LMFDB - Embedded newform 418.2.s.a.107.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(107,418)]

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([9, 25]))

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

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

chi := DirichletCharacter("418.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.s (of order $30$, 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:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.3
Character	$\chi$	$=$	418.107
Dual form			418.2.s.a.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(-1.47425 - 1.32742i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.214664 - 2.04239i) q^{5} +(0.806884 + 1.81229i) q^{6} +(-4.92396 - 1.59989i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0977827 + 0.930340i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(-1.47425 - 1.32742i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.214664 - 2.04239i) q^{5} +(0.806884 + 1.81229i) q^{6} +(-4.92396 - 1.59989i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0977827 + 0.930340i) q^{9} +(-1.02682 + 1.77850i) q^{10} +(1.60644 + 2.90161i) q^{11} -1.98380i q^{12} +(-0.00911533 - 0.0867265i) q^{13} +(3.84752 + 3.46433i) q^{14} +(-3.02758 + 2.72604i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(1.54830 + 0.162733i) q^{17} +(0.289074 - 0.889680i) q^{18} +(-3.46991 - 2.63813i) q^{19} +(1.66143 - 1.20710i) q^{20} +(5.13542 + 8.89480i) q^{21} +(-0.287369 - 3.30415i) q^{22} +(-0.914927 + 1.58470i) q^{23} +(-0.806884 + 1.81229i) q^{24} +(0.765475 + 0.162707i) q^{25} +(-0.0269476 + 0.0829362i) q^{26} +(-2.40735 + 3.31343i) q^{27} +(-2.10582 - 4.72975i) q^{28} +(-3.77259 - 4.18989i) q^{29} +(3.87461 - 1.25894i) q^{30} +(5.37355 + 7.39606i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.48336 - 6.41013i) q^{33} +(-1.34826 - 0.778416i) q^{34} +(-4.32459 + 9.71318i) q^{35} +(-0.625948 + 0.695186i) q^{36} +(4.62071 + 1.50136i) q^{37} +(2.09689 + 3.82139i) q^{38} +(-0.101684 + 0.139957i) q^{39} +(-2.00876 + 0.426975i) q^{40} +(-7.79781 + 8.66035i) q^{41} +(-1.07359 - 10.2146i) q^{42} +(0.359744 - 0.207699i) q^{43} +(-1.08139 + 3.13538i) q^{44} +1.92110 q^{45} +(1.48038 - 1.07556i) q^{46} +(-8.17201 - 1.73701i) q^{47} +(1.47425 - 1.32742i) q^{48} +(16.0226 + 11.6411i) q^{49} +(-0.633117 - 0.459986i) q^{50} +(-2.06657 - 2.29516i) q^{51} +(0.0583510 - 0.0648054i) q^{52} +(-6.86141 + 0.721163i) q^{53} +(3.54692 - 2.04781i) q^{54} +(6.27105 - 2.65811i) q^{55} +5.17735i q^{56} +(1.61360 + 8.49530i) q^{57} +(1.74225 + 5.36211i) q^{58} +(0.191553 + 0.901185i) q^{59} +(-4.05169 - 0.425850i) q^{60} +(-2.07779 - 4.66679i) q^{61} +(-1.90073 - 8.94225i) q^{62} +(1.00696 - 4.73739i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.179086 q^{65} +(-3.96235 + 5.25261i) q^{66} +(-3.98898 - 2.30304i) q^{67} +(0.915083 + 1.25950i) q^{68} +(3.45240 - 1.12175i) q^{69} +(7.90142 - 7.11447i) q^{70} +(-5.62493 - 0.591204i) q^{71} +(0.854590 - 0.380488i) q^{72} +(-3.37249 - 15.8663i) q^{73} +(-3.61057 - 3.25097i) q^{74} +(-0.912521 - 1.25598i) q^{75} +(-0.361305 - 4.34390i) q^{76} +(-3.26781 - 16.8575i) q^{77} +(0.149819 - 0.0864979i) q^{78} +(-7.18987 - 3.20114i) q^{79} +(2.00876 + 0.426975i) q^{80} +(10.6924 - 2.27275i) q^{81} +(10.6461 - 4.73997i) q^{82} +(9.70091 - 13.3522i) q^{83} +(-3.17386 + 9.76815i) q^{84} +(0.664729 - 3.12730i) q^{85} +(-0.413122 + 0.0434208i) q^{86} +11.1848i q^{87} +(2.26318 - 2.42447i) q^{88} +(-1.38239 - 0.798126i) q^{89} +(-1.75502 - 0.781384i) q^{90} +(-0.0938695 + 0.441621i) q^{91} +(-1.78987 + 0.380448i) q^{92} +(1.89572 - 18.0366i) q^{93} +(6.75899 + 4.91070i) q^{94} +(-6.13295 + 6.52058i) q^{95} +(-1.88671 + 0.613028i) q^{96} +(3.19468 - 7.17538i) q^{97} +(-9.90249 - 17.1516i) q^{98} +(-2.54240 + 1.77827i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) $ 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	−1.47425	−	1.32742i	−0.851159	−	0.766387i	0.122962	−	0.992411i	$-0.460761\pi$
$3$	−1.47425	−	1.32742i	−0.851159	−	0.766387i	−0.974122	+	0.226024i	$0.927427\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.214664	−	2.04239i	0.0960004	−	0.913383i	−0.835463	−	0.549547i	$-0.814800\pi$
$5$	0.214664	−	2.04239i	0.0960004	−	0.913383i	0.931463	−	0.363836i	$-0.118533\pi$
$6$	0.806884	+	1.81229i	0.329409	+	0.739865i
$7$	−4.92396	−	1.59989i	−1.86108	−	0.604702i	−0.994380	−	0.105873i	$-0.966236\pi$
$7$	−4.92396	−	1.59989i	−1.86108	−	0.604702i	−0.866700	−	0.498829i	$-0.833764\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.0977827	+	0.930340i	0.0325942	+	0.310113i
$10$	−1.02682	+	1.77850i	−0.324708	+	0.562412i
$11$	1.60644	+	2.90161i	0.484361	+	0.874868i
$11$	1.60644	+	2.90161i	0.484361	+	0.874868i
$12$		−	1.98380i		−	0.572674i
$13$	−0.00911533	−	0.0867265i	−0.00252814	−	0.0240536i	0.993185	−	0.116548i	$-0.0371828\pi$
$13$	−0.00911533	−	0.0867265i	−0.00252814	−	0.0240536i	−0.995713	+	0.0924940i	$0.970516\pi$
$14$	3.84752	+	3.46433i	1.02829	+	0.925880i
$15$	−3.02758	+	2.72604i	−0.781717	+	0.703861i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	1.54830	+	0.162733i	0.375519	+	0.0394686i	0.290408	−	0.956903i	$-0.406209\pi$
$17$	1.54830	+	0.162733i	0.375519	+	0.0394686i	0.0851108	+	0.996371i	$0.472876\pi$
$18$	0.289074	−	0.889680i	0.0681355	−	0.209700i
$19$	−3.46991	−	2.63813i	−0.796051	−	0.605229i
$19$	−3.46991	−	2.63813i	−0.796051	−	0.605229i
$20$	1.66143	−	1.20710i	0.371506	−	0.269915i
$21$	5.13542	+	8.89480i	1.12064	+	1.94101i
$22$	−0.287369	−	3.30415i	−0.0612674	−	0.704448i
$23$	−0.914927	+	1.58470i	−0.190775	+	0.330433i	−0.945507	−	0.325600i	$-0.894434\pi$
$23$	−0.914927	+	1.58470i	−0.190775	+	0.330433i	0.754732	+	0.656033i	$0.227767\pi$
$24$	−0.806884	+	1.81229i	−0.164705	+	0.369933i
$25$	0.765475	+	0.162707i	0.153095	+	0.0325413i
$26$	−0.0269476	+	0.0829362i	−0.00528486	+	0.0162651i
$27$	−2.40735	+	3.31343i	−0.463294	+	0.637670i
$28$	−2.10582	−	4.72975i	−0.397962	−	0.893838i
$29$	−3.77259	−	4.18989i	−0.700553	−	0.778043i	0.282911	−	0.959146i	$-0.408700\pi$
$29$	−3.77259	−	4.18989i	−0.700553	−	0.778043i	−0.983464	+	0.181103i	$0.942033\pi$
$30$	3.87461	−	1.25894i	0.707404	−	0.229849i
$31$	5.37355	+	7.39606i	0.965118	+	1.32837i	0.944475	+	0.328584i	$0.106571\pi$
$31$	5.37355	+	7.39606i	0.965118	+	1.32837i	0.0206434	+	0.999787i	$0.493429\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	1.48336	−	6.41013i	0.258219	−	1.11586i
$34$	−1.34826	−	0.778416i	−0.231224	−	0.133497i
$35$	−4.32459	+	9.71318i	−0.730989	+	1.64183i
$36$	−0.625948	+	0.695186i	−0.104325	+	0.115864i
$37$	4.62071	+	1.50136i	0.759639	+	0.246822i	0.663124	−	0.748510i	$-0.269230\pi$
$37$	4.62071	+	1.50136i	0.759639	+	0.246822i	0.0965156	+	0.995331i	$0.469230\pi$
$38$	2.09689	+	3.82139i	0.340161	+	0.619912i
$39$	−0.101684	+	0.139957i	−0.0162825	+	0.0224110i
$40$	−2.00876	+	0.426975i	−0.317613	+	0.0675107i
$41$	−7.79781	+	8.66035i	−1.21781	+	1.35252i	−0.300788	+	0.953691i	$0.597250\pi$
$41$	−7.79781	+	8.66035i	−1.21781	+	1.35252i	−0.917026	+	0.398828i	$0.869417\pi$
$42$	−1.07359	−	10.2146i	−0.165659	−	1.57614i
$43$	0.359744	−	0.207699i	0.0548605	−	0.0316737i	−0.472319	−	0.881428i	$-0.656583\pi$
$43$	0.359744	−	0.207699i	0.0548605	−	0.0316737i	0.527179	+	0.849754i	$0.323250\pi$
$44$	−1.08139	+	3.13538i	−0.163026	+	0.472676i
$45$	1.92110			0.286381
$46$	1.48038	−	1.07556i	0.218271	−	0.158583i
$47$	−8.17201	−	1.73701i	−1.19201	−	0.253369i	−0.431147	−	0.902282i	$-0.641891\pi$
$47$	−8.17201	−	1.73701i	−1.19201	−	0.253369i	−0.760863	+	0.648912i	$0.775224\pi$
$48$	1.47425	−	1.32742i	0.212790	−	0.191597i
$49$	16.0226	+	11.6411i	2.28894	+	1.66301i
$50$	−0.633117	−	0.459986i	−0.0895363	−	0.0650519i
$51$	−2.06657	−	2.29516i	−0.289378	−	0.321387i
$52$	0.0583510	−	0.0648054i	0.00809183	−	0.00898689i
$53$	−6.86141	+	0.721163i	−0.942487	+	0.0990594i	−0.563293	−	0.826258i	$-0.690466\pi$
$53$	−6.86141	+	0.721163i	−0.942487	+	0.0990594i	−0.379195	+	0.925317i	$0.623799\pi$
$54$	3.54692	−	2.04781i	0.482674	−	0.278672i
$55$	6.27105	−	2.65811i	0.845589	−	0.358420i
$56$			5.17735i			0.691853i
$57$	1.61360	+	8.49530i	0.213726	+	1.12523i
$58$	1.74225	+	5.36211i	0.228769	+	0.704079i
$59$	0.191553	+	0.901185i	0.0249380	+	0.117324i	0.988856	−	0.148875i	$-0.0475653\pi$
$59$	0.191553	+	0.901185i	0.0249380	+	0.117324i	−0.963918	+	0.266200i	$0.914232\pi$
$60$	−4.05169	−	0.425850i	−0.523071	−	0.0549769i
$61$	−2.07779	−	4.66679i	−0.266033	−	0.597521i	0.730295	−	0.683132i	$-0.239382\pi$
$61$	−2.07779	−	4.66679i	−0.266033	−	0.597521i	−0.996329	+	0.0856108i	$0.972716\pi$
$62$	−1.90073	−	8.94225i	−0.241394	−	1.13567i
$63$	1.00696	−	4.73739i	0.126866	−	0.596856i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.179086			−0.0222129
$66$	−3.96235	+	5.25261i	−0.487731	+	0.646552i
$67$	−3.98898	−	2.30304i	−0.487332	−	0.281361i	0.236135	−	0.971720i	$-0.424119\pi$
$67$	−3.98898	−	2.30304i	−0.487332	−	0.281361i	−0.723467	+	0.690359i	$0.757453\pi$
$68$	0.915083	+	1.25950i	0.110970	+	0.152737i
$69$	3.45240	−	1.12175i	0.415620	−	0.135043i
$70$	7.90142	−	7.11447i	0.944400	−	0.850341i
$71$	−5.62493	−	0.591204i	−0.667556	−	0.0701630i	−0.235312	−	0.971920i	$-0.575611\pi$
$71$	−5.62493	−	0.591204i	−0.667556	−	0.0701630i	−0.432244	+	0.901757i	$0.642278\pi$
$72$	0.854590	−	0.380488i	0.100714	−	0.0448409i
$73$	−3.37249	−	15.8663i	−0.394720	−	1.85701i	−0.505011	−	0.863113i	$-0.668511\pi$
$73$	−3.37249	−	15.8663i	−0.394720	−	1.85701i	0.110290	−	0.993899i	$-0.464822\pi$
$74$	−3.61057	−	3.25097i	−0.419720	−	0.377918i
$75$	−0.912521	−	1.25598i	−0.105369	−	0.145028i
$76$	−0.361305	−	4.34390i	−0.0414446	−	0.498279i
$77$	−3.26781	−	16.8575i	−0.372401	−	1.92109i
$78$	0.149819	−	0.0864979i	0.0169636	−	0.00979396i
$79$	−7.18987	−	3.20114i	−0.808923	−	0.360156i	−0.0397609	−	0.999209i	$-0.512660\pi$
$79$	−7.18987	−	3.20114i	−0.808923	−	0.360156i	−0.769162	+	0.639053i	$0.779326\pi$
$80$	2.00876	+	0.426975i	0.224586	+	0.0477373i
$81$	10.6924	−	2.27275i	1.18805	−	0.252527i
$82$	10.6461	−	4.73997i	1.17567	−	0.523442i
$83$	9.70091	−	13.3522i	1.06481	−	1.46559i	0.189595	−	0.981862i	$-0.439283\pi$
$83$	9.70091	−	13.3522i	1.06481	−	1.46559i	0.875219	−	0.483727i	$-0.160717\pi$
$84$	−3.17386	+	9.76815i	−0.346297	+	1.06579i
$85$	0.664729	−	3.12730i	0.0721000	−	0.339204i
$86$	−0.413122	+	0.0434208i	−0.0445480	+	0.00468219i
$87$			11.1848i			1.19913i
$88$	2.26318	−	2.42447i	0.241255	−	0.258449i
$89$	−1.38239	−	0.798126i	−0.146534	−	0.0846012i	0.424941	−	0.905221i	$-0.360295\pi$
$89$	−1.38239	−	0.798126i	−0.146534	−	0.0846012i	−0.571474	+	0.820620i	$0.693628\pi$
$90$	−1.75502	−	0.781384i	−0.184995	−	0.0823651i
$91$	−0.0938695	+	0.441621i	−0.00984019	+	0.0462945i
$92$	−1.78987	+	0.380448i	−0.186607	+	0.0396645i
$93$	1.89572	−	18.0366i	0.196577	−	1.87031i
$94$	6.75899	+	4.91070i	0.697137	+	0.506500i
$95$	−6.13295	+	6.52058i	−0.629228	+	0.668997i
$96$	−1.88671	+	0.613028i	−0.192561	+	0.0625669i
$97$	3.19468	−	7.17538i	0.324371	−	0.728549i	−0.675591	−	0.737277i	$-0.736111\pi$
$97$	3.19468	−	7.17538i	0.324371	−	0.728549i	0.999962	+	0.00872745i	$0.00277807\pi$
$98$	−9.90249	−	17.1516i	−1.00030	−	1.73258i
$99$	−2.54240	+	1.77827i	−0.255521	+	0.178723i
$100$	0.391288	+	0.677730i	0.0391288	+	0.0677730i
$101$	−10.3504	+	1.08787i	−1.02990	+	0.108247i	−0.604377	−	0.796698i	$-0.706578\pi$
$101$	−10.3504	+	1.08787i	−1.02990	+	0.108247i	−0.425527	+	0.904946i	$0.639911\pi$
$102$	0.954382	+	2.93729i	0.0944979	+	0.290835i
$103$	−12.0783	−	3.92449i	−1.19011	−	0.386691i	−0.353999	−	0.935246i	$-0.615178\pi$
$103$	−12.0783	−	3.92449i	−1.19011	−	0.386691i	−0.836115	+	0.548554i	$0.815178\pi$
$104$	−0.0796650	+	0.0354692i	−0.00781180	+	0.00347804i
$105$	19.2690	−	8.57912i	1.88046	−	0.837236i
$106$	6.56153	+	2.13197i	0.637313	+	0.207075i
$107$	4.91130	+	15.1154i	0.474793	+	1.46126i	0.846236	+	0.532808i	$0.178863\pi$
$107$	4.91130	+	15.1154i	0.474793	+	1.46126i	−0.371443	+	0.928456i	$0.621137\pi$
$108$	−4.07319	+	0.428110i	−0.391943	+	0.0411949i
$109$	5.33993	+	9.24903i	0.511472	+	0.885896i	0.999912	+	0.0132983i	$0.00423310\pi$
$109$	5.33993	+	9.24903i	0.511472	+	0.885896i	−0.488439	+	0.872598i	$0.662434\pi$
$110$	−6.81004	−	0.122361i	−0.649312	−	0.0116667i
$111$	−4.81915	−	8.34701i	−0.457413	−	0.792263i
$112$	2.10582	−	4.72975i	0.198981	−	0.446919i
$113$	−9.47141	+	3.07745i	−0.890995	+	0.289502i	−0.718515	−	0.695511i	$-0.755178\pi$
$113$	−9.47141	+	3.07745i	−0.890995	+	0.289502i	−0.172480	+	0.985013i	$0.555178\pi$
$114$	1.98126	−	8.41715i	0.185562	−	0.788339i
$115$	3.04017	+	2.20881i	0.283497	+	0.205973i
$116$	0.589337	−	5.60717i	0.0547186	−	0.520612i
$117$	0.0797939	−	0.0169607i	0.00737694	−	0.00156802i
$118$	0.191553	−	0.901185i	0.0176339	−	0.0829608i
$119$	−7.36343	−	3.27841i	−0.675004	−	0.300531i
$120$	3.52819	+	2.03700i	0.322078	+	0.185952i
$121$	−5.83867	+	9.32255i	−0.530788	+	0.847504i
$122$			5.10843i			0.462496i
$123$	22.9919	−	2.41654i	2.07311	−	0.217892i
$124$	−1.90073	+	8.94225i	−0.170691	+	0.803038i
$125$	3.66967	−	11.2941i	0.328226	−	1.01017i
$126$	−2.84678	+	3.91826i	−0.253611	+	0.349066i
$127$	−5.62141	+	2.50281i	−0.498819	+	0.222089i	−0.640694	−	0.767796i	$-0.721353\pi$
$127$	−5.62141	+	2.50281i	−0.498819	+	0.222089i	0.141875	+	0.989885i	$0.454687\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	−0.806057	−	0.171333i	−0.0709694	−	0.0150850i
$130$	0.163603	+	0.0728408i	0.0143489	+	0.00638856i
$131$	−0.948917	+	0.547858i	−0.0829073	+	0.0478665i	−0.540881	−	0.841099i	$-0.681909\pi$
$131$	−0.948917	+	0.547858i	−0.0829073	+	0.0478665i	0.457973	+	0.888966i	$0.348576\pi$
$132$	5.75621	−	3.18687i	0.501014	−	0.277381i
$133$	12.8649	+	18.5415i	1.11553	+	1.60775i
$134$	2.70739	+	3.72640i	0.233883	+	0.321912i
$135$	6.25054	+	5.62801i	0.537961	+	0.484382i
$136$	−0.323684	−	1.52281i	−0.0277557	−	0.130580i
$137$	−5.89941	+	2.62659i	−0.504021	+	0.224404i	−0.642965	−	0.765896i	$-0.722296\pi$
$137$	−5.89941	+	2.62659i	−0.504021	+	0.224404i	0.138944	+	0.990300i	$0.455629\pi$
$138$	−3.61018	−	0.379445i	−0.307319	−	0.0323005i
$139$	3.80023	−	3.42175i	0.322332	−	0.290229i	−0.492040	−	0.870573i	$-0.663749\pi$
$139$	3.80023	−	3.42175i	0.322332	−	0.290229i	0.814371	+	0.580344i	$0.197082\pi$
$140$	−10.1120	+	3.28559i	−0.854621	+	0.277683i
$141$	9.74184	+	13.4085i	0.820411	+	1.12920i
$142$	4.89816	+	2.82796i	0.411045	+	0.237317i
$143$	0.237003	−	0.165770i	0.0198192	−	0.0138624i
$144$	−0.935465			−0.0779554
$145$	−9.36721	+	6.80568i	−0.777905	+	0.565181i
$146$	−3.37249	+	15.8663i	−0.279109	+	1.31311i
$147$	−8.16867	−	38.4306i	−0.673741	−	3.16970i
$148$	1.97613	+	4.43846i	0.162437	+	0.364839i
$149$	−5.68388	−	0.597400i	−0.465642	−	0.0489409i	−0.131197	−	0.991356i	$-0.541882\pi$
$149$	−5.68388	−	0.597400i	−0.465642	−	0.0489409i	−0.334445	+	0.942415i	$0.608549\pi$
$150$	0.322778	+	1.51855i	0.0263547	+	0.123989i
$151$	−1.35709	−	4.17671i	−0.110439	−	0.339895i	0.880530	−	0.473991i	$-0.157187\pi$
$151$	−1.35709	−	4.17671i	−0.110439	−	0.339895i	−0.990968	+	0.134096i	$0.957187\pi$
$152$	−1.43675	+	4.11531i	−0.116536	+	0.333795i
$153$			1.45636i			0.117740i
$154$	−3.87129	+	16.7293i	−0.311957	+	1.34808i
$155$	16.2591	−	9.38720i	1.30596	−	0.753998i
$156$	−0.172048	+	0.0180830i	−0.0137749	+	0.00144780i
$157$	−4.25653	+	4.72736i	−0.339708	+	0.377284i	−0.888658	−	0.458571i	$-0.848361\pi$
$157$	−4.25653	+	4.72736i	−0.339708	+	0.377284i	0.548949	+	0.835856i	$0.315028\pi$
$158$	5.26625	+	5.84877i	0.418961	+	0.465303i
$159$	11.0727	+	8.04481i	0.878125	+	0.637995i
$160$	−1.66143	−	1.20710i	−0.131347	−	0.0954294i
$161$	7.04041	−	6.33921i	0.554862	−	0.499600i
$162$	−10.6924	−	2.27275i	−0.840076	−	0.178564i
$163$	−1.95549	+	1.42074i	−0.153166	+	0.111281i	−0.661729	−	0.749743i	$-0.730177\pi$
$163$	−1.95549	+	1.42074i	−0.153166	+	0.111281i	0.508563	+	0.861025i	$0.330177\pi$
$164$	−11.6536			−0.909997
$165$	−12.7735	−	4.40561i	−0.994419	−	0.342976i
$166$	−14.2930	+	8.25209i	−1.10935	+	0.640486i
$167$	−1.48991	−	14.1756i	−0.115293	−	1.09694i	−0.887258	−	0.461273i	$-0.847393\pi$
$167$	−1.48991	−	14.1756i	−0.115293	−	1.09694i	0.771965	−	0.635665i	$-0.219274\pi$
$168$	6.87253	−	7.63272i	0.530227	−	0.588877i
$169$	12.7085	−	2.70127i	0.977575	−	0.207790i
$170$	−1.87925	+	2.58656i	−0.144132	+	0.198380i
$171$	2.11506	−	3.48616i	0.161743	−	0.266593i
$172$	0.395066	+	0.128365i	0.0301235	+	0.00978772i
$173$	−10.7102	+	11.8949i	−0.814283	+	0.904353i	−0.996888	−	0.0788336i	$-0.974880\pi$
$173$	−10.7102	+	11.8949i	−0.814283	+	0.904353i	0.182605	+	0.983186i	$0.441547\pi$
$174$	4.54926	−	10.2178i	0.344878	−	0.774609i
$175$	−3.50885	−	2.02584i	−0.265244	−	0.153139i
$176$	−3.05363	+	1.29434i	−0.230176	+	0.0975648i
$177$	0.913855	−	1.58284i	0.0686896	−	0.118974i
$178$	0.938254	+	1.29140i	0.0703251	+	0.0967942i
$179$	−1.61276	+	0.524017i	−0.120543	+	0.0391669i	−0.368667	−	0.929561i	$-0.620186\pi$
$179$	−1.61276	+	0.524017i	−0.120543	+	0.0391669i	0.248124	+	0.968728i	$0.420186\pi$
$180$	1.28547	+	1.42766i	0.0958133	+	0.106411i
$181$	−5.25856	−	11.8109i	−0.390866	−	0.877899i	−0.996612	−	0.0822413i	$-0.973792\pi$
$181$	−5.25856	−	11.8109i	−0.390866	−	0.877899i	0.605747	−	0.795658i	$-0.292874\pi$
$182$	0.265377	−	0.365261i	0.0196711	−	0.0270749i
$183$	−3.13161	+	9.63812i	−0.231496	+	0.712470i
$184$	1.78987	+	0.380448i	0.131951	+	0.0280470i
$185$	4.05825	−	9.11498i	0.298369	−	0.670147i
$186$	−9.06798	+	15.7062i	−0.664897	+	1.15163i
$187$	2.01508	+	4.75400i	0.147357	+	0.347647i
$188$	−4.17729	−	7.23527i	−0.304660	−	0.527687i
$189$	17.1548	−	12.4637i	1.24783	−	0.906600i
$190$	8.25489	−	3.46235i	0.598873	−	0.251185i
$191$	−1.57777	+	4.85588i	−0.114164	+	0.351359i	−0.991772	−	0.128019i	$-0.959138\pi$
$191$	−1.57777	+	4.85588i	−0.114164	+	0.351359i	0.877608	+	0.479379i	$0.159138\pi$
$192$	1.97293	+	0.207364i	0.142384	+	0.0149652i
$193$	−1.59224	+	15.1492i	−0.114612	+	1.09046i	0.774437	+	0.632650i	$0.218033\pi$
$193$	−1.59224	+	15.1492i	−0.114612	+	1.09046i	−0.889050	+	0.457811i	$0.848634\pi$
$194$	−5.83698	+	5.25564i	−0.419071	+	0.377333i
$195$	0.264018	+	0.237722i	0.0189067	+	0.0170237i
$196$	2.07018	+	19.6965i	0.147870	+	1.40689i
$197$			7.29615i			0.519829i	0.965632	+	0.259915i	$0.0836944\pi$
$197$			7.29615i			0.519829i	−0.965632	+	0.259915i	$0.916306\pi$
$198$	3.04589	−	0.590440i	0.216462	−	0.0419608i
$199$	8.45713	−	14.6482i	0.599510	−	1.03838i	−0.393383	−	0.919375i	$-0.628695\pi$
$199$	8.45713	−	14.6482i	0.599510	−	1.03838i	0.992893	−	0.119007i	$-0.0379712\pi$
$200$	−0.0818014	−	0.778289i	−0.00578424	−	0.0550333i
$201$	2.82366	+	8.69033i	0.199165	+	0.612968i
$202$	9.89804	+	3.21607i	0.696424	+	0.226282i
$203$	11.8727	+	26.6666i	0.833301	+	1.87163i
$204$	0.322830	−	3.07153i	0.0226027	−	0.215050i
$205$	16.0139	+	17.7852i	1.11846	+	1.24217i
$206$	9.43788	+	8.49790i	0.657568	+	0.592077i
$207$	−1.56377	−	0.696237i	−0.108690	−	0.0483918i
$208$	0.0872042			0.00604653
$209$	2.08062	−	14.3063i	0.143919	−	0.989589i
$210$	−21.0926			−1.45553
$211$	−0.0317683	−	0.0141442i	−0.00218702	−	0.000973724i	0.405643	−	0.914032i	$-0.367048\pi$
$211$	−0.0317683	−	0.0141442i	−0.00218702	−	0.000973724i	−0.407830	+	0.913058i	$0.633714\pi$
$212$	−5.12711	−	4.61647i	−0.352131	−	0.317060i
$213$	7.50778	+	8.33823i	0.514425	+	0.571326i
$214$	1.66130	−	15.8062i	0.113564	−	1.08049i
$215$	−0.346977	−	0.779323i	−0.0236636	−	0.0531494i
$216$	3.89517	+	1.26562i	0.265033	+	0.0861144i
$217$	−14.6262	−	45.0149i	−0.992894	−	3.05581i
$218$	−1.11635	−	10.6214i	−0.0756087	−	0.719369i
$219$	−16.0894	+	27.8677i	−1.08722	+	1.88312i
$220$	6.17152	+	2.88168i	0.416083	+	0.194283i
$221$		−	0.135762i		−	0.00913237i
$222$	1.00748	+	9.58549i	0.0676173	+	0.643336i
$223$	−10.4572	−	9.41567i	−0.700264	−	0.630520i	0.240077	−	0.970754i	$-0.422827\pi$
$223$	−10.4572	−	9.41567i	−0.700264	−	0.630520i	−0.940341	+	0.340234i	$0.889494\pi$
$224$	−3.84752	+	3.46433i	−0.257073	+	0.231470i
$225$	−0.0765224	+	0.728062i	−0.00510149	+	0.0485374i
$226$	9.90428	+	1.04098i	0.658823	+	0.0692450i
$227$	−3.35129	+	10.3142i	−0.222433	+	0.684578i	0.776109	+	0.630599i	$0.217191\pi$
$227$	−3.35129	+	10.3142i	−0.222433	+	0.684578i	−0.998542	+	0.0539795i	$0.982809\pi$
$228$	−5.23353	+	6.88360i	−0.346599	+	0.455878i
$229$	14.0399	−	10.2006i	0.927785	−	0.674075i	−0.0176643	−	0.999844i	$-0.505623\pi$
$229$	14.0399	−	10.2006i	0.927785	−	0.674075i	0.945450	+	0.325769i	$0.105623\pi$
$230$	−1.87893	−	3.25440i	−0.123893	−	0.214589i
$231$	−17.5595	+	29.1900i	−1.15533	+	1.92056i
$232$	−2.81903	+	4.88270i	−0.185078	+	0.320565i
$233$	−3.42374	+	7.68985i	−0.224297	+	0.503779i	−0.990281	−	0.139081i	$-0.955585\pi$
$233$	−3.42374	+	7.68985i	−0.224297	+	0.503779i	0.765984	+	0.642859i	$0.222252\pi$
$234$	−0.0797939	−	0.0169607i	−0.00521629	−	0.00110876i
$235$	−5.30189	+	16.3175i	−0.345857	+	1.06444i
$236$	−0.541537	+	0.745362i	−0.0352511	+	0.0485189i
$237$	6.35041	+	14.2633i	0.412504	+	0.926499i
$238$	5.39338	+	5.98995i	0.349601	+	0.388271i
$239$	−15.8330	+	5.14447i	−1.02415	+	0.332768i	−0.772477	−	0.635043i	$-0.780982\pi$
$239$	−15.8330	+	5.14447i	−1.02415	+	0.332768i	−0.251678	+	0.967811i	$0.580982\pi$
$240$	−2.39464	−	3.29594i	−0.154573	−	0.212752i
$241$	−9.31765	+	16.1387i	−0.600203	+	1.03958i	0.392587	+	0.919715i	$0.371580\pi$
$241$	−9.31765	+	16.1387i	−0.600203	+	1.03958i	−0.992790	+	0.119867i	$0.961753\pi$
$242$	9.12571	−	6.14177i	0.586623	−	0.394808i
$243$	−8.13946	−	4.69932i	−0.522147	−	0.301462i
$244$	2.07779	−	4.66679i	0.133017	−	0.298760i
$245$	27.2150	−	30.2254i	1.73871	−	1.93103i
$246$	−21.9870	−	7.14401i	−1.40184	−	0.455486i
$247$	−0.197167	+	0.324980i	−0.0125454	+	0.0206780i
$248$	5.37355	−	7.39606i	0.341221	−	0.469650i
$249$	−32.0255	+	6.80724i	−2.02954	+	0.431391i
$250$	−7.94613	+	8.82508i	−0.502558	+	0.558147i
$251$	−0.190399	−	1.81153i	−0.0120179	−	0.114343i	0.986868	−	0.161527i	$-0.0516419\pi$
$251$	−0.190399	−	1.81153i	−0.0120179	−	0.114343i	−0.998886	+	0.0471843i	$0.984975\pi$
$252$	4.19436	−	2.42162i	0.264220	−	0.152547i
$253$	−6.06796	−	0.109028i	−0.381489	−	0.00685451i
$254$	6.15340			0.386098
$255$	−5.13123	+	3.72806i	−0.321330	+	0.233460i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	−9.64603	+	8.68533i	−0.601703	+	0.541776i	−0.912698	−	0.408636i	$-0.866005\pi$
$257$	−9.64603	+	8.68533i	−0.601703	+	0.541776i	0.310994	+	0.950412i	$0.399338\pi$
$258$	0.666683	+	0.484373i	0.0415059	+	0.0301558i
$259$	−20.3501	−	14.7852i	−1.26450	−	0.918710i
$260$	−0.119832	−	0.133087i	−0.00743165	−	0.00825369i
$261$	3.52913	−	3.91949i	0.218448	−	0.242611i
$262$	1.08971	−	0.114533i	0.0673227	−	0.00707590i
$263$	−6.54847	+	3.78076i	−0.403796	+	0.233132i	−0.688121	−	0.725596i	$-0.741564\pi$
$263$	−6.54847	+	3.78076i	−0.403796	+	0.233132i	0.284325	+	0.958728i	$0.408231\pi$
$264$	−6.55478	+	0.570084i	−0.403419	+	0.0350862i
$265$			14.1685i			0.870362i
$266$	−4.21119	−	22.1712i	−0.258205	−	1.35940i
$267$	0.978547	+	3.01166i	0.0598861	+	0.184311i
$268$	−0.957658	−	4.50543i	−0.0584983	−	0.275213i
$269$	13.6394	+	1.43356i	0.831611	+	0.0874059i	0.510760	−	0.859724i	$-0.329364\pi$
$269$	13.6394	+	1.43356i	0.831611	+	0.0874059i	0.320852	+	0.947129i	$0.396031\pi$
$270$	−3.42103	−	7.68377i	−0.208197	−	0.467619i
$271$	−3.59522	−	16.9142i	−0.218394	−	1.02746i	−0.941575	−	0.336804i	$-0.890654\pi$
$271$	−3.59522	−	16.9142i	−0.218394	−	1.02746i	0.723181	−	0.690659i	$-0.242679\pi$
$272$	−0.323684	+	1.52281i	−0.0196262	+	0.0923341i
$273$	0.724605	−	0.526456i	0.0438551	−	0.0318626i
$274$	6.45771			0.390125
$275$	0.757581	+	2.48249i	0.0456839	+	0.149700i
$276$	3.14373	+	1.81503i	0.189230	+	0.109252i
$277$	9.05743	+	12.4665i	0.544208	+	0.749038i	0.989212	−	0.146490i	$-0.0467977\pi$
$277$	9.05743	+	12.4665i	0.544208	+	0.749038i	−0.445004	+	0.895529i	$0.646798\pi$
$278$	−4.86344	+	1.58023i	−0.291690	+	0.0947757i
$279$	−6.35541	+	5.72244i	−0.380488	+	0.342593i
$280$	10.5742	+	1.11139i	0.631927	+	0.0664182i
$281$	3.06119	−	1.36293i	0.182615	−	0.0813055i	−0.313392	−	0.949624i	$-0.601466\pi$
$281$	3.06119	−	1.36293i	0.182615	−	0.0813055i	0.496008	+	0.868318i	$0.334799\pi$
$282$	−3.44589	−	16.2116i	−0.205200	−	0.965389i
$283$	13.9228	+	12.5361i	0.827622	+	0.745195i	0.969605	−	0.244675i	$-0.0786811\pi$
$283$	13.9228	+	12.5361i	0.827622	+	0.745195i	−0.141983	+	0.989869i	$0.545348\pi$
$284$	−3.32446	−	4.57573i	−0.197270	−	0.271519i
$285$	17.6971	−	1.47196i	1.04828	−	0.0871914i
$286$	−0.283938	+	0.0550410i	−0.0167896	+	0.00325464i
$287$	52.2517	−	30.1675i	3.08432	−	1.78073i
$288$	0.854590	+	0.380488i	0.0503572	+	0.0224205i
$289$	−14.2577	−	3.03058i	−0.838691	−	0.178269i
$290$	11.3255	−	2.40731i	0.665056	−	0.141362i
$291$	−14.2345	+	6.33762i	−0.834442	+	0.371518i
$292$	9.53434	−	13.1229i	0.557955	−	0.767959i
$293$	−1.39212	+	4.28451i	−0.0813286	+	0.250304i	−0.983450	−	0.181178i	$-0.942009\pi$
$293$	−1.39212	+	4.28451i	−0.0813286	+	0.250304i	0.902122	+	0.431482i	$0.142009\pi$
$294$	−8.16867	+	38.4306i	−0.476407	+	2.24132i
$295$	1.88169	−	0.197773i	0.109556	−	0.0115148i
$296$		−	4.85850i		−	0.282394i
$297$	−13.4816	−	1.66234i	−0.782279	−	0.0964588i
$298$	4.94950	+	2.85760i	0.286717	+	0.165536i
$299$	0.145775	+	0.0649034i	0.00843041	+	0.00375346i
$300$	0.322778	−	1.51855i	0.0186356	−	0.0876735i
$301$	−2.10366	+	0.447147i	−0.121253	+	0.0257731i
$302$	−0.459052	+	4.36759i	−0.0264155	+	0.251327i
$303$	16.7032	+	12.1356i	0.959572	+	0.697170i
$304$	2.98639	−	3.17514i	0.171281	−	0.182107i
$305$	−9.97741	+	3.24186i	−0.571305	+	0.185628i
$306$	0.592356	−	1.33045i	0.0338627	−	0.0760569i
$307$	−6.68046	−	11.5709i	−0.381274	−	0.660386i	0.609971	−	0.792424i	$-0.291181\pi$
$307$	−6.68046	−	11.5709i	−0.381274	−	0.660386i	−0.991245	+	0.132038i	$0.957848\pi$
$308$	10.3410	−	13.7083i	0.589233	−	0.781105i
$309$	12.5970	+	21.8187i	0.716621	+	1.24122i
$310$	−18.6716	+	1.96246i	−1.06047	+	0.111460i
$311$	0.638515	+	1.96515i	0.0362069	+	0.111433i	0.967526	−	0.252770i	$-0.0813415\pi$
$311$	0.638515	+	1.96515i	0.0362069	+	0.111433i	−0.931320	+	0.364203i	$0.881341\pi$
$312$	0.164529	+	0.0534587i	0.00931461	+	0.00302650i
$313$	7.75030	−	3.45066i	0.438073	−	0.195043i	−0.175836	−	0.984419i	$-0.556263\pi$
$313$	7.75030	−	3.45066i	0.438073	−	0.195043i	0.613909	+	0.789377i	$0.289596\pi$
$314$	5.81133	−	2.58737i	0.327952	−	0.146014i
$315$	−9.45943	−	3.07356i	−0.532979	−	0.173175i
$316$	−2.43205	−	7.48509i	−0.136814	−	0.421069i
$317$	11.4141	−	1.19967i	0.641078	−	0.0673800i	0.221589	−	0.975140i	$-0.428876\pi$
$317$	11.4141	−	1.19967i	0.641078	−	0.0673800i	0.419489	+	0.907760i	$0.362209\pi$
$318$	−6.84332	−	11.8530i	−0.383755	−	0.664682i
$319$	6.09696	−	17.6774i	0.341364	−	0.989745i
$320$	1.02682	+	1.77850i	0.0574009	+	0.0994213i
$321$	12.8241	−	28.8033i	0.715769	−	1.60764i
$322$	−9.01012	+	2.92757i	−0.502114	+	0.163147i
$323$	−4.94316	−	4.64930i	−0.275045	−	0.258694i
$324$	8.84361	+	6.42526i	0.491312	+	0.356959i
$325$	0.00713343	−	0.0678701i	0.000395692	−	0.00376475i
$326$	2.36430	−	0.502547i	0.130946	−	0.0278335i
$327$	4.40496	−	20.7237i	0.243595	−	1.14602i
$328$	10.6461	+	4.73997i	0.587835	+	0.261721i
$329$	37.4596	+	21.6273i	2.06521	+	1.19235i
$330$	9.87729	+	9.22019i	0.543727	+	0.507555i
$331$		−	9.53206i		−	0.523929i	−0.965077	−	0.261965i	$-0.915630\pi$
$331$		−	9.53206i		−	0.523929i	0.965077	−	0.261965i	$-0.0843704\pi$
$332$	16.4138	−	1.72516i	0.900822	−	0.0946802i
$333$	−0.944949	+	4.44564i	−0.0517829	+	0.243619i
$334$	−4.40462	+	13.5560i	−0.241010	+	0.741752i
$335$	−5.55999	+	7.65267i	−0.303775	+	0.418110i
$336$	−9.38288	+	4.17753i	−0.511878	+	0.227903i
$337$	−11.7071	+	2.48843i	−0.637728	+	0.135553i	−0.515418	−	0.856939i	$-0.672363\pi$
$337$	−11.7071	+	2.48843i	−0.637728	+	0.135553i	−0.122310	+	0.992492i	$0.539030\pi$
$338$	−12.7085	−	2.70127i	−0.691250	−	0.146930i
$339$	18.0483	+	8.03562i	0.980250	+	0.436435i
$340$	2.76883	−	1.59858i	0.150161	−	0.0866954i
$341$	−12.8282	+	27.4733i	−0.694684	+	1.48776i
$342$	−3.35016	+	2.32449i	−0.181156	+	0.125694i
$343$	−38.9678	−	53.6345i	−2.10406	−	2.89599i
$344$	−0.308700	−	0.277955i	−0.0166440	−	0.0149863i
$345$	−1.54995	−	7.29193i	−0.0834464	−	0.392584i
$346$	14.6224	−	6.51030i	0.786103	−	0.349996i
$347$	−5.86849	−	0.616804i	−0.315037	−	0.0331118i	−0.0543096	−	0.998524i	$-0.517296\pi$
$347$	−5.86849	−	0.616804i	−0.315037	−	0.0331118i	−0.260728	+	0.965412i	$0.583962\pi$
$348$	−8.31190	+	7.48407i	−0.445565	+	0.401188i
$349$	16.9174	−	5.49679i	0.905566	−	0.294236i	0.181034	−	0.983477i	$-0.442056\pi$
$349$	16.9174	−	5.49679i	0.905566	−	0.294236i	0.724532	+	0.689241i	$0.242056\pi$
$350$	2.38151	+	3.27787i	0.127297	+	0.175210i
$351$	0.309306	+	0.178578i	0.0165095	+	0.00953179i
$352$	3.31609	+	0.0595827i	0.176748	+	0.00317577i
$353$	−18.3852			−0.978546			−0.489273	−	0.872131i	$-0.662738\pi$
$353$	−18.3852			−0.978546			−0.489273	+	0.872131i	$0.662738\pi$
$354$	−1.47865	+	1.07430i	−0.0785893	+	0.0570985i
$355$	−2.41493	+	11.3614i	−0.128171	+	0.602999i
$356$	−0.331879	−	1.56137i	−0.0175896	−	0.0827525i
$357$	6.50371	+	14.6076i	0.344213	+	0.773115i
$358$	1.68647	+	0.177255i	0.0891325	+	0.00936820i
$359$	−4.50712	−	21.2043i	−0.237877	−	1.11912i	−0.921225	−	0.389030i	$-0.872810\pi$
$359$	−4.50712	−	21.2043i	−0.237877	−	1.11912i	0.683348	−	0.730093i	$-0.260523\pi$
$360$	−0.593654	−	1.82708i	−0.0312883	−	0.0962955i
$361$	5.08050	+	18.3082i	0.267395	+	0.963587i
$362$			12.9287i			0.679515i
$363$	20.9826	−	5.99340i	1.10130	−	0.314572i
$364$	−0.390999	+	0.225744i	−0.0204939	+	0.0118322i
$365$	−33.1291	+	3.48201i	−1.73406	+	0.182257i
$366$	6.78105	−	7.53111i	0.354451	−	0.393658i
$367$	14.2703	+	15.8488i	0.744905	+	0.827301i	0.989832	−	0.142241i	$-0.0454307\pi$
$367$	14.2703	+	15.8488i	0.744905	+	0.827301i	−0.244927	+	0.969541i	$0.578764\pi$
$368$	−1.48038	−	1.07556i	−0.0771703	−	0.0560675i
$369$	−8.81956	−	6.40779i	−0.459128	−	0.333576i
$370$	−7.41480	+	6.67631i	−0.385477	+	0.347085i
$371$	34.9391	+	7.42653i	1.81395	+	0.385566i
$372$	14.6723	−	10.6601i	0.760723	−	0.552698i
$373$	18.3420			0.949712			0.474856	−	0.880063i	$-0.342500\pi$
$373$	18.3420			0.949712			0.474856	+	0.880063i	$0.342500\pi$
$374$	0.0927603	−	5.16260i	0.00479652	−	0.266952i
$375$	−20.4020	+	11.7791i	−1.05356	+	0.608271i
$376$	0.873291	+	8.30881i	0.0450365	+	0.428494i
$377$	−0.328986	+	0.365376i	−0.0169436	+	0.0188178i
$378$	−20.7411	+	4.40866i	−1.06681	+	0.226757i
$379$	19.4045	−	26.7080i	0.996741	−	1.37190i	0.0694368	−	0.997586i	$-0.477880\pi$
$379$	19.4045	−	26.7080i	0.996741	−	1.37190i	0.927304	−	0.374309i	$-0.122120\pi$
$380$	−8.94948	−	0.194551i	−0.459099	−	0.00998027i
$381$	11.6097	+	3.77220i	0.594780	+	0.193256i
$382$	3.41643	−	3.79433i	0.174800	−	0.194135i
$383$	0.655228	−	1.47167i	0.0334806	−	0.0751986i	−0.896031	−	0.443991i	$-0.853562\pi$
$383$	0.655228	−	1.47167i	0.0334806	−	0.0751986i	0.929512	+	0.368793i	$0.120229\pi$
$384$	−1.71802	−	0.991900i	−0.0876724	−	0.0506177i
$385$	−35.1311	+	3.05543i	−1.79045	+	0.155719i
$386$	7.61631	−	13.1918i	0.387660	−	0.671447i
$387$	0.228407	+	0.314375i	0.0116106	+	0.0159806i
$388$	7.47001	−	2.42715i	0.379232	−	0.123220i
$389$	−20.8964	−	23.2078i	−1.05949	−	1.17668i	−0.983748	−	0.179552i	$-0.942535\pi$
$389$	−20.8964	−	23.2078i	−1.05949	−	1.17668i	−0.0757391	−	0.997128i	$-0.524132\pi$
$390$	−0.144502	−	0.324556i	−0.00731712	−	0.0164345i
$391$	−1.67447	+	2.30471i	−0.0846815	+	0.116554i
$392$	6.12008	−	18.8357i	0.309111	−	0.951344i
$393$	2.12618	+	0.451934i	0.107252	+	0.0227970i
$394$	2.96761	−	6.66536i	0.149506	−	0.335796i
$395$	−8.08136	+	13.9973i	−0.406617	+	0.704282i
$396$	−3.02271	−	0.699479i	−0.151897	−	0.0351502i
$397$	−5.68320	−	9.84360i	−0.285232	−	0.494036i	0.687434	−	0.726247i	$-0.258737\pi$
$397$	−5.68320	−	9.84360i	−0.285232	−	0.494036i	−0.972665	+	0.232211i	$0.925404\pi$
$398$	−13.6839	+	9.94195i	−0.685913	+	0.498345i
$399$	5.64626	−	44.4121i	0.282667	−	2.22338i
$400$	−0.241829	+	0.744274i	−0.0120915	+	0.0372137i
$401$	−15.3696	−	1.61541i	−0.767523	−	0.0806699i	−0.287329	−	0.957832i	$-0.592767\pi$
$401$	−15.3696	−	1.61541i	−0.767523	−	0.0806699i	−0.480194	+	0.877162i	$0.659434\pi$
$402$	0.955134	−	9.08749i	0.0476378	−	0.453243i
$403$	0.592453	−	0.533447i	0.0295122	−	0.0265729i
$404$	−7.73422	−	6.96392i	−0.384792	−	0.346468i
$405$	−2.34655	−	22.3259i	−0.116601	−	1.10939i
$406$		−	29.1902i		−	1.44868i
$407$	3.06655	+	15.8193i	0.152003	+	0.784135i
$408$	−1.54422	+	2.67467i	−0.0764504	+	0.132416i
$409$	−0.945551	−	8.99631i	−0.0467545	−	0.444839i	−0.992709	−	0.120539i	$-0.961538\pi$
$409$	−0.945551	−	8.99631i	−0.0467545	−	0.444839i	0.945954	−	0.324300i	$-0.105129\pi$
$410$	−7.39551	−	22.7610i	−0.365238	−	1.12409i
$411$	12.1838	+	3.95876i	0.600983	+	0.195271i
$412$	−5.16552	−	11.6019i	−0.254487	−	0.571587i
$413$	0.498599	−	4.74386i	0.0245345	−	0.233430i
$414$	1.14539	+	1.27209i	0.0562930	+	0.0625197i
$415$	−25.1878	−	22.6792i	−1.23642	−	1.11328i
$416$	−0.0796650	−	0.0354692i	−0.00390590	−	0.00173902i
$417$	−10.1446			−0.496783
$418$	−7.71965	+	12.2232i	−0.377580	+	0.597857i
$419$	3.29039			0.160746			0.0803731	−	0.996765i	$-0.474389\pi$
$419$	3.29039			0.160746			0.0803731	+	0.996765i	$0.474389\pi$
$420$	19.2690	+	8.57912i	0.940232	+	0.418618i
$421$	−24.3284	−	21.9054i	−1.18569	−	1.06760i	−0.996321	−	0.0856978i	$-0.972688\pi$
$421$	−24.3284	−	21.9054i	−1.18569	−	1.06760i	−0.189372	−	0.981905i	$-0.560645\pi$
$422$	0.0232688	+	0.0258427i	0.00113271	+	0.00125800i
$423$	0.816933	−	7.77260i	0.0397206	−	0.377917i
$424$	2.80616	+	6.30274i	0.136279	+	0.306088i
$425$	1.15871	+	0.376488i	0.0562057	+	0.0182623i
$426$	−3.46723	−	10.6710i	−0.167988	−	0.517014i
$427$	2.76459	+	26.3033i	0.133788	+	1.27291i
$428$	−7.94665	+	13.7640i	−0.384116	+	0.665308i
$429$	−0.569450	−	0.0702159i	−0.0274933	−	0.00339006i
$430$			0.853075i			0.0411389i
$431$	−0.889197	−	8.46014i	−0.0428311	−	0.407511i	−0.994841	−	0.101444i	$-0.967654\pi$
$431$	−0.889197	−	8.46014i	−0.0428311	−	0.407511i	0.952010	−	0.306067i	$-0.0990130\pi$
$432$	−3.04364	−	2.74051i	−0.146437	−	0.131853i
$433$	6.72064	−	6.05129i	0.322973	−	0.290806i	−0.491655	−	0.870790i	$-0.663608\pi$
$433$	6.72064	−	6.05129i	0.322973	−	0.290806i	0.814628	+	0.579984i	$0.196941\pi$
$434$	−4.94749	+	47.0722i	−0.237487	+	2.25954i
$435$	22.8436	+	2.40096i	1.09527	+	0.115117i
$436$	−3.30026	+	10.1571i	−0.158054	+	0.486439i
$437$	7.35536	−	3.08506i	0.351855	−	0.147579i
$438$	26.0332	−	18.9142i	1.24391	−	0.903757i
$439$	8.92467	+	15.4580i	0.425951	+	0.737769i	0.996509	−	0.0834887i	$-0.0266063\pi$
$439$	8.92467	+	15.4580i	0.425951	+	0.737769i	−0.570558	+	0.821258i	$0.693273\pi$
$440$	−4.46588	−	5.14272i	−0.212902	−	0.245170i
$441$	−9.26343	+	16.0447i	−0.441116	+	0.764035i
$442$	−0.0552196	+	0.124025i	−0.00262653	+	0.00589927i
$443$	24.8580	+	5.28373i	1.18104	+	0.251037i	0.756267	−	0.654263i	$-0.227021\pi$
$443$	24.8580	+	5.28373i	1.18104	+	0.251037i	0.424771	+	0.905301i	$0.360355\pi$
$444$	2.97840	−	9.16656i	0.141348	−	0.435026i
$445$	−1.92683	+	2.65206i	−0.0913406	+	0.125720i
$446$	5.72340	+	12.8550i	0.271011	+	0.608700i
$447$	7.58647	+	8.42563i	0.358828	+	0.398519i
$448$	4.92396	−	1.59989i	0.232635	−	0.0755877i
$449$	−15.6918	−	21.5979i	−0.740541	−	1.01927i	−0.998587	−	0.0531348i	$-0.983079\pi$
$449$	−15.6918	−	21.5979i	−0.740541	−	1.01927i	0.258046	−	0.966133i	$-0.416921\pi$
$450$	0.366036	−	0.633993i	0.0172551	−	0.0298867i
$451$	−37.6557	−	8.71384i	−1.77314	−	0.410318i
$452$	−8.62460	−	4.97942i	−0.405667	−	0.234212i
$453$	−3.54355	+	7.95895i	−0.166491	+	0.373944i
$454$	7.25672	−	8.05941i	0.340575	−	0.378247i
$455$	0.881811	+	0.286518i	0.0413399	+	0.0134322i
$456$	7.58088	−	4.15982i	0.355007	−	0.194801i
$457$	−16.6894	+	22.9710i	−0.780696	+	1.07454i	0.214508	+	0.976722i	$0.431185\pi$
$457$	−16.6894	+	22.9710i	−0.780696	+	1.07454i	−0.995205	+	0.0978142i	$0.968815\pi$
$458$	−16.9751	+	3.60817i	−0.793194	+	0.168599i
$459$	−4.26651	+	4.73844i	−0.199144	+	0.221172i
$460$	0.392803	+	3.73727i	0.0183145	+	0.174251i
$461$	37.1562	−	21.4521i	1.73054	−	0.999126i	0.844369	−	0.535762i	$-0.179976\pi$
$461$	37.1562	−	21.4521i	1.73054	−	0.999126i	0.886168	−	0.463364i	$-0.153358\pi$
$462$	27.9140	−	19.5243i	1.29868	−	0.908352i
$463$	−10.0914			−0.468986			−0.234493	−	0.972118i	$-0.575343\pi$
$463$	−10.0914			−0.468986			−0.234493	+	0.972118i	$0.575343\pi$
$464$	4.56128	−	3.31396i	0.211752	−	0.153847i
$465$	−36.4308	−	7.74360i	−1.68944	−	0.359101i
$466$	6.25548	−	5.63246i	0.289780	−	0.260919i
$467$	−22.8738	−	16.6188i	−1.05847	−	0.769027i	−0.0846690	−	0.996409i	$-0.526983\pi$
$467$	−22.8738	−	16.6188i	−1.05847	−	0.769027i	−0.973806	+	0.227382i	$0.926983\pi$
$468$	0.0659968	+	0.0479495i	0.00305070	+	0.00221646i
$469$	15.9570	+	17.7220i	0.736824	+	0.818326i
$470$	11.4804	−	12.7503i	0.529554	−	0.588129i
$471$	12.5504	−	1.31910i	0.578292	−	0.0607809i
$472$	0.797884	−	0.460659i	0.0367256	−	0.0212035i
$473$	1.18057	+	0.710182i	0.0542827	+	0.0326542i
$474$		−	15.6131i		−	0.717133i
$475$	−2.22688	−	2.58400i	−0.102176	−	0.118562i
$476$	−2.49076	−	7.66578i	−0.114164	−	0.351360i
$477$	−1.34185	−	6.31293i	−0.0614393	−	0.289049i
$478$	16.5567	+	1.74017i	0.757284	+	0.0795937i
$479$	−16.0156	−	35.9716i	−0.731771	−	1.64358i	−0.764913	−	0.644133i	$-0.777218\pi$
$479$	−16.0156	−	35.9716i	−0.731771	−	1.64358i	0.0331425	−	0.999451i	$-0.489448\pi$
$480$	0.847033	+	3.98498i	0.0386616	+	0.181889i
$481$	0.0880884	−	0.414423i	0.00401648	−	0.0188961i
$482$	15.0763	−	10.9536i	0.686706	−	0.498921i
$483$	−18.7941			−0.855163
$484$	−10.8348	+	1.89902i	−0.492493	+	0.0863193i
$485$	−13.9691	−	8.06507i	−0.634305	−	0.366216i
$486$	5.52438	+	7.60366i	0.250591	+	0.344909i
$487$	22.7462	−	7.39068i	1.03073	−	0.334904i	0.255650	−	0.966769i	$-0.417711\pi$
$487$	22.7462	−	7.39068i	1.03073	−	0.334904i	0.775078	+	0.631866i	$0.217711\pi$
$488$	−3.79631	+	3.41821i	−0.171851	+	0.154735i
$489$	4.76881	+	0.501222i	0.215653	+	0.0226660i
$490$	−37.1559	+	16.5429i	−1.67853	+	0.747332i
$491$	3.66839	+	17.2584i	0.165552	+	0.778862i	0.980059	+	0.198708i	$0.0636744\pi$
$491$	3.66839	+	17.2584i	0.165552	+	0.778862i	−0.814507	+	0.580154i	$0.802992\pi$
$492$	17.1804	+	15.4693i	0.774553	+	0.697410i
$493$	−5.15929	−	7.10115i	−0.232363	−	0.319820i
$494$	0.312302	−	0.216689i	0.0140511	−	0.00974932i
$495$	3.08615	+	5.57430i	0.138712	+	0.250546i
$496$	−7.91723	+	4.57101i	−0.355494	+	0.205245i
$497$	26.7510	+	11.9103i	1.19995	+	0.534251i
$498$	32.0255	+	6.80724i	1.43510	+	0.305040i
$499$	20.1551	−	4.28409i	0.902264	−	0.191782i	0.266654	−	0.963792i	$-0.414082\pi$
$499$	20.1551	−	4.28409i	0.902264	−	0.191782i	0.635610	+	0.772010i	$0.280749\pi$
$500$	10.8486	−	4.83012i	0.485166	−	0.216010i
$501$	−16.6204	+	22.8761i	−0.742547	+	1.02203i
$502$	−0.562876	+	1.73236i	−0.0251224	+	0.0773188i
$503$	−5.62244	+	26.4515i	−0.250692	+	1.17941i	0.655050	+	0.755585i	$0.272647\pi$
$503$	−5.62244	+	26.4515i	−0.250692	+	1.17941i	−0.905742	+	0.423829i	$0.860686\pi$
$504$	−4.81670	+	0.506255i	−0.214553	+	0.0225504i
$505$			21.3731i			0.951089i
$506$	5.49901	+	2.56766i	0.244461	+	0.114147i
$507$	−22.3212	−	12.8872i	−0.991320	−	0.572339i
$508$	−5.62141	−	2.50281i	−0.249410	−	0.111044i
$509$	−8.12580	+	38.2289i	−0.360170	+	1.69447i	0.308760	+	0.951140i	$0.400086\pi$
$509$	−8.12580	+	38.2289i	−0.360170	+	1.69447i	−0.668930	+	0.743326i	$0.733247\pi$
$510$	6.20395	−	1.31869i	0.274715	−	0.0583926i
$511$	−8.77838	+	83.5207i	−0.388333	+	3.69474i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	17.0945	−	5.14639i	0.754743	−	0.227219i
$514$	12.3447	−	4.01105i	0.544503	−	0.176920i
$515$	−10.6081	+	23.8262i	−0.467449	+	1.04991i
$516$	−0.412033	−	0.713661i	−0.0181387	−	0.0314172i
$517$	−8.08774	−	26.5024i	−0.355698	−	1.16557i
$518$	12.5771	+	21.7841i	0.552605	+	0.957140i
$519$	31.5791	−	3.31910i	1.38617	−	0.145692i
$520$	0.0553406	+	0.170321i	0.00242684	+	0.00746906i
$521$	1.85103	+	0.601437i	0.0810952	+	0.0263494i	0.349284	−	0.937017i	$-0.386425\pi$
$521$	1.85103	+	0.601437i	0.0810952	+	0.0263494i	−0.268188	+	0.963366i	$0.586425\pi$
$522$	−4.81822	+	2.14521i	−0.210888	+	0.0938933i
$523$	20.6832	−	9.20874i	0.904412	−	0.402670i	0.0987954	−	0.995108i	$-0.468501\pi$
$523$	20.6832	−	9.20874i	0.904412	−	0.402670i	0.805616	+	0.592438i	$0.201834\pi$
$524$	−1.04209	−	0.338595i	−0.0455238	−	0.0147916i
$525$	2.48379	+	7.64431i	0.108401	+	0.333625i
$526$	7.52010	−	0.790394i	0.327892	−	0.0344628i
$527$	7.11631	+	12.3258i	0.309991	+	0.536920i
$528$	6.21996	+	2.14527i	0.270689	+	0.0933609i
$529$	9.82582	+	17.0188i	0.427209	+	0.739948i
$530$	5.76283	−	12.9435i	0.250321	−	0.562231i
$531$	−0.819678	+	0.266329i	−0.0355710	+	0.0115577i
$532$	−5.17071	+	21.9672i	−0.224179	+	0.952399i
$533$	0.822162	+	0.597335i	0.0356118	+	0.0258735i
$534$	0.331005	−	3.14930i	0.0143240	−	0.136283i
$535$	31.9258	−	6.78604i	1.38027	−	0.293386i
$536$	−0.957658	+	4.50543i	−0.0413645	+	0.194605i
$537$	3.07320	+	1.36828i	0.132618	+	0.0590456i
$538$	−11.8772	−	6.85729i	−0.512061	−	0.295639i
$539$	−8.03849	+	65.1920i	−0.346242	+	2.80802i
$540$			8.41093i			0.361949i
$541$	−9.25326	+	0.972557i	−0.397829	+	0.0418135i	−0.301331	−	0.953520i	$-0.597431\pi$
$541$	−9.25326	+	0.972557i	−0.397829	+	0.0418135i	−0.0964981	+	0.995333i	$0.530764\pi$
$542$	−3.59522	+	16.9142i	−0.154428	+	0.726526i
$543$	−7.92563	+	24.3926i	−0.340121	+	1.04679i
$544$	0.915083	−	1.25950i	0.0392339	−	0.0540008i
$545$	20.0364	−	8.92077i	0.858264	−	0.382124i
$546$	−0.876088	+	0.186218i	−0.0374931	+	0.00796941i
$547$	40.9494	+	8.70406i	1.75087	+	0.372159i	0.968180	−	0.250254i	$-0.0805143\pi$
$547$	40.9494	+	8.70406i	1.75087	+	0.372159i	0.782689	+	0.622413i	$0.213848\pi$
$548$	−5.89941	−	2.62659i	−0.252010	−	0.112202i
$549$	4.13853	−	2.38938i	0.176628	−	0.101976i
$550$	0.317633	−	2.57600i	0.0135439	−	0.109841i
$551$	2.03706	+	24.4911i	0.0867816	+	1.04336i
$552$	−2.13370	−	2.93678i	−0.0908163	−	0.124998i
$553$	30.2811	+	27.2652i	1.28768	+	1.15944i
$554$	−3.20380	−	15.0727i	−0.136116	−	0.640377i
$555$	−18.0823	+	8.05076i	−0.767551	+	0.341736i
$556$	5.08571	+	0.534529i	0.215682	+	0.0226691i
$557$	12.1434	−	10.9340i	0.514533	−	0.463288i	−0.370489	−	0.928837i	$-0.620810\pi$
$557$	12.1434	−	10.9340i	0.514533	−	0.463288i	0.885022	+	0.465549i	$0.154143\pi$
$558$	8.13348	−	2.64273i	0.344318	−	0.111876i
$559$	−0.0212922	−	0.0293062i	−0.000900563	−	0.00123952i
$560$	−9.20793	−	5.31620i	−0.389106	−	0.224651i
$561$	3.33983	−	9.68344i	0.141008	−	0.408835i
$562$	−3.35089			−0.141349
$563$	15.3621	−	11.1612i	0.647436	−	0.470390i	−0.214961	−	0.976623i	$-0.568962\pi$
$563$	15.3621	−	11.1612i	0.647436	−	0.470390i	0.862397	+	0.506233i	$0.168962\pi$
$564$	−3.44589	+	16.2116i	−0.145098	+	0.682633i
$565$	4.25217	+	20.0049i	0.178890	+	0.841612i
$566$	−7.62018	−	17.1152i	−0.320300	−	0.719406i
$567$	−56.2852	−	5.91581i	−2.36375	−	0.248441i
$568$	1.17593	+	5.53232i	0.0493409	+	0.232131i
$569$	−0.779967	−	2.40049i	−0.0326979	−	0.100634i	0.933376	−	0.358901i	$-0.116848\pi$
$569$	−0.779967	−	2.40049i	−0.0326979	−	0.100634i	−0.966074	+	0.258267i	$0.916848\pi$
$570$	−16.7658	−	5.85334i	−0.702241	−	0.245170i
$571$			19.1339i			0.800730i	0.916356	+	0.400365i	$0.131117\pi$
$571$			19.1339i			0.800730i	−0.916356	+	0.400365i	$0.868883\pi$
$572$	0.281778	+	0.0652056i	0.0117817	+	0.00272638i
$573$	8.77184	−	5.06442i	0.366449	−	0.211569i
$574$	−60.0045	+	6.30673i	−2.50454	+	0.263238i
$575$	−0.958195	+	1.06418i	−0.0399595	+	0.0443795i
$576$	−0.625948	−	0.695186i	−0.0260812	−	0.0289661i
$577$	−26.2582	−	19.0777i	−1.09314	−	0.794215i	−0.113216	−	0.993570i	$-0.536115\pi$
$577$	−26.2582	−	19.0777i	−1.09314	−	0.794215i	−0.979927	+	0.199355i	$0.936115\pi$
$578$	11.7925	+	8.56772i	0.490501	+	0.356370i
$579$	22.4567	−	20.2201i	0.933269	−	0.840319i
$580$	−11.3255	−	2.40731i	−0.470265	−	0.0999580i
$581$	−69.1288	+	50.2250i	−2.86795	+	2.08369i
$582$	15.5816			0.645879
$583$	−13.1150	−	18.7506i	−0.543168	−	0.776571i
$584$	−14.0476	+	8.11039i	−0.581294	+	0.335610i
$585$	−0.0175115	−	0.166611i	−0.000724011	−	0.00688851i
$586$	3.01443	−	3.34787i	0.124525	−	0.138299i
$587$	16.6799	−	3.54543i	0.688455	−	0.146336i	0.149615	−	0.988744i	$-0.452196\pi$
$587$	16.6799	−	3.54543i	0.688455	−	0.146336i	0.538839	+	0.842409i	$0.318863\pi$
$588$	23.0936	−	31.7856i	0.952363	−	1.31082i
$589$	0.866070	−	39.8398i	0.0356858	−	1.64157i
$590$	−1.79945	−	0.584676i	−0.0740821	−	0.0240707i
$591$	9.68507	−	10.7564i	0.398390	−	0.442457i
$592$	−1.97613	+	4.43846i	−0.0812184	+	0.182420i
$593$	−33.8275	−	19.5303i	−1.38913	−	0.802014i	−0.395912	−	0.918288i	$-0.629572\pi$
$593$	−33.8275	−	19.5303i	−1.38913	−	0.802014i	−0.993217	+	0.116274i	$0.962905\pi$
$594$	11.6399	+	7.00207i	0.477590	+	0.287298i
$595$	−8.27644	+	14.3352i	−0.339301	+	0.587686i
$596$	−3.35931	−	4.62369i	−0.137603	−	0.189394i
$597$	−31.9122	+	10.3689i	−1.30608	+	0.424371i
$598$	−0.106774	−	0.118584i	−0.00436631	−	0.00484928i
$599$	−14.9986	−	33.6874i	−0.612827	−	1.37643i	−0.907183	−	0.420735i	$-0.861772\pi$
$599$	−14.9986	−	33.6874i	−0.612827	−	1.37643i	0.294357	−	0.955696i	$-0.404895\pi$
$600$	−0.912521	+	1.25598i	−0.0372535	+	0.0512751i
$601$	7.23129	−	22.2556i	0.294970	−	0.907825i	−0.688261	−	0.725463i	$-0.741626\pi$
$601$	7.23129	−	22.2556i	0.294970	−	0.907825i	0.983231	−	0.182362i	$-0.0583744\pi$
$602$	2.10366	+	0.447147i	0.0857388	+	0.0182243i
$603$	1.75256	−	3.93631i	0.0713697	−	0.160299i
$604$	2.19582	−	3.80328i	0.0893468	−	0.154753i
$605$	17.7869	+	13.9260i	0.723140	+	0.566174i
$606$	−10.3231	−	17.8802i	−0.419348	−	0.726332i
$607$	33.4742	−	24.3204i	1.35868	−	0.987136i	0.360149	−	0.932895i	$-0.382726\pi$
$607$	33.4742	−	24.3204i	1.35868	−	0.987136i	0.998528	−	0.0542415i	$-0.0172741\pi$
$608$	−4.01964	+	1.68596i	−0.163018	+	0.0683747i
$609$	17.8944	−	55.0733i	0.725118	−	2.23168i
$610$	10.4334	+	1.09659i	0.422436	+	0.0443998i
$611$	−0.0761547	+	0.724563i	−0.00308089	+	0.0293127i
$612$	−1.08229	+	0.974496i	−0.0437489	+	0.0393917i
$613$	−18.4468	−	16.6095i	−0.745057	−	0.670853i	0.206458	−	0.978456i	$-0.433806\pi$
$613$	−18.4468	−	16.6095i	−0.745057	−	0.670853i	−0.951515	+	0.307603i	$0.900473\pi$
$614$	1.39660	+	13.2877i	0.0563620	+	0.536249i
$615$		−	47.4770i		−	1.91446i
$616$	−15.0227	+	8.31713i	−0.605280	+	0.335107i
$617$	4.92976	−	8.53859i	0.198465	−	0.343751i	−0.749566	−	0.661929i	$-0.769738\pi$
$617$	4.92976	−	8.53859i	0.198465	−	0.343751i	0.948031	+	0.318179i	$0.103071\pi$
$618$	−2.63350	−	25.0561i	−0.105935	−	1.00790i
$619$	−3.56454	−	10.9705i	−0.143271	−	0.440943i	0.853514	−	0.521070i	$-0.174467\pi$
$619$	−3.56454	−	10.9705i	−0.143271	−	0.440943i	−0.996785	+	0.0801279i	$0.974467\pi$
$620$	17.8555	+	5.80161i	0.717095	+	0.232998i
$621$	−3.04825	−	6.84647i	−0.122322	−	0.274740i
$622$	0.215985	−	2.05496i	0.00866020	−	0.0823963i
$623$	5.52994	+	6.14162i	0.221552	+	0.246059i
$624$	−0.128561	−	0.115757i	−0.00514656	−	0.00463398i
$625$	−18.7046	−	8.32781i	−0.748183	−	0.333112i
$626$	−8.48376			−0.339079
$627$	−22.0579	+	18.3293i	−0.880907	+	0.732000i
$628$	−6.36129			−0.253843
$629$	6.90994	+	3.07650i	0.275517	+	0.122668i
$630$	7.39149	+	6.65533i	0.294484	+	0.265155i
$631$	8.23109	+	9.14155i	0.327675	+	0.363920i	0.884361	−	0.466803i	$-0.154594\pi$
$631$	8.23109	+	9.14155i	0.327675	+	0.363920i	−0.556687	+	0.830723i	$0.687928\pi$
$632$	−0.822669	+	7.82718i	−0.0327240	+	0.311348i
$633$	0.0280592	+	0.0630220i	0.00111525	+	0.00250490i
$634$	−10.9152	−	3.54657i	−0.433499	−	0.140852i
$635$	3.90500	+	12.0183i	0.154965	+	0.476934i
$636$	1.43064	+	13.6117i	0.0567287	+	0.539738i
$637$	0.863539	−	1.49569i	0.0342147	−	0.0592616i
$638$	−12.7599	+	13.6693i	−0.505169	+	0.541171i
$639$		−	5.29090i		−	0.209305i
$640$	−0.214664	−	2.04239i	−0.00848532	−	0.0807324i
$641$	2.09118	+	1.88291i	0.0825968	+	0.0743705i	0.709395	−	0.704811i	$-0.248968\pi$
$641$	2.09118	+	1.88291i	0.0825968	+	0.0743705i	−0.626798	+	0.779182i	$0.715635\pi$
$642$	−23.4307	+	21.0971i	−0.924737	+	0.832637i
$643$	−0.660162	+	6.28102i	−0.0260343	+	0.247699i	0.973763	+	0.227564i	$0.0730762\pi$
$643$	−0.660162	+	6.28102i	−0.0260343	+	0.247699i	−0.999797	+	0.0201349i	$0.993590\pi$
$644$	9.42190	+	0.990282i	0.371275	+	0.0390226i
$645$	−0.522959	+	1.60950i	−0.0205915	+	0.0633741i
$646$	2.62476	+	6.25791i	0.103270	+	0.246214i
$647$	−15.0434	+	10.9297i	−0.591416	+	0.429689i	−0.842822	−	0.538193i	$-0.819107\pi$
$647$	−15.0434	+	10.9297i	−0.591416	+	0.429689i	0.251406	+	0.967882i	$0.419107\pi$
$648$	−5.46565	−	9.46678i	−0.214711	−	0.371890i
$649$	−2.30717	+	2.00351i	−0.0905642	+	0.0786448i
$650$	−0.0341220	+	0.0591010i	−0.00133837	+	0.00231813i
$651$	−38.1911	+	85.7785i	−1.49683	+	3.36193i
$652$	−2.36430	−	0.502547i	−0.0925930	−	0.0196812i
$653$	0.166246	−	0.511653i	0.00650571	−	0.0200225i	−0.947751	−	0.319011i	$-0.896649\pi$
$653$	0.166246	−	0.511653i	0.00650571	−	0.0200225i	0.954257	+	0.298989i	$0.0966493\pi$
$654$	−12.4532	+	17.1404i	−0.486960	+	0.670243i
$655$	0.915239	+	2.05566i	0.0357614	+	0.0803213i
$656$	−7.79781	−	8.66035i	−0.304453	−	0.338130i
$657$	14.4313	−	4.68902i	0.563019	−	0.182936i
$658$	−25.4244	−	34.9937i	−0.991146	−	1.36420i
$659$	21.6084	−	37.4269i	0.841744	−	1.45794i	−0.0466753	−	0.998910i	$-0.514863\pi$
$659$	21.6084	−	37.4269i	0.841744	−	1.45794i	0.888419	−	0.459033i	$-0.151804\pi$
$660$	−5.27316	−	12.4405i	−0.205258	−	0.484247i
$661$	−33.7150	−	19.4654i	−1.31136	−	0.757115i	−0.329040	−	0.944316i	$-0.606725\pi$
$661$	−33.7150	−	19.4654i	−1.31136	−	0.757115i	−0.982322	+	0.187201i	$0.940058\pi$
$662$	−3.87704	+	8.70797i	−0.150685	+	0.338445i
$663$	−0.180214	+	0.200148i	−0.00699893	+	0.00777310i
$664$	−15.6964	−	5.10007i	−0.609139	−	0.197921i
$665$	40.6306	−	22.2950i	1.57559	−	0.864563i
$666$	2.67146	−	3.67694i	0.103517	−	0.142479i
$667$	10.0914	−	2.14499i	0.390739	−	0.0830542i
$668$	9.53755	−	10.5925i	0.369019	−	0.409837i
$669$	2.91792	+	27.7621i	0.112813	+	1.07335i
$670$	8.19193	−	4.72961i	0.316482	−	0.182721i
$671$	10.2033	−	13.5259i	0.393896	−	0.522160i
$672$	10.2708			0.396206
$673$	−21.1314	+	15.3529i	−0.814557	+	0.591810i	−0.915148	−	0.403117i	$-0.867927\pi$
$673$	−21.1314	+	15.3529i	−0.814557	+	0.591810i	0.100591	+	0.994928i	$0.467927\pi$
$674$	11.7071	+	2.48843i	0.450942	+	0.0958506i
$675$	−2.38188	+	2.14466i	−0.0916787	+	0.0825478i
$676$	10.5111	+	7.63674i	0.404272	+	0.293721i
$677$	31.3847	+	22.8023i	1.20621	+	0.876365i	0.994881	−	0.101049i	$-0.0322200\pi$
$677$	31.3847	+	22.8023i	1.20621	+	0.876365i	0.211332	+	0.977414i	$0.432220\pi$
$678$	−13.2196	−	14.6818i	−0.507694	−	0.563852i
$679$	−27.2103	+	30.2201i	−1.04424	+	1.15974i
$680$	−3.17965	+	0.334195i	−0.121934	+	0.0128158i
$681$	18.6319	−	10.7572i	0.713978	−	0.412215i
$682$	22.8935	−	19.8804i	0.876637	−	0.761261i
$683$			2.04819i			0.0783720i	0.999232	+	0.0391860i	$0.0124765\pi$
$683$			2.04819i			0.0783720i	−0.999232	+	0.0391860i	$0.987524\pi$
$684$	4.00597	−	0.760895i	0.153172	−	0.0290935i
$685$	4.09812	+	12.6127i	0.156581	+	0.481907i
$686$	13.7837	+	64.8472i	0.526264	+	2.47588i
$687$	−34.2389	−	3.59865i	−1.30630	−	0.137297i
$688$	0.168957	+	0.379484i	0.00644143	+	0.0144677i
$689$	0.125088	+	0.588493i	0.00476547	+	0.0224198i
$690$	−1.54995	+	7.29193i	−0.0590055	+	0.277599i
$691$	−35.0067	+	25.4339i	−1.33172	+	0.967550i	−0.332012	+	0.943275i	$0.607728\pi$
$691$	−35.0067	+	25.4339i	−1.33172	+	0.967550i	−0.999705	+	0.0242746i	$0.992272\pi$
$692$	−16.0062			−0.608463
$693$	15.3637	−	4.68855i	0.583619	−	0.178103i
$694$	5.11026	+	2.95041i	0.193983	+	0.111996i
$695$	−6.17276	−	8.49607i	−0.234146	−	0.322274i
$696$	10.6373	−	3.45628i	0.403208	−	0.131010i
$697$	−13.4827	+	12.1399i	−0.510694	+	0.459831i
$698$	−17.6905	−	1.85935i	−0.669596	−	0.0703774i
$699$	15.2551	−	6.79202i	0.577002	−	0.256898i
$700$	−0.842390	−	3.96313i	−0.0318393	−	0.149792i
$701$	−4.29289	−	3.86534i	−0.162140	−	0.145992i	0.584067	−	0.811705i	$-0.301461\pi$
$701$	−4.29289	−	3.86534i	−0.162140	−	0.145992i	−0.746207	+	0.665714i	$0.768127\pi$
$702$	−0.209931	−	0.288945i	−0.00792334	−	0.0109055i
$703$	−12.0726	−	17.3996i	−0.455328	−	0.656239i
$704$	−3.00516	−	1.40321i	−0.113261	−	0.0528853i
$705$	29.4765	−	17.0183i	1.11015	−	0.640946i
$706$	16.7957	+	7.47794i	0.632115	+	0.281436i
$707$	52.7054	+	11.2029i	1.98219	+	0.421328i
$708$	1.78777	−	0.380002i	0.0671885	−	0.0142814i
$709$	3.10429	−	1.38212i	0.116584	−	0.0519066i	−0.347616	−	0.937637i	$-0.613009\pi$
$709$	3.10429	−	1.38212i	0.116584	−	0.0519066i	0.464200	+	0.885730i	$0.346342\pi$
$710$	6.82724	−	9.39688i	0.256222	−	0.352659i
$711$	2.27510	−	7.00204i	0.0853229	−	0.262597i
$712$	−0.331879	+	1.56137i	−0.0124377	+	0.0585148i
$713$	−16.6369	+	1.74861i	−0.623058	+	0.0654861i
$714$		−	15.9900i		−	0.598410i
$715$	−0.287692	−	0.519637i	−0.0107591	−	0.0194333i
$716$	−1.46857	−	0.847877i	−0.0548829	−	0.0316867i
$717$	30.1708	+	13.4329i	1.12675	+	0.501661i
$718$	−4.50712	+	21.2043i	−0.168204	+	0.791339i
$719$	−35.1154	+	7.46400i	−1.30958	+	0.278360i	−0.809246	−	0.587471i	$-0.800124\pi$
$719$	−35.1154	+	7.46400i	−1.30958	+	0.278360i	−0.500337	+	0.865831i	$0.666790\pi$
$720$	−0.200810	+	1.91058i	−0.00748375	+	0.0712031i
$721$	53.1944	+	38.6480i	1.98106	+	1.43933i
$722$	2.80533	−	18.7918i	0.104403	−	0.699357i
$723$	35.1594	−	11.4240i	1.30759	−	0.424862i
$724$	5.25856	−	11.8109i	0.195433	−	0.438949i
$725$	−2.20610	−	3.82108i	−0.0819325	−	0.141911i
$726$	−21.6063	−	3.05916i	−0.801886	−	0.113536i
$727$	22.6043	+	39.1518i	0.838347	+	1.45206i	0.891276	+	0.453461i	$0.149811\pi$
$727$	22.6043	+	39.1518i	0.838347	+	1.45206i	−0.0529295	+	0.998598i	$0.516856\pi$
$728$	0.449014	−	0.0471933i	0.0166416	−	0.00174910i
$729$	−4.37224	−	13.4564i	−0.161935	−	0.498384i
$730$	31.6812	+	10.2939i	1.17257	+	0.380993i
$731$	0.590793	−	0.263038i	0.0218513	−	0.00972882i
$732$	−9.25797	+	4.12192i	−0.342185	+	0.152350i
$733$	2.88032	+	0.935874i	0.106387	+	0.0345673i	0.361727	−	0.932284i	$-0.382187\pi$
$733$	2.88032	+	0.935874i	0.106387	+	0.0345673i	−0.255340	+	0.966851i	$0.582187\pi$
$734$	−6.59030	−	20.2829i	−0.243252	−	0.748654i
$735$	−80.2436	+	8.43394i	−2.95983	+	0.311091i
$736$	0.914927	+	1.58470i	0.0337247	+	0.0584128i
$737$	0.274443	−	15.2742i	0.0101092	−	0.562632i
$738$	5.45079	+	9.44104i	0.200646	+	0.347530i
$739$	−21.2459	+	47.7191i	−0.781544	+	1.75538i	−0.137338	+	0.990524i	$0.543854\pi$
$739$	−21.2459	+	47.7191i	−0.781544	+	1.75538i	−0.644206	+	0.764852i	$0.722812\pi$
$740$	9.48925	−	3.08325i	0.348832	−	0.113342i
$741$	0.722059	−	0.217379i	0.0265255	−	0.00798562i
$742$	−28.8978	−	20.9955i	−1.06087	−	0.770768i
$743$	1.05160	−	10.0053i	0.0385796	−	0.367060i	−0.958151	−	0.286263i	$-0.907587\pi$
$743$	1.05160	−	10.0053i	0.0385796	−	0.367060i	0.996731	−	0.0807969i	$-0.0257465\pi$
$744$	−17.7396	+	3.77068i	−0.650367	+	0.138240i
$745$	−2.44025	+	11.4805i	−0.0894037	+	0.420611i
$746$	−16.7562	−	7.46036i	−0.613490	−	0.273143i
$747$	13.3706	+	7.71954i	0.489206	+	0.282443i
$748$	−2.18456	+	4.67854i	−0.0798754	+	0.171064i
$749$		−	82.2852i		−	3.00664i
$750$	23.4292	−	2.46251i	0.855513	−	0.0899181i
$751$	−0.946407	+	4.45250i	−0.0345349	+	0.162474i	−0.992036	−	0.125956i	$-0.959800\pi$
$751$	−0.946407	+	4.45250i	−0.0345349	+	0.162474i	0.957501	+	0.288430i	$0.0931334\pi$
$752$	2.58171	−	7.94567i	0.0941451	−	0.289749i
$753$	−2.12397	+	2.92339i	−0.0774016	+	0.106534i
$754$	0.449156	−	0.199977i	0.0163573	−	0.00728273i
$755$	−8.82177	+	1.87512i	−0.321057	+	0.0682428i
$756$	20.7411	+	4.40866i	0.754348	+	0.160342i
$757$	−22.5235	−	10.0281i	−0.818630	−	0.364478i	−0.0456893	−	0.998956i	$-0.514548\pi$
$757$	−22.5235	−	10.0281i	−0.818630	−	0.364478i	−0.772941	+	0.634478i	$0.781215\pi$
$758$	−28.5900	+	16.5064i	−1.03843	+	0.599540i
$759$	8.80097	+	8.21548i	0.319455	+	0.298203i
$760$	8.09663	+	3.81781i	0.293696	+	0.138487i
$761$	15.0179	+	20.6703i	0.544397	+	0.749298i	0.989239	−	0.146311i	$-0.0467401\pi$
$761$	15.0179	+	20.6703i	0.544397	+	0.749298i	−0.444842	+	0.895609i	$0.646740\pi$
$762$	−9.07165	−	8.16815i	−0.328631	−	0.295901i
$763$	−11.4961	−	54.0851i	−0.416188	−	1.95801i
$764$	−4.66436	+	2.07671i	−0.168751	+	0.0751326i
$765$	2.97445	+	0.312628i	0.107542	+	0.0113031i
$766$	−1.19716	+	1.07793i	−0.0432552	+	0.0389471i
$767$	0.0764106	−	0.0248273i	0.00275903	−	0.000896462i
$768$	1.16605	+	1.60493i	0.0420762	+	0.0579129i
$769$	−31.7245	−	18.3162i	−1.14402	−	0.660497i	−0.196593	−	0.980485i	$-0.562988\pi$
$769$	−31.7245	−	18.3162i	−1.14402	−	0.660497i	−0.947422	+	0.319988i	$0.896321\pi$
$770$	33.3366	+	11.4978i	1.20137	+	0.414353i
$771$	25.7498			0.927355
$772$	−12.3234	+	8.95351i	−0.443531	+	0.322244i
$773$	−1.67957	+	7.90175i	−0.0604099	+	0.284206i	−0.997975	−	0.0636029i	$-0.979741\pi$
$773$	−1.67957	+	7.90175i	−0.0604099	+	0.284206i	0.937565	+	0.347809i	$0.113074\pi$
$774$	−0.0807923	−	0.380098i	−0.00290402	−	0.0136623i
$775$	2.90993	+	6.53581i	0.104528	+	0.234773i
$776$	−7.81140	−	0.821011i	−0.280413	−	0.0294726i
$777$	10.3750	+	48.8104i	0.372200	+	1.75106i
$778$	9.65033	+	29.7007i	0.345981	+	1.06482i
$779$	49.9048	−	9.47893i	1.78803	−	0.339618i
$780$			0.355271i			0.0127207i
$781$	−7.32069	−	17.2711i	−0.261955	−	0.618008i
$782$	2.46711	−	1.42439i	0.0882238	−	0.0509360i
$783$	22.9649	−	2.41370i	0.820697	−	0.0862587i
$784$	−13.2521	+	14.7180i	−0.473290	+	0.525642i
$785$	8.74137	+	9.70828i	0.311993	+	0.346503i
$786$	−1.75854	−	1.27766i	−0.0627252	−	0.0455725i
$787$	−18.0772	−	13.1338i	−0.644382	−	0.468171i	0.216971	−	0.976178i	$-0.430382\pi$
$787$	−18.0772	−	13.1338i	−0.644382	−	0.468171i	−0.861353	+	0.508007i	$0.830382\pi$
$788$	−5.42210	+	4.88208i	−0.193154	+	0.173917i
$789$	14.6728	+	3.11879i	0.522364	+	0.111032i
$790$	13.0759	−	9.50021i	0.465220	−	0.338002i
$791$	51.5604			1.83328
$792$	2.47688	+	1.86845i	0.0880120	+	0.0663926i
$793$	−0.385795	+	0.222739i	−0.0137000	+	0.00790968i
$794$	1.18811	+	11.3041i	0.0421646	+	0.401169i
$795$	18.8075	−	20.8879i	0.667034	−	0.740816i
$796$	16.5446	−	3.51667i	0.586409	−	0.124645i
$797$	−4.52141	+	6.22319i	−0.160157	+	0.220437i	−0.881552	−	0.472087i	$-0.843501\pi$
$797$	−4.52141	+	6.22319i	−0.160157	+	0.220437i	0.721396	+	0.692523i	$0.243501\pi$
$798$	−23.2221	+	38.2759i	−0.822054	+	1.35495i
$799$	−12.3701	−	4.01928i	−0.437622	−	0.142192i
$800$	0.523645	−	0.581567i	0.0185137	−	0.0205615i
$801$	0.607354	−	1.36414i	0.0214598	−	0.0481995i
$802$	13.3838	+	7.72715i	0.472599	+	0.272855i
$803$	40.6201	−	35.2740i	1.43345	−	1.24479i
$804$	−4.56877	+	7.91335i	−0.161128	+	0.279082i
$805$	−11.4358	−	15.7400i	−0.403059	−	0.554763i
$806$	−0.758205	+	0.246356i	−0.0267066	+	0.00867751i
$807$	−18.2050	−	20.2187i	−0.640847	−	0.711733i
$808$	4.23308	+	9.50765i	0.148919	+	0.334478i
$809$	9.09933	−	12.5242i	0.319915	−	0.440326i	−0.618526	−	0.785764i	$-0.712270\pi$
$809$	9.09933	−	12.5242i	0.319915	−	0.440326i	0.938441	+	0.345439i	$0.112270\pi$
$810$	−6.93710	+	21.3502i	−0.243745	+	0.750169i
$811$	45.9541	+	9.76784i	1.61367	+	0.342995i	0.924374	−	0.381488i	$-0.124588\pi$
$811$	45.9541	+	9.76784i	1.61367	+	0.342995i	0.689292	+	0.724484i	$0.257922\pi$
$812$	−11.8727	+	26.6666i	−0.416651	+	0.935813i
$813$	−17.1520	+	29.7081i	−0.601547	+	1.04191i
$814$	3.63287	−	15.6990i	0.127332	−	0.550248i
$815$	2.48194	+	4.29884i	0.0869385	+	0.150582i
$816$	2.49861	−	1.81534i	0.0874687	−	0.0635497i
$817$	−1.79622	−	0.228359i	−0.0628417	−	0.00798928i
$818$	−2.79533	+	8.60313i	−0.0977363	+	0.300801i
$819$	−0.420037	−	0.0441476i	−0.0146773	−	0.00154264i
$820$	−2.50161	+	23.8013i	−0.0873601	+	0.831176i
$821$	−1.74109	+	1.56769i	−0.0607646	+	0.0547127i	−0.698953	−	0.715167i	$-0.746351\pi$
$821$	−1.74109	+	1.56769i	−0.0607646	+	0.0547127i	0.638189	+	0.769880i	$0.279684\pi$
$822$	−9.52029	−	8.57210i	−0.332058	−	0.298986i
$823$	−1.66892	−	15.8787i	−0.0581748	−	0.553496i	−0.984328	−	0.176348i	$-0.943571\pi$
$823$	−1.66892	−	15.8787i	−0.0581748	−	0.553496i	0.926153	−	0.377148i	$-0.123095\pi$
$824$			12.6999i			0.442422i
$825$	2.17844	−	4.66544i	0.0758436	−	0.162430i
$826$	−2.38499	+	4.13093i	−0.0829845	+	0.143733i
$827$	0.336456	+	3.20117i	0.0116997	+	0.111315i	0.998813	−	0.0487069i	$-0.0155100\pi$
$827$	0.336456	+	3.20117i	0.0116997	+	0.111315i	−0.987113	+	0.160022i	$0.948843\pi$
$828$	−0.528964	−	1.62798i	−0.0183828	−	0.0565764i
$829$	−17.4821	−	5.68029i	−0.607180	−	0.197285i	−0.0107400	−	0.999942i	$-0.503419\pi$
$829$	−17.4821	−	5.68029i	−0.607180	−	0.197285i	−0.596440	+	0.802658i	$0.703419\pi$
$830$	13.7858	+	30.9633i	0.478511	+	1.07475i
$831$	3.19535	−	30.4018i	0.110846	−	1.05463i
$832$	0.0583510	+	0.0648054i	0.00202296	+	0.00224672i
$833$	22.9134	+	20.6313i	0.793903	+	0.714833i
$834$	9.26755	+	4.12618i	0.320909	+	0.142878i
$835$	−29.2718			−1.01299
$836$	12.0239	−	8.02660i	0.415855	−	0.277606i
$837$	−37.4423			−1.29420
$838$	−3.00592	−	1.33832i	−0.103838	−	0.0462316i
$839$	−23.0195	−	20.7269i	−0.794722	−	0.715571i	0.168082	−	0.985773i	$-0.446243\pi$
$839$	−23.0195	−	20.7269i	−0.794722	−	0.715571i	−0.962804	+	0.270202i	$0.912909\pi$
$840$	−14.1137	−	15.6748i	−0.486968	−	0.540833i
$841$	−0.291386	+	2.77235i	−0.0100478	+	0.0955984i
$842$	13.3154	+	29.9068i	0.458878	+	1.03066i
$843$	−6.32214	−	2.05419i	−0.217746	−	0.0707500i
$844$	−0.0107460	−	0.0330727i	−0.000369892	−	0.00113841i
$845$	−2.78899	−	26.5355i	−0.0959443	−	0.912849i
$846$	−3.90770	+	6.76834i	−0.134350	+	0.232700i
$847$	43.6644	−	36.5626i	1.50033	−	1.25631i
$848$		−	6.89921i		−	0.236920i
$849$	−3.88494	−	36.9628i	−0.133331	−	1.26856i
$850$	−0.905403	−	0.815228i	−0.0310551	−	0.0279621i
$851$	−6.60681	+	5.94880i	−0.226479	+	0.203922i
$852$	−1.17283	+	11.1587i	−0.0401805	+	0.382292i
$853$	−56.8538	−	5.97558i	−1.94664	−	0.204600i	−0.951849	−	0.306566i	$-0.900820\pi$
$853$	−56.8538	−	5.97558i	−1.94664	−	0.204600i	−0.994788	+	0.101967i	$0.967487\pi$
$854$	8.17293	−	25.1537i	0.279672	−	0.860742i
$855$	−6.66605	−	5.06813i	−0.227974	−	0.173326i
$856$	12.8580	−	9.34185i	0.439476	−	0.319298i
$857$	−24.1423	−	41.8157i	−0.824685	−	1.42840i	−0.902160	−	0.431402i	$-0.858019\pi$
$857$	−24.1423	−	41.8157i	−0.824685	−	1.42840i	0.0774744	−	0.996994i	$-0.475314\pi$
$858$	0.491659	+	0.295761i	0.0167850	+	0.0100971i
$859$	−5.16981	+	8.95437i	−0.176392	+	0.305519i	−0.940642	−	0.339400i	$-0.889776\pi$
$859$	−5.16981	+	8.95437i	−0.176392	+	0.305519i	0.764250	+	0.644920i	$0.223109\pi$
$860$	0.346977	−	0.779323i	0.0118318	−	0.0265747i
$861$	−117.077	−	24.8855i	−3.98998	−	0.848096i
$862$	−2.62873	+	8.09039i	−0.0895348	+	0.275560i
$863$	24.2016	−	33.3107i	0.823832	−	1.13391i	−0.165207	−	0.986259i	$-0.552829\pi$
$863$	24.2016	−	33.3107i	0.823832	−	1.13391i	0.989040	−	0.147649i	$-0.0471707\pi$
$864$	1.66584	+	3.74154i	0.0566731	+	0.127290i
$865$	21.9949	+	24.4278i	0.747849	+	0.830571i
$866$	−8.60089	+	2.79460i	−0.292270	+	0.0949643i
$867$	16.9966	+	23.3939i	0.577236	+	0.794498i
$868$	23.6658	−	40.9903i	0.803268	−	1.39130i
$869$	−2.26168	−	26.0046i	−0.0767223	−	0.882147i
$870$	−19.8921	−	11.4847i	−0.674406	−	0.389369i
$871$	−0.163374	+	0.366944i	−0.00553571	+	0.0124334i
$872$	7.14622	−	7.93668i	0.242002	−	0.268770i
$873$	6.98793	+	2.27052i	0.236505	+	0.0768453i
$874$	−7.97427	−	0.173351i	−0.269734	−	0.00586369i
$875$	−36.1386	+	49.7405i	−1.22171	+	1.68154i
$876$	−31.4756	+	6.69035i	−1.06346	+	0.226046i
$877$	−4.46693	+	4.96102i	−0.150837	+	0.167522i	−0.813828	−	0.581106i	$-0.802620\pi$
$877$	−4.46693	+	4.96102i	−0.150837	+	0.167522i	0.662991	+	0.748628i	$0.269287\pi$
$878$	−1.86576	−	17.7515i	−0.0629665	−	0.599086i
$879$	7.73969	−	4.46851i	0.261053	−	0.150719i
$880$	1.98805	+	6.51455i	0.0670170	+	0.219605i
$881$	39.7281			1.33847			0.669236	−	0.743050i	$-0.266621\pi$
$881$	39.7281			1.33847			0.669236	+	0.743050i	$0.266621\pi$
$882$	14.9885	−	10.8898i	0.504691	−	0.366679i
$883$	32.5537	+	6.91950i	1.09552	+	0.232860i	0.720013	−	0.693960i	$-0.244136\pi$
$883$	32.5537	+	6.91950i	1.09552	+	0.232860i	0.375506	+	0.926820i	$0.377469\pi$
$884$	0.100891	−	0.0908428i	0.00339334	−	0.00305537i
$885$	−3.03661	−	2.20622i	−0.102074	−	0.0741614i
$886$	−20.5598	−	14.9376i	−0.690720	−	0.501838i
$887$	29.7048	+	32.9905i	0.997389	+	1.10771i	0.994182	+	0.107718i	$0.0343543\pi$
$887$	29.7048	+	32.9905i	0.997389	+	1.10771i	0.00320742	+	0.999995i	$0.498979\pi$
$888$	−6.44928	+	7.16265i	−0.216424	+	0.240363i
$889$	31.6838	−	3.33010i	1.06264	−	0.111688i
$890$	2.83894	−	1.63906i	0.0951614	−	0.0549415i
$891$	23.7714	+	27.3742i	0.796372	+	0.917070i
$892$		−	14.0715i		−	0.471149i
$893$	23.7736	+	27.5861i	0.795554	+	0.923134i
$894$	−3.50357	−	10.7829i	−0.117177	−	0.360634i
$895$	0.724045	+	3.40636i	0.0242022	+	0.113862i
$896$	−5.14899	−	0.541181i	−0.172016	−	0.0180796i
$897$	−0.128755	−	0.289189i	−0.00429902	−	0.00965575i
$898$	5.55051	+	26.1131i	0.185223	+	0.871405i
$899$	10.7164	−	50.4169i	0.357413	−	1.68150i
$900$	−0.592259	+	0.430301i	−0.0197420	+	0.0143434i
$901$	−10.7409			−0.357832
$902$	30.8560	+	23.2764i	1.02739	+	0.775021i
$903$	3.69488	+	2.13324i	0.122958	+	0.0709897i
$904$	5.85365	+	8.05686i	0.194690	+	0.267967i
$905$	−25.2513	+	8.20464i	−0.839381	+	0.272732i
$906$	6.47439	−	5.82957i	0.215097	−	0.193674i
$907$	−7.45078	−	0.783109i	−0.247399	−	0.0260027i	−0.0199829	−	0.999800i	$-0.506361\pi$
$907$	−7.45078	−	0.783109i	−0.247399	−	0.0260027i	−0.227416	+	0.973798i	$0.573028\pi$
$908$	−9.90740	+	4.41106i	−0.328789	+	0.146386i
$909$	−2.02418	−	9.52302i	−0.0671378	−	0.315859i
$910$	−0.689037	−	0.620412i	−0.0228414	−	0.0205664i
$911$	7.15594	+	9.84931i	0.237087	+	0.326322i	0.910937	−	0.412546i	$-0.135360\pi$
$911$	7.15594	+	9.84931i	0.237087	+	0.326322i	−0.673850	+	0.738868i	$0.735360\pi$
$912$	−8.61743	+	0.716758i	−0.285352	+	0.0237342i
$913$	54.3267	+	6.69875i	1.79795	+	0.221696i
$914$	24.5896	−	14.1968i	0.813353	−	0.469590i
$915$	19.0125	+	8.46492i	0.628534	+	0.279842i
$916$	16.9751	+	3.60817i	0.560873	+	0.119217i
$917$	5.54894	−	1.17946i	0.183242	−	0.0389493i
$918$	5.82495	−	2.59344i	0.192252	−	0.0855962i
$919$	13.6663	−	18.8101i	0.450810	−	0.620487i	−0.521761	−	0.853092i	$-0.674725\pi$
$919$	13.6663	−	18.8101i	0.450810	−	0.620487i	0.972571	+	0.232604i	$0.0747247\pi$
$920$	1.16124	−	3.57393i	0.0382850	−	0.117829i
$921$	−5.51078	+	25.9262i	−0.181586	+	0.854297i
$922$	−42.6693	+	4.48472i	−1.40524	+	0.147696i
$923$			0.493219i			0.0162345i
$924$	−33.4420	+	6.48268i	−1.10016	+	0.213264i
$925$	3.29275	+	1.90107i	0.108265	+	0.0625068i
$926$	9.21894	+	4.10454i	0.302953	+	0.134883i
$927$	2.47006	−	11.6207i	0.0811273	−	0.381674i
$928$	−5.51485	+	1.17222i	−0.181034	+	0.0384799i
$929$	4.19386	−	39.9020i	0.137596	−	1.30914i	−0.679942	−	0.733266i	$-0.737995\pi$
$929$	4.19386	−	39.9020i	0.137596	−	1.30914i	0.817538	−	0.575875i	$-0.195338\pi$
$930$	30.1316	+	21.8919i	0.988053	+	0.717863i
$931$	−24.8861	−	82.6631i	−0.815609	−	2.70917i
$932$	−8.00560	+	2.60118i	−0.262232	+	0.0852044i
$933$	1.66725	−	3.74470i	0.0545832	−	0.122596i
$934$	14.1368	+	24.4857i	0.462570	+	0.801195i
$935$	10.1421	−	3.09506i	0.331681	−	0.101219i
$936$	−0.0407882	−	0.0706473i	−0.00133321	−	0.00230918i
$937$	−12.9396	+	1.36001i	−0.422719	+	0.0444296i	−0.313500	−	0.949588i	$-0.601502\pi$
$937$	−12.9396	+	1.36001i	−0.422719	+	0.0444296i	−0.109219	+	0.994018i	$0.534835\pi$
$938$	−7.36923	−	22.6801i	−0.240614	−	0.740533i
$939$	−16.0064	−	5.20078i	−0.522348	−	0.169721i
$940$	−15.6739	+	6.97849i	−0.511227	+	0.227613i
$941$	23.1343	−	10.3000i	0.754155	−	0.335772i	0.00660622	−	0.999978i	$-0.497897\pi$
$941$	23.1343	−	10.3000i	0.754155	−	0.335772i	0.747549	+	0.664207i	$0.231230\pi$
$942$	−12.0019	−	3.89965i	−0.391043	−	0.127057i
$943$	−6.58963	−	20.2808i	−0.214588	−	0.660433i
$944$	−0.916271	+	0.0963039i	−0.0298221	+	0.00313443i
$945$	−21.7732	−	37.7122i	−0.708281	−	1.22678i
$946$	−0.789647	−	1.12896i	−0.0256736	−	0.0367058i
$947$	−13.9274	−	24.1230i	−0.452580	−	0.783891i	0.545966	−	0.837808i	$-0.316163\pi$
$947$	−13.9274	−	24.1230i	−0.452580	−	0.783891i	−0.998545	+	0.0539164i	$0.982830\pi$
$948$	−6.35041	+	14.2633i	−0.206252	+	0.463249i
$949$	−1.34529	+	0.437111i	−0.0436700	+	0.0141892i
$950$	0.983351	+	3.26636i	0.0319041	+	0.105975i
$951$	−18.4197	−	13.3827i	−0.597299	−	0.433963i
$952$	−0.842528	+	8.01612i	−0.0273065	+	0.259804i
$953$	−7.47780	+	1.58946i	−0.242230	+	0.0514875i	−0.327427	−	0.944877i	$-0.606181\pi$
$953$	−7.47780	+	1.58946i	−0.242230	+	0.0514875i	0.0851969	+	0.996364i	$0.472848\pi$
$954$	−1.34185	+	6.31293i	−0.0434441	+	0.204389i
$955$	9.57890	+	4.26480i	0.309966	+	0.138006i
$956$	−14.4175	−	8.32393i	−0.466294	−	0.269215i
$957$	−32.4538	+	17.9677i	−1.04908	+	0.580814i
$958$			39.3758i			1.27217i
$959$	33.2507	−	3.49479i	1.07372	−	0.112853i
$960$	0.847033	−	3.98498i	0.0273379	−	0.128615i
$961$	−16.2471	+	50.0034i	−0.524100	+	1.61301i
$962$	−0.249034	+	0.342766i	−0.00802917	+	0.0110512i
$963$	−13.5823	+	6.04721i	−0.437682	+	0.194869i
$964$	−18.2281	+	3.87450i	−0.587087	+	0.124789i
$965$	30.5987	+	6.50395i	0.985006	+	0.209370i
$966$	17.1693	+	7.64426i	0.552413	+	0.245950i
$967$	20.7765	−	11.9953i	0.668127	−	0.385743i	−0.127240	−	0.991872i	$-0.540612\pi$
$967$	20.7765	−	11.9953i	0.668127	−	0.385743i	0.795367	+	0.606129i	$0.207278\pi$
$968$	10.6705	+	2.67208i	0.342963	+	0.0858839i
$969$	1.11587	+	13.4159i	0.0358470	+	0.430981i
$970$	9.48106	+	13.0496i	0.304419	+	0.418996i
$971$	−39.9922	−	36.0091i	−1.28341	−	1.15559i	−0.979181	−	0.202989i	$-0.934934\pi$
$971$	−39.9922	−	36.0091i	−1.28341	−	1.15559i	−0.304229	−	0.952599i	$-0.598399\pi$
$972$	−1.95409	−	9.19326i	−0.0626774	−	0.294874i
$973$	−24.1866	+	10.7686i	−0.775387	+	0.345224i
$974$	−23.7857	−	2.49998i	−0.762144	−	0.0801046i
$975$	−0.100609	+	0.0905885i	−0.00322206	+	0.00290115i
$976$	4.85841	−	1.57859i	0.155514	−	0.0505295i
$977$	29.1638	+	40.1405i	0.933032	+	1.28421i	0.958665	+	0.284537i	$0.0918398\pi$
$977$	29.1638	+	40.1405i	0.933032	+	1.28421i	−0.0256333	+	0.999671i	$0.508160\pi$
$978$	−4.15266	−	2.39754i	−0.132787	−	0.0766648i
$979$	0.0951090	−	5.29332i	0.00303970	−	0.169175i
$980$	40.6722			1.29923
$981$	−8.08259	+	5.87235i	−0.258057	+	0.187490i
$982$	3.66839	−	17.2584i	0.117063	−	0.550738i
$983$	5.18112	+	24.3753i	0.165252	+	0.777450i	0.980215	+	0.197937i	$0.0634241\pi$
$983$	5.18112	+	24.3753i	0.165252	+	0.777450i	−0.814963	+	0.579514i	$0.803243\pi$
$984$	−9.40315	−	21.1198i	−0.299761	−	0.673275i
$985$	14.9016	+	1.56622i	0.474803	+	0.0499038i
$986$	1.82495	+	8.58569i	0.0581181	+	0.273424i
$987$	−26.5163	−	81.6087i	−0.844022	−	2.59763i
$988$	−0.373438	+	0.0709308i	−0.0118806	+	0.00225661i
$989$			0.760116i			0.0241703i
$990$	−0.552067	−	6.34762i	−0.0175458	−	0.201741i
$991$	0.631510	−	0.364602i	0.0200606	−	0.0115820i	−0.489936	−	0.871758i	$-0.662980\pi$
$991$	0.631510	−	0.364602i	0.0200606	−	0.0115820i	0.509997	+	0.860176i	$0.329647\pi$
$992$	9.09195	−	0.955602i	0.288670	−	0.0303404i
$993$	−12.6531	+	14.0527i	−0.401533	+	0.445947i
$994$	−19.5939	−	21.7612i	−0.621481	−	0.690225i
$995$	−28.1018	−	20.4172i	−0.890887	−	0.647267i
$996$	−26.4880	−	19.2447i	−0.839305	−	0.609791i
$997$	20.5878	−	18.5373i	0.652022	−	0.587083i	−0.275295	−	0.961360i	$-0.588776\pi$
$997$	20.5878	−	18.5373i	0.652022	−	0.587083i	0.927317	+	0.374276i	$0.122109\pi$
$998$	−20.1551	−	4.28409i	−0.637997	−	0.135610i
$999$	−16.0983	+	11.6961i	−0.509328	+	0.370048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.107.3	✓	80
11.7	odd	10		418.2.s.b.183.8	yes	80
19.8	odd	6		418.2.s.b.217.8	yes	80
209.84	even	30	inner	418.2.s.a.293.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.107.3	✓	80	1.1	even	1	trivial
418.2.s.a.293.3	yes	80	209.84	even	30	inner
418.2.s.b.183.8	yes	80	11.7	odd	10
418.2.s.b.217.8	yes	80	19.8	odd	6

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.s (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(-1.47425 - 1.32742i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.214664 - 2.04239i) q^{5} +(0.806884 + 1.81229i) q^{6} +(-4.92396 - 1.59989i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0977827 + 0.930340i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(-1.47425 - 1.32742i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.214664 - 2.04239i) q^{5} +(0.806884 + 1.81229i) q^{6} +(-4.92396 - 1.59989i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0977827 + 0.930340i) q^{9} +(-1.02682 + 1.77850i) q^{10} +(1.60644 + 2.90161i) q^{11} -1.98380i q^{12} +(-0.00911533 - 0.0867265i) q^{13} +(3.84752 + 3.46433i) q^{14} +(-3.02758 + 2.72604i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(1.54830 + 0.162733i) q^{17} +(0.289074 - 0.889680i) q^{18} +(-3.46991 - 2.63813i) q^{19} +(1.66143 - 1.20710i) q^{20} +(5.13542 + 8.89480i) q^{21} +(-0.287369 - 3.30415i) q^{22} +(-0.914927 + 1.58470i) q^{23} +(-0.806884 + 1.81229i) q^{24} +(0.765475 + 0.162707i) q^{25} +(-0.0269476 + 0.0829362i) q^{26} +(-2.40735 + 3.31343i) q^{27} +(-2.10582 - 4.72975i) q^{28} +(-3.77259 - 4.18989i) q^{29} +(3.87461 - 1.25894i) q^{30} +(5.37355 + 7.39606i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.48336 - 6.41013i) q^{33} +(-1.34826 - 0.778416i) q^{34} +(-4.32459 + 9.71318i) q^{35} +(-0.625948 + 0.695186i) q^{36} +(4.62071 + 1.50136i) q^{37} +(2.09689 + 3.82139i) q^{38} +(-0.101684 + 0.139957i) q^{39} +(-2.00876 + 0.426975i) q^{40} +(-7.79781 + 8.66035i) q^{41} +(-1.07359 - 10.2146i) q^{42} +(0.359744 - 0.207699i) q^{43} +(-1.08139 + 3.13538i) q^{44} +1.92110 q^{45} +(1.48038 - 1.07556i) q^{46} +(-8.17201 - 1.73701i) q^{47} +(1.47425 - 1.32742i) q^{48} +(16.0226 + 11.6411i) q^{49} +(-0.633117 - 0.459986i) q^{50} +(-2.06657 - 2.29516i) q^{51} +(0.0583510 - 0.0648054i) q^{52} +(-6.86141 + 0.721163i) q^{53} +(3.54692 - 2.04781i) q^{54} +(6.27105 - 2.65811i) q^{55} +5.17735i q^{56} +(1.61360 + 8.49530i) q^{57} +(1.74225 + 5.36211i) q^{58} +(0.191553 + 0.901185i) q^{59} +(-4.05169 - 0.425850i) q^{60} +(-2.07779 - 4.66679i) q^{61} +(-1.90073 - 8.94225i) q^{62} +(1.00696 - 4.73739i) q^{63} +(-0.809017 + 0.587785i) q^{64} -0.179086 q^{65} +(-3.96235 + 5.25261i) q^{66} +(-3.98898 - 2.30304i) q^{67} +(0.915083 + 1.25950i) q^{68} +(3.45240 - 1.12175i) q^{69} +(7.90142 - 7.11447i) q^{70} +(-5.62493 - 0.591204i) q^{71} +(0.854590 - 0.380488i) q^{72} +(-3.37249 - 15.8663i) q^{73} +(-3.61057 - 3.25097i) q^{74} +(-0.912521 - 1.25598i) q^{75} +(-0.361305 - 4.34390i) q^{76} +(-3.26781 - 16.8575i) q^{77} +(0.149819 - 0.0864979i) q^{78} +(-7.18987 - 3.20114i) q^{79} +(2.00876 + 0.426975i) q^{80} +(10.6924 - 2.27275i) q^{81} +(10.6461 - 4.73997i) q^{82} +(9.70091 - 13.3522i) q^{83} +(-3.17386 + 9.76815i) q^{84} +(0.664729 - 3.12730i) q^{85} +(-0.413122 + 0.0434208i) q^{86} +11.1848i q^{87} +(2.26318 - 2.42447i) q^{88} +(-1.38239 - 0.798126i) q^{89} +(-1.75502 - 0.781384i) q^{90} +(-0.0938695 + 0.441621i) q^{91} +(-1.78987 + 0.380448i) q^{92} +(1.89572 - 18.0366i) q^{93} +(6.75899 + 4.91070i) q^{94} +(-6.13295 + 6.52058i) q^{95} +(-1.88671 + 0.613028i) q^{96} +(3.19468 - 7.17538i) q^{97} +(-9.90249 - 17.1516i) q^{98} +(-2.54240 + 1.77827i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Introduction

L-functions

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