LMFDB - Embedded newform 354.2.e.c.85.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			85.2
Character	$\chi$	$=$	354.85
Dual form			354.2.e.c.25.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.697351 - 0.660566i) q^{5} +(0.161782 + 0.986827i) q^{6} +(-1.30774 - 1.53959i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})$	\(q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.697351 - 0.660566i) q^{5} +(0.161782 + 0.986827i) q^{6} +(-1.30774 - 1.53959i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(0.155399 - 0.947890i) q^{10} +(4.44744 - 2.67594i) q^{11} +(0.725995 + 0.687699i) q^{12} +(2.29120 - 3.37927i) q^{13} +(-1.97281 - 0.434248i) q^{14} +(0.256973 + 0.925532i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(-2.44518 + 2.87869i) q^{17} +(-0.947653 - 0.319302i) q^{18} +(6.22394 + 2.87950i) q^{19} +(-0.449927 - 0.848652i) q^{20} +(1.97281 - 0.434248i) q^{21} +(1.92117 - 4.82177i) q^{22} +(2.12741 - 0.716808i) q^{23} +(0.994138 + 0.108119i) q^{24} +(-0.220744 + 4.07138i) q^{25} +(-0.221037 - 4.07679i) q^{26} +(0.994138 - 0.108119i) q^{27} +(-1.83334 + 0.848191i) q^{28} +(-6.35432 - 4.83043i) q^{29} +(0.764682 + 0.581297i) q^{30} +(-8.42910 + 3.89972i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(0.281003 + 5.18280i) q^{33} +(-0.204483 + 3.77147i) q^{34} +(-1.92896 - 0.209787i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(1.87864 - 4.71503i) q^{37} +(6.69744 - 1.47422i) q^{38} +(1.91241 + 3.60718i) q^{39} +(-0.871766 - 0.403322i) q^{40} +(-10.1849 - 3.43170i) q^{41} +(1.30774 - 1.53959i) q^{42} +(10.9026 + 6.55988i) q^{43} +(-1.38858 - 5.00122i) q^{44} +(-0.938087 - 0.206489i) q^{45} +(1.25982 - 1.85810i) q^{46} +(4.18431 + 3.96359i) q^{47} +(0.856857 - 0.515554i) q^{48} +(0.472315 - 2.88099i) q^{49} +(2.28816 + 3.37478i) q^{50} +(-1.39801 - 3.50875i) q^{51} +(-2.64313 - 3.11174i) q^{52} +(0.601170 + 3.66698i) q^{53} +(0.725995 - 0.687699i) q^{54} +(1.33379 - 4.80389i) q^{55} +(-0.946202 + 1.78473i) q^{56} +(-5.45942 + 4.15015i) q^{57} -7.98188 q^{58} +(-7.04595 + 3.05854i) q^{59} +0.960544 q^{60} +(-9.80612 + 7.45442i) q^{61} +(-4.35034 + 8.20561i) q^{62} +(-0.540417 + 1.94641i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(-0.634458 - 3.87002i) q^{65} +(3.36020 + 3.95593i) q^{66} +(4.03271 + 10.1213i) q^{67} +(2.11961 + 3.12619i) q^{68} +(-0.363189 + 2.21535i) q^{69} +(-1.66259 + 1.00035i) q^{70} +(-6.41054 - 6.07239i) q^{71} +(-0.561187 + 0.827689i) q^{72} +(6.37533 + 1.40332i) q^{73} +(-1.35784 - 4.89051i) q^{74} +(-3.49371 - 2.10210i) q^{75} +(4.43963 - 5.22673i) q^{76} +(-9.93597 - 3.34782i) q^{77} +(3.70543 + 1.71431i) q^{78} +(5.15857 + 9.73010i) q^{79} +(-0.938087 + 0.206489i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(-10.1849 + 3.43170i) q^{82} +(-2.12966 - 0.231615i) q^{83} +(0.109363 - 2.01707i) q^{84} +(0.196415 + 3.62266i) q^{85} +(12.6494 - 1.37570i) q^{86} +(7.24416 - 3.35150i) q^{87} +(-4.13205 - 3.14110i) q^{88} +(8.71037 + 6.62145i) q^{89} +(-0.871766 + 0.403322i) q^{90} +(-8.19901 + 0.891696i) q^{91} +(-0.121538 - 2.24163i) q^{92} +(0.502815 - 9.27387i) q^{93} +(5.72976 + 0.623149i) q^{94} +(6.24237 - 2.10330i) q^{95} +(0.370138 - 0.928977i) q^{96} +(0.915829 - 0.201589i) q^{97} +(-1.36750 - 2.57937i) q^{98} +(-4.71069 - 2.17940i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{23}{29}\right)$	$1$

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 $

$2$	0.796093	−	0.605174i	0.562923	−	0.427923i
$2$	0.796093	−	0.605174i	0.562923	−	0.427923i
$3$	−0.468408	+	0.883512i	−0.270436	+	0.510096i
$3$	−0.468408	+	0.883512i	−0.270436	+	0.510096i
$4$	0.267528	−	0.963550i	0.133764	−	0.481775i
$5$	0.697351	−	0.660566i	0.311865	−	0.295414i	−0.515717	−	0.856759i	$-0.672474\pi$
$5$	0.697351	−	0.660566i	0.311865	−	0.295414i	0.827582	+	0.561345i	$0.189716\pi$
$6$	0.161782	+	0.986827i	0.0660472	+	0.402870i
$7$	−1.30774	−	1.53959i	−0.494281	−	0.581912i	0.457300	−	0.889313i	$-0.348817\pi$
$7$	−1.30774	−	1.53959i	−0.494281	−	0.581912i	−0.951580	+	0.307401i	$0.900541\pi$
$8$	−0.370138	−	0.928977i	−0.130864	−	0.328443i
$9$	−0.561187	−	0.827689i	−0.187062	−	0.275896i
$10$	0.155399	−	0.947890i	0.0491414	−	0.299749i
$11$	4.44744	−	2.67594i	1.34095	−	0.806825i	0.349456	−	0.936953i	$-0.386366\pi$
$11$	4.44744	−	2.67594i	1.34095	−	0.806825i	0.991497	+	0.130127i	$0.0415387\pi$
$12$	0.725995	+	0.687699i	0.209577	+	0.198522i
$13$	2.29120	−	3.37927i	0.635465	−	0.937240i	−0.364517	−	0.931197i	$-0.618766\pi$
$13$	2.29120	−	3.37927i	0.635465	−	0.937240i	0.999982	−	0.00604346i	$-0.00192370\pi$
$14$	−1.97281	−	0.434248i	−0.527255	−	0.116058i
$15$	0.256973	+	0.925532i	0.0663501	+	0.238971i
$16$	−0.856857	−	0.515554i	−0.214214	−	0.128888i
$17$	−2.44518	+	2.87869i	−0.593044	+	0.698185i	−0.974036	−	0.226393i	$-0.927307\pi$
$17$	−2.44518	+	2.87869i	−0.593044	+	0.698185i	0.380992	+	0.924578i	$0.375582\pi$
$18$	−0.947653	−	0.319302i	−0.223364	−	0.0752601i
$19$	6.22394	+	2.87950i	1.42787	+	0.660603i	0.973180	−	0.230046i	$-0.0738877\pi$
$19$	6.22394	+	2.87950i	1.42787	+	0.660603i	0.454691	+	0.890649i	$0.349750\pi$
$20$	−0.449927	−	0.848652i	−0.100607	−	0.189764i
$21$	1.97281	−	0.434248i	0.430502	−	0.0947607i
$22$	1.92117	−	4.82177i	0.409595	−	1.02800i
$23$	2.12741	−	0.716808i	0.443596	−	0.149465i	−0.0886349	−	0.996064i	$-0.528250\pi$
$23$	2.12741	−	0.716808i	0.443596	−	0.149465i	0.532231	+	0.846599i	$0.321354\pi$
$24$	0.994138	+	0.108119i	0.202928	+	0.0220697i
$25$	−0.220744	+	4.07138i	−0.0441487	+	0.814275i
$26$	−0.221037	−	4.07679i	−0.0433489	−	0.799524i
$27$	0.994138	−	0.108119i	0.191322	−	0.0208075i
$28$	−1.83334	+	0.848191i	−0.346468	+	0.160293i
$29$	−6.35432	−	4.83043i	−1.17997	−	0.896988i	−0.183672	−	0.982988i	$-0.558799\pi$
$29$	−6.35432	−	4.83043i	−1.17997	−	0.896988i	−0.996295	+	0.0859994i	$0.972592\pi$
$30$	0.764682	+	0.581297i	0.139611	+	0.106130i
$31$	−8.42910	+	3.89972i	−1.51391	+	0.700410i	−0.988609	−	0.150506i	$-0.951910\pi$
$31$	−8.42910	+	3.89972i	−1.51391	+	0.700410i	−0.525302	+	0.850916i	$0.676048\pi$
$32$	−0.994138	+	0.108119i	−0.175740	+	0.0191129i
$33$	0.281003	+	5.18280i	0.0489164	+	0.902209i
$34$	−0.204483	+	3.77147i	−0.0350685	+	0.646801i
$35$	−1.92896	−	0.209787i	−0.326054	−	0.0354605i
$36$	−0.947653	+	0.319302i	−0.157942	+	0.0532169i
$37$	1.87864	−	4.71503i	0.308847	−	0.775147i	−0.689842	−	0.723960i	$-0.742320\pi$
$37$	1.87864	−	4.71503i	0.308847	−	0.775147i	0.998689	−	0.0511872i	$-0.0163005\pi$
$38$	6.69744	−	1.47422i	1.08647	−	0.239150i
$39$	1.91241	+	3.60718i	0.306230	+	0.577611i
$40$	−0.871766	−	0.403322i	−0.137838	−	0.0637708i
$41$	−10.1849	−	3.43170i	−1.59062	−	0.535941i	−0.621685	−	0.783268i	$-0.713551\pi$
$41$	−10.1849	−	3.43170i	−1.59062	−	0.535941i	−0.968932	+	0.247326i	$0.920448\pi$
$42$	1.30774	−	1.53959i	0.201789	−	0.237565i
$43$	10.9026	+	6.55988i	1.66263	+	1.00037i	0.956254	+	0.292537i	$0.0944994\pi$
$43$	10.9026	+	6.55988i	1.66263	+	1.00037i	0.706377	+	0.707836i	$0.250328\pi$
$44$	−1.38858	−	5.00122i	−0.209337	−	0.753962i
$45$	−0.938087	−	0.206489i	−0.139842	−	0.0307815i
$46$	1.25982	−	1.85810i	0.185751	−	0.273962i
$47$	4.18431	+	3.96359i	0.610344	+	0.578149i	0.929164	−	0.369667i	$-0.120528\pi$
$47$	4.18431	+	3.96359i	0.610344	+	0.578149i	−0.318820	+	0.947815i	$0.603287\pi$
$48$	0.856857	−	0.515554i	0.123677	−	0.0744138i
$49$	0.472315	−	2.88099i	0.0674736	−	0.411571i
$50$	2.28816	+	3.37478i	0.323595	+	0.477266i
$51$	−1.39801	−	3.50875i	−0.195761	−	0.491323i
$52$	−2.64313	−	3.11174i	−0.366536	−	0.431520i
$53$	0.601170	+	3.66698i	0.0825771	+	0.503698i	0.995437	+	0.0954244i	$0.0304208\pi$
$53$	0.601170	+	3.66698i	0.0825771	+	0.503698i	−0.912860	+	0.408274i	$0.866131\pi$
$54$	0.725995	−	0.687699i	0.0987955	−	0.0935840i
$55$	1.33379	−	4.80389i	0.179849	−	0.647757i
$56$	−0.946202	+	1.78473i	−0.126442	+	0.238494i
$57$	−5.45942	+	4.15015i	−0.723118	+	0.549700i
$58$	−7.98188			−1.04807
$59$	−7.04595	+	3.05854i	−0.917304	+	0.398187i
$59$	−7.04595	+	3.05854i	−0.917304	+	0.398187i
$60$	0.960544			0.124006
$61$	−9.80612	+	7.45442i	−1.25555	+	0.954441i	−0.999924	−	0.0123362i	$-0.996073\pi$
$61$	−9.80612	+	7.45442i	−1.25555	+	0.954441i	−0.255621	+	0.966777i	$0.582280\pi$
$62$	−4.35034	+	8.20561i	−0.552494	+	1.04211i
$63$	−0.540417	+	1.94641i	−0.0680861	+	0.245224i
$64$	−0.725995	+	0.687699i	−0.0907494	+	0.0859624i
$65$	−0.634458	−	3.87002i	−0.0786948	−	0.480017i
$66$	3.36020	+	3.95593i	0.413612	+	0.486942i
$67$	4.03271	+	10.1213i	0.492674	+	1.23652i	0.939701	+	0.341998i	$0.111104\pi$
$67$	4.03271	+	10.1213i	0.492674	+	1.23652i	−0.447026	+	0.894521i	$0.647517\pi$
$68$	2.11961	+	3.12619i	0.257040	+	0.379106i
$69$	−0.363189	+	2.21535i	−0.0437228	+	0.266697i
$70$	−1.66259	+	1.00035i	−0.198717	+	0.119564i
$71$	−6.41054	−	6.07239i	−0.760792	−	0.720660i	0.205345	−	0.978690i	$-0.434168\pi$
$71$	−6.41054	−	6.07239i	−0.760792	−	0.720660i	−0.966137	+	0.258029i	$0.916927\pi$
$72$	−0.561187	+	0.827689i	−0.0661365	+	0.0975441i
$73$	6.37533	+	1.40332i	0.746176	+	0.164246i	0.571754	−	0.820425i	$-0.306263\pi$
$73$	6.37533	+	1.40332i	0.746176	+	0.164246i	0.174422	+	0.984671i	$0.444194\pi$
$74$	−1.35784	−	4.89051i	−0.157846	−	0.568510i
$75$	−3.49371	−	2.10210i	−0.403419	−	0.242729i
$76$	4.43963	−	5.22673i	0.509260	−	0.599547i
$77$	−9.93597	−	3.34782i	−1.13231	−	0.381519i
$78$	3.70543	+	1.71431i	0.419557	+	0.194108i
$79$	5.15857	+	9.73010i	0.580385	+	1.09472i	0.983727	+	0.179672i	$0.0575037\pi$
$79$	5.15857	+	9.73010i	0.580385	+	1.09472i	−0.403342	+	0.915049i	$0.632151\pi$
$80$	−0.938087	+	0.206489i	−0.104881	+	0.0230861i
$81$	−0.370138	+	0.928977i	−0.0411265	+	0.103220i
$82$	−10.1849	+	3.43170i	−1.12474	+	0.378968i
$83$	−2.12966	−	0.231615i	−0.233761	−	0.0254230i	−0.00951121	−	0.999955i	$-0.503028\pi$
$83$	−2.12966	−	0.231615i	−0.233761	−	0.0254230i	−0.224250	+	0.974532i	$0.571993\pi$
$84$	0.109363	−	2.01707i	0.0119324	−	0.220081i
$85$	0.196415	+	3.62266i	0.0213042	+	0.392933i
$86$	12.6494	−	1.37570i	1.36402	−	0.148346i
$87$	7.24416	−	3.35150i	0.776655	−	0.359319i
$88$	−4.13205	−	3.14110i	−0.440478	−	0.334843i
$89$	8.71037	+	6.62145i	0.923298	+	0.701873i	0.954680	−	0.297635i	$-0.0961978\pi$
$89$	8.71037	+	6.62145i	0.923298	+	0.701873i	−0.0313823	+	0.999507i	$0.509991\pi$
$90$	−0.871766	+	0.403322i	−0.0918922	+	0.0425139i
$91$	−8.19901	+	0.891696i	−0.859489	+	0.0934751i
$92$	−0.121538	−	2.24163i	−0.0126712	−	0.233706i
$93$	0.502815	−	9.27387i	0.0521395	−	0.961656i
$94$	5.72976	+	0.623149i	0.590979	+	0.0642729i
$95$	6.24237	−	2.10330i	0.640454	−	0.215794i
$96$	0.370138	−	0.928977i	0.0377771	−	0.0948133i
$97$	0.915829	−	0.201589i	0.0929883	−	0.0204683i	−0.168233	−	0.985747i	$-0.553806\pi$
$97$	0.915829	−	0.201589i	0.0929883	−	0.0204683i	0.261221	+	0.965279i	$0.415875\pi$
$98$	−1.36750	−	2.57937i	−0.138138	−	0.260556i
$99$	−4.71069	−	2.17940i	−0.473442	−	0.219038i
$100$	3.86392	+	1.30191i	0.386392	+	0.130191i
$101$	3.44514	−	4.05594i	0.342805	−	0.403581i	−0.563561	−	0.826074i	$-0.690569\pi$
$101$	3.44514	−	4.05594i	0.342805	−	0.403581i	0.906366	+	0.422493i	$0.138845\pi$
$102$	−3.23635	−	1.94725i	−0.320447	−	0.192806i
$103$	1.22511	+	4.41246i	0.120714	+	0.434773i	0.999065	−	0.0432446i	$-0.0137695\pi$
$103$	1.22511	+	4.41246i	0.120714	+	0.434773i	−0.878351	+	0.478017i	$0.841356\pi$
$104$	−3.98732	−	0.877676i	−0.390989	−	0.0860632i
$105$	1.08889	−	1.60599i	0.106265	−	0.156729i
$106$	2.69775	+	2.55544i	0.262028	+	0.248206i
$107$	−4.72775	+	2.84460i	−0.457049	+	0.274997i	−0.725405	−	0.688323i	$-0.758347\pi$
$107$	−4.72775	+	2.84460i	−0.457049	+	0.274997i	0.268356	+	0.963320i	$0.413520\pi$
$108$	0.161782	−	0.986827i	0.0155675	−	0.0949574i
$109$	−0.267578	−	0.394648i	−0.0256294	−	0.0378005i	0.814659	−	0.579941i	$-0.196924\pi$
$109$	−0.267578	−	0.394648i	−0.0256294	−	0.0378005i	−0.840288	+	0.542141i	$0.817614\pi$
$110$	−1.84537	−	4.63152i	−0.175949	−	0.441598i
$111$	3.28582	+	3.86836i	0.311876	+	0.367169i
$112$	0.326806	+	1.99343i	0.0308802	+	0.188361i
$113$	5.04897	−	4.78263i	0.474967	−	0.449912i	−0.412382	−	0.911011i	$-0.635303\pi$
$113$	5.04897	−	4.78263i	0.474967	−	0.449912i	0.887349	+	0.461099i	$0.152545\pi$
$114$	−1.83465	+	6.60780i	−0.171831	+	0.618878i
$115$	1.01005	−	1.90516i	0.0941879	−	0.177657i
$116$	−6.35432	+	4.83043i	−0.589984	+	0.448494i
$117$	−4.08277			−0.377453
$118$	−3.75828	+	6.69890i	−0.345978	+	0.616684i
$119$	7.62969			0.699412
$120$	0.764682	−	0.581297i	0.0698056	−	0.0530649i
$121$	7.46660	−	14.0835i	0.678782	−	1.28032i
$122$	−3.29536	+	11.8688i	−0.298348	+	1.07455i
$123$	7.80265	−	7.39106i	0.703541	−	0.666430i
$124$	1.50255	+	9.16514i	0.134933	+	0.823054i
$125$	5.64469	+	6.64544i	0.504876	+	0.594387i
$126$	0.747692	+	1.87657i	0.0666097	+	0.167178i
$127$	6.66246	+	9.82639i	0.591197	+	0.871951i	0.999157	−	0.0410490i	$-0.0130700\pi$
$127$	6.66246	+	9.82639i	0.591197	+	0.871951i	−0.407960	+	0.913000i	$0.633760\pi$
$128$	−0.161782	+	0.986827i	−0.0142996	+	0.0872240i
$129$	−10.9026	+	6.55988i	−0.959921	+	0.577565i
$130$	−2.84713	−	2.69694i	−0.249709	−	0.236537i
$131$	6.38257	−	9.41359i	0.557648	−	0.822469i	−0.439476	−	0.898254i	$-0.644836\pi$
$131$	6.38257	−	9.41359i	0.557648	−	0.822469i	0.997124	+	0.0757851i	$0.0241463\pi$
$132$	5.06906	+	1.11578i	0.441205	+	0.0971166i
$133$	−3.70606	−	13.3480i	−0.321356	−	1.15742i
$134$	9.33559	+	5.61704i	0.806472	+	0.485238i
$135$	0.621843	−	0.732090i	0.0535197	−	0.0630083i
$136$	3.57929	+	1.20600i	0.306922	+	0.103414i
$137$	−2.54033	−	1.17528i	−0.217035	−	0.100411i	0.308359	−	0.951270i	$-0.400220\pi$
$137$	−2.54033	−	1.17528i	−0.217035	−	0.100411i	−0.525394	+	0.850859i	$0.676082\pi$
$138$	1.05154	+	1.98342i	0.0895132	+	0.168840i
$139$	8.32869	−	1.83328i	0.706431	−	0.155497i	0.152797	−	0.988258i	$-0.451172\pi$
$139$	8.32869	−	1.83328i	0.706431	−	0.155497i	0.553634	+	0.832760i	$0.313241\pi$
$140$	−0.718192	+	1.80253i	−0.0606983	+	0.152341i
$141$	−5.46184	+	1.84031i	−0.459970	+	0.154982i
$142$	−8.77824	−	0.954692i	−0.736654	−	0.0801159i
$143$	1.14727	−	21.1602i	0.0959397	−	1.76950i
$144$	0.0541389	+	0.998533i	0.00451158	+	0.0832111i
$145$	−7.62200	+	0.828943i	−0.632973	+	0.0688400i
$146$	5.92460	−	2.74101i	0.490324	−	0.226848i
$147$	2.32416	+	1.76678i	0.191693	+	0.145721i
$148$	−4.04058	−	3.07157i	−0.332134	−	0.252481i
$149$	−8.58200	+	3.97046i	−0.703065	+	0.325272i	−0.738645	−	0.674094i	$-0.764534\pi$
$149$	−8.58200	+	3.97046i	−0.703065	+	0.325272i	0.0355804	+	0.999367i	$0.488672\pi$
$150$	−4.05345	+	0.440840i	−0.330963	+	0.0359944i
$151$	−0.872537	−	16.0930i	−0.0710061	−	1.30963i	−0.789351	−	0.613943i	$-0.789583\pi$
$151$	−0.872537	−	16.0930i	−0.0710061	−	1.30963i	0.718344	−	0.695688i	$-0.244900\pi$
$152$	0.371272	−	6.84771i	0.0301141	−	0.555423i
$153$	3.75486	+	0.408366i	0.303563	+	0.0330144i
$154$	−9.93597	+	3.34782i	−0.800663	+	0.269775i
$155$	−3.30202	+	8.28744i	−0.265225	+	0.665664i
$156$	3.98732	−	0.877676i	0.319241	−	0.0702703i
$157$	1.62097	+	3.05747i	0.129367	+	0.244013i	0.939731	−	0.341914i	$-0.111075\pi$
$157$	1.62097	+	3.05747i	0.129367	+	0.244013i	−0.810364	+	0.585927i	$0.800730\pi$
$158$	9.99511	+	4.62423i	0.795168	+	0.367884i
$159$	−3.52141	−	1.18650i	−0.279266	−	0.0940957i
$160$	−0.621843	+	0.732090i	−0.0491610	+	0.0578768i
$161$	−3.88570	−	2.33795i	−0.306236	−	0.184256i
$162$	0.267528	+	0.963550i	0.0210190	+	0.0757036i
$163$	−11.8607	−	2.61073i	−0.929001	−	0.204489i	−0.275401	−	0.961329i	$-0.588811\pi$
$163$	−11.8607	−	2.61073i	−0.929001	−	0.204489i	−0.653599	+	0.756841i	$0.726742\pi$
$164$	−6.03137	+	8.89560i	−0.470971	+	0.694630i
$165$	3.61954	+	3.42861i	0.281781	+	0.266917i
$166$	−1.83558	+	1.10443i	−0.142468	+	0.0857204i
$167$	1.09145	−	6.65753i	0.0844587	−	0.515175i	−0.910386	−	0.413761i	$-0.864215\pi$
$167$	1.09145	−	6.65753i	0.0844587	−	0.515175i	0.994844	−	0.101414i	$-0.0323368\pi$
$168$	−1.13362	−	1.67196i	−0.0874605	−	0.128995i
$169$	−1.35805	−	3.40846i	−0.104466	−	0.262189i
$170$	2.34870	+	2.76511i	0.180137	+	0.212074i
$171$	−1.10946	−	6.76743i	−0.0848428	−	0.517518i
$172$	9.23753	−	8.75025i	0.704355	−	0.667200i
$173$	−2.72605	+	9.81836i	−0.207258	+	0.746476i	0.784696	+	0.619880i	$0.212819\pi$
$173$	−2.72605	+	9.81836i	−0.207258	+	0.746476i	−0.991954	+	0.126596i	$0.959595\pi$
$174$	3.73878	−	7.05209i	0.283436	−	0.534617i
$175$	6.55694	−	4.98446i	0.495658	−	0.376790i
$176$	−5.19041			−0.391242
$177$	0.598128	−	7.65782i	0.0449580	−	0.575597i
$178$	10.9414			0.820092
$179$	0.868873	−	0.660500i	0.0649426	−	0.0493681i	−0.572199	−	0.820115i	$-0.693910\pi$
$179$	0.868873	−	0.660500i	0.0649426	−	0.0493681i	0.637142	+	0.770747i	$0.280117\pi$
$180$	−0.449927	+	0.848652i	−0.0335356	+	0.0632548i
$181$	−0.873265	+	3.14522i	−0.0649093	+	0.233782i	−0.988888	−	0.148661i	$-0.952504\pi$
$181$	−0.873265	+	3.14522i	−0.0649093	+	0.233782i	0.923979	+	0.382444i	$0.124917\pi$
$182$	−5.98754	+	5.67170i	−0.443826	+	0.420414i
$183$	−1.99280	−	12.1555i	−0.147312	−	0.898563i
$184$	−1.45333	−	1.71100i	−0.107141	−	0.126136i
$185$	−1.80452	−	4.52900i	−0.132671	−	0.332979i
$186$	−5.21202	−	7.68716i	−0.382164	−	0.563650i
$187$	−3.17161	+	19.3460i	−0.231931	+	1.41472i
$188$	4.93853	−	2.97142i	0.360180	−	0.216713i
$189$	−1.46654	−	1.38918i	−0.106675	−	0.101048i
$190$	3.69665	−	5.45214i	0.268183	−	0.395540i
$191$	−19.2951	−	4.24717i	−1.39614	−	0.307314i	−0.547733	−	0.836653i	$-0.684509\pi$
$191$	−19.2951	−	4.24717i	−1.39614	−	0.307314i	−0.848410	+	0.529339i	$0.822440\pi$
$192$	−0.267528	−	0.963550i	−0.0193072	−	0.0695382i
$193$	−3.24758	−	1.95400i	−0.233766	−	0.140652i	0.393852	−	0.919174i	$-0.371142\pi$
$193$	−3.24758	−	1.95400i	−0.233766	−	0.140652i	−0.627618	+	0.778522i	$0.715970\pi$
$194$	0.607088	−	0.714720i	0.0435864	−	0.0513139i
$195$	3.71640	+	1.25220i	0.266137	+	0.0896719i
$196$	−2.64962	−	1.22585i	−0.189259	−	0.0875605i
$197$	−7.02230	−	13.2455i	−0.500318	−	0.943701i	−0.997120	−	0.0758367i	$-0.975837\pi$
$197$	−7.02230	−	13.2455i	−0.500318	−	0.943701i	0.496802	−	0.867864i	$-0.334508\pi$
$198$	−5.06906	+	1.11578i	−0.360243	+	0.0792954i
$199$	1.56321	−	3.92337i	0.110813	−	0.278120i	−0.863103	−	0.505028i	$-0.831482\pi$
$199$	1.56321	−	3.92337i	0.110813	−	0.278120i	0.973916	+	0.226908i	$0.0728615\pi$
$200$	3.86392	−	1.30191i	0.273220	−	0.0920586i
$201$	−10.8313	−	1.17797i	−0.763980	−	0.0830878i
$202$	0.288107	−	5.31382i	0.0202711	−	0.373879i
$203$	0.872919	+	16.1000i	0.0612669	+	1.13000i
$204$	−3.75486	+	0.408366i	−0.262893	+	0.0285913i
$205$	−9.36932	+	4.33471i	−0.654382	+	0.302749i
$206$	3.64561	+	2.77132i	0.254002	+	0.193087i
$207$	−1.78717	−	1.35857i	−0.124217	−	0.0944272i
$208$	−3.70543	+	1.71431i	−0.256925	+	0.118866i
$209$	35.3860	−	3.84846i	2.44770	−	0.266203i
$210$	−0.105048	−	1.93749i	−0.00724897	−	0.133699i
$211$	1.53529	−	28.3167i	0.105694	−	1.94940i	−0.164010	−	0.986459i	$-0.552443\pi$
$211$	1.53529	−	28.3167i	0.105694	−	1.94940i	0.269703	−	0.962943i	$-0.413074\pi$
$212$	3.69415	+	0.401763i	0.253715	+	0.0275932i
$213$	8.36778	−	2.81943i	0.573351	−	0.193184i
$214$	−2.04226	+	5.12568i	−0.139606	+	0.350384i
$215$	11.9362	−	2.62735i	0.814040	−	0.179184i
$216$	−0.468408	−	0.883512i	−0.0318712	−	0.0601154i
$217$	17.0271	+	7.87757i	1.15587	+	0.534764i
$218$	−0.451848	−	0.152245i	−0.0306030	−	0.0103114i
$219$	−4.22610	+	4.97535i	−0.285574	+	0.336203i
$220$	−4.27196	−	2.57035i	−0.288016	−	0.173293i
$221$	4.12546	+	14.8586i	0.277509	+	0.999496i
$222$	4.95685	+	1.09109i	0.332682	+	0.0732289i
$223$	−2.94776	+	4.34761i	−0.197396	+	0.291138i	−0.913486	−	0.406871i	$-0.866620\pi$
$223$	−2.94776	+	4.34761i	−0.197396	+	0.291138i	0.716089	+	0.698009i	$0.245930\pi$
$224$	1.46654	+	1.38918i	0.0979871	+	0.0928183i
$225$	3.49371	−	2.10210i	0.232914	−	0.140140i
$226$	1.12512	−	6.86293i	0.0748418	−	0.456515i
$227$	14.4637	+	21.3324i	0.959992	+	1.41588i	0.908818	+	0.417193i	$0.136986\pi$
$227$	14.4637	+	21.3324i	0.959992	+	1.41588i	0.0511745	+	0.998690i	$0.483704\pi$
$228$	2.53832	+	6.37071i	0.168104	+	0.421910i
$229$	−15.7972	−	18.5979i	−1.04391	−	1.22898i	−0.972833	−	0.231510i	$-0.925633\pi$
$229$	−15.7972	−	18.5979i	−1.04391	−	1.22898i	−0.0710733	−	0.997471i	$-0.522642\pi$
$230$	−0.348859	−	2.12794i	−0.0230031	−	0.140312i
$231$	7.61193	−	7.21040i	0.500828	−	0.474410i
$232$	−2.13538	+	7.69094i	−0.140195	+	0.504935i
$233$	−3.96374	+	7.47640i	−0.259673	+	0.489795i	−0.978729	−	0.205157i	$-0.934230\pi$
$233$	−3.96374	+	7.47640i	−0.259673	+	0.489795i	0.719056	+	0.694952i	$0.244574\pi$
$234$	−3.25027	+	2.47079i	−0.212477	+	0.161521i
$235$	5.53614			0.361138
$236$	1.06206	+	7.60737i	0.0691343	+	0.495197i
$237$	−11.0130			−0.715370
$238$	6.07394	−	4.61729i	0.393715	−	0.299295i
$239$	10.2979	−	19.4239i	0.666116	−	1.25643i	−0.288183	−	0.957575i	$-0.593051\pi$
$239$	10.2979	−	19.4239i	0.666116	−	1.25643i	0.954299	−	0.298853i	$-0.0966041\pi$
$240$	0.256973	−	0.925532i	0.0165875	−	0.0597429i
$241$	−5.87331	+	5.56350i	−0.378333	+	0.358376i	−0.853111	−	0.521729i	$-0.825287\pi$
$241$	−5.87331	+	5.56350i	−0.378333	+	0.358376i	0.474778	+	0.880106i	$0.342528\pi$
$242$	−2.57886	−	15.7304i	−0.165776	−	1.01119i
$243$	−0.647386	−	0.762162i	−0.0415298	−	0.0488927i
$244$	4.55929	+	11.4430i	0.291879	+	0.732560i
$245$	−1.57372	−	2.32106i	−0.100541	−	0.148287i
$246$	1.73875	−	10.6059i	0.110859	−	0.676210i
$247$	23.9909	−	14.4349i	1.52650	−	0.918468i
$248$	6.74268	+	6.38700i	0.428161	+	0.405575i
$249$	1.20219	−	1.77309i	0.0761854	−	0.112365i
$250$	8.51535	+	1.87437i	0.538558	+	0.118546i
$251$	4.36879	+	15.7349i	0.275755	+	0.993181i	0.963605	+	0.267328i	$0.0861409\pi$
$251$	4.36879	+	15.7349i	0.275755	+	0.993181i	−0.687850	+	0.725853i	$0.741445\pi$
$252$	1.73088	+	1.04144i	0.109035	+	0.0656044i
$253$	7.54340	−	8.88078i	0.474250	−	0.558330i
$254$	11.2506	+	3.79077i	0.705926	+	0.237854i
$255$	−3.29267	−	1.52335i	−0.206195	−	0.0953958i
$256$	0.468408	+	0.883512i	0.0292755	+	0.0552195i
$257$	−18.2361	+	4.01407i	−1.13754	+	0.250391i	−0.743521	−	0.668713i	$-0.766846\pi$
$257$	−18.2361	+	4.01407i	−1.13754	+	0.250391i	−0.394016	+	0.919104i	$0.628915\pi$
$258$	−4.70962	+	11.8202i	−0.293208	+	0.735897i
$259$	−9.71602	+	3.27371i	−0.603724	+	0.203418i
$260$	−3.89870	−	0.424009i	−0.241787	−	0.0262959i
$261$	−0.432130	+	7.97017i	−0.0267482	+	0.493341i
$262$	−0.615740	−	11.3567i	−0.0380406	−	0.701617i
$263$	4.15407	−	0.451782i	0.256151	−	0.0278581i	0.0208573	−	0.999782i	$-0.493360\pi$
$263$	4.15407	−	0.451782i	0.256151	−	0.0278581i	0.235293	+	0.971924i	$0.424395\pi$
$264$	4.71069	−	2.17940i	0.289923	−	0.134133i
$265$	2.84151	+	2.16006i	0.174552	+	0.132691i
$266$	−11.0282	−	8.38344i	−0.676184	−	0.514022i
$267$	−9.93014	+	4.59417i	−0.607715	+	0.281159i
$268$	10.8313	−	1.17797i	0.661626	−	0.0719562i
$269$	1.04028	+	19.1868i	0.0634268	+	1.16984i	0.840996	+	0.541042i	$0.181970\pi$
$269$	1.04028	+	19.1868i	0.0634268	+	1.16984i	−0.777569	+	0.628798i	$0.783547\pi$
$270$	0.0520028	−	0.959135i	0.00316479	−	0.0583711i
$271$	−3.90407	−	0.424593i	−0.237155	−	0.0257922i	−0.0112305	−	0.999937i	$-0.503575\pi$
$271$	−3.90407	−	0.424593i	−0.237155	−	0.0257922i	−0.225925	+	0.974145i	$0.572540\pi$
$272$	3.57929	−	1.20600i	0.217026	−	0.0731247i
$273$	3.05266	−	7.66160i	0.184755	−	0.463701i
$274$	−2.73358	+	0.601707i	−0.165142	+	0.0363505i
$275$	9.91300	+	18.6979i	0.597776	+	1.12753i
$276$	2.03744	+	0.942620i	0.122639	+	0.0567390i
$277$	3.05510	+	1.02938i	0.183563	+	0.0618496i	0.409582	−	0.912273i	$-0.365675\pi$
$277$	3.05510	+	1.02938i	0.183563	+	0.0618496i	−0.226019	+	0.974123i	$0.572571\pi$
$278$	5.52096	−	6.49978i	0.331125	−	0.389831i
$279$	7.95806	+	4.78820i	0.476436	+	0.286662i
$280$	0.519094	+	1.86961i	0.0310218	+	0.111730i
$281$	−9.92481	−	2.18462i	−0.592065	−	0.130323i	−0.0911757	−	0.995835i	$-0.529063\pi$
$281$	−9.92481	−	2.18462i	−0.592065	−	0.130323i	−0.500889	+	0.865512i	$0.666994\pi$
$282$	−3.23443	+	4.77042i	−0.192607	+	0.284075i
$283$	1.81892	+	1.72297i	0.108123	+	0.102420i	0.739852	−	0.672770i	$-0.234896\pi$
$283$	1.81892	+	1.72297i	0.108123	+	0.102420i	−0.631728	+	0.775190i	$0.717654\pi$
$284$	−7.56605	+	4.55234i	−0.448963	+	0.270132i
$285$	−1.06569	+	6.50041i	−0.0631260	+	0.385051i
$286$	−11.8923	−	17.5398i	−0.703205	−	1.03715i
$287$	8.03584	+	20.1684i	0.474340	+	1.19050i
$288$	0.647386	+	0.762162i	0.0381476	+	0.0449108i
$289$	0.442349	+	2.69821i	0.0260205	+	0.158718i
$290$	−5.56617	+	5.27256i	−0.326857	+	0.309615i
$291$	−0.250875	+	0.903572i	−0.0147066	+	0.0529683i
$292$	3.05775	−	5.76752i	0.178941	−	0.337519i
$293$	−15.6155	+	11.8706i	−0.912268	+	0.693488i	−0.952122	−	0.305717i	$-0.901104\pi$
$293$	−15.6155	+	11.8706i	−0.912268	+	0.693488i	0.0398540	+	0.999206i	$0.487311\pi$
$294$	2.91945			0.170266
$295$	−2.89313	+	6.78718i	−0.168445	+	0.395165i
$296$	−5.07551			−0.295008
$297$	4.13205	−	3.14110i	0.239766	−	0.182265i
$298$	−4.42925	+	8.35446i	−0.256580	+	0.483961i
$299$	2.45204	−	8.83144i	0.141805	−	0.510735i
$300$	−2.96014	+	2.80399i	−0.170904	+	0.161889i
$301$	−4.15826	−	25.3642i	−0.239678	−	1.46197i
$302$	−10.4337	−	12.2835i	−0.600392	−	0.706836i
$303$	1.96974	+	4.94366i	0.113158	+	0.284006i
$304$	−3.84849	−	5.67610i	−0.220726	−	0.325547i
$305$	−1.91417	+	11.6759i	−0.109605	+	0.668562i
$306$	3.23635	−	1.94725i	0.185010	−	0.111317i
$307$	−18.4259	−	17.4539i	−1.05162	−	0.996147i	−0.0516223	−	0.998667i	$-0.516439\pi$
$307$	−18.4259	−	17.4539i	−1.05162	−	0.996147i	−0.999997	+	0.00252009i	$0.999198\pi$
$308$	−5.88394	+	8.67817i	−0.335269	+	0.494485i
$309$	−4.47231	−	0.984431i	−0.254421	−	0.0560023i
$310$	2.38663	+	8.59587i	0.135552	+	0.488213i
$311$	20.4043	+	12.2768i	1.15702	+	0.696156i	0.958822	−	0.284007i	$-0.0916638\pi$
$311$	20.4043	+	12.2768i	1.15702	+	0.696156i	0.198197	+	0.980162i	$0.436491\pi$
$312$	2.64313	−	3.11174i	0.149638	−	0.176167i
$313$	9.00282	+	3.03340i	0.508869	+	0.171458i	0.562012	−	0.827129i	$-0.310027\pi$
$313$	9.00282	+	3.03340i	0.508869	+	0.171458i	−0.0531429	+	0.998587i	$0.516924\pi$
$314$	3.14074	+	1.45306i	0.177242	+	0.0820011i
$315$	0.908869	+	1.71431i	0.0512090	+	0.0965903i
$316$	10.7555	−	2.36746i	0.605044	−	0.133180i
$317$	8.08876	−	20.3013i	0.454310	−	1.14023i	−0.506306	−	0.862354i	$-0.668989\pi$
$317$	8.08876	−	20.3013i	0.454310	−	1.14023i	0.960616	−	0.277879i	$-0.0896313\pi$
$318$	−3.52141	+	1.18650i	−0.197471	+	0.0665357i
$319$	−41.1864	−	4.47929i	−2.30599	−	0.250792i
$320$	−0.0520028	+	0.959135i	−0.00290705	+	0.0536173i
$321$	−0.298714	−	5.50946i	−0.0166726	−	0.307508i
$322$	−4.50825	+	0.490302i	−0.251235	+	0.0273234i
$323$	−23.5079	+	10.8759i	−1.30801	+	0.605151i
$324$	0.796093	+	0.605174i	0.0442274	+	0.0336208i
$325$	13.2525	+	10.0743i	0.735116	+	0.558821i
$326$	−11.0222	+	5.09939i	−0.610461	+	0.282429i
$327$	0.474013	−	0.0515520i	0.0262130	−	0.00285083i
$328$	0.581859	+	10.7318i	0.0321278	+	0.592562i
$329$	0.630316	−	11.6255i	0.0347504	−	0.640934i
$330$	4.95639	+	0.539040i	0.272840	+	0.0296732i
$331$	−4.83281	+	1.62836i	−0.265636	+	0.0895030i	−0.448968	−	0.893548i	$-0.648208\pi$
$331$	−4.83281	+	1.62836i	−0.265636	+	0.0895030i	0.183332	+	0.983051i	$0.441312\pi$
$332$	−0.792917	+	1.99007i	−0.0435170	+	0.109219i
$333$	−4.95685	+	1.09109i	−0.271634	+	0.0597911i
$334$	−3.16007	−	5.96053i	−0.172912	−	0.326146i
$335$	9.49803	+	4.39426i	0.518933	+	0.240084i
$336$	−1.91429	−	0.645001i	−0.104433	−	0.0351877i
$337$	21.0432	−	24.7740i	1.14630	−	1.34953i	0.218769	−	0.975777i	$-0.429796\pi$
$337$	21.0432	−	24.7740i	1.14630	−	1.34953i	0.927529	−	0.373750i	$-0.121928\pi$
$338$	−3.14385	−	1.89159i	−0.171003	−	0.102889i
$339$	1.86054	+	6.70105i	0.101050	+	0.363951i
$340$	3.54316	+	0.779909i	0.192155	+	0.0422965i
$341$	−27.0525	+	39.8995i	−1.46498	+	2.16068i
$342$	−4.97871	−	4.71608i	−0.269218	−	0.255017i
$343$	−17.1694	+	10.3305i	−0.927061	+	0.557794i
$344$	2.05851	−	12.5563i	0.110987	−	0.676992i
$345$	1.21012	+	1.78479i	0.0651504	+	0.0960897i
$346$	3.77163	+	9.46606i	0.202764	+	0.508899i
$347$	−4.11192	−	4.84093i	−0.220739	−	0.259875i	0.640634	−	0.767846i	$-0.278671\pi$
$347$	−4.11192	−	4.84093i	−0.220739	−	0.259875i	−0.861374	+	0.507971i	$0.830396\pi$
$348$	−1.29132	−	7.87673i	−0.0692223	−	0.422237i
$349$	−7.30186	+	6.91668i	−0.390859	+	0.370242i	−0.857744	−	0.514076i	$-0.828135\pi$
$349$	−7.30186	+	6.91668i	−0.390859	+	0.370242i	0.466885	+	0.884318i	$0.345376\pi$
$350$	2.20347	−	7.93619i	0.117781	−	0.424207i
$351$	1.91241	−	3.60718i	0.102077	−	0.192537i
$352$	−4.13205	+	3.14110i	−0.220239	+	0.167421i
$353$	3.56993			0.190008			0.0950042	−	0.995477i	$-0.469714\pi$
$353$	3.56993			0.190008			0.0950042	+	0.995477i	$0.469714\pi$
$354$	−4.15815	−	6.45831i	−0.221003	−	0.343255i
$355$	−8.48161			−0.450157
$356$	8.71037	−	6.62145i	0.461649	−	0.350936i
$357$	−3.57381	+	6.74092i	−0.189146	+	0.356767i
$358$	0.291986	−	1.05164i	0.0154319	−	0.0555808i
$359$	1.43730	−	1.36148i	0.0758579	−	0.0718564i	−0.648831	−	0.760932i	$-0.724742\pi$
$359$	1.43730	−	1.36148i	0.0758579	−	0.0718564i	0.724689	+	0.689076i	$0.241983\pi$
$360$	0.155399	+	0.947890i	0.00819023	+	0.0499582i
$361$	18.1456	+	21.3626i	0.955031	+	1.12435i
$362$	1.20820	+	3.03236i	0.0635018	+	0.159377i
$363$	8.94552	+	13.1937i	0.469518	+	0.692488i
$364$	−1.33427	+	8.13871i	−0.0699349	+	0.426584i
$365$	5.37282	−	3.23272i	0.281226	−	0.169208i
$366$	−8.94267	−	8.47095i	−0.467441	−	0.442784i
$367$	−9.83129	+	14.5001i	−0.513189	+	0.756897i	−0.992696	−	0.120641i	$-0.961505\pi$
$367$	−9.83129	+	14.5001i	−0.513189	+	0.756897i	0.479507	+	0.877538i	$0.340815\pi$
$368$	−2.19244	−	0.482593i	−0.114289	−	0.0251569i
$369$	2.87527	+	10.3558i	0.149680	+	0.539100i
$370$	−4.17740	−	2.51346i	−0.217173	−	0.130668i
$371$	4.85948	−	5.72102i	0.252292	−	0.297021i
$372$	−8.80132	−	2.96551i	−0.456327	−	0.153755i
$373$	27.3138	+	12.6367i	1.41426	+	0.654304i	0.970336	−	0.241762i	$-0.0777254\pi$
$373$	27.3138	+	12.6367i	1.41426	+	0.654304i	0.443920	+	0.896067i	$0.353587\pi$
$374$	9.18278	+	17.3206i	0.474830	+	0.895625i
$375$	−8.51535	+	1.87437i	−0.439731	+	0.0967921i
$376$	2.13331	−	5.35420i	0.110017	−	0.276122i
$377$	−30.8823	+	10.4055i	−1.59052	+	0.535909i
$378$	−2.00819	−	0.218404i	−0.103290	−	0.0112335i
$379$	−1.21608	+	22.4293i	−0.0624658	+	1.15211i	0.784382	+	0.620278i	$0.212980\pi$
$379$	−1.21608	+	22.4293i	−0.0624658	+	1.15211i	−0.846848	+	0.531835i	$0.821503\pi$
$380$	−0.356623	−	6.57753i	−0.0182944	−	0.337420i
$381$	−11.8025	+	1.28360i	−0.604660	+	0.0657607i
$382$	−17.9310	+	8.29574i	−0.917428	+	0.424447i
$383$	−16.4057	−	12.4713i	−0.838291	−	0.637252i	0.0953574	−	0.995443i	$-0.469601\pi$
$383$	−16.4057	−	12.4713i	−0.838291	−	0.637252i	−0.933648	+	0.358191i	$0.883394\pi$
$384$	−0.796093	−	0.605174i	−0.0406255	−	0.0308827i
$385$	−9.14031	+	4.22876i	−0.465833	+	0.215517i
$386$	−3.76789	+	0.409782i	−0.191780	+	0.0208574i
$387$	−0.688861	−	12.7053i	−0.0350167	−	0.645846i
$388$	0.0507689	−	0.936377i	0.00257740	−	0.0475374i
$389$	33.3704	+	3.62925i	1.69195	+	0.184010i	0.902760	−	0.430144i	$-0.141537\pi$
$389$	33.3704	+	3.62925i	1.69195	+	0.184010i	0.789186	+	0.614154i	$0.210503\pi$
$390$	3.71640	−	1.25220i	0.188187	−	0.0634076i
$391$	−3.13844	+	7.87688i	−0.158718	+	0.398351i
$392$	−2.85120	+	0.627596i	−0.144007	+	0.0316984i
$393$	5.32737	+	10.0485i	0.268730	+	0.506879i
$394$	−13.6062	−	6.29491i	−0.685472	−	0.317133i
$395$	10.0247	+	3.37772i	0.504398	+	0.169951i
$396$	−3.36020	+	3.95593i	−0.168856	+	0.198793i
$397$	−24.4934	−	14.7372i	−1.22929	−	0.739638i	−0.255436	−	0.966826i	$-0.582219\pi$
$397$	−24.4934	−	14.7372i	−1.22929	−	0.739638i	−0.973851	+	0.227188i	$0.927047\pi$
$398$	−1.12986	−	4.06938i	−0.0566347	−	0.203980i
$399$	13.5291	+	2.97797i	0.677301	+	0.149085i
$400$	2.28816	−	3.37478i	0.114408	−	0.168739i
$401$	−21.6734	−	20.5301i	−1.08232	−	1.02523i	−0.999589	−	0.0286536i	$-0.990878\pi$
$401$	−21.6734	−	20.5301i	−1.08232	−	1.02523i	−0.0827282	−	0.996572i	$-0.526363\pi$
$402$	−9.33559	+	5.61704i	−0.465617	+	0.280152i
$403$	−6.13457	+	37.4192i	−0.305585	+	1.86398i
$404$	−2.98642	−	4.40465i	−0.148580	−	0.219139i
$405$	0.355534	+	0.892323i	0.0176666	+	0.0443399i
$406$	10.4383	+	12.2889i	0.518042	+	0.609886i
$407$	−4.26198	−	25.9970i	−0.211259	−	1.28862i
$408$	−2.74209	+	2.59744i	−0.135754	+	0.128593i
$409$	−0.317645	+	1.14405i	−0.0157065	+	0.0565699i	−0.970988	−	0.239128i	$-0.923138\pi$
$409$	−0.317645	+	1.14405i	−0.0157065	+	0.0565699i	0.955281	+	0.295698i	$0.0955522\pi$
$410$	−4.83560	+	9.12090i	−0.238813	+	0.450449i
$411$	2.22828	−	1.69390i	0.109913	−	0.0835538i
$412$	4.57938			0.225610
$413$	13.9232	+	6.84812i	0.685116	+	0.336974i
$414$	−2.24493			−0.110332
$415$	−1.63812	+	1.24526i	−0.0804120	+	0.0611276i
$416$	−1.91241	+	3.60718i	−0.0937634	+	0.176857i
$417$	−2.28150	+	8.21723i	−0.111726	+	0.402399i
$418$	25.8415	−	24.4784i	1.26395	−	1.19728i
$419$	−4.90086	−	29.8939i	−0.239423	−	1.46041i	−0.783506	−	0.621384i	$-0.786571\pi$
$419$	−4.90086	−	29.8939i	−0.239423	−	1.46041i	0.544084	−	0.839031i	$-0.316877\pi$
$420$	−1.25615	−	1.47885i	−0.0612936	−	0.0721604i
$421$	−9.56625	−	24.0095i	−0.466230	−	1.17015i	−0.954700	−	0.297569i	$-0.903824\pi$
$421$	−9.56625	−	24.0095i	−0.466230	−	1.17015i	0.488470	−	0.872581i	$-0.337555\pi$
$422$	−15.9143	−	23.4718i	−0.774696	−	1.14259i
$423$	0.932438	−	5.68762i	0.0453367	−	0.276541i
$424$	3.18402	−	1.91576i	0.154630	−	0.0930376i
$425$	−11.1805	−	10.5907i	−0.542332	−	0.513725i
$426$	4.95528	−	7.30850i	0.240084	−	0.354098i
$427$	24.3007	+	5.34899i	1.17599	+	0.258856i
$428$	1.47610	+	5.31644i	0.0713501	+	0.256980i
$429$	18.1579	+	10.9252i	0.876671	+	0.527476i
$430$	7.91230	−	9.31508i	0.381565	−	0.449213i
$431$	−0.761408	−	0.256548i	−0.0366757	−	0.0123575i	0.300904	−	0.953654i	$-0.402712\pi$
$431$	−0.761408	−	0.256548i	−0.0366757	−	0.0123575i	−0.337580	+	0.941297i	$0.609608\pi$
$432$	−0.907575	−	0.419889i	−0.0436657	−	0.0202019i
$433$	2.48542	+	4.68800i	0.119442	+	0.225291i	0.936022	−	0.351940i	$-0.114478\pi$
$433$	2.48542	+	4.68800i	0.119442	+	0.225291i	−0.816581	+	0.577231i	$0.804133\pi$
$434$	18.3225	−	4.03308i	0.879506	−	0.193594i
$435$	2.83783	−	7.12242i	0.136064	−	0.341494i
$436$	−0.451848	+	0.152245i	−0.0216396	+	0.00729123i
$437$	15.3049	+	1.66451i	0.732134	+	0.0796244i
$438$	−0.353416	+	6.51837i	−0.0168869	+	0.311460i
$439$	0.534245	+	9.85358i	0.0254981	+	0.470285i	0.983201	+	0.182526i	$0.0584275\pi$
$439$	0.534245	+	9.85358i	0.0254981	+	0.470285i	−0.957703	+	0.287759i	$0.907090\pi$
$440$	−4.95639	+	0.539040i	−0.236287	+	0.0256977i
$441$	−2.64962	+	1.22585i	−0.126173	+	0.0583737i
$442$	12.2763	+	9.33219i	0.583923	+	0.443887i
$443$	−6.04516	−	4.59541i	−0.287214	−	0.218334i	0.451639	−	0.892201i	$-0.350839\pi$
$443$	−6.04516	−	4.59541i	−0.287214	−	0.218334i	−0.738853	+	0.673866i	$0.764632\pi$
$444$	4.60641	−	2.13115i	0.218611	−	0.101140i
$445$	10.4481	−	1.13630i	0.495287	−	0.0538657i
$446$	0.284376	+	5.24501i	0.0134656	+	0.248359i
$447$	0.511935	−	9.44209i	0.0242137	−	0.446596i
$448$	2.00819	+	0.218404i	0.0948783	+	0.0103186i
$449$	−17.2177	+	5.80133i	−0.812556	+	0.273782i	−0.694747	−	0.719254i	$-0.744484\pi$
$449$	−17.2177	+	5.80133i	−0.812556	+	0.273782i	−0.117809	+	0.993036i	$0.537587\pi$
$450$	1.50918	−	3.78777i	0.0711436	−	0.178557i
$451$	−54.4798	+	11.9919i	−2.56535	+	0.564677i
$452$	−3.25757	−	6.14442i	−0.153223	−	0.289009i
$453$	14.6271	+	6.76720i	0.687240	+	0.317951i
$454$	24.4243	+	8.22951i	1.14629	+	0.386230i
$455$	−5.12856	+	6.03781i	−0.240431	+	0.283057i
$456$	5.87613	+	3.53555i	0.275175	+	0.165567i
$457$	3.46666	+	12.4858i	0.162164	+	0.584061i	0.999312	+	0.0370849i	$0.0118072\pi$
$457$	3.46666	+	12.4858i	0.162164	+	0.584061i	−0.837149	+	0.546976i	$0.815779\pi$
$458$	−23.8310	−	5.24559i	−1.11355	−	0.245110i
$459$	−2.11961	+	3.12619i	−0.0989348	+	0.145918i
$460$	−1.56550	−	1.48292i	−0.0729918	−	0.0691415i
$461$	19.3722	−	11.6559i	0.902255	−	0.542869i	0.0128137	−	0.999918i	$-0.495921\pi$
$461$	19.3722	−	11.6559i	0.902255	−	0.542869i	0.889442	+	0.457049i	$0.151094\pi$
$462$	1.69625	−	10.3467i	0.0789169	−	0.481372i
$463$	−0.810121	−	1.19484i	−0.0376495	−	0.0555289i	0.808398	−	0.588636i	$-0.200335\pi$
$463$	−0.810121	−	1.19484i	−0.0376495	−	0.0555289i	−0.846048	+	0.533107i	$0.821024\pi$
$464$	2.95440	+	7.41498i	0.137155	+	0.344232i
$465$	−5.77536	−	6.79928i	−0.267826	−	0.315309i
$466$	1.36902	+	8.35067i	0.0634187	+	0.386837i
$467$	10.4378	−	9.88719i	0.483003	−	0.457525i	−0.407034	−	0.913413i	$-0.633437\pi$
$467$	10.4378	−	9.88719i	0.483003	−	0.457525i	0.890037	+	0.455888i	$0.150678\pi$
$468$	−1.09226	+	3.93396i	−0.0504896	+	0.181847i
$469$	10.3090	−	19.4449i	0.476026	−	0.897881i
$470$	4.40728	−	3.35033i	0.203293	−	0.154539i
$471$	−3.46059			−0.159455
$472$	5.44928	+	5.41344i	0.250824	+	0.249174i
$473$	66.0425			3.03664
$474$	−8.76736	+	6.66477i	−0.402698	+	0.306123i
$475$	−13.0974	+	24.7044i	−0.600951	+	1.13351i
$476$	2.04116	−	7.35159i	0.0935563	−	0.336959i
$477$	2.69775	−	2.55544i	0.123521	−	0.117006i
$478$	−3.55676	−	21.6953i	−0.162682	−	0.992319i
$479$	19.3002	+	22.7220i	0.881851	+	1.03819i	0.998983	+	0.0450787i	$0.0143539\pi$
$479$	19.3002	+	22.7220i	0.881851	+	1.03819i	−0.117133	+	0.993116i	$0.537370\pi$
$480$	−0.355534	−	0.892323i	−0.0162278	−	0.0407288i
$481$	−11.6290	−	17.1515i	−0.530238	−	0.782042i
$482$	−1.30882	+	7.98344i	−0.0596150	+	0.363636i
$483$	3.88570	−	2.33795i	0.176806	−	0.106380i
$484$	−11.5726	−	10.9622i	−0.526029	−	0.498281i
$485$	0.505491	−	0.745543i	0.0229532	−	0.0338534i
$486$	−0.976621	−	0.214970i	−0.0443004	−	0.00975126i
$487$	−9.29215	−	33.4673i	−0.421068	−	1.51655i	−0.805050	−	0.593208i	$-0.797861\pi$
$487$	−9.29215	−	33.4673i	−0.421068	−	1.51655i	0.383982	−	0.923341i	$-0.374552\pi$
$488$	10.5546	+	6.35049i	0.477784	+	0.287473i
$489$	7.86226	−	9.25617i	0.355544	−	0.418578i
$490$	−2.65747	−	0.895406i	−0.120052	−	0.0404503i
$491$	−19.9657	−	9.23713i	−0.901041	−	0.416866i	−0.0860172	−	0.996294i	$-0.527414\pi$
$491$	−19.9657	−	9.23713i	−0.901041	−	0.416866i	−0.815024	+	0.579428i	$0.803276\pi$
$492$	−5.03423	−	9.49556i	−0.226960	−	0.428093i
$493$	29.4428	−	6.48085i	1.32604	−	0.291883i
$494$	10.3634	−	26.0102i	0.466271	−	1.17025i
$495$	−4.72464	+	1.59192i	−0.212357	+	0.0715513i
$496$	9.23305	+	1.00415i	0.414576	+	0.0450879i
$497$	−0.965672	+	17.8108i	−0.0433163	+	0.798922i
$498$	−0.115977	−	2.13908i	−0.00519707	−	0.0958544i
$499$	−5.92385	+	0.644258i	−0.265188	+	0.0288409i	−0.239747	−	0.970835i	$-0.577065\pi$
$499$	−5.92385	+	0.644258i	−0.265188	+	0.0288409i	−0.0254410	+	0.999676i	$0.508099\pi$
$500$	7.91333	−	3.66110i	0.353895	−	0.163729i
$501$	5.37077	+	4.08275i	0.239948	+	0.182404i
$502$	13.0003	+	9.88261i	0.580234	+	0.441082i
$503$	13.3622	−	6.18200i	0.595790	−	0.275642i	−0.0987313	−	0.995114i	$-0.531478\pi$
$503$	13.3622	−	6.18200i	0.595790	−	0.275642i	0.694521	+	0.719472i	$0.255616\pi$
$504$	2.00819	−	0.218404i	0.0894521	−	0.00972850i
$505$	−0.276739	−	5.10416i	−0.0123147	−	0.227132i
$506$	0.630831	−	11.6350i	0.0280439	−	0.517239i
$507$	3.64754	+	0.396694i	0.161993	+	0.0176178i
$508$	11.2506	−	3.79077i	0.499165	−	0.168188i
$509$	6.02307	−	15.1168i	0.266968	−	0.670039i	−0.732980	−	0.680250i	$-0.761871\pi$
$509$	6.02307	−	15.1168i	0.266968	−	0.670039i	0.999948	+	0.0102115i	$0.00325048\pi$
$510$	−3.54316	+	0.779909i	−0.156894	+	0.0345349i
$511$	−6.17676	−	11.6506i	−0.273244	−	0.515392i
$512$	0.907575	+	0.419889i	0.0401095	+	0.0185567i
$513$	6.49879	+	2.18970i	0.286928	+	0.0966775i
$514$	−12.0884	+	14.2316i	−0.533197	+	0.627729i
$515$	3.76905	+	2.26776i	0.166084	+	0.0999296i
$516$	3.40402	+	12.2602i	0.149853	+	0.539723i
$517$	29.2158	+	6.43088i	1.28491	+	0.282830i
$518$	−5.75369	+	8.48606i	−0.252803	+	0.372856i
$519$	−7.39773	−	7.00750i	−0.324724	−	0.307595i
$520$	−3.36032	+	2.02184i	−0.147360	+	0.0886635i
$521$	2.41994	−	14.7610i	0.106019	−	0.646690i	−0.879339	−	0.476196i	$-0.842015\pi$
$521$	2.41994	−	14.7610i	0.106019	−	0.646690i	0.985359	−	0.170494i	$-0.0545364\pi$
$522$	4.47933	+	6.60652i	0.196055	+	0.289159i
$523$	10.5127	+	26.3848i	0.459686	+	1.15373i	0.958010	+	0.286735i	$0.0925698\pi$
$523$	10.5127	+	26.3848i	0.459686	+	1.15373i	−0.498324	+	0.866991i	$0.666051\pi$
$524$	−7.36295	−	8.66833i	−0.321652	−	0.378678i
$525$	1.33250	+	8.12790i	0.0581552	+	0.354731i
$526$	3.03362	−	2.87359i	0.132272	−	0.125295i
$527$	9.38460	−	33.8003i	0.408800	−	1.47236i
$528$	2.43123	−	4.58579i	0.105806	−	0.199571i
$529$	−14.2981	+	10.8691i	−0.621656	+	0.472570i
$530$	3.56931			0.155041
$531$	6.48561	+	4.11544i	0.281452	+	0.178595i
$532$	−13.8529			−0.600601
$533$	−34.9323	+	26.5549i	−1.51309	+	1.15022i
$534$	−5.12504	+	9.66686i	−0.221782	+	0.418326i
$535$	−1.41786	+	5.10667i	−0.0612995	+	0.220781i
$536$	7.90983	−	7.49259i	0.341653	−	0.323631i
$537$	0.176572	+	1.07704i	0.00761965	+	0.0464778i
$538$	12.4395	+	14.6449i	0.536305	+	0.631387i
$539$	−5.60876	−	14.0769i	−0.241587	−	0.606336i
$540$	−0.539045	−	0.795032i	−0.0231968	−	0.0342127i
$541$	−0.0614711	+	0.374957i	−0.00264285	+	0.0161207i	−0.988115	−	0.153716i	$-0.950876\pi$
$541$	−0.0614711	+	0.374957i	−0.00264285	+	0.0161207i	0.985472	+	0.169837i	$0.0543241\pi$
$542$	−3.36496	+	2.02463i	−0.144537	+	0.0869652i
$543$	−2.36979	−	2.24479i	−0.101698	−	0.0963330i
$544$	2.11961	−	3.12619i	0.0908774	−	0.134034i
$545$	−0.447287	−	0.0984553i	−0.0191597	−	0.00421736i
$546$	−2.20640	−	7.94674i	−0.0944252	−	0.340089i
$547$	−9.86264	−	5.93415i	−0.421696	−	0.253726i	0.288853	−	0.957373i	$-0.406726\pi$
$547$	−9.86264	−	5.93415i	−0.421696	−	0.253726i	−0.710549	+	0.703647i	$0.751554\pi$
$548$	−1.81205	+	2.13331i	−0.0774069	+	0.0911305i
$549$	11.6730	+	3.93310i	0.498192	+	0.167860i
$550$	19.2072	+	8.88617i	0.818996	+	0.378908i
$551$	−25.6397	−	48.3616i	−1.09229	−	2.06027i
$552$	2.19244	−	0.482593i	0.0933165	−	0.0205405i
$553$	8.23432	−	20.6666i	0.350159	−	0.878833i
$554$	3.05510	−	1.02938i	0.129799	−	0.0437343i
$555$	4.84668	+	0.527108i	0.205730	+	0.0223745i
$556$	0.461701	−	8.51557i	0.0195805	−	0.361141i
$557$	−1.91871	−	35.3885i	−0.0812983	−	1.49946i	−0.700175	−	0.713971i	$-0.746895\pi$
$557$	−1.91871	−	35.3885i	−0.0812983	−	1.49946i	0.618877	−	0.785488i	$-0.287588\pi$
$558$	9.23305	−	1.00415i	0.390866	−	0.0425093i
$559$	47.1476	−	21.8128i	1.99413	−	0.922584i
$560$	1.54469	+	1.17424i	0.0652749	+	0.0496207i
$561$	−15.6068	−	11.8640i	−0.658919	−	0.500897i
$562$	−9.22315	+	4.26708i	−0.389055	+	0.179996i
$563$	−33.0372	+	3.59301i	−1.39235	+	0.151427i	−0.773359	−	0.633968i	$-0.781425\pi$
$563$	−33.0372	+	3.59301i	−1.39235	+	0.151427i	−0.618994	+	0.785396i	$0.712459\pi$
$564$	0.312032	+	5.75509i	0.0131389	+	0.242333i
$565$	0.361656	−	6.67035i	0.0152150	−	0.280624i
$566$	2.49072	+	0.270883i	0.104693	+	0.0113860i
$567$	1.91429	−	0.645001i	0.0803928	−	0.0270875i
$568$	−3.26832	+	8.20287i	−0.137136	+	0.344185i
$569$	−33.5242	+	7.37924i	−1.40541	+	0.309354i	−0.851994	−	0.523552i	$-0.824607\pi$
$569$	−33.5242	+	7.37924i	−1.40541	+	0.309354i	−0.553415	+	0.832905i	$0.686676\pi$
$570$	3.08550	+	5.81986i	0.129237	+	0.243767i
$571$	29.5278	+	13.6610i	1.23570	+	0.571695i	0.925417	−	0.378950i	$-0.123715\pi$
$571$	29.5278	+	13.6610i	1.23570	+	0.571695i	0.310282	+	0.950645i	$0.399577\pi$
$572$	−20.0820	−	6.76641i	−0.839670	−	0.282918i
$573$	12.7904	−	15.0580i	0.534327	−	0.629058i
$574$	18.6027	+	11.1929i	0.776461	+	0.467181i
$575$	2.44878	+	8.81972i	0.102121	+	0.367808i
$576$	0.976621	+	0.214970i	0.0406925	+	0.00895710i
$577$	−12.1349	+	17.8977i	−0.505185	+	0.745091i	−0.991699	−	0.128581i	$-0.958958\pi$
$577$	−12.1349	+	17.8977i	−0.505185	+	0.745091i	0.486514	+	0.873673i	$0.338268\pi$
$578$	1.98504	+	1.88033i	0.0825667	+	0.0782113i
$579$	3.24758	−	1.95400i	0.134965	−	0.0812056i
$580$	−1.24037	+	7.56595i	−0.0515037	+	0.314159i
$581$	2.42846	+	3.58171i	0.100749	+	0.148594i
$582$	0.347098	+	0.871150i	0.0143877	+	0.0361103i
$583$	12.4863	+	14.7000i	0.517128	+	0.608810i
$584$	−1.05610	−	6.44195i	−0.0437019	−	0.266570i
$585$	−2.84713	+	2.69694i	−0.117714	+	0.111505i
$586$	−5.24762	+	18.9002i	−0.216777	+	0.780761i
$587$	−3.12437	+	5.89319i	−0.128957	+	0.243238i	−0.939580	−	0.342330i	$-0.888784\pi$
$587$	−3.12437	+	5.89319i	−0.128957	+	0.243238i	0.810623	+	0.585568i	$0.199129\pi$
$588$	2.32416	−	1.76678i	0.0958466	−	0.0728607i
$589$	−63.6915			−2.62436
$590$	1.80423	+	7.15408i	0.0742788	+	0.294529i
$591$	14.9918			0.616682
$592$	−4.04058	+	3.07157i	−0.166067	+	0.126241i
$593$	7.02901	−	13.2581i	0.288647	−	0.544446i	−0.696205	−	0.717843i	$-0.745130\pi$
$593$	7.02901	−	13.2581i	0.288647	−	0.544446i	0.984852	+	0.173397i	$0.0554744\pi$
$594$	1.38858	−	5.00122i	0.0569742	−	0.205203i
$595$	5.32057	−	5.03991i	0.218122	−	0.206616i
$596$	1.52980	+	9.33139i	0.0626632	+	0.382229i
$597$	2.73412	+	3.21886i	0.111900	+	0.131739i
$598$	−3.39251	−	8.51456i	−0.138730	−	0.348186i
$599$	2.04418	+	3.01494i	0.0835230	+	0.123187i	0.867156	−	0.498037i	$-0.165946\pi$
$599$	2.04418	+	3.01494i	0.0835230	+	0.123187i	−0.783633	+	0.621225i	$0.786635\pi$
$600$	−0.659643	+	4.02364i	−0.0269298	+	0.164265i
$601$	21.4667	−	12.9161i	0.875646	−	0.526859i	−0.00534848	−	0.999986i	$-0.501702\pi$
$601$	21.4667	−	12.9161i	0.875646	−	0.526859i	0.880994	+	0.473127i	$0.156875\pi$
$602$	−18.6601	−	17.6758i	−0.760531	−	0.720413i
$603$	6.11422	−	9.01780i	0.248990	−	0.367233i
$604$	−15.7398	−	3.46460i	−0.640445	−	0.140973i
$605$	−4.09624	−	14.7533i	−0.166536	−	0.599808i
$606$	4.55987	+	2.74358i	0.185232	+	0.111450i
$607$	23.2322	−	27.3510i	0.942964	−	1.11014i	−0.0508078	−	0.998708i	$-0.516180\pi$
$607$	23.2322	−	27.3510i	0.942964	−	1.11014i	0.993772	−	0.111435i	$-0.0355445\pi$
$608$	−6.49879	−	2.18970i	−0.263561	−	0.0888039i
$609$	−14.6335	−	6.77016i	−0.592978	−	0.274341i
$610$	5.54211	+	10.4535i	0.224394	+	0.423251i
$611$	22.9811	−	5.05852i	0.929716	−	0.204646i
$612$	1.39801	−	3.50875i	0.0565114	−	0.141833i
$613$	20.9864	−	7.07113i	0.847631	−	0.285600i	0.138225	−	0.990401i	$-0.455860\pi$
$613$	20.9864	−	7.07113i	0.847631	−	0.285600i	0.709405	+	0.704801i	$0.248964\pi$
$614$	−25.2313	−	2.74407i	−1.01825	−	0.110742i
$615$	0.558901	−	10.3083i	0.0225371	−	0.415672i
$616$	0.567637	+	10.4694i	0.0228707	+	0.421826i
$617$	29.7028	−	3.23038i	1.19579	−	0.130050i	0.511516	−	0.859274i	$-0.329084\pi$
$617$	29.7028	−	3.23038i	1.19579	−	0.130050i	0.684275	+	0.729224i	$0.260119\pi$
$618$	−4.15613	+	1.92283i	−0.167184	+	0.0773476i
$619$	−19.9560	−	15.1702i	−0.802100	−	0.609741i	0.121721	−	0.992564i	$-0.461159\pi$
$619$	−19.9560	−	15.1702i	−0.802100	−	0.609741i	−0.923821	+	0.382824i	$0.874952\pi$
$620$	7.10198	+	5.39879i	0.285223	+	0.216821i
$621$	2.03744	−	0.942620i	0.0817596	−	0.0378260i
$622$	23.6733	−	2.57463i	0.949214	−	0.103233i
$623$	−1.19658	−	22.0696i	−0.0479399	−	0.884200i
$624$	0.221037	−	4.07679i	0.00884856	−	0.163202i
$625$	−11.9412	−	1.29868i	−0.477647	−	0.0519473i
$626$	9.00282	−	3.03340i	0.359825	−	0.121239i
$627$	−13.1749	+	33.0666i	−0.526156	+	1.32055i
$628$	3.37968	−	0.743924i	0.134864	−	0.0296858i
$629$	8.97950	+	16.9371i	0.358036	+	0.675328i
$630$	1.76100	+	0.814725i	0.0701599	+	0.0324594i
$631$	−21.2317	−	7.15379i	−0.845220	−	0.284788i	−0.136818	−	0.990596i	$-0.543687\pi$
$631$	−21.2317	−	7.15379i	−0.845220	−	0.284788i	−0.708403	+	0.705808i	$0.750584\pi$
$632$	7.12965	−	8.39367i	0.283602	−	0.333882i
$633$	24.2990	+	14.6202i	0.965799	+	0.581102i
$634$	−5.84639	−	21.0568i	−0.232190	−	0.836273i
$635$	11.1370	+	2.45145i	0.441960	+	0.0972828i
$636$	−2.08533	+	3.07563i	−0.0826888	+	0.121957i
$637$	−8.65348	−	8.19701i	−0.342863	−	0.324777i
$638$	−35.4989	+	21.3590i	−1.40542	+	0.845611i
$639$	−1.42854	+	8.71368i	−0.0565120	+	0.344708i
$640$	0.539045	+	0.795032i	0.0213076	+	0.0314264i
$641$	−14.6831	−	36.8518i	−0.579948	−	1.45556i	−0.867325	−	0.497742i	$-0.834163\pi$
$641$	−14.6831	−	36.8518i	−0.579948	−	1.45556i	0.287377	−	0.957818i	$-0.407217\pi$
$642$	−3.57199	−	4.20527i	−0.140975	−	0.165969i
$643$	1.54143	+	9.40232i	0.0607881	+	0.370791i	0.999649	+	0.0264943i	$0.00843439\pi$
$643$	1.54143	+	9.40232i	0.0607881	+	0.370791i	−0.938861	+	0.344297i	$0.888117\pi$
$644$	−3.29227	+	3.11860i	−0.129734	+	0.122890i
$645$	−3.26971	+	11.7764i	−0.128745	+	0.463696i
$646$	−12.1326	+	22.8846i	−0.477352	+	0.900382i
$647$	−18.8957	+	14.3641i	−0.742866	+	0.564712i	−0.906700	−	0.421776i	$-0.861407\pi$
$647$	−18.8957	+	14.3641i	−0.742866	+	0.564712i	0.163834	+	0.986488i	$0.447614\pi$
$648$	1.00000			0.0392837
$649$	−23.1520	+	32.4572i	−0.908795	+	1.27405i
$650$	16.6469			0.652946
$651$	−14.9356	+	11.3537i	−0.585371	+	0.444987i
$652$	−5.68864	+	10.7299i	−0.222784	+	0.420216i
$653$	1.15067	−	4.14434i	0.0450292	−	0.162180i	−0.937617	−	0.347669i	$-0.886973\pi$
$653$	1.15067	−	4.14434i	0.0450292	−	0.162180i	0.982646	+	0.185489i	$0.0593869\pi$
$654$	0.346160	−	0.327900i	0.0135359	−	0.0128219i
$655$	−1.76740	−	10.7807i	−0.0690581	−	0.421236i
$656$	6.95779	+	8.19135i	0.271656	+	0.319818i
$657$	−2.41624	−	6.06431i	−0.0942666	−	0.236591i
$658$	−6.53366	−	9.63643i	−0.254709	−	0.375667i
$659$	−1.66970	+	10.1847i	−0.0650422	+	0.396740i	0.934162	+	0.356849i	$0.116149\pi$
$659$	−1.66970	+	10.1847i	−0.0650422	+	0.396740i	−0.999204	+	0.0398902i	$0.987299\pi$
$660$	4.27196	−	2.57035i	0.166286	−	0.100051i
$661$	21.5816	+	20.4432i	0.839427	+	0.795147i	0.980842	−	0.194803i	$-0.0624067\pi$
$661$	21.5816	+	20.4432i	0.839427	+	0.795147i	−0.141415	+	0.989950i	$0.545165\pi$
$662$	−2.86193	+	4.22102i	−0.111232	+	0.164055i
$663$	−15.0601	−	3.31499i	−0.584887	−	0.128743i
$664$	0.573104	+	2.06414i	0.0222408	+	0.0801040i
$665$	−11.4017	−	6.86015i	−0.442137	−	0.266025i
$666$	−3.28582	+	3.86836i	−0.127323	+	0.149896i
$667$	−16.9807	−	5.72148i	−0.657497	−	0.221537i
$668$	−6.12287	−	2.83274i	−0.236901	−	0.109602i
$669$	−2.46042	−	4.64084i	−0.0951252	−	0.179425i
$670$	10.2206	−	2.24973i	0.394856	−	0.0869145i
$671$	−23.6646	+	59.3937i	−0.913562	+	2.29287i
$672$	−1.91429	+	0.645001i	−0.0738455	+	0.0248814i
$673$	−18.0705	−	1.96529i	−0.696568	−	0.0757563i	−0.247017	−	0.969011i	$-0.579450\pi$
$673$	−18.0705	−	1.96529i	−0.696568	−	0.0757563i	−0.449551	+	0.893255i	$0.648416\pi$
$674$	1.75978	−	32.4572i	0.0677842	−	1.25021i
$675$	0.220744	+	4.07138i	0.00849642	+	0.156707i
$676$	−3.64754	+	0.396694i	−0.140290	+	0.0152574i
$677$	−4.73509	+	2.19069i	−0.181984	+	0.0841950i	−0.508766	−	0.860905i	$-0.669898\pi$
$677$	−4.73509	+	2.19069i	−0.181984	+	0.0841950i	0.326781	+	0.945100i	$0.394036\pi$
$678$	5.53646	+	4.20871i	0.212627	+	0.161634i
$679$	−1.50803	−	1.14638i	−0.0578731	−	0.0439940i
$680$	3.29267	−	1.52335i	0.126268	−	0.0584178i
$681$	−25.6224	+	2.78660i	−0.981852	+	0.106783i
$682$	2.60981	+	48.1352i	0.0999350	+	1.84319i
$683$	−0.407144	+	7.50933i	−0.0155789	+	0.287337i	0.980354	+	0.197244i	$0.0631991\pi$
$683$	−0.407144	+	7.50933i	−0.0155789	+	0.287337i	−0.995933	+	0.0900927i	$0.971284\pi$
$684$	−6.81757	−	0.741455i	−0.260676	−	0.0283503i
$685$	−2.54785	+	0.858470i	−0.0973482	+	0.0328004i
$686$	−7.41670	+	18.6145i	−0.283171	+	0.710706i
$687$	23.8310	−	5.24559i	0.909208	−	0.200132i
$688$	−5.96000	−	11.2418i	−0.227223	−	0.428588i
$689$	13.7691	+	6.37026i	0.524561	+	0.242688i
$690$	2.04347	+	0.688526i	0.0777937	+	0.0262117i
$691$	−11.5077	+	13.5480i	−0.437775	+	0.515388i	−0.936163	−	0.351565i	$-0.885649\pi$
$691$	−11.5077	+	13.5480i	−0.437775	+	0.515388i	0.498388	+	0.866954i	$0.333925\pi$
$692$	8.73118	+	5.25338i	0.331910	+	0.199703i
$693$	2.80499	+	10.1026i	0.106553	+	0.383768i
$694$	−6.20307	−	1.36540i	−0.235465	−	0.0518299i
$695$	4.59702	−	6.78009i	0.174375	−	0.257184i
$696$	−5.79481	−	5.48914i	−0.219652	−	0.208065i
$697$	34.7828	−	20.9281i	1.31749	−	0.792708i
$698$	−1.62716	+	9.92522i	−0.0615888	+	0.375675i
$699$	−4.74884	−	7.00402i	−0.179618	−	0.264916i
$700$	−3.04861	−	7.65143i	−0.115227	−	0.289197i
$701$	19.8610	+	23.3822i	0.750139	+	0.883132i	0.996286	−	0.0861007i	$-0.0274407\pi$
$701$	19.8610	+	23.3822i	0.750139	+	0.883132i	−0.246148	+	0.969232i	$0.579165\pi$
$702$	−0.660519	−	4.02899i	−0.0249297	−	0.152064i
$703$	25.2695	−	23.9366i	0.953058	−	0.902784i
$704$	−1.38858	+	5.00122i	−0.0523341	+	0.188491i
$705$	−2.59317	+	4.89125i	−0.0976646	+	0.184215i
$706$	2.84200	−	2.16043i	0.106960	−	0.0813089i
$707$	−10.7499			−0.404290
$708$	−7.21868	−	2.62501i	−0.271295	−	0.0986539i
$709$	14.3058			0.537265			0.268633	−	0.963243i	$-0.413428\pi$
$709$	14.3058			0.537265			0.268633	+	0.963243i	$0.413428\pi$
$710$	−6.75215	+	5.13285i	−0.253404	+	0.192632i
$711$	5.15857	−	9.73010i	0.193462	−	0.364907i
$712$	2.92713	−	10.5426i	0.109699	−	0.395100i
$713$	−15.1368	+	14.3384i	−0.566878	+	0.536975i
$714$	1.23435	+	7.52918i	0.0461942	+	0.281772i
$715$	−13.1776	−	15.5139i	−0.492816	−	0.580188i
$716$	−0.403977	−	1.01390i	−0.0150973	−	0.0378914i
$717$	12.3376	+	18.1967i	0.460757	+	0.679566i
$718$	0.320291	−	1.95369i	0.0119531	−	0.0729109i
$719$	11.6091	−	6.98494i	0.432945	−	0.260494i	−0.282358	−	0.959309i	$-0.591117\pi$
$719$	11.6091	−	6.98494i	0.432945	−	0.260494i	0.715302	+	0.698815i	$0.246289\pi$
$720$	0.697351	+	0.660566i	0.0259887	+	0.0246178i
$721$	5.19127	−	7.65654i	0.193333	−	0.285145i
$722$	27.3737	+	6.02541i	1.01874	+	0.224242i
$723$	−2.16431	−	7.79513i	−0.0804914	−	0.289904i
$724$	2.79695	+	1.68287i	0.103948	+	0.0625434i
$725$	21.0692	−	24.8045i	0.782489	−	0.921217i
$726$	15.1059	+	5.08978i	0.560634	+	0.188900i
$727$	29.7589	+	13.7679i	1.10370	+	0.510624i	0.885199	−	0.465213i	$-0.154022\pi$
$727$	29.7589	+	13.7679i	1.10370	+	0.510624i	0.218498	+	0.975837i	$0.429884\pi$
$728$	3.86313	+	7.28663i	0.143177	+	0.270061i
$729$	0.976621	−	0.214970i	0.0361711	−	0.00796187i
$730$	2.32091	−	5.82504i	0.0859006	−	0.215594i
$731$	−45.5427	+	15.3451i	−1.68446	+	0.567560i
$732$	−12.2456	−	1.33179i	−0.452610	−	0.0492244i
$733$	1.15688	−	21.3374i	0.0427303	−	0.788114i	−0.896125	−	0.443802i	$-0.853629\pi$
$733$	1.15688	−	21.3374i	0.0427303	−	0.788114i	0.938855	−	0.344312i	$-0.111888\pi$
$734$	0.948445	+	17.4930i	0.0350078	+	0.645680i
$735$	2.78783	−	0.303194i	0.102830	−	0.0111835i
$736$	−2.03744	+	0.942620i	−0.0751010	+	0.0347454i
$737$	45.0193	+	34.2228i	1.65831	+	1.26061i
$738$	8.55602	+	6.50412i	0.314952	+	0.239420i
$739$	−43.5937	+	20.1686i	−1.60362	+	0.741914i	−0.998528	−	0.0542406i	$-0.982726\pi$
$739$	−43.5937	+	20.1686i	−1.60362	+	0.741914i	−0.605093	+	0.796155i	$0.706864\pi$
$740$	−4.84668	+	0.527108i	−0.178167	+	0.0193769i
$741$	1.51582	+	27.9577i	0.0556851	+	1.02705i
$742$	0.406383	−	7.49530i	0.0149188	−	0.275161i
$743$	−4.46991	−	0.486132i	−0.163985	−	0.0178345i	0.0257580	−	0.999668i	$-0.491800\pi$
$743$	−4.46991	−	0.486132i	−0.163985	−	0.0178345i	−0.189743	+	0.981834i	$0.560766\pi$
$744$	−8.80132	+	2.96551i	−0.322672	+	0.108721i
$745$	−3.36192	+	8.43777i	−0.123171	+	0.309136i
$746$	29.3917	−	6.46961i	1.07611	−	0.236869i
$747$	1.00343	+	1.89268i	0.0367137	+	0.0692494i
$748$	17.7923	+	8.23159i	0.650551	+	0.300977i
$749$	10.5622	+	3.55883i	0.385935	+	0.130037i
$750$	−5.64469	+	6.64544i	−0.206115	+	0.242657i
$751$	−6.24272	−	3.75612i	−0.227800	−	0.137063i	0.397079	−	0.917785i	$-0.370024\pi$
$751$	−6.24272	−	3.75612i	−0.227800	−	0.137063i	−0.624879	+	0.780722i	$0.714852\pi$
$752$	−1.54191	−	5.55346i	−0.0562277	−	0.202514i
$753$	−15.9484	−	3.51051i	−0.581192	−	0.127930i
$754$	−18.2881	+	26.9729i	−0.666013	+	0.982295i
$755$	−11.2390	−	10.6461i	−0.409027	−	0.387451i
$756$	−1.73088	+	1.04144i	−0.0629516	+	0.0378767i
$757$	5.75529	−	35.1057i	0.209179	−	1.27594i	−0.648286	−	0.761397i	$-0.724514\pi$
$757$	5.75529	−	35.1057i	0.209179	−	1.27594i	0.857465	−	0.514541i	$-0.172038\pi$
$758$	12.6055	+	18.5917i	0.457852	+	0.675282i
$759$	4.31288	+	10.8245i	0.156548	+	0.392905i
$760$	−4.26446	−	5.02051i	−0.154688	−	0.182113i
$761$	1.75637	+	10.7134i	0.0636683	+	0.388360i	0.999368	+	0.0355607i	$0.0113217\pi$
$761$	1.75637	+	10.7134i	0.0636683	+	0.388360i	−0.935699	+	0.352799i	$0.885230\pi$
$762$	−8.61907	+	8.16442i	−0.312236	+	0.295766i
$763$	−0.257675	+	0.928061i	−0.00932846	+	0.0335981i
$764$	−9.25434	+	17.4555i	−0.334810	+	0.631519i
$765$	2.88821	−	2.19556i	0.104423	−	0.0793806i
$766$	−20.6077			−0.744588
$767$	−5.80806	+	30.8179i	−0.209717	+	1.11277i
$768$	−1.00000			−0.0360844
$769$	18.1090	−	13.7661i	0.653027	−	0.496418i	−0.225418	−	0.974262i	$-0.572375\pi$
$769$	18.1090	−	13.7661i	0.653027	−	0.496418i	0.878445	+	0.477844i	$0.158582\pi$
$770$	−4.71740	+	8.89796i	−0.170003	+	0.320660i
$771$	4.99547	−	17.9920i	0.179907	−	0.647967i
$772$	−2.75160	+	2.60645i	−0.0990322	+	0.0938083i
$773$	−0.481179	−	2.93506i	−0.0173068	−	0.105567i	0.976760	−	0.214334i	$-0.0687580\pi$
$773$	−0.481179	−	2.93506i	−0.0173068	−	0.105567i	−0.994067	+	0.108767i	$0.965310\pi$
$774$	−8.23731	−	9.69771i	−0.296084	−	0.348577i
$775$	−14.0165	−	35.1789i	−0.503489	−	1.26366i
$776$	−0.526255	−	0.776168i	−0.0188914	−	0.0278628i
$777$	1.65871	−	10.1177i	0.0595057	−	0.362969i
$778$	28.7623	−	17.3057i	1.03118	−	0.620439i
$779$	−53.5088	−	50.6862i	−1.91715	−	1.81602i
$780$	2.20080	−	3.24594i	0.0788012	−	0.116223i
$781$	−44.7598	−	9.85239i	−1.60163	−	0.352546i
$782$	2.26840	+	8.17003i	0.0811178	+	0.292160i
$783$	−6.83933	−	4.11509i	−0.244418	−	0.147061i
$784$	−1.89001	+	2.22510i	−0.0675005	+	0.0794677i
$785$	3.15004	+	1.06137i	0.112430	+	0.0378820i
$786$	10.3222	+	4.77554i	0.368179	+	0.170338i
$787$	−2.81884	−	5.31690i	−0.100481	−	0.189527i	0.828175	−	0.560470i	$-0.189379\pi$
$787$	−2.81884	−	5.31690i	−0.100481	−	0.189527i	−0.928656	+	0.370943i	$0.879035\pi$
$788$	−14.6413	+	3.22280i	−0.521576	+	0.114808i
$789$	−1.54664	+	3.88179i	−0.0550620	+	0.138195i
$790$	10.0247	−	3.37772i	0.356663	−	0.120174i
$791$	−13.9661	−	1.51890i	−0.496576	−	0.0540059i
$792$	−0.281003	+	5.18280i	−0.00998501	+	0.184163i
$793$	2.72269	+	50.2171i	0.0966856	+	1.78326i
$794$	−28.4176	+	3.09060i	−1.00850	+	0.109681i
$795$	−3.23942	+	1.49872i	−0.114890	+	0.0531540i
$796$	−3.36216	−	2.55585i	−0.119169	−	0.0905896i
$797$	−32.1650	−	24.4512i	−1.13934	−	0.866105i	−0.146940	−	0.989145i	$-0.546942\pi$
$797$	−32.1650	−	24.4512i	−1.13934	−	0.866105i	−0.992402	+	0.123041i	$0.960735\pi$
$798$	12.5726	−	5.81670i	0.445065	−	0.205909i
$799$	−21.6413	+	2.35364i	−0.765615	+	0.0832657i
$800$	−0.220744	−	4.07138i	−0.00780446	−	0.143945i
$801$	0.592355	−	10.9254i	0.0209298	−	0.386028i
$802$	−29.6783	−	3.22771i	−1.04798	−	0.113975i
$803$	32.1091	−	10.8188i	1.13310	−	0.381787i
$804$	−4.03271	+	10.1213i	−0.142223	+	0.356952i
$805$	−4.25407	+	0.936391i	−0.149936	+	0.0330034i
$806$	17.7615	+	33.5017i	0.625621	+	1.18005i
$807$	−17.4390	−	8.06816i	−0.613883	−	0.284013i
$808$	−5.04305	−	1.69920i	−0.177414	−	0.0597777i
$809$	19.1602	−	22.5571i	0.673637	−	0.793066i	−0.314068	−	0.949401i	$-0.601692\pi$
$809$	19.1602	−	22.5571i	0.673637	−	0.793066i	0.987704	+	0.156334i	$0.0499677\pi$
$810$	0.823049	+	0.495212i	0.0289190	+	0.0174000i
$811$	9.21732	+	33.1978i	0.323664	+	1.16573i	0.929097	+	0.369836i	$0.120586\pi$
$811$	9.21732	+	33.1978i	0.323664	+	1.16573i	−0.605433	+	0.795896i	$0.707000\pi$
$812$	15.7467	+	3.46612i	0.552602	+	0.121637i
$813$	2.20383	−	3.25041i	0.0772918	−	0.113997i
$814$	−19.1256	−	18.1168i	−0.670353	−	0.634992i
$815$	−9.99562	+	6.01416i	−0.350131	+	0.210667i
$816$	−0.611052	+	3.72725i	−0.0213911	+	0.130480i
$817$	48.9680	+	72.2224i	1.71317	+	2.52674i
$818$	0.439477	+	1.10300i	0.0153660	+	0.0385657i
$819$	5.33922	+	6.28582i	0.186568	+	0.219644i
$820$	1.67015	+	10.1875i	0.0583242	+	0.355762i
$821$	−12.9057	+	12.2250i	−0.450414	+	0.426655i	−0.878982	−	0.476855i	$-0.841777\pi$
$821$	−12.9057	+	12.2250i	−0.450414	+	0.426655i	0.428568	+	0.903509i	$0.359018\pi$
$822$	0.748818	−	2.69700i	0.0261180	−	0.0940687i
$823$	−18.8820	+	35.6153i	−0.658187	+	1.24147i	0.299620	+	0.954059i	$0.403140\pi$
$823$	−18.8820	+	35.6153i	−0.658187	+	1.24147i	−0.957807	+	0.287413i	$0.907205\pi$
$824$	3.64561	−	2.77132i	0.127001	−	0.0965436i
$825$	−21.1631			−0.736806
$826$	15.2285	−	2.97422i	0.529866	−	0.103486i
$827$	9.54738			0.331995			0.165998	−	0.986126i	$-0.446916\pi$
$827$	9.54738			0.331995			0.165998	+	0.986126i	$0.446916\pi$
$828$	−1.78717	+	1.35857i	−0.0621084	+	0.0472136i
$829$	13.6313	−	25.7114i	0.473435	−	0.892994i	−0.525669	−	0.850689i	$-0.676185\pi$
$829$	13.6313	−	25.7114i	0.473435	−	0.892994i	0.999105	−	0.0423048i	$-0.0134700\pi$
$830$	−0.550492	+	1.98269i	−0.0191079	+	0.0688203i
$831$	−2.34051	+	2.21704i	−0.0811912	+	0.0769084i
$832$	0.660519	+	4.02899i	0.0228994	+	0.139680i
$833$	7.13859	+	8.40420i	0.247338	+	0.291188i
$834$	3.15657	+	7.92238i	0.109303	+	0.274330i
$835$	−3.63662	−	5.36361i	−0.125850	−	0.185615i
$836$	5.75857	−	35.1257i	0.199164	−	1.21485i
$837$	−7.95806	+	4.78820i	−0.275071	+	0.165505i
$838$	−21.9926	−	20.8325i	−0.759721	−	0.719646i
$839$	11.5094	−	16.9751i	0.397349	−	0.586045i	−0.575410	−	0.817865i	$-0.695158\pi$
$839$	11.5094	−	16.9751i	0.397349	−	0.586045i	0.972759	+	0.231820i	$0.0744679\pi$
$840$	−1.89497	−	0.417114i	−0.0653827	−	0.0143918i
$841$	9.28602	+	33.4452i	0.320208	+	1.15328i
$842$	−22.1455	−	13.3245i	−0.763185	−	0.459193i
$843$	6.57900	−	7.74540i	0.226593	−	0.266766i
$844$	−26.8738	−	9.05485i	−0.925035	−	0.311681i
$845$	−3.19855	−	1.47981i	−0.110033	−	0.0509069i
$846$	−2.69969	−	5.09216i	−0.0928174	−	0.175072i
$847$	−31.4473	+	6.92207i	−1.08054	+	0.237845i
$848$	1.37541	−	3.45201i	0.0472317	−	0.118543i
$849$	−2.37426	+	0.799982i	−0.0814844	+	0.0274553i
$850$	−15.3099	−	1.66505i	−0.525126	−	0.0571109i
$851$	0.616867	−	11.3774i	0.0211459	−	0.390014i
$852$	−0.478047	−	8.81706i	−0.0163776	−	0.302067i
$853$	−9.97542	+	1.08489i	−0.341552	+	0.0371460i	−0.277288	−	0.960787i	$-0.589436\pi$
$853$	−9.97542	+	1.08489i	−0.341552	+	0.0371460i	−0.0642642	+	0.997933i	$0.520470\pi$
$854$	22.5827	−	10.4479i	0.772763	−	0.357518i
$855$	−5.24402	−	3.98640i	−0.179342	−	0.136332i
$856$	4.39249	+	3.33908i	0.150132	+	0.114127i
$857$	−25.8445	+	11.9570i	−0.882833	+	0.408442i	−0.808296	−	0.588776i	$-0.799610\pi$
$857$	−25.8445	+	11.9570i	−0.882833	+	0.408442i	−0.0745369	+	0.997218i	$0.523748\pi$
$858$	21.0670	−	2.29118i	0.719217	−	0.0782196i
$859$	−0.968956	−	17.8713i	−0.0330604	−	0.609762i	−0.967381	−	0.253328i	$-0.918475\pi$
$859$	−0.968956	−	17.8713i	−0.0330604	−	0.609762i	0.934320	−	0.356435i	$-0.116008\pi$
$860$	0.661681	−	12.2040i	0.0225631	−	0.416152i
$861$	−21.5831	−	2.34730i	−0.735550	−	0.0799959i
$862$	−0.761408	+	0.256548i	−0.0259337	+	0.00873807i
$863$	5.87610	−	14.7479i	0.200025	−	0.502024i	−0.794410	−	0.607382i	$-0.792220\pi$
$863$	5.87610	−	14.7479i	0.200025	−	0.502024i	0.994434	+	0.105358i	$0.0335989\pi$
$864$	−0.976621	+	0.214970i	−0.0332253	+	0.00731344i
$865$	4.58466	+	8.64758i	0.155883	+	0.294026i
$866$	4.81569	+	2.22797i	0.163644	+	0.0757096i
$867$	−2.59110	−	0.873043i	−0.0879984	−	0.0296501i
$868$	12.1457	−	14.2990i	0.412251	−	0.485339i
$869$	48.9796	+	29.4700i	1.66152	+	0.999702i
$870$	−2.05113	−	7.38749i	−0.0695397	−	0.250459i
$871$	43.4425	+	9.56241i	1.47199	+	0.324010i
$872$	−0.267578	+	0.394648i	−0.00906135	+	0.0133645i
$873$	−0.680804	−	0.644892i	−0.0230417	−	0.0218263i
$874$	13.1915	−	7.93705i	0.446208	−	0.268475i
$875$	2.84948	−	17.3811i	0.0963301	−	0.587588i
$876$	3.66340	+	5.40311i	0.123775	+	0.182554i
$877$	−0.237760	−	0.596733i	−0.00802859	−	0.0201502i	0.924908	−	0.380192i	$-0.124142\pi$
$877$	−0.237760	−	0.596733i	−0.00802859	−	0.0201502i	−0.932936	+	0.360041i	$0.882763\pi$
$878$	6.38844	+	7.52105i	0.215599	+	0.253823i
$879$	−3.17339	−	19.3568i	−0.107036	−	0.652888i
$880$	−3.61954	+	3.42861i	−0.122015	+	0.115578i
$881$	−4.05466	+	14.6036i	−0.136605	+	0.492006i	−0.999920	−	0.0126592i	$-0.995970\pi$
$881$	−4.05466	+	14.6036i	−0.136605	+	0.492006i	0.863315	+	0.504665i	$0.168384\pi$
$882$	−1.36750	+	2.57937i	−0.0460460	+	0.0868520i
$883$	−1.14090	+	0.867291i	−0.0383944	+	0.0291867i	−0.624195	−	0.781268i	$-0.714573\pi$
$883$	−1.14090	+	0.867291i	−0.0383944	+	0.0291867i	0.585801	+	0.810455i	$0.300780\pi$
$884$	15.4207			0.518653
$885$	−4.64139	−	5.73529i	−0.156019	−	0.192790i
$886$	−7.59353			−0.255110
$887$	25.0013	−	19.0055i	0.839462	−	0.638143i	−0.0944957	−	0.995525i	$-0.530124\pi$
$887$	25.0013	−	19.0055i	0.839462	−	0.638143i	0.933958	+	0.357383i	$0.116331\pi$
$888$	2.37741	−	4.48428i	0.0797808	−	0.150482i
$889$	6.41587	−	23.1079i	0.215181	−	0.775013i
$890$	7.62999	−	7.22751i	0.255758	−	0.242267i
$891$	0.839715	+	5.12203i	0.0281315	+	0.171595i
$892$	3.40054	+	4.00342i	0.113858	+	0.134044i
$893$	14.6297	+	36.7179i	0.489565	+	1.22872i
$894$	−5.30656	−	7.82660i	−0.177478	−	0.261761i
$895$	0.169605	−	1.03455i	0.00566928	−	0.0345811i
$896$	1.73088	−	1.04144i	0.0578247	−	0.0347920i
$897$	6.65413	+	6.30313i	0.222175	+	0.210455i
$898$	−10.1961	+	15.0381i	−0.340249	+	0.501829i
$899$	72.3985	+	15.9361i	2.41463	+	0.531499i
$900$	−1.09081	−	3.92874i	−0.0363603	−	0.130958i
$901$	−12.0261	−	7.23584i	−0.400646	−	0.241061i
$902$	−36.1138	+	42.5165i	−1.20246	+	1.41564i
$903$	24.3574	+	8.20695i	0.810563	+	0.273110i
$904$	−6.31177	−	2.92014i	−0.209926	−	0.0971223i
$905$	1.46865	+	2.77017i	0.0488196	+	0.0920835i
$906$	15.7398	−	3.46460i	0.522921	−	0.115104i
$907$	10.2367	−	25.6921i	0.339903	−	0.853093i	−0.655310	−	0.755360i	$-0.727462\pi$
$907$	10.2367	−	25.6921i	0.339903	−	0.853093i	0.995213	−	0.0977322i	$-0.0311589\pi$
$908$	24.4243	−	8.22951i	0.810550	−	0.273106i
$909$	−5.29043	−	0.575368i	−0.175472	−	0.0190838i
$910$	−0.428885	+	7.91033i	−0.0142174	+	0.262225i
$911$	1.87998	+	34.6741i	0.0622864	+	1.14881i	0.847924	+	0.530118i	$0.177852\pi$
$911$	1.87998	+	34.6741i	0.0622864	+	1.14881i	−0.785637	+	0.618687i	$0.787665\pi$
$912$	6.81757	−	0.741455i	0.225752	−	0.0245520i
$913$	−10.0913	+	4.66875i	−0.333974	+	0.154513i
$914$	10.3159	+	7.84192i	0.341218	+	0.259388i
$915$	−9.41921	−	7.16030i	−0.311390	−	0.236712i
$916$	−22.1462	+	10.2459i	−0.731729	+	0.338534i
$917$	−22.8399	+	2.48399i	−0.754239	+	0.0820285i
$918$	0.204483	+	3.77147i	0.00674894	+	0.124477i
$919$	0.120441	−	2.22141i	0.00397298	−	0.0732774i	−0.995875	−	0.0907411i	$-0.971076\pi$
$919$	0.120441	−	2.22141i	0.00397298	−	0.0732774i	0.999847	+	0.0174638i	$0.00555917\pi$
$920$	−2.14371	−	0.233142i	−0.0706760	−	0.00768648i
$921$	24.0516	−	8.10391i	0.792526	−	0.267033i
$922$	8.36826	−	21.0028i	0.275594	−	0.691689i
$923$	−35.2081	+	7.74988i	−1.15889	+	0.255090i
$924$	−4.91118	−	9.26346i	−0.161566	−	0.304746i
$925$	18.7820	+	8.68947i	0.617547	+	0.285708i
$926$	−1.36802	−	0.460939i	−0.0449559	−	0.0151474i
$927$	2.96463	−	3.49023i	0.0973711	−	0.114634i
$928$	6.83933	+	4.11509i	0.224512	+	0.135084i
$929$	0.213925	+	0.770488i	0.00701865	+	0.0252789i	0.966976	−	0.254866i	$-0.0820313\pi$
$929$	0.213925	+	0.770488i	0.00701865	+	0.0252789i	−0.959958	+	0.280145i	$0.909618\pi$
$930$	−8.71248	−	1.91776i	−0.285693	−	0.0628859i
$931$	11.2355	−	16.5711i	0.368228	−	0.543096i
$932$	6.14348	+	5.81941i	0.201236	+	0.190621i
$933$	−20.4043	+	12.2768i	−0.668006	+	0.401926i
$934$	2.32597	−	14.1878i	0.0761081	−	0.464239i
$935$	10.5675	+	15.5860i	0.345596	+	0.509716i
$936$	1.51119	+	3.79280i	0.0493948	+	0.123972i
$937$	−12.8796	−	15.1630i	−0.420757	−	0.495354i	0.510418	−	0.859927i	$-0.329491\pi$
$937$	−12.8796	−	15.1630i	−0.420757	−	0.495354i	−0.931175	+	0.364573i	$0.881215\pi$
$938$	−3.56060	−	21.7187i	−0.116258	−	0.709140i
$939$	−6.89704	+	6.53323i	−0.225077	+	0.213204i
$940$	1.48107	−	5.33435i	0.0483073	−	0.173987i
$941$	−8.20101	+	15.4687i	−0.267345	+	0.504267i	−0.980444	−	0.196797i	$-0.936946\pi$
$941$	−8.20101	+	15.4687i	−0.267345	+	0.504267i	0.713099	+	0.701063i	$0.247291\pi$
$942$	−2.75495	+	2.09426i	−0.0897611	+	0.0682346i
$943$	−24.1274			−0.785695
$944$	7.61421	+	1.01184i	0.247821	+	0.0329325i
$945$	−1.94033			−0.0631191
$946$	52.5760	−	39.9672i	1.70939	−	1.29945i
$947$	−25.5360	+	48.1659i	−0.829807	+	1.56518i	−0.00484870	+	0.999988i	$0.501543\pi$
$947$	−25.5360	+	48.1659i	−0.829807	+	1.56518i	−0.824958	+	0.565194i	$0.808801\pi$
$948$	−2.94628	+	10.6116i	−0.0956908	+	0.344647i
$949$	19.3493	−	18.3287i	0.628106	−	0.594973i
$950$	4.52368	+	27.5932i	0.146767	+	0.895242i
$951$	14.1476	+	16.6558i	0.458766	+	0.540101i
$952$	−2.82404	−	7.08780i	−0.0915276	−	0.229717i
$953$	−3.66579	−	5.40664i	−0.118747	−	0.175138i	0.763670	−	0.645606i	$-0.223395\pi$
$953$	−3.66579	−	5.40664i	−0.118747	−	0.175138i	−0.882417	+	0.470468i	$0.844085\pi$
$954$	0.601170	−	3.66698i	0.0194636	−	0.118723i
$955$	−16.2610	+	9.78390i	−0.526193	+	0.316600i
$956$	−15.9609	−	15.1190i	−0.516213	−	0.488983i
$957$	23.2496	−	34.2905i	0.751551	−	1.10846i
$958$	29.1156	+	6.40882i	0.940681	+	0.207060i
$959$	1.51264	+	5.44804i	0.0488457	+	0.175926i
$960$	−0.823049	−	0.495212i	−0.0265638	−	0.0159829i
$961$	35.7730	−	42.1152i	1.15397	−	1.35855i
$962$	−19.6374	−	6.61662i	−0.633136	−	0.213328i
$963$	5.00760	+	2.31676i	0.161367	+	0.0746566i
$964$	3.78943	+	7.14762i	0.122049	+	0.230209i
$965$	−3.55545	+	0.782613i	−0.114454	+	0.0251932i
$966$	1.67851	−	4.21275i	0.0540053	−	0.135543i
$967$	−25.5071	+	8.59435i	−0.820254	+	0.276376i	−0.697977	−	0.716120i	$-0.745916\pi$
$967$	−25.5071	+	8.59435i	−0.820254	+	0.276376i	−0.122277	+	0.992496i	$0.539020\pi$
$968$	−15.8469	−	1.72346i	−0.509339	−	0.0553940i
$969$	1.40230	−	25.8638i	0.0450483	−	0.830867i
$970$	−0.0487658	−	0.899432i	−0.00156577	−	0.0288790i
$971$	−42.7513	+	4.64949i	−1.37196	+	0.149209i	−0.764233	−	0.644940i	$-0.776882\pi$
$971$	−42.7513	+	4.64949i	−1.37196	+	0.149209i	−0.607722	+	0.794150i	$0.707917\pi$
$972$	−0.907575	+	0.419889i	−0.0291105	+	0.0134679i
$973$	−13.7143	−	10.4254i	−0.439661	−	0.334221i
$974$	−27.6510	−	21.0197i	−0.885994	−	0.673515i
$975$	−15.1083	+	6.98986i	−0.483854	+	0.223855i
$976$	12.2456	−	1.33179i	0.391972	−	0.0426295i
$977$	−1.65316	−	30.4907i	−0.0528892	−	0.975485i	−0.897752	−	0.440501i	$-0.854801\pi$
$977$	−1.65316	−	30.4907i	−0.0528892	−	0.975485i	0.844863	−	0.534983i	$-0.179682\pi$
$978$	0.657497	−	12.1268i	0.0210244	−	0.387773i
$979$	56.4574	+	6.14012i	1.80439	+	0.196239i
$980$	−2.65747	+	0.895406i	−0.0848897	+	0.0286027i
$981$	−0.176485	+	0.442943i	−0.00563472	+	0.0141421i
$982$	−21.4847	+	4.72913i	−0.685603	+	0.150913i
$983$	−1.12098	−	2.11440i	−0.0357538	−	0.0674388i	0.864991	−	0.501787i	$-0.167324\pi$
$983$	−1.12098	−	2.11440i	−0.0357538	−	0.0674388i	−0.900745	+	0.434348i	$0.856979\pi$
$984$	−9.75418	−	4.51276i	−0.310952	−	0.143862i
$985$	−13.6465	−	4.59805i	−0.434814	−	0.146506i
$986$	19.5171	−	22.9774i	0.621553	−	0.731748i
$987$	9.97602	+	6.00237i	0.317540	+	0.191058i
$988$	−7.49045	−	26.9782i	−0.238303	−	0.858290i
$989$	27.8965	+	6.14048i	0.887057	+	0.195256i
$990$	−2.79786	+	4.12654i	−0.0889220	+	0.131150i
$991$	10.2355	+	9.69558i	0.325141	+	0.307990i	0.832806	−	0.553564i	$-0.186733\pi$
$991$	10.2355	+	9.69558i	0.325141	+	0.307990i	−0.507665	+	0.861554i	$0.669491\pi$
$992$	7.95806	−	4.78820i	0.252669	−	0.152026i
$993$	0.825051	−	5.03259i	0.0261822	−	0.159704i
$994$	10.0099	+	14.7634i	0.317493	+	0.468268i
$995$	−1.50154	−	3.76857i	−0.0476019	−	0.119472i
$996$	−1.38684	−	1.63272i	−0.0439438	−	0.0517347i
$997$	0.338353	+	2.06386i	0.0107158	+	0.0653632i	0.991643	−	0.129012i	$-0.0411805\pi$
$997$	0.338353	+	2.06386i	0.0107158	+	0.0653632i	−0.980927	+	0.194375i	$0.937732\pi$
$998$	−4.32605	+	4.09785i	−0.136939	+	0.129715i
$999$	1.35784	−	4.89051i	0.0429603	−	0.154729i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.85.2	yes	84
59.25	even	29	inner	354.2.e.c.25.2	✓	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.25.2	✓	84	59.25	even	29	inner
354.2.e.c.85.2	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.697351 - 0.660566i) q^{5} +(0.161782 + 0.986827i) q^{6} +(-1.30774 - 1.53959i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +O(q^{10})\)	\(q+(0.796093 - 0.605174i) q^{2} +(-0.468408 + 0.883512i) q^{3} +(0.267528 - 0.963550i) q^{4} +(0.697351 - 0.660566i) q^{5} +(0.161782 + 0.986827i) q^{6} +(-1.30774 - 1.53959i) q^{7} +(-0.370138 - 0.928977i) q^{8} +(-0.561187 - 0.827689i) q^{9} +(0.155399 - 0.947890i) q^{10} +(4.44744 - 2.67594i) q^{11} +(0.725995 + 0.687699i) q^{12} +(2.29120 - 3.37927i) q^{13} +(-1.97281 - 0.434248i) q^{14} +(0.256973 + 0.925532i) q^{15} +(-0.856857 - 0.515554i) q^{16} +(-2.44518 + 2.87869i) q^{17} +(-0.947653 - 0.319302i) q^{18} +(6.22394 + 2.87950i) q^{19} +(-0.449927 - 0.848652i) q^{20} +(1.97281 - 0.434248i) q^{21} +(1.92117 - 4.82177i) q^{22} +(2.12741 - 0.716808i) q^{23} +(0.994138 + 0.108119i) q^{24} +(-0.220744 + 4.07138i) q^{25} +(-0.221037 - 4.07679i) q^{26} +(0.994138 - 0.108119i) q^{27} +(-1.83334 + 0.848191i) q^{28} +(-6.35432 - 4.83043i) q^{29} +(0.764682 + 0.581297i) q^{30} +(-8.42910 + 3.89972i) q^{31} +(-0.994138 + 0.108119i) q^{32} +(0.281003 + 5.18280i) q^{33} +(-0.204483 + 3.77147i) q^{34} +(-1.92896 - 0.209787i) q^{35} +(-0.947653 + 0.319302i) q^{36} +(1.87864 - 4.71503i) q^{37} +(6.69744 - 1.47422i) q^{38} +(1.91241 + 3.60718i) q^{39} +(-0.871766 - 0.403322i) q^{40} +(-10.1849 - 3.43170i) q^{41} +(1.30774 - 1.53959i) q^{42} +(10.9026 + 6.55988i) q^{43} +(-1.38858 - 5.00122i) q^{44} +(-0.938087 - 0.206489i) q^{45} +(1.25982 - 1.85810i) q^{46} +(4.18431 + 3.96359i) q^{47} +(0.856857 - 0.515554i) q^{48} +(0.472315 - 2.88099i) q^{49} +(2.28816 + 3.37478i) q^{50} +(-1.39801 - 3.50875i) q^{51} +(-2.64313 - 3.11174i) q^{52} +(0.601170 + 3.66698i) q^{53} +(0.725995 - 0.687699i) q^{54} +(1.33379 - 4.80389i) q^{55} +(-0.946202 + 1.78473i) q^{56} +(-5.45942 + 4.15015i) q^{57} -7.98188 q^{58} +(-7.04595 + 3.05854i) q^{59} +0.960544 q^{60} +(-9.80612 + 7.45442i) q^{61} +(-4.35034 + 8.20561i) q^{62} +(-0.540417 + 1.94641i) q^{63} +(-0.725995 + 0.687699i) q^{64} +(-0.634458 - 3.87002i) q^{65} +(3.36020 + 3.95593i) q^{66} +(4.03271 + 10.1213i) q^{67} +(2.11961 + 3.12619i) q^{68} +(-0.363189 + 2.21535i) q^{69} +(-1.66259 + 1.00035i) q^{70} +(-6.41054 - 6.07239i) q^{71} +(-0.561187 + 0.827689i) q^{72} +(6.37533 + 1.40332i) q^{73} +(-1.35784 - 4.89051i) q^{74} +(-3.49371 - 2.10210i) q^{75} +(4.43963 - 5.22673i) q^{76} +(-9.93597 - 3.34782i) q^{77} +(3.70543 + 1.71431i) q^{78} +(5.15857 + 9.73010i) q^{79} +(-0.938087 + 0.206489i) q^{80} +(-0.370138 + 0.928977i) q^{81} +(-10.1849 + 3.43170i) q^{82} +(-2.12966 - 0.231615i) q^{83} +(0.109363 - 2.01707i) q^{84} +(0.196415 + 3.62266i) q^{85} +(12.6494 - 1.37570i) q^{86} +(7.24416 - 3.35150i) q^{87} +(-4.13205 - 3.14110i) q^{88} +(8.71037 + 6.62145i) q^{89} +(-0.871766 + 0.403322i) q^{90} +(-8.19901 + 0.891696i) q^{91} +(-0.121538 - 2.24163i) q^{92} +(0.502815 - 9.27387i) q^{93} +(5.72976 + 0.623149i) q^{94} +(6.24237 - 2.10330i) q^{95} +(0.370138 - 0.928977i) q^{96} +(0.915829 - 0.201589i) q^{97} +(-1.36750 - 2.57937i) q^{98} +(-4.71069 - 2.17940i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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