LMFDB - Embedded newform 418.2.n.c.311.1

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			311.1
Root			$-0.104528 - 0.994522i$ of defining polynomial
Character	$\chi$	$=$	418.311
Dual form			418.2.n.c.125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.913545 + 0.406737i) q^{2} +(1.33826 - 1.48629i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.0399263 - 0.379874i) q^{5} +(1.82709 - 0.813473i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(0.913545 + 0.406737i) q^{2} +(1.33826 - 1.48629i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.0399263 - 0.379874i) q^{5} +(1.82709 - 0.813473i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.190983 - 0.330792i) q^{10} +(-2.54508 + 2.12663i) q^{11} +2.00000 q^{12} +(0.193806 + 1.84395i) q^{13} +(2.83448 - 3.14801i) q^{14} +(-0.511170 - 0.567712i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(0.562569 - 5.35248i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-3.06539 + 3.09893i) q^{19} +(0.309017 - 0.224514i) q^{20} +(-4.23607 - 7.33708i) q^{21} +(-3.19003 + 0.907591i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.82709 + 0.813473i) q^{24} +(4.74803 + 1.00922i) q^{25} +(-0.572949 + 1.76336i) q^{26} +(3.23607 + 2.35114i) q^{27} +(3.86984 - 1.72296i) q^{28} +(1.49622 + 1.66172i) q^{29} +(-0.236068 - 0.726543i) q^{30} +(-7.97214 + 5.79210i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.245205 + 6.62872i) q^{33} +(2.69098 - 4.66092i) q^{34} +(-1.47815 - 0.658114i) q^{35} +(0.669131 - 0.743145i) q^{36} +(-1.04508 + 3.21644i) q^{37} +(-4.06082 + 1.58421i) q^{38} +(3.00000 + 2.17963i) q^{39} +(0.373619 - 0.0794152i) q^{40} +(6.65402 - 7.39003i) q^{41} +(-0.885579 - 8.42572i) q^{42} +(5.35410 + 9.27358i) q^{43} +(-3.28339 - 0.468375i) q^{44} -0.381966 q^{45} +(0.809017 - 0.587785i) q^{46} +(-0.978148 - 0.207912i) q^{47} +(1.33826 + 1.48629i) q^{48} +(-8.85410 - 6.43288i) q^{49} +(3.92705 + 2.85317i) q^{50} +(-7.20248 - 7.99916i) q^{51} +(-1.24064 + 1.37787i) q^{52} +(-0.707023 - 6.72688i) q^{53} +(2.00000 + 3.46410i) q^{54} +(0.706234 + 1.05172i) q^{55} +4.23607 q^{56} +(0.503613 + 8.70324i) q^{57} +(0.690983 + 2.12663i) q^{58} +(-8.51791 + 1.81054i) q^{59} +(0.0798526 - 0.759747i) q^{60} +(-6.52810 + 2.90650i) q^{61} +(-9.63877 + 2.04878i) q^{62} +(-4.14350 - 0.880728i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.708204 q^{65} +(-2.92015 + 5.95590i) q^{66} +(-6.16312 + 10.6748i) q^{67} +(4.35410 - 3.16344i) q^{68} +(-0.618034 - 1.90211i) q^{69} +(-1.08268 - 1.20243i) q^{70} +(0.661272 - 6.29158i) q^{71} +(0.913545 - 0.406737i) q^{72} +(10.9905 - 2.33611i) q^{73} +(-2.26298 + 2.51329i) 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} +(3.38761 + 1.50826i) q^{79} +(0.373619 + 0.0794152i) q^{80} +(10.7596 - 2.28703i) q^{81} +(9.08454 - 4.04470i) q^{82} +(-9.28115 - 6.74315i) q^{83} +(2.61803 - 8.05748i) q^{84} +(-2.01081 - 0.427410i) q^{85} +(1.11931 + 10.6495i) q^{86} +4.47214 q^{87} +(-2.80902 - 1.76336i) q^{88} +(-7.35410 + 12.7377i) q^{89} +(-0.348943 - 0.155360i) q^{90} +(7.68247 + 1.63296i) q^{91} +(0.978148 - 0.207912i) q^{92} +(-2.06007 + 19.6002i) q^{93} +(-0.809017 - 0.587785i) q^{94} +(1.05481 + 1.28819i) q^{95} +(0.618034 + 1.90211i) q^{96} +(-14.7815 - 6.58114i) q^{97} +(-5.47214 - 9.47802i) q^{98} +(2.38101 + 2.30885i) 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 $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$2$	0.913545	+	0.406737i	0.645974	+	0.287606i
$3$	1.33826	−	1.48629i	0.772645	−	0.858110i	−0.220452	−	0.975398i	$-0.570753\pi$
$3$	1.33826	−	1.48629i	0.772645	−	0.858110i	0.993098	+	0.117288i	$0.0374201\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.0399263	−	0.379874i	0.0178556	−	0.169885i	−0.981960	−	0.189089i	$-0.939447\pi$
$5$	0.0399263	−	0.379874i	0.0178556	−	0.169885i	0.999816	+	0.0192042i	$0.00611326\pi$
$6$	1.82709	−	0.813473i	0.745907	−	0.332099i
$7$	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
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	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
$13$	0.193806	+	1.84395i	0.0537522	+	0.511418i	0.987962	+	0.154695i	$0.0494395\pi$
$13$	0.193806	+	1.84395i	0.0537522	+	0.511418i	−0.934210	+	0.356723i	$0.883894\pi$
$14$	2.83448	−	3.14801i	0.757547	−	0.841342i
$15$	−0.511170	−	0.567712i	−0.131984	−	0.146583i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	0.562569	−	5.35248i	0.136443	−	1.29817i	−0.685280	−	0.728280i	$-0.740320\pi$
$17$	0.562569	−	5.35248i	0.136443	−	1.29817i	0.821723	−	0.569888i	$-0.193013\pi$
$18$	0.309017	−	0.951057i	0.0728360	−	0.224166i
$19$	−3.06539	+	3.09893i	−0.703249	+	0.710943i
$19$	−3.06539	+	3.09893i	−0.703249	+	0.710943i
$20$	0.309017	−	0.224514i	0.0690983	−	0.0502029i
$21$	−4.23607	−	7.33708i	−0.924386	−	1.60108i
$22$	−3.19003	+	0.907591i	−0.680116	+	0.193499i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	1.82709	+	0.813473i	0.372953	+	0.166050i
$25$	4.74803	+	1.00922i	0.949606	+	0.201845i
$26$	−0.572949	+	1.76336i	−0.112365	+	0.345823i
$27$	3.23607	+	2.35114i	0.622782	+	0.452477i
$28$	3.86984	−	1.72296i	0.731331	−	0.325610i
$29$	1.49622	+	1.66172i	0.277841	+	0.308574i	0.865873	−	0.500264i	$-0.166764\pi$
$29$	1.49622	+	1.66172i	0.277841	+	0.308574i	−0.588032	+	0.808838i	$0.700097\pi$
$30$	−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
$33$	−0.245205	+	6.62872i	−0.0426847	+	1.15391i
$34$	2.69098	−	4.66092i	0.461500	−	0.799341i
$35$	−1.47815	−	0.658114i	−0.249853	−	0.111242i
$36$	0.669131	−	0.743145i	0.111522	−	0.123857i
$37$	−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	$0.189670\pi$
$38$	−4.06082	+	1.58421i	−0.658753	+	0.256992i
$39$	3.00000	+	2.17963i	0.480384	+	0.349020i
$40$	0.373619	−	0.0794152i	0.0590744	−	0.0125566i
$41$	6.65402	−	7.39003i	1.03918	−	1.15413i	0.0513388	−	0.998681i	$-0.483651\pi$
$41$	6.65402	−	7.39003i	1.03918	−	1.15413i	0.987844	−	0.155448i	$-0.0496822\pi$
$42$	−0.885579	−	8.42572i	−0.136648	−	1.30012i
$43$	5.35410	+	9.27358i	0.816493	+	1.41421i	0.908251	+	0.418426i	$0.137418\pi$
$43$	5.35410	+	9.27358i	0.816493	+	1.41421i	−0.0917581	+	0.995781i	$0.529249\pi$
$44$	−3.28339	−	0.468375i	−0.494989	−	0.0706103i
$45$	−0.381966			−0.0569401
$46$	0.809017	−	0.587785i	0.119283	−	0.0866642i
$47$	−0.978148	−	0.207912i	−0.142677	−	0.0303270i	0.136019	−	0.990706i	$-0.456569\pi$
$47$	−0.978148	−	0.207912i	−0.142677	−	0.0303270i	−0.278697	+	0.960379i	$0.589902\pi$
$48$	1.33826	+	1.48629i	0.193161	+	0.214527i
$49$	−8.85410	−	6.43288i	−1.26487	−	0.918983i
$50$	3.92705	+	2.85317i	0.555369	+	0.403499i
$51$	−7.20248	−	7.99916i	−1.00855	−	1.12011i
$52$	−1.24064	+	1.37787i	−0.172045	+	0.191076i
$53$	−0.707023	−	6.72688i	−0.0971171	−	0.924008i	−0.929255	−	0.369439i	$-0.879550\pi$
$53$	−0.707023	−	6.72688i	−0.0971171	−	0.924008i	0.832138	−	0.554569i	$-0.187117\pi$
$54$	2.00000	+	3.46410i	0.272166	+	0.471405i
$55$	0.706234	+	1.05172i	0.0952285	+	0.141814i
$56$	4.23607			0.566068
$57$	0.503613	+	8.70324i	0.0667052	+	1.15277i
$58$	0.690983	+	2.12663i	0.0907305	+	0.279240i
$59$	−8.51791	+	1.81054i	−1.10894	+	0.235712i	−0.725750	−	0.687959i	$-0.758507\pi$
$59$	−8.51791	+	1.81054i	−1.10894	+	0.235712i	−0.383187	+	0.923671i	$0.625174\pi$
$60$	0.0798526	−	0.759747i	0.0103089	−	0.0980829i
$61$	−6.52810	+	2.90650i	−0.835838	+	0.372139i	−0.779600	−	0.626278i	$-0.784577\pi$
$61$	−6.52810	+	2.90650i	−0.835838	+	0.372139i	−0.0562384	+	0.998417i	$0.517911\pi$
$62$	−9.63877	+	2.04878i	−1.22412	+	0.260196i
$63$	−4.14350	−	0.880728i	−0.522032	−	0.110961i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	0.708204			0.0878419
$66$	−2.92015	+	5.95590i	−0.359445	+	0.733121i
$67$	−6.16312	+	10.6748i	−0.752945	+	1.30414i	0.193445	+	0.981111i	$0.438034\pi$
$67$	−6.16312	+	10.6748i	−0.752945	+	1.30414i	−0.946390	+	0.323028i	$0.895299\pi$
$68$	4.35410	−	3.16344i	0.528012	−	0.383623i
$69$	−0.618034	−	1.90211i	−0.0744025	−	0.228988i
$70$	−1.08268	−	1.20243i	−0.129405	−	0.143718i
$71$	0.661272	−	6.29158i	0.0784785	−	0.746673i	−0.882549	−	0.470221i	$-0.844174\pi$
$71$	0.661272	−	6.29158i	0.0784785	−	0.746673i	0.961027	−	0.276453i	$-0.0891590\pi$
$72$	0.913545	−	0.406737i	0.107662	−	0.0479344i
$73$	10.9905	−	2.33611i	1.28634	−	0.273421i	0.486528	−	0.873665i	$-0.338263\pi$
$73$	10.9905	−	2.33611i	1.28634	−	0.273421i	0.799817	+	0.600244i	$0.204930\pi$
$74$	−2.26298	+	2.51329i	−0.263066	+	0.292164i
$75$	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
$79$	3.38761	+	1.50826i	0.381136	+	0.169693i	0.588357	−	0.808601i	$-0.299775\pi$
$79$	3.38761	+	1.50826i	0.381136	+	0.169693i	−0.207221	+	0.978294i	$0.566442\pi$
$80$	0.373619	+	0.0794152i	0.0417719	+	0.00887889i
$81$	10.7596	−	2.28703i	1.19551	−	0.254114i
$82$	9.08454	−	4.04470i	1.00322	−	0.446662i
$83$	−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
$85$	−2.01081	−	0.427410i	−0.218102	−	0.0463591i
$86$	1.11931	+	10.6495i	0.120699	+	1.14837i
$87$	4.47214			0.479463
$88$	−2.80902	−	1.76336i	−0.299442	−	0.187974i
$89$	−7.35410	+	12.7377i	−0.779533	+	1.35019i	0.152678	+	0.988276i	$0.451210\pi$
$89$	−7.35410	+	12.7377i	−0.779533	+	1.35019i	−0.932211	+	0.361915i	$0.882123\pi$
$90$	−0.348943	−	0.155360i	−0.0367819	−	0.0163763i
$91$	7.68247	+	1.63296i	0.805342	+	0.171181i
$92$	0.978148	−	0.207912i	0.101979	−	0.0216763i
$93$	−2.06007	+	19.6002i	−0.213619	+	2.03245i
$94$	−0.809017	−	0.587785i	−0.0834437	−	0.0606254i
$95$	1.05481	+	1.28819i	0.108221	+	0.132166i
$96$	0.618034	+	1.90211i	0.0630778	+	0.194134i
$97$	−14.7815	−	6.58114i	−1.50083	−	0.668213i	−0.518451	−	0.855107i	$-0.673491\pi$
$97$	−14.7815	−	6.58114i	−1.50083	−	0.668213i	−0.982380	+	0.186894i	$0.940158\pi$
$98$	−5.47214	−	9.47802i	−0.552769	−	0.957424i
$99$	2.38101	+	2.30885i	0.239301	+	0.232048i
$100$	2.42705	+	4.20378i	0.242705	+	0.420378i
$101$	−0.288910	−	2.74879i	−0.0287476	−	0.273515i	−0.999448	−	0.0332220i	$-0.989423\pi$
$101$	−0.288910	−	2.74879i	−0.0287476	−	0.273515i	0.970700	−	0.240293i	$-0.0772435\pi$
$102$	−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	$-0.0452529\pi$
$104$	−1.69381	+	0.754131i	−0.166091	+	0.0739486i
$105$	−2.95630	+	1.31623i	−0.288505	+	0.128451i
$106$	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	$0.804887\pi$
$108$	0.418114	+	3.97809i	0.0402330	+	0.382792i
$109$	−3.95492	−	6.85011i	−0.378812	−	0.656122i	0.612078	−	0.790798i	$-0.290334\pi$
$109$	−3.95492	−	6.85011i	−0.378812	−	0.656122i	−0.990890	+	0.134676i	$0.957001\pi$
$110$	0.217404	+	1.24804i	0.0207286	+	0.118996i
$111$	3.38197	+	5.85774i	0.321002	+	0.555992i
$112$	3.86984	+	1.72296i	0.365666	+	0.162805i
$113$	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	$0.726298\pi$
$114$	−3.07985	+	8.15564i	−0.288455	+	0.763846i
$115$	−0.309017	−	0.224514i	−0.0288160	−	0.0209360i
$116$	−0.233733	+	2.22382i	−0.0217015	+	0.206476i
$117$	1.81359	−	0.385489i	0.167666	−	0.0356385i
$118$	−8.51791	−	1.81054i	−0.784137	−	0.166673i
$119$	−20.8274	−	9.27293i	−1.90924	−	0.850048i
$120$	0.381966	−	0.661585i	0.0348686	−	0.0603941i
$121$	1.95492	−	10.8249i	0.177720	−	0.984081i
$122$	−7.14590			−0.646959
$123$	−2.07892	−	19.7796i	−0.187450	−	1.78347i
$124$	−9.63877	−	2.04878i	−0.865587	−	0.183986i
$125$	1.16312	−	3.57971i	0.104033	−	0.320179i
$126$	−3.42705	−	2.48990i	−0.305306	−	0.221818i
$127$	−0.513692	+	0.228710i	−0.0455828	+	0.0202948i	−0.429401	−	0.903114i	$-0.641275\pi$
$127$	−0.513692	+	0.228710i	−0.0455828	+	0.0202948i	0.383819	+	0.923408i	$0.374609\pi$
$128$	−0.978148	+	0.207912i	−0.0864569	+	0.0183770i
$129$	20.9484	+	4.45272i	1.84440	+	0.392040i
$130$	0.646976	+	0.288052i	0.0567436	+	0.0252639i
$131$	−1.73607	−	3.00696i	−0.151681	−	0.262719i	0.780165	−	0.625574i	$-0.215135\pi$
$131$	−1.73607	−	3.00696i	−0.151681	−	0.262719i	−0.931846	+	0.362855i	$0.881802\pi$
$132$	−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
$135$	1.02234	−	1.13542i	0.0879891	−	0.0977218i
$136$	5.26436	−	1.11897i	0.451415	−	0.0959512i
$137$	−10.0805	+	4.48811i	−0.861232	+	0.383445i	−0.789332	−	0.613967i	$-0.789573\pi$
$137$	−10.0805	+	4.48811i	−0.861232	+	0.383445i	−0.0719001	+	0.997412i	$0.522906\pi$
$138$	0.209057	−	1.98904i	0.0177961	−	0.169319i
$139$	−6.96994	−	7.74090i	−0.591182	−	0.656575i	0.371111	−	0.928589i	$-0.378977\pi$
$139$	−6.96994	−	7.74090i	−0.591182	−	0.656575i	−0.962293	+	0.272014i	$0.912310\pi$
$140$	−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
$143$	−4.41464	−	4.28084i	−0.369170	−	0.357982i
$144$	1.00000			0.0833333
$145$	0.690983	−	0.502029i	0.0573830	−	0.0416912i
$146$	10.9905	+	2.33611i	0.909583	+	0.193338i
$147$	−21.4102	+	4.55088i	−1.76589	+	0.375351i
$148$	−3.08958	+	1.37557i	−0.253962	+	0.113071i
$149$	0.950181	−	9.04037i	0.0778419	−	0.740616i	−0.884088	−	0.467320i	$-0.845220\pi$
$149$	0.950181	−	9.04037i	0.0778419	−	0.740616i	0.961930	−	0.273296i	$-0.0881138\pi$
$150$	9.49606	−	2.01845i	0.775350	−	0.164806i
$151$	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	$0.797690\pi$
$152$	−3.89452	−	1.95774i	−0.315887	−	0.158794i
$153$	−5.38197			−0.435106
$154$	−0.519352	+	14.0398i	−0.0418506	+	1.13136i
$155$	1.88197	+	3.25966i	0.151163	+	0.261822i
$156$	0.387613	+	3.68789i	0.0310339	+	0.295268i
$157$	5.76659	−	6.40445i	0.460224	−	0.511131i	−0.467706	−	0.883884i	$-0.654920\pi$
$157$	5.76659	−	6.40445i	0.460224	−	0.511131i	0.927930	+	0.372753i	$0.121586\pi$
$158$	2.48127	+	2.75573i	0.197399	+	0.219234i
$159$	−10.9443	−	7.95148i	−0.867937	−	0.630593i
$160$	0.309017	+	0.224514i	0.0244299	+	0.0177494i
$161$	−2.83448	−	3.14801i	−0.223389	−	0.248098i
$162$	10.7596	+	2.28703i	0.845356	+	0.179686i
$163$	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
$165$	2.50828	+	0.357807i	0.195270	+	0.0278552i
$166$	−5.73607	−	9.93516i	−0.445205	−	0.771118i
$167$	−1.77698	−	16.9069i	−0.137507	−	1.30829i	−0.817864	−	0.575412i	$-0.804842\pi$
$167$	−1.77698	−	16.9069i	−0.137507	−	1.30829i	0.680357	−	0.732881i	$-0.261825\pi$
$168$	5.66897	−	6.29602i	0.437370	−	0.485749i
$169$	9.35335	−	1.98812i	0.719488	−	0.152932i
$170$	−1.66312	−	1.20833i	−0.127555	−	0.0926744i
$171$	3.40238	+	2.72467i	0.260186	+	0.208361i
$172$	−3.30902	+	10.1841i	−0.252310	+	0.776531i
$173$	14.1351	−	15.6986i	1.07467	−	1.19355i	0.0944754	−	0.995527i	$-0.469883\pi$
$173$	14.1351	−	15.6986i	1.07467	−	1.19355i	0.980198	−	0.198019i	$-0.0634507\pi$
$174$	4.08550	+	1.81898i	0.309721	+	0.137897i
$175$	10.2812	−	17.8075i	0.777182	−	1.34612i
$176$	−1.84894	−	2.75344i	−0.139369	−	0.207548i
$177$	−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	$0.920334\pi$
$180$	−0.255585	−	0.283856i	−0.0190502	−	0.0211574i
$181$	9.83334	−	4.37809i	0.730906	−	0.325421i	−0.00732023	−	0.999973i	$-0.502330\pi$
$181$	9.83334	−	4.37809i	0.730906	−	0.325421i	0.738227	+	0.674553i	$0.235663\pi$
$182$	6.35410	+	4.61653i	0.470997	+	0.342200i
$183$	−4.41641	+	13.5923i	−0.326470	+	1.00477i
$184$	0.978148	+	0.207912i	0.0721100	+	0.0153275i
$185$	1.18011	+	0.525421i	0.0867637	+	0.0386297i
$186$	−9.85410	+	17.0678i	−0.722538	+	1.25147i
$187$	9.95095	+	14.8189i	0.727686	+	1.08367i
$188$	−0.500000	−	0.866025i	−0.0364662	−	0.0631614i
$189$	13.7082	−	9.95959i	0.997125	−	0.724454i
$190$	0.439665	+	1.60585i	0.0318966	+	0.116501i
$191$	−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	$0.103360\pi$
$192$	−0.209057	+	1.98904i	−0.0150874	+	0.143547i
$193$	−0.879754	+	8.37030i	−0.0633261	+	0.602508i	0.916134	+	0.400871i	$0.131293\pi$
$193$	−0.879754	+	8.37030i	−0.0633261	+	0.602508i	−0.979460	+	0.201636i	$0.935374\pi$
$194$	−10.8268	−	12.0243i	−0.777316	−	0.863297i
$195$	0.947762	−	1.05260i	0.0678706	−	0.0753780i
$196$	−1.14399	−	10.8843i	−0.0817134	−	0.777451i
$197$	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	0.213723	+	0.976894i	$0.431441\pi$
$199$	−10.4271	+	18.0602i	−0.739154	+	1.28025i	−0.952877	+	0.303358i	$0.901892\pi$
$200$	0.507392	+	4.82751i	0.0358780	+	0.341357i
$201$	7.61803	+	23.4459i	0.537335	+	1.65375i
$202$	0.854102	−	2.62866i	0.0600944	−	0.184952i
$203$	8.65323	−	3.85266i	0.607337	−	0.270404i
$204$	1.12514	−	10.7050i	0.0787754	−	0.749498i
$205$	−2.54161	−	2.82274i	−0.177514	−	0.197149i
$206$	5.98489	−	6.64689i	0.416987	−	0.463111i
$207$	−0.913545	−	0.406737i	−0.0634958	−	0.0282702i
$208$	−1.85410			−0.128559
$209$	1.21141	−	14.4060i	0.0837952	−	0.996483i
$210$	−3.23607			−0.223310
$211$	8.13953	+	3.62395i	0.560349	+	0.249483i	0.667310	−	0.744780i	$-0.267446\pi$
$211$	8.13953	+	3.62395i	0.560349	+	0.249483i	−0.106962	+	0.994263i	$0.534112\pi$
$212$	4.52595	−	5.02658i	0.310844	−	0.345227i
$213$	−8.46616	−	9.40262i	−0.580092	−	0.644257i
$214$	−0.636596	+	6.05681i	−0.0435168	+	0.414035i
$215$	3.73656	−	1.66362i	0.254831	−	0.113458i
$216$	−1.23607	+	3.80423i	−0.0841038	+	0.258845i
$217$	12.8992	+	39.6996i	0.875654	+	2.69499i
$218$	−0.826802	−	7.86650i	−0.0559981	−	0.532787i
$219$	11.2361	−	19.4614i	0.759263	−	1.31508i
$220$	−0.309017	+	1.22857i	−0.0208339	+	0.0828302i
$221$	9.97871			0.671241
$222$	0.707023	+	6.72688i	0.0474523	+	0.451479i
$223$	13.6985	−	15.2138i	0.917322	−	1.01879i	−0.0824321	−	0.996597i	$-0.526269\pi$
$223$	13.6985	−	15.2138i	0.917322	−	1.01879i	0.999754	−	0.0221922i	$-0.00706457\pi$
$224$	2.83448	+	3.14801i	0.189387	+	0.210335i
$225$	0.507392	−	4.82751i	0.0338261	−	0.321834i
$226$	−1.15341	+	10.9740i	−0.0767239	+	0.729979i
$227$	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	$0.0253739\pi$
$228$	−6.13078	+	6.19786i	−0.406021	+	0.410463i
$229$	−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
$231$	26.3844	+	9.66497i	1.73597	+	0.635908i
$232$	−1.11803	+	1.93649i	−0.0734025	+	0.127137i
$233$	−9.26874	−	4.12671i	−0.607215	−	0.270350i	0.0800100	−	0.996794i	$-0.474505\pi$
$233$	−9.26874	−	4.12671i	−0.607215	−	0.270350i	−0.687225	+	0.726444i	$0.741171\pi$
$234$	1.81359	+	0.385489i	0.118558	+	0.0252002i
$235$	−0.118034	+	0.363271i	−0.00769969	+	0.0236972i
$236$	−7.04508	−	5.11855i	−0.458596	−	0.333189i
$237$	6.77523	−	3.01652i	0.440098	−	0.195944i
$238$	−15.2551	−	16.9425i	−0.988841	−	1.09822i
$239$	−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	−0.767414	−	0.641152i	$-0.778457\pi$
$241$	2.66312	−	4.61266i	0.171547	−	0.297127i	0.938961	+	0.344024i	$0.111790\pi$
$242$	6.18878	−	9.09390i	0.397830	−	0.584578i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−6.52810	−	2.90650i	−0.417919	−	0.186070i
$245$	−2.79719	+	3.10660i	−0.178706	+	0.198473i
$246$	6.14590	−	18.9151i	0.391848	−	1.20598i
$247$	−6.30835	−	5.05182i	−0.401391	−	0.321440i
$248$	−7.97214	−	5.79210i	−0.506231	−	0.367798i
$249$	−22.4429	+	4.77038i	−1.42226	+	0.302311i
$250$	2.51856	−	2.79715i	0.159288	−	0.176907i
$251$	2.17985	+	20.7399i	0.137591	+	1.30909i	0.817558	+	0.575846i	$0.195327\pi$
$251$	2.17985	+	20.7399i	0.137591	+	1.30909i	−0.679967	+	0.733242i	$0.738006\pi$
$252$	−2.11803	−	3.66854i	−0.133424	−	0.231096i
$253$	0.569171	+	3.26742i	0.0357834	+	0.205421i
$254$	−0.562306			−0.0352822
$255$	−3.32624	+	2.41665i	−0.208297	+	0.151337i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	9.36783	+	10.4040i	0.584349	+	0.648985i	0.960732	−	0.277479i	$-0.0894989\pi$
$257$	9.36783	+	10.4040i	0.584349	+	0.648985i	−0.376383	+	0.926464i	$0.622832\pi$
$258$	17.3262	+	12.5882i	1.07868	+	0.783710i
$259$	11.5902	+	8.42075i	0.720178	+	0.523240i
$260$	0.473881	+	0.526298i	0.0293888	+	0.0326396i
$261$	1.49622	−	1.66172i	0.0926138	−	0.102858i
$262$	−0.362937	−	3.45312i	−0.0224223	−	0.213334i
$263$	−8.39919	−	14.5478i	−0.517916	−	0.897057i	−0.999783	−	0.0208127i	$-0.993375\pi$
$263$	−8.39919	−	14.5478i	−0.517916	−	0.897057i	0.481867	−	0.876244i	$-0.339959\pi$
$264$	−6.38006	+	1.81518i	−0.392665	+	0.111717i
$265$	−2.58359			−0.158709
$266$	1.06667	+	18.4338i	0.0654017	+	1.13025i
$267$	9.09017	+	27.9767i	0.556309	+	1.71214i
$268$	−12.0569	+	2.56277i	−0.736491	+	0.156546i
$269$	1.60203	−	15.2423i	0.0976774	−	0.929338i	−0.830454	−	0.557087i	$-0.811919\pi$
$269$	1.60203	−	15.2423i	0.0976774	−	0.929338i	0.928132	−	0.372252i	$-0.121414\pi$
$270$	1.39577	−	0.621438i	0.0849441	−	0.0378195i
$271$	−2.56082	+	0.544320i	−0.155559	+	0.0330651i	−0.285033	−	0.958518i	$-0.592005\pi$
$271$	−2.56082	+	0.544320i	−0.155559	+	0.0330651i	0.129474	+	0.991583i	$0.458671\pi$
$272$	5.26436	+	1.11897i	0.319199	+	0.0678477i
$273$	12.7082	−	9.23305i	0.769135	−	0.558810i
$274$	−11.0344			−0.666615
$275$	−14.2304	+	7.52872i	−0.858124	+	0.453999i
$276$	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
$279$	6.59368	+	7.32302i	0.394753	+	0.438418i
$280$	0.169131	−	1.60917i	0.0101075	−	0.0961663i
$281$	−3.25433	+	1.44892i	−0.194137	+	0.0864353i	−0.501503	−	0.865156i	$-0.667219\pi$
$281$	−3.25433	+	1.44892i	−0.194137	+	0.0864353i	0.307366	+	0.951591i	$0.400553\pi$
$282$	−1.95630	+	0.415823i	−0.116496	+	0.0247619i
$283$	10.5481	−	11.7149i	0.627021	−	0.696378i	−0.343017	−	0.939329i	$-0.611449\pi$
$283$	10.5481	−	11.7149i	0.627021	−	0.696378i	0.970038	+	0.242952i	$0.0781156\pi$
$284$	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
$288$	0.913545	+	0.406737i	0.0538312	+	0.0239672i
$289$	−11.7041	−	2.48778i	−0.688475	−	0.146340i
$290$	0.835438	−	0.177578i	0.0490586	−	0.0104277i
$291$	−29.5630	+	13.1623i	−1.73301	+	0.771586i
$292$	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	$0.919199\pi$
$294$	−21.4102	−	4.55088i	−1.24867	−	0.265413i
$295$	0.347687	+	3.30802i	0.0202431	+	0.192600i
$296$	−3.38197			−0.196573
$297$	−13.2361	+	0.898056i	−0.768035	+	0.0521105i
$298$	4.54508	−	7.87232i	0.263290	−	0.456031i
$299$	1.69381	+	0.754131i	0.0979554	+	0.0436125i
$300$	9.49606	+	2.01845i	0.548255	+	0.116535i
$301$	44.3694	−	9.43102i	2.55741	−	0.543595i
$302$	−0.811552	+	7.72140i	−0.0466996	+	0.444317i
$303$	−4.47214	−	3.24920i	−0.256917	−	0.186661i
$304$	−2.76153	−	3.37253i	−0.158385	−	0.193428i
$305$	0.843459	+	2.59590i	0.0482963	+	0.148641i
$306$	−4.91667	−	2.18904i	−0.281067	−	0.125139i
$307$	−4.13525	−	7.16247i	−0.236011	−	0.408784i	0.723555	−	0.690267i	$-0.242507\pi$
$307$	−4.13525	−	7.16247i	−0.236011	−	0.408784i	−0.959566	+	0.281483i	$0.909174\pi$
$308$	−6.18497	+	12.6148i	−0.352421	+	0.718795i
$309$	−8.94427	−	15.4919i	−0.508822	−	0.881305i
$310$	0.393438	+	3.74331i	0.0223458	+	0.212606i
$311$	−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
$313$	−4.61864	+	2.05635i	−0.261061	+	0.116232i	−0.533094	−	0.846056i	$-0.678971\pi$
$313$	−4.61864	+	2.05635i	−0.261061	+	0.116232i	0.272033	+	0.962288i	$0.412304\pi$
$314$	7.87297	−	3.50527i	0.444297	−	0.197814i
$315$	−0.500000	+	1.53884i	−0.0281718	+	0.0867039i
$316$	1.14590	+	3.52671i	0.0644618	+	0.198393i
$317$	0.135029	+	1.28472i	0.00758401	+	0.0721570i	0.997659	−	0.0683811i	$-0.0217834\pi$
$317$	0.135029	+	1.28472i	0.00758401	+	0.0721570i	−0.990075	+	0.140538i	$0.955117\pi$
$318$	−6.76393	−	11.7155i	−0.379302	−	0.656971i
$319$	−7.34187	−	1.04732i	−0.411066	−	0.0586386i
$320$	0.190983	+	0.330792i	0.0106763	+	0.0184919i
$321$	11.1273	+	4.95419i	0.621065	+	0.276516i
$322$	−1.30902	−	4.02874i	−0.0729487	−	0.224513i
$323$	14.8625	+	18.1508i	0.826971	+	1.00994i
$324$	8.89919	+	6.46564i	0.494399	+	0.359202i
$325$	−0.940756	+	8.95070i	−0.0521838	+	0.496495i
$326$	4.83623	−	1.02797i	0.267854	−	0.0569341i
$327$	−15.4740	−	3.28909i	−0.855712	−	0.181887i
$328$	9.08454	+	4.04470i	0.501610	+	0.223331i
$329$	−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	$0.392703\pi$
$332$	−1.19916	−	11.4093i	−0.0658127	−	0.626166i
$333$	3.30806	+	0.703150i	0.181281	+	0.0385324i
$334$	5.25329	−	16.1680i	0.287447	−	0.884671i
$335$	3.80902	+	2.76741i	0.208109	+	0.151200i
$336$	7.73968	−	3.44593i	0.422234	−	0.187991i
$337$	−22.4974	+	4.78197i	−1.22551	+	0.260490i	−0.774816	−	0.632187i	$-0.782157\pi$
$337$	−22.4974	+	4.78197i	−1.22551	+	0.260490i	−0.450696	+	0.892678i	$0.648824\pi$
$338$	9.35335	+	1.98812i	0.508755	+	0.108139i
$339$	20.1609	+	8.97622i	1.09499	+	0.487522i
$340$	−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
$344$	−7.16519	+	7.95775i	−0.386321	+	0.429053i
$345$	−0.747238	+	0.158830i	−0.0402300	+	0.00855114i
$346$	19.2983	−	8.59215i	1.03748	−	0.461917i
$347$	−0.547318	+	5.20738i	−0.0293816	+	0.279547i	0.969960	+	0.243264i	$0.0782183\pi$
$347$	−0.547318	+	5.20738i	−0.0293816	+	0.279547i	−0.999342	+	0.0362825i	$0.988448\pi$
$348$	2.99244	+	3.32344i	0.160412	+	0.178155i
$349$	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
$352$	−0.569171	−	3.26742i	−0.0303369	−	0.174154i
$353$	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
$355$	−2.36360	−	0.502399i	−0.125447	−	0.0266646i
$356$	−14.3868	+	3.05801i	−0.762499	+	0.162074i
$357$	−41.6547	+	18.5459i	−2.20460	+	0.981551i
$358$	0.178556	−	1.69885i	0.00943697	−	0.0897868i
$359$	−22.6738	+	4.81946i	−1.19668	+	0.254362i	−0.762814	−	0.646617i	$-0.776183\pi$
$359$	−22.6738	+	4.81946i	−1.19668	+	0.254362i	−0.433863	+	0.900979i	$0.642850\pi$
$360$	−0.118034	−	0.363271i	−0.00622094	−	0.0191461i
$361$	−0.206743	−	18.9989i	−0.0108812	−	0.999941i
$362$	10.7639			0.565740
$363$	−13.4727	−	17.3921i	−0.707135	−	0.912849i
$364$	3.92705	+	6.80185i	0.205833	+	0.356514i
$365$	−0.448615	−	4.26829i	−0.0234816	−	0.223412i
$366$	−9.56308	+	10.6209i	−0.499870	+	0.555162i
$367$	−18.2102	−	20.2245i	−0.950567	−	1.05571i	−0.998382	−	0.0568554i	$-0.981893\pi$
$367$	−18.2102	−	20.2245i	−0.950567	−	1.05571i	0.0478155	−	0.998856i	$-0.484774\pi$
$368$	0.809017	+	0.587785i	0.0421729	+	0.0306404i
$369$	−8.04508	−	5.84510i	−0.418810	−	0.304284i
$370$	0.864380	+	0.959992i	0.0449370	+	0.0499076i
$371$	−28.0264	−	5.95718i	−1.45506	−	0.309282i
$372$	−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	$0.630182\pi$
$374$	3.06326	+	17.5852i	0.158397	+	0.909307i
$375$	−3.76393	−	6.51932i	−0.194369	−	0.336656i
$376$	−0.104528	−	0.994522i	−0.00539064	−	0.0512886i
$377$	−2.77415	+	3.08100i	−0.142876	+	0.158680i
$378$	16.5740	−	3.52291i	0.852475	−	0.181199i
$379$	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	$0.562272\pi$
$380$	−0.251505	+	1.64585i	−0.0129019	+	0.0844301i
$381$	−0.347524	+	1.06957i	−0.0178042	+	0.0547957i
$382$	−0.195250	+	0.216847i	−0.00998984	+	0.0110948i
$383$	23.0543	+	10.2644i	1.17802	+	0.524488i	0.899916	−	0.436063i	$-0.143628\pi$
$383$	23.0543	+	10.2644i	1.17802	+	0.524488i	0.278103	+	0.960551i	$0.410294\pi$
$384$	−1.00000	+	1.73205i	−0.0510310	+	0.0883883i
$385$	5.16157	−	1.46851i	0.263058	−	0.0748424i
$386$	−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
$389$	−9.23291	−	10.2542i	−0.468127	−	0.519908i	0.462132	−	0.886811i	$-0.347085\pi$
$389$	−9.23291	−	10.2542i	−0.468127	−	0.519908i	−0.930259	+	0.366903i	$0.880418\pi$
$390$	1.29395	−	0.576105i	0.0655219	−	0.0291722i
$391$	−4.35410	−	3.16344i	−0.220196	−	0.159982i
$392$	3.38197	−	10.4086i	0.170815	−	0.525715i
$393$	−6.79252	−	1.44380i	−0.342637	−	0.0728298i
$394$	23.3523	+	10.3971i	1.17647	+	0.523800i
$395$	0.708204	−	1.22665i	0.0356336	−	0.0617192i
$396$	−0.122602	+	3.31436i	−0.00616100	+	0.166553i
$397$	0.527864	+	0.914287i	0.0264927	+	0.0458868i	0.878968	−	0.476881i	$-0.158233\pi$
$397$	0.527864	+	0.914287i	0.0264927	+	0.0458868i	−0.852475	+	0.522768i	$0.824899\pi$
$398$	−16.8713	+	12.2577i	−0.845683	+	0.614425i
$399$	35.7223	+	9.36376i	1.78835	+	0.468774i
$400$	−1.50000	+	4.61653i	−0.0750000	+	0.230826i
$401$	−1.98022	+	18.8405i	−0.0988872	+	0.940849i	0.826784	+	0.562520i	$0.190168\pi$
$401$	−1.98022	+	18.8405i	−0.0988872	+	0.940849i	−0.925671	+	0.378329i	$0.876499\pi$
$402$	−2.57689	+	24.5174i	−0.128523	+	1.22282i
$403$	−12.2254	−	13.5776i	−0.608988	−	0.676350i
$404$	1.84943	−	2.05400i	0.0920127	−	0.102190i
$405$	−0.439190	−	4.17861i	−0.0218235	−	0.207637i
$406$	9.47214			0.470094
$407$	−4.18034	−	10.4086i	−0.207212	−	0.515936i
$408$	5.38197	−	9.32184i	0.266447	−	0.461500i
$409$	2.35840	+	22.4387i	0.116616	+	1.10952i	0.883725	+	0.468006i	$0.155028\pi$
$409$	2.35840	+	22.4387i	0.116616	+	1.10952i	−0.767110	+	0.641516i	$0.778306\pi$
$410$	−1.17376	−	3.61247i	−0.0579680	−	0.178407i
$411$	−6.81966	+	20.9888i	−0.336389	+	1.03530i
$412$	8.17100	−	3.63796i	0.402556	−	0.179230i
$413$	−3.85590	+	36.6865i	−0.189737	+	1.80522i
$414$	−0.669131	−	0.743145i	−0.0328860	−	0.0365236i
$415$	−2.93211	+	3.25644i	−0.143931	+	0.159852i
$416$	−1.69381	−	0.754131i	−0.0830457	−	0.0369743i
$417$	−20.8328			−1.02019
$418$	6.96612	−	12.6678i	0.340724	−	0.619602i
$419$	−33.6525			−1.64403			−0.822016	−	0.569465i	$-0.807150\pi$
$419$	−33.6525			−1.64403			−0.822016	+	0.569465i	$0.807150\pi$
$420$	−2.95630	−	1.31623i	−0.144252	−	0.0642253i
$421$	1.69147	−	1.87857i	0.0824373	−	0.0915559i	−0.700515	−	0.713638i	$-0.747046\pi$
$421$	1.69147	−	1.87857i	0.0824373	−	0.0915559i	0.782952	+	0.622082i	$0.213713\pi$
$422$	5.96184	+	6.62129i	0.290218	+	0.322320i
$423$	−0.104528	+	0.994522i	−0.00508235	+	0.0483553i
$424$	6.17916	−	2.75114i	0.300087	−	0.133607i
$425$	8.07295	−	24.8460i	0.391596	−	1.20521i
$426$	−3.90983	−	12.0332i	−0.189432	−	0.583011i
$427$	3.16413	+	30.1047i	0.153123	+	1.45687i
$428$	−3.04508	+	5.27424i	−0.147190	+	0.254940i
$429$	−12.2705	+	0.832544i	−0.592426	+	0.0401956i
$430$	4.09017			0.197246
$431$	2.24445	+	21.3545i	0.108111	+	1.02861i	0.905269	+	0.424839i	$0.139669\pi$
$431$	2.24445	+	21.3545i	0.108111	+	1.02861i	−0.797158	+	0.603771i	$0.793664\pi$
$432$	−2.67652	+	2.97258i	−0.128774	+	0.143018i
$433$	−1.78910	−	1.98699i	−0.0859785	−	0.0954888i	0.698620	−	0.715493i	$-0.253798\pi$
$433$	−1.78910	−	1.98699i	−0.0859785	−	0.0954888i	−0.784599	+	0.620004i	$0.787131\pi$
$434$	−4.36329	+	41.5140i	−0.209445	+	1.99273i
$435$	0.178556	−	1.69885i	0.00856110	−	0.0814534i
$436$	2.44427	−	7.52270i	0.117059	−	0.360272i
$437$	1.15106	+	4.20417i	0.0550625	+	0.201113i
$438$	18.1803	−	13.2088i	0.868690	−	0.631140i
$439$	17.9164	+	31.0321i	0.855103	+	1.48108i	0.876549	+	0.481313i	$0.159840\pi$
$439$	17.9164	+	31.0321i	0.855103	+	1.48108i	−0.0214455	+	0.999770i	$0.506827\pi$
$440$	−0.782006	+	0.996667i	−0.0372807	+	0.0475142i
$441$	−5.47214	+	9.47802i	−0.260578	+	0.451334i
$442$	9.11601	+	4.05871i	0.433604	+	0.193053i
$443$	−11.9479	−	2.53960i	−0.567660	−	0.120660i	−0.0848637	−	0.996393i	$-0.527045\pi$
$443$	−11.9479	−	2.53960i	−0.567660	−	0.120660i	−0.482796	+	0.875733i	$0.660379\pi$
$444$	−2.09017	+	6.43288i	−0.0991951	+	0.305291i
$445$	4.54508	+	3.30220i	0.215458	+	0.156539i
$446$	18.7022	−	8.32677i	0.885576	−	0.394284i
$447$	−12.1650	−	13.5106i	−0.575386	−	0.639031i
$448$	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
$451$	−1.21919	+	32.9589i	−0.0574095	+	1.55197i
$452$	−5.51722	+	9.55611i	−0.259508	+	0.449481i
$453$	14.1854	+	6.31575i	0.666489	+	0.296740i
$454$	4.68391	−	5.20201i	0.219827	−	0.244143i
$455$	0.927051	−	2.85317i	0.0434608	−	0.133759i
$456$	−8.12165	+	3.16841i	−0.380331	+	0.148375i
$457$	−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	$0.781968\pi$
$458$	−18.2994	+	3.88965i	−0.855074	+	0.181752i
$459$	14.4050	−	15.9983i	0.672366	−	0.746738i
$460$	−0.0399263	−	0.379874i	−0.00186157	−	0.0177117i
$461$	−1.82624	−	3.16314i	−0.0850564	−	0.147322i	0.820359	−	0.571849i	$-0.193774\pi$
$461$	−1.82624	−	3.16314i	−0.0850564	−	0.147322i	−0.905415	+	0.424527i	$0.860440\pi$
$462$	20.1722	+	19.5609i	0.938498	+	0.910055i
$463$	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
$465$	7.36336	+	1.56513i	0.341468	+	0.0725812i
$466$	−6.78893	−	7.53987i	−0.314491	−	0.349278i
$467$	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
$469$	34.9385	+	38.8031i	1.61331	+	1.79176i
$470$	−0.255585	+	0.283856i	−0.0117893	+	0.0130933i
$471$	−1.80166	−	17.1416i	−0.0830161	−	0.789845i
$472$	−4.35410	−	7.54153i	−0.200414	−	0.347127i
$473$	−33.3481	−	12.2159i	−1.53335	−	0.561686i
$474$	7.41641			0.340647
$475$	−17.6821	+	11.6201i	−0.811310	+	0.533169i
$476$	−7.04508	−	21.6825i	−0.322911	−	0.993818i
$477$	−6.61612	+	1.40630i	−0.302932	+	0.0643901i
$478$	2.64731	−	25.1875i	0.121085	−	1.15205i
$479$	29.0807	−	12.9476i	1.32873	−	0.591590i	0.385189	−	0.922838i	$-0.374136\pi$
$479$	29.0807	−	12.9476i	1.32873	−	0.591590i	0.943544	+	0.331248i	$0.107470\pi$
$480$	0.747238	−	0.158830i	0.0341066	−	0.00724958i
$481$	−6.13348	−	1.30371i	−0.279663	−	0.0594442i
$482$	4.30902	−	3.13068i	0.196270	−	0.142599i
$483$	−8.47214			−0.385496
$484$	9.35256	−	5.79048i	0.425116	−	0.263204i
$485$	−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	$0.796833\pi$
$488$	−4.78154	−	5.31044i	−0.216450	−	0.240392i
$489$	1.03363	−	9.83437i	0.0467426	−	0.444726i
$490$	−3.81893	+	1.70030i	−0.172522	+	0.0768116i
$491$	−10.8815	+	2.31294i	−0.491076	+	0.104381i	−0.446792	−	0.894638i	$-0.647434\pi$
$491$	−10.8815	+	2.31294i	−0.491076	+	0.104381i	−0.0442833	+	0.999019i	$0.514100\pi$
$492$	13.3080	−	14.7801i	0.599972	−	0.666337i
$493$	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
$497$	−24.4815	−	10.8999i	−1.09815	−	0.488926i
$498$	−22.4429	−	4.77038i	−1.00569	−	0.213766i
$499$	−41.2378	+	8.76536i	−1.84606	+	0.392391i	−0.991836	−	0.127520i	$-0.959298\pi$
$499$	−41.2378	+	8.76536i	−1.84606	+	0.392391i	−0.854220	+	0.519911i	$0.825965\pi$
$500$	3.43852	−	1.53093i	0.153775	−	0.0684652i
$501$	−27.5066	−	19.9847i	−1.22890	−	0.892850i
$502$	−6.44427	+	19.8334i	−0.287622	+	0.885209i
$503$	17.5858	+	3.73798i	0.784114	+	0.166669i	0.582537	−	0.812804i	$-0.302060\pi$
$503$	17.5858	+	3.73798i	0.784114	+	0.166669i	0.201577	+	0.979473i	$0.435393\pi$
$504$	−0.442790	−	4.21286i	−0.0197234	−	0.187656i
$505$	−1.05573			−0.0469793
$506$	−0.809017	+	3.21644i	−0.0359652	+	0.142988i
$507$	9.56231	−	16.5624i	0.424677	−	0.735562i
$508$	−0.513692	−	0.228710i	−0.0227914	−	0.0101474i
$509$	−24.3447	−	5.17462i	−1.07906	−	0.229361i	−0.366106	−	0.930573i	$-0.619309\pi$
$509$	−24.3447	−	5.17462i	−1.07906	−	0.229361i	−0.712953	+	0.701212i	$0.752643\pi$
$510$	−4.02161	+	0.854820i	−0.178080	+	0.0378521i
$511$	4.97521	−	47.3360i	0.220091	−	2.09402i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	−17.2058	+	2.82118i	−0.759656	+	0.124558i
$514$	4.32624	+	13.3148i	0.190822	+	0.587290i
$515$	−3.12104	−	1.38958i	−0.137530	−	0.0612321i
$516$	10.7082	+	18.5472i	0.471402	+	0.816493i
$517$	2.93162	−	1.55100i	0.128932	−	0.0682130i
$518$	7.16312	+	12.4069i	0.314729	+	0.545127i
$519$	−4.41625	−	42.0178i	−0.193852	−	1.84438i
$520$	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	$0.932825\pi$
$522$	2.04275	−	0.909491i	0.0894087	−	0.0398073i
$523$	−18.0358	+	8.03006i	−0.788651	+	0.351130i	−0.761220	−	0.648494i	$-0.775399\pi$
$523$	−18.0358	+	8.03006i	−0.788651	+	0.351130i	−0.0274307	+	0.999624i	$0.508733\pi$
$524$	1.07295	−	3.30220i	0.0468720	−	0.144257i
$525$	−12.7082	−	39.1118i	−0.554631	−	1.70698i
$526$	−1.75591	−	16.7064i	−0.0765612	−	0.728432i
$527$	26.5172	+	45.9292i	1.15511	+	2.00071i
$528$	−6.56677	−	0.936751i	−0.285782	−	0.0407669i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−2.36023	−	1.05084i	−0.102522	−	0.0456456i
$531$	2.69098	+	8.28199i	0.116779	+	0.359408i
$532$	−6.52323	+	17.2739i	−0.282818	+	0.748920i
$533$	14.9164	+	10.8374i	0.646101	+	0.469420i
$534$	−3.07485	+	29.2553i	−0.133062	+	1.26600i
$535$	2.27540	−	0.483652i	0.0983743	−	0.0209101i
$536$	−12.0569	−	2.56277i	−0.520778	−	0.110695i
$537$	−3.12104	−	1.38958i	−0.134683	−	0.0599647i
$538$	7.66312	−	13.2729i	0.330381	−	0.572236i
$539$	36.2148	−	2.45714i	1.55988	−	0.105837i
$540$	1.52786			0.0657488
$541$	−3.02910	−	28.8200i	−0.130231	−	1.23907i	−0.843095	−	0.537765i	$-0.819269\pi$
$541$	−3.02910	−	28.8200i	−0.130231	−	1.23907i	0.712864	−	0.701302i	$-0.247398\pi$
$542$	−2.56082	−	0.544320i	−0.109997	−	0.0233805i
$543$	6.65248	−	20.4742i	0.285485	−	0.878633i
$544$	4.35410	+	3.16344i	0.186681	+	0.135631i
$545$	−2.76008	+	1.22887i	−0.118229	+	0.0526389i
$546$	15.3649	−	3.26592i	0.657559	−	0.139768i
$547$	−7.59427	−	1.61421i	−0.324708	−	0.0690187i	0.0426739	−	0.999089i	$-0.486412\pi$
$547$	−7.59427	−	1.61421i	−0.324708	−	0.0690187i	−0.367382	+	0.930070i	$0.619746\pi$
$548$	−10.0805	−	4.48811i	−0.430616	−	0.191723i
$549$	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
$553$	10.5108	−	11.6735i	0.446966	−	0.496406i
$554$	12.1451	−	2.58152i	0.515995	−	0.109678i
$555$	2.36023	−	1.05084i	0.100186	−	0.0446057i
$556$	1.08881	−	10.3593i	0.0461759	−	0.439334i
$557$	−17.7967	−	19.7652i	−0.754070	−	0.837480i	0.236904	−	0.971533i	$-0.423867\pi$
$557$	−17.7967	−	19.7652i	−0.754070	−	0.837480i	−0.990974	+	0.134053i	$0.957201\pi$
$558$	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
$561$	35.3421	+	5.04156i	1.49215	+	0.212855i
$562$	−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	$0.210803\pi$
$564$	−1.95630	−	0.415823i	−0.0823749	−	0.0175093i
$565$	4.12268	−	0.876302i	0.173442	−	0.0368663i
$566$	14.4011	−	6.41177i	0.605322	−	0.269507i
$567$	4.87069	−	46.3415i	0.204550	−	1.94616i
$568$	6.18799	−	1.31530i	0.259642	−	0.0551887i
$569$	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	$0.743357\pi$
$570$	2.97515	+	1.49558i	0.124615	+	0.0626429i
$571$	1.03444			0.0432900			0.0216450	−	0.999766i	$-0.493110\pi$
$571$	1.03444			0.0432900			0.0216450	+	0.999766i	$0.493110\pi$
$572$	0.227317	−	6.14516i	0.00950461	−	0.256942i
$573$	0.291796	+	0.505406i	0.0121900	+	0.0211136i
$574$	−4.40322	−	41.8938i	−0.183787	−	1.74862i
$575$	3.24803	−	3.60730i	0.135452	−	0.150435i
$576$	0.669131	+	0.743145i	0.0278804	+	0.0309644i
$577$	−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
$579$	11.2634	+	12.5092i	0.468089	+	0.519865i
$580$	0.835438	+	0.177578i	0.0346897	+	0.00737352i
$581$	−39.3156	+	28.5645i	−1.63109	+	1.18505i
$582$	−32.3607			−1.34139
$583$	16.1050	+	15.6169i	0.667001	+	0.646786i
$584$	5.61803	+	9.73072i	0.232476	+	0.402660i
$585$	−0.0740275	−	0.704324i	−0.00306066	−	0.0291202i
$586$	−12.3230	+	13.6861i	−0.509058	+	0.565366i
$587$	19.3866	−	4.12074i	0.800169	−	0.170081i	0.210360	−	0.977624i	$-0.432536\pi$
$587$	19.3866	−	4.12074i	0.800169	−	0.170081i	0.589809	+	0.807543i	$0.299203\pi$
$588$	−17.7082	−	12.8658i	−0.730274	−	0.530575i
$589$	6.48842	−	42.4601i	0.267351	−	1.74954i
$590$	−1.02786	+	3.16344i	−0.0423165	+	0.130237i
$591$	34.2090	−	37.9930i	1.40717	−	1.56282i
$592$	−3.08958	−	1.37557i	−0.126981	−	0.0565356i
$593$	18.2361	−	31.5858i	0.748866	−	1.29707i	−0.199501	−	0.979898i	$-0.563932\pi$
$593$	18.2361	−	31.5858i	0.748866	−	1.29707i	0.948367	−	0.317176i	$-0.102734\pi$
$594$	−12.4570	−	4.56318i	−0.511118	−	0.187229i
$595$	−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
$598$	1.24064	+	1.37787i	0.0507334	+	0.0563451i
$599$	−12.7702	+	5.68566i	−0.521776	+	0.232310i	−0.650686	−	0.759347i	$-0.725519\pi$
$599$	−12.7702	+	5.68566i	−0.521776	+	0.232310i	0.128910	+	0.991656i	$0.458852\pi$
$600$	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	$-0.0383966\pi$
$602$	44.3694	+	9.43102i	1.80836	+	0.384380i
$603$	11.2606	+	5.01353i	0.458566	+	0.204167i
$604$	−3.88197	+	6.72376i	−0.157955	+	0.273586i
$605$	−4.03404	−	1.17482i	−0.164007	−	0.0477632i
$606$	−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	$0.969078\pi$
$608$	−1.15106	−	4.20417i	−0.0466815	−	0.170502i
$609$	5.85410	−	18.0171i	0.237220	−	0.730089i
$610$	−0.285309	+	2.71454i	−0.0115518	+	0.109908i
$611$	0.193806	−	1.84395i	0.00784057	−	0.0745980i
$612$	−3.60124	−	3.99958i	−0.145571	−	0.161673i
$613$	5.53405	−	6.14619i	0.223518	−	0.248242i	−0.620947	−	0.783853i	$-0.713252\pi$
$613$	5.53405	−	6.14619i	0.223518	−	0.248242i	0.844465	+	0.535610i	$0.179918\pi$
$614$	−0.864504	−	8.22520i	−0.0348885	−	0.331942i
$615$	−7.59675			−0.306330
$616$	−10.7812	+	9.00854i	−0.434385	+	0.362964i
$617$	−1.56231	+	2.70599i	−0.0628961	+	0.108939i	−0.895759	−	0.444540i	$-0.853367\pi$
$617$	−1.56231	+	2.70599i	−0.0628961	+	0.108939i	0.832863	+	0.553480i	$0.186700\pi$
$618$	−1.86986	−	17.7905i	−0.0752169	−	0.715641i
$619$	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
$621$	3.65418	−	1.62695i	0.146637	−	0.0652871i
$622$	1.62670	−	15.4771i	0.0652249	−	0.620573i
$623$	41.6902	+	46.3016i	1.67028	+	1.85503i
$624$	−2.48127	+	2.75573i	−0.0993304	+	0.110318i
$625$	20.8588	+	9.28694i	0.834353	+	0.371478i
$626$	−5.05573			−0.202068
$627$	−19.7903	−	21.0795i	−0.790348	−	0.841834i
$628$	8.61803			0.343897
$629$	16.6280	+	7.40327i	0.663002	+	0.295188i
$630$	−1.08268	+	1.20243i	−0.0431348	+	0.0479061i
$631$	23.8562	+	26.4950i	0.949699	+	1.05475i	0.998434	+	0.0559357i	$0.0178142\pi$
$631$	23.8562	+	26.4950i	0.949699	+	1.05475i	−0.0487355	+	0.998812i	$0.515519\pi$
$632$	−0.387613	+	3.68789i	−0.0154184	+	0.146696i
$633$	16.2791	−	7.24791i	0.647035	−	0.288079i
$634$	−0.399187	+	1.22857i	−0.0158537	+	0.0487928i
$635$	0.0663712	+	0.204270i	0.00263386	+	0.00810619i
$636$	−1.41405	−	13.4538i	−0.0560706	−	0.533476i
$637$	10.1459	−	17.5732i	0.401995	−	0.696276i
$638$	−6.28115	−	3.94298i	−0.248673	−	0.156104i
$639$	−6.32624			−0.250262
$640$	0.0399263	+	0.379874i	0.00157823	+	0.0150158i
$641$	−10.5712	+	11.7405i	−0.417536	+	0.463721i	−0.914817	−	0.403869i	$-0.867665\pi$
$641$	−10.5712	+	11.7405i	−0.417536	+	0.463721i	0.497281	+	0.867590i	$0.334332\pi$
$642$	8.15024	+	9.05176i	0.321664	+	0.357244i
$643$	−1.42125	+	13.5223i	−0.0560485	+	0.533266i	0.930089	+	0.367335i	$0.119730\pi$
$643$	−1.42125	+	13.5223i	−0.0560485	+	0.533266i	−0.986137	+	0.165931i	$0.946937\pi$
$644$	0.442790	−	4.21286i	0.0174484	−	0.166010i
$645$	2.52786	−	7.77997i	0.0995345	−	0.306336i
$646$	6.19495	+	22.6267i	0.243737	+	0.890236i
$647$	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
$649$	17.8285	−	22.7224i	0.699828	−	0.891932i
$650$	−4.50000	+	7.79423i	−0.176505	+	0.305715i
$651$	76.2676	+	33.9565i	2.98916	+	1.33086i
$652$	4.83623	+	1.02797i	0.189401	+	0.0402585i
$653$	−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
$655$	−1.21158	+	0.539430i	−0.0473403	+	0.0210773i
$656$	6.65402	+	7.39003i	0.259796	+	0.288532i
$657$	−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	−0.999016	−	0.0443504i	$-0.985878\pi$
$659$	−11.8369	+	20.5021i	−0.461099	+	0.798648i	0.537917	+	0.842998i	$0.319212\pi$
$660$	1.41247	+	2.10344i	0.0549802	+	0.0818762i
$661$	2.92705	−	5.06980i	0.113849	−	0.197192i	−0.803470	−	0.595345i	$-0.797015\pi$
$661$	2.92705	−	5.06980i	0.113849	−	0.197192i	0.917319	+	0.398153i	$0.130349\pi$
$662$	10.9940	+	4.89485i	0.427294	+	0.190244i
$663$	13.3541	−	14.8313i	0.518631	−	0.575998i
$664$	3.54508	−	10.9106i	0.137576	−	0.423415i
$665$	6.57055	−	2.56330i	0.254795	−	0.0994005i
$666$	2.73607	+	1.98787i	0.106020	+	0.0770284i
$667$	2.18720	−	0.464905i	0.0846889	−	0.0180012i
$668$	11.3752	−	12.6335i	0.440120	−	0.488803i
$669$	−4.27984	−	40.7200i	−0.165468	−	1.57433i
$670$	2.35410	+	4.07742i	0.0909469	+	0.157525i
$671$	10.4335	−	21.2801i	0.402782	−	0.821510i
$672$	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	$0.0208566\pi$
$674$	−22.4974	−	4.78197i	−0.866567	−	0.184195i
$675$	12.9921	+	14.4292i	0.500067	+	0.555380i
$676$	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	$0.778176\pi$
$678$	14.7670	+	16.4004i	0.567122	+	0.629853i
$679$	−45.8629	+	50.9359i	−1.76006	+	1.95474i
$680$	−0.214882	−	2.04447i	−0.00824035	−	0.0784017i
$681$	−7.00000	−	12.1244i	−0.268241	−	0.464606i
$682$	20.1745	−	25.7124i	0.772521	−	0.984578i
$683$	14.7082			0.562794			0.281397	−	0.959591i	$-0.409202\pi$
$683$	14.7082			0.562794			0.281397	+	0.959591i	$0.409202\pi$
$684$	0.251807	+	4.35162i	0.00962807	+	0.166388i
$685$	1.30244	+	4.00850i	0.0497636	+	0.153157i
$686$	−16.3431	+	3.47383i	−0.623982	+	0.132631i
$687$	−3.91108	+	37.2114i	−0.149217	+	1.41970i
$688$	−9.78243	+	4.35542i	−0.372952	+	0.166049i
$689$	12.2670	−	2.60742i	0.467334	−	0.0993350i
$690$	−0.747238	−	0.158830i	−0.0284469	−	0.00604657i
$691$	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
$693$	12.4185	−	6.57015i	0.471741	−	0.249579i
$694$	−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
$697$	−35.8117	−	39.7729i	−1.35646	−	1.50651i
$698$	−1.80748	+	17.1971i	−0.0684143	+	0.650919i
$699$	−18.5375	+	8.25342i	−0.701152	+	0.312173i
$700$	20.1130	−	4.27514i	0.760199	−	0.161585i
$701$	5.82693	−	6.47146i	0.220080	−	0.244424i	−0.622987	−	0.782232i	$-0.714081\pi$
$701$	5.82693	−	6.47146i	0.220080	−	0.244424i	0.843067	+	0.537809i	$0.180748\pi$
$702$	−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
$706$	3.65418	+	1.62695i	0.137527	+	0.0612309i
$707$	−11.4524	−	2.43427i	−0.430710	−	0.0915502i
$708$	−17.0358	+	3.62107i	−0.640245	+	0.136088i
$709$	44.7637	−	19.9301i	1.68114	−	0.748490i	0.681273	−	0.732030i	$-0.261427\pi$
$709$	44.7637	−	19.9301i	1.68114	−	0.748490i	0.999865	−	0.0164606i	$-0.00523981\pi$
$710$	−1.95492	−	1.42033i	−0.0733667	−	0.0533040i
$711$	1.14590	−	3.52671i	0.0429745	−	0.132262i
$712$	−14.3868	−	3.05801i	−0.539168	−	0.114604i
$713$	1.03003	+	9.80012i	0.0385751	+	0.367017i
$714$	−45.5967			−1.70642
$715$	−1.80244	+	1.50609i	−0.0674074	+	0.0563244i
$716$	0.854102	−	1.47935i	0.0319193	−	0.0552858i
$717$	−46.2733	−	20.6022i	−1.72811	−	0.769404i
$718$	−22.6738	−	4.81946i	−0.846178	−	0.179861i
$719$	9.58426	−	2.03720i	0.357432	−	0.0759746i	−0.0256957	−	0.999670i	$-0.508180\pi$
$719$	9.58426	−	2.03720i	0.357432	−	0.0759746i	0.383128	+	0.923695i	$0.374847\pi$
$720$	0.0399263	−	0.379874i	0.00148797	−	0.0141571i
$721$	−30.6525	−	22.2703i	−1.14156	−	0.829390i
$722$	7.53867	−	17.4404i	0.280560	−	0.649065i
$723$	−3.29180	−	10.1311i	−0.122423	−	0.376780i
$724$	9.83334	+	4.37809i	0.365453	+	0.162710i
$725$	5.42705	+	9.39993i	0.201556	+	0.349105i
$726$	−5.23395	−	21.3683i	−0.194250	−	0.793053i
$727$	−15.7812	−	27.3338i	−0.585291	−	1.01375i	−0.994839	−	0.101465i	$-0.967647\pi$
$727$	−15.7812	−	27.3338i	−0.585291	−	1.01375i	0.409549	−	0.912288i	$-0.365686\pi$
$728$	0.820977	+	7.81108i	0.0304274	+	0.289498i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	1.32624	−	4.08174i	0.0490863	−	0.151072i
$731$	52.6487	−	23.4407i	1.94728	−	0.866986i
$732$	−13.0562	+	5.81300i	−0.482571	+	0.214855i
$733$	−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
$735$	0.873929	+	8.31488i	0.0322354	+	0.306699i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−7.01573	−	40.2750i	−0.258428	−	1.48355i
$738$	−4.97214	−	8.61199i	−0.183027	−	0.317012i
$739$	−14.4640	−	6.43979i	−0.532067	−	0.236891i	0.123075	−	0.992397i	$-0.460724\pi$
$739$	−14.4640	−	6.43979i	−0.532067	−	0.236891i	−0.655142	+	0.755506i	$0.727391\pi$
$740$	0.399187	+	1.22857i	0.0146744	+	0.0451632i
$741$	−15.9507	+	2.61538i	−0.585963	+	0.0960783i
$742$	−23.1803	−	16.8415i	−0.850977	−	0.618271i
$743$	−4.90119	+	46.6317i	−0.179807	+	1.71075i	0.417449	+	0.908700i	$0.362924\pi$
$743$	−4.90119	+	46.6317i	−0.179807	+	1.71075i	−0.597256	+	0.802050i	$0.703743\pi$
$744$	−19.2775	+	4.09757i	−0.706749	+	0.150224i
$745$	−3.39626	−	0.721898i	−0.124429	−	0.0264483i
$746$	−14.0327	−	6.24775i	−0.513773	−	0.228746i
$747$	−5.73607	+	9.93516i	−0.209872	+	0.363509i
$748$	−4.35410	+	17.3108i	−0.159202	+	0.632945i
$749$	25.7984			0.942652
$750$	−0.786876	−	7.48663i	−0.0287327	−	0.273373i
$751$	35.5116	+	7.54822i	1.29584	+	0.275439i	0.803677	−	0.595066i	$-0.202874\pi$
$751$	35.5116	+	7.54822i	1.29584	+	0.275439i	0.492160	+	0.870505i	$0.336207\pi$
$752$	0.309017	−	0.951057i	0.0112687	−	0.0346815i
$753$	33.7426	+	24.5155i	1.22965	+	0.893393i
$754$	−3.78747	+	1.68629i	−0.137931	+	0.0614110i
$755$	2.90075	−	0.616574i	0.105569	−	0.0224394i
$756$	16.5740	+	3.52291i	0.602791	+	0.128127i
$757$	4.66955	+	2.07902i	0.169718	+	0.0755631i	0.489837	−	0.871814i	$-0.337056\pi$
$757$	4.66955	+	2.07902i	0.169718	+	0.0755631i	−0.320119	+	0.947377i	$0.603723\pi$
$758$	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	$0.180461\pi$
$762$	−0.752512	+	0.835749i	−0.0272606	+	0.0302760i
$763$	−32.7744	+	6.96641i	−1.18651	+	0.252201i
$764$	−0.266569	+	0.118684i	−0.00964413	+	0.00429384i
$765$	−0.214882	+	2.04447i	−0.00776908	+	0.0739178i
$766$	16.8862	+	18.7541i	0.610124	+	0.677611i
$767$	−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	−0.781782	−	0.623552i	$-0.785689\pi$
$769$	4.13525	−	7.16247i	0.149121	−	0.258285i	0.930903	+	0.365267i	$0.119022\pi$
$770$	5.31263	+	0.757847i	0.191454	+	0.0273109i
$771$	28.0000			1.00840
$772$	−6.80902	+	4.94704i	−0.245062	+	0.178048i
$773$	0.264599	+	0.0562422i	0.00951695	+	0.00202289i	0.212668	−	0.977125i	$-0.431785\pi$
$773$	0.264599	+	0.0562422i	0.00951695	+	0.00202289i	−0.203151	+	0.979147i	$0.565118\pi$
$774$	10.4742	−	2.22636i	0.376487	−	0.0800249i
$775$	−43.6975	+	19.4554i	−1.56966	+	0.698857i
$776$	1.69131	−	16.0917i	0.0607143	−	0.577658i
$777$	28.0264	−	5.95718i	1.00544	−	0.213713i
$778$	−4.26393	−	13.1230i	−0.152869	−	0.470484i
$779$	2.50403	+	43.2737i	0.0897163	+	1.55044i
$780$	1.41641			0.0507155
$781$	11.6969	+	17.4189i	0.418546	+	0.623297i
$782$	−2.69098	−	4.66092i	−0.0962294	−	0.166674i
$783$	0.934931	+	8.89527i	0.0334117	+	0.317891i
$784$	7.32315	−	8.13318i	0.261541	−	0.290471i
$785$	−2.20264	−	2.44628i	−0.0786156	−	0.0873115i
$786$	−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	$0.603087\pi$
$788$	17.1045	+	18.9965i	0.609323	+	0.676722i
$789$	−32.8626	−	6.98516i	−1.16994	−	0.248678i
$790$	1.14590	−	0.832544i	0.0407692	−	0.0296206i
$791$	46.7426			1.66198
$792$	−1.46007	+	2.97795i	−0.0518815	+	0.105817i
$793$	−6.62461	−	11.4742i	−0.235247	−	0.407460i
$794$	0.110354	+	1.04994i	0.00391630	+	0.0372611i
$795$	−3.45752	+	3.83997i	−0.122626	+	0.136190i
$796$	−20.3984	+	4.33581i	−0.723002	+	0.153679i
$797$	−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	$0.768171\pi$
$798$	28.8254	+	23.0838i	1.02041	+	0.817158i
$799$	−1.66312	+	5.11855i	−0.0588369	+	0.181081i
$800$	−3.24803	+	3.60730i	−0.114835	+	0.127537i
$801$	13.4366	+	5.98237i	0.474759	+	0.211376i
$802$	−9.47214	+	16.4062i	−0.334473	+	0.579324i
$803$	−23.0038	+	29.3184i	−0.811787	+	1.03462i
$804$	−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
$807$	−20.5105	−	22.7792i	−0.722004	−	0.801867i
$808$	2.52498	−	1.12419i	0.0888284	−	0.0395490i
$809$	−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
$811$	7.71616	+	1.64012i	0.270951	+	0.0575924i	0.341383	−	0.939924i	$-0.389105\pi$
$811$	7.71616	+	1.64012i	0.270951	+	0.0575924i	−0.0704324	+	0.997517i	$0.522438\pi$
$812$	8.65323	+	3.85266i	0.303669	+	0.135202i
$813$	−2.61803	+	4.53457i	−0.0918185	+	0.159034i
$814$	0.414637	−	11.2090i	0.0145330	−	0.392877i
$815$	−0.944272	−	1.63553i	−0.0330764	−	0.0572900i
$816$	8.70820	−	6.32688i	0.304848	−	0.221485i
$817$	−45.1506	−	11.8352i	−1.57962	−	0.414060i
$818$	−6.97214	+	21.4580i	−0.243775	+	0.750262i
$819$	0.820977	−	7.81108i	0.0286873	−	0.272941i
$820$	0.397038	−	3.77757i	0.0138652	−	0.131918i
$821$	29.9990	+	33.3173i	1.04697	+	1.16278i	0.986357	+	0.164620i	$0.0526397\pi$
$821$	29.9990	+	33.3173i	1.04697	+	1.16278i	0.0606155	+	0.998161i	$0.480694\pi$
$822$	−14.7670	+	16.4004i	−0.515057	+	0.572029i
$823$	1.46117	+	13.9021i	0.0509333	+	0.484598i	0.990021	+	0.140920i	$0.0450061\pi$
$823$	1.46117	+	13.9021i	0.0509333	+	0.484598i	−0.939088	+	0.343678i	$0.888327\pi$
$824$	8.94427			0.311588
$825$	−7.85410	+	31.2259i	−0.273445	+	1.08715i
$826$	−18.4443	+	31.9464i	−0.641758	+	1.11156i
$827$	2.19870	+	20.9192i	0.0764562	+	0.727432i	0.963855	+	0.266429i	$0.0858438\pi$
$827$	2.19870	+	20.9192i	0.0764562	+	0.727432i	−0.887398	+	0.461003i	$0.847490\pi$
$828$	−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	$0.920963\pi$
$830$	−4.00313	+	1.78231i	−0.138951	+	0.0618647i
$831$	2.59574	−	24.6968i	0.0900451	−	0.856722i
$832$	−1.24064	−	1.37787i	−0.0430113	−	0.0477689i
$833$	−39.4129	+	43.7725i	−1.36558	+	1.51663i
$834$	−19.0317	−	8.47347i	−0.659015	−	0.293412i
$835$	−6.49342			−0.224714
$836$	11.5163	−	8.73923i	0.398301	−	0.302253i
$837$	−39.4164			−1.36243
$838$	−30.7431	−	13.6877i	−1.06200	−	0.472834i
$839$	33.4423	−	37.1414i	1.15456	−	1.28226i	0.201494	−	0.979490i	$-0.435420\pi$
$839$	33.4423	−	37.1414i	1.15456	−	1.28226i	0.953062	−	0.302775i	$-0.0979129\pi$
$840$	−2.16535	−	2.40487i	−0.0747117	−	0.0829758i
$841$	2.50868	−	23.8685i	0.0865063	−	0.823053i
$842$	2.30932	−	1.02817i	0.0795844	−	0.0354332i
$843$	−2.20163	+	6.77591i	−0.0758280	+	0.233375i
$844$	2.75329	+	8.47375i	0.0947721	+	0.291679i
$845$	−0.381788	−	3.63247i	−0.0131339	−	0.124961i
$846$	−0.500000	+	0.866025i	−0.0171904	+	0.0297746i
$847$	−41.0517	−	22.0458i	−1.41055	−	0.757503i
$848$	6.76393			0.232274
$849$	−3.29556	−	31.3552i	−0.113103	−	1.07611i
$850$	17.4808	−	19.4144i	0.599586	−	0.665907i
$851$	2.26298	+	2.51329i	0.0775739	+	0.0861545i
$852$	1.32254	−	12.5832i	0.0453096	−	0.431092i
$853$	−3.00082	+	28.5509i	−0.102746	+	0.977565i	0.814748	+	0.579816i	$0.196875\pi$
$853$	−3.00082	+	28.5509i	−0.102746	+	0.977565i	−0.917494	+	0.397750i	$0.869791\pi$
$854$	−9.35410	+	28.7890i	−0.320091	+	0.985138i
$855$	1.17088	−	1.18369i	0.0400431	−	0.0404812i
$856$	−4.92705	+	3.57971i	−0.168403	+	0.122352i
$857$	20.2705	+	35.1096i	0.692427	+	1.19932i	0.971040	+	0.238916i	$0.0767921\pi$
$857$	20.2705	+	35.1096i	0.692427	+	1.19932i	−0.278613	+	0.960404i	$0.589875\pi$
$858$	−11.5483	−	4.23030i	−0.394252	−	0.144420i
$859$	28.3885	−	49.1704i	0.968605	−	1.67767i	0.269003	−	0.963139i	$-0.413306\pi$
$859$	28.3885	−	49.1704i	0.968605	−	1.67767i	0.699602	−	0.714533i	$-0.253361\pi$
$860$	3.73656	+	1.66362i	0.127416	+	0.0567290i
$861$	−82.4082	−	17.5164i	−2.80846	−	0.596957i
$862$	−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	$0.985491\pi$
$864$	−3.65418	+	1.62695i	−0.124318	+	0.0553498i
$865$	−5.39914	−	5.99635i	−0.183576	−	0.203882i
$866$	−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
$869$	−11.8293	+	3.36553i	−0.401281	+	0.114168i
$870$	0.854102	−	1.47935i	0.0289568	−	0.0501546i
$871$	−20.8783	−	9.29560i	−0.707433	−	0.314969i
$872$	5.29271	−	5.87815i	0.179234	−	0.199059i
$873$	−5.00000	+	15.3884i	−0.169224	+	0.520819i
$874$	−0.658449	+	4.30888i	−0.0222724	+	0.145750i
$875$	−12.8992	−	9.37181i	−0.436072	−	0.316825i
$876$	21.9811	−	4.67222i	0.742671	−	0.157860i
$877$	−36.3744	+	40.3979i	−1.22828	+	1.36414i	−0.319103	+	0.947720i	$0.603382\pi$
$877$	−36.3744	+	40.3979i	−1.22828	+	1.36414i	−0.909173	+	0.416419i	$0.863285\pi$
$878$	3.74555	+	35.6365i	0.126406	+	1.20267i
$879$	18.4164	+	31.8982i	0.621170	+	1.07590i
$880$	−1.11978	+	0.592430i	−0.0377477	+	0.0199708i
$881$	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
$883$	2.64902	+	0.563067i	0.0891467	+	0.0189487i	0.252269	−	0.967657i	$-0.418823\pi$
$883$	2.64902	+	0.563067i	0.0891467	+	0.0189487i	−0.163122	+	0.986606i	$0.552157\pi$
$884$	6.67706	+	7.41563i	0.224574	+	0.249415i
$885$	5.38197	+	3.91023i	0.180913	+	0.131441i
$886$	−9.88197	−	7.17967i	−0.331991	−	0.241206i
$887$	−30.8634	−	34.2773i	−1.03629	−	1.15092i	−0.988370	−	0.152067i	$-0.951407\pi$
$887$	−30.8634	−	34.2773i	−1.03629	−	1.15092i	−0.0479210	−	0.998851i	$-0.515260\pi$
$888$	−4.52595	+	5.02658i	−0.151881	+	0.168681i
$889$	0.248983	+	2.36892i	0.00835063	+	0.0794509i
$890$	2.80902	+	4.86536i	0.0941585	+	0.163087i
$891$	−22.5205	+	28.7024i	−0.754465	+	0.961566i
$892$	20.4721			0.685458
$893$	3.64271	−	2.39388i	0.121899	−	0.0801082i
$894$	−5.61803	−	17.2905i	−0.187895	−	0.578282i
$895$	−0.638218	+	0.135657i	−0.0213333	+	0.00453453i
$896$	−0.442790	+	4.21286i	−0.0147926	+	0.140742i
$897$	3.38761	−	1.50826i	0.113109	−	0.0503594i
$898$	−4.97894	+	1.05831i	−0.166149	+	0.0353161i
$899$	−21.5529	−	4.58122i	−0.718831	−	0.152792i
$900$	3.92705	−	2.85317i	0.130902	−	0.0951057i
$901$	−36.4033			−1.21277
$902$	−14.5194	+	29.6135i	−0.483442	+	0.986023i
$903$	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
$906$	10.3902	+	11.5395i	0.345190	+	0.383373i
$907$	0.0435265	−	0.414127i	0.00144527	−	0.0137509i	−0.993775	−	0.111401i	$-0.964466\pi$
$907$	0.0435265	−	0.414127i	0.00144527	−	0.0137509i	0.995221	+	0.0976505i	$0.0311327\pi$
$908$	6.39482	−	2.84716i	0.212219	−	0.0944862i
$909$	−2.70353	+	0.574654i	−0.0896705	+	0.0190601i
$910$	2.00739	−	2.22943i	0.0665444	−	0.0739050i
$911$	−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
$915$	4.98703	+	2.22037i	0.164866	+	0.0734031i
$916$	−18.2994	−	3.88965i	−0.604629	−	0.128518i
$917$	−14.3868	+	3.05801i	−0.475094	+	0.100984i
$918$	19.6667	−	8.75617i	0.649097	−	0.288997i
$919$	−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
$921$	−16.1796	−	3.43907i	−0.533135	−	0.113321i
$922$	−0.381788	−	3.63247i	−0.0125735	−	0.119629i
$923$	11.7295			0.386081
$924$	10.4721	+	26.0746i	0.344508	+	0.857790i
$925$	−8.20820	+	14.2170i	−0.269884	+	0.467453i
$926$	9.78243	+	4.35542i	0.321471	+	0.143128i
$927$	−8.74882	−	1.85962i	−0.287349	−	0.0610779i
$928$	−2.18720	+	0.464905i	−0.0717985	+	0.0152612i
$929$	−2.79759	+	26.6173i	−0.0917860	+	0.873286i	0.847649	+	0.530558i	$0.178018\pi$
$929$	−2.79759	+	26.6173i	−0.0917860	+	0.873286i	−0.939435	+	0.342728i	$0.888649\pi$
$930$	6.09017	+	4.42477i	0.199705	+	0.145094i
$931$	47.0763	−	7.71894i	1.54286	−	0.252978i
$932$	−3.13525	−	9.64932i	−0.102699	−	0.316074i
$933$	−28.4337	−	12.6595i	−0.930879	−	0.414454i
$934$	9.18034	+	15.9008i	0.300390	+	0.520291i
$935$	6.02661	−	3.18844i	0.197091	−	0.104273i
$936$	0.927051	+	1.60570i	0.0303016	+	0.0524839i
$937$	3.89583	+	37.0663i	0.127271	+	1.21090i	0.852623	+	0.522526i	$0.175010\pi$
$937$	3.89583	+	37.0663i	0.127271	+	1.21090i	−0.725352	+	0.688378i	$0.758323\pi$
$938$	16.1353	+	49.6592i	0.526835	+	1.62143i
$939$	−3.12461	+	9.61657i	−0.101968	+	0.313825i
$940$	−0.348943	+	0.155360i	−0.0113813	+	0.00506727i
$941$	9.56677	−	4.25940i	0.311868	−	0.138853i	−0.244834	−	0.969565i	$-0.578733\pi$
$941$	9.56677	−	4.25940i	0.311868	−	0.138853i	0.556702	+	0.830713i	$0.312067\pi$
$942$	5.32624	−	16.3925i	0.173538	−	0.534096i
$943$	−3.07295	−	9.45756i	−0.100069	−	0.307981i
$944$	−0.910255	−	8.66050i	−0.0296263	−	0.281875i
$945$	−3.23607	−	5.60503i	−0.105269	−	0.182332i
$946$	−25.4964	−	24.7236i	−0.828958	−	0.803835i
$947$	−7.33688	−	12.7079i	−0.238417	−	0.412950i	0.721844	−	0.692056i	$-0.243295\pi$
$947$	−7.33688	−	12.7079i	−0.238417	−	0.412950i	−0.960260	+	0.279107i	$0.909962\pi$
$948$	6.77523	+	3.01652i	0.220049	+	0.0979722i
$949$	6.43769	+	19.8132i	0.208976	+	0.643163i
$950$	−20.8797	+	3.42358i	−0.677428	+	0.111075i
$951$	2.09017	+	1.51860i	0.0677784	+	0.0492439i
$952$	2.38308	−	22.6735i	0.0772360	−	0.734852i
$953$	43.6222	−	9.27219i	1.41306	−	0.300356i	0.562747	−	0.826629i	$-0.309745\pi$
$953$	43.6222	−	9.27219i	1.41306	−	0.300356i	0.850315	+	0.526274i	$0.176411\pi$
$954$	−6.61612	−	1.40630i	−0.214205	−	0.0455307i
$955$	0.101820	+	0.0453333i	0.00329483	+	0.00146695i
$956$	12.6631	−	21.9332i	0.409555	−	0.709369i
$957$	−11.3820	+	9.51057i	−0.367927	+	0.307433i
$958$	31.8328			1.02847
$959$	4.88594	+	46.4866i	0.157775	+	1.50113i
$960$	0.747238	+	0.158830i	0.0241170	+	0.00512623i
$961$	20.4271	−	62.8680i	0.658937	−	2.02800i
$962$	−5.07295	−	3.68571i	−0.163558	−	0.118832i
$963$	5.56365	−	2.47710i	0.179286	−	0.0798233i
$964$	5.20985	−	1.10739i	0.167798	−	0.0356665i
$965$	3.14453	+	0.668391i	0.101226	+	0.0215163i
$966$	−7.73968	−	3.44593i	−0.249020	−	0.110871i
$967$	12.0172	+	20.8144i	0.386448	+	0.669347i	0.991969	−	0.126482i	$-0.0403686\pi$
$967$	12.0172	+	20.8144i	0.386448	+	0.669347i	−0.605521	+	0.795829i	$0.707035\pi$
$968$	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
$971$	2.69077	−	2.98840i	0.0863508	−	0.0959023i	−0.698421	−	0.715687i	$-0.746114\pi$
$971$	2.69077	−	2.98840i	0.0863508	−	0.0959023i	0.784772	+	0.619785i	$0.212780\pi$
$972$	9.78148	−	2.07912i	0.313741	−	0.0666877i
$973$	−40.3098	+	17.9471i	−1.29227	+	0.575357i
$974$	−1.46922	+	13.9787i	−0.0470770	+	0.447907i
$975$	12.0444	+	13.3766i	0.385728	+	0.428394i
$976$	−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
$979$	−8.37148	−	48.0579i	−0.267554	−	1.53594i
$980$	−4.18034			−0.133536
$981$	−6.39919	+	4.64928i	−0.204310	+	0.148440i
$982$	−10.8815	−	2.31294i	−0.347243	−	0.0738088i
$983$	42.8750	−	9.11335i	1.36750	−	0.290671i	0.535072	−	0.844806i	$-0.320284\pi$
$983$	42.8750	−	9.11335i	1.36750	−	0.290671i	0.832427	+	0.554135i	$0.186951\pi$
$984$	18.1691	−	8.08940i	0.579209	−	0.257881i
$985$	1.02061	−	9.71044i	0.0325193	−	0.309400i
$986$	11.7715	−	2.50210i	0.374880	−	0.0796831i
$987$	2.61803	+	8.05748i	0.0833329	+	0.256472i
$988$	−0.466875	−	8.06835i	−0.0148533	−	0.256688i
$989$	10.7082			0.340501
$990$	1.21848	−	0.346669i	0.0387259	−	0.0110179i
$991$	−1.13525	−	1.96632i	−0.0360626	−	0.0624622i	0.847431	−	0.530906i	$-0.178148\pi$
$991$	−1.13525	−	1.96632i	−0.0360626	−	0.0624622i	−0.883493	+	0.468444i	$0.844815\pi$
$992$	−1.03003	−	9.80012i	−0.0327036	−	0.311154i
$993$	16.1052	−	17.8867i	0.511084	−	0.567616i
$994$	−17.9316	−	19.9151i	−0.568756	−	0.631668i
$995$	6.44427	+	4.68204i	0.204297	+	0.148431i
$996$	−18.5623	−	13.4863i	−0.588169	−	0.427330i
$997$	−1.24064	−	1.37787i	−0.0392913	−	0.0436375i	0.723179	−	0.690661i	$-0.242680\pi$
$997$	−1.24064	−	1.37787i	−0.0392913	−	0.0436375i	−0.762470	+	0.647023i	$0.776014\pi$
$998$	−41.2378	−	8.76536i	−1.30536	−	0.277463i
$999$	−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.311.1	yes	8
11.4	even	5	inner	418.2.n.c.235.1	yes	8
19.11	even	3	inner	418.2.n.c.201.1	yes	8
209.125	even	15	inner	418.2.n.c.125.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.c.125.1	✓	8	209.125	even	15	inner
418.2.n.c.201.1	yes	8	19.11	even	3	inner
418.2.n.c.235.1	yes	8	11.4	even	5	inner
418.2.n.c.311.1	yes	8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.913545 + 0.406737i) q^{2} +(1.33826 - 1.48629i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.0399263 - 0.379874i) q^{5} +(1.82709 - 0.813473i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(0.913545 + 0.406737i) q^{2} +(1.33826 - 1.48629i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.0399263 - 0.379874i) q^{5} +(1.82709 - 0.813473i) q^{6} +(1.30902 - 4.02874i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.190983 - 0.330792i) q^{10} +(-2.54508 + 2.12663i) q^{11} +2.00000 q^{12} +(0.193806 + 1.84395i) q^{13} +(2.83448 - 3.14801i) q^{14} +(-0.511170 - 0.567712i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(0.562569 - 5.35248i) q^{17} +(0.309017 - 0.951057i) q^{18} +(-3.06539 + 3.09893i) q^{19} +(0.309017 - 0.224514i) q^{20} +(-4.23607 - 7.33708i) q^{21} +(-3.19003 + 0.907591i) q^{22} +(0.500000 - 0.866025i) q^{23} +(1.82709 + 0.813473i) q^{24} +(4.74803 + 1.00922i) q^{25} +(-0.572949 + 1.76336i) q^{26} +(3.23607 + 2.35114i) q^{27} +(3.86984 - 1.72296i) q^{28} +(1.49622 + 1.66172i) q^{29} +(-0.236068 - 0.726543i) q^{30} +(-7.97214 + 5.79210i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.245205 + 6.62872i) q^{33} +(2.69098 - 4.66092i) q^{34} +(-1.47815 - 0.658114i) q^{35} +(0.669131 - 0.743145i) q^{36} +(-1.04508 + 3.21644i) q^{37} +(-4.06082 + 1.58421i) q^{38} +(3.00000 + 2.17963i) q^{39} +(0.373619 - 0.0794152i) q^{40} +(6.65402 - 7.39003i) q^{41} +(-0.885579 - 8.42572i) q^{42} +(5.35410 + 9.27358i) q^{43} +(-3.28339 - 0.468375i) q^{44} -0.381966 q^{45} +(0.809017 - 0.587785i) q^{46} +(-0.978148 - 0.207912i) q^{47} +(1.33826 + 1.48629i) q^{48} +(-8.85410 - 6.43288i) q^{49} +(3.92705 + 2.85317i) q^{50} +(-7.20248 - 7.99916i) q^{51} +(-1.24064 + 1.37787i) q^{52} +(-0.707023 - 6.72688i) q^{53} +(2.00000 + 3.46410i) q^{54} +(0.706234 + 1.05172i) q^{55} +4.23607 q^{56} +(0.503613 + 8.70324i) q^{57} +(0.690983 + 2.12663i) q^{58} +(-8.51791 + 1.81054i) q^{59} +(0.0798526 - 0.759747i) q^{60} +(-6.52810 + 2.90650i) q^{61} +(-9.63877 + 2.04878i) q^{62} +(-4.14350 - 0.880728i) q^{63} +(-0.809017 + 0.587785i) q^{64} +0.708204 q^{65} +(-2.92015 + 5.95590i) q^{66} +(-6.16312 + 10.6748i) q^{67} +(4.35410 - 3.16344i) q^{68} +(-0.618034 - 1.90211i) q^{69} +(-1.08268 - 1.20243i) q^{70} +(0.661272 - 6.29158i) q^{71} +(0.913545 - 0.406737i) q^{72} +(10.9905 - 2.33611i) q^{73} +(-2.26298 + 2.51329i) 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} +(3.38761 + 1.50826i) q^{79} +(0.373619 + 0.0794152i) q^{80} +(10.7596 - 2.28703i) q^{81} +(9.08454 - 4.04470i) q^{82} +(-9.28115 - 6.74315i) q^{83} +(2.61803 - 8.05748i) q^{84} +(-2.01081 - 0.427410i) q^{85} +(1.11931 + 10.6495i) q^{86} +4.47214 q^{87} +(-2.80902 - 1.76336i) q^{88} +(-7.35410 + 12.7377i) q^{89} +(-0.348943 - 0.155360i) q^{90} +(7.68247 + 1.63296i) q^{91} +(0.978148 - 0.207912i) q^{92} +(-2.06007 + 19.6002i) q^{93} +(-0.809017 - 0.587785i) q^{94} +(1.05481 + 1.28819i) q^{95} +(0.618034 + 1.90211i) q^{96} +(-14.7815 - 6.58114i) q^{97} +(-5.47214 - 9.47802i) q^{98} +(2.38101 + 2.30885i) 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

Modular forms

Varieties

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