926i	−0.951827	+	0.306635i	$0.900797\pi$
$588$	−17.7082	−	12.8658i	−0.730274	−	0.530575i
$589$	−38.3770	+	19.2918i	−1.58130	+	0.794903i
$590$	−1.02786	+	3.16344i	−0.0423165	+	0.130237i
$591$	−50.0074	−	10.6294i	−2.05703	−	0.437235i
$592$	0.353512	+	3.36344i	0.0145292	+	0.138237i
$593$	18.2361	+	31.5858i	0.748866	+	1.29707i	0.948367	+	0.317176i	$0.102734\pi$
$593$	18.2361	+	31.5858i	0.748866	+	1.29707i	−0.199501	+	0.979898i	$0.563932\pi$
$594$	2.27668	+	13.0697i	0.0934134	+	0.536256i
$595$	−4.35410	−	7.54153i	−0.178501	−	0.309172i
$596$	7.35410	−	5.34307i	0.301236	−	0.218861i
$597$	12.8885	+	39.6669i	0.527493	+	1.62346i
$598$	−1.81359	+	0.385489i	−0.0741630	+	0.0157638i
$599$	1.46117	−	13.9021i	0.0597019	−	0.568026i	−0.923255	−	0.384188i	$-0.874481\pi$
$599$	1.46117	−	13.9021i	0.0597019	−	0.568026i	0.982957	−	0.183838i	$-0.0588520\pi$
$600$	7.85410	+	5.70634i	0.320642	+	0.232960i
$601$	6.38197	−	19.6417i	0.260326	−	0.801201i	−0.732408	−	0.680866i	$-0.761603\pi$
$601$	6.38197	−	19.6417i	0.260326	−	0.801201i	0.992733	−	0.120334i	$-0.0383966\pi$
$602$	−30.3522	+	33.7096i	−1.23706	+	1.37390i
$603$	−1.28844	−	12.2587i	−0.0524694	−	0.499213i
$604$	−3.88197	−	6.72376i	−0.157955	−	0.273586i
$605$	0.999596	+	4.08099i	0.0406394	+	0.165916i
$606$	−2.76393	+	4.78727i	−0.112277	+	0.194470i
$607$	−34.3713	+	24.9722i	−1.39509	+	1.01359i	−0.399804	+	0.916601i	$0.630922\pi$
$607$	−34.3713	+	24.9722i	−1.39509	+	1.01359i	−0.995285	+	0.0969907i	$0.969078\pi$
$608$	−1.53993	−	4.07782i	−0.0624523	−	0.165377i
$609$	5.85410	−	18.0171i	0.237220	−	0.730089i
$610$	2.49351	−	1.11018i	0.100959	−	0.0449500i
$611$	−1.69381	+	0.754131i	−0.0685241	+	0.0305089i
$612$	5.26436	−	1.11897i	0.212799	−	0.0452318i
$613$	−8.08978	−	1.71954i	−0.326743	−	0.0694514i	0.0416197	−	0.999134i	$-0.486748\pi$
$613$	−8.08978	−	1.71954i	−0.326743	−	0.0694514i	−0.368363	+	0.929682i	$0.620082\pi$
$614$	7.55549	+	3.36392i	0.304915	+	0.135757i
$615$	−7.59675			−0.306330
$616$	−10.7812	+	9.00854i	−0.434385	+	0.362964i
$617$	−1.56231	−	2.70599i	−0.0628961	−	0.108939i	0.832863	−	0.553480i	$-0.186700\pi$
$617$	−1.56231	−	2.70599i	−0.0628961	−	0.108939i	−0.895759	+	0.444540i	$0.853367\pi$
$618$	16.3420	+	7.27593i	0.657372	+	0.292681i
$619$	11.7812	+	36.2587i	0.473525	+	1.45736i	0.847937	+	0.530096i	$0.177844\pi$
$619$	11.7812	+	36.2587i	0.473525	+	1.45736i	−0.374413	+	0.927262i	$0.622156\pi$
$620$	−1.16312	+	3.57971i	−0.0467120	+	0.143765i
$621$	−0.418114	+	3.97809i	−0.0167783	+	0.159635i
$622$	−14.2169	+	6.32976i	−0.570045	+	0.253800i
$623$	−60.9434	+	12.9539i	−2.44165	+	0.518988i
$624$	3.62717	+	0.770979i	0.145203	+	0.0308639i
$625$	−2.38668	−	22.7077i	−0.0954672	−	0.908309i
$626$	−5.05573			−0.202068
$627$	27.4083	−	9.20783i	1.09458	−	0.367725i
$628$	8.61803			0.343897
$629$	−1.90259	−	18.1019i	−0.0758612	−	0.721771i
$630$	1.58268	+	0.336408i	0.0630553	+	0.0134028i
$631$	−34.8734	+	7.41257i	−1.38829	+	0.295090i	−0.840629	−	0.541612i	$-0.817814\pi$
$631$	−34.8734	+	7.41257i	−1.38829	+	0.295090i	−0.547659	+	0.836702i	$0.684481\pi$
$632$	3.38761	−	1.50826i	0.134752	−	0.0599955i
$633$	−1.86266	+	17.7220i	−0.0740342	+	0.704388i
$634$	−0.399187	+	1.22857i	−0.0158537	+	0.0487928i
$635$	0.0663712	+	0.204270i	0.00263386	+	0.00810619i
$636$	12.3583	+	5.50228i	0.490039	+	0.218180i
$637$	10.1459	+	17.5732i	0.401995	+	0.696276i
$638$	−6.28115	−	3.94298i	−0.248673	−	0.156104i
$639$	−6.32624			−0.250262
$640$	−0.348943	−	0.155360i	−0.0137932	−	0.00614113i
$641$	15.4531	+	3.28467i	0.610362	+	0.129737i	0.502714	−	0.864453i	$-0.332335\pi$
$641$	15.4531	+	3.28467i	0.610362	+	0.129737i	0.107648	+	0.994189i	$0.465668\pi$
$642$	−11.9142	+	2.53244i	−0.470215	+	0.0999472i
$643$	12.4212	−	5.53030i	0.489846	−	0.218094i	−0.146923	−	0.989148i	$-0.546937\pi$
$643$	12.4212	−	5.53030i	0.489846	−	0.218094i	0.636769	+	0.771054i	$0.280270\pi$
$644$	−3.86984	+	1.72296i	−0.152493	+	0.0678943i
$645$	2.52786	−	7.77997i	0.0995345	−	0.306336i
$646$	8.28783	+	21.9467i	0.326080	+	0.863481i
$647$	8.54508	−	6.20837i	0.335942	−	0.244076i	−0.407006	−	0.913426i	$-0.633427\pi$
$647$	8.54508	−	6.20837i	0.335942	−	0.244076i	0.742948	+	0.669349i	$0.233427\pi$
$648$	5.50000	−	9.52628i	0.216060	−	0.374228i
$649$	−28.5924	−	4.07871i	−1.12235	−	0.160103i
$650$	−4.50000	−	7.79423i	−0.176505	−	0.305715i
$651$	−8.72659	−	83.0280i	−0.342022	−	3.25412i
$652$	−3.30836	+	3.67431i	−0.129566	+	0.143897i
$653$	−1.50658	+	4.63677i	−0.0589569	+	0.181451i	−0.976198	−	0.216882i	$-0.930411\pi$
$653$	−1.50658	+	4.63677i	−0.0589569	+	0.181451i	0.917241	+	0.398333i	$0.130411\pi$
$654$	−12.7984	−	9.29856i	−0.500456	−	0.363603i
$655$	0.138630	−	1.31897i	0.00541671	−	0.0515365i
$656$	−9.72697	+	2.06753i	−0.379774	+	0.0807235i
$657$	−3.47214	−	10.6861i	−0.135461	−	0.416906i
$658$	−3.42705	+	2.48990i	−0.133600	+	0.0970663i
$659$	−11.8369	−	20.5021i	−0.461099	−	0.798648i	0.537917	−	0.842998i	$-0.319212\pi$
$659$	−11.8369	−	20.5021i	−0.461099	−	0.798648i	−0.999016	+	0.0443504i	$0.985878\pi$
$660$	1.11540	−	2.27495i	0.0434168	−	0.0885524i
$661$	2.92705	+	5.06980i	0.113849	+	0.197192i	0.917319	−	0.398153i	$-0.130349\pi$
$661$	2.92705	+	5.06980i	0.113849	+	0.197192i	−0.803470	+	0.595345i	$0.797015\pi$
$662$	−1.25794	−	11.9685i	−0.0488913	−	0.465170i
$663$	−19.5213	−	4.14938i	−0.758145	−	0.161149i
$664$	3.54508	−	10.9106i	0.137576	−	0.423415i
$665$	−0.407432	+	7.04107i	−0.0157995	+	0.273041i
$666$	2.73607	+	1.98787i	0.106020	+	0.0770284i
$667$	−1.49622	−	1.66172i	−0.0579339	−	0.0643421i
$668$	−16.6285	−	3.53450i	−0.643376	−	0.136754i
$669$	37.4045	+	16.6535i	1.44614	+	0.643863i
$670$	2.35410	−	4.07742i	0.0909469	−	0.157525i
$671$	13.2124	+	19.6758i	0.510058	+	0.759575i
$672$	8.47214			0.326820
$673$	32.2705	−	23.4459i	1.24394	−	0.903773i	0.246083	−	0.969249i	$-0.420857\pi$
$673$	32.2705	−	23.4459i	1.24394	−	0.903773i	0.997854	+	0.0654759i	$0.0208566\pi$
$674$	15.3900	−	17.0923i	0.592801	−	0.658372i
$675$	−18.9921	+	4.03690i	−0.731007	+	0.155380i
$676$	7.73607	+	5.62058i	0.297541	+	0.216176i
$677$	−10.2361	−	7.43694i	−0.393404	−	0.285825i	0.373445	−	0.927652i	$-0.378176\pi$
$677$	−10.2361	−	7.43694i	−0.393404	−	0.285825i	−0.766849	+	0.641828i	$0.778176\pi$
$678$	−21.5866	+	4.58838i	−0.829029	+	0.176216i
$679$	67.0432	+	14.2505i	2.57288	+	0.546883i
$680$	1.87800	+	0.836140i	0.0720181	+	0.0320645i
$681$	−7.00000	+	12.1244i	−0.268241	+	0.464606i
$682$	−32.3548	−	4.61542i	−1.23893	−	0.176734i
$683$	14.7082			0.562794			0.281397	−	0.959591i	$-0.409202\pi$
$683$	14.7082			0.562794			0.281397	+	0.959591i	$0.409202\pi$
$684$	−4.06082	−	1.58421i	−0.155269	−	0.0605737i
$685$	1.30244	+	4.00850i	0.0497636	+	0.153157i
$686$	11.1800	+	12.4166i	0.426853	+	0.474069i
$687$	34.1816	−	15.2186i	1.30411	−	0.580627i
$688$	1.11931	−	10.6495i	0.0426734	−	0.406010i
$689$	−8.39158	−	9.31979i	−0.319694	−	0.355056i
$690$	0.511170	−	0.567712i	0.0194599	−	0.0216124i
$691$	18.9894	−	13.7966i	0.722389	−	0.524846i	−0.164757	−	0.986334i	$-0.552684\pi$
$691$	18.9894	−	13.7966i	0.722389	−	0.524846i	0.887147	+	0.461488i	$0.152684\pi$
$692$	21.1246			0.803037
$693$	−0.519352	+	14.0398i	−0.0197286	+	0.533330i
$694$	−2.61803	−	4.53457i	−0.0993792	−	0.172130i
$695$	−3.21885	+	2.33863i	−0.122098	+	0.0887093i
$696$	1.38197	+	4.25325i	0.0523833	+	0.161219i
$697$	52.3502	−	11.1274i	1.98291	−	0.421480i
$698$	15.7968	−	7.03321i	0.597919	−	0.266211i
$699$	2.12107	−	20.1806i	0.0802262	−	0.763302i
$700$	−13.7589	−	15.2808i	−0.520036	−	0.577559i
$701$	−8.51791	−	1.81054i	−0.321717	−	0.0683831i	0.0442225	−	0.999022i	$-0.485919\pi$
$701$	−8.51791	−	1.81054i	−0.321717	−	0.0683831i	−0.365939	+	0.930639i	$0.619252\pi$
$702$	−6.00000	+	4.35926i	−0.226455	+	0.164529i
$703$	−6.76393	+	13.0983i	−0.255107	+	0.494012i
$704$	0.809017	−	3.21644i	0.0304910	−	0.121224i
$705$	0.381966	−	0.661585i	0.0143857	−	0.0249167i
$706$	−0.418114	−	3.97809i	−0.0157359	−	0.149717i
$707$	7.83432	−	8.70089i	0.294640	−	0.327231i
$708$	11.6539	+	12.9429i	0.437979	+	0.486424i
$709$	−5.12189	+	48.7316i	−0.192357	+	1.83015i	0.293320	+	0.956014i	$0.405240\pi$
$709$	−5.12189	+	48.7316i	−0.192357	+	1.83015i	−0.485677	+	0.874138i	$0.661427\pi$
$710$	−1.95492	−	1.42033i	−0.0733667	−	0.0533040i
$711$	1.14590	−	3.52671i	0.0429745	−	0.132262i
$712$	9.84171	−	10.9303i	0.368834	−	0.409631i
$713$	−9.00217	−	4.00802i	−0.337134	−	0.150102i
$714$	−45.5967			−1.70642
$715$	−1.80244	+	1.50609i	−0.0674074	+	0.0563244i
$716$	0.854102	+	1.47935i	0.0319193	+	0.0552858i
$717$	5.29463	+	50.3750i	0.197731	+	1.88129i
$718$	15.5107	−	17.2263i	0.578853	−	0.642882i
$719$	−6.55639	−	7.28161i	−0.244512	−	0.271558i	0.608379	−	0.793646i	$-0.291820\pi$
$719$	−6.55639	−	7.28161i	−0.244512	−	0.271558i	−0.852892	+	0.522088i	$0.825153\pi$
$720$	−0.348943	+	0.155360i	−0.0130043	+	0.00578991i
$721$	−30.6525	−	22.2703i	−1.14156	−	0.829390i
$722$	4.15231	−	18.5407i	0.154533	−	0.690014i
$723$	−3.29180	−	10.1311i	−0.122423	−	0.376780i
$724$	−1.12514	−	10.7050i	−0.0418154	−	0.397847i
$725$	5.42705	−	9.39993i	0.201556	−	0.349105i
$726$	21.1225	+	6.15143i	0.783929	+	0.228301i
$727$	−15.7812	+	27.3338i	−0.585291	+	1.01375i	0.409549	+	0.912288i	$0.365686\pi$
$727$	−15.7812	+	27.3338i	−0.585291	+	1.01375i	−0.994839	+	0.101465i	$0.967647\pi$
$728$	−7.17508	−	3.19455i	−0.265926	−	0.118398i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	1.32624	−	4.08174i	0.0490863	−	0.151072i
$731$	−6.02410	+	57.3155i	−0.222809	+	2.11989i
$732$	1.49390	−	14.2135i	0.0552161	−	0.525346i
$733$	−5.98278	+	18.4131i	−0.220979	+	0.680103i	0.777696	+	0.628641i	$0.216388\pi$
$733$	−5.98278	+	18.4131i	−0.220979	+	0.680103i	−0.998675	+	0.0514628i	$0.983612\pi$
$734$	−8.40983	−	25.8828i	−0.310412	−	0.955351i
$735$	−7.63786	−	3.40059i	−0.281727	−	0.125433i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	38.3871	+	14.0617i	1.41401	+	0.517970i
$738$	−4.97214	+	8.61199i	−0.183027	+	0.317012i
$739$	1.65498	+	15.7461i	0.0608794	+	0.579229i	0.981858	+	0.189616i	$0.0607244\pi$
$739$	1.65498	+	15.7461i	0.0608794	+	0.579229i	−0.920979	+	0.389613i	$0.872609\pi$
$740$	0.399187	+	1.22857i	0.0146744	+	0.0451632i
$741$	11.3671	+	11.4915i	0.417581	+	0.422150i
$742$	−23.1803	−	16.8415i	−0.850977	−	0.618271i
$743$	42.8348	−	19.0713i	1.57146	−	0.699658i	0.578233	−	0.815872i	$-0.303743\pi$
$743$	42.8348	−	19.0713i	1.57146	−	0.699658i	0.993224	+	0.116214i	$0.0370759\pi$
$744$	13.1874	+	14.6460i	0.483472	+	0.536950i
$745$	2.32331	−	2.58030i	0.0851196	−	0.0945349i
$746$	1.60563	+	15.2765i	0.0587862	+	0.559314i
$747$	−5.73607	−	9.93516i	−0.209872	−	0.363509i
$748$	−4.35410	+	17.3108i	−0.159202	+	0.632945i
$749$	25.7984			0.942652
$750$	6.87705	+	3.06186i	0.251114	+	0.111803i
$751$	−24.2928	+	26.9798i	−0.886455	+	0.984508i	−0.999959	−	0.00902930i	$-0.997126\pi$
$751$	−24.2928	+	26.9798i	−0.886455	+	0.984508i	0.113504	+	0.993538i	$0.463793\pi$
$752$	0.309017	−	0.951057i	0.0112687	−	0.0346815i
$753$	33.7426	+	24.5155i	1.22965	+	0.893393i
$754$	0.433364	−	4.12319i	0.0157822	−	0.150158i
$755$	−1.98435	−	2.20384i	−0.0722177	−	0.0802059i
$756$	−11.3379	+	12.5920i	−0.412357	+	0.457968i
$757$	−0.534293	−	5.08346i	−0.0194192	−	0.184761i	0.980512	−	0.196457i	$-0.0629437\pi$
$757$	−0.534293	−	5.08346i	−0.0194192	−	0.184761i	−0.999932	+	0.0116959i	$0.996277\pi$
$758$	8.16312	−	14.1389i	0.296498	−	0.513549i
$759$	5.61803	+	3.52671i	0.203922	+	0.128012i
$760$	−0.899187	−	1.40126i	−0.0326169	−	0.0508290i
$761$	16.3713	−	11.8945i	0.593460	−	0.431174i	−0.250092	−	0.968222i	$-0.580461\pi$
$761$	16.3713	−	11.8945i	0.593460	−	0.431174i	0.843552	+	0.537048i	$0.180461\pi$
$762$	1.10004	+	0.233820i	0.0398501	+	0.00847040i
$763$	22.4203	+	24.9002i	0.811669	+	0.901449i
$764$	0.0305010	−	0.290198i	0.00110349	−	0.0104990i
$765$	1.87800	−	0.836140i	0.0678993	−	0.0302307i
$766$	−24.6846	+	5.24687i	−0.891891	+	0.189577i
$767$	−4.98936	−	15.3557i	−0.180155	−	0.554461i
$768$	−1.61803	+	1.17557i	−0.0583858	+	0.0424197i
$769$	4.13525	+	7.16247i	0.149121	+	0.258285i	0.930903	−	0.365267i	$-0.119022\pi$
$769$	4.13525	+	7.16247i	0.149121	+	0.258285i	−0.781782	+	0.623552i	$0.785689\pi$
$770$	−3.31263	+	4.22195i	−0.119379	+	0.152148i
$771$	28.0000			1.00840
$772$	−6.80902	+	4.94704i	−0.245062	+	0.178048i
$773$	−0.181006	+	0.201028i	−0.00651035	+	0.00723047i	−0.746391	−	0.665507i	$-0.768215\pi$
$773$	−0.181006	+	0.201028i	−0.00651035	+	0.00723047i	0.739881	+	0.672738i	$0.234882\pi$
$774$	−7.16519	−	7.95775i	−0.257547	−	0.286035i
$775$	4.99989	−	47.5708i	0.179601	−	1.70879i
$776$	−14.7815	+	6.58114i	−0.530624	+	0.236249i
$777$	−19.1722	−	21.2929i	−0.687801	−	0.763880i
$778$	−4.26393	−	13.1230i	−0.152869	−	0.470484i
$779$	−40.3819	−	15.7538i	−1.44683	−	0.564438i
$780$	1.41641			0.0507155
$781$	9.23677	−	18.8392i	0.330518	−	0.674120i
$782$	−2.69098	+	4.66092i	−0.0962294	+	0.166674i
$783$	−8.17100	−	3.63796i	−0.292008	−	0.130010i
$784$	−10.7051	−	2.27544i	−0.382325	−	0.0812658i
$785$	3.21986	−	0.684403i	0.114922	−	0.0244274i
$786$	−5.61803	−	4.08174i	−0.200389	−	0.145591i
$787$	13.6074	+	9.88635i	0.485051	+	0.352410i	0.803278	−	0.595604i	$-0.203087\pi$
$787$	13.6074	+	9.88635i	0.485051	+	0.352410i	−0.318227	+	0.948015i	$0.603087\pi$
$788$	−25.0037	+	5.31470i	−0.890720	+	0.189328i
$789$	22.4806	−	24.9672i	0.800331	−	0.888858i
$790$	1.14590	−	0.832544i	0.0407692	−	0.0296206i
$791$	46.7426			1.66198
$792$	−1.84894	−	2.75344i	−0.0656993	−	0.0978391i
$793$	−6.62461	+	11.4742i	−0.235247	+	0.407460i
$794$	−0.964456	−	0.429403i	−0.0342272	−	0.0152390i
$795$	5.05427	+	1.07432i	0.179256	+	0.0381021i
$796$	13.9541	+	15.4976i	0.494591	+	0.549299i
$797$	−9.70820	−	7.05342i	−0.343882	−	0.249845i	0.402416	−	0.915457i	$-0.368171\pi$
$797$	−9.70820	−	7.05342i	−0.343882	−	0.249845i	−0.746298	+	0.665612i	$0.768171\pi$
$798$	30.8615	+	20.2813i	1.09249	+	0.717950i
$799$	−1.66312	+	5.11855i	−0.0588369	+	0.181081i
$800$	4.74803	+	1.00922i	0.167868	+	0.0356815i
$801$	−1.53743	−	14.6276i	−0.0543223	−	0.516842i
$802$	−9.47214	−	16.4062i	−0.334473	−	0.579324i
$803$	36.8923	+	5.26270i	1.30190	+	0.185717i
$804$	−12.3262	−	21.3497i	−0.434713	−	0.752945i
$805$	−1.30902	+	0.951057i	−0.0461368	+	0.0335203i
$806$	−5.64590	−	17.3763i	−0.198868	−	0.612054i
$807$	29.9826	−	6.37301i	1.05544	−	0.224341i
$808$	−0.288910	+	2.74879i	−0.0101638	+	0.0967021i
$809$	−9.97214	−	7.24518i	−0.350602	−	0.254727i	0.398520	−	0.917160i	$-0.369524\pi$
$809$	−9.97214	−	7.24518i	−0.350602	−	0.254727i	−0.749121	+	0.662433i	$0.769524\pi$
$810$	1.29837	−	3.99598i	0.0456202	−	0.140405i
$811$	−5.27847	+	5.86233i	−0.185352	+	0.205854i	−0.828659	−	0.559754i	$-0.810895\pi$
$811$	−5.27847	+	5.86233i	−0.185352	+	0.205854i	0.643306	+	0.765609i	$0.277562\pi$
$812$	−0.990108	−	9.42025i	−0.0347460	−	0.330586i
$813$	−2.61803	−	4.53457i	−0.0918185	−	0.159034i
$814$	−9.91464	+	5.24544i	−0.347508	+	0.183852i
$815$	−0.944272	+	1.63553i	−0.0330764	+	0.0572900i
$816$	8.70820	−	6.32688i	0.304848	−	0.221485i
$817$	29.5711	−	36.1137i	1.03456	−	1.26346i
$818$	−6.97214	+	21.4580i	−0.243775	+	0.750262i
$819$	−7.17508	+	3.19455i	−0.250718	+	0.111627i
$820$	−3.46999	+	1.54494i	−0.121177	+	0.0539516i
$821$	−43.8531	+	9.32127i	−1.53048	+	0.325314i	−0.894741	−	0.446586i	$-0.852640\pi$
$821$	−43.8531	+	9.32127i	−1.53048	+	0.325314i	−0.635743	+	0.771900i	$0.719306\pi$
$822$	21.5866	+	4.58838i	0.752920	+	0.160038i
$823$	−12.7702	−	5.68566i	−0.445141	−	0.198189i	0.171910	−	0.985113i	$-0.445006\pi$
$823$	−12.7702	−	5.68566i	−0.445141	−	0.198189i	−0.617051	+	0.786923i	$0.711673\pi$
$824$	8.94427			0.311588
$825$	−7.85410	+	31.2259i	−0.273445	+	1.08715i
$826$	−18.4443	−	31.9464i	−0.641758	−	1.11156i
$827$	−19.2159	−	8.55548i	−0.668203	−	0.297503i	0.0444585	−	0.999011i	$-0.485844\pi$
$827$	−19.2159	−	8.55548i	−0.668203	−	0.297503i	−0.712661	+	0.701508i	$0.752510\pi$
$828$	−0.309017	−	0.951057i	−0.0107391	−	0.0330515i
$829$	−9.48936	+	29.2052i	−0.329579	+	1.01434i	0.639752	+	0.768581i	$0.279037\pi$
$829$	−9.48936	+	29.2052i	−0.329579	+	1.01434i	−0.969331	+	0.245759i	$0.920963\pi$
$830$	0.458040	−	4.35796i	0.0158988	−	0.151267i
$831$	−22.6859	+	10.1004i	−0.786965	+	0.350380i
$832$	1.81359	−	0.385489i	0.0628748	−	0.0133644i
$833$	57.6146	+	12.2464i	1.99623	+	0.424311i
$834$	2.17762	+	20.7187i	0.0754049	+	0.717430i
$835$	−6.49342			−0.224714
$836$	10.6468	−	9.77987i	0.368227	−	0.338244i
$837$	−39.4164			−1.36243
$838$	3.51764	+	33.4681i	0.121515	+	1.15614i
$839$	−48.8866	−	10.3912i	−1.68775	−	0.358743i	−0.738742	−	0.673989i	$-0.764580\pi$
$839$	−48.8866	−	10.3912i	−1.68775	−	0.358743i	−0.949010	+	0.315246i	$0.897913\pi$
$840$	3.16535	−	0.672816i	0.109215	−	0.0232144i
$841$	−21.9251	+	9.76168i	−0.756038	+	0.336610i
$842$	−0.264234	+	2.51402i	−0.00910610	+	0.0866387i
$843$	−2.20163	+	6.77591i	−0.0758280	+	0.233375i
$844$	2.75329	+	8.47375i	0.0947721	+	0.291679i
$845$	3.33670	+	1.48560i	0.114786	+	0.0511060i
$846$	−0.500000	−	0.866025i	−0.0171904	−	0.0297746i
$847$	−41.0517	−	22.0458i	−1.41055	−	0.757503i
$848$	6.76393			0.232274
$849$	28.8021	+	12.8235i	0.988487	+	0.440103i
$850$	−25.5537	−	5.43161i	−0.876486	−	0.186303i
$851$	−3.30806	+	0.703150i	−0.113399	+	0.0241037i
$852$	−11.5586	+	5.14623i	−0.395992	+	0.176307i
$853$	26.2262	−	11.6767i	0.897970	−	0.399802i	0.0947613	−	0.995500i	$-0.469791\pi$
$853$	26.2262	−	11.6767i	0.897970	−	0.399802i	0.803208	+	0.595698i	$0.203125\pi$
$854$	−9.35410	+	28.7890i	−0.320091	+	0.985138i
$855$	−1.64301	−	0.269399i	−0.0561898	−	0.00921325i
$856$	−4.92705	+	3.57971i	−0.168403	+	0.122352i
$857$	20.2705	−	35.1096i	0.692427	−	1.19932i	−0.278613	−	0.960404i	$-0.589875\pi$
$857$	20.2705	−	35.1096i	0.692427	−	1.19932i	0.971040	−	0.238916i	$-0.0767921\pi$
$858$	2.11060	+	12.1163i	0.0720547	+	0.413643i
$859$	28.3885	+	49.1704i	0.968605	+	1.67767i	0.699602	+	0.714533i	$0.253361\pi$
$859$	28.3885	+	49.1704i	0.968605	+	1.67767i	0.269003	+	0.963139i	$0.413306\pi$
$860$	−0.427539	−	4.06776i	−0.0145790	−	0.138710i
$861$	56.3737	−	62.6094i	1.92121	−	2.13372i
$862$	−6.63525	+	20.4212i	−0.225998	+	0.695549i
$863$	−37.1418	−	26.9851i	−1.26432	−	0.918584i	−0.265361	−	0.964149i	$-0.585491\pi$
$863$	−37.1418	−	26.9851i	−1.26432	−	0.918584i	−0.998961	+	0.0455648i	$0.985491\pi$
$864$	0.418114	−	3.97809i	0.0142245	−	0.135337i
$865$	7.89256	−	1.67762i	0.268355	−	0.0570406i
$866$	−0.826238	−	2.54290i	−0.0280767	−	0.0864112i
$867$	−19.3607	+	14.0664i	−0.657523	+	0.477719i
$868$	−20.8713	−	36.1502i	−0.708419	−	1.22702i
$869$	8.82927	+	8.56169i	0.299513	+	0.290435i
$870$	0.854102	+	1.47935i	0.0289568	+	0.0501546i
$871$	2.38890	+	22.7289i	0.0809449	+	0.770140i
$872$	−7.73698	−	1.64455i	−0.262007	−	0.0556914i
$873$	−5.00000	+	15.3884i	−0.169224	+	0.520819i
$874$	3.89452	−	1.95774i	0.131734	−	0.0662215i
$875$	−12.8992	−	9.37181i	−0.436072	−	0.316825i
$876$	−15.0368	−	16.7001i	−0.508046	−	0.564242i
$877$	53.1728	+	11.3022i	1.79552	+	0.381649i	0.980301	−	0.197509i	$-0.0632850\pi$
$877$	53.1728	+	11.3022i	1.79552	+	0.381649i	0.815216	+	0.579158i	$0.196618\pi$
$878$	−32.7349	−	14.5745i	−1.10475	−	0.491866i
$879$	18.4164	−	31.8982i	0.621170	−	1.07590i
$880$	0.0468299	−	1.26597i	0.00157864	−	0.0426759i
$881$	37.4164			1.26059			0.630295	−	0.776355i	$-0.282934\pi$
$881$	37.4164			1.26059			0.630295	+	0.776355i	$0.282934\pi$
$882$	−8.85410	+	6.43288i	−0.298133	+	0.216606i
$883$	−1.81214	+	2.01259i	−0.0609834	+	0.0677290i	−0.772865	−	0.634571i	$-0.781177\pi$
$883$	−1.81214	+	2.01259i	−0.0609834	+	0.0677290i	0.711881	+	0.702300i	$0.247843\pi$
$884$	−9.76065	+	2.07469i	−0.328286	+	0.0697794i
$885$	5.38197	+	3.91023i	0.180913	+	0.131441i
$886$	−9.88197	−	7.17967i	−0.331991	−	0.241206i
$887$	45.1167	−	9.58985i	1.51487	−	0.321996i	0.625879	−	0.779920i	$-0.284740\pi$
$887$	45.1167	−	9.58985i	1.51487	−	0.321996i	0.888991	+	0.457925i	$0.151407\pi$
$888$	6.61612	+	1.40630i	0.222023	+	0.0471924i
$889$	−2.17603	−	0.968833i	−0.0729818	−	0.0324936i
$890$	2.80902	−	4.86536i	0.0941585	−	0.163087i
$891$	36.1172	+	5.15213i	1.20997	+	0.172603i
$892$	20.4721			0.685458
$893$	3.40238	−	2.72467i	0.113856	−	0.0911777i
$894$	−5.61803	−	17.2905i	−0.187895	−	0.578282i
$895$	0.436592	+	0.484884i	0.0145936	+	0.0162079i
$896$	3.86984	−	1.72296i	0.129282	−	0.0575602i
$897$	−0.387613	+	3.68789i	−0.0129420	+	0.123135i
$898$	3.40599	+	3.78273i	0.113659	+	0.126231i
$899$	14.7439	−	16.3748i	0.491737	−	0.546130i
$900$	3.92705	−	2.85317i	0.130902	−	0.0951057i
$901$	−36.4033			−1.21277
$902$	−18.3864	−	27.3809i	−0.612200	−	0.911685i
$903$	45.3607	+	78.5670i	1.50951	+	2.61455i
$904$	−8.92705	+	6.48588i	−0.296909	+	0.215717i
$905$	−1.27051	−	3.91023i	−0.0422332	−	0.129980i
$906$	−15.1885	+	3.22842i	−0.504606	+	0.107257i
$907$	−0.380408	+	0.169368i	−0.0126312	+	0.00562378i	−0.413043	−	0.910712i	$-0.635534\pi$
$907$	−0.380408	+	0.169368i	−0.0126312	+	0.00562378i	0.400411	+	0.916336i	$0.368867\pi$
$908$	−0.731699	+	6.96165i	−0.0242823	+	0.231031i
$909$	1.84943	+	2.05400i	0.0613418	+	0.0681269i
$910$	−2.93444	−	0.623735i	−0.0972758	−	0.0206766i
$911$	−8.68034	+	6.30664i	−0.287592	+	0.208948i	−0.722222	−	0.691661i	$-0.756879\pi$
$911$	−8.68034	+	6.30664i	−0.287592	+	0.208948i	0.434630	+	0.900609i	$0.356879\pi$
$912$	−8.70820	+	0.408882i	−0.288357	+	0.0135394i
$913$	37.9615	−	2.57565i	1.25634	−	0.0852417i
$914$	−5.44427	+	9.42976i	−0.180081	+	0.311909i
$915$	−0.570619	−	5.42908i	−0.0188641	−	0.179480i
$916$	12.5182	−	13.9029i	0.413614	−	0.459365i
$917$	9.84171	+	10.9303i	0.325002	+	0.360951i
$918$	−2.25027	+	21.4099i	−0.0742701	+	0.706633i
$919$	−44.2705	−	32.1644i	−1.46035	−	1.06101i	−0.983272	−	0.182145i	$-0.941696\pi$
$919$	−44.2705	−	32.1644i	−1.46035	−	1.06101i	−0.477078	−	0.878861i	$-0.658304\pi$
$920$	0.118034	−	0.363271i	0.00389147	−	0.0119767i
$921$	11.0681	−	12.2924i	0.364706	−	0.405047i
$922$	3.33670	+	1.48560i	0.109888	+	0.0489255i
$923$	11.7295			0.386081
$924$	10.4721	+	26.0746i	0.344508	+	0.857790i
$925$	−8.20820	−	14.2170i	−0.269884	−	0.467453i
$926$	−1.11931	−	10.6495i	−0.0367829	−	0.349966i
$927$	5.98489	−	6.64689i	0.196569	−	0.218312i
$928$	1.49622	+	1.66172i	0.0491159	+	0.0545487i
$929$	24.4501	−	10.8859i	0.802181	−	0.357154i	0.0356523	−	0.999364i	$-0.488649\pi$
$929$	24.4501	−	10.8859i	0.802181	−	0.357154i	0.766528	+	0.642210i	$0.221982\pi$
$930$	6.09017	+	4.42477i	0.199705	+	0.145094i
$931$	−33.5485	−	33.9155i	−1.09951	−	1.11154i
$932$	−3.13525	−	9.64932i	−0.102699	−	0.316074i
$933$	3.25341	+	30.9541i	0.106512	+	1.01339i
$934$	9.18034	−	15.9008i	0.300390	−	0.520291i
$935$	−0.252037	+	6.81342i	−0.00824250	+	0.222823i
$936$	0.927051	−	1.60570i	0.0303016	−	0.0524839i
$937$	−34.0483	−	15.1593i	−1.11231	−	0.495232i	−0.233477	−	0.972362i	$-0.575010\pi$
$937$	−34.0483	−	15.1593i	−1.11231	−	0.495232i	−0.878833	+	0.477130i	$0.841677\pi$
$938$	16.1353	+	49.6592i	0.526835	+	1.62143i
$939$	−3.12461	+	9.61657i	−0.101968	+	0.313825i
$940$	0.0399263	−	0.379874i	0.00130225	−	0.0123901i
$941$	−1.09464	+	10.4148i	−0.0356841	+	0.339512i	0.962085	+	0.272750i	$0.0879333\pi$
$941$	−1.09464	+	10.4148i	−0.0356841	+	0.339512i	−0.997769	+	0.0667614i	$0.978733\pi$
$942$	5.32624	−	16.3925i	0.173538	−	0.534096i
$943$	−3.07295	−	9.45756i	−0.100069	−	0.307981i
$944$	7.95534	+	3.54195i	0.258924	+	0.115281i
$945$	−3.23607	+	5.60503i	−0.105269	+	0.182332i
$946$	34.1595	−	9.71867i	1.11062	−	0.315981i
$947$	−7.33688	+	12.7079i	−0.238417	+	0.412950i	−0.960260	−	0.279107i	$-0.909962\pi$
$947$	−7.33688	+	12.7079i	−0.238417	+	0.412950i	0.721844	+	0.692056i	$0.243295\pi$
$948$	−0.775226	−	7.37578i	−0.0251782	−	0.239554i
$949$	6.43769	+	19.8132i	0.208976	+	0.643163i
$950$	14.8797	+	15.0425i	0.482762	+	0.488044i
$951$	2.09017	+	1.51860i	0.0677784	+	0.0492439i
$952$	−20.8274	+	9.27293i	−0.675018	+	0.300538i
$953$	−29.8410	−	33.1418i	−0.966646	−	1.07357i	−0.997255	−	0.0740381i	$-0.976411\pi$
$953$	−29.8410	−	33.1418i	−0.966646	−	1.07357i	0.0306090	−	0.999531i	$-0.490255\pi$
$954$	4.52595	−	5.02658i	0.146533	−	0.162742i
$955$	−0.0116503	−	0.110846i	−0.000376996	−	0.00358688i
$956$	12.6631	+	21.9332i	0.409555	+	0.709369i
$957$	−11.3820	+	9.51057i	−0.367927	+	0.307433i
$958$	31.8328			1.02847
$959$	−42.7015	−	19.0119i	−1.37890	−	0.613928i
$960$	−0.511170	+	0.567712i	−0.0164980	+	0.0183228i
$961$	20.4271	−	62.8680i	0.658937	−	2.02800i
$962$	−5.07295	−	3.68571i	−0.163558	−	0.118832i
$963$	−0.636596	+	6.05681i	−0.0205140	+	0.195178i
$964$	−3.56395	−	3.95817i	−0.114787	−	0.127484i
$965$	−2.15111	+	2.38905i	−0.0692466	+	0.0769062i
$966$	0.885579	+	8.42572i	0.0284930	+	0.271093i
$967$	12.0172	−	20.8144i	0.386448	−	0.669347i	−0.605521	−	0.795829i	$-0.707035\pi$
$967$	12.0172	−	20.8144i	0.386448	−	0.669347i	0.991969	+	0.126482i	$0.0403686\pi$
$968$	10.8992	−	1.48584i	0.350313	−	0.0477567i
$969$	46.8673	−	2.20059i	1.50559	−	0.0706931i
$970$	−5.00000	+	3.63271i	−0.160540	+	0.116639i
$971$	−3.93341	−	0.836072i	−0.126229	−	0.0268308i	0.144364	−	0.989525i	$-0.453886\pi$
$971$	−3.93341	−	0.836072i	−0.126229	−	0.0268308i	−0.270593	+	0.962694i	$0.587220\pi$
$972$	−6.69131	−	7.43145i	−0.214624	−	0.238364i
$973$	4.61228	−	43.8829i	0.147863	−	1.40682i
$974$	12.8405	−	5.71698i	0.411438	−	0.183184i
$975$	−17.6067	+	3.74241i	−0.563864	+	0.119853i
$976$	−2.20820	−	6.79615i	−0.0706829	−	0.217540i
$977$	−17.1180	+	12.4370i	−0.547654	+	0.397894i	−0.826920	−	0.562320i	$-0.809909\pi$
$977$	−17.1180	+	12.4370i	−0.547654	+	0.397894i	0.279265	+	0.960214i	$0.409909\pi$
$978$	4.94427	+	8.56373i	0.158100	+	0.273838i
$979$	45.8051	+	16.7790i	1.46394	+	0.536260i
$980$	−4.18034			−0.133536
$981$	−6.39919	+	4.64928i	−0.204310	+	0.148440i
$982$	7.44382	−	8.26720i	0.237542	−	0.263817i
$983$	−29.3299	−	32.5741i	−0.935478	−	1.03895i	−0.999160	−	0.0409832i	$-0.986951\pi$
$983$	−29.3299	−	32.5741i	−0.935478	−	1.03895i	0.0636820	−	0.997970i	$-0.479716\pi$
$984$	−2.07892	+	19.7796i	−0.0662735	+	0.630550i
$985$	−8.91980	+	3.97135i	−0.284208	+	0.126538i
$986$	−8.05261	−	8.94333i	−0.256447	−	0.284814i
$987$	2.61803	+	8.05748i	0.0833329	+	0.256472i
$988$	7.52918	+	2.93728i	0.239535	+	0.0934474i
$989$	10.7082			0.340501
$990$	−0.909465	−	0.881902i	−0.0289047	−	0.0280287i
$991$	−1.13525	+	1.96632i	−0.0360626	+	0.0624622i	−0.883493	−	0.468444i	$-0.844815\pi$
$991$	−1.13525	+	1.96632i	−0.0360626	+	0.0624622i	0.847431	+	0.530906i	$0.178148\pi$
$992$	9.00217	+	4.00802i	0.285819	+	0.127255i
$993$	−23.5429	−	5.00420i	−0.747112	−	0.158804i
$994$	26.2128	−	5.57170i	0.831418	−	0.176723i
$995$	6.44427	+	4.68204i	0.204297	+	0.148431i
$996$	−18.5623	−	13.4863i	−0.588169	−	0.427330i
$997$	1.81359	−	0.385489i	0.0574368	−	0.0122086i	−0.179104	−	0.983830i	$-0.557320\pi$
$997$	1.81359	−	0.385489i	0.0574368	−	0.0122086i	0.236540	+	0.971622i	$0.423986\pi$
$998$	28.2099	−	31.3303i	0.892969	−	0.991743i
$999$	−10.9443	+	7.95148i	−0.346261	+	0.251574i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.c.201.1	yes	8
11.4	even	5	inner	418.2.n.c.125.1	✓	8
19.7	even	3	inner	418.2.n.c.311.1	yes	8
209.26	even	15	inner	418.2.n.c.235.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.c.125.1	✓	8	11.4	even	5	inner
418.2.n.c.201.1	yes	8	1.1	even	1	trivial
418.2.n.c.235.1	yes	8	209.26	even	15	inner
418.2.n.c.311.1	yes	8	19.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.104528 - 0.994522i) q^{2} +(-1.95630 - 0.415823i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.348943 + 0.155360i) q^{5} +(-0.209057 + 1.98904i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +O(q^{10})\)	\(q+(-0.104528 - 0.994522i) q^{2} +(-1.95630 - 0.415823i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(-0.348943 + 0.155360i) q^{5} +(-0.209057 + 1.98904i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(0.913545 + 0.406737i) q^{9} +(0.190983 + 0.330792i) q^{10} +(-2.54508 + 2.12663i) q^{11} +2.00000 q^{12} +(-1.69381 - 0.754131i) q^{13} +(-4.14350 - 0.880728i) q^{14} +(0.747238 - 0.158830i) q^{15} +(0.913545 - 0.406737i) q^{16} +(-4.91667 + 2.18904i) q^{17} +(0.309017 - 0.951057i) q^{18} +(4.30146 + 0.705295i) q^{19} +(0.309017 - 0.224514i) q^{20} +(-4.23607 + 7.33708i) q^{21} +(2.38101 + 2.30885i) q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.209057 - 1.98904i) q^{24} +(-3.24803 + 3.60730i) q^{25} +(-0.572949 + 1.76336i) q^{26} +(3.23607 + 2.35114i) q^{27} +(-0.442790 + 4.21286i) q^{28} +(-2.18720 + 0.464905i) q^{29} +(-0.236068 - 0.726543i) q^{30} +(-7.97214 + 5.79210i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(5.86324 - 3.10200i) q^{33} +(2.69098 + 4.66092i) q^{34} +(0.169131 + 1.60917i) q^{35} +(-0.978148 - 0.207912i) q^{36} +(-1.04508 + 3.21644i) q^{37} +(0.251807 - 4.35162i) q^{38} +(3.00000 + 2.17963i) q^{39} +(-0.255585 - 0.283856i) q^{40} +(-9.72697 - 2.06753i) q^{41} +(7.73968 + 3.44593i) q^{42} +(5.35410 - 9.27358i) q^{43} +(2.04732 - 2.60931i) q^{44} -0.381966 q^{45} +(0.809017 - 0.587785i) q^{46} +(0.669131 - 0.743145i) q^{47} +(-1.95630 + 0.415823i) q^{48} +(-8.85410 - 6.43288i) q^{49} +(3.92705 + 2.85317i) q^{50} +(10.5287 - 2.23795i) q^{51} +(1.81359 + 0.385489i) q^{52} +(6.17916 + 2.75114i) q^{53} +(2.00000 - 3.46410i) q^{54} +(0.557699 - 1.13748i) q^{55} +4.23607 q^{56} +(-8.12165 - 3.16841i) q^{57} +(0.690983 + 2.12663i) q^{58} +(5.82693 + 6.47146i) q^{59} +(-0.697887 + 0.310719i) q^{60} +(0.746950 - 7.10675i) q^{61} +(6.59368 + 7.32302i) q^{62} +(2.83448 - 3.14801i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.708204 q^{65} +(-3.69789 - 5.50687i) q^{66} +(-6.16312 - 10.6748i) q^{67} +(4.35410 - 3.16344i) q^{68} +(-0.618034 - 1.90211i) q^{69} +(1.58268 - 0.336408i) q^{70} +(-5.77931 + 2.57311i) q^{71} +(-0.104528 + 0.994522i) q^{72} +(-7.51840 - 8.35003i) q^{73} +(3.30806 + 0.703150i) q^{74} +(7.85410 - 5.70634i) q^{75} +(-4.35410 + 0.204441i) q^{76} +(5.23607 + 13.0373i) q^{77} +(1.85410 - 3.21140i) q^{78} +(-0.387613 - 3.68789i) q^{79} +(-0.255585 + 0.283856i) q^{80} +(-7.36044 - 8.17459i) q^{81} +(-1.03946 + 9.88980i) q^{82} +(-9.28115 - 6.74315i) q^{83} +(2.61803 - 8.05748i) q^{84} +(1.37555 - 1.52770i) q^{85} +(-9.78243 - 4.35542i) q^{86} +4.47214 q^{87} +(-2.80902 - 1.76336i) q^{88} +(-7.35410 - 12.7377i) q^{89} +(0.0399263 + 0.379874i) q^{90} +(-5.25542 + 5.83674i) q^{91} +(-0.669131 - 0.743145i) q^{92} +(18.0043 - 8.01605i) q^{93} +(-0.809017 - 0.587785i) q^{94} +(-1.61054 + 0.422165i) q^{95} +(0.618034 + 1.90211i) q^{96} +(1.69131 + 16.0917i) q^{97} +(-5.47214 + 9.47802i) q^{98} +(-3.19003 + 0.907591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9	\( 8 q + q^{2} + 2 q^{3} + q^{4} + q^{5} + 2 q^{6} + 6 q^{7} - 2 q^{8} + q^{9} + 6 q^{10} + 2 q^{11} + 16 q^{12} - 6 q^{13} - 3 q^{14} - 8 q^{15} + q^{16} - 4 q^{17} - 2 q^{18} - 4 q^{19} - 2 q^{20} - 16 q^{21} - q^{22} + 4 q^{23} + 2 q^{24} + 6 q^{25} - 18 q^{26} + 8 q^{27} + 7 q^{28} - 5 q^{29} + 16 q^{30} - 28 q^{31} - 4 q^{32} + 18 q^{33} + 26 q^{34} - 3 q^{35} + q^{36} + 14 q^{37} - 13 q^{38} + 24 q^{39} - 4 q^{40} - 19 q^{41} + 14 q^{42} + 16 q^{43} + 4 q^{44} - 12 q^{45} + 2 q^{46} + q^{47} + 2 q^{48} - 44 q^{49} + 18 q^{50} - 18 q^{51} + 9 q^{52} + 4 q^{53} + 16 q^{54} + 14 q^{55} + 16 q^{56} - 26 q^{57} + 10 q^{58} - 13 q^{59} + 2 q^{60} - 3 q^{61} - q^{62} - 3 q^{63} - 2 q^{64} - 48 q^{65} - 22 q^{66} - 18 q^{67} + 8 q^{68} + 4 q^{69} + 2 q^{70} - 16 q^{71} + q^{72} - 4 q^{73} - 7 q^{74} + 36 q^{75} - 8 q^{76} + 24 q^{77} - 12 q^{78} + 12 q^{79} - 4 q^{80} - 11 q^{81} + 21 q^{82} - 34 q^{83} + 12 q^{84} + 31 q^{85} - 19 q^{86} - 18 q^{88} - 32 q^{89} + q^{90} + 3 q^{91} - q^{92} + 28 q^{93} - 2 q^{94} - 38 q^{95} - 4 q^{96} - 30 q^{97} - 8 q^{98} - q^{99}+O(q^{100}) \) 8 * q + q^2 + 2 * q^3 + q^4 + q^5 + 2 * q^6 + 6 * q^7 - 2 * q^8 + q^9 + 6 * q^10 + 2 * q^11 + 16 * q^12 - 6 * q^13 - 3 * q^14 - 8 * q^15 + q^16 - 4 * q^17 - 2 * q^18 - 4 * q^19 - 2 * q^20 - 16 * q^21 - q^22 + 4 * q^23 + 2 * q^24 + 6 * q^25 - 18 * q^26 + 8 * q^27 + 7 * q^28 - 5 * q^29 + 16 * q^30 - 28 * q^31 - 4 * q^32 + 18 * q^33 + 26 * q^34 - 3 * q^35 + q^36 + 14 * q^37 - 13 * q^38 + 24 * q^39 - 4 * q^40 - 19 * q^41 + 14 * q^42 + 16 * q^43 + 4 * q^44 - 12 * q^45 + 2 * q^46 + q^47 + 2 * q^48 - 44 * q^49 + 18 * q^50 - 18 * q^51 + 9 * q^52 + 4 * q^53 + 16 * q^54 + 14 * q^55 + 16 * q^56 - 26 * q^57 + 10 * q^58 - 13 * q^59 + 2 * q^60 - 3 * q^61 - q^62 - 3 * q^63 - 2 * q^64 - 48 * q^65 - 22 * q^66 - 18 * q^67 + 8 * q^68 + 4 * q^69 + 2 * q^70 - 16 * q^71 + q^72 - 4 * q^73 - 7 * q^74 + 36 * q^75 - 8 * q^76 + 24 * q^77 - 12 * q^78 + 12 * q^79 - 4 * q^80 - 11 * q^81 + 21 * q^82 - 34 * q^83 + 12 * q^84 + 31 * q^85 - 19 * q^86 - 18 * q^88 - 32 * q^89 + q^90 + 3 * q^91 - q^92 + 28 * q^93 - 2 * q^94 - 38 * q^95 - 4 * q^96 - 30 * q^97 - 8 * q^98 - q^99

Introduction

L-functions

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