LMFDB - Embedded newform 418.2.u.b.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, 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:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	418.5
Dual form			418.2.u.b.251.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.615661 - 0.788011i) q^{2} +(1.20057 - 1.15938i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-2.39453 + 1.49627i) q^{5} +(-1.65275 - 0.232278i) q^{6} +(2.61504 + 1.16429i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.00748509 + 0.214345i) q^{9} +O(q^{10})$	\(q+(-0.615661 - 0.788011i) q^{2} +(1.20057 - 1.15938i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-2.39453 + 1.49627i) q^{5} +(-1.65275 - 0.232278i) q^{6} +(2.61504 + 1.16429i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.00748509 + 0.214345i) q^{9} +(2.65330 + 0.965720i) q^{10} +(-0.230878 - 3.30858i) q^{11} +(0.834495 + 1.44539i) q^{12} +(5.51978 - 2.93492i) q^{13} +(-0.692507 - 2.77749i) q^{14} +(-1.14006 + 4.57254i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(0.0973339 + 2.78728i) q^{17} +(0.173514 - 0.126066i) q^{18} +(3.77584 - 2.17785i) q^{19} +(-0.872534 - 2.68538i) q^{20} +(4.48940 - 1.63401i) q^{21} +(-2.46505 + 2.21890i) q^{22} +(6.61248 - 5.54853i) q^{23} +(0.625214 - 1.54746i) q^{24} +(1.30310 - 2.67175i) q^{25} +(-5.71106 - 2.54273i) q^{26} +(3.58984 + 3.98692i) q^{27} +(-1.76234 + 2.25570i) q^{28} +(-4.42511 + 1.26888i) q^{29} +(4.30510 - 1.91675i) q^{30} +(-0.618020 + 0.686381i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.11308 - 3.70451i) q^{33} +(2.13648 - 1.79272i) q^{34} +(-8.00390 + 1.12487i) q^{35} +(-0.206167 - 0.0591175i) q^{36} +(-2.96494 + 2.15416i) q^{37} +(-4.04081 - 1.63458i) q^{38} +(3.22420 - 9.92308i) q^{39} +(-1.57892 + 2.34085i) q^{40} +(-8.19481 + 7.91363i) q^{41} +(-4.05157 - 2.53170i) q^{42} +(3.86050 + 3.23934i) q^{43} +(3.26615 + 0.576398i) q^{44} +(-0.302794 - 0.524455i) q^{45} +(-8.44335 - 1.79469i) q^{46} +(-3.79034 - 5.61941i) q^{47} +(-1.60434 + 0.460036i) q^{48} +(0.798964 + 0.887340i) q^{49} +(-2.90763 + 0.618037i) q^{50} +(3.34836 + 3.23348i) q^{51} +(1.51238 + 6.06584i) q^{52} +(8.09265 + 5.05685i) q^{53} +(0.931609 - 5.28342i) q^{54} +(5.50337 + 7.57704i) q^{55} +2.86252 q^{56} +(2.00821 - 6.99228i) q^{57} +(3.72426 + 2.70584i) q^{58} +(5.54524 - 8.22116i) q^{59} +(-4.16091 - 2.21239i) q^{60} +(-2.68635 - 6.64896i) q^{61} +(0.921366 + 0.0644282i) q^{62} +(-0.269134 + 0.551807i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-8.82585 + 15.2868i) q^{65} +(-0.386929 + 5.52187i) q^{66} +(-0.957233 - 0.348404i) q^{67} +(-2.72803 - 0.579861i) q^{68} +(1.50591 - 14.3278i) q^{69} +(5.81410 + 5.61461i) q^{70} +(-1.96324 + 1.22677i) q^{71} +(0.0803440 + 0.198858i) q^{72} +(0.623780 + 1.27894i) q^{73} +(3.52290 + 1.01018i) q^{74} +(-1.53310 - 4.71840i) q^{75} +(1.19970 + 4.19055i) q^{76} +(3.24840 - 8.92089i) q^{77} +(-9.80451 + 3.56855i) q^{78} +(-12.1730 + 1.71081i) q^{79} +(2.81670 - 0.196963i) q^{80} +(8.29033 + 0.579716i) q^{81} +(11.2813 + 1.58548i) q^{82} +(-4.27619 + 0.908932i) q^{83} +(0.499387 + 4.75135i) q^{84} +(-4.40359 - 6.52859i) q^{85} +(0.175877 - 5.03645i) q^{86} +(-3.84155 + 6.65376i) q^{87} +(-1.55664 - 2.92863i) q^{88} +(2.08231 + 11.8094i) q^{89} +(-0.226858 + 0.561492i) q^{90} +(17.8516 - 1.24830i) q^{91} +(3.78401 + 7.75838i) q^{92} +(0.0537978 + 1.54057i) q^{93} +(-2.09459 + 6.44648i) q^{94} +(-5.78271 + 10.8646i) q^{95} +(1.35024 + 0.981007i) q^{96} +(-0.0681272 - 0.0871988i) q^{97} +(0.207342 - 1.17589i) q^{98} +(0.710906 - 0.0247225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$2$	−0.615661	−	0.788011i	−0.435338	−	0.557208i
$3$	1.20057	−	1.15938i	0.693150	−	0.669367i	−0.262143	−	0.965029i	$-0.584429\pi$
$3$	1.20057	−	1.15938i	0.693150	−	0.669367i	0.955293	+	0.295662i	$0.0955403\pi$
$4$	−0.241922	+	0.970296i	−0.120961	+	0.485148i
$5$	−2.39453	+	1.49627i	−1.07087	+	0.669152i	−0.946375	−	0.323069i	$-0.895285\pi$
$5$	−2.39453	+	1.49627i	−1.07087	+	0.669152i	−0.124491	+	0.992221i	$0.539730\pi$
$6$	−1.65275	−	0.232278i	−0.674731	−	0.0948273i
$7$	2.61504	+	1.16429i	0.988394	+	0.440061i	0.836281	−	0.548302i	$-0.184725\pi$
$7$	2.61504	+	1.16429i	0.988394	+	0.440061i	0.152113	+	0.988363i	$0.451392\pi$
$8$	0.913545	−	0.406737i	0.322987	−	0.143803i
$9$	−0.00748509	+	0.214345i	−0.00249503	+	0.0714483i
$10$	2.65330	+	0.965720i	0.839046	+	0.305388i
$11$	−0.230878	−	3.30858i	−0.0696122	−	0.997574i
$11$	−0.230878	−	3.30858i	−0.0696122	−	0.997574i
$12$	0.834495	+	1.44539i	0.240898	+	0.417247i
$13$	5.51978	−	2.93492i	1.53091	−	0.814000i	0.531458	−	0.847084i	$-0.321644\pi$
$13$	5.51978	−	2.93492i	1.53091	−	0.814000i	0.999453	+	0.0330848i	$0.0105331\pi$
$14$	−0.692507	−	2.77749i	−0.185080	−	0.742316i
$15$	−1.14006	+	4.57254i	−0.294363	+	1.18062i
$16$	−0.882948	−	0.469472i	−0.220737	−	0.117368i
$17$	0.0973339	+	2.78728i	0.0236069	+	0.676015i	0.952300	+	0.305164i	$0.0987114\pi$
$17$	0.0973339	+	2.78728i	0.0236069	+	0.676015i	−0.928693	+	0.370850i	$0.879066\pi$
$18$	0.173514	−	0.126066i	0.0408977	−	0.0297140i
$19$	3.77584	−	2.17785i	0.866237	−	0.499633i
$19$	3.77584	−	2.17785i	0.866237	−	0.499633i
$20$	−0.872534	−	2.68538i	−0.195104	−	0.600470i
$21$	4.48940	−	1.63401i	0.979667	−	0.356570i
$22$	−2.46505	+	2.21890i	−0.525551	+	0.473071i
$23$	6.61248	−	5.54853i	1.37880	−	1.15695i	0.409143	−	0.912470i	$-0.365828\pi$
$23$	6.61248	−	5.54853i	1.37880	−	1.15695i	0.969655	−	0.244479i	$-0.0786168\pi$
$24$	0.625214	−	1.54746i	0.127621	−	0.315874i
$25$	1.30310	−	2.67175i	0.260620	−	0.534350i
$26$	−5.71106	−	2.54273i	−1.12003	−	0.498670i
$27$	3.58984	+	3.98692i	0.690864	+	0.767282i
$28$	−1.76234	+	2.25570i	−0.333052	+	0.426287i
$29$	−4.42511	+	1.26888i	−0.821723	+	0.235625i	−0.660053	−	0.751219i	$-0.729466\pi$
$29$	−4.42511	+	1.26888i	−0.821723	+	0.235625i	−0.161671	+	0.986845i	$0.551688\pi$
$30$	4.30510	−	1.91675i	0.786000	−	0.349950i
$31$	−0.618020	+	0.686381i	−0.111000	+	0.123278i	−0.796084	−	0.605186i	$-0.793099\pi$
$31$	−0.618020	+	0.686381i	−0.111000	+	0.123278i	0.685084	+	0.728464i	$0.259765\pi$
$32$	0.173648	+	0.984808i	0.0306970	+	0.174091i
$33$	−4.11308	−	3.70451i	−0.715995	−	0.644872i
$34$	2.13648	−	1.79272i	0.366404	−	0.307449i
$35$	−8.00390	+	1.12487i	−1.35291	+	0.190138i
$36$	−0.206167	−	0.0591175i	−0.0343612	−	0.00985292i
$37$	−2.96494	+	2.15416i	−0.487434	+	0.354141i	−0.804197	−	0.594364i	$-0.797404\pi$
$37$	−2.96494	+	2.15416i	−0.487434	+	0.354141i	0.316763	+	0.948505i	$0.397404\pi$
$38$	−4.04081	−	1.63458i	−0.655506	−	0.265165i
$39$	3.22420	−	9.92308i	0.516286	−	1.58896i
$40$	−1.57892	+	2.34085i	−0.249650	+	0.370121i
$41$	−8.19481	+	7.91363i	−1.27981	+	1.23590i	−0.322595	+	0.946537i	$0.604555\pi$
$41$	−8.19481	+	7.91363i	−1.27981	+	1.23590i	−0.957219	+	0.289364i	$0.906556\pi$
$42$	−4.05157	−	2.53170i	−0.625170	−	0.390650i
$43$	3.86050	+	3.23934i	0.588721	+	0.493995i	0.887798	−	0.460234i	$-0.152234\pi$
$43$	3.86050	+	3.23934i	0.588721	+	0.493995i	−0.299077	+	0.954229i	$0.596679\pi$
$44$	3.26615	+	0.576398i	0.492391	+	0.0868953i
$45$	−0.302794	−	0.524455i	−0.0451379	−	0.0781812i
$46$	−8.44335	−	1.79469i	−1.24490	−	0.264613i
$47$	−3.79034	−	5.61941i	−0.552878	−	0.819675i	0.444211	−	0.895922i	$-0.353484\pi$
$47$	−3.79034	−	5.61941i	−0.552878	−	0.819675i	−0.997089	+	0.0762468i	$0.975706\pi$
$48$	−1.60434	+	0.460036i	−0.231566	+	0.0664004i
$49$	0.798964	+	0.887340i	0.114138	+	0.126763i
$50$	−2.90763	+	0.618037i	−0.411201	+	0.0874036i
$51$	3.34836	+	3.23348i	0.468865	+	0.452777i
$52$	1.51238	+	6.06584i	0.209730	+	0.841180i
$53$	8.09265	+	5.05685i	1.11161	+	0.694611i	0.956047	−	0.293214i	$-0.0947250\pi$
$53$	8.09265	+	5.05685i	1.11161	+	0.694611i	0.155564	+	0.987826i	$0.450281\pi$
$54$	0.931609	−	5.28342i	0.126776	−	0.718982i
$55$	5.50337	+	7.57704i	0.742074	+	1.02169i
$56$	2.86252			0.382521
$57$	2.00821	−	6.99228i	0.265994	−	0.926151i
$58$	3.72426	+	2.70584i	0.489020	+	0.355294i
$59$	5.54524	−	8.22116i	0.721929	−	1.07030i	−0.272215	−	0.962237i	$-0.587756\pi$
$59$	5.54524	−	8.22116i	0.721929	−	1.07030i	0.994144	−	0.108067i	$-0.0344662\pi$
$60$	−4.16091	−	2.21239i	−0.537171	−	0.285619i
$61$	−2.68635	−	6.64896i	−0.343952	−	0.851312i	−0.995679	−	0.0928585i	$-0.970400\pi$
$61$	−2.68635	−	6.64896i	−0.343952	−	0.851312i	0.651727	−	0.758454i	$-0.274045\pi$
$62$	0.921366	+	0.0644282i	0.117014	+	0.00818239i
$63$	−0.269134	+	0.551807i	−0.0339077	+	0.0695211i
$64$	0.669131	−	0.743145i	0.0836413	−	0.0928931i
$65$	−8.82585	+	15.2868i	−1.09471	+	1.89610i
$66$	−0.386929	+	5.52187i	−0.0476277	+	0.679695i
$67$	−0.957233	−	0.348404i	−0.116945	−	0.0425644i	0.282885	−	0.959154i	$-0.408709\pi$
$67$	−0.957233	−	0.348404i	−0.116945	−	0.0425644i	−0.399830	+	0.916589i	$0.630931\pi$
$68$	−2.72803	−	0.579861i	−0.330823	−	0.0703185i
$69$	1.50591	−	14.3278i	0.181290	−	1.72486i
$70$	5.81410	+	5.61461i	0.694918	+	0.671075i
$71$	−1.96324	+	1.22677i	−0.232994	+	0.145591i	−0.641392	−	0.767213i	$-0.721643\pi$
$71$	−1.96324	+	1.22677i	−0.232994	+	0.145591i	0.408399	+	0.912804i	$0.366087\pi$
$72$	0.0803440	+	0.198858i	0.00946863	+	0.0234357i
$73$	0.623780	+	1.27894i	0.0730079	+	0.149688i	0.932176	−	0.362004i	$-0.117907\pi$
$73$	0.623780	+	1.27894i	0.0730079	+	0.149688i	−0.859168	+	0.511693i	$0.829019\pi$
$74$	3.52290	+	1.01018i	0.409529	+	0.117430i
$75$	−1.53310	−	4.71840i	−0.177027	−	0.544834i
$76$	1.19970	+	4.19055i	0.137615	+	0.480689i
$77$	3.24840	−	8.92089i	0.370189	−	1.01663i
$78$	−9.80451	+	3.56855i	−1.11014	+	0.404059i
$79$	−12.1730	+	1.71081i	−1.36957	+	0.192481i	−0.785319	−	0.619091i	$-0.787501\pi$
$79$	−12.1730	+	1.71081i	−1.36957	+	0.192481i	−0.584253	+	0.811572i	$0.698612\pi$
$80$	2.81670	−	0.196963i	0.314917	−	0.0220211i
$81$	8.29033	+	0.579716i	0.921148	+	0.0644129i
$82$	11.2813	+	1.58548i	1.24581	+	0.175087i
$83$	−4.27619	+	0.908932i	−0.469373	+	0.0997682i	−0.436525	−	0.899692i	$-0.643791\pi$
$83$	−4.27619	+	0.908932i	−0.469373	+	0.0997682i	−0.0328477	+	0.999460i	$0.510458\pi$
$84$	0.499387	+	4.75135i	0.0544875	+	0.518414i
$85$	−4.40359	−	6.52859i	−0.477636	−	0.708125i
$86$	0.175877	−	5.03645i	0.0189653	−	0.543095i
$87$	−3.84155	+	6.65376i	−0.411857	+	0.713358i
$88$	−1.55664	−	2.92863i	−0.165938	−	0.312193i
$89$	2.08231	+	11.8094i	0.220725	+	1.25179i	0.870692	+	0.491829i	$0.163672\pi$
$89$	2.08231	+	11.8094i	0.220725	+	1.25179i	−0.649967	+	0.759962i	$0.725217\pi$
$90$	−0.226858	+	0.561492i	−0.0239129	+	0.0591865i
$91$	17.8516	−	1.24830i	1.87135	−	0.130858i
$92$	3.78401	+	7.75838i	0.394511	+	0.808867i
$93$	0.0537978	+	1.54057i	0.00557857	+	0.159749i
$94$	−2.09459	+	6.44648i	−0.216040	+	0.664904i
$95$	−5.78271	+	10.8646i	−0.593294	+	1.11468i
$96$	1.35024	+	0.981007i	0.137808	+	0.100124i
$97$	−0.0681272	−	0.0871988i	−0.00691727	−	0.00885370i	0.784540	−	0.620079i	$-0.212899\pi$
$97$	−0.0681272	−	0.0871988i	−0.00691727	−	0.00885370i	−0.791457	+	0.611225i	$0.790677\pi$
$98$	0.207342	−	1.17589i	0.0209447	−	0.118783i
$99$	0.710906	−	0.0247225i	0.0714487	−	0.00248470i
$100$	2.27714	+	1.91074i	0.227714	+	0.191074i
$101$	11.8622	−	6.30722i	1.18033	−	0.627592i	0.240972	−	0.970532i	$-0.422534\pi$
$101$	11.8622	−	6.30722i	1.18033	−	0.627592i	0.939357	+	0.342940i	$0.111423\pi$
$102$	0.486556	−	4.62927i	0.0481763	−	0.458367i
$103$	−0.0980939	−	0.933301i	−0.00966548	−	0.0919609i	0.988626	−	0.150397i	$-0.0480552\pi$
$103$	−0.0980939	−	0.933301i	−0.00966548	−	0.0919609i	−0.998291	+	0.0584362i	$0.981389\pi$
$104$	3.84883	−	4.92628i	0.377409	−	0.483061i
$105$	−8.30509	+	10.6300i	−0.810493	+	1.03738i
$106$	−0.997481	−	9.49040i	−0.0968839	−	0.921789i
$107$	−2.02145	+	19.2328i	−0.195421	+	1.85930i	0.255591	+	0.966785i	$0.417730\pi$
$107$	−2.02145	+	19.2328i	−0.195421	+	1.85930i	−0.451011	+	0.892518i	$0.648937\pi$
$108$	−4.73695	+	2.51868i	−0.455813	+	0.242360i
$109$	−5.05028	−	4.23769i	−0.483729	−	0.405897i	0.368044	−	0.929808i	$-0.380028\pi$
$109$	−5.05028	−	4.23769i	−0.483729	−	0.405897i	−0.851772	+	0.523912i	$0.824472\pi$
$110$	2.58258	−	9.00160i	0.246239	−	0.858269i
$111$	−1.06214	+	6.02370i	−0.100814	+	0.571745i
$112$	−1.76234	−	2.25570i	−0.166526	−	0.213143i
$113$	−11.9332	−	8.66999i	−1.12258	−	0.815604i	−0.137984	−	0.990434i	$-0.544062\pi$
$113$	−11.9332	−	8.66999i	−1.12258	−	0.815604i	−0.984599	+	0.174831i	$0.944062\pi$
$114$	−6.74637	+	2.72239i	−0.631856	+	0.254975i
$115$	−7.53169	+	23.1802i	−0.702334	+	2.16156i
$116$	−0.160658	−	4.60064i	−0.0149167	−	0.427159i
$117$	0.587769	+	1.20510i	0.0543393	+	0.111412i
$118$	−9.89235	+	0.691741i	−0.910665	+	0.0636799i
$119$	−2.99068	+	7.40218i	−0.274155	+	0.678557i
$120$	0.818321	+	4.64093i	0.0747021	+	0.423657i
$121$	−10.8934	+	1.52775i	−0.990308	+	0.138887i
$122$	−3.58557	+	6.21039i	−0.324622	+	0.562262i
$123$	−0.663555	+	19.0017i	−0.0598308	+	1.71333i
$124$	−0.516480	−	0.765712i	−0.0463812	−	0.0687630i
$125$	−0.598378	−	5.69319i	−0.0535206	−	0.509214i
$126$	0.600525	−	0.127646i	0.0534990	−	0.0113716i
$127$	−14.4027	−	2.02417i	−1.27803	−	0.179616i	−0.532697	−	0.846306i	$-0.678821\pi$
$127$	−14.4027	−	2.02417i	−1.27803	−	0.179616i	−0.745335	+	0.666691i	$0.767710\pi$
$128$	−0.997564	−	0.0697565i	−0.0881730	−	0.00616566i
$129$	8.39042	−	0.586715i	0.738735	−	0.0516574i
$130$	17.4799	−	2.45664i	1.53309	−	0.215462i
$131$	−16.2600	+	5.91817i	−1.42065	+	0.517073i	−0.934235	−	0.356657i	$-0.883916\pi$
$131$	−16.2600	+	5.91817i	−1.42065	+	0.517073i	−0.486411	+	0.873730i	$0.661694\pi$
$132$	4.58951	−	3.09470i	0.399466	−	0.269359i
$133$	12.4096	−	1.29899i	1.07605	−	0.112637i
$134$	0.314785	+	0.968809i	0.0271933	+	0.0836924i
$135$	−14.5615	−	4.17543i	−1.25325	−	0.359364i
$136$	1.22261	+	2.50672i	0.104838	+	0.214949i
$137$	−4.43149	−	10.9683i	−0.378608	−	0.937087i	−0.989389	−	0.145288i	$-0.953589\pi$
$137$	−4.43149	−	10.9683i	−0.378608	−	0.937087i	0.610782	−	0.791799i	$-0.290855\pi$
$138$	−12.2176	+	7.63438i	−1.04003	+	0.649882i
$139$	5.98937	+	5.78386i	0.508011	+	0.490581i	0.903916	−	0.427711i	$-0.140680\pi$
$139$	5.98937	+	5.78386i	0.508011	+	0.490581i	−0.395904	+	0.918292i	$0.629569\pi$
$140$	0.844857	−	8.03828i	0.0714034	−	0.679358i
$141$	−11.0656	−	2.35206i	−0.931891	−	0.198079i
$142$	2.17540	+	0.791780i	0.182555	+	0.0664447i
$143$	−10.9848	−	17.5850i	−0.918595	−	1.47053i
$144$	0.107238	−	0.185741i	0.00893649	−	0.0154784i
$145$	8.69748	−	9.65953i	0.722287	−	0.802181i
$146$	0.623780	−	1.27894i	0.0516244	−	0.105846i
$147$	1.98797	+	0.139013i	0.163965	+	0.0114656i
$148$	−1.37288	−	3.39801i	−0.112850	−	0.279315i
$149$	−5.33553	−	2.83695i	−0.437103	−	0.232412i	0.236311	−	0.971678i	$-0.424062\pi$
$149$	−5.33553	−	2.83695i	−0.437103	−	0.232412i	−0.673414	+	0.739266i	$0.735173\pi$
$150$	−2.77428	+	4.11304i	−0.226519	+	0.335828i
$151$	11.8549	+	8.61309i	0.964738	+	0.700923i	0.954246	−	0.299022i	$-0.0966603\pi$
$151$	11.8549	+	8.61309i	0.964738	+	0.700923i	0.0104917	+	0.999945i	$0.496660\pi$
$152$	2.56359	−	3.52534i	0.207935	−	0.285943i
$153$	−0.598168			−0.0483590
$154$	−9.02967	+	2.93247i	−0.727632	+	0.236306i
$155$	0.452857	−	2.56828i	0.0363744	−	0.206289i
$156$	8.84832	+	5.52904i	0.708432	+	0.442678i
$157$	1.19629	+	4.79804i	0.0954740	+	0.382925i	0.998955	−	0.0457026i	$-0.0145527\pi$
$157$	1.19629	+	4.79804i	0.0954740	+	0.382925i	−0.903481	+	0.428628i	$0.858997\pi$
$158$	8.84260	+	8.53920i	0.703479	+	0.679342i
$159$	15.5786	−	3.31133i	1.23546	−	0.262606i
$160$	−1.88934	−	2.09833i	−0.149366	−	0.165887i
$161$	23.7521	−	6.81079i	1.87192	−	0.536766i
$162$	−4.64721	−	6.88978i	−0.365120	−	0.541312i
$163$	−12.3516	−	2.62542i	−0.967455	−	0.205639i	−0.303019	−	0.952984i	$-0.597995\pi$
$163$	−12.3516	−	2.62542i	−0.967455	−	0.205639i	−0.664436	+	0.747345i	$0.731328\pi$
$164$	−5.69606	−	9.86587i	−0.444788	−	0.770395i
$165$	15.3918	+	2.71629i	1.19825	+	0.211463i
$166$	3.34893	+	2.81009i	0.259928	+	0.218105i
$167$	−8.43168	−	5.26870i	−0.652463	−	0.407704i	0.162910	−	0.986641i	$-0.447912\pi$
$167$	−8.43168	−	5.26870i	−0.652463	−	0.407704i	−0.815372	+	0.578937i	$0.803468\pi$
$168$	3.43666	−	3.31874i	0.265144	−	0.256047i
$169$	14.5847	−	21.6227i	1.12190	−	1.66328i
$170$	−2.43348	+	7.48947i	−0.186639	+	0.574416i
$171$	0.438549	+	0.825634i	0.0335367	+	0.0631378i
$172$	−4.07706	+	2.96216i	−0.310873	+	0.225862i
$173$	−0.210275	−	0.0602955i	−0.0159869	−	0.00458418i	0.267634	−	0.963521i	$-0.413758\pi$
$173$	−0.210275	−	0.0602955i	−0.0159869	−	0.00458418i	−0.283621	+	0.958936i	$0.591536\pi$
$174$	7.60833	−	1.06928i	0.576786	−	0.0810620i
$175$	6.51836	−	5.46955i	0.492741	−	0.413459i
$176$	−1.34943	+	3.02969i	−0.101717	+	0.228372i
$177$	−2.87397	−	16.2991i	−0.216021	−	1.22512i
$178$	8.02392	−	8.91146i	0.601418	−	0.667942i
$179$	5.79586	−	2.58048i	0.433203	−	0.192874i	−0.178537	−	0.983933i	$-0.557137\pi$
$179$	5.79586	−	2.58048i	0.433203	−	0.192874i	0.611740	+	0.791059i	$0.290470\pi$
$180$	0.582129	−	0.166923i	0.0433893	−	0.0124417i
$181$	−9.95346	+	12.7398i	−0.739835	+	0.946945i	−0.999826	−	0.0186659i	$-0.994058\pi$
$181$	−9.95346	+	12.7398i	−0.739835	+	0.946945i	0.259991	+	0.965611i	$0.416280\pi$
$182$	−11.9742	−	13.2987i	−0.887587	−	0.985765i
$183$	−10.9338	−	4.86805i	−0.808251	−	0.359856i
$184$	3.78401	−	7.75838i	0.278961	−	0.571955i
$185$	3.87645	−	9.59454i	0.285002	−	0.705405i
$186$	1.18086	−	0.990860i	0.0865850	−	0.0726534i
$187$	9.19946	−	0.965558i	0.672731	−	0.0706086i
$188$	6.36946	−	2.31829i	0.464540	−	0.169079i
$189$	4.74564	+	14.6056i	0.345195	+	1.06240i
$190$	12.1216	−	2.13207i	0.879394	−	0.154677i
$191$	11.3365	−	8.23642i	0.820277	−	0.595966i	−0.0965147	−	0.995332i	$-0.530769\pi$
$191$	11.3365	−	8.23642i	0.820277	−	0.595966i	0.916792	+	0.399365i	$0.130769\pi$
$192$	−0.0582469	−	1.66797i	−0.00420361	−	0.120376i
$193$	20.4903	+	10.8949i	1.47492	+	0.784231i	0.995627	−	0.0934206i	$-0.0297801\pi$
$193$	20.4903	+	10.8949i	1.47492	+	0.784231i	0.479298	+	0.877652i	$0.340891\pi$
$194$	−0.0267703	+	0.107370i	−0.00192200	+	0.00770871i
$195$	7.12714	+	28.5854i	0.510385	+	2.04704i
$196$	−1.05427	+	0.560565i	−0.0753049	+	0.0400403i
$197$	−5.25904	−	9.10893i	−0.374691	−	0.648984i	0.615590	−	0.788067i	$-0.288918\pi$
$197$	−5.25904	−	9.10893i	−0.374691	−	0.648984i	−0.990281	+	0.139083i	$0.955585\pi$
$198$	−0.457159	−	0.544981i	−0.0324889	−	0.0387301i
$199$	−7.86659	−	2.86320i	−0.557648	−	0.202967i	0.0477934	−	0.998857i	$-0.484781\pi$
$199$	−7.86659	−	2.86320i	−0.557648	−	0.202967i	−0.605441	+	0.795890i	$0.707003\pi$
$200$	0.103742	−	2.97078i	0.00733566	−	0.210066i
$201$	−1.55316	+	0.691510i	−0.109551	+	0.0487754i
$202$	−12.2732	−	5.46440i	−0.863542	−	0.384474i
$203$	−13.0492	−	1.83395i	−0.915876	−	0.128718i
$204$	−3.94747	+	2.46665i	−0.276378	+	0.172700i
$205$	7.78179	−	31.2111i	0.543504	−	2.17987i
$206$	−0.675059	+	0.651897i	−0.0470336	+	0.0454198i
$207$	1.13981	+	1.45888i	0.0792219	+	0.101399i
$208$	−6.25153			−0.433466
$209$	−8.07735	−	11.9898i	−0.558722	−	0.829355i
$210$	13.4897			0.930877
$211$	4.21967	+	5.40093i	0.290494	+	0.371816i	0.911014	−	0.412375i	$-0.135301\pi$
$211$	4.21967	+	5.40093i	0.290494	+	0.371816i	−0.620520	+	0.784191i	$0.713078\pi$
$212$	−6.86443	+	6.62890i	−0.471451	+	0.455275i
$213$	−0.934720	+	3.74896i	−0.0640460	+	0.256874i
$214$	16.4002	−	10.2480i	1.12109	−	0.700536i
$215$	−14.0910	−	1.98036i	−0.960999	−	0.135060i
$216$	4.90110	+	2.18211i	0.333478	+	0.148474i
$217$	−2.41530	+	1.07536i	−0.163961	+	0.0730002i
$218$	−0.230081	+	6.58865i	−0.0155830	+	0.446240i
$219$	2.23166	+	0.812259i	0.150802	+	0.0548874i
$220$	−8.68335	+	3.50684i	−0.585431	+	0.236431i
$221$	8.71770	+	15.0995i	0.586416	+	1.01570i
$222$	5.40066	−	2.87158i	0.362469	−	0.192728i
$223$	−3.63607	−	14.5835i	−0.243489	−	0.976582i	−0.960223	−	0.279235i	$-0.909919\pi$
$223$	−3.63607	−	14.5835i	−0.243489	−	0.976582i	0.716733	−	0.697347i	$-0.245636\pi$
$224$	−0.692507	+	2.77749i	−0.0462701	+	0.185579i
$225$	0.562922	+	0.299311i	0.0375281	+	0.0199541i
$226$	0.514777	+	14.7413i	0.0342424	+	0.980575i
$227$	16.8623	−	12.2512i	1.11919	−	0.813141i	0.135106	−	0.990831i	$-0.456863\pi$
$227$	16.8623	−	12.2512i	1.11919	−	0.813141i	0.984086	+	0.177691i	$0.0568626\pi$
$228$	6.29875	+	3.64015i	0.417145	+	0.241075i
$229$	−2.43847	−	7.50483i	−0.161139	−	0.495933i	0.837592	−	0.546296i	$-0.183962\pi$
$229$	−2.43847	−	7.50483i	−0.161139	−	0.495933i	−0.998731	+	0.0503621i	$0.983962\pi$
$230$	22.9032	−	8.33608i	1.51019	−	0.549665i
$231$	−6.44274	−	14.4763i	−0.423901	−	0.952469i
$232$	−3.52644	+	2.95904i	−0.231522	+	0.194270i
$233$	−6.77653	+	16.7725i	−0.443945	+	1.09880i	0.524906	+	0.851160i	$0.324100\pi$
$233$	−6.77653	+	16.7725i	−0.443945	+	1.09880i	−0.968851	+	0.247643i	$0.920344\pi$
$234$	0.587769	−	1.20510i	0.0384237	−	0.0787802i
$235$	17.4842	+	7.78448i	1.14055	+	0.507804i
$236$	6.63544	+	7.36940i	0.431930	+	0.479707i
$237$	−12.6311	+	16.1671i	−0.820478	+	1.05016i
$238$	7.67424	−	2.20055i	0.497447	−	0.142641i
$239$	−11.5792	+	5.15539i	−0.748996	+	0.333474i	−0.745488	−	0.666519i	$-0.767783\pi$
$239$	−11.5792	+	5.15539i	−0.748996	+	0.333474i	−0.00350808	+	0.999994i	$0.501117\pi$
$240$	3.15329	−	3.50209i	0.203544	−	0.226059i
$241$	−0.993270	−	5.63312i	−0.0639822	−	0.362861i	−0.999942	−	0.0107545i	$-0.996577\pi$
$241$	−0.993270	−	5.63312i	−0.0639822	−	0.362861i	0.935960	−	0.352106i	$-0.114534\pi$
$242$	7.91053	+	7.64353i	0.508508	+	0.491345i
$243$	−1.70408	+	1.42989i	−0.109317	+	0.0917277i
$244$	7.10135	−	0.998029i	0.454617	−	0.0638923i
$245$	−3.24084	−	0.929297i	−0.207050	−	0.0593706i
$246$	15.3821	−	11.1758i	0.980727	−	0.712540i
$247$	14.4500	−	23.1030i	0.919431	−	1.47001i
$248$	−0.285413	+	0.878411i	−0.0181237	+	0.0557792i
$249$	−4.08007	+	6.04895i	−0.258564	+	0.383337i
$250$	−4.11789	+	3.97660i	−0.260438	+	0.251502i
$251$	15.3260	+	9.57673i	0.967367	+	0.604478i	0.918960	−	0.394350i	$-0.129030\pi$
$251$	15.3260	+	9.57673i	0.967367	+	0.604478i	0.0484064	+	0.998828i	$0.484586\pi$
$252$	−0.470306	−	0.394634i	−0.0296265	−	0.0248596i
$253$	−19.8844	−	20.5969i	−1.25012	−	1.29492i
$254$	7.27211	+	12.5957i	0.456293	+	0.790323i
$255$	−12.8559	−	2.73261i	−0.805068	−	0.171123i
$256$	0.559193	+	0.829038i	0.0349496	+	0.0518148i
$257$	−14.2781	+	4.09418i	−0.890644	+	0.255388i	−0.689597	−	0.724194i	$-0.742212\pi$
$257$	−14.2781	+	4.09418i	−0.890644	+	0.255388i	−0.201047	+	0.979582i	$0.564434\pi$
$258$	−5.62800	−	6.25052i	−0.350384	−	0.389141i
$259$	−10.2615	+	2.18115i	−0.637620	+	0.135530i
$260$	−12.6976	−	12.2619i	−0.787470	−	0.760451i
$261$	−0.238856	−	0.957999i	−0.0147848	−	0.0592986i
$262$	14.6743	+	9.16949i	0.906579	+	0.566493i
$263$	3.17460	−	18.0041i	0.195754	−	1.11018i	−0.715586	−	0.698525i	$-0.753840\pi$
$263$	3.17460	−	18.0041i	0.195754	−	1.11018i	0.911340	−	0.411654i	$-0.135049\pi$
$264$	−5.26424	−	1.71130i	−0.323992	−	0.105323i
$265$	−26.9445			−1.65519
$266$	−8.66376	−	8.97919i	−0.531209	−	0.550550i
$267$	16.1915	+	11.7638i	0.990903	+	0.719933i
$268$	0.569631	−	0.844513i	0.0347957	−	0.0515868i
$269$	−21.5562	−	11.4616i	−1.31430	−	0.698827i	−0.343601	−	0.939116i	$-0.611647\pi$
$269$	−21.5562	−	11.4616i	−1.31430	−	0.698827i	−0.970701	+	0.240289i	$0.922758\pi$
$270$	5.67465	+	14.0452i	0.345348	+	0.854766i
$271$	−14.8394	−	1.03767i	−0.901432	−	0.0630342i	−0.388485	−	0.921455i	$-0.627002\pi$
$271$	−14.8394	−	1.03767i	−0.901432	−	0.0630342i	−0.512946	+	0.858421i	$0.671446\pi$
$272$	1.22261	−	2.50672i	0.0741315	−	0.151992i
$273$	19.9848	−	22.1954i	1.20954	−	1.34333i
$274$	−5.91486	+	10.2448i	−0.357330	+	0.618913i
$275$	−9.14054	−	3.69456i	−0.551196	−	0.222790i
$276$	13.5379	+	4.92738i	0.814883	+	0.296593i
$277$	8.91990	+	1.89598i	0.535945	+	0.113919i	0.467930	−	0.883766i	$-0.345000\pi$
$277$	8.91990	+	1.89598i	0.535945	+	0.113919i	0.0680151	+	0.997684i	$0.478333\pi$
$278$	0.870325	−	8.28059i	0.0521986	−	0.496637i
$279$	−0.142496	−	0.137607i	−0.00853103	−	0.00823832i
$280$	−6.85439	+	4.28310i	−0.409628	+	0.255964i
$281$	6.27332	+	15.5270i	0.374235	+	0.926263i	0.990348	+	0.138605i	$0.0442620\pi$
$281$	6.27332	+	15.5270i	0.374235	+	0.926263i	−0.616113	+	0.787658i	$0.711294\pi$
$282$	4.95921	+	10.1679i	0.295316	+	0.605488i
$283$	−19.6738	−	5.64137i	−1.16949	−	0.335345i	−0.365970	−	0.930627i	$-0.619263\pi$
$283$	−19.6738	−	5.64137i	−1.16949	−	0.335345i	−0.803517	+	0.595282i	$0.797040\pi$
$284$	−0.715378	−	2.20171i	−0.0424498	−	0.130647i
$285$	5.65361	+	19.7481i	0.334891	+	1.16977i
$286$	−7.09426	+	19.4826i	−0.419492	+	1.15203i
$287$	−30.6436	+	11.1533i	−1.80883	+	0.658361i
$288$	−0.212388	+	0.0298492i	−0.0125151	+	0.00175888i
$289$	9.19914	−	0.643266i	0.541126	−	0.0378392i
$290$	−12.9665	−	0.906707i	−0.761420	−	0.0532437i
$291$	−0.182888	−	0.0257032i	−0.0107211	−	0.00150675i
$292$	−1.39185	+	0.295848i	−0.0814521	+	0.0173132i
$293$	−0.422798	−	4.02265i	−0.0247001	−	0.235006i	−0.999906	−	0.0137067i	$-0.995637\pi$
$293$	−0.422798	−	4.02265i	−0.0247001	−	0.235006i	0.975206	−	0.221299i	$-0.0710298\pi$
$294$	−1.11438	−	1.65213i	−0.0649917	−	0.0963542i
$295$	−0.977187	+	27.9830i	−0.0568940	+	1.62923i
$296$	−1.83244	+	3.17387i	−0.106508	+	0.184478i
$297$	12.3622	−	12.7977i	0.717328	−	0.742600i
$298$	1.04933	+	5.95105i	0.0607861	+	0.344735i
$299$	20.2149	−	50.0338i	1.16906	−	2.89353i
$300$	4.94914	−	0.346077i	0.285739	−	0.0199808i
$301$	6.32383	+	12.9658i	0.364500	+	0.747335i
$302$	−0.511398	−	14.6445i	−0.0294277	−	0.842698i
$303$	6.92891	−	21.3250i	0.398055	−	1.22509i
$304$	−4.35631	+	0.150278i	−0.249851	+	0.00861902i
$305$	16.3812	+	11.9016i	0.937984	+	0.681485i
$306$	0.368269	+	0.471363i	0.0210525	+	0.0269460i
$307$	−2.67931	+	15.1951i	−0.152916	+	0.867231i	0.807750	+	0.589525i	$0.200685\pi$
$307$	−2.67931	+	15.1951i	−0.152916	+	0.867231i	−0.960666	+	0.277706i	$0.910426\pi$
$308$	7.87004	+	5.31007i	0.448437	+	0.302569i
$309$	−1.19982	−	1.00677i	−0.0682552	−	0.0572729i
$310$	−2.30264	+	1.22434i	−0.130781	+	0.0695376i
$311$	−1.65237	+	15.7212i	−0.0936971	+	0.891468i	0.842193	+	0.539176i	$0.181264\pi$
$311$	−1.65237	+	15.7212i	−0.0936971	+	0.891468i	−0.935890	+	0.352292i	$0.885402\pi$
$312$	−1.09062	−	10.3766i	−0.0617444	−	0.587458i
$313$	−3.35126	+	4.28941i	−0.189424	+	0.242452i	−0.873342	−	0.487107i	$-0.838052\pi$
$313$	−3.35126	+	4.28941i	−0.189424	+	0.242452i	0.683918	+	0.729559i	$0.260275\pi$
$314$	3.04440	−	3.89665i	0.171805	−	0.219901i
$315$	−0.181201	−	1.72401i	−0.0102095	−	0.0971372i
$316$	1.28493	−	12.2253i	0.0722831	−	0.687728i
$317$	13.2196	−	7.02901i	0.742489	−	0.394788i	−0.0547121	−	0.998502i	$-0.517424\pi$
$317$	13.2196	−	7.02901i	0.742489	−	0.394788i	0.797201	+	0.603714i	$0.206313\pi$
$318$	−12.2005	−	10.2374i	−0.684170	−	0.574087i
$319$	5.21985	+	14.3479i	0.292256	+	0.803327i
$320$	−0.490309	+	2.78068i	−0.0274091	+	0.155445i
$321$	19.8712	+	25.4339i	1.10910	+	1.41958i
$322$	−19.9902	−	14.5237i	−1.11401	−	0.809376i
$323$	6.43779	+	10.3123i	0.358208	+	0.573794i
$324$	−2.56811	+	7.90382i	−0.142673	+	0.439101i
$325$	−0.648546	−	18.5719i	−0.0359749	−	1.03019i
$326$	5.53557	+	11.3496i	0.306587	+	0.628596i
$327$	−10.9763	+	0.767537i	−0.606990	+	0.0424449i
$328$	−4.26756	+	10.5626i	−0.235637	+	0.583221i
$329$	−3.36927	−	19.1081i	−0.185754	−	1.05346i
$330$	−7.33569	−	13.8012i	−0.403816	−	0.759733i
$331$	−8.98838	+	15.5683i	−0.494046	+	0.855712i	−0.999976	−	0.00686173i	$-0.997816\pi$
$331$	−8.98838	+	15.5683i	−0.494046	+	0.855712i	0.505931	+	0.862574i	$0.331149\pi$
$332$	0.152571	−	4.36906i	0.00837341	−	0.239783i
$333$	−0.439540	−	0.651645i	−0.0240866	−	0.0357099i
$334$	1.03927	+	9.88798i	0.0568663	+	0.541046i
$335$	2.81343	−	0.598013i	0.153714	−	0.0326729i
$336$	−4.73102	−	0.664902i	−0.258099	−	0.0362734i
$337$	−9.33368	−	0.652675i	−0.508438	−	0.0355535i	−0.186766	−	0.982404i	$-0.559801\pi$
$337$	−9.33368	−	0.652675i	−0.508438	−	0.0355535i	−0.321672	+	0.946851i	$0.604245\pi$
$338$	−26.0182	+	1.81937i	−1.41520	+	0.0989605i
$339$	−24.3784	+	3.42617i	−1.32406	+	0.186084i
$340$	7.39998	−	2.69337i	0.401320	−	0.146069i
$341$	2.41363	+	1.88630i	0.130705	+	0.102149i
$342$	0.380611	−	0.853892i	0.0205811	−	0.0461732i
$343$	−5.13577	−	15.8063i	−0.277306	−	0.853459i
$344$	4.84430	+	1.38908i	0.261187	+	0.0748942i
$345$	17.8322	+	36.5615i	0.960055	+	1.96841i
$346$	0.0819450	+	0.202821i	0.00440539	+	0.0109037i
$347$	−1.23475	+	0.771557i	−0.0662848	+	0.0414194i	−0.562657	−	0.826691i	$-0.690221\pi$
$347$	−1.23475	+	0.771557i	−0.0662848	+	0.0414194i	0.496372	+	0.868110i	$0.334665\pi$
$348$	−5.52676	−	5.33713i	−0.296265	−	0.286100i
$349$	−0.265528	+	2.52633i	−0.0142134	+	0.135231i	−0.999327	−	0.0366709i	$-0.988325\pi$
$349$	−0.265528	+	2.52633i	−0.0142134	+	0.135231i	0.985114	+	0.171902i	$0.0549913\pi$
$350$	−8.32316	−	1.76914i	−0.444892	−	0.0945647i
$351$	31.5164	+	11.4710i	1.68222	+	0.612278i
$352$	3.21822	−	0.801899i	0.171532	−	0.0427414i
$353$	5.98650	−	10.3689i	0.318629	−	0.551882i	−0.661573	−	0.749881i	$-0.730111\pi$
$353$	5.98650	−	10.3689i	0.318629	−	0.551882i	0.980202	+	0.197999i	$0.0634441\pi$
$354$	−11.0745	+	12.2995i	−0.588602	+	0.653709i
$355$	2.86546	−	5.87507i	0.152083	−	0.311816i
$356$	−11.9623	−	0.836489i	−0.634003	−	0.0443338i
$357$	4.99141	+	12.3542i	0.264173	+	0.653852i
$358$	−5.60173	−	2.97849i	−0.296061	−	0.157418i
$359$	−11.7638	+	17.4406i	−0.620872	+	0.920480i	−0.999988	−	0.00486859i	$-0.998450\pi$
$359$	−11.7638	+	17.4406i	−0.620872	+	0.920480i	0.379116	+	0.925349i	$0.376228\pi$
$360$	−0.489932	−	0.355956i	−0.0258217	−	0.0187605i
$361$	9.51394	−	16.4464i	0.500734	−	0.865601i
$362$	16.1671			0.849724
$363$	−11.3070	+	14.4637i	−0.593466	+	0.759149i
$364$	−3.10746	+	17.6233i	−0.162875	+	0.923711i
$365$	−3.40729	−	2.12911i	−0.178346	−	0.111443i
$366$	2.89545	+	11.6130i	0.151348	+	0.607023i
$367$	6.72164	+	6.49101i	0.350866	+	0.338828i	0.849117	−	0.528206i	$-0.177135\pi$
$367$	6.72164	+	6.49101i	0.350866	+	0.338828i	−0.498250	+	0.867033i	$0.666024\pi$
$368$	−8.44335	+	1.79469i	−0.440140	+	0.0935547i
$369$	−1.63491	−	1.81575i	−0.0851099	−	0.0945242i
$370$	−9.94718	+	2.85231i	−0.517129	+	0.148284i
$371$	15.2750	+	22.6461i	0.793037	+	1.17573i
$372$	−1.50782	−	0.320497i	−0.0781768	−	0.0166170i
$373$	5.55655	+	9.62423i	0.287707	+	0.498324i	0.973262	−	0.229697i	$-0.0737736\pi$
$373$	5.55655	+	9.62423i	0.287707	+	0.498324i	−0.685555	+	0.728021i	$0.740440\pi$
$374$	−6.42462	−	6.65482i	−0.332209	−	0.344112i
$375$	−7.31894	−	6.14132i	−0.377949	−	0.317137i
$376$	−5.74827	−	3.59192i	−0.296444	−	0.185239i
$377$	−20.7016	+	19.9913i	−1.06619	+	1.02960i
$378$	8.58765	−	12.7317i	0.441701	−	0.654848i
$379$	3.49326	−	10.7512i	0.179437	−	0.552250i	−0.820371	−	0.571831i	$-0.806233\pi$
$379$	3.49326	−	10.7512i	0.179437	−	0.552250i	0.999808	+	0.0195811i	$0.00623325\pi$
$380$	−9.14291	−	8.23933i	−0.469021	−	0.422669i
$381$	−19.6382	+	14.2680i	−1.00610	+	0.730971i
$382$	−13.4698	−	3.86240i	−0.689175	−	0.197618i
$383$	−7.86487	+	1.10534i	−0.401876	+	0.0564800i	−0.337216	−	0.941427i	$-0.609485\pi$
$383$	−7.86487	+	1.10534i	−0.401876	+	0.0564800i	−0.0646603	+	0.997907i	$0.520596\pi$
$384$	−1.27852	+	1.07281i	−0.0652442	+	0.0547464i
$385$	5.56966	+	26.2218i	0.283856	+	1.33639i
$386$	−4.02980	−	22.8542i	−0.205112	−	1.16325i
$387$	−0.723233	+	0.803232i	−0.0367640	+	0.0408306i
$388$	0.101090	−	0.0450082i	0.00513207	−	0.00228495i
$389$	16.6707	−	4.78025i	0.845238	−	0.242368i	0.175050	−	0.984560i	$-0.443991\pi$
$389$	16.6707	−	4.78025i	0.845238	−	0.242368i	0.670188	+	0.742191i	$0.266213\pi$
$390$	18.1377	−	23.2152i	0.918437	−	1.17555i
$391$	16.1089	+	17.8908i	0.814663	+	0.904775i
$392$	1.09080	+	0.485657i	0.0550939	+	0.0245294i
$393$	−12.6599	+	25.9567i	−0.638609	+	1.30934i
$394$	−3.94014	+	9.75220i	−0.198502	+	0.491309i
$395$	26.5888	−	22.3107i	1.33783	−	1.12257i
$396$	−0.147996	+	0.695769i	−0.00743705	+	0.0349637i
$397$	−28.5137	+	10.3781i	−1.43106	+	0.520863i	−0.937235	−	0.348699i	$-0.886624\pi$
$397$	−28.5137	+	10.3781i	−1.43106	+	0.520863i	−0.493824	+	0.869562i	$0.664401\pi$
$398$	2.58692	+	7.96172i	0.129671	+	0.399085i
$399$	13.3926	−	15.9470i	0.670470	−	0.798348i
$400$	−2.40488	+	1.74725i	−0.120244	+	0.0873623i
$401$	−0.698077	−	19.9903i	−0.0348603	−	0.998269i	−0.883252	−	0.468899i	$-0.844651\pi$
$401$	−0.698077	−	19.9903i	−0.0348603	−	0.998269i	0.848391	−	0.529369i	$-0.177571\pi$
$402$	1.50114	+	0.798169i	0.0748699	+	0.0398090i
$403$	−1.39686	+	5.60250i	−0.0695826	+	0.279081i
$404$	3.25015	+	13.0357i	0.161701	+	0.648548i
$405$	−20.7189	+	11.0164i	−1.02953	+	0.547410i
$406$	6.58873	+	11.4120i	0.326993	+	0.566369i
$407$	7.81174	+	9.31240i	0.387213	+	0.461599i
$408$	4.37406	+	1.59203i	0.216548	+	0.0788171i
$409$	−0.697807	+	19.9826i	−0.0345043	+	0.988074i	0.851488	+	0.524374i	$0.175701\pi$
$409$	−0.697807	+	19.9826i	−0.0345043	+	0.988074i	−0.885992	+	0.463700i	$0.846522\pi$
$410$	−29.3856	+	13.0833i	−1.45125	+	0.646139i
$411$	−18.0367	−	8.03047i	−0.889687	−	0.396114i
$412$	0.929309	+	0.130606i	0.0457838	+	0.00643449i
$413$	24.0729	−	15.0424i	1.18455	−	0.740189i
$414$	0.447882	−	1.79636i	0.0220122	−	0.0882861i
$415$	8.87945	−	8.57479i	0.435875	−	0.420920i
$416$	3.84883	+	4.92628i	0.188704	+	0.241531i
$417$	13.8963			0.680506
$418$	−4.47522	+	13.7467i	−0.218890	+	0.672374i
$419$	22.4564			1.09707			0.548533	−	0.836129i	$-0.315186\pi$
$419$	22.4564			1.09707			0.548533	+	0.836129i	$0.315186\pi$
$420$	−8.30509	−	10.6300i	−0.405247	−	0.518692i
$421$	8.26017	−	7.97676i	0.402576	−	0.388763i	−0.465620	−	0.884985i	$-0.654169\pi$
$421$	8.26017	−	7.97676i	0.402576	−	0.388763i	0.868196	+	0.496222i	$0.165280\pi$
$422$	1.65810	−	6.65029i	0.0807153	−	0.323731i
$423$	1.23286	−	0.770379i	0.0599439	−	0.0374571i
$424$	9.44981	+	1.32808i	0.458923	+	0.0644974i
$425$	7.57374	+	3.37205i	0.367380	+	0.163568i
$426$	3.52969	−	1.57152i	0.171014	−	0.0761404i
$427$	0.716401	−	20.5150i	0.0346691	−	0.992792i
$428$	−18.1725	−	6.61423i	−0.878399	−	0.319711i
$429$	−33.5757	−	8.37652i	−1.62105	−	0.404422i
$430$	7.11474	+	12.3231i	0.343103	+	0.594272i
$431$	22.3895	−	11.9047i	1.07846	−	0.573429i	0.167482	−	0.985875i	$-0.446437\pi$
$431$	22.3895	−	11.9047i	1.07846	−	0.573429i	0.910982	+	0.412446i	$0.135325\pi$
$432$	−1.29789	−	5.20556i	−0.0624449	−	0.250453i
$433$	4.51426	−	18.1057i	0.216941	−	0.870105i	−0.758826	−	0.651294i	$-0.774227\pi$
$433$	4.51426	−	18.1057i	0.216941	−	0.870105i	0.975767	−	0.218811i	$-0.0702178\pi$
$434$	2.33440	+	1.24122i	0.112055	+	0.0595806i
$435$	−0.757104	−	21.6806i	−0.0363003	−	1.03951i
$436$	5.33358	−	3.87507i	0.255432	−	0.185582i
$437$	12.8838	−	35.3514i	0.616316	−	1.69109i
$438$	−0.733880	−	2.25865i	−0.0350662	−	0.107923i
$439$	−8.98858	+	3.27158i	−0.429002	+	0.156144i	−0.547491	−	0.836811i	$-0.684417\pi$
$439$	−8.98858	+	3.27158i	−0.429002	+	0.156144i	0.118490	+	0.992955i	$0.462195\pi$
$440$	8.10943	+	4.68355i	0.386602	+	0.223279i
$441$	−0.196177	+	0.164612i	−0.00934177	+	0.00783868i
$442$	6.53141	−	16.1658i	0.310668	−	0.768929i
$443$	−3.46251	+	7.09920i	−0.164509	+	0.337293i	−0.965085	−	0.261938i	$-0.915638\pi$
$443$	−3.46251	+	7.09920i	−0.164509	+	0.337293i	0.800576	+	0.599232i	$0.204527\pi$
$444$	−5.58782	−	2.48786i	−0.265186	−	0.118068i
$445$	−22.6562	−	25.1622i	−1.07400	−	1.19280i
$446$	−9.25335	+	11.8438i	−0.438159	+	0.560818i
$447$	−9.69477	+	2.77993i	−0.458547	+	0.131486i
$448$	2.61504	−	1.16429i	0.123549	−	0.0550077i
$449$	−1.75183	+	1.94561i	−0.0826741	+	0.0918189i	−0.783062	−	0.621943i	$-0.786344\pi$
$449$	−1.75183	+	1.94561i	−0.0826741	+	0.0918189i	0.700388	+	0.713762i	$0.253010\pi$
$450$	−0.110709	−	0.627863i	−0.00521888	−	0.0295977i
$451$	28.0749	+	25.2861i	1.32199	+	1.19068i
$452$	11.2994	−	9.48129i	0.531477	−	0.445962i
$453$	24.2185	−	3.40368i	1.13788	−	0.159919i
$454$	−20.0356	−	5.74510i	−0.940315	−	0.269631i
$455$	−40.8783	+	29.6998i	−1.91640	+	1.39235i
$456$	−1.00943	−	7.20458i	−0.0472707	−	0.337386i
$457$	0.761660	−	2.34415i	0.0356289	−	0.109655i	−0.931660	−	0.363330i	$-0.881640\pi$
$457$	0.761660	−	2.34415i	0.0356289	−	0.109655i	0.967289	+	0.253676i	$0.0816396\pi$
$458$	−4.41262	+	6.54198i	−0.206188	+	0.305687i
$459$	−10.7632	+	10.3939i	−0.502385	+	0.485147i
$460$	−20.6695	−	12.9158i	−0.963722	−	0.602201i
$461$	−7.14302	−	5.99371i	−0.332684	−	0.279155i	0.461109	−	0.887344i	$-0.347452\pi$
$461$	−7.14302	−	5.99371i	−0.332684	−	0.279155i	−0.793792	+	0.608189i	$0.791896\pi$
$462$	−7.44091	+	13.9894i	−0.346182	+	0.650847i
$463$	6.71560	+	11.6318i	0.312100	+	0.540574i	0.978817	−	0.204738i	$-0.0656341\pi$
$463$	6.71560	+	11.6318i	0.312100	+	0.540574i	−0.666716	+	0.745311i	$0.732301\pi$
$464$	4.50285	+	0.957110i	0.209039	+	0.0444327i
$465$	−2.43392	−	3.60844i	−0.112870	−	0.167337i
$466$	17.3890	−	4.98620i	0.805528	−	0.230981i
$467$	21.5399	+	23.9225i	0.996748	+	1.10700i	0.994259	+	0.107004i	$0.0341258\pi$
$467$	21.5399	+	23.9225i	0.996748	+	1.10700i	0.00248961	+	0.999997i	$0.499208\pi$
$468$	−1.31150	+	0.278768i	−0.0606242	+	0.0128861i
$469$	−2.09756	−	2.02559i	−0.0968564	−	0.0935332i
$470$	−4.63011	−	18.5704i	−0.213571	−	0.856587i
$471$	6.99896	+	4.37344i	0.322495	+	0.201517i
$472$	1.72198	−	9.76586i	0.0792607	−	0.449510i
$473$	9.82632	−	13.5207i	0.451815	−	0.621680i
$474$	20.5163			0.942345
$475$	−0.898374	−	12.9260i	−0.0412202	−	0.593088i
$476$	−6.45880	−	4.69259i	−0.296038	−	0.215085i
$477$	−1.14448	+	1.69677i	−0.0524023	+	0.0776896i
$478$	11.1914	+	5.95055i	0.511881	+	0.272172i
$479$	7.64328	+	18.9178i	0.349230	+	0.864376i	0.994910	+	0.100767i	$0.0321297\pi$
$479$	7.64328	+	18.9178i	0.349230	+	0.864376i	−0.645680	+	0.763608i	$0.723426\pi$
$480$	−4.70104	−	0.328729i	−0.214572	−	0.0150043i
$481$	−10.0436	+	20.5923i	−0.457946	+	0.938929i
$482$	−3.82744	+	4.25080i	−0.174335	+	0.193619i
$483$	20.6197	−	35.7144i	0.938230	−	1.62506i
$484$	1.15298	−	10.9394i	0.0524080	−	0.497246i
$485$	0.293605	+	0.106864i	0.0133319	+	0.00485243i
$486$	2.17591	+	0.462503i	0.0987012	+	0.0209796i
$487$	2.52294	−	24.0042i	0.114325	−	1.08773i	−0.775473	−	0.631380i	$-0.782489\pi$
$487$	2.52294	−	24.0042i	0.114325	−	1.08773i	0.889799	−	0.456353i	$-0.150845\pi$
$488$	−5.15848	−	4.98149i	−0.233514	−	0.225501i
$489$	−17.8729	+	11.1682i	−0.808239	+	0.505044i
$490$	1.26297	+	3.12595i	0.0570550	+	0.141216i
$491$	−3.90290	−	8.00213i	−0.176135	−	0.361131i	0.792402	−	0.609999i	$-0.208830\pi$
$491$	−3.90290	−	8.00213i	−0.176135	−	0.361131i	−0.968537	+	0.248868i	$0.919941\pi$
$492$	−18.2768	−	5.24078i	−0.823981	−	0.236273i
$493$	−3.96744	−	12.2105i	−0.178685	−	0.549934i
$494$	−27.1017	+	2.83690i	−1.21936	+	0.127638i
$495$	−1.66529	+	1.12290i	−0.0748494	+	0.0504708i
$496$	0.867915	−	0.315895i	0.0389705	−	0.0141841i
$497$	−6.56228	+	0.922268i	−0.294358	+	0.0413694i
$498$	7.27858	−	0.508968i	0.326161	−	0.0228074i
$499$	−2.19898	−	0.153768i	−0.0984398	−	0.00688358i	0.0204516	−	0.999791i	$-0.493490\pi$
$499$	−2.19898	−	0.153768i	−0.0984398	−	0.00688358i	−0.118891	+	0.992907i	$0.537934\pi$
$500$	5.66883	+	0.796703i	0.253518	+	0.0356296i
$501$	−16.2312	+	3.45005i	−0.725158	+	0.154137i
$502$	−1.88904	−	17.9731i	−0.0843122	−	0.802177i
$503$	12.7405	+	18.8885i	0.568070	+	0.842199i	0.998163	−	0.0605859i	$-0.0192969\pi$
$503$	12.7405	+	18.8885i	0.568070	+	0.842199i	−0.430093	+	0.902785i	$0.641519\pi$
$504$	−0.0214262	+	0.613567i	−0.000954401	+	0.0273305i
$505$	−18.9670	+	32.8518i	−0.844020	+	1.46189i
$506$	−3.98849	+	28.3499i	−0.177310	+	1.26030i
$507$	−7.55891	−	42.8687i	−0.335703	−	1.90387i
$508$	5.44836	−	13.4852i	0.241732	−	0.598308i
$509$	−17.4279	+	1.21868i	−0.772480	+	0.0540170i	−0.450556	−	0.892748i	$-0.648774\pi$
$509$	−17.4279	+	1.21868i	−0.772480	+	0.0540170i	−0.321924	+	0.946765i	$0.604330\pi$
$510$	5.76156	+	11.8130i	0.255126	+	0.523086i
$511$	0.142153	+	4.07074i	0.00628850	+	0.180079i
$512$	0.309017	−	0.951057i	0.0136568	−	0.0420312i
$513$	22.2375	+	7.23583i	0.981812	+	0.319470i
$514$	12.0167	+	8.73067i	0.530035	+	0.385093i
$515$	1.63136	+	2.08804i	0.0718862	+	0.0920101i
$516$	−1.46054	+	8.28313i	−0.0642966	+	0.364644i
$517$	−17.7172	+	13.8380i	−0.779200	+	0.608596i
$518$	8.03640	+	6.74334i	0.353099	+	0.296285i
$519$	−0.322356	+	0.171400i	−0.0141498	+	0.00752360i
$520$	−1.84510	+	17.5550i	−0.0809132	+	0.769838i
$521$	0.500413	+	4.76111i	0.0219235	+	0.208588i	1.00000		0.000341953i	$0.000108847\pi$
$521$	0.500413	+	4.76111i	0.0219235	+	0.208588i	−0.978076	+	0.208246i	$0.933224\pi$
$522$	−0.607859	+	0.778024i	−0.0266053	+	0.0340532i
$523$	2.41630	−	3.09272i	0.105657	−	0.135235i	−0.732276	−	0.681008i	$-0.761542\pi$
$523$	2.41630	−	3.09272i	0.105657	−	0.135235i	0.837933	+	0.545773i	$0.183764\pi$
$524$	−1.80872	−	17.2088i	−0.0790141	−	0.751769i
$525$	1.48447	−	14.1238i	0.0647877	−	0.616414i
$526$	−16.1419	+	8.58279i	−0.703820	+	0.374228i
$527$	−1.97329	−	1.65579i	−0.0859578	−	0.0721272i
$528$	1.89247	+	5.20186i	0.0823592	+	0.226382i
$529$	8.94482	−	50.7286i	0.388905	−	2.20559i
$530$	16.5887	+	21.2325i	0.720566	+	0.922283i
$531$	1.72066	+	1.25013i	0.0746702	+	0.0542511i
$532$	−1.74176	+	12.3553i	−0.0755148	+	0.535669i
$533$	−22.0076	+	67.7326i	−0.953257	+	2.93382i
$534$	−0.698471	−	20.0016i	−0.0302258	−	0.865553i
$535$	−23.9370	−	49.0781i	−1.03489	−	2.12183i
$536$	−1.01618	+	0.0710586i	−0.0438925	+	0.00306926i
$537$	3.96658	−	9.81764i	0.171171	−	0.423662i
$538$	4.23942	+	24.0430i	0.182774	+	1.03657i
$539$	2.75137	−	2.84830i	0.118510	−	0.122685i
$540$	7.57414	−	13.1188i	0.325939	−	0.564543i
$541$	−0.308507	+	8.83448i	−0.0132637	+	0.379824i	0.974549	+	0.224176i	$0.0719689\pi$
$541$	−0.308507	+	8.83448i	−0.0132637	+	0.379824i	−0.987813	+	0.155648i	$0.950253\pi$
$542$	8.31837	+	12.3325i	0.357305	+	0.529726i
$543$	2.82046	+	26.8349i	0.121038	+	1.15160i
$544$	−2.72803	+	0.579861i	−0.116963	+	0.0248613i
$545$	18.4338	+	2.59069i	0.789615	+	0.110973i
$546$	−29.7941	−	2.08340i	−1.27507	−	0.0891615i
$547$	2.36867	−	0.165633i	0.101277	−	0.00708198i	−0.0190281	−	0.999819i	$-0.506057\pi$
$547$	2.36867	−	0.165633i	0.101277	−	0.00708198i	0.120305	+	0.992737i	$0.461613\pi$
$548$	11.7146	−	1.64638i	0.500422	−	0.0703298i
$549$	1.44528	−	0.526039i	0.0616830	−	0.0224508i
$550$	2.71613	+	9.47744i	0.115816	+	0.404120i
$551$	−13.9451	+	14.4283i	−0.594081	+	0.614667i
$552$	−4.45191	−	13.7016i	−0.189486	−	0.583178i
$553$	−33.8249	−	9.69913i	−1.43838	−	0.412449i
$554$	−3.99758	−	8.19626i	−0.169841	−	0.348226i
$555$	−6.46975	−	16.0132i	−0.274625	−	0.679722i
$556$	−7.06102	+	4.41221i	−0.299454	+	0.187119i
$557$	22.6188	+	21.8427i	0.958390	+	0.925506i	0.997278	−	0.0737372i	$-0.0234926\pi$
$557$	22.6188	+	21.8427i	0.958390	+	0.925506i	−0.0388878	+	0.999244i	$0.512381\pi$
$558$	−0.0207064	+	0.197008i	−0.000876571	+	0.00834001i
$559$	30.8163	+	6.55021i	1.30339	+	0.277044i
$560$	7.59512	+	2.76440i	0.320952	+	0.116817i
$561$	9.92515	−	11.8249i	0.419040	−	0.499246i
$562$	8.37320	−	14.5028i	0.353202	−	0.611764i
$563$	−10.8520	+	12.0524i	−0.457357	+	0.507946i	−0.927078	−	0.374869i	$-0.877688\pi$
$563$	−10.8520	+	12.0524i	−0.457357	+	0.507946i	0.469721	+	0.882815i	$0.344354\pi$
$564$	4.95921	−	10.1679i	0.208820	−	0.428145i
$565$	41.5471	+	2.90525i	1.74790	+	0.122225i
$566$	7.66694	+	18.9764i	0.322266	+	0.797636i
$567$	21.0046	+	11.1684i	0.882111	+	0.469027i
$568$	−1.29454	+	1.91923i	−0.0543176	+	0.0805291i
$569$	−6.62574	−	4.81388i	−0.277766	−	0.201808i	0.440177	−	0.897911i	$-0.354916\pi$
$569$	−6.62574	−	4.81388i	−0.277766	−	0.201808i	−0.717942	+	0.696103i	$0.754916\pi$
$570$	12.0810	−	16.6132i	0.506016	−	0.695851i
$571$	16.7807			0.702250			0.351125	−	0.936329i	$-0.385799\pi$
$571$	16.7807			0.702250			0.351125	+	0.936329i	$0.385799\pi$
$572$	19.7201	−	6.40431i	0.824540	−	0.267777i
$573$	4.06110	−	23.0316i	0.169655	−	0.962160i
$574$	27.6550	+	17.2808i	1.15430	+	0.721285i
$575$	−6.20756	−	24.8972i	−0.258873	−	1.03828i
$576$	0.154281	+	0.148987i	0.00642837	+	0.00620780i
$577$	−40.6911	+	8.64917i	−1.69399	+	0.360070i	−0.950991	−	0.309219i	$-0.899933\pi$
$577$	−40.6911	+	8.64917i	−1.69399	+	0.360070i	−0.743003	+	0.669288i	$0.766599\pi$
$578$	−6.17045	−	6.85298i	−0.256657	−	0.285047i
$579$	37.2313	−	10.6759i	1.54728	−	0.443676i
$580$	7.26849	+	10.7760i	0.301808	+	0.447448i
$581$	−12.2407	−	2.60184i	−0.507829	−	0.107942i
$582$	0.0923426	+	0.159942i	0.00382772	+	0.00662981i
$583$	14.8626	−	27.9427i	0.615545	−	1.15727i
$584$	1.09004	+	0.914654i	0.0451063	+	0.0378487i
$585$	−3.21059	−	2.00620i	−0.132742	−	0.0829461i
$586$	−2.90959	+	2.80976i	−0.120194	+	0.116070i
$587$	20.7887	−	30.8206i	0.858043	−	1.27210i	−0.102714	−	0.994711i	$-0.532753\pi$
$587$	20.7887	−	30.8206i	0.858043	−	1.27210i	0.960757	−	0.277390i	$-0.0894696\pi$
$588$	−0.615818	+	1.89529i	−0.0253959	+	0.0781606i
$589$	−0.838710	+	3.93762i	−0.0345584	+	0.162247i
$590$	22.6525	−	16.4580i	0.932589	−	0.677566i
$591$	−16.8745	−	4.83869i	−0.694126	−	0.199037i
$592$	3.62920	−	0.510051i	0.149159	−	0.0209630i
$593$	−12.1029	+	10.1556i	−0.497008	+	0.417039i	−0.856530	−	0.516098i	$-0.827384\pi$
$593$	−12.1029	+	10.1556i	−0.497008	+	0.417039i	0.359522	+	0.933137i	$0.382940\pi$
$594$	−17.6957	−	1.86248i	−0.726063	−	0.0764185i
$595$	−3.91439	−	22.1996i	−0.160474	−	0.910095i
$596$	4.04346	−	4.49072i	0.165627	−	0.183947i
$597$	−12.7639	+	5.68287i	−0.522393	+	0.232584i
$598$	−51.8727	+	14.8743i	−2.12123	+	0.608254i
$599$	7.31801	−	9.36662i	0.299006	−	0.382710i	−0.614921	−	0.788589i	$-0.710812\pi$
$599$	7.31801	−	9.36662i	0.299006	−	0.382710i	0.913927	+	0.405879i	$0.133034\pi$
$600$	−3.31971	−	3.68691i	−0.135526	−	0.150517i
$601$	−13.0204	−	5.79707i	−0.531114	−	0.236467i	0.123616	−	0.992330i	$-0.460551\pi$
$601$	−13.0204	−	5.79707i	−0.531114	−	0.236467i	−0.654730	+	0.755863i	$0.727218\pi$
$602$	6.32383	−	12.9658i	0.257740	−	0.528446i
$603$	0.0818437	−	0.202570i	0.00333293	−	0.00824930i
$604$	−11.2252	+	9.41906i	−0.456747	+	0.383256i
$605$	23.7986	−	19.9577i	0.967551	−	0.811395i
$606$	−21.0702	+	7.66892i	−0.855917	+	0.311528i
$607$	10.5058	+	32.3337i	0.426419	+	1.31238i	0.901629	+	0.432511i	$0.142372\pi$
$607$	10.5058	+	32.3337i	0.426419	+	1.31238i	−0.475210	+	0.879873i	$0.657628\pi$
$608$	2.80043	+	3.34030i	0.113572	+	0.135467i
$609$	−17.7927	+	12.9272i	−0.720998	+	0.523836i
$610$	−0.706654	−	20.2359i	−0.0286116	−	0.819329i
$611$	−37.4143	−	19.8936i	−1.51362	−	0.804807i
$612$	0.144710	−	0.580400i	0.00584955	−	0.0234613i
$613$	−0.706162	−	2.83226i	−0.0285216	−	0.114394i	0.954348	−	0.298698i	$-0.0965524\pi$
$613$	−0.706162	−	2.83226i	−0.0285216	−	0.114394i	−0.982869	+	0.184304i	$0.940997\pi$
$614$	13.6235	−	7.24372i	0.549798	−	0.292333i
$615$	−26.8428	−	46.4931i	−1.08241	−	1.87478i
$616$	−0.660892	−	9.47088i	−0.0266281	−	0.381593i
$617$	18.1205	+	6.59531i	0.729502	+	0.265517i	0.679954	−	0.733255i	$-0.262000\pi$
$617$	18.1205	+	6.59531i	0.729502	+	0.265517i	0.0495482	+	0.998772i	$0.484222\pi$
$618$	−0.0546613	+	1.56530i	−0.00219880	+	0.0629654i
$619$	−13.8288	+	6.15696i	−0.555825	+	0.247469i	−0.665372	−	0.746512i	$-0.731727\pi$
$619$	−13.8288	+	6.15696i	−0.555825	+	0.247469i	0.109546	+	0.993982i	$0.465060\pi$
$620$	2.38244	+	1.06073i	0.0956810	+	0.0425999i
$621$	45.8593	+	6.44510i	1.84027	+	0.258633i
$622$	13.4058	−	8.37687i	0.537523	−	0.335882i
$623$	−8.30424	+	33.3065i	−0.332702	+	1.33440i
$624$	−7.50541	+	7.24789i	−0.300457	+	0.290148i
$625$	19.1019	+	24.4493i	0.764077	+	0.977974i
$626$	5.44334			0.217560
$627$	−23.5982	−	5.02996i	−0.942420	−	0.200877i
$628$	−4.94493			−0.197324
$629$	−6.29283	−	8.05445i	−0.250911	−	0.321152i
$630$	−1.24698	+	1.20420i	−0.0496810	+	0.0479764i
$631$	6.33038	−	25.3898i	0.252008	−	1.01075i	−0.702289	−	0.711892i	$-0.747839\pi$
$631$	6.33038	−	25.3898i	0.252008	−	1.01075i	0.954297	−	0.298858i	$-0.0966058\pi$
$632$	−10.4248	+	6.51412i	−0.414675	+	0.259118i
$633$	11.3277	+	1.59201i	0.450237	+	0.0632767i
$634$	−13.6778	−	6.08973i	−0.543213	−	0.241854i
$635$	37.5163	−	16.7034i	1.48879	−	0.662852i
$636$	−0.555831	+	15.9169i	−0.0220401	+	0.631147i
$637$	7.01438	+	2.55302i	0.277920	+	0.101154i
$638$	8.09262	−	12.9467i	0.320390	−	0.512566i
$639$	−0.248257	−	0.429993i	−0.00982088	−	0.0170103i
$640$	2.49307	−	1.32559i	0.0985473	−	0.0523985i
$641$	11.5922	+	46.4936i	0.457862	+	1.83639i	0.542611	+	0.839984i	$0.317436\pi$
$641$	11.5922	+	46.4936i	0.457862	+	1.83639i	−0.0847490	+	0.996402i	$0.527009\pi$
$642$	7.80830	−	31.3174i	0.308169	−	1.23600i
$643$	−13.5415	−	7.20015i	−0.534025	−	0.283946i	0.180477	−	0.983579i	$-0.442236\pi$
$643$	−13.5415	−	7.20015i	−0.534025	−	0.283946i	−0.714503	+	0.699633i	$0.753347\pi$
$644$	0.862340	+	24.6942i	0.0339810	+	0.973087i
$645$	−19.2132	+	13.9592i	−0.756520	+	0.549644i
$646$	4.16274	−	11.4220i	0.163781	−	0.449391i
$647$	−1.56106	−	4.80445i	−0.0613717	−	0.188883i	0.915670	−	0.401931i	$-0.131661\pi$
$647$	−1.56106	−	4.80445i	−0.0613717	−	0.188883i	−0.977042	+	0.213048i	$0.931661\pi$
$648$	7.80938	−	2.84238i	0.306782	−	0.111659i
$649$	−28.4806	−	16.4488i	−1.11796	−	0.645671i
$650$	−14.2356	+	11.9451i	−0.558366	+	0.468525i
$651$	−1.65299	+	4.09128i	−0.0647856	+	0.160350i
$652$	5.53557	−	11.3496i	0.216790	−	0.444484i
$653$	43.4782	+	19.3577i	1.70143	+	0.757526i	0.998949	+	0.0458247i	$0.0145916\pi$
$653$	43.4782	+	19.3577i	1.70143	+	0.757526i	0.702482	+	0.711701i	$0.252075\pi$
$654$	7.36250	+	8.17689i	0.287897	+	0.319742i
$655$	30.0800	−	38.5006i	1.17532	−	1.50434i
$656$	10.9508	−	3.14009i	0.427557	−	0.122600i
$657$	−0.278803	+	0.124131i	−0.0108771	+	0.00484282i
$658$	−12.9830	+	14.4191i	−0.506132	+	0.562116i
$659$	4.81988	+	27.3349i	0.187756	+	1.06482i	0.922363	+	0.386323i	$0.126255\pi$
$659$	4.81988	+	27.3349i	0.187756	+	1.06482i	−0.734608	+	0.678492i	$0.762634\pi$
$660$	−6.35922	+	14.2775i	−0.247532	+	0.555750i
$661$	5.42959	−	4.55597i	0.211187	−	0.177207i	−0.531058	−	0.847335i	$-0.678206\pi$
$661$	5.42959	−	4.55597i	0.211187	−	0.177207i	0.742245	+	0.670129i	$0.233761\pi$
$662$	17.8018	−	2.50188i	0.691887	−	0.0972383i
$663$	27.9722	+	8.02090i	1.08635	+	0.311506i
$664$	−3.53680	+	2.56963i	−0.137254	+	0.0997211i
$665$	−27.7716	+	21.6786i	−1.07694	+	0.840661i
$666$	−0.242895	+	0.747555i	−0.00941200	+	0.0289672i
$667$	−22.2206	+	32.9433i	−0.860384	+	1.27557i
$668$	7.15200	−	6.90661i	0.276719	−	0.267225i
$669$	−21.2731	−	13.2929i	−0.822466	−	0.513934i
$670$	−2.20336	−	1.84884i	−0.0851233	−	0.0714269i
$671$	−21.3784	+	10.4231i	−0.825304	+	0.402380i
$672$	2.38876	+	4.13745i	0.0921484	+	0.159606i
$673$	−10.4100	−	2.21271i	−0.401275	−	0.0852936i	0.00285338	−	0.999996i	$-0.499092\pi$
$673$	−10.4100	−	2.21271i	−0.401275	−	0.0852936i	−0.404128	+	0.914702i	$0.632425\pi$
$674$	5.23207	+	7.75687i	0.201532	+	0.298783i
$675$	15.3299	−	4.39579i	0.590050	−	0.169194i
$676$	17.4521	+	19.3825i	0.671233	+	0.745480i
$677$	5.76398	−	1.22517i	0.221528	−	0.0470871i	−0.0958106	−	0.995400i	$-0.530544\pi$
$677$	5.76398	−	1.22517i	0.221528	−	0.0470871i	0.317338	+	0.948312i	$0.397211\pi$
$678$	17.7087	+	17.1011i	0.680100	+	0.656765i
$679$	−0.0766307	−	0.307349i	−0.00294081	−	0.0117950i
$680$	−6.67829	−	4.17306i	−0.256101	−	0.160030i
$681$	6.04065	−	34.2582i	0.231478	−	1.31278i
$682$	0.000442924	−	3.06329i	1.69605e−5	−	0.117299i
$683$	−12.9719			−0.496357			−0.248178	−	0.968714i	$-0.579832\pi$
$683$	−12.9719			−0.496357			−0.248178	+	0.968714i	$0.579832\pi$
$684$	−0.907204	+	0.225783i	−0.0346878	+	0.00863303i
$685$	27.0229	+	19.6333i	1.03249	+	0.750149i
$686$	−9.29362	+	13.7784i	−0.354832	+	0.526060i
$687$	−11.6285	−	6.18298i	−0.443654	−	0.235895i
$688$	−1.88784	−	4.67256i	−0.0719732	−	0.178140i
$689$	59.5110	+	4.16142i	2.26719	+	0.158537i
$690$	17.8322	−	36.5615i	0.678862	−	1.39187i
$691$	8.48023	−	9.41825i	0.322603	−	0.358287i	−0.559928	−	0.828541i	$-0.689171\pi$
$691$	8.48023	−	9.41825i	0.322603	−	0.358287i	0.882531	+	0.470254i	$0.155838\pi$
$692$	0.109375	−	0.189443i	0.00415780	−	0.00720152i
$693$	1.88783	+	0.763052i	0.0717129	+	0.0289859i
$694$	1.36818	+	0.497978i	0.0519355	+	0.0189030i
$695$	−22.9959	−	4.88793i	−0.872285	−	0.185410i
$696$	−0.803102	+	7.64101i	−0.0304415	+	0.289632i
$697$	−22.8551	−	22.0709i	−0.865700	−	0.835997i
$698$	2.15425	−	1.34613i	0.0815396	−	0.0509516i
$699$	11.3100	+	27.9931i	0.427782	+	1.05880i
$700$	3.73015	+	7.64794i	0.140986	+	0.289065i
$701$	26.4010	+	7.57035i	0.997150	+	0.285928i	0.734238	−	0.678892i	$-0.237539\pi$
$701$	26.4010	+	7.57035i	0.997150	+	0.285928i	0.262912	+	0.964820i	$0.415317\pi$
$702$	−10.3641	−	31.8975i	−0.391169	−	1.20389i
$703$	−6.50372	+	14.5910i	−0.245292	+	0.550308i
$704$	−2.61324	−	2.04230i	−0.0984902	−	0.0769719i
$705$	30.0162	−	10.9250i	1.13048	−	0.411459i
$706$	−11.8565	+	1.66632i	−0.446225	+	0.0627128i
$707$	38.3635	−	2.68264i	1.44281	−	0.100891i
$708$	16.5102	+	1.15451i	0.620492	+	0.0433891i
$709$	19.7239	+	2.77201i	0.740747	+	0.104105i	0.499446	−	0.866345i	$-0.333537\pi$
$709$	19.7239	+	2.77201i	0.740747	+	0.104105i	0.241301	+	0.970450i	$0.422426\pi$
$710$	−6.39377	+	1.35904i	−0.239954	+	0.0510038i
$711$	−0.275587	−	2.62203i	−0.0103353	−	0.0983339i
$712$	6.70559	+	9.94145i	0.251303	+	0.372572i
$713$	−0.278241	+	7.96778i	−0.0104202	+	0.298396i
$714$	6.66220	−	11.5393i	0.249326	−	0.431846i
$715$	52.6153	+	25.6716i	1.96770	+	0.960064i
$716$	1.10169	+	6.24797i	0.0411719	+	0.233498i
$717$	−7.92459	+	19.6141i	−0.295949	+	0.732500i
$718$	20.9859	−	1.46748i	0.783188	−	0.0547659i
$719$	−7.04806	−	14.4507i	−0.262848	−	0.538919i	0.726027	−	0.687666i	$-0.241365\pi$
$719$	−7.04806	−	14.4507i	−0.262848	−	0.538919i	−0.988875	+	0.148747i	$0.952476\pi$
$720$	0.0211347	+	0.605220i	0.000787645	+	0.0225552i
$721$	0.830116	−	2.55483i	0.0309151	−	0.0951470i
$722$	−18.8173	+	2.62835i	−0.700308	+	0.0978169i
$723$	−7.72340	−	5.61138i	−0.287236	−	0.208689i
$724$	−9.95346	−	12.7398i	−0.369917	−	0.473473i
$725$	−2.37623	+	13.4763i	−0.0882509	+	0.500496i
$726$	18.3589	+	0.00530906i	0.681362	+	0.000197038i
$727$	−8.42514	−	7.06953i	−0.312471	−	0.262194i	0.473041	−	0.881040i	$-0.343156\pi$
$727$	−8.42514	−	7.06953i	−0.312471	−	0.262194i	−0.785512	+	0.618846i	$0.787601\pi$
$728$	15.8005	−	8.40127i	0.585605	−	0.311372i
$729$	−2.99416	+	28.4875i	−0.110895	+	1.05509i
$730$	0.419975	+	3.99580i	0.0155440	+	0.147891i
$731$	−8.65320	+	11.0756i	−0.320050	+	0.409645i
$732$	7.36857	−	9.43134i	0.272350	−	0.348593i
$733$	−5.52843	−	52.5995i	−0.204197	−	1.94281i	−0.315287	−	0.948996i	$-0.602101\pi$
$733$	−5.52843	−	52.5995i	−0.204197	−	1.94281i	0.111090	−	0.993810i	$-0.464566\pi$
$734$	0.976732	−	9.29298i	0.0360518	−	0.343010i
$735$	−4.96826	+	2.64167i	−0.183257	+	0.0974396i
$736$	6.61248	+	5.54853i	0.243739	+	0.204522i
$737$	−0.931720	+	3.24752i	−0.0343203	+	0.119624i
$738$	−0.424280	+	2.40621i	−0.0156180	+	0.0885739i
$739$	−22.7335	−	29.0975i	−0.836264	−	1.07037i	−0.996525	−	0.0832939i	$-0.973456\pi$
$739$	−22.7335	−	29.0975i	−0.836264	−	1.07037i	0.160261	−	0.987075i	$-0.448766\pi$
$740$	8.37175	+	6.08243i	0.307752	+	0.223595i
$741$	−9.43690	−	44.4898i	−0.346673	−	1.63437i
$742$	8.44115	−	25.9792i	0.309884	−	0.953725i
$743$	−0.0233715	−	0.669271i	−0.000857416	−	0.0245532i	0.998887	−	0.0471735i	$-0.0150214\pi$
$743$	−0.0233715	−	0.669271i	−0.000857416	−	0.0245532i	−0.999744	+	0.0226203i	$0.992799\pi$
$744$	0.675751	+	1.38550i	0.0247742	+	0.0507947i
$745$	17.0209	−	1.19022i	0.623598	−	0.0436062i
$746$	4.16304	−	10.3039i	0.152420	−	0.377252i
$747$	−0.162817	−	0.923383i	−0.00595717	−	0.0337848i
$748$	−1.28867	+	9.15979i	−0.0471186	+	0.334915i
$749$	−27.6788	+	47.9410i	−1.01136	+	1.75173i
$750$	−0.333437	+	9.54838i	−0.0121754	+	0.348658i
$751$	2.28744	+	3.39127i	0.0834699	+	0.123749i	0.868460	−	0.495759i	$-0.165110\pi$
$751$	2.28744	+	3.39127i	0.0834699	+	0.123749i	−0.784990	+	0.619508i	$0.787332\pi$
$752$	0.708519	+	6.74110i	0.0258370	+	0.245823i
$753$	29.5030	−	6.27105i	1.07515	−	0.228530i
$754$	28.4985	+	4.00521i	1.03785	+	0.145861i
$755$	−41.2744	−	2.88619i	−1.50213	−	0.105039i
$756$	−15.3198	+	1.07127i	−0.557176	+	0.0389615i
$757$	−21.8844	+	3.07565i	−0.795402	+	0.111786i	−0.525157	−	0.851005i	$-0.675994\pi$
$757$	−21.8844	+	3.07565i	−0.795402	+	0.111786i	−0.270245	+	0.962792i	$0.587105\pi$
$758$	−10.6227	+	3.86635i	−0.385834	+	0.140432i
$759$	−47.7522	−	1.67446i	−1.73330	−	0.0607790i
$760$	−0.863742	+	12.2773i	−0.0313312	+	0.445346i
$761$	−11.4780	−	35.3257i	−0.416077	−	1.28055i	−0.911284	−	0.411779i	$-0.864908\pi$
$761$	−11.4780	−	35.3257i	−0.416077	−	1.28055i	0.495207	−	0.868775i	$-0.335092\pi$
$762$	23.3338	+	6.69086i	0.845295	+	0.242384i
$763$	−8.27279	−	16.9617i	−0.299495	−	0.614056i
$764$	5.24922	+	12.9923i	0.189910	+	0.470044i
$765$	1.43233	−	0.895020i	0.0517860	−	0.0323595i
$766$	5.71312	+	5.51709i	0.206423	+	0.199341i
$767$	6.48008	−	61.6538i	0.233982	−	2.22619i
$768$	1.63252	+	0.347002i	0.0589084	+	0.0125214i
$769$	−20.4965	−	7.46013i	−0.739124	−	0.269019i	−0.0551021	−	0.998481i	$-0.517548\pi$
$769$	−20.4965	−	7.46013i	−0.739124	−	0.269019i	−0.684022	+	0.729462i	$0.739771\pi$
$770$	17.2340	−	20.5327i	0.621072	−	0.739947i
$771$	−12.3952	+	21.4691i	−0.446401	+	0.773189i
$772$	−15.5283	+	17.2459i	−0.558877	+	0.620695i
$773$	−4.09032	+	8.38639i	−0.147118	+	0.301638i	−0.959609	−	0.281337i	$-0.909222\pi$
$773$	−4.09032	+	8.38639i	−0.147118	+	0.301638i	0.812491	+	0.582974i	$0.198111\pi$
$774$	1.07822	+	0.0753966i	0.0387559	+	0.00271008i
$775$	1.02849	+	2.54561i	0.0369446	+	0.0914412i
$776$	−0.0977042	−	0.0519503i	−0.00350738	−	0.00186491i
$777$	−9.79090	+	14.5156i	−0.351247	+	0.520745i
$778$	−14.0304	−	10.1937i	−0.503014	−	0.365461i
$779$	−13.7076	+	47.7277i	−0.491125	+	1.71002i
$780$	−29.4605			−1.05485
$781$	4.51213	+	6.21230i	0.161457	+	0.222294i
$782$	4.18048	−	23.7087i	0.149494	−	0.847820i
$783$	−20.9444	−	13.0875i	−0.748490	−	0.467709i
$784$	−0.288863	−	1.15857i	−0.0103165	−	0.0413773i
$785$	−10.0437	−	9.69909i	−0.358475	−	0.346175i
$786$	28.2484	−	6.00438i	1.00759	−	0.214169i
$787$	−7.55082	−	8.38603i	−0.269158	−	0.298930i	0.593380	−	0.804922i	$-0.297793\pi$
$787$	−7.55082	−	8.38603i	−0.269158	−	0.298930i	−0.862538	+	0.505992i	$0.831126\pi$
$788$	10.1106	−	2.89918i	0.360176	−	0.103279i
$789$	−17.0622	−	25.2957i	−0.607430	−	0.900552i
$790$	−33.9508	−	7.21646i	−1.20792	−	0.256750i
$791$	−21.1115	−	36.5662i	−0.750638	−	1.30014i
$792$	0.639389	−	0.311736i	0.0227197	−	0.0110771i
$793$	−34.3422	−	28.8166i	−1.21953	−	1.02331i
$794$	25.7328	+	16.0797i	0.913224	+	0.570646i
$795$	−32.3487	+	31.2388i	−1.14729	+	1.10793i
$796$	4.68126	−	6.94025i	0.165923	−	0.245991i
$797$	6.75861	−	20.8009i	0.239402	−	0.736804i	−0.757105	−	0.653294i	$-0.773387\pi$
$797$	6.75861	−	20.8009i	0.239402	−	0.736804i	0.996507	−	0.0835106i	$-0.0266132\pi$
$798$	−20.8117	−	0.735589i	−0.736727	−	0.0260396i
$799$	15.2939	−	11.1117i	0.541061	−	0.393104i
$800$	2.85744	+	0.819357i	0.101026	+	0.0289687i
$801$	−2.54687	+	0.357939i	−0.0899891	+	0.0126471i
$802$	−15.3228	+	12.8574i	−0.541067	+	0.454009i
$803$	4.08745	−	2.35910i	0.144243	−	0.0832510i
$804$	−0.295227	−	1.67431i	−0.0104118	−	0.0590485i
$805$	−46.6842	+	51.8481i	−1.64540	+	1.82740i
$806$	5.27483	−	2.34850i	0.185798	−	0.0827225i
$807$	−39.1680	+	11.2312i	−1.37878	+	0.395359i
$808$	8.27124	−	10.5867i	0.290981	−	0.372439i
$809$	26.2462	+	29.1493i	0.922766	+	1.02484i	0.999614	+	0.0277928i	$0.00884786\pi$
$809$	26.2462	+	29.1493i	0.922766	+	1.02484i	−0.0768476	+	0.997043i	$0.524485\pi$
$810$	21.4368	+	9.54430i	0.753214	+	0.335352i
$811$	8.98730	−	18.4267i	0.315587	−	0.647049i	−0.680755	−	0.732512i	$-0.738348\pi$
$811$	8.98730	−	18.4267i	0.315587	−	0.647049i	0.996341	+	0.0854628i	$0.0272369\pi$
$812$	4.93636	−	12.2179i	0.173232	−	0.428765i
$813$	−19.0188	+	15.9587i	−0.667020	+	0.559696i
$814$	2.52889	−	11.8890i	0.0886374	−	0.416710i
$815$	33.5047	−	12.1947i	1.17362	−	0.427162i
$816$	−1.43840	−	4.42695i	−0.0503542	−	0.154974i
$817$	21.6314	+	3.82365i	0.756788	+	0.133773i
$818$	16.1761	−	11.7526i	0.565584	−	0.410921i
$819$	0.133947	+	3.83574i	0.00468048	+	0.134032i
$820$	28.4014	+	15.1013i	0.991819	+	0.527359i
$821$	5.03534	−	20.1956i	0.175734	−	0.704832i	−0.816166	−	0.577817i	$-0.803905\pi$
$821$	5.03534	−	20.1956i	0.175734	−	0.704832i	0.991901	−	0.127015i	$-0.0405398\pi$
$822$	4.77642	+	19.1572i	0.166597	+	0.668184i
$823$	41.0260	−	21.8139i	1.43008	−	0.760385i	0.439617	−	0.898186i	$-0.355114\pi$
$823$	41.0260	−	21.8139i	1.43008	−	0.760385i	0.990460	+	0.137800i	$0.0440032\pi$
$824$	−0.469221	−	0.812715i	−0.0163461	−	0.0283123i
$825$	−15.2573	+	6.16176i	−0.531189	+	0.214525i
$826$	−26.6743	−	9.70866i	−0.928119	−	0.337808i
$827$	−0.546241	+	15.6423i	−0.0189947	+	0.543936i	0.952176	+	0.305550i	$0.0988404\pi$
$827$	−0.546241	+	15.6423i	−0.0189947	+	0.543936i	−0.971171	+	0.238386i	$0.923382\pi$
$828$	−1.69129	+	0.753012i	−0.0587765	+	0.0261690i
$829$	24.0089	+	10.6894i	0.833862	+	0.371259i	0.778838	−	0.627226i	$-0.215810\pi$
$829$	24.0089	+	10.6894i	0.833862	+	0.371259i	0.0550247	+	0.998485i	$0.482476\pi$
$830$	−12.2238	−	1.71794i	−0.424293	−	0.0596305i
$831$	12.9071	−	8.06527i	0.447743	−	0.279781i
$832$	1.51238	−	6.06584i	0.0524324	−	0.210295i
$833$	−2.39550	+	2.31331i	−0.0829991	+	0.0801513i
$834$	−8.55544	−	10.9505i	−0.296251	−	0.379183i
$835$	28.0733			0.971516
$836$	13.5878	−	4.93681i	0.469943	−	0.170743i
$837$	−4.95513			−0.171274
$838$	−13.8255	−	17.6959i	−0.477595	−	0.611294i
$839$	−20.1866	+	19.4939i	−0.696918	+	0.673006i	−0.956173	−	0.292803i	$-0.905412\pi$
$839$	−20.1866	+	19.4939i	−0.696918	+	0.673006i	0.259255	+	0.965809i	$0.416523\pi$
$840$	−3.26345	+	13.0890i	−0.112600	+	0.451613i
$841$	−6.62181	+	4.13777i	−0.228338	+	0.142682i
$842$	−11.3712	−	1.59812i	−0.391879	−	0.0550750i
$843$	25.5332	+	11.3681i	0.879410	+	0.391539i
$844$	−6.26134	+	2.78773i	−0.215524	+	0.0959575i
$845$	−2.57013	+	73.5988i	−0.0884150	+	2.53188i
$846$	−1.36609	−	0.497217i	−0.0469673	−	0.0170947i
$847$	−30.2655	−	8.68795i	−1.03993	−	0.298522i
$848$	−4.77134	−	8.26420i	−0.163848	−	0.283794i
$849$	−30.1603	+	16.0365i	−1.03510	+	0.550371i
$850$	−2.00565	−	8.04423i	−0.0687933	−	0.275915i
$851$	−7.65322	+	30.6954i	−0.262349	+	1.05223i
$852$	−3.41147	−	1.81391i	−0.116875	−	0.0621435i
$853$	−0.453211	−	12.9783i	−0.0155176	−	0.444367i	−0.982139	−	0.188157i	$-0.939748\pi$
$853$	−0.453211	−	12.9783i	−0.0155176	−	0.444367i	0.966621	−	0.256210i	$-0.0824737\pi$
$854$	−16.6071	+	12.0658i	−0.568284	+	0.412883i
$855$	−2.28549	−	1.32082i	−0.0781620	−	0.0451710i
$856$	5.97599	+	18.3922i	0.204255	+	0.628633i
$857$	−20.4588	+	7.44638i	−0.698858	+	0.254363i	−0.666923	−	0.745127i	$-0.732389\pi$
$857$	−20.4588	+	7.44638i	−0.698858	+	0.254363i	−0.0319346	+	0.999490i	$0.510167\pi$
$858$	14.0705	+	31.6151i	0.480358	+	1.07932i
$859$	9.49431	−	7.96667i	0.323942	−	0.271819i	−0.466284	−	0.884635i	$-0.654408\pi$
$859$	9.49431	−	7.96667i	0.323942	−	0.271819i	0.790226	+	0.612816i	$0.209963\pi$
$860$	5.33046	−	13.1933i	0.181767	−	0.449889i
$861$	−23.8588	+	48.9178i	−0.813106	+	1.66711i
$862$	−23.1654	−	10.3139i	−0.789016	−	0.351293i
$863$	−8.04912	−	8.93945i	−0.273995	−	0.304303i	0.590405	−	0.807107i	$-0.298968\pi$
$863$	−8.04912	−	8.93945i	−0.273995	−	0.304303i	−0.864400	+	0.502805i	$0.832301\pi$
$864$	−3.30298	+	4.22762i	−0.112370	+	0.143826i
$865$	0.593729	−	0.170249i	0.0201874	−	0.00578864i
$866$	−17.0467	+	7.58970i	−0.579272	+	0.257908i
$867$	10.2984	−	11.4376i	0.349753	−	0.388440i
$868$	−0.459103	−	2.60371i	−0.0155830	−	0.0883755i
$869$	8.47082	+	39.8804i	0.287353	+	1.35285i
$870$	−16.6184	+	13.9445i	−0.563418	+	0.472764i
$871$	−6.30625	+	0.886286i	−0.213679	+	0.0300307i
$872$	−6.33728	−	1.81719i	−0.214607	−	0.0615377i
$873$	0.0192006	−	0.0139500i	0.000649841	−	0.000472137i
$874$	−35.7893	+	11.6119i	−1.21059	+	0.392778i
$875$	5.06375	−	15.5846i	0.171186	−	0.526856i
$876$	−1.32802	+	1.96887i	−0.0448696	+	0.0665220i
$877$	24.9150	−	24.0601i	0.841318	−	0.812452i	−0.142840	−	0.989746i	$-0.545623\pi$
$877$	24.9150	−	24.0601i	0.841318	−	0.812452i	0.984158	+	0.177294i	$0.0567344\pi$
$878$	8.11196	+	5.06892i	0.273765	+	0.171068i
$879$	−5.17137	−	4.33930i	−0.174426	−	0.146361i
$880$	−1.30198	−	9.27380i	−0.0438897	−	0.312620i
$881$	−22.9162	−	39.6921i	−0.772068	−	1.33726i	−0.936428	−	0.350861i	$-0.885889\pi$
$881$	−22.9162	−	39.6921i	−0.772068	−	1.33726i	0.164360	−	0.986400i	$-0.447444\pi$
$882$	0.250495	+	0.0532443i	0.00843460	+	0.00179283i
$883$	−24.6664	−	36.5695i	−0.830091	−	1.23066i	−0.970628	−	0.240585i	$-0.922661\pi$
$883$	−24.6664	−	36.5695i	−0.830091	−	1.23066i	0.140537	−	0.990075i	$-0.455117\pi$
$884$	−16.7600	+	4.80585i	−0.563699	+	0.161638i
$885$	31.2696	+	34.7285i	1.05112	+	1.16738i
$886$	7.72599	−	1.64221i	0.259560	−	0.0551711i
$887$	17.9074	+	17.2930i	0.601271	+	0.580641i	0.931717	−	0.363184i	$-0.118310\pi$
$887$	17.9074	+	17.2930i	0.601271	+	0.580641i	−0.330446	+	0.943825i	$0.607199\pi$
$888$	1.47975	+	5.93494i	0.0496570	+	0.199164i
$889$	−35.3069	−	22.0622i	−1.18416	−	0.739943i
$890$	−5.87957	+	33.3447i	−0.197084	+	1.11772i
$891$	0.00398538	−	27.5631i	0.000133515	−	0.923397i
$892$	15.0299			0.503239
$893$	−26.5500	−	12.9632i	−0.888460	−	0.433797i
$894$	8.15931	+	5.92809i	0.272888	+	0.198265i
$895$	−10.0173	+	14.8512i	−0.334840	+	0.496421i
$896$	−2.52746	−	1.34387i	−0.0844364	−	0.0448956i
$897$	−33.7385	−	83.5058i	−1.12650	−	2.78818i
$898$	2.61170	+	0.182628i	0.0871534	+	0.00609436i
$899$	1.86387	−	3.82151i	0.0621636	−	0.127454i
$900$	−0.426603	+	0.473791i	−0.0142201	+	0.0157930i
$901$	−13.3072	+	23.0487i	−0.443326	+	0.767863i
$902$	2.64109	−	37.6910i	0.0879385	−	1.25497i
$903$	22.6244	+	8.23462i	0.752894	+	0.274031i
$904$	−14.4279	−	3.06675i	−0.479866	−	0.101999i
$905$	4.77162	−	45.3990i	0.158614	−	1.50911i
$906$	−17.5925	−	16.9889i	−0.584472	−	0.564418i
$907$	19.3590	−	12.0969i	0.642806	−	0.401670i	−0.168984	−	0.985619i	$-0.554049\pi$
$907$	19.3590	−	12.0969i	0.642806	−	0.401670i	0.811790	+	0.583949i	$0.198493\pi$
$908$	7.80792	+	19.3253i	0.259115	+	0.641332i
$909$	1.26313	+	2.58980i	0.0418954	+	0.0858984i
$910$	48.5710	+	13.9275i	1.61011	+	0.461692i
$911$	13.9150	+	42.8259i	0.461024	+	1.41889i	0.863915	+	0.503638i	$0.168006\pi$
$911$	13.9150	+	42.8259i	0.461024	+	1.41889i	−0.402890	+	0.915248i	$0.631994\pi$
$912$	−5.05582	+	5.23102i	−0.167415	+	0.173216i
$913$	3.99455	+	13.9383i	0.132200	+	0.461289i
$914$	−2.31614	+	0.843005i	−0.0766110	+	0.0278841i
$915$	33.4652	−	4.70323i	1.10633	−	0.155484i
$916$	7.87183	−	0.550452i	0.260093	−	0.0181874i
$917$	−49.4112	−	3.45517i	−1.63170	−	0.114100i
$918$	14.8170	+	2.08240i	0.489035	+	0.0687294i
$919$	1.97575	−	0.419958i	0.0651738	−	0.0138531i	−0.175209	−	0.984531i	$-0.556060\pi$
$919$	1.97575	−	0.419958i	0.0651738	−	0.0138531i	0.240383	+	0.970678i	$0.422727\pi$
$920$	2.54768	+	24.2396i	0.0839945	+	0.799155i
$921$	14.4002	+	21.3491i	0.474502	+	0.703478i
$922$	−0.325422	+	9.31887i	−0.0107172	+	0.306901i
$923$	−7.23618	+	12.5334i	−0.238182	+	0.412543i
$924$	15.6049	−	2.74924i	0.513364	−	0.0904434i
$925$	1.89175	+	10.7287i	0.0622004	+	0.352756i
$926$	5.03142	−	12.4532i	0.165343	−	0.409237i
$927$	0.200783	−	0.0140401i	0.00659457	−	0.000461137i
$928$	−2.01802	−	4.13755i	−0.0662447	−	0.135822i
$929$	−1.08013	−	30.9309i	−0.0354379	−	1.01481i	−0.878720	−	0.477337i	$-0.841602\pi$
$929$	−1.08013	−	30.9309i	−0.0354379	−	1.01481i	0.843282	−	0.537471i	$-0.180620\pi$
$930$	−1.34501	+	4.13953i	−0.0441048	+	0.135741i
$931$	4.94926	+	1.61043i	0.162205	+	0.0527797i
$932$	−14.6349	−	10.6329i	−0.479382	−	0.348291i
$933$	16.2430	+	20.7901i	0.531773	+	0.680639i
$934$	5.58989	−	31.7018i	0.182907	−	1.03732i
$935$	−20.5837	+	16.0769i	−0.673157	+	0.525771i
$936$	1.02711	+	0.861851i	0.0335723	+	0.0281705i
$937$	−12.3222	+	6.55183i	−0.402549	+	0.214039i	−0.658385	−	0.752681i	$-0.728760\pi$
$937$	−12.3222	+	6.55183i	−0.402549	+	0.214039i	0.255837	+	0.966720i	$0.417649\pi$
$938$	−0.304800	+	2.89998i	−0.00995208	+	0.0946877i
$939$	0.949629	+	9.03511i	0.0309900	+	0.294850i
$940$	−11.7831	+	15.0816i	−0.384321	+	0.491909i
$941$	−25.2224	+	32.2833i	−0.822228	+	1.05240i	0.175463	+	0.984486i	$0.443858\pi$
$941$	−25.2224	+	32.2833i	−0.822228	+	1.05240i	−0.997691	+	0.0679179i	$0.978364\pi$
$942$	−0.862676	−	8.20782i	−0.0281075	−	0.267425i
$943$	−10.2790	+	97.7979i	−0.334729	+	3.18474i
$944$	−8.75576	+	4.65552i	−0.284976	+	0.151524i
$945$	−33.2174	−	27.8727i	−1.08056	−	0.906700i
$946$	−16.7041	+	0.580902i	−0.543097	+	0.0188868i
$947$	5.83666	−	33.1013i	0.189666	−	1.07565i	−0.730147	−	0.683290i	$-0.760548\pi$
$947$	5.83666	−	33.1013i	0.189666	−	1.07565i	0.919813	−	0.392358i	$-0.128341\pi$
$948$	−12.6311	−	16.1671i	−0.410239	−	0.525082i
$949$	7.19671	+	5.22871i	0.233615	+	0.169731i
$950$	−9.63277	+	8.66600i	−0.312528	+	0.281162i
$951$	7.72184	−	23.7654i	0.250398	−	0.770645i
$952$	0.278621	+	7.97865i	0.00903014	+	0.258590i
$953$	12.6667	+	25.9705i	0.410314	+	0.841268i	0.999448	+	0.0332322i	$0.0105801\pi$
$953$	12.6667	+	25.9705i	0.410314	+	0.841268i	−0.589134	+	0.808035i	$0.700531\pi$
$954$	2.04169	−	0.142769i	0.0661020	−	0.00462230i
$955$	−14.8216	+	36.6847i	−0.479615	+	1.18709i
$956$	−2.20099	−	12.4824i	−0.0711851	−	0.403711i
$957$	22.9014	+	11.1739i	0.740298	+	0.361200i
$958$	10.2017	−	17.6699i	0.329603	−	0.570890i
$959$	1.18180	−	33.8422i	0.0381622	−	1.09282i
$960$	2.63521	+	3.90686i	0.0850510	+	0.126093i
$961$	3.15121	+	29.9818i	0.101652	+	0.967154i
$962$	22.4104	−	4.76348i	0.722540	−	0.153581i
$963$	−4.10732	−	0.577246i	−0.132357	−	0.0186015i
$964$	5.70608	+	0.399008i	0.183781	+	0.0128512i
$965$	−65.3663	+	4.57086i	−2.10422	+	0.147141i
$966$	−40.8381	+	5.73942i	−1.31394	+	0.184663i
$967$	−31.7186	+	11.5446i	−1.02000	+	0.371250i	−0.797265	−	0.603629i	$-0.793721\pi$
$967$	−31.7186	+	11.5446i	−1.02000	+	0.371250i	−0.222736	+	0.974879i	$0.571499\pi$
$968$	−9.33021	+	5.82641i	−0.299884	+	0.187268i
$969$	19.6849	+	4.91686i	0.632371	+	0.157952i
$970$	−0.0965519	−	0.297156i	−0.00310009	−	0.00954111i
$971$	46.3767	+	13.2983i	1.48830	+	0.426763i	0.918633	−	0.395113i	$-0.129294\pi$
$971$	46.3767	+	13.2983i	1.48830	+	0.426763i	0.569667	+	0.821876i	$0.307072\pi$
$972$	−0.975165	−	1.99938i	−0.0312784	−	0.0641303i
$973$	8.92835	+	22.0984i	0.286230	+	0.708443i
$974$	−20.4688	+	12.7903i	−0.655864	+	0.409829i
$975$	−22.3105	−	21.5450i	−0.714508	−	0.689992i
$976$	−0.749588	+	7.13185i	−0.0239937	+	0.228285i
$977$	14.9548	+	3.17874i	0.478446	+	0.101697i	0.440821	−	0.897595i	$-0.354687\pi$
$977$	14.9548	+	3.17874i	0.478446	+	0.101697i	0.0376253	+	0.999292i	$0.488021\pi$
$978$	19.8043	+	7.20818i	0.633272	+	0.230492i
$979$	38.5915	−	9.61602i	1.23339	−	0.307329i
$980$	1.68572	−	2.91976i	0.0538485	−	0.0932683i
$981$	0.946128	−	1.05078i	0.0302076	−	0.0335489i
$982$	−3.90290	+	8.00213i	−0.124547	+	0.255358i
$983$	2.25322	+	0.157560i	0.0718665	+	0.00502539i	0.105644	−	0.994404i	$-0.466309\pi$
$983$	2.25322	+	0.157560i	0.0718665	+	0.00502539i	−0.0337780	+	0.999429i	$0.510754\pi$
$984$	7.12252	+	17.6288i	0.227058	+	0.561987i
$985$	26.2223	+	13.9427i	0.835513	+	0.444250i
$986$	−7.17943	+	10.6439i	−0.228639	+	0.338972i
$987$	−26.1985	−	19.0343i	−0.833908	−	0.605870i
$988$	18.9210	+	19.6099i	0.601957	+	0.623874i
$989$	43.5011			1.38325
$990$	1.91012	+	0.620940i	0.0607075	+	0.0197348i
$991$	−7.19519	+	40.8060i	−0.228563	+	1.29624i	0.627193	+	0.778864i	$0.284204\pi$
$991$	−7.19519	+	40.8060i	−0.228563	+	1.29624i	−0.855756	+	0.517380i	$0.826907\pi$
$992$	−0.783271	−	0.489442i	−0.0248689	−	0.0155398i
$993$	7.25838	+	29.1118i	0.230338	+	0.923834i
$994$	4.76690	+	4.60334i	0.151197	+	0.146009i
$995$	23.1209	−	4.91450i	0.732982	−	0.155800i
$996$	−4.88221	−	5.42225i	−0.154699	−	0.171810i
$997$	−9.53560	+	2.73429i	−0.301995	+	0.0865958i	−0.423213	−	0.906030i	$-0.639098\pi$
$997$	−9.53560	+	2.73429i	−0.301995	+	0.0865958i	0.121218	+	0.992626i	$0.461320\pi$
$998$	1.23266	+	1.82749i	0.0390190	+	0.0578481i
$999$	−19.2321	−	4.08791i	−0.608477	−	0.129336i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.5.8	✓	264
11.9	even	5	inner	418.2.u.b.119.4	yes	264
19.4	even	9	inner	418.2.u.b.137.4	yes	264
209.42	even	45	inner	418.2.u.b.251.8	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.5.8	✓	264	1.1	even	1	trivial
418.2.u.b.119.4	yes	264	11.9	even	5	inner
418.2.u.b.137.4	yes	264	19.4	even	9	inner
418.2.u.b.251.8	yes	264	209.42	even	45	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.615661 - 0.788011i) q^{2} +(1.20057 - 1.15938i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-2.39453 + 1.49627i) q^{5} +(-1.65275 - 0.232278i) q^{6} +(2.61504 + 1.16429i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.00748509 + 0.214345i) q^{9} +O(q^{10})\)	\(q+(-0.615661 - 0.788011i) q^{2} +(1.20057 - 1.15938i) q^{3} +(-0.241922 + 0.970296i) q^{4} +(-2.39453 + 1.49627i) q^{5} +(-1.65275 - 0.232278i) q^{6} +(2.61504 + 1.16429i) q^{7} +(0.913545 - 0.406737i) q^{8} +(-0.00748509 + 0.214345i) q^{9} +(2.65330 + 0.965720i) q^{10} +(-0.230878 - 3.30858i) q^{11} +(0.834495 + 1.44539i) q^{12} +(5.51978 - 2.93492i) q^{13} +(-0.692507 - 2.77749i) q^{14} +(-1.14006 + 4.57254i) q^{15} +(-0.882948 - 0.469472i) q^{16} +(0.0973339 + 2.78728i) q^{17} +(0.173514 - 0.126066i) q^{18} +(3.77584 - 2.17785i) q^{19} +(-0.872534 - 2.68538i) q^{20} +(4.48940 - 1.63401i) q^{21} +(-2.46505 + 2.21890i) q^{22} +(6.61248 - 5.54853i) q^{23} +(0.625214 - 1.54746i) q^{24} +(1.30310 - 2.67175i) q^{25} +(-5.71106 - 2.54273i) q^{26} +(3.58984 + 3.98692i) q^{27} +(-1.76234 + 2.25570i) q^{28} +(-4.42511 + 1.26888i) q^{29} +(4.30510 - 1.91675i) q^{30} +(-0.618020 + 0.686381i) q^{31} +(0.173648 + 0.984808i) q^{32} +(-4.11308 - 3.70451i) q^{33} +(2.13648 - 1.79272i) q^{34} +(-8.00390 + 1.12487i) q^{35} +(-0.206167 - 0.0591175i) q^{36} +(-2.96494 + 2.15416i) q^{37} +(-4.04081 - 1.63458i) q^{38} +(3.22420 - 9.92308i) q^{39} +(-1.57892 + 2.34085i) q^{40} +(-8.19481 + 7.91363i) q^{41} +(-4.05157 - 2.53170i) q^{42} +(3.86050 + 3.23934i) q^{43} +(3.26615 + 0.576398i) q^{44} +(-0.302794 - 0.524455i) q^{45} +(-8.44335 - 1.79469i) q^{46} +(-3.79034 - 5.61941i) q^{47} +(-1.60434 + 0.460036i) q^{48} +(0.798964 + 0.887340i) q^{49} +(-2.90763 + 0.618037i) q^{50} +(3.34836 + 3.23348i) q^{51} +(1.51238 + 6.06584i) q^{52} +(8.09265 + 5.05685i) q^{53} +(0.931609 - 5.28342i) q^{54} +(5.50337 + 7.57704i) q^{55} +2.86252 q^{56} +(2.00821 - 6.99228i) q^{57} +(3.72426 + 2.70584i) q^{58} +(5.54524 - 8.22116i) q^{59} +(-4.16091 - 2.21239i) q^{60} +(-2.68635 - 6.64896i) q^{61} +(0.921366 + 0.0644282i) q^{62} +(-0.269134 + 0.551807i) q^{63} +(0.669131 - 0.743145i) q^{64} +(-8.82585 + 15.2868i) q^{65} +(-0.386929 + 5.52187i) q^{66} +(-0.957233 - 0.348404i) q^{67} +(-2.72803 - 0.579861i) q^{68} +(1.50591 - 14.3278i) q^{69} +(5.81410 + 5.61461i) q^{70} +(-1.96324 + 1.22677i) q^{71} +(0.0803440 + 0.198858i) q^{72} +(0.623780 + 1.27894i) q^{73} +(3.52290 + 1.01018i) q^{74} +(-1.53310 - 4.71840i) q^{75} +(1.19970 + 4.19055i) q^{76} +(3.24840 - 8.92089i) q^{77} +(-9.80451 + 3.56855i) q^{78} +(-12.1730 + 1.71081i) q^{79} +(2.81670 - 0.196963i) q^{80} +(8.29033 + 0.579716i) q^{81} +(11.2813 + 1.58548i) q^{82} +(-4.27619 + 0.908932i) q^{83} +(0.499387 + 4.75135i) q^{84} +(-4.40359 - 6.52859i) q^{85} +(0.175877 - 5.03645i) q^{86} +(-3.84155 + 6.65376i) q^{87} +(-1.55664 - 2.92863i) q^{88} +(2.08231 + 11.8094i) q^{89} +(-0.226858 + 0.561492i) q^{90} +(17.8516 - 1.24830i) q^{91} +(3.78401 + 7.75838i) q^{92} +(0.0537978 + 1.54057i) q^{93} +(-2.09459 + 6.44648i) q^{94} +(-5.78271 + 10.8646i) q^{95} +(1.35024 + 0.981007i) q^{96} +(-0.0681272 - 0.0871988i) q^{97} +(0.207342 - 1.17589i) q^{98} +(0.710906 - 0.0247225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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