LMFDB - Embedded newform 418.2.s.a.145.5

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			145.5
Character	$\chi$	$=$	418.145
Dual form			418.2.s.a.369.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.978148 - 0.207912i) q^{2} +(-0.167101 + 0.375316i) q^{3} +(0.913545 - 0.406737i) q^{4} +(1.82285 - 2.02448i) q^{5} +(-0.0854173 + 0.401857i) q^{6} +(0.891945 - 1.22766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.89445 + 2.10400i) q^{9} +O(q^{10})$	\(q+(0.978148 - 0.207912i) q^{2} +(-0.167101 + 0.375316i) q^{3} +(0.913545 - 0.406737i) q^{4} +(1.82285 - 2.02448i) q^{5} +(-0.0854173 + 0.401857i) q^{6} +(0.891945 - 1.22766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.89445 + 2.10400i) q^{9} +(1.36210 - 2.35923i) q^{10} +(-3.31337 - 0.146957i) q^{11} +0.410835i q^{12} +(-3.18834 - 3.54101i) q^{13} +(0.617210 - 1.38628i) q^{14} +(0.455218 + 1.02244i) q^{15} +(0.669131 - 0.743145i) q^{16} +(0.516163 + 0.464755i) q^{17} +(2.29050 + 1.66415i) q^{18} +(2.72449 + 3.40252i) q^{19} +(0.841825 - 2.59087i) q^{20} +(0.311714 + 0.539905i) q^{21} +(-3.27152 + 0.545142i) q^{22} +(-0.303875 + 0.526328i) q^{23} +(0.0854173 + 0.401857i) q^{24} +(-0.253092 - 2.40801i) q^{25} +(-3.85488 - 2.80074i) q^{26} +(-2.27841 + 0.740301i) q^{27} +(0.315499 - 1.48431i) q^{28} +(4.57247 - 2.03580i) q^{29} +(0.657847 + 0.905449i) q^{30} +(4.73360 + 1.53804i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.608824 - 1.21900i) q^{33} +(0.601512 + 0.347283i) q^{34} +(-0.859484 - 4.04355i) q^{35} +(2.58644 + 1.15156i) q^{36} +(1.56727 - 2.15716i) q^{37} +(3.37238 + 2.76171i) q^{38} +(1.86177 - 0.604927i) q^{39} +(0.284757 - 2.70928i) q^{40} +(-4.00607 - 1.78362i) q^{41} +(0.417155 + 0.463298i) q^{42} +(-9.72125 + 5.61257i) q^{43} +(-3.08668 + 1.21342i) q^{44} +7.71280 q^{45} +(-0.187805 + 0.578005i) q^{46} +(1.30084 + 12.3766i) q^{47} +(0.167101 + 0.375316i) q^{48} +(1.45154 + 4.46739i) q^{49} +(-0.748216 - 2.30277i) q^{50} +(-0.260682 + 0.116063i) q^{51} +(-4.35295 - 1.93806i) q^{52} +(-7.90283 + 7.11574i) q^{53} +(-2.07471 + 1.19783i) q^{54} +(-6.33727 + 6.43996i) q^{55} -1.51747i q^{56} +(-1.73229 + 0.453979i) q^{57} +(4.04929 - 2.94198i) q^{58} +(1.29133 + 0.135724i) q^{59} +(0.831725 + 0.748889i) q^{60} +(2.38442 - 11.2178i) q^{61} +(4.94994 + 0.520259i) q^{62} +(4.27274 - 0.449083i) q^{63} +(0.309017 - 0.951057i) q^{64} -12.9805 q^{65} +(0.342074 - 1.31895i) q^{66} +(-9.19960 - 5.31139i) q^{67} +(0.660571 + 0.214633i) q^{68} +(-0.146761 - 0.201999i) q^{69} +(-1.68140 - 3.77650i) q^{70} +(-3.64882 - 3.28542i) q^{71} +(2.76935 + 0.588643i) q^{72} +(6.89774 + 0.724981i) q^{73} +(1.08452 - 2.43588i) q^{74} +(0.946058 + 0.307393i) q^{75} +(3.87288 + 2.00021i) q^{76} +(-3.13576 + 3.93660i) q^{77} +(1.69532 - 0.978792i) q^{78} +(-5.05996 + 1.07553i) q^{79} +(-0.284757 - 2.70928i) q^{80} +(-0.784948 + 7.46829i) q^{81} +(-4.28936 - 0.911732i) q^{82} +(-9.77485 + 3.17604i) q^{83} +(0.504364 + 0.366442i) q^{84} +(1.88177 - 0.197782i) q^{85} +(-8.34190 + 7.51108i) q^{86} +2.05631i q^{87} +(-2.76695 + 1.82866i) q^{88} +(-4.21116 - 2.43132i) q^{89} +(7.54426 - 1.60358i) q^{90} +(-7.19097 + 0.755802i) q^{91} +(-0.0635273 + 0.604421i) q^{92} +(-1.36824 + 1.51959i) q^{93} +(3.84566 + 11.8357i) q^{94} +(11.8547 + 0.686609i) q^{95} +(0.241483 + 0.332372i) q^{96} +(-1.84026 - 8.65775i) q^{97} +(2.34865 + 4.06797i) q^{98} +(-5.96782 - 7.24974i) 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 $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.978148	−	0.207912i	0.691655	−	0.147016i
$2$	0.978148	−	0.207912i	0.691655	−	0.147016i
$3$	−0.167101	+	0.375316i	−0.0964761	+	0.216689i	−0.955336	−	0.295522i	$-0.904507\pi$
$3$	−0.167101	+	0.375316i	−0.0964761	+	0.216689i	0.858860	+	0.512210i	$0.171173\pi$
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	1.82285	−	2.02448i	0.815202	−	0.905373i	−0.181754	−	0.983344i	$-0.558177\pi$
$5$	1.82285	−	2.02448i	0.815202	−	0.905373i	0.996956	+	0.0779706i	$0.0248440\pi$
$6$	−0.0854173	+	0.401857i	−0.0348715	+	0.164057i
$7$	0.891945	−	1.22766i	0.337124	−	0.464011i	−0.606475	−	0.795103i	$-0.707417\pi$
$7$	0.891945	−	1.22766i	0.337124	−	0.464011i	0.943599	+	0.331092i	$0.107417\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	1.89445	+	2.10400i	0.631484	+	0.701334i
$10$	1.36210	−	2.35923i	0.430734	−	0.746053i
$11$	−3.31337	−	0.146957i	−0.999018	−	0.0443091i
$11$	−3.31337	−	0.146957i	−0.999018	−	0.0443091i
$12$			0.410835i			0.118598i
$13$	−3.18834	−	3.54101i	−0.884286	−	0.982099i	0.115651	−	0.993290i	$-0.463105\pi$
$13$	−3.18834	−	3.54101i	−0.884286	−	0.982099i	−0.999937	+	0.0111905i	$0.996438\pi$
$14$	0.617210	−	1.38628i	0.164956	−	0.370498i
$15$	0.455218	+	1.02244i	0.117537	+	0.263992i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	0.516163	+	0.464755i	0.125188	+	0.112720i	0.729347	−	0.684144i	$-0.239824\pi$
$17$	0.516163	+	0.464755i	0.125188	+	0.112720i	−0.604159	+	0.796864i	$0.706491\pi$
$18$	2.29050	+	1.66415i	0.539876	+	0.392243i
$19$	2.72449	+	3.40252i	0.625041	+	0.780592i
$19$	2.72449	+	3.40252i	0.625041	+	0.780592i
$20$	0.841825	−	2.59087i	0.188238	−	0.579336i
$21$	0.311714	+	0.539905i	0.0680216	+	0.117817i
$22$	−3.27152	+	0.545142i	−0.697490	+	0.116225i
$23$	−0.303875	+	0.526328i	−0.0633624	+	0.109747i	−0.895966	−	0.444122i	$-0.853516\pi$
$23$	−0.303875	+	0.526328i	−0.0633624	+	0.109747i	0.832604	+	0.553869i	$0.186849\pi$
$24$	0.0854173	+	0.401857i	0.0174357	+	0.0820287i
$25$	−0.253092	−	2.40801i	−0.0506185	−	0.481602i
$26$	−3.85488	−	2.80074i	−0.756005	−	0.549270i
$27$	−2.27841	+	0.740301i	−0.438481	+	0.142471i
$28$	0.315499	−	1.48431i	0.0596238	−	0.280508i
$29$	4.57247	−	2.03580i	0.849087	−	0.378038i	0.0643953	−	0.997924i	$-0.479488\pi$
$29$	4.57247	−	2.03580i	0.849087	−	0.378038i	0.784691	+	0.619887i	$0.212821\pi$
$30$	0.657847	+	0.905449i	0.120106	+	0.165312i
$31$	4.73360	+	1.53804i	0.850180	+	0.276240i	0.701521	−	0.712648i	$-0.252505\pi$
$31$	4.73360	+	1.53804i	0.850180	+	0.276240i	0.148658	+	0.988889i	$0.452505\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.608824	−	1.21900i	0.105983	−	0.212201i
$34$	0.601512	+	0.347283i	0.103158	+	0.0595585i
$35$	−0.859484	−	4.04355i	−0.145279	−	0.683485i
$36$	2.58644	+	1.15156i	0.431074	+	0.191926i
$37$	1.56727	−	2.15716i	0.257658	−	0.354636i	−0.660517	−	0.750811i	$-0.729663\pi$
$37$	1.56727	−	2.15716i	0.257658	−	0.354636i	0.918175	+	0.396176i	$0.129663\pi$
$38$	3.37238	+	2.76171i	0.547072	+	0.448009i
$39$	1.86177	−	0.604927i	0.298122	−	0.0968658i
$40$	0.284757	−	2.70928i	0.0450240	−	0.428375i
$41$	−4.00607	−	1.78362i	−0.625643	−	0.278554i	0.0693260	−	0.997594i	$-0.477915\pi$
$41$	−4.00607	−	1.78362i	−0.625643	−	0.278554i	−0.694969	+	0.719040i	$0.744582\pi$
$42$	0.417155	+	0.463298i	0.0643684	+	0.0714884i
$43$	−9.72125	+	5.61257i	−1.48248	+	0.855908i	−0.999802	−	0.0198913i	$-0.993668\pi$
$43$	−9.72125	+	5.61257i	−1.48248	+	0.855908i	−0.482675	+	0.875800i	$0.660335\pi$
$44$	−3.08668	+	1.21342i	−0.465335	+	0.182929i
$45$	7.71280			1.14976
$46$	−0.187805	+	0.578005i	−0.0276904	+	0.0852222i
$47$	1.30084	+	12.3766i	0.189747	+	1.80532i	0.512342	+	0.858782i	$0.328778\pi$
$47$	1.30084	+	12.3766i	0.189747	+	1.80532i	−0.322595	+	0.946537i	$0.604555\pi$
$48$	0.167101	+	0.375316i	0.0241190	+	0.0541722i
$49$	1.45154	+	4.46739i	0.207363	+	0.638198i
$50$	−0.748216	−	2.30277i	−0.105814	−	0.325661i
$51$	−0.260682	+	0.116063i	−0.0365027	+	0.0162521i
$52$	−4.35295	−	1.93806i	−0.603646	−	0.268760i
$53$	−7.90283	+	7.11574i	−1.08554	+	0.977422i	−0.999821	−	0.0188974i	$-0.993984\pi$
$53$	−7.90283	+	7.11574i	−1.08554	+	0.977422i	−0.0857159	+	0.996320i	$0.527318\pi$
$54$	−2.07471	+	1.19783i	−0.282332	+	0.163004i
$55$	−6.33727	+	6.43996i	−0.854518	+	0.868363i
$56$		−	1.51747i		−	0.202780i
$57$	−1.73229	+	0.453979i	−0.229447	+	0.0601309i
$58$	4.04929	−	2.94198i	0.531697	−	0.386301i
$59$	1.29133	+	0.135724i	0.168117	+	0.0176698i	0.188213	−	0.982128i	$-0.439730\pi$
$59$	1.29133	+	0.135724i	0.168117	+	0.0176698i	−0.0200959	+	0.999798i	$0.506397\pi$
$60$	0.831725	+	0.748889i	0.107375	+	0.0966811i
$61$	2.38442	−	11.2178i	0.305293	−	1.43629i	−0.511461	−	0.859307i	$-0.670895\pi$
$61$	2.38442	−	11.2178i	0.305293	−	1.43629i	0.816754	−	0.576986i	$-0.195771\pi$
$62$	4.94994	+	0.520259i	0.628643	+	0.0660730i
$63$	4.27274	−	0.449083i	0.538315	−	0.0565792i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−12.9805			−1.61004
$66$	0.342074	−	1.31895i	0.0421065	−	0.162351i
$67$	−9.19960	−	5.31139i	−1.12391	−	0.648889i	−0.181513	−	0.983388i	$-0.558100\pi$
$67$	−9.19960	−	5.31139i	−1.12391	−	0.648889i	−0.942396	+	0.334499i	$0.891433\pi$
$68$	0.660571	+	0.214633i	0.0801060	+	0.0260280i
$69$	−0.146761	−	0.201999i	−0.0176680	−	0.0243179i
$70$	−1.68140	−	3.77650i	−0.200966	−	0.451378i
$71$	−3.64882	−	3.28542i	−0.433036	−	0.389907i	0.423583	−	0.905857i	$-0.360772\pi$
$71$	−3.64882	−	3.28542i	−0.433036	−	0.389907i	−0.856619	+	0.515950i	$0.827439\pi$
$72$	2.76935	+	0.588643i	0.326371	+	0.0693722i
$73$	6.89774	+	0.724981i	0.807319	+	0.0848526i	0.499191	−	0.866492i	$-0.333631\pi$
$73$	6.89774	+	0.724981i	0.807319	+	0.0848526i	0.308128	+	0.951345i	$0.400297\pi$
$74$	1.08452	−	2.43588i	0.126073	−	0.283165i
$75$	0.946058	+	0.307393i	0.109241	+	0.0354947i
$76$	3.87288	+	2.00021i	0.444249	+	0.229440i
$77$	−3.13576	+	3.93660i	−0.357353	+	0.448618i
$78$	1.69532	−	0.978792i	0.191957	−	0.110826i
$79$	−5.05996	+	1.07553i	−0.569289	+	0.121006i	−0.483558	−	0.875312i	$-0.660656\pi$
$79$	−5.05996	+	1.07553i	−0.569289	+	0.121006i	−0.0857311	+	0.996318i	$0.527323\pi$
$80$	−0.284757	−	2.70928i	−0.0318368	−	0.302907i
$81$	−0.784948	+	7.46829i	−0.0872165	+	0.829810i
$82$	−4.28936	−	0.911732i	−0.473681	−	0.100684i
$83$	−9.77485	+	3.17604i	−1.07293	+	0.348616i	−0.791628	−	0.611004i	$-0.790766\pi$
$83$	−9.77485	+	3.17604i	−1.07293	+	0.348616i	−0.281301	+	0.959620i	$0.590766\pi$
$84$	0.504364	+	0.366442i	0.0550306	+	0.0399821i
$85$	1.88177	−	0.197782i	0.204107	−	0.0214525i
$86$	−8.34190	+	7.51108i	−0.899530	+	0.809941i
$87$			2.05631i			0.220459i
$88$	−2.76695	+	1.82866i	−0.294958	+	0.194936i
$89$	−4.21116	−	2.43132i	−0.446383	−	0.257719i	0.259919	−	0.965631i	$-0.416304\pi$
$89$	−4.21116	−	2.43132i	−0.446383	−	0.257719i	−0.706301	+	0.707911i	$0.749638\pi$
$90$	7.54426	−	1.60358i	0.795235	−	0.169032i
$91$	−7.19097	+	0.755802i	−0.753819	+	0.0792295i
$92$	−0.0635273	+	0.604421i	−0.00662317	+	0.0630153i
$93$	−1.36824	+	1.51959i	−0.141880	+	0.157574i
$94$	3.84566	+	11.8357i	0.396649	+	1.22076i
$95$	11.8547	+	0.686609i	1.21626	+	0.0704446i
$96$	0.241483	+	0.332372i	0.0246462	+	0.0339226i
$97$	−1.84026	−	8.65775i	−0.186850	−	0.879062i	−0.967259	−	0.253792i	$-0.918322\pi$
$97$	−1.84026	−	8.65775i	−0.186850	−	0.879062i	0.780409	−	0.625270i	$-0.215011\pi$
$98$	2.34865	+	4.06797i	0.237249	+	0.410927i
$99$	−5.96782	−	7.24974i	−0.599788	−	0.728626i
$100$	−1.21064	−	2.09689i	−0.121064	−	0.209689i
$101$	−0.606404	+	0.546008i	−0.0603394	+	0.0543299i	−0.698749	−	0.715367i	$-0.746259\pi$
$101$	−0.606404	+	0.546008i	−0.0603394	+	0.0543299i	0.638409	+	0.769697i	$0.279593\pi$
$102$	−0.230854	+	0.167726i	−0.0228580	+	0.0166073i
$103$	−0.310060	+	0.426760i	−0.0305511	+	0.0420499i	−0.824019	−	0.566562i	$-0.808273\pi$
$103$	−0.310060	+	0.426760i	−0.0305511	+	0.0420499i	0.793468	+	0.608612i	$0.208273\pi$
$104$	−4.66077	−	0.990678i	−0.457026	−	0.0971440i
$105$	1.66123	+	0.353106i	0.162120	+	0.0344596i
$106$	−6.25069	+	8.60334i	−0.607121	+	0.835630i
$107$	−0.326922	+	0.237523i	−0.0316048	+	0.0229622i	−0.603476	−	0.797382i	$-0.706218\pi$
$107$	−0.326922	+	0.237523i	−0.0316048	+	0.0229622i	0.571871	+	0.820344i	$0.306218\pi$
$108$	−1.78033	+	1.60301i	−0.171312	+	0.154250i
$109$	2.11976	+	3.67153i	0.203036	+	0.351669i	0.949505	−	0.313751i	$-0.101586\pi$
$109$	2.11976	+	3.67153i	0.203036	+	0.351669i	−0.746469	+	0.665420i	$0.768252\pi$
$110$	−4.85985	+	7.61682i	−0.463368	+	0.726235i
$111$	0.547725	+	0.948688i	0.0519878	+	0.0900454i
$112$	−0.315499	−	1.48431i	−0.0298119	−	0.140254i
$113$	5.01384	+	6.90096i	0.471663	+	0.649188i	0.976876	−	0.213806i	$-0.0685862\pi$
$113$	5.01384	+	6.90096i	0.471663	+	0.649188i	−0.505213	+	0.862995i	$0.668586\pi$
$114$	−1.60005	+	0.804221i	−0.149858	+	0.0753222i
$115$	0.511620	+	1.57460i	0.0477088	+	0.146833i
$116$	3.34913	−	3.71958i	0.310959	−	0.345355i
$117$	1.41014	−	13.4165i	0.130367	−	1.24036i
$118$	1.29133	−	0.135724i	0.118877	−	0.0124944i
$119$	1.03095	−	0.219135i	0.0945070	−	0.0200881i
$120$	0.969252	+	0.559598i	0.0884802	+	0.0510841i
$121$	10.9568	+	0.973843i	0.996073	+	0.0885312i
$122$		−	11.4684i		−	1.03830i
$123$	1.33884	−	1.20550i	0.120719	−	0.108696i
$124$	4.94994	−	0.520259i	0.444517	−	0.0467207i
$125$	5.68332	+	4.12917i	0.508331	+	0.369324i
$126$	4.08600	−	1.32762i	0.364010	−	0.118274i
$127$	3.00156	+	0.638001i	0.266345	+	0.0566135i	0.339148	−	0.940733i	$-0.389861\pi$
$127$	3.00156	+	0.638001i	0.266345	+	0.0566135i	−0.0728030	+	0.997346i	$0.523194\pi$
$128$	0.104528	−	0.994522i	0.00923910	−	0.0879041i
$129$	−0.482051	−	4.58641i	−0.0424422	−	0.403811i
$130$	−12.6969	+	2.69881i	−1.11359	+	0.236701i
$131$	5.05062	−	2.91598i	0.441275	−	0.254770i	−0.262863	−	0.964833i	$-0.584667\pi$
$131$	5.05062	−	2.91598i	0.441275	−	0.254770i	0.704138	+	0.710063i	$0.251333\pi$
$132$	0.0603749	−	1.36125i	0.00525496	−	0.118481i
$133$	6.60723	−	0.309878i	0.572919	−	0.0268698i
$134$	−10.1029	−	3.28262i	−0.872754	−	0.283575i
$135$	−2.65447	+	5.96205i	−0.228461	+	0.513131i
$136$	0.690761	+	0.0726019i	0.0592323	+	0.00622556i
$137$	−5.05054	−	1.07353i	−0.431497	−	0.0917176i	−0.0129575	−	0.999916i	$-0.504125\pi$
$137$	−5.05054	−	1.07353i	−0.431497	−	0.0917176i	−0.418540	+	0.908198i	$0.637458\pi$
$138$	−0.185552	−	0.167072i	−0.0157952	−	0.0142221i
$139$	8.46955	+	19.0229i	0.718378	+	1.61350i	0.787811	+	0.615917i	$0.211214\pi$
$139$	8.46955	+	19.0229i	0.718378	+	1.61350i	−0.0694332	+	0.997587i	$0.522119\pi$
$140$	−2.42984	−	3.34439i	−0.205359	−	0.282652i
$141$	−4.86252	−	1.57993i	−0.409498	−	0.133054i
$142$	−4.25216	−	2.45499i	−0.356834	−	0.206018i
$143$	10.0438	+	12.2012i	0.839902	+	1.02032i
$144$	2.83121			0.235935
$145$	4.21350	−	12.9678i	0.349912	−	1.07692i
$146$	6.89774	−	0.724981i	0.570861	−	0.0599999i
$147$	−1.91924	−	0.201720i	−0.158296	−	0.0166376i
$148$	0.554376	−	2.60813i	0.0455694	−	0.214387i
$149$	−9.61485	−	8.65725i	−0.787679	−	0.709230i	0.173597	−	0.984817i	$-0.444461\pi$
$149$	−9.61485	−	8.65725i	−0.787679	−	0.709230i	−0.961276	+	0.275587i	$0.911128\pi$
$150$	0.989295	+	0.103979i	0.0807756	+	0.00848985i
$151$	18.0435	−	13.1094i	1.46836	−	1.06683i	0.487273	−	0.873249i	$-0.337991\pi$
$151$	18.0435	−	13.1094i	1.46836	−	1.06683i	0.981085	−	0.193576i	$-0.0620085\pi$
$152$	4.20411	+	1.15128i	0.340998	+	0.0933813i
$153$			1.96647i			0.158979i
$154$	−2.24877	+	4.50254i	−0.181211	+	0.362825i
$155$	11.7424	−	6.77945i	0.943169	−	0.544539i
$156$	1.45477	−	1.30988i	0.116475	−	0.104874i
$157$	16.4345	+	7.31709i	1.31161	+	0.583967i	0.938967	−	0.344007i	$-0.111784\pi$
$157$	16.4345	+	7.31709i	1.31161	+	0.583967i	0.372645	+	0.927974i	$0.378451\pi$
$158$	−4.72577	+	2.10405i	−0.375962	+	0.167389i
$159$	−1.35008	−	4.15511i	−0.107068	−	0.329522i
$160$	−0.841825	−	2.59087i	−0.0665521	−	0.204826i
$161$	0.375110	+	0.842510i	0.0295628	+	0.0663991i
$162$	0.784948	+	7.46829i	0.0616714	+	0.586764i
$163$	−1.30355	+	4.01192i	−0.102102	+	0.314238i	−0.989039	−	0.147652i	$-0.952829\pi$
$163$	−1.30355	+	4.01192i	−0.102102	+	0.314238i	0.886937	+	0.461890i	$0.152829\pi$
$164$	−4.38519			−0.342426
$165$	−1.35805	−	3.45461i	−0.105724	−	0.268941i
$166$	−8.90091	+	5.13894i	−0.690844	+	0.398859i
$167$	−13.5904	−	15.0937i	−1.05166	−	1.16799i	−0.985413	−	0.170182i	$-0.945564\pi$
$167$	−13.5904	−	15.0937i	−1.05166	−	1.16799i	−0.0662460	−	0.997803i	$-0.521102\pi$
$168$	0.569530	+	0.253571i	0.0439402	+	0.0195634i
$169$	−1.01437	+	9.65110i	−0.0780285	+	0.742392i
$170$	1.79953	−	0.584703i	0.138018	−	0.0448447i
$171$	−1.99750	+	12.1783i	−0.152752	+	0.931294i
$172$	−6.59797	+	9.08132i	−0.503090	+	0.692444i
$173$	−15.0749	−	6.71178i	−1.14612	−	0.510287i	−0.256302	−	0.966597i	$-0.582504\pi$
$173$	−15.0749	−	6.71178i	−1.14612	−	0.510287i	−0.889821	+	0.456310i	$0.849171\pi$
$174$	0.427530	+	2.01137i	0.0324110	+	0.152482i
$175$	−3.18196	−	1.83710i	−0.240533	−	0.138872i
$176$	−2.32629	+	2.36398i	−0.175350	+	0.178192i
$177$	−0.266723	+	0.461978i	−0.0200481	+	0.0347244i
$178$	−4.62464	−	1.50264i	−0.346631	−	0.112627i
$179$	−1.63931	−	2.25631i	−0.122528	−	0.168645i	0.743347	−	0.668906i	$-0.233237\pi$
$179$	−1.63931	−	2.25631i	−0.122528	−	0.168645i	−0.865874	+	0.500261i	$0.833237\pi$
$180$	7.04599	−	3.13708i	0.525177	−	0.233824i
$181$	2.00284	−	9.42264i	0.148870	−	0.700380i	−0.838877	−	0.544320i	$-0.816788\pi$
$181$	2.00284	−	9.42264i	0.148870	−	0.700380i	0.987748	−	0.156059i	$-0.0498791\pi$
$182$	−6.87669	+	2.23437i	−0.509734	+	0.165623i
$183$	3.81178	+	2.76942i	0.281775	+	0.204722i
$184$	0.0635273	+	0.604421i	0.00468329	+	0.0445585i
$185$	−1.51023	−	7.10509i	−0.111035	−	0.522376i
$186$	−1.02240	+	1.77085i	−0.0749662	+	0.129845i
$187$	−1.64194	−	1.61576i	−0.120070	−	0.118156i
$188$	6.22241	+	10.7775i	0.453816	+	0.786032i
$189$	−1.12338	+	3.45742i	−0.0817141	+	0.251490i
$190$	11.7384	−	1.79312i	0.851590	−	0.130086i
$191$	5.15296	+	3.74385i	0.372855	+	0.270895i	0.758394	−	0.651796i	$-0.225984\pi$
$191$	5.15296	+	3.74385i	0.372855	+	0.270895i	−0.385539	+	0.922692i	$0.625984\pi$
$192$	0.305310	+	0.274902i	0.0220338	+	0.0198393i
$193$	6.04515	−	6.71382i	0.435140	−	0.483271i	−0.485194	−	0.874407i	$-0.661251\pi$
$193$	6.04515	−	6.71382i	0.435140	−	0.483271i	0.920333	+	0.391135i	$0.127918\pi$
$194$	−3.60010	−	8.08595i	−0.258472	−	0.580537i
$195$	2.16907	−	4.87181i	0.155330	−	0.348877i
$196$	3.14310	+	3.49077i	0.224507	+	0.249340i
$197$		−	27.0069i		−	1.92416i	−0.272770	−	0.962079i	$-0.587940\pi$
$197$		−	27.0069i		−	1.92416i	0.272770	−	0.962079i	$-0.412060\pi$
$198$	−7.34471	−	5.85053i	−0.521966	−	0.415779i
$199$	−7.88169	+	13.6515i	−0.558718	+	0.967728i	0.438886	+	0.898543i	$0.355373\pi$
$199$	−7.88169	+	13.6515i	−0.558718	+	0.967728i	−0.997604	+	0.0691854i	$0.977960\pi$
$200$	−1.62015	−	1.79936i	−0.114562	−	0.127234i
$201$	3.53072	−	2.56521i	0.249037	−	0.180936i
$202$	−0.479631	+	0.660155i	−0.0337467	+	0.0464484i
$203$	1.57914	−	7.42925i	0.110834	−	0.521431i
$204$	−0.190938	+	0.212058i	−0.0133683	+	0.0148470i
$205$	−10.9133	+	4.85893i	−0.762221	+	0.339362i
$206$	−0.214556	+	0.481900i	−0.0149488	+	0.0335755i
$207$	−1.68307	+	0.357748i	−0.116982	+	0.0248652i
$208$	−4.76490			−0.330386
$209$	−8.52721	−	11.6742i	−0.589840	−	0.807520i
$210$	1.69834			0.117197
$211$	12.5064	−	2.65832i	0.860976	−	0.183006i	0.243795	−	0.969827i	$-0.421608\pi$
$211$	12.5064	−	2.65832i	0.860976	−	0.183006i	0.617182	+	0.786821i	$0.288274\pi$
$212$	−4.32536	+	9.71492i	−0.297067	+	0.667224i
$213$	1.84279	−	0.820464i	0.126266	−	0.0562173i
$214$	−0.270395	+	0.300304i	−0.0184838	+	0.0205283i
$215$	−6.35784	+	29.9113i	−0.433601	+	2.03993i
$216$	−1.40814	+	1.93813i	−0.0958115	+	0.131873i
$217$	6.11030	−	4.43939i	0.414794	−	0.301366i
$218$	2.83679	+	3.15058i	0.192132	+	0.213384i
$219$	−1.42472	+	2.46769i	−0.0962736	+	0.166751i
$220$	−3.17002	+	8.46079i	−0.213723	+	0.570427i
$221$		−	3.30954i		−	0.222623i
$222$	0.732999	+	0.814078i	0.0491957	+	0.0546373i
$223$	8.97040	−	20.1478i	0.600702	−	1.34920i	−0.315669	−	0.948869i	$-0.602229\pi$
$223$	8.97040	−	20.1478i	0.600702	−	1.34920i	0.916371	−	0.400330i	$-0.131104\pi$
$224$	−0.617210	−	1.38628i	−0.0412391	−	0.0926245i
$225$	4.58699	−	5.09437i	0.305800	−	0.339625i
$226$	6.33907	+	5.70772i	0.421669	+	0.379672i
$227$	4.66091	+	3.38635i	0.309355	+	0.224760i	0.731620	−	0.681713i	$-0.238765\pi$
$227$	4.66091	+	3.38635i	0.309355	+	0.224760i	−0.422264	+	0.906473i	$0.638765\pi$
$228$	−1.39787	+	1.11931i	−0.0925764	+	0.0741284i
$229$	5.34760	−	16.4582i	0.353380	−	1.08759i	−0.603564	−	0.797315i	$-0.706253\pi$
$229$	5.34760	−	16.4582i	0.353380	−	1.08759i	0.956943	−	0.290276i	$-0.0937470\pi$
$230$	0.827818	+	1.43382i	0.0545847	+	0.0945435i
$231$	−0.953481	−	1.83471i	−0.0627344	−	0.120715i
$232$	2.50260	−	4.33462i	0.164304	−	0.284582i
$233$	−2.12086	−	9.97787i	−0.138942	−	0.653672i	−0.991399	−	0.130874i	$-0.958222\pi$
$233$	−2.12086	−	9.97787i	−0.138942	−	0.653672i	0.852457	−	0.522798i	$-0.175112\pi$
$234$	−1.41014	−	13.4165i	−0.0921835	−	0.877067i
$235$	27.4274	+	19.9272i	1.78917	+	1.29991i
$236$	1.23489	−	0.401241i	0.0803848	−	0.0261186i
$237$	0.441864	−	2.07880i	0.0287021	−	0.135033i
$238$	0.962860	−	0.428693i	0.0624130	−	0.0277880i
$239$	−8.32962	−	11.4647i	−0.538798	−	0.741592i	0.449641	−	0.893209i	$-0.351552\pi$
$239$	−8.32962	−	11.4647i	−0.538798	−	0.741592i	−0.988439	+	0.151617i	$0.951552\pi$
$240$	1.06442	+	0.345851i	0.0687079	+	0.0223246i
$241$	−14.3186	+	24.8005i	−0.922340	+	1.59754i	−0.126556	+	0.991959i	$0.540392\pi$
$241$	−14.3186	+	24.8005i	−0.922340	+	1.59754i	−0.795784	+	0.605581i	$0.792941\pi$
$242$	10.9198	−	1.32549i	0.701954	−	0.0852055i
$243$	−8.89592	−	5.13606i	−0.570674	−	0.329479i
$244$	−2.38442	−	11.2178i	−0.152647	−	0.718146i
$245$	11.6901	+	5.20475i	0.746851	+	0.332519i
$246$	1.05895	−	1.45751i	0.0675159	−	0.0929277i
$247$	3.36176	−	20.4958i	0.213904	−	1.30412i
$248$	4.73360	−	1.53804i	0.300584	−	0.0976656i
$249$	0.441372	−	4.19938i	0.0279708	−	0.266125i
$250$	6.41762	+	2.85731i	0.405886	+	0.180712i
$251$	−4.90838	−	5.45131i	−0.309814	−	0.344083i	0.568049	−	0.822995i	$-0.307698\pi$
$251$	−4.90838	−	5.45131i	−0.309814	−	0.344083i	−0.877863	+	0.478911i	$0.841032\pi$
$252$	3.72069	−	2.14814i	0.234381	−	0.135320i
$253$	1.08420	−	1.69926i	0.0681630	−	0.106832i
$254$	3.06862			0.192542
$255$	−0.240216	+	0.739309i	−0.0150429	+	0.0462973i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	−5.24369	−	11.7775i	−0.327092	−	0.734662i	0.672895	−	0.739738i	$-0.265051\pi$
$257$	−5.24369	−	11.7775i	−0.327092	−	0.734662i	−0.999987	+	0.00507658i	$0.998384\pi$
$258$	−1.42509	−	4.38596i	−0.0887219	−	0.273058i
$259$	−1.25034	−	3.84815i	−0.0776923	−	0.239112i
$260$	−11.8583	+	5.27966i	−0.735422	+	0.327431i
$261$	12.9456	+	5.76377i	0.801316	+	0.356769i
$262$	4.33399	−	3.90234i	0.267755	−	0.241087i
$263$	−12.5239	+	7.23069i	−0.772258	+	0.445863i	−0.833680	−	0.552248i	$-0.813770\pi$
$263$	−12.5239	+	7.23069i	−0.772258	+	0.445863i	0.0614214	+	0.998112i	$0.480437\pi$
$264$	−0.223963	−	1.34405i	−0.0137840	−	0.0827207i
$265$			28.9700i			1.77961i
$266$	6.39842	−	1.67683i	0.392312	−	0.102813i
$267$	1.61620	−	1.17424i	0.0989101	−	0.0718624i
$268$	−10.5646	−	1.11038i	−0.645335	−	0.0678274i
$269$	17.7836	+	16.0125i	1.08429	+	0.976297i	0.999797	−	0.0201277i	$-0.00640729\pi$
$269$	17.7836	+	16.0125i	1.08429	+	0.976297i	0.0844898	+	0.996424i	$0.473074\pi$
$270$	−1.35689	+	6.38366i	−0.0825776	+	0.388497i
$271$	21.1087	+	2.21861i	1.28226	+	0.134771i	0.721039	−	0.692894i	$-0.243665\pi$
$271$	21.1087	+	2.21861i	1.28226	+	0.134771i	0.561222	+	0.827665i	$0.310331\pi$
$272$	0.690761	−	0.0726019i	0.0418835	−	0.00440214i
$273$	0.917958	−	2.82518i	0.0555573	−	0.170988i
$274$	−5.16338			−0.311931
$275$	0.484714	+	8.01582i	0.0292294	+	0.483372i
$276$	−0.216234	−	0.124843i	−0.0130157	−	0.00751464i
$277$	−15.8776	−	5.15894i	−0.953992	−	0.309971i	−0.209655	−	0.977775i	$-0.567234\pi$
$277$	−15.8776	−	5.15894i	−0.953992	−	0.309971i	−0.744336	+	0.667805i	$0.767234\pi$
$278$	12.2396	+	16.8463i	0.734080	+	1.01037i
$279$	5.73154	+	12.8733i	0.343138	+	0.770701i
$280$	−3.07208	−	2.76611i	−0.183592	−	0.165307i
$281$	−13.8515	−	2.94424i	−0.826314	−	0.175638i	−0.224703	−	0.974427i	$-0.572141\pi$
$281$	−13.8515	−	2.94424i	−0.826314	−	0.175638i	−0.601611	+	0.798789i	$0.705474\pi$
$282$	−5.08475	−	0.534429i	−0.302793	−	0.0318248i
$283$	5.34431	−	12.0035i	0.317686	−	0.713535i	−0.682158	−	0.731205i	$-0.738958\pi$
$283$	5.34431	−	12.0035i	0.317686	−	0.713535i	0.999844	+	0.0176700i	$0.00562484\pi$
$284$	−4.66967	−	1.51727i	−0.277094	−	0.0900332i
$285$	−2.23863	+	4.33451i	−0.132605	+	0.256754i
$286$	12.3611	+	9.84637i	0.730925	+	0.582228i
$287$	−5.76286	+	3.32719i	−0.340171	+	0.196398i
$288$	2.76935	−	0.588643i	0.163185	−	0.0346861i
$289$	−1.72656	−	16.4271i	−0.101562	−	0.966300i
$290$	1.42526	−	13.5605i	0.0836943	−	0.796298i
$291$	3.55690	+	0.756043i	0.208509	+	0.0443200i
$292$	6.59627	−	2.14326i	0.386018	−	0.125425i
$293$	19.0098	+	13.8114i	1.11056	+	0.806872i	0.982752	−	0.184926i	$-0.0592047\pi$
$293$	19.0098	+	13.8114i	1.11056	+	0.806872i	0.127812	+	0.991798i	$0.459205\pi$
$294$	−1.91924	+	0.201720i	−0.111932	+	0.0117645i
$295$	2.62867	−	2.36687i	0.153047	−	0.137804i
$296$		−	2.66640i		−	0.154981i
$297$	7.65801	−	2.11806i	0.444363	−	0.122902i
$298$	−11.2047	−	6.46903i	−0.649070	−	0.374741i
$299$	2.83259	−	0.602085i	0.163813	−	0.0348195i
$300$	0.989295	−	0.103979i	0.0571170	−	0.00600323i
$301$	−1.78052	+	16.9405i	−0.102627	+	0.976433i
$302$	14.9236	−	16.5743i	0.858757	−	0.953747i
$303$	−0.103595	−	0.318832i	−0.00595136	−	0.0183164i
$304$	4.35161	+	0.252040i	0.249582	+	0.0144555i
$305$	−18.3638	−	25.2755i	−1.05151	−	1.44727i
$306$	0.408851	+	1.92349i	0.0233725	+	0.109959i
$307$	−2.18854	−	3.79066i	−0.124906	−	0.216344i	0.796790	−	0.604256i	$-0.206530\pi$
$307$	−2.18854	−	3.79066i	−0.124906	−	0.216344i	−0.921696	+	0.387912i	$0.873196\pi$
$308$	−1.26349	+	4.87169i	−0.0719943	+	0.277590i
$309$	−0.108359	−	0.187683i	−0.00616431	−	0.0106769i
$310$	10.0762	−	9.07268i	0.572291	−	0.515293i
$311$	−5.49745	+	3.99413i	−0.311732	+	0.226487i	−0.732639	−	0.680617i	$-0.761712\pi$
$311$	−5.49745	+	3.99413i	−0.311732	+	0.226487i	0.420907	+	0.907104i	$0.361712\pi$
$312$	1.15064	−	1.58372i	0.0651421	−	0.0896605i
$313$	28.1016	+	5.97317i	1.58839	+	0.337624i	0.915564	−	0.402173i	$-0.131745\pi$
$313$	28.1016	+	5.97317i	1.58839	+	0.337624i	0.672831	+	0.739796i	$0.265078\pi$
$314$	17.5966	+	3.74028i	0.993035	+	0.211076i
$315$	6.87940	−	9.46868i	0.387610	−	0.533500i
$316$	−4.18504	+	3.04061i	−0.235427	+	0.171048i
$317$	−18.7338	+	16.8680i	−1.05220	+	0.947401i	−0.998690	−	0.0511668i	$-0.983706\pi$
$317$	−18.7338	+	16.8680i	−1.05220	+	0.947401i	−0.0535050	+	0.998568i	$0.517039\pi$
$318$	−2.18447	−	3.78361i	−0.122499	−	0.212175i
$319$	−15.4495	+	6.07338i	−0.865003	+	0.340044i
$320$	−1.36210	−	2.35923i	−0.0761438	−	0.131885i
$321$	−0.0345170	−	0.162390i	−0.00192655	−	0.00906371i
$322$	0.542081	+	0.746110i	0.0302090	+	0.0415791i
$323$	−0.175059	+	3.02248i	−0.00974052	+	0.168175i
$324$	2.32054	+	7.14189i	0.128919	+	0.396771i
$325$	−7.71985	+	8.57376i	−0.428220	+	0.475587i
$326$	−0.440941	+	4.19528i	−0.0244215	+	0.232355i
$327$	−1.73220	+	0.182062i	−0.0957909	+	0.0100680i
$328$	−4.28936	+	0.911732i	−0.236840	+	0.0503420i
$329$	16.3546	+	9.44231i	0.901656	+	0.520571i
$330$	−2.04663	−	3.09676i	−0.112663	−	0.170471i
$331$		−	23.2765i		−	1.27939i	−0.768627	−	0.639697i	$-0.779060\pi$
$331$		−	23.2765i		−	1.27939i	0.768627	−	0.639697i	$-0.220940\pi$
$332$	−7.63796	+	6.87725i	−0.419187	+	0.377438i
$333$	7.50780	−	0.789102i	0.411425	−	0.0432425i
$334$	−16.4316	−	11.9383i	−0.899097	−	0.653232i
$335$	−27.5222	+	8.94252i	−1.50370	+	0.488582i
$336$	0.609805	+	0.129618i	0.0332676	+	0.00707124i
$337$	2.97951	−	28.3482i	0.162305	−	1.54422i	−0.545678	−	0.837995i	$-0.683728\pi$
$337$	2.97951	−	28.3482i	0.162305	−	1.54422i	0.707983	−	0.706230i	$-0.249605\pi$
$338$	1.01437	+	9.65110i	0.0551745	+	0.524950i
$339$	−3.42786	+	0.728615i	−0.186176	+	0.0395729i
$340$	1.63864	−	0.946069i	0.0888677	−	0.0513078i
$341$	−15.4581	−	5.79173i	−0.837105	−	0.313640i
$342$	0.578154	+	12.3274i	0.0312630	+	0.666591i
$343$	16.8815	+	5.48513i	0.911516	+	0.296169i
$344$	−4.56567	+	10.2547i	−0.246165	+	0.552895i
$345$	−0.676466	−	0.0710995i	−0.0364197	−	0.00382787i
$346$	−16.1409	−	3.43086i	−0.867742	−	0.184444i
$347$	−16.8184	−	15.1434i	−0.902859	−	0.812938i	0.0800955	−	0.996787i	$-0.474477\pi$
$347$	−16.8184	−	15.1434i	−0.902859	−	0.812938i	−0.982954	+	0.183849i	$0.941144\pi$
$348$	0.836375	+	1.87853i	0.0448344	+	0.100700i
$349$	5.21251	+	7.17441i	0.279019	+	0.384037i	0.925409	−	0.378970i	$-0.123722\pi$
$349$	5.21251	+	7.17441i	0.279019	+	0.384037i	−0.646389	+	0.763008i	$0.723722\pi$
$350$	−3.49438	−	1.13539i	−0.186783	−	0.0606893i
$351$	9.88577	+	5.70755i	0.527663	+	0.304646i
$352$	−1.78395	+	2.79598i	−0.0950850	+	0.149026i
$353$	10.0931			0.537201			0.268601	−	0.963252i	$-0.413439\pi$
$353$	10.0931			0.537201			0.268601	+	0.963252i	$0.413439\pi$
$354$	−0.164844	+	0.507337i	−0.00876135	+	0.0269647i
$355$	−13.3025	+	1.39815i	−0.706023	+	0.0742060i
$356$	−4.83600	−	0.508284i	−0.256307	−	0.0269390i
$357$	−0.0900283	+	0.423550i	−0.00476480	+	0.0224166i
$358$	−2.07260	−	1.86618i	−0.109540	−	0.0986304i
$359$	−11.1138	−	1.16811i	−0.586565	−	0.0616505i	−0.193403	−	0.981119i	$-0.561952\pi$
$359$	−11.1138	−	1.16811i	−0.586565	−	0.0616505i	−0.393162	+	0.919469i	$0.628619\pi$
$360$	6.23979	−	4.53347i	0.328866	−	0.238935i
$361$	−4.15430	+	18.5403i	−0.218648	+	0.975804i
$362$		−	9.63315i		−	0.506307i
$363$	−2.19640	+	3.94954i	−0.115281	+	0.207297i
$364$	−6.26187	+	3.61529i	−0.328211	+	0.189493i
$365$	14.0412	−	12.6428i	0.734951	−	0.661753i
$366$	4.30428	+	1.91639i	0.224988	+	0.100171i
$367$	−19.6024	+	8.72757i	−1.02324	+	0.455575i	−0.848588	−	0.529055i	$-0.822547\pi$
$367$	−19.6024	+	8.72757i	−1.02324	+	0.455575i	−0.174652	+	0.984630i	$0.555880\pi$
$368$	0.187805	+	0.578005i	0.00979003	+	0.0301306i
$369$	−3.83657	−	11.8078i	−0.199724	−	0.614687i
$370$	−2.95446	−	6.63583i	−0.153595	−	0.344980i
$371$	1.68680	+	16.0488i	0.0875743	+	0.833213i
$372$	−0.631880	+	1.94473i	−0.0327615	+	0.100829i
$373$	0.921303			0.0477033			0.0238516	−	0.999716i	$-0.492407\pi$
$373$	0.921303			0.0477033			0.0238516	+	0.999716i	$0.492407\pi$
$374$	−1.94199	−	1.23907i	−0.100418	−	0.0640709i
$375$	−2.49943	+	1.44305i	−0.129070	+	0.0745187i
$376$	8.32721	+	9.24830i	0.429443	+	0.476945i
$377$	−21.7874	−	9.70036i	−1.12211	−	0.499594i
$378$	−0.379997	+	3.61543i	−0.0195449	+	0.185958i
$379$	0.356081	−	0.115698i	0.0182906	−	0.00594299i	−0.299857	−	0.953984i	$-0.596939\pi$
$379$	0.356081	−	0.115698i	0.0182906	−	0.00594299i	0.318148	+	0.948041i	$0.396939\pi$
$380$	11.1090	−	4.19447i	0.569881	−	0.215172i
$381$	−0.741017	+	1.01992i	−0.0379635	+	0.0522522i
$382$	5.81875	+	2.59067i	0.297713	+	0.132550i
$383$	−0.143488	−	0.675056i	−0.00733187	−	0.0344937i	0.974330	−	0.225126i	$-0.0722795\pi$
$383$	−0.143488	−	0.675056i	−0.00733187	−	0.0344937i	−0.981661	+	0.190632i	$0.938946\pi$
$384$	0.355793	+	0.205417i	0.0181565	+	0.0104827i
$385$	2.25356	+	13.5241i	0.114852	+	0.689251i
$386$	4.51717	−	7.82397i	0.229918	−	0.398229i
$387$	−30.2253	−	9.82080i	−1.53644	−	0.499219i
$388$	−5.20259	−	7.16075i	−0.264121	−	0.363532i
$389$	−11.9798	+	5.33377i	−0.607402	+	0.270433i	−0.687304	−	0.726370i	$-0.741206\pi$
$389$	−11.9798	+	5.33377i	−0.607402	+	0.270433i	0.0799021	+	0.996803i	$0.474539\pi$
$390$	1.10876	−	5.21632i	0.0561444	−	0.264139i
$391$	−0.401463	+	0.130443i	−0.0203028	+	0.00659679i
$392$	3.80019	+	2.76100i	0.191938	+	0.139451i
$393$	0.250447	+	2.38284i	0.0126334	+	0.120199i
$394$	−5.61504	−	26.4167i	−0.282882	−	1.33085i
$395$	−7.04615	+	12.2043i	−0.354530	+	0.614064i
$396$	−8.40061	−	4.19563i	−0.422146	−	0.210838i
$397$	13.1348	+	22.7502i	0.659217	+	1.14180i	0.980819	+	0.194922i	$0.0624455\pi$
$397$	13.1348	+	22.7502i	0.659217	+	1.14180i	−0.321602	+	0.946875i	$0.604221\pi$
$398$	−4.87115	+	14.9919i	−0.244169	+	0.751474i
$399$	−0.987775	+	2.53158i	−0.0494506	+	0.126738i
$400$	−1.95885	−	1.42319i	−0.0979427	−	0.0711595i
$401$	25.0029	+	22.5127i	1.24859	+	1.12423i	0.987283	+	0.158975i	$0.0508188\pi$
$401$	25.0029	+	22.5127i	1.24859	+	1.12423i	0.261303	+	0.965257i	$0.415848\pi$
$402$	2.92022	−	3.24324i	0.145647	−	0.161758i
$403$	−9.64611	−	21.6655i	−0.480507	−	1.07924i
$404$	−0.331896	+	0.745450i	−0.0165124	+	0.0370875i
$405$	13.6885	+	15.2027i	0.680188	+	0.755426i
$406$		−	7.59522i		−	0.376945i
$407$	−5.50996	+	6.91716i	−0.273118	+	0.342871i
$408$	−0.142676	+	0.247122i	−0.00706351	+	0.0122344i
$409$	−4.52735	−	5.02813i	−0.223863	−	0.248625i	0.620742	−	0.784015i	$-0.286831\pi$
$409$	−4.52735	−	5.02813i	−0.223863	−	0.248625i	−0.844605	+	0.535390i	$0.820165\pi$
$410$	−9.66463	+	7.02176i	−0.477302	+	0.346780i
$411$	1.24687	−	1.71616i	0.0615033	−	0.0846521i
$412$	−0.109674	+	0.515978i	−0.00540327	+	0.0254204i
$413$	1.31842	−	1.46425i	0.0648752	−	0.0720512i
$414$	−1.57191	+	0.699861i	−0.0772553	+	0.0343963i
$415$	−11.3882	+	25.5784i	−0.559026	+	1.25559i
$416$	−4.66077	+	0.990678i	−0.228513	+	0.0485720i
$417$	−8.55488			−0.418934
$418$	−10.7681	−	9.64617i	−0.526684	−	0.471810i
$419$	29.3424			1.43347			0.716735	−	0.697345i	$-0.245636\pi$
$419$	29.3424			1.43347			0.716735	+	0.697345i	$0.245636\pi$
$420$	1.66123	−	0.353106i	0.0810598	−	0.0172298i
$421$	4.26738	−	9.58469i	0.207979	−	0.467129i	−0.779194	−	0.626783i	$-0.784371\pi$
$421$	4.26738	−	9.58469i	0.207979	−	0.467129i	0.987173	+	0.159654i	$0.0510378\pi$
$422$	11.6804	−	5.20046i	0.568594	−	0.253154i
$423$	−23.5761	+	26.1839i	−1.14631	+	1.27311i
$424$	−2.21100	+	10.4019i	−0.107376	+	0.505162i
$425$	0.988500	−	1.36055i	0.0479493	−	0.0659965i
$426$	1.63194	−	1.18567i	0.0790677	−	0.0574461i
$427$	−11.6449	−	12.9329i	−0.563534	−	0.625868i
$428$	−0.202049	+	0.349959i	−0.00976642	+	0.0169159i
$429$	−6.25764	+	1.73075i	−0.302122	+	0.0835612i
$430$			30.5795i			1.47468i
$431$	−5.95077	−	6.60900i	−0.286639	−	0.318344i	0.582579	−	0.812774i	$-0.302044\pi$
$431$	−5.95077	−	6.60900i	−0.286639	−	0.318344i	−0.869218	+	0.494430i	$0.835377\pi$
$432$	−0.974405	+	2.18855i	−0.0468811	+	0.105297i
$433$	11.7541	+	26.4002i	0.564868	+	1.26871i	0.939820	+	0.341670i	$0.110993\pi$
$433$	11.7541	+	26.4002i	0.564868	+	1.26871i	−0.374952	+	0.927044i	$0.622341\pi$
$434$	5.05377	−	5.61278i	0.242589	−	0.269422i
$435$	4.16294	+	3.74833i	0.199598	+	0.179719i
$436$	3.42985	+	2.49193i	0.164260	+	0.119342i
$437$	−2.61875	+	0.400032i	−0.125272	+	0.0191361i
$438$	−0.880525	+	2.70998i	−0.0420731	+	0.129488i
$439$	11.1594	+	19.3286i	0.532607	+	0.922502i	0.999275	+	0.0380697i	$0.0121209\pi$
$439$	11.1594	+	19.3286i	0.532607	+	0.922502i	−0.466668	+	0.884432i	$0.654546\pi$
$440$	−1.34165	+	8.93499i	−0.0639607	+	0.425959i
$441$	−6.64952	+	11.5173i	−0.316644	+	0.548443i
$442$	−0.688091	−	3.23721i	−0.0327292	−	0.153979i
$443$	0.487975	+	4.64278i	0.0231844	+	0.220585i	0.999979	+	0.00640877i	$0.00203999\pi$
$443$	0.487975	+	4.64278i	0.0231844	+	0.220585i	−0.976795	+	0.214176i	$0.931293\pi$
$444$	0.886238	+	0.643889i	0.0420590	+	0.0305576i
$445$	−12.5985	+	4.09349i	−0.597224	+	0.194050i
$446$	4.58540	−	21.5726i	0.217125	−	1.02149i
$447$	4.85586	−	2.16197i	0.229674	−	0.102258i
$448$	−0.891945	−	1.22766i	−0.0421405	−	0.0580014i
$449$	−31.7784	−	10.3254i	−1.49971	−	0.487287i	−0.559779	−	0.828642i	$-0.689114\pi$
$449$	−31.7784	−	10.3254i	−1.49971	−	0.487287i	−0.939934	+	0.341355i	$0.889114\pi$
$450$	3.42758	−	5.93674i	0.161578	−	0.279860i
$451$	13.0115	+	6.49849i	0.612686	+	0.306002i
$452$	7.38725	+	4.26503i	0.347467	+	0.200610i
$453$	1.90506	+	8.96261i	0.0895076	+	0.421100i
$454$	5.26312	+	2.34329i	0.247010	+	0.109976i
$455$	−11.5779	+	15.9357i	−0.542782	+	0.747076i
$456$	−1.13461	+	1.38549i	−0.0531329	+	0.0648815i
$457$	−11.1520	+	3.62351i	−0.521669	+	0.169501i	−0.558003	−	0.829839i	$-0.688432\pi$
$457$	−11.1520	+	3.62351i	−0.521669	+	0.169501i	0.0363336	+	0.999340i	$0.488432\pi$
$458$	1.80889	−	17.2104i	0.0845237	−	0.804190i
$459$	−1.52009	−	0.676788i	−0.0709518	−	0.0315898i
$460$	1.10784	+	1.23038i	0.0516532	+	0.0573666i
$461$	2.68901	−	1.55250i	0.125240	−	0.0723072i	−0.436071	−	0.899912i	$-0.643630\pi$
$461$	2.68901	−	1.55250i	0.125240	−	0.0723072i	0.561311	+	0.827605i	$0.310297\pi$
$462$	−1.31410	−	1.59638i	−0.0611376	−	0.0742703i
$463$	19.4113			0.902118			0.451059	−	0.892494i	$-0.351046\pi$
$463$	19.4113			0.902118			0.451059	+	0.892494i	$0.351046\pi$
$464$	1.54669	−	4.76022i	0.0718033	−	0.220988i
$465$	0.582272	+	5.53995i	0.0270022	+	0.256909i
$466$	−4.14903	−	9.31888i	−0.192200	−	0.431689i
$467$	−5.35271	−	16.4739i	−0.247694	−	0.762323i	−0.995182	−	0.0980476i	$-0.968740\pi$
$467$	−5.35271	−	16.4739i	−0.247694	−	0.762323i	0.747488	−	0.664275i	$-0.231260\pi$
$468$	−4.16878	−	12.8302i	−0.192702	−	0.593075i
$469$	−14.7261	+	6.55648i	−0.679988	+	0.302750i
$470$	30.9712	+	13.7893i	1.42859	+	0.636051i
$471$	−5.49244	+	4.94542i	−0.253078	+	0.227873i
$472$	1.12449	−	0.649222i	0.0517587	−	0.0298829i
$473$	33.0349	−	17.1679i	1.51895	−	0.789381i
$474$		−	2.12525i		−	0.0976158i
$475$	7.50377	−	7.42176i	0.344296	−	0.340534i
$476$	0.852689	−	0.619515i	0.0390829	−	0.0283954i
$477$	−29.9431	−	3.14714i	−1.37100	−	0.144098i
$478$	−10.5312	−	9.48238i	−0.481688	−	0.433714i
$479$	1.26898	−	5.97007i	0.0579811	−	0.272780i	−0.939601	−	0.342270i	$-0.888804\pi$
$479$	1.26898	−	5.97007i	0.0579811	−	0.272780i	0.997583	+	0.0694908i	$0.0221374\pi$
$480$	1.11307	+	0.116988i	0.0508042	+	0.00533974i
$481$	−12.6355	+	1.32805i	−0.576131	+	0.0605538i
$482$	−8.84936	+	27.2355i	−0.403077	+	1.24054i
$483$	−0.378889			−0.0172401
$484$	10.4056	−	3.56689i	0.472984	−	0.162131i
$485$	−20.8819	−	12.0562i	−0.948200	−	0.547443i
$486$	−9.76937	−	3.17426i	−0.443148	−	0.143987i
$487$	11.8254	+	16.2763i	0.535860	+	0.737547i	0.988009	−	0.154395i	$-0.0493427\pi$
$487$	11.8254	+	16.2763i	0.535860	+	0.737547i	−0.452150	+	0.891942i	$0.649343\pi$
$488$	−4.66463	−	10.4769i	−0.211158	−	0.474268i
$489$	−1.28791	−	1.15964i	−0.0582415	−	0.0524409i
$490$	12.5167	+	2.66051i	0.565448	+	0.120190i
$491$	10.5642	+	1.11034i	0.476756	+	0.0501090i	0.339859	−	0.940476i	$-0.389621\pi$
$491$	10.5642	+	1.11034i	0.476756	+	0.0501090i	0.136896	+	0.990585i	$0.456287\pi$
$492$	0.732771	−	1.64583i	0.0330359	−	0.0741998i
$493$	3.30629	+	1.07428i	0.148908	+	0.0483830i
$494$	−0.973026	−	20.7469i	−0.0437785	−	0.933447i
$495$	−25.5553	−	1.13345i	−1.14863	−	0.0509447i
$496$	4.31038	−	2.48860i	0.193542	−	0.111741i
$497$	−7.28792	+	1.54909i	−0.326908	+	0.0694864i
$498$	−0.441372	−	4.19938i	−0.0197784	−	0.188179i
$499$	3.83714	−	36.5080i	0.171774	−	1.63432i	−0.480966	−	0.876739i	$-0.659714\pi$
$499$	3.83714	−	36.5080i	0.171774	−	1.63432i	0.652740	−	0.757582i	$-0.273619\pi$
$500$	6.87145	+	1.46057i	0.307301	+	0.0653188i
$501$	7.93589	−	2.57853i	0.354549	−	0.115200i
$502$	−5.93451	−	4.31167i	−0.264870	−	0.192439i
$503$	−18.1837	+	1.91118i	−0.810770	+	0.0852154i	−0.500836	−	0.865542i	$-0.666974\pi$
$503$	−18.1837	+	1.91118i	−0.810770	+	0.0852154i	−0.309935	+	0.950758i	$0.600307\pi$
$504$	3.19276	−	2.87477i	0.142217	−	0.128053i
$505$			2.22294i			0.0989195i
$506$	0.707210	−	1.88754i	0.0314393	−	0.0839116i
$507$	−3.45271	−	1.99342i	−0.153340	−	0.0885310i
$508$	3.00156	−	0.638001i	0.133173	−	0.0283067i
$509$	−33.0393	+	3.47257i	−1.46444	+	0.153919i	−0.802956	−	0.596039i	$-0.796740\pi$
$509$	−33.0393	+	3.47257i	−1.46444	+	0.153919i	−0.661486	+	0.749958i	$0.730074\pi$
$510$	−0.0812558	+	0.773097i	−0.00359807	+	0.0342333i
$511$	7.04243	−	7.82141i	0.311539	−	0.345999i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−8.72640	−	5.73540i	−0.385280	−	0.253224i
$514$	−7.57779	−	10.4299i	−0.334242	−	0.460045i
$515$	0.298775	+	1.40563i	0.0131656	+	0.0619393i
$516$	−2.30584	−	3.99383i	−0.101509	−	0.175818i
$517$	−2.49132	−	41.1995i	−0.109568	−	1.81195i
$518$	−2.02309	−	3.50410i	−0.0888895	−	0.153961i
$519$	5.03808	−	4.53630i	0.221147	−	0.199122i
$520$	−10.5015	+	7.62977i	−0.460520	+	0.334588i
$521$	−10.4686	+	14.4088i	−0.458637	+	0.631259i	−0.974225	−	0.225577i	$-0.927573\pi$
$521$	−10.4686	+	14.4088i	−0.458637	+	0.631259i	0.515589	+	0.856836i	$0.327573\pi$
$522$	13.8611	+	2.94627i	0.606684	+	0.128955i
$523$	−42.9895	−	9.13770i	−1.87980	−	0.399564i	−0.882329	−	0.470633i	$-0.844025\pi$
$523$	−42.9895	−	9.13770i	−1.87980	−	0.399564i	−0.997471	+	0.0710695i	$0.977359\pi$
$524$	3.42794	−	4.71815i	0.149750	−	0.206113i
$525$	1.22121	−	0.887257i	0.0532978	−	0.0387231i
$526$	−10.7469	+	9.67655i	−0.468587	+	0.421918i
$527$	1.72850	+	2.99385i	0.0752945	+	0.130414i
$528$	−0.498513	−	1.26812i	−0.0216950	−	0.0551877i
$529$	11.3153	+	19.5987i	0.491970	+	0.852118i
$530$	6.02320	+	28.3369i	0.261631	+	1.23088i
$531$	2.16080	+	2.97409i	0.0937708	+	0.129064i
$532$	5.90996	−	2.97049i	0.256229	−	0.128787i
$533$	6.45690	+	19.8723i	0.279679	+	0.860765i
$534$	1.33675	−	1.48461i	0.0578467	−	0.0642453i
$535$	−0.115070	+	1.09482i	−0.00497490	+	0.0473330i
$536$	−10.5646	+	1.11038i	−0.456321	+	0.0479612i
$537$	1.12076	−	0.238225i	0.0483644	−	0.0102802i
$538$	20.7242	+	11.9651i	0.893483	+	0.515853i
$539$	−4.15298	−	15.0154i	−0.178882	−	0.646760i
$540$			6.52627i			0.280846i
$541$	−0.933395	+	0.840433i	−0.0401298	+	0.0361330i	−0.688952	−	0.724807i	$-0.741929\pi$
$541$	−0.933395	+	0.840433i	−0.0401298	+	0.0361330i	0.648822	+	0.760940i	$0.275262\pi$
$542$	21.1087	−	2.21861i	0.906696	−	0.0952976i
$543$	3.20179	+	2.32624i	0.137402	+	0.0998284i
$544$	0.660571	−	0.214633i	0.0283218	−	0.00920230i
$545$	11.2969	+	2.40124i	0.483908	+	0.102858i
$546$	0.310509	−	2.95430i	0.0132886	−	0.126432i
$547$	−1.32062	−	12.5649i	−0.0564658	−	0.537236i	−0.985791	−	0.167975i	$-0.946277\pi$
$547$	−1.32062	−	12.5649i	−0.0564658	−	0.537236i	0.929325	−	0.369262i	$-0.120389\pi$
$548$	−5.05054	+	1.07353i	−0.215749	+	0.0458588i
$549$	28.1195	−	16.2348i	1.20011	−	0.692883i
$550$	2.14071	+	7.73988i	0.0912800	+	0.330030i
$551$	19.3845	+	10.0114i	0.825807	+	0.426501i
$552$	−0.237465	−	0.0771569i	−0.0101072	−	0.00328402i
$553$	−3.19283	+	7.17120i	−0.135773	+	0.304951i
$554$	−16.6032	−	1.74507i	−0.705403	−	0.0741409i
$555$	2.91901	+	0.620456i	0.123905	+	0.0263369i
$556$	15.4746	+	13.9334i	0.656271	+	0.590909i
$557$	−2.40218	−	5.39538i	−0.101784	−	0.228610i	0.855474	−	0.517845i	$-0.173266\pi$
$557$	−2.40218	−	5.39538i	−0.101784	−	0.228610i	−0.957258	+	0.289235i	$0.906599\pi$
$558$	8.28279	+	11.4003i	0.350639	+	0.482613i
$559$	50.8688	+	16.5283i	2.15152	+	0.699072i
$560$	−3.58005	−	2.06695i	−0.151285	−	0.0873444i
$561$	0.880791	−	0.346250i	0.0371870	−	0.0146187i
$562$	−14.1610			−0.597346
$563$	1.41454	−	4.35350i	0.0596157	−	0.183478i	−0.916814	−	0.399315i	$-0.869248\pi$
$563$	1.41454	−	4.35350i	0.0596157	−	0.183478i	0.976429	+	0.215837i	$0.0692479\pi$
$564$	−5.08475	+	0.534429i	−0.214107	+	0.0225035i
$565$	23.1103	+	2.42899i	0.972258	+	0.102188i
$566$	2.73185	−	12.8524i	0.114828	−	0.540225i
$567$	8.46837	+	7.62495i	0.355638	+	0.320218i
$568$	−4.88308	−	0.513232i	−0.204889	−	0.0215347i
$569$	27.9290	−	20.2916i	1.17085	−	0.850669i	0.179736	−	0.983715i	$-0.442476\pi$
$569$	27.9290	−	20.2916i	1.17085	−	0.850669i	0.991110	+	0.133046i	$0.0424758\pi$
$570$	−1.28851	+	4.70523i	−0.0539698	+	0.197080i
$571$			11.5970i			0.485321i	0.970111	+	0.242660i	$0.0780201\pi$
$571$			11.5970i			0.485321i	−0.970111	+	0.242660i	$0.921980\pi$
$572$	14.1381	+	7.06120i	0.591144	+	0.295243i
$573$	−2.26619	+	1.30839i	−0.0946716	+	0.0546587i
$574$	−4.94517	+	4.45265i	−0.206407	+	0.185850i
$575$	1.34431	+	0.598526i	0.0560617	+	0.0249603i
$576$	2.58644	−	1.15156i	0.107768	−	0.0479816i
$577$	2.58582	+	7.95832i	0.107649	+	0.331309i	0.990343	−	0.138639i	$-0.0442727\pi$
$577$	2.58582	+	7.95832i	0.107649	+	0.331309i	−0.882694	+	0.469948i	$0.844273\pi$
$578$	−5.10421	−	15.7092i	−0.212307	−	0.653415i
$579$	1.50965	+	3.39073i	0.0627390	+	0.140914i
$580$	−1.42526	−	13.5605i	−0.0591808	−	0.563068i
$581$	−4.81954	+	14.8330i	−0.199948	+	0.615377i
$582$	3.63637			0.150732
$583$	27.2307	−	22.4157i	1.12778	−	0.928363i
$584$	6.00652	−	3.46787i	0.248552	−	0.143501i
$585$	−24.5910	−	27.3111i	−1.01671	−	1.12918i
$586$	21.4659	+	9.55725i	0.886750	+	0.394806i
$587$	0.0474455	−	0.451414i	0.00195828	−	0.0186318i	−0.993499	−	0.113840i	$-0.963685\pi$
$587$	0.0474455	−	0.451414i	0.00195828	−	0.0186318i	0.995457	+	0.0952080i	$0.0303516\pi$
$588$	−1.83536	+	0.596344i	−0.0756889	+	0.0245928i
$589$	7.66343	+	20.2966i	0.315766	+	0.836305i
$590$	2.07913	−	2.86168i	0.0855964	−	0.117813i
$591$	10.1361	+	4.51289i	0.416944	+	0.185635i
$592$	−0.554376	−	2.60813i	−0.0227847	−	0.107194i
$593$	18.7965	+	10.8522i	0.771879	+	0.445645i	0.833544	−	0.552452i	$-0.186308\pi$
$593$	18.7965	+	10.8522i	0.771879	+	0.445645i	−0.0616655	+	0.998097i	$0.519641\pi$
$594$	7.05029	−	3.66397i	0.289277	−	0.150334i
$595$	1.43563	−	2.48658i	0.0588551	−	0.101940i
$596$	−12.3048	−	3.99808i	−0.504025	−	0.163768i
$597$	−3.80658	−	5.23931i	−0.155793	−	0.214431i
$598$	2.64551	−	1.17786i	0.108183	−	0.0481661i
$599$	−6.42580	+	30.2310i	−0.262551	+	1.23521i	0.627236	+	0.778830i	$0.284186\pi$
$599$	−6.42580	+	30.2310i	−0.262551	+	1.23521i	−0.889787	+	0.456377i	$0.849147\pi$
$600$	0.946058	−	0.307393i	0.0386226	−	0.0125493i
$601$	−18.5529	−	13.4795i	−0.756788	−	0.549838i	0.141136	−	0.989990i	$-0.454925\pi$
$601$	−18.5529	−	13.4795i	−0.756788	−	0.549838i	−0.897923	+	0.440152i	$0.854925\pi$
$602$	1.78052	+	16.9405i	0.0725684	+	0.690442i
$603$	−6.25302	−	29.4181i	−0.254643	−	1.19800i
$604$	11.1515	−	19.3150i	0.453748	−	0.785914i
$605$	21.9441	−	20.4066i	0.892155	−	0.829648i
$606$	−0.167620	−	0.290326i	−0.00680909	−	0.0117937i
$607$	−0.428312	+	1.31821i	−0.0173846	+	0.0535044i	−0.959373	−	0.282142i	$-0.908955\pi$
$607$	−0.428312	+	1.31821i	−0.0173846	+	0.0535044i	0.941988	+	0.335647i	$0.108955\pi$
$608$	4.30892	−	0.658217i	0.174750	−	0.0266942i
$609$	2.52444	+	1.83411i	0.102295	+	0.0743220i
$610$	−23.2175	−	20.9052i	−0.940051	−	0.846425i
$611$	39.6783	−	44.0672i	1.60521	−	1.78277i
$612$	0.799834	+	1.79646i	0.0323314	+	0.0726174i
$613$	−3.17208	+	7.12462i	−0.128119	+	0.287761i	−0.966204	−	0.257780i	$-0.917009\pi$
$613$	−3.17208	+	7.12462i	−0.128119	+	0.287761i	0.838084	+	0.545541i	$0.183676\pi$
$614$	−2.92883	−	3.25280i	−0.118198	−	0.131272i
$615$		−	4.90789i		−	0.197905i
$616$	−0.223002	+	5.02793i	−0.00898501	+	0.202581i
$617$	−19.5045	+	33.7827i	−0.785220	+	1.36004i	0.143648	+	0.989629i	$0.454117\pi$
$617$	−19.5045	+	33.7827i	−0.785220	+	1.36004i	−0.928868	+	0.370412i	$0.879217\pi$
$618$	−0.145012	−	0.161052i	−0.00583324	−	0.00647847i
$619$	12.6547	−	9.19416i	0.508634	−	0.369545i	−0.303671	−	0.952777i	$-0.598212\pi$
$619$	12.6547	−	9.19416i	0.508634	−	0.369545i	0.812305	+	0.583232i	$0.198212\pi$
$620$	7.96972	−	10.9694i	0.320072	−	0.440541i
$621$	0.302713	−	1.42415i	0.0121474	−	0.0571492i
$622$	−4.54689	+	5.04984i	−0.182314	+	0.202480i
$623$	−6.74095	+	3.00127i	−0.270071	+	0.120243i
$624$	0.796222	−	1.78834i	0.0318744	−	0.0715910i
$625$	30.5611	−	6.49595i	1.22244	−	0.259838i
$626$	28.7294			1.14826
$627$	5.80642	−	1.24963i	0.231886	−	0.0499053i
$628$	17.9898			0.717869
$629$	1.81152	−	0.385051i	0.0722301	−	0.0153530i
$630$	4.76042	−	10.6921i	0.189660	−	0.425982i
$631$	21.1177	−	9.40222i	0.840683	−	0.374296i	0.0592181	−	0.998245i	$-0.481139\pi$
$631$	21.1177	−	9.40222i	0.840683	−	0.374296i	0.781465	+	0.623949i	$0.214473\pi$
$632$	−3.46141	+	3.84429i	−0.137688	+	0.152918i
$633$	−1.09213	+	5.13806i	−0.0434082	+	0.204220i
$634$	−14.8174	+	20.3944i	−0.588473	+	0.809964i
$635$	6.76300	−	4.91361i	0.268382	−	0.194991i
$636$	−2.92339	−	3.24676i	−0.115920	−	0.128742i
$637$	11.1911	−	19.3835i	0.443406	−	0.768001i
$638$	−13.8491	+	9.15279i	−0.548292	+	0.362362i
$639$		−	13.9012i		−	0.549923i
$640$	−1.82285	−	2.02448i	−0.0720544	−	0.0800245i
$641$	−6.25823	+	14.0562i	−0.247185	+	0.555187i	−0.993941	−	0.109911i	$-0.964944\pi$
$641$	−6.25823	+	14.0562i	−0.247185	+	0.555187i	0.746756	+	0.665098i	$0.231610\pi$
$642$	−0.0675254	−	0.151665i	−0.00266502	−	0.00598573i
$643$	15.7657	−	17.5096i	0.621739	−	0.690512i	−0.347205	−	0.937789i	$-0.612869\pi$
$643$	15.7657	−	17.5096i	0.621739	−	0.690512i	0.968945	+	0.247278i	$0.0795360\pi$
$644$	0.685360	+	0.617101i	0.0270070	+	0.0243172i
$645$	−10.1638	−	7.38442i	−0.400199	−	0.290761i
$646$	0.457175	+	2.99283i	0.0179873	+	0.117751i
$647$	12.3059	−	37.8736i	0.483794	−	1.48896i	−0.349927	−	0.936777i	$-0.613794\pi$
$647$	12.3059	−	37.8736i	0.483794	−	1.48896i	0.833721	−	0.552187i	$-0.186206\pi$
$648$	3.75471	+	6.50335i	0.147499	+	0.255476i
$649$	−4.25871	−	0.639475i	−0.167169	−	0.0251016i
$650$	−5.76857	+	9.99145i	−0.226262	+	0.391897i
$651$	0.645135	+	3.03512i	0.0252848	+	0.118956i
$652$	0.440941	+	4.19528i	0.0172686	+	0.164300i
$653$	−8.56178	−	6.22050i	−0.335049	−	0.243427i	0.407521	−	0.913196i	$-0.366393\pi$
$653$	−8.56178	−	6.22050i	−0.335049	−	0.243427i	−0.742570	+	0.669769i	$0.766393\pi$
$654$	−1.65650	+	0.538228i	−0.0647741	+	0.0210464i
$655$	3.30318	−	15.5403i	0.129066	−	0.607208i
$656$	−4.00607	+	1.78362i	−0.156411	+	0.0696385i
$657$	11.5421	+	15.8863i	0.450299	+	0.619784i
$658$	17.9603	+	5.83567i	0.700167	+	0.227498i
$659$	9.67581	−	16.7590i	0.376916	−	0.652837i	−0.613696	−	0.789542i	$-0.710318\pi$
$659$	9.67581	−	16.7590i	0.376916	−	0.652837i	0.990612	+	0.136705i	$0.0436512\pi$
$660$	−2.64576	−	2.60357i	−0.102986	−	0.101344i
$661$	−30.0208	−	17.3325i	−1.16768	−	0.674158i	−0.214544	−	0.976714i	$-0.568827\pi$
$661$	−30.0208	−	17.3325i	−1.16768	−	0.674158i	−0.953131	+	0.302557i	$0.902160\pi$
$662$	−4.83946	−	22.7679i	−0.188091	−	0.884899i
$663$	1.24212	+	0.553028i	0.0482400	+	0.0214778i
$664$	−6.04119	+	8.31498i	−0.234444	+	0.322684i
$665$	11.4166	−	13.9410i	0.442718	−	0.540610i
$666$	7.17968	−	2.33282i	0.278207	−	0.0903949i
$667$	−0.317966	+	3.02525i	−0.0123117	+	0.117138i
$668$	−18.5546	−	8.26105i	−0.717900	−	0.319630i
$669$	6.06284	+	6.73347i	0.234403	+	0.260331i
$670$	−25.0616	+	14.4693i	−0.968212	+	0.558998i
$671$	−9.54898	+	36.8183i	−0.368634	+	1.42135i
$672$	0.623428			0.0240493
$673$	−6.69413	+	20.6024i	−0.258040	+	0.794164i	0.735176	+	0.677876i	$0.237100\pi$
$673$	−6.69413	+	20.6024i	−0.258040	+	0.794164i	−0.993216	+	0.116288i	$0.962900\pi$
$674$	−2.97951	−	28.3482i	−0.114767	−	1.09193i
$675$	2.35930	+	5.29908i	0.0908096	+	0.203962i
$676$	2.99878	+	9.22930i	0.115338	+	0.354973i
$677$	−4.20772	−	12.9500i	−0.161716	−	0.497710i	0.837064	−	0.547106i	$-0.184270\pi$
$677$	−4.20772	−	12.9500i	−0.161716	−	0.497710i	−0.998779	+	0.0493960i	$0.984270\pi$
$678$	−3.20147	+	1.42539i	−0.122952	+	0.0547416i
$679$	−12.2702	−	5.46303i	−0.470886	−	0.209652i
$680$	1.40613	−	1.26609i	0.0539227	−	0.0485522i
$681$	−2.04980	+	1.18345i	−0.0785483	+	0.0453499i
$682$	−16.3245	−	2.45124i	−0.625097	−	0.0938627i
$683$		−	46.2976i		−	1.77153i	−0.464134	−	0.885765i	$-0.653634\pi$
$683$		−	46.2976i		−	1.77153i	0.464134	−	0.885765i	$-0.346366\pi$
$684$	3.12854	+	11.9378i	0.119623	+	0.456455i
$685$	−11.3797	+	8.26784i	−0.434796	+	0.315898i
$686$	17.6530	+	1.85541i	0.673996	+	0.0708398i
$687$	5.28345	+	4.75724i	0.201576	+	0.181500i
$688$	−2.33384	+	10.9798i	−0.0889767	+	0.418602i
$689$	50.3938	+	5.29660i	1.91985	+	0.201785i
$690$	−0.676466	+	0.0710995i	−0.0257526	+	0.00270671i
$691$	−0.309933	+	0.953876i	−0.0117904	+	0.0362872i	−0.956779	−	0.290817i	$-0.906073\pi$
$691$	−0.309933	+	0.953876i	−0.0117904	+	0.0362872i	0.944988	+	0.327104i	$0.106073\pi$
$692$	−16.5015			−0.627294
$693$	−14.2232	+	0.860070i	−0.540293	+	0.0326714i
$694$	−19.5994	−	11.3157i	−0.743981	−	0.429538i
$695$	53.9502	+	17.5295i	2.04645	+	0.664931i
$696$	1.20867	+	1.66359i	0.0458144	+	0.0630581i
$697$	−1.23884	−	2.78248i	−0.0469244	−	0.105394i
$698$	6.59025	+	5.93389i	0.249445	+	0.224601i
$699$	4.09925	+	0.871323i	0.155048	+	0.0329565i
$700$	−3.65408	−	0.384060i	−0.138111	−	0.0145161i
$701$	−18.3252	+	41.1590i	−0.692132	+	1.55455i	0.133940	+	0.990989i	$0.457237\pi$
$701$	−18.3252	+	41.1590i	−0.692132	+	1.55455i	−0.826072	+	0.563565i	$0.809430\pi$
$702$	10.8564	+	3.52746i	0.409749	+	0.133135i
$703$	11.6098	−	0.544498i	0.437872	−	0.0205361i
$704$	−1.16365	+	3.10579i	−0.0438567	+	0.117054i
$705$	−12.0622	+	6.96410i	−0.454288	+	0.262283i
$706$	9.87254	−	2.09847i	0.371558	−	0.0789771i
$707$	0.129432	+	1.23147i	0.00486780	+	0.0463140i
$708$	−0.0557603	+	0.530524i	−0.00209560	+	0.0199383i
$709$	−37.7002	−	8.01342i	−1.41586	−	0.300950i	−0.564457	−	0.825462i	$-0.690915\pi$
$709$	−37.7002	−	8.01342i	−1.41586	−	0.300950i	−0.851403	+	0.524512i	$0.824248\pi$
$710$	−12.7211	+	4.13334i	−0.477415	+	0.155121i
$711$	−11.8488	−	8.60863i	−0.444363	−	0.322849i
$712$	−4.83600	+	0.508284i	−0.181237	+	0.0190487i
$713$	−2.24794	+	2.02405i	−0.0841859	+	0.0758013i
$714$			0.433012i			0.0162051i
$715$	43.0093	+	1.90758i	1.60846	+	0.0713394i
$716$	−2.41531	−	1.39448i	−0.0902642	−	0.0521141i
$717$	5.69479	−	1.21047i	0.212676	−	0.0452057i
$718$	−11.1138	+	1.16811i	−0.414764	+	0.0435935i
$719$	1.21244	−	11.5356i	0.0452164	−	0.430206i	−0.948373	−	0.317157i	$-0.897272\pi$
$719$	1.21244	−	11.5356i	0.0452164	−	0.430206i	0.993589	−	0.113049i	$-0.0360616\pi$
$720$	5.16087	−	5.73173i	0.192334	−	0.213609i
$721$	0.247359	+	0.761294i	0.00921214	+	0.0283521i
$722$	−0.208783	+	18.9989i	−0.00777011	+	0.707064i
$723$	−6.91537	−	9.51819i	−0.257185	−	0.353985i
$724$	−2.00284	−	9.42264i	−0.0744351	−	0.350190i
$725$	−6.05948	−	10.4953i	−0.225043	−	0.389787i
$726$	−1.32725	+	4.31989i	−0.0492587	+	0.160326i
$727$	−12.3977	−	21.4735i	−0.459806	−	0.796407i	0.539145	−	0.842213i	$-0.318748\pi$
$727$	−12.3977	−	21.4735i	−0.459806	−	0.796407i	−0.998950	+	0.0458064i	$0.985414\pi$
$728$	−5.37337	+	4.83820i	−0.199150	+	0.179316i
$729$	−14.8116	+	10.7612i	−0.548577	+	0.398565i
$730$	11.1058	−	15.2858i	0.411044	−	0.565754i
$731$	−7.62622	−	1.62100i	−0.282066	−	0.0599550i
$732$	4.60866	+	0.979601i	0.170341	+	0.0362071i
$733$	−28.5506	+	39.2965i	−1.05454	+	1.45145i	−0.169732	+	0.985490i	$0.554290\pi$
$733$	−28.5506	+	39.2965i	−1.05454	+	1.45145i	−0.884807	+	0.465958i	$0.845710\pi$
$734$	−17.3595	+	12.6124i	−0.640751	+	0.465533i
$735$	−3.90685	+	3.51775i	−0.144106	+	0.129754i
$736$	0.303875	+	0.526328i	0.0112010	+	0.0194007i
$737$	29.7011	+	18.9505i	1.09405	+	0.698052i
$738$	−6.20770	−	10.7521i	−0.228509	−	0.395789i
$739$	−4.52758	−	21.3006i	−0.166550	−	0.783555i	−0.979535	−	0.201272i	$-0.935493\pi$
$739$	−4.52758	−	21.3006i	−0.166550	−	0.783555i	0.812986	−	0.582284i	$-0.197841\pi$
$740$	−4.26956	−	5.87655i	−0.156952	−	0.216026i
$741$	7.13066	+	4.68661i	0.261951	+	0.172167i
$742$	4.98668	+	15.3474i	0.183067	+	0.563421i
$743$	−25.3745	+	28.1812i	−0.930899	+	1.03387i	0.0684447	+	0.997655i	$0.478196\pi$
$743$	−25.3745	+	28.1812i	−0.930899	+	1.03387i	−0.999344	+	0.0362136i	$0.988470\pi$
$744$	−0.213740	+	2.03360i	−0.00783611	+	0.0745556i
$745$	−35.0528	+	3.68420i	−1.28424	+	0.134979i
$746$	0.901170	−	0.191550i	0.0329942	−	0.00701313i
$747$	−25.2004	−	14.5494i	−0.922034	−	0.532336i
$748$	−2.15717	−	0.808232i	−0.0788741	−	0.0295519i
$749$			0.613207i			0.0224061i
$750$	−2.14479	+	1.93118i	−0.0783166	+	0.0705166i
$751$	−20.0891	+	2.11145i	−0.733062	+	0.0770479i	−0.463701	−	0.885992i	$-0.653479\pi$
$751$	−20.0891	+	2.11145i	−0.733062	+	0.0770479i	−0.269360	+	0.963039i	$0.586812\pi$
$752$	10.0681	+	7.31488i	0.367145	+	0.266746i
$753$	2.86616	−	0.931272i	0.104449	−	0.0339374i
$754$	−23.3281	−	4.95854i	−0.849558	−	0.180579i
$755$	6.35092	−	60.4250i	0.231134	−	2.19909i
$756$	0.379997	+	3.61543i	0.0138204	+	0.131492i
$757$	37.2601	−	7.91988i	1.35424	−	0.287853i	0.527079	−	0.849816i	$-0.323287\pi$
$757$	37.2601	−	7.91988i	1.35424	−	0.287853i	0.827162	+	0.561964i	$0.189954\pi$
$758$	0.324244	−	0.187203i	0.0117771	−	0.00679951i
$759$	0.456589	+	0.690866i	0.0165731	+	0.0250768i
$760$	9.99419	−	6.41251i	0.362528	−	0.232606i
$761$	18.2398	+	5.92646i	0.661191	+	0.214834i	0.620342	−	0.784331i	$-0.286994\pi$
$761$	18.2398	+	5.92646i	0.661191	+	0.214834i	0.0408489	+	0.999165i	$0.486994\pi$
$762$	−0.512770	+	1.15170i	−0.0185757	+	0.0417217i
$763$	6.39810	+	0.672467i	0.231627	+	0.0243449i
$764$	6.23023	+	1.32428i	0.225402	+	0.0479106i
$765$	3.98106	+	3.58457i	0.143936	+	0.129600i
$766$	−0.280704	−	0.630471i	−0.0101422	−	0.0227799i
$767$	−3.63660	−	5.00535i	−0.131310	−	0.180733i
$768$	0.390727	+	0.126955i	0.0140991	+	0.00458109i
$769$	1.70089	+	0.982009i	0.0613357	+	0.0354122i	0.530354	−	0.847776i	$-0.322059\pi$
$769$	1.70089	+	0.982009i	0.0613357	+	0.0354122i	−0.469019	+	0.883188i	$0.655392\pi$
$770$	5.01613	+	12.7600i	0.180769	+	0.459839i
$771$	5.29652			0.190750
$772$	2.79176	−	8.59217i	0.100478	−	0.309239i
$773$	49.8459	−	5.23901i	1.79283	−	0.188434i	0.851146	−	0.524930i	$-0.175908\pi$
$773$	49.8459	−	5.23901i	1.79283	−	0.188434i	0.941685	+	0.336496i	$0.109242\pi$
$774$	−31.6067	−	3.32199i	−1.13608	−	0.119407i
$775$	2.50558	−	11.7878i	0.0900031	−	0.423431i
$776$	−6.57770	−	5.92259i	−0.236126	−	0.212609i
$777$	1.65320	+	0.173759i	0.0593084	+	0.00623356i
$778$	−10.6091	+	7.70796i	−0.380354	+	0.276344i
$779$	−4.84570	−	18.4902i	−0.173615	−	0.662479i
$780$		−	5.33286i		−	0.190947i
$781$	11.6071	+	11.4220i	0.415334	+	0.408712i
$782$	−0.365569	+	0.211061i	−0.0130727	+	0.00754754i
$783$	−8.91087	+	8.02339i	−0.318449	+	0.286732i
$784$	4.29119	+	1.91056i	0.153257	+	0.0682343i
$785$	44.7708	−	19.9332i	1.59794	−	0.711448i
$786$	0.740395	+	2.27870i	0.0264090	+	0.0812786i
$787$	12.2687	+	37.7592i	0.437332	+	1.34597i	0.890678	+	0.454634i	$0.150230\pi$
$787$	12.2687	+	37.7592i	0.437332	+	1.34597i	−0.453346	+	0.891334i	$0.649770\pi$
$788$	−10.9847	−	24.6720i	−0.391313	−	0.878903i
$789$	−0.621028	−	5.90869i	−0.0221092	−	0.210355i
$790$	−4.35476	+	13.4026i	−0.154935	+	0.476842i
$791$	12.9441			0.460239
$792$	−9.08936	−	2.35736i	−0.322976	−	0.0837653i
$793$	−47.3247	+	27.3229i	−1.68055	+	0.970265i
$794$	17.5778	+	19.5221i	0.623813	+	0.692814i
$795$	−10.8729	−	4.84093i	−0.385622	−	0.171690i
$796$	−1.64772	+	15.6770i	−0.0584020	+	0.555658i
$797$	4.23596	−	1.37635i	0.150045	−	0.0487527i	−0.233031	−	0.972469i	$-0.574864\pi$
$797$	4.23596	−	1.37635i	0.150045	−	0.0487527i	0.383077	+	0.923717i	$0.374864\pi$
$798$	−0.439845	+	2.68163i	−0.0155703	+	0.0949286i
$799$	−5.08067	+	6.99294i	−0.179741	+	0.247392i
$800$	−2.21195	−	0.984822i	−0.0782041	−	0.0348187i
$801$	−2.86235	−	13.4663i	−0.101136	−	0.475809i
$802$	29.1372	+	16.8224i	1.02887	+	0.594018i
$803$	−22.7482	−	3.41580i	−0.802766	−	0.120541i
$804$	2.18210	−	3.77951i	0.0769568	−	0.133293i
$805$	2.38941	+	0.776367i	0.0842157	+	0.0273633i
$806$	−13.9398	−	19.1865i	−0.491010	−	0.675817i
$807$	−8.98140	+	3.99878i	−0.316160	+	0.140764i
$808$	−0.169655	+	0.798165i	−0.00596845	+	0.0280793i
$809$	−5.57460	+	1.81130i	−0.195993	+	0.0636819i	−0.405369	−	0.914153i	$-0.632857\pi$
$809$	−5.57460	+	1.81130i	−0.195993	+	0.0636819i	0.209376	+	0.977835i	$0.432857\pi$
$810$	16.5502	+	12.0244i	0.581515	+	0.422495i
$811$	−2.52920	−	24.0637i	−0.0888122	−	0.844991i	−0.944723	−	0.327869i	$-0.893670\pi$
$811$	−2.52920	−	24.0637i	−0.0888122	−	0.844991i	0.855911	−	0.517123i	$-0.172997\pi$
$812$	−1.57914	−	7.42925i	−0.0554168	−	0.260715i
$813$	−4.35997	+	7.55170i	−0.152911	+	0.264850i
$814$	−3.95139	+	7.91159i	−0.138496	+	0.277301i
$815$	5.74587	+	9.95214i	0.201269	+	0.348608i
$816$	−0.0881785	+	0.271386i	−0.00308687	+	0.00950040i
$817$	−45.5823	−	17.7854i	−1.59472	−	0.622232i
$818$	−5.47382	−	3.97696i	−0.191388	−	0.139051i
$819$	−15.2132	−	13.6980i	−0.531591	−	0.478647i
$820$	−7.99353	+	8.87771i	−0.279146	+	0.310023i
$821$	10.3824	+	23.3192i	0.362348	+	0.813847i	0.999085	+	0.0427658i	$0.0136169\pi$
$821$	10.3824	+	23.3192i	0.362348	+	0.813847i	−0.636737	+	0.771081i	$0.719716\pi$
$822$	0.862808	−	1.93790i	0.0300939	−	0.0675920i
$823$	−21.8524	−	24.2695i	−0.761727	−	0.845983i	0.230154	−	0.973154i	$-0.426077\pi$
$823$	−21.8524	−	24.2695i	−0.761727	−	0.845983i	−0.991881	+	0.127171i	$0.959410\pi$
$824$			0.527505i			0.0183765i
$825$	−3.08946	−	1.15753i	−0.107561	−	0.0403002i
$826$	0.985174	−	1.70637i	0.0342786	−	0.0593723i
$827$	30.5562	+	33.9361i	1.06254	+	1.18007i	0.983069	+	0.183236i	$0.0586572\pi$
$827$	30.5562	+	33.9361i	1.06254	+	1.18007i	0.0794735	+	0.996837i	$0.474676\pi$
$828$	−1.39205	+	1.01139i	−0.0483772	+	0.0351481i
$829$	−3.70353	+	5.09747i	−0.128629	+	0.177042i	−0.868474	−	0.495735i	$-0.834899\pi$
$829$	−3.70353	+	5.09747i	−0.128629	+	0.177042i	0.739845	+	0.672777i	$0.234899\pi$
$830$	−5.82133	+	27.3872i	−0.202061	+	0.950623i
$831$	4.58940	−	5.09705i	0.159205	−	0.176815i
$832$	−4.35295	+	1.93806i	−0.150911	+	0.0671901i
$833$	−1.32701	+	2.98051i	−0.0459782	+	0.103269i
$834$	−8.36794	+	1.77866i	−0.289758	+	0.0615900i
$835$	−55.3301			−1.91478
$836$	−12.5383	−	7.19657i	−0.433647	−	0.248899i
$837$	−11.9237			−0.412144
$838$	28.7012	−	6.10063i	0.991467	−	0.210743i
$839$	8.31198	−	18.6690i	0.286961	−	0.644526i	−0.711336	−	0.702852i	$-0.751910\pi$
$839$	8.31198	−	18.6690i	0.286961	−	0.644526i	0.998298	+	0.0583260i	$0.0185763\pi$
$840$	1.55152	−	0.690779i	0.0535324	−	0.0238341i
$841$	−2.64176	+	2.93397i	−0.0910950	+	0.101171i
$842$	2.18136	−	10.2625i	0.0751746	−	0.353668i
$843$	3.41963	−	4.70672i	0.117778	−	0.162108i
$844$	10.3439	−	7.51531i	0.356053	−	0.258688i
$845$	17.6894	+	19.6460i	0.608533	+	0.675844i
$846$	−17.6170	+	30.5135i	−0.605684	+	1.04908i
$847$	10.9684	−	12.5826i	0.376879	−	0.432343i
$848$			10.6343i			0.365184i
$849$	3.61207	+	4.01161i	0.123966	+	0.137678i
$850$	0.684024	−	1.53634i	0.0234618	−	0.0526961i
$851$	0.659120	+	1.48041i	0.0225943	+	0.0507477i
$852$	1.34976	−	1.49906i	0.0462421	−	0.0513571i
$853$	−11.0093	−	9.91283i	−0.376952	−	0.339409i	0.458777	−	0.888551i	$-0.348288\pi$
$853$	−11.0093	−	9.91283i	−0.376952	−	0.339409i	−0.835729	+	0.549143i	$0.814954\pi$
$854$	−14.0793	−	10.2292i	−0.481783	−	0.350036i
$855$	21.0135	+	26.2430i	0.718645	+	0.897491i
$856$	−0.124873	+	0.384320i	−0.00426808	+	0.0131358i
$857$	−0.700167	−	1.21272i	−0.0239172	−	0.0414259i	0.853819	−	0.520570i	$-0.174280\pi$
$857$	−0.700167	−	1.21272i	−0.0239172	−	0.0414259i	−0.877736	+	0.479144i	$0.840947\pi$
$858$	−5.76105	+	2.99396i	−0.196679	+	0.102212i
$859$	−2.61836	+	4.53513i	−0.0893372	+	0.154737i	−0.907231	−	0.420632i	$-0.861808\pi$
$859$	−2.61836	+	4.53513i	−0.0893372	+	0.154737i	0.817894	+	0.575369i	$0.195142\pi$
$860$	6.35784	+	29.9113i	0.216801	+	1.01997i
$861$	−0.285765	−	2.71887i	−0.00973885	−	0.0926590i
$862$	−7.19482	−	5.22734i	−0.245057	−	0.178044i
$863$	−19.4667	+	6.32512i	−0.662655	+	0.215310i	−0.620986	−	0.783822i	$-0.713268\pi$
$863$	−19.4667	+	6.32512i	−0.662655	+	0.215310i	−0.0416690	+	0.999131i	$0.513268\pi$
$864$	−0.498087	+	2.34331i	−0.0169453	+	0.0797211i
$865$	−41.0671	+	18.2842i	−1.39632	+	0.621683i
$866$	16.9862	+	23.3795i	0.577215	+	0.794468i
$867$	6.45386	+	2.09699i	0.219185	+	0.0712174i
$868$	3.77637	−	6.54087i	0.128178	−	0.222012i
$869$	16.9235	−	2.82002i	0.574092	−	0.0956627i
$870$	4.85130	+	2.80090i	0.164474	+	0.0949593i
$871$	10.5238	+	49.5104i	0.356584	+	1.67759i
$872$	3.87300	+	1.72437i	0.131156	+	0.0583945i
$873$	14.7296	−	20.2736i	0.498523	−	0.686158i
$874$	−2.47835	+	0.935758i	−0.0838314	+	0.0316525i
$875$	10.1384	−	3.29417i	0.342741	−	0.111363i
$876$	−0.297847	+	2.83383i	−0.0100633	+	0.0957462i
$877$	−18.7474	−	8.34688i	−0.633055	−	0.281854i	0.0650147	−	0.997884i	$-0.479291\pi$
$877$	−18.7474	−	8.34688i	−0.633055	−	0.281854i	−0.698069	+	0.716030i	$0.745957\pi$
$878$	14.9341	+	16.5860i	0.504002	+	0.559751i
$879$	−8.36021	+	4.82677i	−0.281983	+	0.162803i
$880$	0.545357	+	9.01868i	0.0183840	+	0.304020i
$881$	42.2923			1.42486			0.712432	−	0.701741i	$-0.247594\pi$
$881$	42.2923			1.42486			0.712432	+	0.701741i	$0.247594\pi$
$882$	−4.10963	+	12.6481i	−0.138378	+	0.425885i
$883$	1.21117	+	11.5235i	0.0407591	+	0.387797i	0.995816	+	0.0913760i	$0.0291265\pi$
$883$	1.21117	+	11.5235i	0.0407591	+	0.387797i	−0.955057	+	0.296421i	$0.904207\pi$
$884$	−1.34611	−	3.02341i	−0.0452746	−	0.101688i
$885$	0.449068	+	1.38209i	0.0150953	+	0.0464584i
$886$	1.44260	+	4.43986i	0.0484651	+	0.149160i
$887$	−24.7236	+	11.0077i	−0.830138	+	0.369601i	−0.777400	−	0.629007i	$-0.783462\pi$
$887$	−24.7236	+	11.0077i	−0.830138	+	0.369601i	−0.0527385	+	0.998608i	$0.516795\pi$
$888$	1.00074	+	0.445560i	0.0335828	+	0.0149520i
$889$	3.46047	−	3.11583i	0.116061	−	0.104501i
$890$	−11.4721	+	6.62340i	−0.384544	+	0.222017i
$891$	3.69834	−	24.6298i	0.123899	−	0.825130i
$892$		−	22.0546i		−	0.738441i
$893$	−38.5677	+	38.1462i	−1.29062	+	1.27651i
$894$	4.30025	−	3.12432i	0.143822	−	0.104493i
$895$	−7.55606	−	0.794173i	−0.252571	−	0.0265463i
$896$	−1.12770	−	1.01538i	−0.0376738	−	0.0339216i
$897$	−0.247357	+	1.16373i	−0.00825903	+	0.0388557i
$898$	−33.2307	−	3.49269i	−1.10892	−	0.116552i
$899$	24.7754	−	2.60400i	0.826305	−	0.0868482i
$900$	2.11836	−	6.51964i	0.0706120	−	0.217321i
$901$	−7.38623			−0.246071
$902$	14.0782	+	3.65125i	0.468754	+	0.121573i
$903$	−6.06050	−	3.49903i	−0.201681	−	0.116441i
$904$	8.11257	+	2.63593i	0.269820	+	0.0876698i
$905$	−15.4250	−	21.2307i	−0.512746	−	0.705734i
$906$	3.72686	+	8.37067i	0.123817	+	0.278097i
$907$	−37.8935	−	34.1195i	−1.25823	−	1.13292i	−0.985291	−	0.170887i	$-0.945337\pi$
$907$	−37.8935	−	34.1195i	−1.25823	−	1.13292i	−0.272942	−	0.962030i	$-0.587997\pi$
$908$	5.63530	+	1.19782i	0.187014	+	0.0397511i
$909$	−2.29761	−	0.241488i	−0.0762068	−	0.00800965i
$910$	−8.01172	+	17.9946i	−0.265586	+	0.596516i
$911$	6.25480	+	2.03231i	0.207231	+	0.0673334i	0.410793	−	0.911729i	$-0.365252\pi$
$911$	6.25480	+	2.03231i	0.207231	+	0.0673334i	−0.203562	+	0.979062i	$0.565252\pi$
$912$	−0.821755	+	1.59111i	−0.0272110	+	0.0526870i
$913$	32.8544	−	9.08691i	1.08732	−	0.300733i
$914$	−10.1549	+	5.86296i	−0.335896	+	0.193929i
$915$	12.5549	−	2.66863i	0.415053	−	0.0882222i
$916$	−1.80889	−	17.2104i	−0.0597673	−	0.568648i
$917$	0.925057	−	8.80133i	0.0305481	−	0.290646i
$918$	−1.62759	−	0.345954i	−0.0537183	−	0.0114182i
$919$	−18.8949	+	6.13933i	−0.623286	+	0.202518i	−0.603599	−	0.797288i	$-0.706267\pi$
$919$	−18.8949	+	6.13933i	−0.623286	+	0.202518i	−0.0196871	+	0.999806i	$0.506267\pi$
$920$	1.33944	+	0.973158i	0.0441599	+	0.0320841i
$921$	1.78840	−	0.187969i	0.0589298	−	0.00619378i
$922$	2.30747	−	2.07765i	0.0759923	−	0.0684238i
$923$			23.3955i			0.770074i
$924$	−1.61729	−	1.28828i	−0.0532050	−	0.0423812i
$925$	−5.59114	−	3.22805i	−0.183836	−	0.106138i
$926$	18.9871	−	4.03583i	0.623954	−	0.132626i
$927$	−1.48530	+	0.156111i	−0.0487836	+	0.00512736i
$928$	0.523185	−	4.97777i	0.0171744	−	0.163403i
$929$	−23.4661	+	26.0618i	−0.769899	+	0.855059i	−0.992800	−	0.119782i	$-0.961780\pi$
$929$	−23.4661	+	26.0618i	−0.769899	+	0.855059i	0.222902	+	0.974841i	$0.428447\pi$
$930$	1.72137	+	5.29783i	0.0564459	+	0.173723i
$931$	−11.2457	+	17.1103i	−0.368562	+	0.560766i
$932$	−5.99587	−	8.25261i	−0.196401	−	0.270323i
$933$	−0.580430	−	2.73071i	−0.0190024	−	0.0893994i
$934$	−8.66086	−	15.0011i	−0.283392	−	0.490849i
$935$	−6.26407	+	0.378786i	−0.204857	+	0.0123876i
$936$	−6.74523	−	11.6831i	−0.220475	−	0.381873i
$937$	−27.6746	+	24.9183i	−0.904089	+	0.814045i	−0.983145	−	0.182825i	$-0.941476\pi$
$937$	−27.6746	+	24.9183i	−0.904089	+	0.814045i	0.0790568	+	0.996870i	$0.474809\pi$
$938$	−13.0411	+	9.47494i	−0.425808	+	0.309368i
$939$	−6.93764	+	9.54884i	−0.226401	+	0.311615i
$940$	33.1613	+	7.04866i	1.08160	+	0.229902i
$941$	55.3812	+	11.7716i	1.80538	+	0.383744i	0.982765	−	0.184861i	$-0.0591835\pi$
$941$	55.3812	+	11.7716i	1.80538	+	0.383744i	0.822610	+	0.568605i	$0.192517\pi$
$942$	−4.34421	+	5.97929i	−0.141542	+	0.194816i
$943$	2.15611	−	1.56651i	0.0702127	−	0.0510125i
$944$	0.964932	−	0.868829i	0.0314059	−	0.0282780i
$945$	4.95171	+	8.57661i	0.161079	+	0.278997i
$946$	28.7436	−	23.6611i	0.934534	−	0.769288i
$947$	1.41013	+	2.44243i	0.0458232	+	0.0793681i	0.888027	−	0.459791i	$-0.152076\pi$
$947$	1.41013	+	2.44243i	0.0458232	+	0.0793681i	−0.842204	+	0.539159i	$0.818742\pi$
$948$	−0.441864	−	2.07880i	−0.0143511	−	0.0675164i
$949$	−19.4252	−	26.7364i	−0.630567	−	0.867901i
$950$	5.79672	−	8.81970i	0.188070	−	0.286149i
$951$	−3.20038	−	9.84976i	−0.103779	−	0.319400i
$952$	0.705251	−	0.783261i	0.0228573	−	0.0253856i
$953$	−2.29588	+	21.8439i	−0.0743709	+	0.707592i	0.892278	+	0.451487i	$0.149106\pi$
$953$	−2.29588	+	21.8439i	−0.0743709	+	0.707592i	−0.966649	+	0.256105i	$0.917561\pi$
$954$	−29.9431	+	3.14714i	−0.969443	+	0.101893i
$955$	16.9724	−	3.60759i	0.549214	−	0.116739i
$956$	−12.2726	−	7.08560i	−0.396925	−	0.229165i
$957$	0.302188	−	6.81330i	0.00976835	−	0.220243i
$958$		−	6.10345i		−	0.197194i
$959$	−5.82273	+	5.24281i	−0.188026	+	0.169299i
$960$	1.11307	−	0.116988i	0.0359240	−	0.00377577i
$961$	−5.03812	−	3.66041i	−0.162520	−	0.118078i
$962$	−12.0833	+	3.92610i	−0.389581	+	0.126583i
$963$	−1.11909	−	0.237870i	−0.0360621	−	0.00766524i
$964$	−2.99340	+	28.4803i	−0.0964108	+	0.917288i
$965$	−2.57259	−	24.4765i	−0.0828145	−	0.787928i
$966$	−0.370609	+	0.0787755i	−0.0119242	+	0.00253456i
$967$	12.6149	−	7.28322i	0.405668	−	0.234213i	−0.283259	−	0.959044i	$-0.591416\pi$
$967$	12.6149	−	7.28322i	0.405668	−	0.234213i	0.688927	+	0.724831i	$0.258082\pi$
$968$	9.43665	−	5.65239i	0.303306	−	0.181675i
$969$	−1.10513	−	0.570763i	−0.0355019	−	0.0183355i
$970$	−22.9322	−	7.45114i	−0.736310	−	0.239242i
$971$	−15.4194	+	34.6326i	−0.494833	+	1.11141i	0.477673	+	0.878538i	$0.341480\pi$
$971$	−15.4194	+	34.6326i	−0.494833	+	1.11141i	−0.972506	+	0.232876i	$0.925186\pi$
$972$	−10.2159	−	1.07373i	−0.327674	−	0.0344399i
$973$	30.9080	+	6.56970i	0.990866	+	0.210615i
$974$	14.9510	+	13.4619i	0.479061	+	0.431348i
$975$	−1.92787	−	4.33007i	−0.0617413	−	0.138673i
$976$	−6.74097	−	9.27814i	−0.215773	−	0.296986i
$977$	0.555732	+	0.180568i	0.0177794	+	0.00577689i	0.317893	−	0.948127i	$-0.397025\pi$
$977$	0.555732	+	0.180568i	0.0177794	+	0.00577689i	−0.300114	+	0.953903i	$0.597025\pi$
$978$	−1.50087	−	0.866530i	−0.0479926	−	0.0277086i
$979$	13.5958	+	8.67471i	0.434525	+	0.277245i
$980$	12.7964			0.408765
$981$	−3.70913	+	11.4155i	−0.118423	+	0.364470i
$982$	10.5642	−	1.11034i	0.337117	−	0.0354324i
$983$	−5.12027	−	0.538162i	−0.163311	−	0.0171647i	0.0225199	−	0.999746i	$-0.492831\pi$
$983$	−5.12027	−	0.538162i	−0.163311	−	0.0171647i	−0.185831	+	0.982582i	$0.559498\pi$
$984$	0.374571	−	1.76222i	0.0119409	−	0.0561774i
$985$	−54.6747	−	49.2294i	−1.74208	−	1.56858i
$986$	3.45739	+	0.363387i	0.110106	+	0.0115726i
$987$	−6.27672	+	4.56030i	−0.199790	+	0.145156i
$988$	−5.26529	−	20.0912i	−0.167511	−	0.639187i
$989$		−	6.82208i		−	0.216930i
$990$	−25.2326	+	4.20458i	−0.801943	+	0.133630i
$991$	16.2949	−	9.40788i	0.517626	−	0.298851i	−0.218337	−	0.975873i	$-0.570063\pi$
$991$	16.2949	−	9.40788i	0.517626	−	0.298851i	0.735963	+	0.677022i	$0.236730\pi$
$992$	3.69878	−	3.33040i	0.117436	−	0.105740i
$993$	8.73605	+	3.88954i	0.277230	+	0.123431i
$994$	−6.80658	+	3.03049i	−0.215892	+	0.0961212i
$995$	13.2700	+	40.8409i	0.420687	+	1.29474i
$996$	−1.30483	−	4.01585i	−0.0413450	−	0.127247i
$997$	6.80640	+	15.2874i	0.215561	+	0.484157i	0.988668	−	0.150118i	$-0.0479653\pi$
$997$	6.80640	+	15.2874i	0.215561	+	0.484157i	−0.773107	+	0.634275i	$0.781299\pi$
$998$	−3.83714	−	36.5080i	−0.121463	−	1.15564i
$999$	−1.97394	+	6.07516i	−0.0624527	+	0.192210i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.145.5	✓	80
11.6	odd	10		418.2.s.b.259.5	yes	80
19.8	odd	6		418.2.s.b.255.5	yes	80
209.160	even	30	inner	418.2.s.a.369.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.145.5	✓	80	1.1	even	1	trivial
418.2.s.a.369.5	yes	80	209.160	even	30	inner
418.2.s.b.255.5	yes	80	19.8	odd	6
418.2.s.b.259.5	yes	80	11.6	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.978148 - 0.207912i) q^{2} +(-0.167101 + 0.375316i) q^{3} +(0.913545 - 0.406737i) q^{4} +(1.82285 - 2.02448i) q^{5} +(-0.0854173 + 0.401857i) q^{6} +(0.891945 - 1.22766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.89445 + 2.10400i) q^{9} +O(q^{10})\)	\(q+(0.978148 - 0.207912i) q^{2} +(-0.167101 + 0.375316i) q^{3} +(0.913545 - 0.406737i) q^{4} +(1.82285 - 2.02448i) q^{5} +(-0.0854173 + 0.401857i) q^{6} +(0.891945 - 1.22766i) q^{7} +(0.809017 - 0.587785i) q^{8} +(1.89445 + 2.10400i) q^{9} +(1.36210 - 2.35923i) q^{10} +(-3.31337 - 0.146957i) q^{11} +0.410835i q^{12} +(-3.18834 - 3.54101i) q^{13} +(0.617210 - 1.38628i) q^{14} +(0.455218 + 1.02244i) q^{15} +(0.669131 - 0.743145i) q^{16} +(0.516163 + 0.464755i) q^{17} +(2.29050 + 1.66415i) q^{18} +(2.72449 + 3.40252i) q^{19} +(0.841825 - 2.59087i) q^{20} +(0.311714 + 0.539905i) q^{21} +(-3.27152 + 0.545142i) q^{22} +(-0.303875 + 0.526328i) q^{23} +(0.0854173 + 0.401857i) q^{24} +(-0.253092 - 2.40801i) q^{25} +(-3.85488 - 2.80074i) q^{26} +(-2.27841 + 0.740301i) q^{27} +(0.315499 - 1.48431i) q^{28} +(4.57247 - 2.03580i) q^{29} +(0.657847 + 0.905449i) q^{30} +(4.73360 + 1.53804i) q^{31} +(0.500000 - 0.866025i) q^{32} +(0.608824 - 1.21900i) q^{33} +(0.601512 + 0.347283i) q^{34} +(-0.859484 - 4.04355i) q^{35} +(2.58644 + 1.15156i) q^{36} +(1.56727 - 2.15716i) q^{37} +(3.37238 + 2.76171i) q^{38} +(1.86177 - 0.604927i) q^{39} +(0.284757 - 2.70928i) q^{40} +(-4.00607 - 1.78362i) q^{41} +(0.417155 + 0.463298i) q^{42} +(-9.72125 + 5.61257i) q^{43} +(-3.08668 + 1.21342i) q^{44} +7.71280 q^{45} +(-0.187805 + 0.578005i) q^{46} +(1.30084 + 12.3766i) q^{47} +(0.167101 + 0.375316i) q^{48} +(1.45154 + 4.46739i) q^{49} +(-0.748216 - 2.30277i) q^{50} +(-0.260682 + 0.116063i) q^{51} +(-4.35295 - 1.93806i) q^{52} +(-7.90283 + 7.11574i) q^{53} +(-2.07471 + 1.19783i) q^{54} +(-6.33727 + 6.43996i) q^{55} -1.51747i q^{56} +(-1.73229 + 0.453979i) q^{57} +(4.04929 - 2.94198i) q^{58} +(1.29133 + 0.135724i) q^{59} +(0.831725 + 0.748889i) q^{60} +(2.38442 - 11.2178i) q^{61} +(4.94994 + 0.520259i) q^{62} +(4.27274 - 0.449083i) q^{63} +(0.309017 - 0.951057i) q^{64} -12.9805 q^{65} +(0.342074 - 1.31895i) q^{66} +(-9.19960 - 5.31139i) q^{67} +(0.660571 + 0.214633i) q^{68} +(-0.146761 - 0.201999i) q^{69} +(-1.68140 - 3.77650i) q^{70} +(-3.64882 - 3.28542i) q^{71} +(2.76935 + 0.588643i) q^{72} +(6.89774 + 0.724981i) q^{73} +(1.08452 - 2.43588i) q^{74} +(0.946058 + 0.307393i) q^{75} +(3.87288 + 2.00021i) q^{76} +(-3.13576 + 3.93660i) q^{77} +(1.69532 - 0.978792i) q^{78} +(-5.05996 + 1.07553i) q^{79} +(-0.284757 - 2.70928i) q^{80} +(-0.784948 + 7.46829i) q^{81} +(-4.28936 - 0.911732i) q^{82} +(-9.77485 + 3.17604i) q^{83} +(0.504364 + 0.366442i) q^{84} +(1.88177 - 0.197782i) q^{85} +(-8.34190 + 7.51108i) q^{86} +2.05631i q^{87} +(-2.76695 + 1.82866i) q^{88} +(-4.21116 - 2.43132i) q^{89} +(7.54426 - 1.60358i) q^{90} +(-7.19097 + 0.755802i) q^{91} +(-0.0635273 + 0.604421i) q^{92} +(-1.36824 + 1.51959i) q^{93} +(3.84566 + 11.8357i) q^{94} +(11.8547 + 0.686609i) q^{95} +(0.241483 + 0.332372i) q^{96} +(-1.84026 - 8.65775i) q^{97} +(2.34865 + 4.06797i) q^{98} +(-5.96782 - 7.24974i) 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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