LMFDB - Embedded newform 125.2.h.a.104.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(4,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("125.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.h (of order $50$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			104.6
Character	$\chi$	$=$	125.104
Dual form			125.2.h.a.119.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.150619 - 0.586621i) q^{2} +(-2.96797 + 0.566170i) q^{3} +(1.43117 - 0.786795i) q^{4} +(1.03654 + 1.98131i) q^{5} +(0.779158 + 1.65580i) q^{6} +(2.97825 - 4.09921i) q^{7} +(-1.50630 - 1.60405i) q^{8} +(5.69894 - 2.25637i) q^{9} +O(q^{10})$	\(q+(-0.150619 - 0.586621i) q^{2} +(-2.96797 + 0.566170i) q^{3} +(1.43117 - 0.786795i) q^{4} +(1.03654 + 1.98131i) q^{5} +(0.779158 + 1.65580i) q^{6} +(2.97825 - 4.09921i) q^{7} +(-1.50630 - 1.60405i) q^{8} +(5.69894 - 2.25637i) q^{9} +(1.00616 - 0.906479i) q^{10} +(0.644855 - 0.165571i) q^{11} +(-3.80222 + 3.14547i) q^{12} +(0.641704 + 1.62076i) q^{13} +(-2.85327 - 1.12969i) q^{14} +(-4.19817 - 5.29360i) q^{15} +(1.03612 - 1.63267i) q^{16} +(-0.790438 + 1.43780i) q^{17} +(-2.18200 - 3.00327i) q^{18} +(-0.166592 + 0.873305i) q^{19} +(3.04235 + 2.02005i) q^{20} +(-6.51850 + 13.8525i) q^{21} +(-0.194254 - 0.353347i) q^{22} +(3.83432 + 0.241235i) q^{23} +(5.37882 + 3.90794i) q^{24} +(-2.85117 + 4.10741i) q^{25} +(0.854119 - 0.620554i) q^{26} +(-7.98340 + 5.06642i) q^{27} +(1.03716 - 8.20997i) q^{28} +(-4.85783 - 0.613686i) q^{29} +(-2.47301 + 3.26005i) q^{30} +(-4.26257 - 2.34337i) q^{31} +(-5.29930 - 1.72185i) q^{32} +(-1.82017 + 0.856505i) q^{33} +(0.962499 + 0.247128i) q^{34} +(11.2089 + 1.65184i) q^{35} +(6.38088 - 7.71316i) q^{36} +(1.87620 + 1.19068i) q^{37} +(0.537391 - 0.0338098i) q^{38} +(-2.82218 - 4.44704i) q^{39} +(1.61677 - 4.64711i) q^{40} +(0.0553140 + 0.879191i) q^{41} +(9.10799 + 1.73744i) q^{42} +(-5.21297 + 1.69380i) q^{43} +(0.792630 - 0.744329i) q^{44} +(10.3777 + 8.95254i) q^{45} +(-0.436007 - 2.28563i) q^{46} +(-4.01220 + 4.27256i) q^{47} +(-2.15081 + 5.43232i) q^{48} +(-5.77044 - 17.7596i) q^{49} +(2.83893 + 1.05390i) q^{50} +(1.53195 - 4.71486i) q^{51} +(2.19360 + 1.81470i) q^{52} +(5.99702 + 2.82199i) q^{53} +(4.17452 + 3.92013i) q^{54} +(0.996464 + 1.10604i) q^{55} +(-11.0615 + 1.39739i) q^{56} -2.68626i q^{57} +(0.371678 + 2.94214i) q^{58} +(2.85719 + 3.45375i) q^{59} +(-10.1733 - 4.27296i) q^{60} +(-0.497506 + 7.90763i) q^{61} +(-0.732646 + 2.85347i) q^{62} +(7.72354 - 30.0812i) q^{63} +(0.0309366 - 0.491723i) q^{64} +(-2.54607 + 2.95140i) q^{65} +(0.776595 + 0.938742i) q^{66} +(0.307262 + 2.43223i) q^{67} +2.67966i q^{68} +(-11.5167 + 1.45490i) q^{69} +(-0.719264 - 6.82417i) q^{70} +(0.971397 + 0.912203i) q^{71} +(-12.2037 - 5.74261i) q^{72} +(10.6537 + 8.81348i) q^{73} +(0.415884 - 1.27996i) q^{74} +(6.13668 - 13.8049i) q^{75} +(0.448690 + 1.38093i) q^{76} +(1.24183 - 3.13651i) q^{77} +(-2.18366 + 2.32536i) q^{78} +(0.614971 + 3.22379i) q^{79} +(4.30880 + 0.360552i) q^{80} +(7.42165 - 6.96939i) q^{81} +(0.507421 - 0.164871i) q^{82} +(-11.9766 - 2.28466i) q^{83} +(1.56998 + 24.9541i) q^{84} +(-3.66805 - 0.0757628i) q^{85} +(1.77879 + 2.80292i) q^{86} +(14.7653 - 0.928955i) q^{87} +(-1.23693 - 0.784979i) q^{88} +(-1.29962 + 1.57097i) q^{89} +(3.68867 - 7.43623i) q^{90} +(8.55500 + 2.19655i) q^{91} +(5.67739 - 2.67158i) q^{92} +(13.9779 + 4.54170i) q^{93} +(3.11069 + 1.71011i) q^{94} +(-1.90296 + 0.575146i) q^{95} +(16.7030 + 2.11008i) q^{96} +(2.12322 - 16.8070i) q^{97} +(-9.54902 + 6.05999i) q^{98} +(3.30140 - 2.39861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{21}{50}\right)$

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 $

$2$	−0.150619	−	0.586621i	−0.106504	−	0.414804i	0.892865	−	0.450324i	$-0.148691\pi$
$2$	−0.150619	−	0.586621i	−0.106504	−	0.414804i	−0.999369	+	0.0355197i	$0.988691\pi$
$3$	−2.96797	+	0.566170i	−1.71356	+	0.326878i	−0.948426	−	0.316998i	$-0.897325\pi$
$3$	−2.96797	+	0.566170i	−1.71356	+	0.326878i	−0.765129	+	0.643877i	$0.777325\pi$
$4$	1.43117	−	0.786795i	0.715587	−	0.393398i
$5$	1.03654	+	1.98131i	0.463555	+	0.886068i
$5$	1.03654	+	1.98131i	0.463555	+	0.886068i
$6$	0.779158	+	1.65580i	0.318090	+	0.675976i
$7$	2.97825	−	4.09921i	1.12567	−	1.54936i	0.329638	−	0.944107i	$-0.393073\pi$
$7$	2.97825	−	4.09921i	1.12567	−	1.54936i	0.796036	−	0.605250i	$-0.206927\pi$
$8$	−1.50630	−	1.60405i	−0.532558	−	0.567117i
$9$	5.69894	−	2.25637i	1.89965	−	0.752123i
$10$	1.00616	−	0.906479i	0.318174	−	0.286654i
$11$	0.644855	−	0.165571i	0.194431	−	0.0499214i	−0.150219	−	0.988653i	$-0.547998\pi$
$11$	0.644855	−	0.165571i	0.194431	−	0.0499214i	0.344650	+	0.938731i	$0.387998\pi$
$12$	−3.80222	+	3.14547i	−1.09761	+	0.908019i
$13$	0.641704	+	1.62076i	0.177977	+	0.449518i	0.991190	−	0.132448i	$-0.0422838\pi$
$13$	0.641704	+	1.62076i	0.177977	+	0.449518i	−0.813213	+	0.581966i	$0.802284\pi$
$14$	−2.85327	−	1.12969i	−0.762567	−	0.301922i
$15$	−4.19817	−	5.29360i	−1.08396	−	1.36680i
$16$	1.03612	−	1.63267i	0.259030	−	0.408167i
$17$	−0.790438	+	1.43780i	−0.191709	+	0.348718i	−0.954640	−	0.297762i	$-0.903760\pi$
$17$	−0.790438	+	1.43780i	−0.191709	+	0.348718i	0.762931	+	0.646480i	$0.223760\pi$
$18$	−2.18200	−	3.00327i	−0.514303	−	0.707877i
$19$	−0.166592	+	0.873305i	−0.0382188	+	0.200350i	−0.996275	−	0.0862295i	$-0.972518\pi$
$19$	−0.166592	+	0.873305i	−0.0382188	+	0.200350i	0.958057	+	0.286579i	$0.0925182\pi$
$20$	3.04235	+	2.02005i	0.680291	+	0.451698i
$21$	−6.51850	+	13.8525i	−1.42245	+	3.02287i
$22$	−0.194254	−	0.353347i	−0.0414152	−	0.0753339i
$23$	3.83432	+	0.241235i	0.799512	+	0.0503010i	0.457289	−	0.889318i	$-0.348820\pi$
$23$	3.83432	+	0.241235i	0.799512	+	0.0503010i	0.342222	+	0.939619i	$0.388820\pi$
$24$	5.37882	+	3.90794i	1.09795	+	0.797705i
$25$	−2.85117	+	4.10741i	−0.570234	+	0.821482i
$26$	0.854119	−	0.620554i	0.167507	−	0.121701i
$27$	−7.98340	+	5.06642i	−1.53641	+	0.975033i
$28$	1.03716	−	8.20997i	0.196005	−	1.55154i
$29$	−4.85783	−	0.613686i	−0.902076	−	0.113959i	−0.339405	−	0.940640i	$-0.610226\pi$
$29$	−4.85783	−	0.613686i	−0.902076	−	0.113959i	−0.562670	+	0.826682i	$0.690226\pi$
$30$	−2.47301	+	3.26005i	−0.451508	+	0.595201i
$31$	−4.26257	−	2.34337i	−0.765580	−	0.420881i	0.0505703	−	0.998721i	$-0.483896\pi$
$31$	−4.26257	−	2.34337i	−0.765580	−	0.420881i	−0.816151	+	0.577839i	$0.803896\pi$
$32$	−5.29930	−	1.72185i	−0.936792	−	0.304382i
$33$	−1.82017	+	0.856505i	−0.316850	+	0.149098i
$34$	0.962499	+	0.247128i	0.165067	+	0.0423821i
$35$	11.2089	+	1.65184i	1.89465	+	0.279212i
$36$	6.38088	−	7.71316i	1.06348	−	1.28553i
$37$	1.87620	+	1.19068i	0.308446	+	0.195746i	0.681035	−	0.732250i	$-0.261530\pi$
$37$	1.87620	+	1.19068i	0.308446	+	0.195746i	−0.372589	+	0.927996i	$0.621530\pi$
$38$	0.537391	−	0.0338098i	0.0871763	−	0.00548467i
$39$	−2.82218	−	4.44704i	−0.451910	−	0.712097i
$40$	1.61677	−	4.64711i	0.255634	−	0.734773i
$41$	0.0553140	+	0.879191i	0.00863860	+	0.137307i	0.999982	+	0.00601150i	$0.00191353\pi$
$41$	0.0553140	+	0.879191i	0.00863860	+	0.137307i	−0.991343	+	0.131295i	$0.958086\pi$
$42$	9.10799	+	1.73744i	1.40539	+	0.268093i
$43$	−5.21297	+	1.69380i	−0.794970	+	0.258302i	−0.678219	−	0.734860i	$-0.737248\pi$
$43$	−5.21297	+	1.69380i	−0.794970	+	0.258302i	−0.116751	+	0.993161i	$0.537248\pi$
$44$	0.792630	−	0.744329i	0.119493	−	0.112212i
$45$	10.3777	+	8.95254i	1.54702	+	1.33457i
$46$	−0.436007	−	2.28563i	−0.0642858	−	0.336998i
$47$	−4.01220	+	4.27256i	−0.585240	+	0.623217i	−0.951631	−	0.307244i	$-0.900593\pi$
$47$	−4.01220	+	4.27256i	−0.585240	+	0.623217i	0.366391	+	0.930461i	$0.380593\pi$
$48$	−2.15081	+	5.43232i	−0.310442	+	0.784088i
$49$	−5.77044	−	17.7596i	−0.824349	−	2.53708i
$50$	2.83893	+	1.05390i	0.401486	+	0.149044i
$51$	1.53195	−	4.71486i	0.214516	−	0.660213i
$52$	2.19360	+	1.81470i	0.304197	+	0.251654i
$53$	5.99702	+	2.82199i	0.823755	+	0.387629i	0.790987	−	0.611834i	$-0.209568\pi$
$53$	5.99702	+	2.82199i	0.823755	+	0.387629i	0.0327680	+	0.999463i	$0.489568\pi$
$54$	4.17452	+	3.92013i	0.568080	+	0.533463i
$55$	0.996464	+	1.10604i	0.134363	+	0.149138i
$56$	−11.0615	+	1.39739i	−1.47815	+	0.186734i
$57$		−	2.68626i		−	0.355803i
$58$	0.371678	+	2.94214i	0.0488037	+	0.386321i
$59$	2.85719	+	3.45375i	0.371974	+	0.449639i	0.922972	−	0.384867i	$-0.125753\pi$
$59$	2.85719	+	3.45375i	0.371974	+	0.449639i	−0.550998	+	0.834507i	$0.685753\pi$
$60$	−10.1733	−	4.27296i	−1.31337	−	0.551637i
$61$	−0.497506	+	7.90763i	−0.0636991	+	1.01247i	0.828258	+	0.560347i	$0.189332\pi$
$61$	−0.497506	+	7.90763i	−0.0636991	+	1.01247i	−0.891957	+	0.452121i	$0.850668\pi$
$62$	−0.732646	+	2.85347i	−0.0930462	+	0.362391i
$63$	7.72354	−	30.0812i	0.973075	−	3.78988i
$64$	0.0309366	−	0.491723i	0.00386707	−	0.0614654i
$65$	−2.54607	+	2.95140i	−0.315801	+	0.366076i
$66$	0.776595	+	0.938742i	0.0955922	+	0.115551i
$67$	0.307262	+	2.43223i	0.0375381	+	0.297144i	0.999696	+	0.0246523i	$0.00784786\pi$
$67$	0.307262	+	2.43223i	0.0375381	+	0.297144i	−0.962158	+	0.272492i	$0.912152\pi$
$68$			2.67966i			0.324956i
$69$	−11.5167	+	1.45490i	−1.38645	+	0.175149i
$70$	−0.719264	−	6.82417i	−0.0859685	−	0.815644i
$71$	0.971397	+	0.912203i	0.115284	+	0.108259i	0.740045	−	0.672557i	$-0.234804\pi$
$71$	0.971397	+	0.912203i	0.115284	+	0.108259i	−0.624762	+	0.780815i	$0.714804\pi$
$72$	−12.2037	−	5.74261i	−1.43821	−	0.676772i
$73$	10.6537	+	8.81348i	1.24692	+	1.03154i	0.998013	+	0.0630124i	$0.0200708\pi$
$73$	10.6537	+	8.81348i	1.24692	+	1.03154i	0.248905	+	0.968528i	$0.419929\pi$
$74$	0.415884	−	1.27996i	0.0483455	−	0.148792i
$75$	6.13668	−	13.8049i	0.708603	−	1.59405i
$76$	0.448690	+	1.38093i	0.0514682	+	0.158403i
$77$	1.24183	−	3.13651i	0.141520	−	0.357438i
$78$	−2.18366	+	2.32536i	−0.247250	+	0.263295i
$79$	0.614971	+	3.22379i	0.0691896	+	0.362705i	0.999996	−	0.00280775i	$-0.000893737\pi$
$79$	0.614971	+	3.22379i	0.0691896	+	0.362705i	−0.930806	+	0.365513i	$0.880894\pi$
$80$	4.30880	+	0.360552i	0.481738	+	0.0403110i
$81$	7.42165	−	6.96939i	0.824628	−	0.774377i
$82$	0.507421	−	0.164871i	0.0560352	−	0.0182070i
$83$	−11.9766	−	2.28466i	−1.31461	−	0.250775i	−0.518056	−	0.855347i	$-0.673344\pi$
$83$	−11.9766	−	2.28466i	−1.31461	−	0.250775i	−0.796550	+	0.604572i	$0.793344\pi$
$84$	1.56998	+	24.9541i	0.171299	+	2.72272i
$85$	−3.66805	−	0.0757628i	−0.397856	−	0.00821763i
$86$	1.77879	+	2.80292i	0.191812	+	0.302247i
$87$	14.7653	−	0.928955i	1.58301	−	0.0995944i
$88$	−1.23693	−	0.784979i	−0.131857	−	0.0836791i
$89$	−1.29962	+	1.57097i	−0.137760	+	0.166523i	−0.834881	−	0.550430i	$-0.814464\pi$
$89$	−1.29962	+	1.57097i	−0.137760	+	0.166523i	0.697122	+	0.716953i	$0.254464\pi$
$90$	3.68867	−	7.43623i	0.388820	−	0.783847i
$91$	8.55500	+	2.19655i	0.896807	+	0.230261i
$92$	5.67739	−	2.67158i	0.591909	−	0.278531i
$93$	13.9779	+	4.54170i	1.44944	+	0.470952i
$94$	3.11069	+	1.71011i	0.320843	+	0.176385i
$95$	−1.90296	+	0.575146i	−0.195240	+	0.0590087i
$96$	16.7030	+	2.11008i	1.70474	+	0.215359i
$97$	2.12322	−	16.8070i	0.215580	−	1.70649i	−0.398432	−	0.917198i	$-0.630446\pi$
$97$	2.12322	−	16.8070i	0.215580	−	1.70649i	0.614012	−	0.789296i	$-0.289554\pi$
$98$	−9.54902	+	6.05999i	−0.964596	+	0.612151i
$99$	3.30140	−	2.39861i	0.331803	−	0.241069i
$100$	−0.848830	+	8.12171i	−0.0848830	+	0.812171i
$101$	−1.74107	−	1.26496i	−0.173243	−	0.125869i	0.497785	−	0.867301i	$-0.334147\pi$
$101$	−1.74107	−	1.26496i	−0.173243	−	0.125869i	−0.671028	+	0.741432i	$0.734147\pi$
$102$	−2.99658	−	0.188529i	−0.296706	−	0.0186671i
$103$	3.15628	+	5.74126i	0.310998	+	0.565703i	0.984901	−	0.173116i	$-0.0553836\pi$
$103$	3.15628	+	5.74126i	0.310998	+	0.565703i	−0.673903	+	0.738819i	$0.735384\pi$
$104$	1.63318	−	3.47068i	0.160146	−	0.340328i
$105$	−34.2028	+	1.44353i	−3.33785	+	0.140874i
$106$	0.752172	−	3.94302i	0.0730574	−	0.382980i
$107$	−10.8720	−	14.9640i	−1.05103	−	1.44663i	−0.887908	−	0.460020i	$-0.847842\pi$
$107$	−10.8720	−	14.9640i	−1.05103	−	1.44663i	−0.163127	−	0.986605i	$-0.552158\pi$
$108$	−7.43941	+	13.5322i	−0.715857	+	1.30214i
$109$	−1.18329	+	1.86457i	−0.113339	+	0.178593i	−0.896262	−	0.443525i	$-0.853728\pi$
$109$	−1.18329	+	1.86457i	−0.113339	+	0.178593i	0.782923	+	0.622118i	$0.213728\pi$
$110$	0.498738	−	0.751137i	0.0475528	−	0.0716181i
$111$	−6.24264	−	2.47163i	−0.592525	−	0.234597i
$112$	−3.60682	−	9.10978i	−0.340812	−	0.860793i
$113$	−11.0522	+	9.14314i	−1.03970	+	0.860114i	−0.990339	−	0.138667i	$-0.955718\pi$
$113$	−11.0522	+	9.14314i	−1.03970	+	0.860114i	−0.0493600	+	0.998781i	$0.515718\pi$
$114$	−1.57582	+	0.404601i	−0.147589	+	0.0378943i
$115$	3.49647	+	7.84703i	0.326047	+	0.731739i
$116$	−7.43524	+	2.94382i	−0.690345	+	0.273327i
$117$	7.31407	+	7.78869i	0.676186	+	0.720065i
$118$	1.59569	−	2.19628i	0.146896	−	0.202184i
$119$	3.53973	+	7.52231i	0.324486	+	0.689569i
$120$	−2.16747	+	14.7078i	−0.197862	+	1.34264i
$121$	−9.25095	+	5.08575i	−0.840995	+	0.462341i
$122$	4.71372	−	0.899189i	0.426760	−	0.0814088i
$123$	−0.661941	−	2.57809i	−0.0596852	−	0.232459i
$124$	−7.94424			−0.713413
$125$	−11.0934	−	1.39155i	−0.992224	−	0.124464i
$126$	−18.8096			−1.67569
$127$	3.02034	+	11.7634i	0.268012	+	1.04384i	0.949944	+	0.312421i	$0.101140\pi$
$127$	3.02034	+	11.7634i	0.268012	+	1.04384i	−0.681932	+	0.731416i	$0.738860\pi$
$128$	−11.2397	+	2.14410i	−0.993462	+	0.189513i
$129$	14.5129	−	7.97855i	1.27779	−	0.702473i
$130$	2.11484	+	1.04904i	0.185484	+	0.0920073i
$131$	−0.890013	−	1.89137i	−0.0777608	−	0.165250i	0.862166	−	0.506625i	$-0.169107\pi$
$131$	−0.890013	−	1.89137i	−0.0777608	−	0.165250i	−0.939927	+	0.341375i	$0.889107\pi$
$132$	−1.93108	+	2.65791i	−0.168079	+	0.231341i
$133$	3.08371	+	3.28382i	0.267392	+	0.284743i
$134$	1.38052	−	0.546586i	0.119259	−	0.0472178i
$135$	−18.3133	−	10.5660i	−1.57615	−	0.909379i
$136$	3.49694	−	0.897862i	0.299860	−	0.0769910i
$137$	14.6433	−	12.1140i	1.25107	−	1.03497i	0.253353	−	0.967374i	$-0.418467\pi$
$137$	14.6433	−	12.1140i	1.25107	−	1.03497i	0.997713	−	0.0675971i	$-0.0215333\pi$
$138$	2.58811	+	6.53682i	0.220314	+	0.556451i
$139$	−15.4724	−	6.12595i	−1.31235	−	0.519596i	−0.395367	−	0.918523i	$-0.629383\pi$
$139$	−15.4724	−	6.12595i	−1.31235	−	0.519596i	−0.916983	+	0.398927i	$0.869383\pi$
$140$	17.3415	−	6.45503i	1.46563	−	0.545549i
$141$	9.48908	−	14.9524i	0.799125	−	1.25922i
$142$	0.388807	−	0.707237i	0.0326279	−	0.0593500i
$143$	0.682156	+	0.938907i	0.0570447	+	0.0785153i
$144$	2.22090	−	11.6423i	0.185075	−	0.970195i
$145$	−3.81943	−	10.2610i	−0.317186	−	0.852127i
$146$	3.56553	−	7.57714i	0.295086	−	0.627089i
$147$	27.1814	+	49.4428i	2.24189	+	4.07797i
$148$	3.62200	+	0.227877i	0.297726	+	0.0187313i
$149$	11.2607	+	8.18140i	0.922515	+	0.670246i	0.944149	−	0.329520i	$-0.106887\pi$
$149$	11.2607	+	8.18140i	0.922515	+	0.670246i	−0.0216339	+	0.999766i	$0.506887\pi$
$150$	−9.02255	−	1.52063i	−0.736688	−	0.124159i
$151$	−9.19910	+	6.68354i	−0.748612	+	0.543899i	−0.895396	−	0.445270i	$-0.853108\pi$
$151$	−9.19910	+	6.68354i	−0.748612	+	0.543899i	0.146784	+	0.989169i	$0.453108\pi$
$152$	1.65176	−	1.04824i	0.133976	−	0.0850234i
$153$	−1.26045	+	9.97746i	−0.101901	+	0.806630i
$154$	−2.02698	−	0.256068i	−0.163339	−	0.0206345i
$155$	0.224610	−	10.8745i	0.0180411	−	0.873458i
$156$	−7.53795	−	4.14402i	−0.603519	−	0.331787i
$157$	10.5682	+	3.43380i	0.843431	+	0.274047i	0.698692	−	0.715423i	$-0.253766\pi$
$157$	10.5682	+	3.43380i	0.843431	+	0.274047i	0.144739	+	0.989470i	$0.453766\pi$
$158$	1.79852	−	0.846318i	0.143082	−	0.0673295i
$159$	−19.3967	−	4.98022i	−1.53826	−	0.394957i
$160$	−2.08143	−	12.2843i	−0.164551	−	0.971159i
$161$	12.4085	−	14.9993i	0.977924	−	1.18211i
$162$	−5.20623	−	3.30398i	−0.409040	−	0.259585i
$163$	9.14909	−	0.575612i	0.716612	−	0.0450854i	0.299702	−	0.954033i	$-0.403113\pi$
$163$	9.14909	−	0.575612i	0.716612	−	0.0450854i	0.416910	+	0.908948i	$0.363113\pi$
$164$	0.770907	+	1.21476i	0.0601977	+	0.0948565i
$165$	−3.58367	−	2.71851i	−0.278989	−	0.211636i
$166$	0.463672	+	7.36986i	0.0359879	+	0.572012i
$167$	−17.2353	−	3.28781i	−1.33371	−	0.254418i	−0.529269	−	0.848454i	$-0.677534\pi$
$167$	−17.2353	−	3.28781i	−1.33371	−	0.254418i	−0.804438	+	0.594036i	$0.797534\pi$
$168$	32.0390	−	10.4101i	2.47186	−	0.803156i
$169$	7.26152	−	6.81902i	0.558578	−	0.524540i
$170$	0.508033	+	2.16317i	0.0389643	+	0.165907i
$171$	1.02110	+	5.35280i	0.0780856	+	0.409339i
$172$	−6.12800	+	6.52566i	−0.467256	+	0.497577i
$173$	6.50798	−	16.4373i	0.494793	−	1.24970i	−0.441113	−	0.897452i	$-0.645416\pi$
$173$	6.50798	−	16.4373i	0.494793	−	1.24970i	0.935905	−	0.352252i	$-0.114584\pi$
$174$	−2.76888	−	8.52172i	−0.209908	−	0.646030i
$175$	8.34566	+	23.9205i	0.630872	+	1.80822i
$176$	0.397826	−	1.22438i	0.0299873	−	0.0922914i
$177$	−10.4354	−	8.63294i	−0.784375	−	0.648892i
$178$	1.11731	+	0.525768i	0.0837462	+	0.0394080i
$179$	14.5648	+	13.6773i	1.08862	+	1.02229i	0.999655	+	0.0262521i	$0.00835727\pi$
$179$	14.5648	+	13.6773i	1.08862	+	1.02229i	0.0889692	+	0.996034i	$0.471643\pi$
$180$	21.8962	+	4.64749i	1.63205	+	0.346404i
$181$	15.9309	−	2.01254i	1.18413	−	0.149591i	0.491499	−	0.870878i	$-0.336449\pi$
$181$	15.9309	−	2.01254i	1.18413	−	0.149591i	0.692636	+	0.721287i	$0.256449\pi$
$182$		−	5.34938i		−	0.396523i
$183$	−3.00048	−	23.7512i	−0.221802	−	1.75574i
$184$	−5.38870	−	6.51382i	−0.397260	−	0.480205i
$185$	−0.414335	+	4.95152i	−0.0304625	+	0.364043i
$186$	0.558921	−	8.88380i	0.0409821	−	0.651392i
$187$	−0.271660	+	1.05805i	−0.0198657	+	0.0773720i
$188$	−2.38053	+	9.27156i	−0.173618	+	0.676198i
$189$	−3.00825	+	47.8147i	−0.218818	+	3.47801i
$190$	0.624015	+	1.02969i	0.0452708	+	0.0747017i
$191$	2.11643	+	2.55832i	0.153139	+	0.185113i	0.841504	−	0.540252i	$-0.181671\pi$
$191$	2.11643	+	2.55832i	0.153139	+	0.185113i	−0.688364	+	0.725365i	$0.741671\pi$
$192$	0.186580	+	1.47693i	0.0134652	+	0.106588i
$193$		−	6.52727i		−	0.469843i	−0.972014	−	0.234921i	$-0.924517\pi$
$193$		−	6.52727i		−	0.469843i	0.972014	−	0.234921i	$-0.0754833\pi$
$194$	−10.1791	+	1.28593i	−0.730820	+	0.0923241i
$195$	5.88566	−	10.2011i	0.421481	−	0.730519i
$196$	−22.2317	−	20.8769i	−1.58798	−	1.49121i
$197$	−10.6047	−	4.99019i	−0.755553	−	0.355536i	0.00911707	−	0.999958i	$-0.497098\pi$
$197$	−10.6047	−	4.99019i	−0.755553	−	0.355536i	−0.764670	+	0.644422i	$0.777098\pi$
$198$	−1.90433	−	1.57540i	−0.135335	−	0.111958i
$199$	−0.0563377	+	0.173389i	−0.00399367	+	0.0122913i	−0.953033	−	0.302865i	$-0.902057\pi$
$199$	−0.0563377	+	0.173389i	−0.00399367	+	0.0122913i	0.949040	+	0.315156i	$0.102057\pi$
$200$	10.8832	−	1.61359i	0.769559	−	0.114098i
$201$	−2.28900	−	7.04482i	−0.161454	−	0.496903i
$202$	−0.479816	+	1.21188i	−0.0337598	+	0.0852674i
$203$	−16.9835	+	18.0856i	−1.19201	+	1.26936i
$204$	−1.51714	−	7.95313i	−0.106221	−	0.556830i
$205$	−1.68461	+	1.02091i	−0.117659	+	0.0713035i
$206$	2.89255	−	2.71628i	0.201533	−	0.189253i
$207$	22.3959	−	7.27687i	1.55662	−	0.505777i
$208$	3.31104	+	0.631615i	0.229580	+	0.0437946i
$209$	0.0371660	+	0.590737i	0.00257083	+	0.0408621i
$210$	5.99839	+	19.8467i	0.413928	+	1.36955i
$211$	−5.12515	−	8.07594i	−0.352830	−	0.555971i	0.620839	−	0.783938i	$-0.286792\pi$
$211$	−5.12515	−	8.07594i	−0.352830	−	0.555971i	−0.973669	+	0.227967i	$0.926792\pi$
$212$	10.8031	−	0.679674i	0.741961	−	0.0466802i
$213$	−3.39954	−	2.15741i	−0.232932	−	0.147823i
$214$	−7.14068	+	8.63160i	−0.488127	+	0.590044i
$215$	−8.75939	−	8.57281i	−0.597385	−	0.584661i
$216$	20.1522	+	5.17421i	1.37118	+	0.352060i
$217$	−22.3010	+	10.4940i	−1.51389	+	0.712382i
$218$	1.27202	+	0.413304i	0.0861521	+	0.0279925i
$219$	−36.6097	−	20.1263i	−2.47385	−	1.36001i
$220$	2.29634	+	0.798917i	0.154819	+	0.0538630i
$221$	−2.83756	−	0.358467i	−0.190875	−	0.0241131i
$222$	−0.509655	+	4.03434i	−0.0342058	+	0.270767i
$223$	1.34297	−	0.852276i	0.0899320	−	0.0570726i	−0.490100	−	0.871666i	$-0.663040\pi$
$223$	1.34297	−	0.852276i	0.0899320	−	0.0570726i	0.580032	+	0.814593i	$0.303040\pi$
$224$	−22.8409	+	16.5949i	−1.52612	+	1.10879i
$225$	−6.98080	+	29.8412i	−0.465387	+	1.98941i
$226$	7.02822	+	5.10630i	0.467510	+	0.339666i
$227$	2.76481	+	0.173947i	0.183507	+	0.0115453i	0.154278	−	0.988027i	$-0.450695\pi$
$227$	2.76481	+	0.173947i	0.183507	+	0.0115453i	0.0292289	+	0.999573i	$0.490695\pi$
$228$	−2.11353	−	3.84450i	−0.139972	−	0.254608i
$229$	6.79097	−	14.4315i	0.448760	−	0.953663i	−0.544609	−	0.838690i	$-0.683322\pi$
$229$	6.79097	−	14.4315i	0.448760	−	0.953663i	0.993369	−	0.114973i	$-0.0366782\pi$
$230$	4.07660	−	3.23301i	0.268803	−	0.213178i
$231$	−1.90992	+	10.0121i	−0.125663	+	0.658750i
$232$	6.33297	+	8.71659i	0.415780	+	0.572272i
$233$	7.28020	−	13.2426i	0.476942	−	0.867554i	−0.522943	−	0.852368i	$-0.675166\pi$
$233$	7.28020	−	13.2426i	0.476942	−	0.867554i	0.999885	−	0.0151865i	$-0.00483420\pi$
$234$	3.46737	−	5.46371i	0.226669	−	0.357174i
$235$	−12.6241	−	3.52073i	−0.823504	−	0.229667i
$236$	6.80652	+	2.69489i	0.443067	+	0.175423i
$237$	−3.65042	−	9.21992i	−0.237121	−	0.598898i
$238$	3.87959	−	3.20948i	0.251477	−	0.208040i
$239$	20.2709	−	5.20467i	1.31121	−	0.336662i	0.472546	−	0.881306i	$-0.343335\pi$
$239$	20.2709	−	5.20467i	1.31121	−	0.336662i	0.838668	+	0.544644i	$0.183335\pi$
$240$	−12.9925	+	1.36940i	−0.838662	+	0.0883946i
$241$	1.97779	−	0.783063i	0.127401	−	0.0504415i	−0.303559	−	0.952813i	$-0.598175\pi$
$241$	1.97779	−	0.783063i	0.127401	−	0.0504415i	0.430960	+	0.902371i	$0.358175\pi$
$242$	4.37678	+	4.66079i	0.281350	+	0.299607i
$243$	−1.40823	+	1.93826i	−0.0903381	+	0.124340i
$244$	5.50967	+	11.7086i	0.352720	+	0.749569i
$245$	29.2059	−	29.8416i	1.86590	−	1.90651i
$246$	−1.41266	+	0.776618i	−0.0900680	+	0.0495153i
$247$	−1.52232	+	0.290398i	−0.0968628	+	0.0184776i
$248$	2.66184	+	10.3672i	0.169027	+	0.658318i
$249$	36.8397			2.33462
$250$	0.854563	+	6.71722i	0.0540473	+	0.424834i
$251$	5.31387			0.335408			0.167704	−	0.985837i	$-0.446365\pi$
$251$	5.31387			0.335408			0.167704	+	0.985837i	$0.446365\pi$
$252$	−12.6140	−	49.1283i	−0.794608	−	3.09479i
$253$	2.51252	−	0.479289i	0.157961	−	0.0301327i
$254$	6.44576	−	3.54359i	0.404443	−	0.222345i
$255$	10.9295	−	1.85188i	0.684434	−	0.115969i
$256$	2.53113	+	5.37892i	0.158196	+	0.336183i
$257$	−12.4960	+	17.1993i	−0.779480	+	1.07286i	0.215860	+	0.976424i	$0.430745\pi$
$257$	−12.4960	+	17.1993i	−0.779480	+	1.07286i	−0.995339	+	0.0964371i	$0.969255\pi$
$258$	−6.86631	−	7.31188i	−0.427478	−	0.455217i
$259$	10.4686	−	4.14483i	0.650490	−	0.257547i
$260$	−1.32173	+	6.22720i	−0.0819703	+	0.386195i
$261$	−29.0692	+	7.46369i	−1.79934	+	0.461991i
$262$	−0.975468	+	0.806977i	−0.0602646	+	0.0498552i
$263$	1.08150	+	2.73157i	0.0666884	+	0.168436i	0.959299	−	0.282393i	$-0.0911284\pi$
$263$	1.08150	+	2.73157i	0.0666884	+	0.168436i	−0.892610	+	0.450829i	$0.851128\pi$
$264$	4.11560	+	1.62948i	0.253297	+	0.100288i
$265$	0.624932	+	14.8071i	0.0383893	+	0.909590i
$266$	1.46189	−	2.30357i	0.0896344	−	0.141241i
$267$	2.96780	−	5.39840i	0.181626	−	0.330377i
$268$	2.35341	+	3.23920i	0.143758	+	0.197865i
$269$	2.39895	−	12.5757i	0.146267	−	0.766756i	−0.831250	−	0.555899i	$-0.812374\pi$
$269$	2.39895	−	12.5757i	0.146267	−	0.766756i	0.977517	−	0.210858i	$-0.0676257\pi$
$270$	−3.43994	+	12.3344i	−0.209348	+	0.750647i
$271$	−3.01455	+	6.40625i	−0.183121	+	0.389152i	−0.975219	−	0.221242i	$-0.928989\pi$
$271$	−3.01455	+	6.40625i	−0.183121	+	0.389152i	0.792098	+	0.610394i	$0.208989\pi$
$272$	1.52846	+	2.78026i	0.0926765	+	0.168578i
$273$	−26.6345	−	1.67570i	−1.61200	−	0.101418i
$274$	−9.31191	−	6.76550i	−0.562553	−	0.408719i
$275$	−1.15852	+	3.12075i	−0.0698616	+	0.188189i
$276$	−15.3377	+	11.1435i	−0.923223	+	0.670761i
$277$	−20.8755	+	13.2480i	−1.25429	+	0.795994i	−0.985903	−	0.167319i	$-0.946489\pi$
$277$	−20.8755	+	13.2480i	−1.25429	+	0.795994i	−0.268382	+	0.963312i	$0.586489\pi$
$278$	−1.26318	+	9.99910i	−0.0757605	+	0.599706i
$279$	−29.5796	−	3.73678i	−1.77089	−	0.223715i
$280$	−14.2343	−	20.4678i	−0.850665	−	1.22318i
$281$	−12.0429	−	6.62064i	−0.718419	−	0.394954i	0.0802100	−	0.996778i	$-0.474441\pi$
$281$	−12.0429	−	6.62064i	−0.718419	−	0.394954i	−0.798629	+	0.601824i	$0.794441\pi$
$282$	−10.2006	−	3.31438i	−0.607438	−	0.197369i
$283$	1.30946	−	0.616186i	0.0778394	−	0.0366285i	−0.386466	−	0.922304i	$-0.626304\pi$
$283$	1.30946	−	0.616186i	0.0778394	−	0.0366285i	0.464305	+	0.885675i	$0.346304\pi$
$284$	2.10796	+	0.541231i	0.125084	+	0.0321162i
$285$	5.32230	−	2.78441i	0.315266	−	0.164934i
$286$	0.448037	−	0.541584i	0.0264930	−	0.0320245i
$287$	3.76873	+	2.39171i	0.222461	+	0.141178i
$288$	−34.0855	+	2.14448i	−2.00851	+	0.126365i
$289$	7.66658	+	12.0806i	0.450975	+	0.710623i
$290$	−5.44402	+	3.78605i	−0.319684	+	0.222325i
$291$	3.21398	+	51.0847i	0.188407	+	2.99464i
$292$	22.1817	+	4.23138i	1.29808	+	0.247623i
$293$	1.66657	−	0.541500i	0.0973619	−	0.0316348i	−0.259931	−	0.965627i	$-0.583700\pi$
$293$	1.66657	−	0.541500i	0.0973619	−	0.0316348i	0.357293	+	0.933992i	$0.383700\pi$
$294$	24.9102	−	23.3922i	1.45279	−	1.36426i
$295$	−3.88135	+	9.24091i	−0.225981	+	0.538027i
$296$	−0.916229	−	4.80304i	−0.0532548	−	0.279171i
$297$	−4.30928	+	4.58892i	−0.250050	+	0.266276i
$298$	3.10330	−	7.83805i	0.179770	−	0.454046i
$299$	2.06952	+	6.36932i	0.119683	+	0.368347i
$300$	−2.07897	−	24.5855i	−0.120029	−	1.41945i
$301$	−8.58231	+	26.4136i	−0.494676	+	1.52246i
$302$	5.30626	+	4.38972i	0.305341	+	0.252600i
$303$	5.88363	+	2.76863i	0.338006	+	0.159053i
$304$	1.25321	+	1.17684i	0.0718763	+	0.0674963i
$305$	−16.1831	+	7.21086i	−0.926644	+	0.412893i
$306$	6.04284	−	0.763388i	0.345446	−	0.0436400i
$307$			16.7007i			0.953162i	0.879131	+	0.476581i	$0.158124\pi$
$307$			16.7007i			0.953162i	−0.879131	+	0.476581i	$0.841876\pi$
$308$	−0.690511	−	5.46596i	−0.0393455	−	0.311452i
$309$	−12.6183	−	15.2529i	−0.717828	−	0.867705i
$310$	−6.41302	+	1.50614i	−0.364235	+	0.0855428i
$311$	1.44691	−	22.9979i	0.0820465	−	1.30409i	−0.714552	−	0.699583i	$-0.753369\pi$
$311$	1.44691	−	22.9979i	0.0820465	−	1.30409i	0.796598	−	0.604509i	$-0.206631\pi$
$312$	−2.88222	+	11.2255i	−0.163174	+	0.635519i
$313$	−4.60472	+	17.9342i	−0.260274	+	1.01370i	0.695245	+	0.718772i	$0.255296\pi$
$313$	−4.60472	+	17.9342i	−0.260274	+	1.01370i	−0.955519	+	0.294928i	$0.904704\pi$
$314$	0.422579	−	6.71670i	0.0238475	−	0.379045i
$315$	67.6059	−	15.8777i	3.80916	−	0.894605i
$316$	3.41659	+	4.12995i	0.192198	+	0.232328i
$317$	−3.38040	−	26.7586i	−0.189862	−	1.50291i	−0.742700	−	0.669624i	$-0.766455\pi$
$317$	−3.38040	−	26.7586i	−0.189862	−	1.50291i	0.552838	−	0.833288i	$-0.313545\pi$
$318$			12.1286i			0.680139i
$319$	−3.23420	+	0.408574i	−0.181080	+	0.0228758i
$320$	1.00632	−	0.448396i	0.0562551	−	0.0250661i
$321$	40.7399	+	38.2573i	2.27388	+	2.13531i
$322$	−10.6678	−	5.01990i	−0.594495	−	0.279748i
$323$	−1.12396	−	0.929818i	−0.0625387	−	0.0517365i
$324$	5.13820	−	15.8137i	0.285455	−	0.878541i
$325$	−8.48673	−	1.98532i	−0.470759	−	0.110125i
$326$	−1.71569	−	5.28035i	−0.0950233	−	0.292452i
$327$	2.45630	−	6.20391i	0.135834	−	0.343077i
$328$	1.32695	−	1.41305i	0.0732683	−	0.0780229i
$329$	5.56479	+	29.1716i	0.306797	+	1.60828i
$330$	−1.05497	+	2.51172i	−0.0580739	+	0.138265i
$331$	−2.19697	+	2.06309i	−0.120757	+	0.113398i	−0.742573	−	0.669765i	$-0.766395\pi$
$331$	−2.19697	+	2.06309i	−0.120757	+	0.113398i	0.621817	+	0.783163i	$0.286395\pi$
$332$	−18.9382	+	6.15340i	−1.03937	+	0.337712i
$333$	13.3790	+	2.55218i	0.733164	+	0.139858i
$334$	0.667260	+	10.6058i	0.0365108	+	0.580323i
$335$	−4.50051	+	3.12989i	−0.245889	+	0.171004i
$336$	15.8626	+	24.9954i	0.865375	+	1.36361i
$337$	10.0385	−	0.631568i	0.546831	−	0.0344037i	0.213027	−	0.977046i	$-0.431668\pi$
$337$	10.0385	−	0.631568i	0.546831	−	0.0344037i	0.333804	+	0.942643i	$0.391668\pi$
$338$	−5.09390	−	3.23269i	−0.277072	−	0.175835i
$339$	27.6258	−	33.3939i	1.50043	−	1.81371i
$340$	−5.30923	+	2.77757i	−0.287933	+	0.150635i
$341$	−3.13673	−	0.805376i	−0.169864	−	0.0436135i
$342$	2.98627	−	1.40523i	0.161479	−	0.0759863i
$343$	−56.2538	−	18.2780i	−3.03742	−	0.986917i
$344$	10.5692	+	5.81049i	0.569855	+	0.313281i
$345$	−14.8201	−	21.3101i	−0.797890	−	1.14730i
$346$	−10.6227	−	1.34196i	−0.571079	−	0.0721441i
$347$	1.51271	−	11.9743i	0.0812063	−	0.642814i	−0.898007	−	0.439981i	$-0.854985\pi$
$347$	1.51271	−	11.9743i	0.0812063	−	0.642814i	0.979213	−	0.202833i	$-0.0650149\pi$
$348$	20.4008	−	12.9468i	1.09360	−	0.694020i
$349$	−14.3734	+	10.4429i	−0.769393	+	0.558997i	−0.901777	−	0.432202i	$-0.857737\pi$
$349$	−14.3734	+	10.4429i	−0.769393	+	0.558997i	0.132384	+	0.991199i	$0.457737\pi$
$350$	12.7752	−	8.49861i	0.682865	−	0.454270i
$351$	−13.3344	−	9.68803i	−0.711739	−	0.517109i
$352$	−3.70236	−	0.232933i	−0.197337	−	0.0124154i
$353$	−4.74605	−	8.63303i	−0.252607	−	0.459490i	0.719351	−	0.694647i	$-0.244439\pi$
$353$	−4.74605	−	8.63303i	−0.252607	−	0.459490i	−0.971957	+	0.235157i	$0.924439\pi$
$354$	−3.49250	+	7.42193i	−0.185624	+	0.394471i
$355$	−0.800463	+	2.87017i	−0.0424842	+	0.152333i
$356$	−0.623953	+	3.27088i	−0.0330694	+	0.173356i
$357$	−14.7647	−	20.3219i	−0.781430	−	1.07555i
$358$	5.82964	−	10.6041i	0.308106	−	0.560443i
$359$	−7.39451	+	11.6519i	−0.390267	+	0.614963i	−0.981483	−	0.191551i	$-0.938648\pi$
$359$	−7.39451	+	11.6519i	−0.390267	+	0.614963i	0.591215	+	0.806514i	$0.298648\pi$
$360$	−1.27171	−	30.1317i	−0.0670249	−	1.58808i
$361$	16.9308	+	6.70340i	0.891097	+	0.352810i
$362$	−3.58009	−	9.04228i	−0.188165	−	0.475252i
$363$	24.5771	−	20.3319i	1.28996	−	1.06715i
$364$	13.9719	−	3.58738i	0.732328	−	0.188030i
$365$	−6.41927	+	30.2437i	−0.336000	+	1.58303i
$366$	−13.4811	+	5.33753i	−0.704666	+	0.278997i
$367$	−15.1801	−	16.1652i	−0.792395	−	0.843815i	0.198268	−	0.980148i	$-0.436468\pi$
$367$	−15.1801	−	16.1652i	−0.792395	−	0.843815i	−0.990663	+	0.136333i	$0.956468\pi$
$368$	4.36668	−	6.01022i	0.227629	−	0.313304i
$369$	2.29901	+	4.88565i	0.119682	+	0.254337i
$370$	2.96708	−	0.502735i	0.154251	−	0.0261359i
$371$	29.4286	−	16.1785i	1.52786	−	0.839946i
$372$	23.5782	−	4.49779i	1.22247	−	0.233199i
$373$	5.22449	+	20.3480i	0.270514	+	1.05358i	0.948057	+	0.318099i	$0.103044\pi$
$373$	5.22449	+	20.3480i	0.270514	+	1.05358i	−0.677544	+	0.735483i	$0.736956\pi$
$374$	0.661589			0.0342100
$375$	33.7127	−	2.15068i	1.74092	−	0.111061i
$376$	12.8970			0.665111
$377$	−2.12265	−	8.26717i	−0.109322	−	0.425781i
$378$	28.5022	−	5.43709i	1.46600	−	0.279654i
$379$	22.6406	−	12.4468i	1.16297	−	0.639348i	0.221075	−	0.975257i	$-0.429043\pi$
$379$	22.6406	−	12.4468i	1.16297	−	0.639348i	0.941894	+	0.335909i	$0.109043\pi$
$380$	−2.27095	+	2.32038i	−0.116497	+	0.119033i
$381$	−15.6244	−	33.2035i	−0.800460	−	1.70107i
$382$	1.18199	−	1.62687i	0.0604759	−	0.0832380i
$383$	15.5365	+	16.5447i	0.793878	+	0.845394i	0.990843	−	0.135016i	$-0.0431087\pi$
$383$	15.5365	+	16.5447i	0.793878	+	0.845394i	−0.196966	+	0.980410i	$0.563109\pi$
$384$	32.1452	−	12.7272i	1.64040	−	0.649482i
$385$	7.50160	−	0.790665i	0.382317	−	0.0402960i
$386$	−3.82903	+	0.983128i	−0.194893	+	0.0500399i
$387$	−25.8866	+	21.4152i	−1.31589	+	1.08860i
$388$	−10.1850	−	25.7243i	−0.517064	−	1.30595i
$389$	−27.9452	−	11.0643i	−1.41688	−	0.560983i	−0.470028	−	0.882651i	$-0.655756\pi$
$389$	−27.9452	−	11.0643i	−1.41688	−	0.560983i	−0.946852	+	0.321669i	$0.895756\pi$
$390$	−6.87070	−	1.91617i	−0.347911	−	0.0970291i
$391$	−3.37764	+	5.32231i	−0.170815	+	0.269161i
$392$	−19.7952	+	36.0074i	−0.999810	+	1.81865i
$393$	3.71237	+	5.10964i	0.187264	+	0.257747i
$394$	−1.33008	+	6.97255i	−0.0670087	+	0.351272i
$395$	−5.74988	+	4.56004i	−0.289308	+	0.229440i
$396$	2.83767	−	6.03035i	0.142598	−	0.303037i
$397$	−6.24773	−	11.3646i	−0.313565	−	0.570372i	0.671820	−	0.740714i	$-0.265513\pi$
$397$	−6.24773	−	11.3646i	−0.313565	−	0.570372i	−0.985385	+	0.170342i	$0.945513\pi$
$398$	0.110199	+	0.00693316i	0.00552380	+	0.000347528i
$399$	−11.0115	−	8.00035i	−0.551266	−	0.400519i
$400$	3.75188	+	8.91079i	0.187594	+	0.445539i
$401$	12.3695	−	8.98695i	0.617702	−	0.448787i	−0.234416	−	0.972136i	$-0.575318\pi$
$401$	12.3695	−	8.98695i	0.617702	−	0.448787i	0.852118	+	0.523349i	$0.175318\pi$
$402$	−3.78787	+	2.40386i	−0.188922	+	0.119893i
$403$	1.06273	−	8.41235i	0.0529382	−	0.419049i
$404$	−3.48705	−	0.440517i	−0.173487	−	0.0219165i
$405$	21.5014	+	7.48052i	1.06841	+	0.371710i
$406$	13.1674	+	7.23884i	0.653487	+	0.359257i
$407$	1.40702	+	0.457169i	0.0697434	+	0.0226610i
$408$	−9.87046	+	4.64469i	−0.488660	+	0.229946i
$409$	3.94533	+	1.01299i	0.195084	+	0.0500890i	0.344968	−	0.938615i	$-0.387890\pi$
$409$	3.94533	+	1.01299i	0.195084	+	0.0500890i	−0.149884	+	0.988704i	$0.547890\pi$
$410$	0.852622	+	0.834462i	0.0421080	+	0.0412111i
$411$	−36.6023	+	44.2446i	−1.80546	+	2.18243i
$412$	9.03439	+	5.73340i	0.445093	+	0.282464i
$413$	22.6671	−	1.42609i	1.11537	−	0.0701733i
$414$	−7.64201	−	12.0419i	−0.375584	−	0.591826i
$415$	−7.88763	−	26.0976i	−0.387189	−	1.28108i
$416$	−0.609882	−	9.69380i	−0.0299019	−	0.475278i
$417$	49.3898	+	9.42161i	2.41863	+	0.461378i
$418$	0.340941	−	0.110778i	0.0166760	−	0.00541835i
$419$	−23.0686	+	21.6629i	−1.12698	+	1.05830i	−0.129201	+	0.991618i	$0.541241\pi$
$419$	−23.0686	+	21.6629i	−1.12698	+	1.05830i	−0.997774	+	0.0666819i	$0.978759\pi$
$420$	−47.8144	+	28.9765i	−2.33311	+	1.41391i
$421$	−2.20847	−	11.5772i	−0.107634	−	0.564238i	−0.994719	−	0.102632i	$-0.967274\pi$
$421$	−2.20847	−	11.5772i	−0.107634	−	0.564238i	0.887085	−	0.461606i	$-0.152726\pi$
$422$	−3.96558	+	4.22291i	−0.193041	+	0.205568i
$423$	−13.2248	+	33.4021i	−0.643013	+	1.62406i
$424$	−4.50673	−	13.8703i	−0.218866	−	0.673601i
$425$	−3.65197	−	7.34607i	−0.177147	−	0.356337i
$426$	−0.753549	+	2.31919i	−0.0365096	+	0.112365i
$427$	30.9334	+	25.5903i	1.49697	+	1.23840i
$428$	−27.3333	−	12.8621i	−1.32121	−	0.621713i
$429$	−2.55620	−	2.40043i	−0.123414	−	0.115894i
$430$	−3.70967	+	6.42967i	−0.178896	+	0.310066i
$431$	25.6653	−	3.24229i	1.23626	−	0.156175i	0.520093	−	0.854109i	$-0.325897\pi$
$431$	25.6653	−	3.24229i	1.23626	−	0.156175i	0.716162	+	0.697934i	$0.245897\pi$
$432$			18.2837i			0.879673i
$433$	−3.12301	−	24.7212i	−0.150082	−	1.18802i	−0.869674	−	0.493627i	$-0.835671\pi$
$433$	−3.12301	−	24.7212i	−0.150082	−	1.18802i	0.719592	−	0.694397i	$-0.244329\pi$
$434$	9.51497	+	11.5016i	0.456733	+	0.552096i
$435$	17.1454	+	28.2917i	0.822058	+	1.35648i
$436$	−0.226463	+	3.59953i	−0.0108456	+	0.172386i
$437$	−0.849438	+	3.30834i	−0.0406342	+	0.158260i
$438$	−6.29243	+	24.5074i	−0.300664	+	1.17101i
$439$	0.738554	−	11.7390i	0.0352493	−	0.560271i	−0.940280	−	0.340402i	$-0.889437\pi$
$439$	0.738554	−	11.7390i	0.0352493	−	0.560271i	0.975529	−	0.219869i	$-0.0705631\pi$
$440$	0.273159	−	3.26440i	0.0130224	−	0.155624i
$441$	−72.9576	−	88.1906i	−3.47417	−	4.19955i
$442$	0.217105	+	1.71856i	0.0103266	+	0.0817437i
$443$			11.9763i			0.569012i	0.958674	+	0.284506i	$0.0918296\pi$
$443$			11.9763i			0.569012i	−0.958674	+	0.284506i	$0.908170\pi$
$444$	−10.8790	+	1.37433i	−0.516293	+	0.0652230i
$445$	−4.45970	−	0.946576i	−0.211410	−	0.0448720i
$446$	−0.702240	−	0.659447i	−0.0332520	−	0.0312257i
$447$	−38.0535	−	17.9066i	−1.79987	−	0.846954i
$448$	−1.92354	−	1.59129i	−0.0908788	−	0.0751814i
$449$	−0.461268	+	1.41964i	−0.0217686	+	0.0669967i	−0.961351	−	0.275327i	$-0.911214\pi$
$449$	−0.461268	+	1.41964i	−0.0217686	+	0.0669967i	0.939582	+	0.342324i	$0.111214\pi$
$450$	18.5569	−	0.399557i	0.874781	−	0.0188353i
$451$	0.181238	+	0.557792i	0.00853415	+	0.0262654i
$452$	−8.62379	+	21.7812i	−0.405629	+	1.02450i
$453$	23.5186	−	25.0448i	1.10500	−	1.17671i
$454$	−0.314391	−	1.64810i	−0.0147551	−	0.0773490i
$455$	4.51555	+	19.2269i	0.211692	+	0.901371i
$456$	−4.30889	+	4.04632i	−0.201782	+	0.189486i
$457$	20.8891	−	6.78729i	0.977152	−	0.317496i	0.223452	−	0.974715i	$-0.428267\pi$
$457$	20.8891	−	6.78729i	0.977152	−	0.317496i	0.753700	+	0.657219i	$0.228267\pi$
$458$	−9.48870	−	1.81007i	−0.443378	−	0.0845788i
$459$	−0.974122	−	15.4832i	−0.0454681	−	0.722695i
$460$	11.1781	+	8.47947i	0.521180	+	0.395357i
$461$	−10.0445	−	15.8276i	−0.467820	−	0.737166i	0.525719	−	0.850658i	$-0.323796\pi$
$461$	−10.0445	−	15.8276i	−0.467820	−	0.737166i	−0.993539	+	0.113492i	$0.963796\pi$
$462$	6.16100	−	0.387617i	0.286636	−	0.0180336i
$463$	−10.5369	−	6.68691i	−0.489690	−	0.310767i	0.267957	−	0.963431i	$-0.413651\pi$
$463$	−10.5369	−	6.68691i	−0.489690	−	0.310767i	−0.757648	+	0.652664i	$0.773651\pi$
$464$	−6.03524	+	7.29536i	−0.280179	+	0.338678i
$465$	5.49016	+	32.4022i	0.254600	+	1.50262i
$466$	−8.86495	−	2.27613i	−0.410661	−	0.105440i
$467$	−2.32964	+	1.09624i	−0.107803	+	0.0507281i	−0.478925	−	0.877856i	$-0.658973\pi$
$467$	−2.32964	+	1.09624i	−0.107803	+	0.0507281i	0.371122	+	0.928584i	$0.378973\pi$
$468$	16.5958	+	5.39231i	0.767142	+	0.249259i
$469$	10.8853	+	5.98427i	0.502638	+	0.276328i
$470$	−0.163913	+	7.93583i	−0.00756075	+	0.366053i
$471$	−33.3100	−	4.20804i	−1.53485	−	0.193896i
$472$	1.23619	−	9.78545i	0.0569003	−	0.450412i
$473$	−3.08116	+	1.95537i	−0.141672	+	0.0899078i
$474$	−4.85878	+	3.53011i	−0.223171	+	0.162143i
$475$	−3.11204	−	3.17420i	−0.142790	−	0.145642i
$476$	10.9845	+	7.98070i	0.503473	+	0.365795i
$477$	40.5441	+	2.55082i	1.85639	+	0.116794i
$478$	−6.10634	−	11.1074i	−0.279298	−	0.508041i
$479$	9.81904	−	20.8665i	0.448644	−	0.953416i	−0.544744	−	0.838603i	$-0.683373\pi$
$479$	9.81904	−	20.8665i	0.448644	−	0.953416i	0.993387	−	0.114813i	$-0.0366270\pi$
$480$	13.1326	+	35.2809i	0.599418	+	1.61035i
$481$	−0.725831	+	3.80494i	−0.0330950	+	0.173490i
$482$	−0.757254	−	1.04227i	−0.0344920	−	0.0474741i
$483$	−28.3358	+	51.5425i	−1.28932	+	2.34527i
$484$	−9.23828	+	14.5572i	−0.419922	+	0.661691i
$485$	35.5007	−	13.2144i	1.61200	−	0.600035i
$486$	1.34913	+	0.534160i	0.0611979	+	0.0242300i
$487$	−1.58550	−	4.00452i	−0.0718460	−	0.181462i	0.889416	−	0.457099i	$-0.151111\pi$
$487$	−1.58550	−	4.00452i	−0.0718460	−	0.181462i	−0.961262	+	0.275636i	$0.911111\pi$
$488$	13.4336	−	11.1133i	0.608111	−	0.503073i
$489$	−26.8283	+	6.88833i	−1.21322	+	0.311501i
$490$	−21.9047	−	12.6381i	−0.989551	−	0.570932i
$491$	−9.24795	+	3.66152i	−0.417354	+	0.165242i	−0.567410	−	0.823435i	$-0.692055\pi$
$491$	−9.24795	+	3.66152i	−0.417354	+	0.165242i	0.150056	+	0.988677i	$0.452055\pi$
$492$	−2.97578	−	3.16889i	−0.134159	−	0.142864i
$493$	4.72217	−	6.49950i	0.212676	−	0.292723i
$494$	0.399643	+	0.849285i	0.0179808	+	0.0382111i
$495$	8.17441	+	4.05484i	0.367413	+	0.182251i
$496$	−8.24248	+	4.53134i	−0.370098	+	0.203463i
$497$	6.63238	−	1.26519i	0.297503	−	0.0567517i
$498$	−5.54875	−	21.6110i	−0.248646	−	0.968411i
$499$	30.2890			1.35592			0.677961	−	0.735098i	$-0.262864\pi$
$499$	30.2890			1.35592			0.677961	+	0.735098i	$0.262864\pi$
$500$	−16.9715	+	6.73669i	−0.758987	+	0.301274i
$501$	53.0152			2.36854
$502$	−0.800368	−	3.11723i	−0.0357222	−	0.139129i
$503$	−10.0000	+	1.90761i	−0.445879	+	0.0850560i	−0.405431	−	0.914126i	$-0.632879\pi$
$503$	−10.0000	+	1.90761i	−0.445879	+	0.0850560i	−0.0404481	+	0.999182i	$0.512879\pi$
$504$	−59.8857	+	32.9225i	−2.66752	+	1.46648i
$505$	0.701591	−	4.76079i	0.0312204	−	0.211852i
$506$	−0.659594	−	1.40171i	−0.0293225	−	0.0623136i
$507$	−17.6912	+	24.3499i	−0.785694	+	1.08142i
$508$	13.5781	+	14.4592i	0.602429	+	0.641521i
$509$	−27.5175	+	10.8949i	−1.21969	+	0.482910i	−0.887722	−	0.460381i	$-0.847713\pi$
$509$	−27.5175	+	10.8949i	−1.21969	+	0.482910i	−0.331969	+	0.943290i	$0.607713\pi$
$510$	−2.73254	−	6.13257i	−0.120999	−	0.271555i
$511$	67.8577	−	17.4229i	3.00185	−	0.770743i
$512$	−14.8589	+	12.2924i	−0.656677	+	0.543251i
$513$	−3.09456	−	7.81596i	−0.136628	−	0.345083i
$514$	11.9716	+	4.73989i	0.528044	+	0.209068i
$515$	−8.10359	+	12.2046i	−0.357087	+	0.537800i
$516$	14.4931	−	22.8374i	0.638022	−	1.00536i
$517$	−1.87988	+	3.41948i	−0.0826769	+	0.150389i
$518$	−4.00822	−	5.51684i	−0.176111	−	0.242396i
$519$	−10.0092	+	52.4699i	−0.439354	+	2.30317i
$520$	8.56934	−	0.361669i	0.375790	−	0.0158602i
$521$	3.16922	−	6.73493i	0.138846	−	0.295063i	−0.823296	−	0.567613i	$-0.807867\pi$
$521$	3.16922	−	6.73493i	0.138846	−	0.295063i	0.962142	+	0.272550i	$0.0878671\pi$
$522$	8.75672	+	15.9284i	0.383271	+	0.697168i
$523$	30.3194	+	1.90754i	1.32578	+	0.0834107i	0.709827	−	0.704376i	$-0.248773\pi$
$523$	30.3194	+	1.90754i	1.32578	+	0.0834107i	0.615948	+	0.787787i	$0.288773\pi$
$524$	−2.76189	−	2.00663i	−0.120654	−	0.0876600i
$525$	−38.3127	−	66.2700i	−1.67210	−	2.89226i
$526$	1.43950	−	1.04586i	0.0627652	−	0.0456016i
$527$	6.73859	−	4.27644i	0.293538	−	0.186285i
$528$	−0.487526	+	3.85917i	−0.0212168	+	0.167949i
$529$	−8.17480	−	1.03272i	−0.355426	−	0.0449007i
$530$	8.59201	−	2.59682i	0.373213	−	0.112799i
$531$	24.0759	+	13.2358i	1.04480	+	0.574386i
$532$	6.99702	+	2.27347i	0.303359	+	0.0985674i
$533$	−1.38946	+	0.653831i	−0.0601843	+	0.0283206i
$534$	−3.61382	−	0.927872i	−0.156385	−	0.0401530i
$535$	18.3791	−	37.0516i	0.794597	−	1.60188i
$536$	3.43859	−	4.15654i	0.148524	−	0.179535i
$537$	−50.9715	−	32.3475i	−2.19958	−	1.39590i
$538$	−7.73852	+	0.486867i	−0.333631	+	0.0209903i
$539$	−6.66156	−	10.4969i	−0.286934	−	0.452135i
$540$	−34.5228	−	0.713061i	−1.48562	−	0.0306853i
$541$	0.216848	+	3.44670i	0.00932301	+	0.148185i	0.999934	+	0.0114753i	$0.00365278\pi$
$541$	0.216848	+	3.44670i	0.00932301	+	0.148185i	−0.990611	+	0.136710i	$0.956347\pi$
$542$	4.21209	+	0.803499i	0.180925	+	0.0345132i
$543$	−46.1429	+	14.9927i	−1.98018	+	0.643400i
$544$	6.66443	−	6.25832i	0.285735	−	0.268323i
$545$	−4.92081	−	0.411765i	−0.210784	−	0.0176381i
$546$	3.02866	+	15.8768i	0.129615	+	0.679464i
$547$	17.7091	−	18.8583i	0.757187	−	0.806323i	−0.228742	−	0.973487i	$-0.573461\pi$
$547$	17.7091	−	18.8583i	0.757187	−	0.806323i	0.985929	+	0.167164i	$0.0534611\pi$
$548$	11.4259	−	28.8586i	0.488092	−	1.23278i
$549$	15.0073	+	46.1877i	0.640495	+	1.97124i
$550$	2.00520	+	0.209570i	0.0855018	+	0.00893611i
$551$	1.34521	−	4.14013i	0.0573078	−	0.176375i
$552$	19.6814	+	16.2819i	0.837696	+	0.693002i
$553$	15.0465	+	7.08037i	0.639844	+	0.301088i
$554$	10.9158	+	10.2506i	0.463767	+	0.435506i
$555$	−1.57367	−	14.9305i	−0.0667987	−	0.633766i
$556$	−26.9635	+	3.40629i	−1.14351	+	0.144459i
$557$		−	33.5203i		−	1.42030i	−0.704050	−	0.710150i	$-0.748627\pi$
$557$		−	33.5203i		−	1.42030i	0.704050	−	0.710150i	$-0.251373\pi$
$558$	2.26317	+	17.9149i	0.0958078	+	0.758397i
$559$	−6.09042	−	7.36205i	−0.257597	−	0.311382i
$560$	14.3107	−	16.5889i	0.604736	−	0.701008i
$561$	0.207244	−	3.29405i	0.00874985	−	0.139075i
$562$	−2.06992	+	8.06181i	−0.0873143	+	0.340067i
$563$	−4.91231	+	19.1322i	−0.207029	+	0.806326i	0.777174	+	0.629285i	$0.216652\pi$
$563$	−4.91231	+	19.1322i	−0.207029	+	0.806326i	−0.984204	+	0.177040i	$0.943348\pi$
$564$	1.81606	−	28.8655i	0.0764700	−	1.21546i
$565$	−29.5714	−	12.4205i	−1.24408	−	0.522534i
$566$	−0.558697	−	0.675349i	−0.0234838	−	0.0283870i
$567$	−6.46548	−	51.1795i	−0.271525	−	2.14934i
$568$		−	2.93222i		−	0.123033i
$569$	24.9817	−	3.15592i	1.04729	−	0.132303i	0.417189	−	0.908820i	$-0.363015\pi$
$569$	24.9817	−	3.15592i	1.04729	−	0.132303i	0.630097	+	0.776517i	$0.283015\pi$
$570$	−2.43503	−	2.70279i	−0.101992	−	0.113207i
$571$	−14.4344	−	13.5548i	−0.604060	−	0.567250i	0.320996	−	0.947080i	$-0.395982\pi$
$571$	−14.4344	−	13.5548i	−0.604060	−	0.567250i	−0.925056	+	0.379831i	$0.875982\pi$
$572$	1.71501	+	0.807023i	0.0717082	+	0.0337433i
$573$	−7.72992	−	6.39475i	−0.322922	−	0.267144i
$574$	0.835386	−	2.57105i	0.0348683	−	0.107314i
$575$	−11.9232	+	15.0613i	−0.497230	+	0.628102i
$576$	−0.933203	−	2.87210i	−0.0388835	−	0.119671i
$577$	−4.84646	+	12.2408i	−0.201761	+	0.509589i	−0.995064	−	0.0992377i	$-0.968360\pi$
$577$	−4.84646	+	12.2408i	−0.201761	+	0.509589i	0.793303	+	0.608827i	$0.208360\pi$
$578$	5.93200	−	6.31694i	0.246739	−	0.262750i
$579$	3.69554	+	19.3727i	0.153581	+	0.805102i
$580$	−13.5395	−	11.6801i	−0.562199	−	0.484991i
$581$	−45.0348	+	42.2905i	−1.86836	+	1.75450i
$582$	29.4833	−	9.57971i	1.22212	−	0.397092i
$583$	4.33445	+	0.826840i	0.179514	+	0.0342442i
$584$	−1.91039	−	30.3648i	−0.0790525	−	1.25650i
$585$	−7.85047	+	22.5647i	−0.324577	+	0.932936i
$586$	−0.568672	−	0.896083i	−0.0234916	−	0.0370169i
$587$	−27.0134	+	1.69954i	−1.11496	+	0.0701474i	−0.609562	−	0.792738i	$-0.708655\pi$
$587$	−27.0134	+	1.69954i	−1.11496	+	0.0701474i	−0.505399	+	0.862886i	$0.668655\pi$
$588$	77.8027	+	49.3751i	3.20853	+	2.03619i
$589$	2.75658	−	3.33214i	0.113583	−	0.137298i
$590$	6.00552	+	0.885026i	0.247243	+	0.0364359i
$591$	34.2996	+	8.80665i	1.41090	+	0.362257i
$592$	3.88795	−	1.82953i	0.159794	−	0.0751933i
$593$	4.17281	+	1.35583i	0.171357	+	0.0556772i	0.393439	−	0.919351i	$-0.371285\pi$
$593$	4.17281	+	1.35583i	0.171357	+	0.0556772i	−0.222082	+	0.975028i	$0.571285\pi$
$594$	3.34102	+	1.83674i	0.137084	+	0.0753623i
$595$	−11.2349	+	14.8105i	−0.460588	+	0.607170i
$596$	22.5532	+	2.84913i	0.923813	+	0.116705i
$597$	0.0690403	−	0.546511i	0.00282563	−	0.0223672i
$598$	3.42467	−	2.17336i	0.140045	−	0.0888753i
$599$	17.9820	−	13.0647i	0.734726	−	0.533810i	−0.156329	−	0.987705i	$-0.549966\pi$
$599$	17.9820	−	13.0647i	0.734726	−	0.533810i	0.891055	+	0.453895i	$0.149966\pi$
$600$	−31.3874	+	10.9508i	−1.28139	+	0.447066i
$601$	−13.2817	−	9.64971i	−0.541771	−	0.393620i	0.282971	−	0.959128i	$-0.408680\pi$
$601$	−13.2817	−	9.64971i	−0.541771	−	0.393620i	−0.824742	+	0.565508i	$0.808680\pi$
$602$	16.7874	+	1.05618i	0.684205	+	0.0430466i
$603$	7.23908	+	13.1678i	0.294798	+	0.536236i
$604$	−7.90695	+	16.8031i	−0.321729	+	0.683709i
$605$	−19.6654	−	13.0574i	−0.799513	−	0.530859i
$606$	0.737950	−	3.86847i	0.0299772	−	0.157146i
$607$	−8.61693	−	11.8602i	−0.349751	−	0.481390i	0.597507	−	0.801864i	$-0.296158\pi$
$607$	−8.61693	−	11.8602i	−0.349751	−	0.481390i	−0.947258	+	0.320473i	$0.896158\pi$
$608$	2.38651	−	4.34105i	0.0967859	−	0.176053i
$609$	40.1668	−	63.2928i	1.62764	−	2.56475i
$610$	6.66753	+	8.40728i	0.269960	+	0.340401i
$611$	−9.49944	−	3.76109i	−0.384306	−	0.152158i
$612$	6.04630	+	15.2712i	0.244407	+	0.617302i
$613$	−23.1818	+	19.1777i	−0.936305	+	0.774579i	−0.974429	−	0.224694i	$-0.927862\pi$
$613$	−23.1818	+	19.1777i	−0.936305	+	0.774579i	0.0381242	+	0.999273i	$0.487862\pi$
$614$	9.79701	−	2.51545i	0.395375	−	0.101515i
$615$	4.42187	−	3.98381i	0.178307	−	0.160643i
$616$	−6.90169	+	2.73257i	−0.278077	+	0.110098i
$617$	28.9089	+	30.7849i	1.16383	+	1.23935i	0.965838	+	0.259148i	$0.0834419\pi$
$617$	28.9089	+	30.7849i	1.16383	+	1.23935i	0.197992	+	0.980204i	$0.436558\pi$
$618$	−7.04711	+	9.69951i	−0.283476	+	0.390172i
$619$	8.70626	+	18.5017i	0.349934	+	0.743648i	0.999866	−	0.0163442i	$-0.00520274\pi$
$619$	8.70626	+	18.5017i	0.349934	+	0.743648i	−0.649932	+	0.759992i	$0.725203\pi$
$620$	−8.23452	−	15.7400i	−0.330706	−	0.632133i
$621$	−31.8331	+	17.5004i	−1.27742	+	0.702267i
$622$	−13.7090	+	2.61513i	−0.549680	+	0.104857i
$623$	2.56915	+	10.0062i	0.102931	+	0.400890i
$624$	−10.1847			−0.407713
$625$	−8.74167	−	23.4219i	−0.349667	−	0.936874i
$626$	11.2141			0.448207
$627$	−0.444765	−	1.73225i	−0.0177622	−	0.0691792i
$628$	17.8266	−	3.40060i	0.711358	−	0.135699i
$629$	−3.19498	+	1.75645i	−0.127392	+	0.0700344i
$630$	−19.4969	−	37.2676i	−0.776775	−	1.48478i
$631$	−0.326567	−	0.693991i	−0.0130004	−	0.0276273i	0.898221	−	0.439543i	$-0.144860\pi$
$631$	−0.326567	−	0.693991i	−0.0130004	−	0.0276273i	−0.911222	+	0.411916i	$0.864860\pi$
$632$	4.24479	−	5.84245i	0.168849	−	0.232400i
$633$	19.7836	+	21.0674i	0.786328	+	0.837354i
$634$	−15.1880	+	6.01336i	−0.603193	+	0.238821i
$635$	−20.1763	+	18.1775i	−0.800672	+	0.721352i
$636$	−31.6785	+	8.13365i	−1.25613	+	0.322520i
$637$	25.0811	−	20.7489i	0.993750	−	0.822101i
$638$	0.726809	+	1.83571i	0.0287747	+	0.0726765i
$639$	7.59420	+	3.00676i	0.300422	+	0.118945i
$640$	−15.8986	−	20.0470i	−0.628446	−	0.792426i
$641$	−2.81519	+	4.43603i	−0.111193	+	0.175213i	−0.895367	−	0.445328i	$-0.853087\pi$
$641$	−2.81519	+	4.43603i	−0.111193	+	0.175213i	0.784174	+	0.620541i	$0.213087\pi$
$642$	16.3063	−	29.6611i	0.643560	−	1.17063i
$643$	−2.80023	−	3.85419i	−0.110430	−	0.151994i	0.750224	−	0.661183i	$-0.229945\pi$
$643$	−2.80023	−	3.85419i	−0.110430	−	0.151994i	−0.860655	+	0.509189i	$0.829945\pi$
$644$	5.95734	−	31.2295i	0.234752	−	1.23061i
$645$	30.8512	+	20.4845i	1.21477	+	0.806577i
$646$	−0.376162	+	0.799385i	−0.0147999	+	0.0314514i
$647$	6.92825	+	12.6024i	0.272378	+	0.495453i	0.976751	−	0.214376i	$-0.0687719\pi$
$647$	6.92825	+	12.6024i	0.272378	+	0.495453i	−0.704373	+	0.709830i	$0.748772\pi$
$648$	−22.3585	−	1.40668i	−0.878325	−	0.0552595i
$649$	2.41431	+	1.75410i	0.0947699	+	0.0688544i
$650$	0.113633	+	5.27752i	0.00445704	+	0.207001i
$651$	60.2471	−	43.7721i	2.36127	−	1.71556i
$652$	12.6411	−	8.02226i	0.495062	−	0.314176i
$653$	1.87202	−	14.8186i	0.0732579	−	0.579896i	−0.912171	−	0.409809i	$-0.865595\pi$
$653$	1.87202	−	14.8186i	0.0732579	−	0.579896i	0.985429	−	0.170087i	$-0.0544048\pi$
$654$	−4.00931	−	0.506494i	−0.156777	−	0.0198055i
$655$	2.82486	−	3.72388i	0.110377	−	0.145504i
$656$	1.49274	+	0.820639i	0.0582816	+	0.0320406i
$657$	80.6011	+	26.1889i	3.14455	+	1.02173i
$658$	16.2745	−	7.65822i	0.634448	−	0.298548i
$659$	34.7931	+	8.93335i	1.35535	+	0.347994i	0.855358	−	0.518038i	$-0.173337\pi$
$659$	34.7931	+	8.93335i	1.35535	+	0.347994i	0.499989	+	0.866032i	$0.333337\pi$
$660$	−7.26777	−	1.07104i	−0.282898	−	0.0416903i
$661$	−7.37640	+	8.91654i	−0.286909	+	0.346813i	−0.894201	−	0.447665i	$-0.852256\pi$
$661$	−7.37640	+	8.91654i	−0.286909	+	0.346813i	0.607292	+	0.794478i	$0.292256\pi$
$662$	1.54116	+	0.978050i	0.0598989	+	0.0380130i
$663$	8.62472	−	0.542621i	0.334956	−	0.0210737i
$664$	14.3757	+	22.6525i	0.557886	+	0.879088i
$665$	−3.30987	+	9.51359i	−0.128351	+	0.368921i
$666$	−0.517964	−	8.23280i	−0.0200707	−	0.319015i
$667$	−18.4784	−	3.52495i	−0.715488	−	0.136487i
$668$	−27.2536	+	8.85522i	−1.05447	+	0.342619i
$669$	−3.50336	+	3.28987i	−0.135448	+	0.127194i
$670$	2.51392	+	2.16868i	0.0971212	+	0.0837833i
$671$	0.988451	+	5.18164i	0.0381587	+	0.200035i
$672$	58.3954	−	62.1847i	2.25265	−	2.39883i
$673$	−5.58131	+	14.0968i	−0.215144	+	0.543391i	−0.996766	−	0.0803613i	$-0.974393\pi$
$673$	−5.58131	+	14.0968i	−0.215144	+	0.543391i	0.781622	+	0.623752i	$0.214393\pi$
$674$	−1.88248	−	5.79366i	−0.0725102	−	0.223164i
$675$	1.95215	−	47.2363i	0.0751381	−	1.81813i
$676$	5.02733	−	15.4725i	0.193359	−	0.595097i
$677$	−27.4839	−	22.7367i	−1.05629	−	0.873840i	−0.0640230	−	0.997948i	$-0.520393\pi$
$677$	−27.4839	−	22.7367i	−1.05629	−	0.873840i	−0.992269	+	0.124108i	$0.960393\pi$
$678$	−23.7505	−	11.1762i	−0.912134	−	0.429218i
$679$	−62.5721	−	58.7591i	−2.40130	−	2.25497i
$680$	5.40366	+	5.99785i	0.207221	+	0.230007i
$681$	−8.30435	+	1.04908i	−0.318223	+	0.0402010i
$682$			1.96138i			0.0751050i
$683$	4.23962	+	33.5601i	0.162225	+	1.28414i	0.837444	+	0.546524i	$0.184049\pi$
$683$	4.23962	+	33.5601i	0.162225	+	1.28414i	−0.675219	+	0.737617i	$0.735951\pi$
$684$	5.67293	+	6.85740i	0.216910	+	0.262199i
$685$	39.1800	+	16.4563i	1.49699	+	0.628763i
$686$	−2.24937	+	35.7527i	−0.0858812	+	1.36504i
$687$	−11.9847	+	46.6772i	−0.457243	+	1.78085i
$688$	−2.63587	+	10.2660i	−0.100491	+	0.391388i
$689$	−0.725445	+	11.5306i	−0.0276372	+	0.439281i
$690$	−10.2688	+	11.9035i	−0.390925	+	0.453159i
$691$	−20.3157	−	24.5574i	−0.772844	−	0.934208i	0.226362	−	0.974043i	$-0.427317\pi$
$691$	−20.3157	−	24.5574i	−0.772844	−	0.934208i	−0.999206	+	0.0398351i	$0.987317\pi$
$692$	−3.61872	−	28.6451i	−0.137563	−	1.08892i
$693$		−	20.6768i		−	0.785447i
$694$	−7.25222	+	0.916169i	−0.275291	+	0.0347773i
$695$	−3.90035	−	37.0053i	−0.147949	−	1.40369i
$696$	−23.7311	−	22.2850i	−0.899525	−	0.844711i
$697$	−1.30782	−	0.615415i	−0.0495374	−	0.0233105i
$698$	8.29095	+	6.85887i	0.313817	+	0.259612i
$699$	−14.1098	+	43.4255i	−0.533682	+	1.64250i
$700$	30.7646	+	27.6680i	1.16279	+	1.04575i
$701$	−6.75025	−	20.7751i	−0.254953	−	0.784666i	−0.993839	−	0.110835i	$-0.964648\pi$
$701$	−6.75025	−	20.7751i	−0.254953	−	0.784666i	0.738885	−	0.673831i	$-0.235352\pi$
$702$	−3.67479	+	9.28145i	−0.138696	+	0.350306i
$703$	−1.35238	+	1.44014i	−0.0510061	+	0.0543160i
$704$	−0.0614652	−	0.322212i	−0.00231656	−	0.0121438i
$705$	39.4611	+	3.30204i	1.48619	+	0.124362i
$706$	−4.34948	+	4.08443i	−0.163695	+	0.153720i
$707$	−10.3707	+	3.36965i	−0.390031	+	0.126729i
$708$	−21.7273	−	4.14470i	−0.816562	−	0.155767i
$709$	3.10132	+	49.2940i	0.116472	+	1.85128i	0.431400	+	0.902161i	$0.358020\pi$
$709$	3.10132	+	49.2940i	0.116472	+	1.85128i	−0.314927	+	0.949116i	$0.601980\pi$
$710$	1.80427	+	0.0372668i	0.0677130	+	0.00139860i
$711$	10.7787	+	16.9846i	0.404235	+	0.636972i
$712$	4.47755	−	0.281703i	0.167803	−	0.0105573i
$713$	−15.7788	−	10.0135i	−0.590920	−	0.375009i
$714$	−9.69739	+	11.7221i	−0.362916	+	0.438690i
$715$	−1.15318	+	2.32478i	−0.0431266	+	0.0869417i
$716$	31.6060	+	8.11504i	1.18117	+	0.303273i
$717$	−57.2165	+	26.9240i	−2.13679	+	1.00550i
$718$	7.94899	+	2.58278i	0.296654	+	0.0963887i
$719$	45.9783	+	25.2768i	1.71470	+	0.942664i	0.957013	+	0.290046i	$0.0936706\pi$
$719$	45.9783	+	25.2768i	1.71470	+	0.942664i	0.757687	+	0.652618i	$0.226329\pi$
$720$	25.3691	−	7.66748i	0.945451	−	0.285750i
$721$	32.9349	+	4.16064i	1.22656	+	0.154950i
$722$	1.38225	−	10.9416i	0.0514421	−	0.407206i
$723$	−5.42667	+	3.44387i	−0.201820	+	0.128079i
$724$	21.2165	−	15.4147i	0.788503	−	0.572881i
$725$	16.3711	−	18.2034i	0.608009	−	0.676056i
$726$	−15.6289	−	11.3551i	−0.580044	−	0.421426i
$727$	11.2969	+	0.710738i	0.418977	+	0.0263598i	0.270880	−	0.962613i	$-0.412685\pi$
$727$	11.2969	+	0.710738i	0.418977	+	0.0263598i	0.148097	+	0.988973i	$0.452685\pi$
$728$	−9.36304	−	17.0313i	−0.347017	−	0.631222i
$729$	−9.92242	+	21.0862i	−0.367497	+	0.780971i
$730$	18.7085	−	0.789592i	0.692432	−	0.0292241i
$731$	1.68519	−	8.83405i	0.0623288	−	0.326739i
$732$	−22.9816	−	31.6314i	−0.849423	−	1.16913i
$733$	25.0434	−	45.5537i	0.924997	−	1.68256i	0.217227	−	0.976121i	$-0.430299\pi$
$733$	25.0434	−	45.5537i	0.924997	−	1.68256i	0.707770	−	0.706443i	$-0.249701\pi$
$734$	−7.19642	+	11.3397i	−0.265625	+	0.418558i
$735$	−69.7868	+	105.104i	−2.57413	+	3.87683i
$736$	−19.9038	−	7.88049i	−0.733665	−	0.290479i
$737$	0.600845	+	1.51756i	0.0221324	+	0.0559001i
$738$	2.51975	−	2.08452i	0.0927533	−	0.0767322i
$739$	−22.3267	+	5.73252i	−0.821300	+	0.210874i	−0.635883	−	0.771786i	$-0.719364\pi$
$739$	−22.3267	+	5.73252i	−0.821300	+	0.210874i	−0.185418	+	0.982660i	$0.559364\pi$
$740$	3.30285	+	7.41249i	0.121415	+	0.272489i
$741$	4.35378	−	1.72378i	0.159940	−	0.0633247i
$742$	−13.9231	−	14.8266i	−0.511135	−	0.544303i
$743$	0.644746	−	0.887417i	0.0236534	−	0.0325562i	−0.797026	−	0.603944i	$-0.793595\pi$
$743$	0.644746	−	0.887417i	0.0236534	−	0.0325562i	0.820680	+	0.571388i	$0.193595\pi$
$744$	−13.7699	−	29.2624i	−0.504827	−	1.07281i
$745$	−4.53768	+	30.7913i	−0.166248	+	1.12811i
$746$	11.1497	−	6.12959i	0.408219	−	0.224420i
$747$	−73.4092	+	14.0035i	−2.68590	+	0.512363i
$748$	0.443672	+	1.72799i	0.0162223	+	0.0631815i
$749$	−93.7202			−3.42446
$750$	−6.33940	−	19.4526i	−0.231482	−	0.710310i
$751$	10.7779			0.393290			0.196645	−	0.980475i	$-0.436995\pi$
$751$	10.7779			0.393290			0.196645	+	0.980475i	$0.436995\pi$
$752$	2.81854	+	10.9775i	0.102781	+	0.400307i
$753$	−15.7714	+	3.00855i	−0.574741	+	0.109638i
$754$	−4.52999	+	2.49038i	−0.164972	+	0.0906943i
$755$	−22.7774	−	11.2985i	−0.828954	−	0.411195i
$756$	33.3151	+	70.7981i	1.21166	+	2.57490i
$757$	−10.9043	+	15.0084i	−0.396322	+	0.545490i	−0.959816	−	0.280630i	$-0.909457\pi$
$757$	−10.9043	+	15.0084i	−0.396322	+	0.545490i	0.563494	+	0.826120i	$0.309457\pi$
$758$	−10.7116	−	11.4067i	−0.389064	−	0.414311i
$759$	−7.18572	+	2.84503i	−0.260825	+	0.103268i
$760$	3.78900	+	2.18611i	0.137442	+	0.0792984i
$761$	−30.2903	+	7.77722i	−1.09802	+	0.281924i	−0.753892	−	0.656998i	$-0.771826\pi$
$761$	−30.2903	+	7.77722i	−1.09802	+	0.281924i	−0.344129	+	0.938922i	$0.611826\pi$
$762$	−17.1245	+	14.1666i	−0.620356	+	0.513203i
$763$	4.11912	+	10.4037i	0.149122	+	0.376640i
$764$	5.04185	+	1.99621i	0.182408	+	0.0722203i
$765$	−21.0749	+	7.84470i	−0.761966	+	0.283626i
$766$	7.36538	−	11.6060i	0.266122	−	0.419341i
$767$	−3.76422	+	6.84709i	−0.135918	+	0.247234i
$768$	−10.5577	−	14.5314i	−0.380968	−	0.524357i
$769$	−1.37352	+	7.20024i	−0.0495304	+	0.259647i	−0.998436	−	0.0559139i	$-0.982193\pi$
$769$	−1.37352	+	7.20024i	−0.0495304	+	0.259647i	0.948905	+	0.315561i	$0.102193\pi$
$770$	−1.59370	−	4.28151i	−0.0574330	−	0.154295i
$771$	27.3500	−	58.1217i	0.984986	−	2.09320i
$772$	−5.13562	−	9.34166i	−0.184835	−	0.336214i
$773$	11.7859	+	0.741506i	0.423910	+	0.0266701i	0.273313	−	0.961925i	$-0.411881\pi$
$773$	11.7859	+	0.741506i	0.423910	+	0.0266701i	0.150597	+	0.988595i	$0.451881\pi$
$774$	16.4616	+	11.9601i	0.591701	+	0.429896i
$775$	21.7785	−	10.8268i	0.782306	−	0.388910i
$776$	−30.1575	+	21.9107i	−1.08259	+	0.786548i
$777$	−28.7239	+	18.2287i	−1.03046	+	0.653953i
$778$	−2.28148	+	18.0598i	−0.0817950	+	0.647474i
$779$	−0.777016	−	0.0981600i	−0.0278395	−	0.00351695i
$780$	0.397201	−	19.2304i	0.0142221	−	0.688560i
$781$	0.777444	+	0.427403i	0.0278191	+	0.0152937i
$782$	3.63092	+	1.17976i	0.129841	+	0.0421880i
$783$	41.8912	−	19.7125i	1.49707	−	0.704467i
$784$	−34.9744	−	8.97989i	−1.24908	−	0.320710i
$785$	4.15090	+	24.4981i	0.148152	+	0.874373i
$786$	2.43827	−	2.94736i	0.0869702	−	0.105129i
$787$	19.2473	+	12.2147i	0.686091	+	0.435406i	0.832653	−	0.553795i	$-0.186821\pi$
$787$	19.2473	+	12.2147i	0.686091	+	0.435406i	−0.146562	+	0.989201i	$0.546821\pi$
$788$	−19.1034	+	1.20189i	−0.680531	+	0.0428154i
$789$	−4.75640	−	7.49488i	−0.169332	−	0.266825i
$790$	3.54105	+	2.68618i	0.125985	+	0.0955698i
$791$	4.56356	+	72.5357i	0.162261	+	2.57907i
$792$	−8.82039	−	1.68258i	−0.313419	−	0.0597879i
$793$	−13.1356	+	4.26802i	−0.466459	+	0.151562i
$794$	−5.72568	+	5.37677i	−0.203197	+	0.190814i
$795$	−10.2381	−	43.5930i	−0.363107	−	1.54608i
$796$	0.0557929	+	0.292477i	0.00197753	+	0.0103666i
$797$	16.1498	−	17.1978i	0.572056	−	0.609178i	−0.376257	−	0.926515i	$-0.622789\pi$
$797$	16.1498	−	17.1978i	0.572056	−	0.609178i	0.948313	+	0.317338i	$0.102789\pi$
$798$	−3.03463	+	7.66460i	−0.107425	+	0.271324i
$799$	−2.97170	−	9.14594i	−0.105131	−	0.323560i
$800$	22.1815	−	16.8571i	0.784235	−	0.595989i
$801$	−3.86177	+	11.8853i	−0.136449	+	0.419947i
$802$	−7.13501	−	5.90260i	−0.251946	−	0.208428i
$803$	8.32932	+	3.91948i	0.293935	+	0.138316i
$804$	−8.81879	−	8.28139i	−0.311015	−	0.292062i
$805$	42.5800	+	9.03766i	1.50075	+	0.318536i
$806$	−5.09493	+	0.643639i	−0.179461	+	0.0226712i
$807$			38.6826i			1.36169i
$808$	0.593519	+	4.69819i	0.0208799	+	0.165282i
$809$	−6.09362	−	7.36593i	−0.214240	−	0.258972i	0.652435	−	0.757845i	$-0.273748\pi$
$809$	−6.09362	−	7.36593i	−0.214240	−	0.258972i	−0.866675	+	0.498873i	$0.833748\pi$
$810$	1.14973	−	13.7399i	0.0403973	−	0.482769i
$811$	0.944752	−	15.0164i	0.0331747	−	0.527297i	−0.945986	−	0.324208i	$-0.894902\pi$
$811$	0.944752	−	15.0164i	0.0331747	−	0.527297i	0.979160	−	0.203089i	$-0.0650979\pi$
$812$	−10.0767	+	39.2461i	−0.353622	+	1.37727i
$813$	5.32006	−	20.7203i	0.186583	−	0.726692i
$814$	0.0562612	−	0.894246i	0.00197195	−	0.0313433i
$815$	10.6239	+	17.5305i	0.372138	+	0.614068i
$816$	−6.11051	−	7.38634i	−0.213911	−	0.258574i
$817$	−0.610762	−	4.83468i	−0.0213679	−	0.169144i
$818$		−	2.46699i		−	0.0862562i
$819$	53.7106	−	6.78523i	1.87680	−	0.237095i
$820$	−1.60773	+	2.78655i	−0.0561443	+	0.0973105i
$821$	−18.2565	−	17.1440i	−0.637155	−	0.598328i	0.297138	−	0.954835i	$-0.403968\pi$
$821$	−18.2565	−	17.1440i	−0.637155	−	0.598328i	−0.934293	+	0.356506i	$0.883968\pi$
$822$	31.4678	+	14.8076i	1.09757	+	0.516476i
$823$	−43.3976	−	35.9016i	−1.51274	−	1.25145i	−0.877933	−	0.478784i	$-0.841078\pi$
$823$	−43.3976	−	35.9016i	−1.51274	−	1.25145i	−0.634812	−	0.772667i	$-0.718922\pi$
$824$	4.45495	−	13.7109i	0.155195	−	0.477642i
$825$	1.67158	−	9.91821i	0.0581970	−	0.345308i
$826$	−4.25066	−	13.0822i	−0.147899	−	0.455187i
$827$	5.70993	−	14.4216i	0.198554	−	0.501489i	−0.796051	−	0.605230i	$-0.793081\pi$
$827$	5.70993	−	14.4216i	0.198554	−	0.501489i	0.994604	+	0.103741i	$0.0330812\pi$
$828$	26.3270	−	28.0355i	0.914928	−	0.974299i
$829$	−9.23884	−	48.4317i	−0.320878	−	1.68210i	−0.667904	−	0.744247i	$-0.732808\pi$
$829$	−9.23884	−	48.4317i	−0.320878	−	1.68210i	0.347026	−	0.937855i	$-0.387192\pi$
$830$	−14.1213	+	8.55783i	−0.490159	+	0.297047i
$831$	54.4571	−	51.1386i	1.88909	−	1.77398i
$832$	0.816817	−	0.265400i	0.0283180	−	0.00920109i
$833$	30.0959	+	5.74111i	1.04276	+	0.198918i
$834$	−1.91211	−	30.3922i	−0.0662111	−	1.05239i
$835$	−11.3509	−	37.5564i	−0.392814	−	1.29969i
$836$	0.517980	+	0.816206i	0.0179147	+	0.0282291i
$837$	45.9023	−	2.88793i	1.58662	−	0.0998214i
$838$	16.1825	+	10.2697i	0.559014	+	0.354761i
$839$	14.8710	−	17.9759i	0.513403	−	0.620597i	−0.448568	−	0.893748i	$-0.648066\pi$
$839$	14.8710	−	17.9759i	0.513403	−	0.620597i	0.961971	+	0.273151i	$0.0880660\pi$
$840$	53.8353	+	52.6886i	1.85749	+	1.81793i
$841$	−4.86705	−	1.24965i	−0.167829	−	0.0430912i
$842$	−6.45879	+	3.03928i	−0.222585	+	0.104740i
$843$	39.4913	+	12.8315i	1.36015	+	0.441940i
$844$	−13.6891	−	7.52564i	−0.471198	−	0.259043i
$845$	21.0374	+	7.31912i	0.723710	+	0.251785i
$846$	21.5863	+	2.72698i	0.742151	+	0.0937555i
$847$	−6.70408	+	53.0683i	−0.230355	+	1.82345i
$848$	10.8210	−	6.86722i	0.371595	−	0.235821i
$849$	−3.53757	+	2.57020i	−0.121409	+	0.0882089i
$850$	−3.75930	+	3.24878i	−0.128943	+	0.111432i
$851$	6.90674	+	5.01804i	0.236760	+	0.172016i
$852$	−6.56277	−	0.412894i	−0.224837	−	0.0141455i
$853$	23.2921	+	42.3681i	0.797505	+	1.45066i	0.890496	+	0.454990i	$0.150357\pi$
$853$	23.2921	+	42.3681i	0.797505	+	1.45066i	−0.0929910	+	0.995667i	$0.529643\pi$
$854$	10.3527	−	22.0005i	0.354261	−	0.752843i
$855$	−9.54714	+	7.57151i	−0.326505	+	0.258940i
$856$	−7.62650	+	39.9795i	−0.260669	+	1.36647i
$857$	8.56148	+	11.7839i	0.292455	+	0.402529i	0.929809	−	0.368041i	$-0.119971\pi$
$857$	8.56148	+	11.7839i	0.292455	+	0.402529i	−0.637355	+	0.770570i	$0.719971\pi$
$858$	−1.02313	+	1.86107i	−0.0349291	+	0.0635358i
$859$	−24.4135	+	38.4695i	−0.832978	+	1.31256i	0.114722	+	0.993398i	$0.463402\pi$
$859$	−24.4135	+	38.4695i	−0.832978	+	1.31256i	−0.947699	+	0.319165i	$0.896598\pi$
$860$	−19.2813	−	5.37735i	−0.657486	−	0.183366i
$861$	−12.5396	−	4.96477i	−0.427348	−	0.169199i
$862$	−5.76767	−	14.5675i	−0.196448	−	0.496170i
$863$	−5.83007	+	4.82306i	−0.198458	+	0.164179i	−0.731345	−	0.682008i	$-0.761107\pi$
$863$	−5.83007	+	4.82306i	−0.198458	+	0.164179i	0.532887	+	0.846186i	$0.321107\pi$
$864$	51.0300	−	13.1023i	1.73607	−	0.445748i
$865$	39.3131	−	4.14359i	1.33669	−	0.140886i
$866$	−14.0316	+	5.55550i	−0.476813	+	0.188783i
$867$	−29.5938	−	31.5142i	−1.00506	−	1.07028i
$868$	−23.6599	+	32.5651i	−0.803071	+	1.10533i
$869$	0.930332	+	1.97706i	0.0315593	+	0.0670670i
$870$	14.0141	−	14.3191i	0.475123	−	0.485463i
$871$	−3.74489	+	2.05877i	−0.126891	+	0.0697588i
$872$	4.77325	−	0.910546i	0.161643	−	0.0308350i
$873$	−25.8227	−	100.573i	−0.873968	−	3.40388i
$874$	2.06869			0.0699743
$875$	−38.7432	+	41.3298i	−1.30976	+	1.39720i
$876$	−68.2301			−2.30528
$877$	0.384575	+	1.49782i	0.0129862	+	0.0505778i	0.974746	−	0.223316i	$-0.0716882\pi$
$877$	0.384575	+	1.49782i	0.0129862	+	0.0505778i	−0.961760	+	0.273894i	$0.911688\pi$
$878$	−6.99758	+	1.33486i	−0.236157	+	0.0450493i
$879$	−4.63973	+	2.55071i	−0.156494	+	0.0860335i
$880$	2.83825	−	0.480906i	0.0956772	−	0.0162113i
$881$	−10.9419	−	23.2527i	−0.368642	−	0.783405i	−0.999969	−	0.00788785i	$-0.997489\pi$
$881$	−10.9419	−	23.2527i	−0.368642	−	0.783405i	0.631326	−	0.775517i	$-0.282511\pi$
$882$	−40.7457	+	56.0816i	−1.37198	+	1.88837i
$883$	−23.9280	−	25.4808i	−0.805243	−	0.857496i	0.186930	−	0.982373i	$-0.440146\pi$
$883$	−23.9280	−	25.4808i	−0.805243	−	0.857496i	−0.992172	+	0.124877i	$0.960146\pi$
$884$	−4.34308	+	1.71955i	−0.146074	+	0.0578346i
$885$	6.28778	−	29.6242i	0.211361	−	0.995807i
$886$	7.02557	−	1.80386i	0.236029	−	0.0606018i
$887$	18.3442	−	15.1756i	0.615937	−	0.509548i	−0.276326	−	0.961064i	$-0.589117\pi$
$887$	18.3442	−	15.1756i	0.615937	−	0.509548i	0.892263	+	0.451517i	$0.149117\pi$
$888$	5.43867	+	13.7365i	0.182510	+	0.460968i
$889$	57.2162	+	22.6535i	1.91897	+	0.759774i
$890$	0.116432	+	2.75872i	0.00390281	+	0.0924726i
$891$	3.63196	−	5.72305i	0.121675	−	0.191729i
$892$	1.25146	−	2.27640i	0.0419020	−	0.0762195i
$893$	−3.06285	−	4.21565i	−0.102494	−	0.141071i
$894$	−4.77283	+	25.0201i	−0.159627	+	0.836796i
$895$	−12.0019	+	43.0344i	−0.401178	+	1.43848i
$896$	−24.6857	+	52.4598i	−0.824691	+	1.75256i
$897$	−9.74837	−	17.7322i	−0.325489	−	0.592061i
$898$	0.902264	+	0.0567656i	0.0301089	+	0.00189429i
$899$	19.2687	+	13.9996i	0.642648	+	0.466911i
$900$	13.4882	+	48.2004i	0.449605	+	1.60668i
$901$	−8.79773	+	6.39192i	−0.293095	+	0.212946i
$902$	0.299915	−	0.190332i	0.00998607	−	0.00633735i
$903$	10.5174	−	83.2538i	0.349997	−	2.77051i
$904$	31.3139	+	3.95587i	1.04149	+	0.131570i
$905$	20.5005	+	29.4780i	0.681459	+	0.979881i
$906$	−18.2341	−	10.0243i	−0.605788	−	0.333035i
$907$	−37.6614	−	12.2369i	−1.25053	−	0.406320i	−0.392416	−	0.919788i	$-0.628361\pi$
$907$	−37.6614	−	12.2369i	−1.25053	−	0.406320i	−0.858109	+	0.513467i	$0.828361\pi$
$908$	4.09379	−	1.92639i	0.135857	−	0.0639296i
$909$	−12.7765	−	3.28045i	−0.423770	−	0.108806i
$910$	10.5988	−	5.54485i	0.351346	−	0.183810i
$911$	−6.62982	+	8.01408i	−0.219656	+	0.265518i	−0.868818	−	0.495132i	$-0.835120\pi$
$911$	−6.62982	+	8.01408i	−0.219656	+	0.265518i	0.649162	+	0.760650i	$0.275120\pi$
$912$	−4.38576	−	2.78329i	−0.145227	−	0.0921639i
$913$	−8.10146	+	0.509701i	−0.268119	+	0.0168686i
$914$	−7.12786	−	11.2317i	−0.235769	−	0.371512i
$915$	43.9484	−	30.5640i	1.45289	−	1.01041i
$916$	−1.63560	−	25.9972i	−0.0540419	−	0.858971i
$917$	−10.4038	−	1.98464i	−0.343565	−	0.0655385i
$918$	−8.93607	+	2.90350i	−0.294934	+	0.0958299i
$919$	19.2213	−	18.0500i	0.634051	−	0.595414i	−0.299396	−	0.954129i	$-0.596785\pi$
$919$	19.2213	−	18.0500i	0.634051	−	0.595414i	0.933447	+	0.358715i	$0.116785\pi$
$920$	7.32028	−	17.4285i	0.241342	−	0.574601i
$921$	−9.45546	−	49.5672i	−0.311568	−	1.63330i
$922$	−7.77193	+	8.27626i	−0.255955	+	0.272564i
$923$	−0.855112	+	2.15977i	−0.0281463	+	0.0710896i
$924$	5.14407	+	15.8318i	0.169228	+	0.520829i
$925$	−10.2400	+	4.31153i	−0.336688	+	0.141762i
$926$	−2.33563	+	7.18833i	−0.0767536	+	0.236223i
$927$	30.9419	+	25.5974i	1.01626	+	0.840727i
$928$	24.6864	+	11.6165i	0.810370	+	0.381331i
$929$	23.7024	+	22.2581i	0.777651	+	0.730263i	0.967862	−	0.251480i	$-0.0809173\pi$
$929$	23.7024	+	22.2581i	0.777651	+	0.730263i	−0.190211	+	0.981743i	$0.560917\pi$
$930$	18.1809	−	8.10102i	0.596175	−	0.265643i
$931$	16.4708	−	2.08075i	0.539810	−	0.0681939i
$932$		−	24.6806i		−	0.808439i
$933$	8.72635	+	69.0762i	0.285688	+	2.26145i
$934$	0.993967	+	1.20150i	0.0325236	+	0.0393143i
$935$	−2.37790	+	0.558465i	−0.0777657	+	0.0182637i
$936$	1.47625	−	23.4642i	0.0482526	−	0.766953i
$937$	8.70136	−	33.8896i	0.284261	−	1.10712i	−0.652679	−	0.757634i	$-0.726355\pi$
$937$	8.70136	−	33.8896i	0.284261	−	1.10712i	0.936940	−	0.349489i	$-0.113645\pi$
$938$	1.87096	−	7.28691i	0.0610891	−	0.237926i
$939$	3.51285	−	55.8351i	0.114637	−	1.82211i
$940$	−20.8373	+	4.89378i	−0.679639	+	0.159617i
$941$	20.8845	+	25.2450i	0.680816	+	0.822965i	0.991847	−	0.127435i	$-0.0406744\pi$
$941$	20.8845	+	25.2450i	0.680816	+	0.822965i	−0.311031	+	0.950400i	$0.600674\pi$
$942$	2.54859	+	20.1742i	0.0830376	+	0.657311i
$943$			3.38445i			0.110213i
$944$	8.59921	−	1.08633i	0.279880	−	0.0353571i
$945$	−97.8539	+	43.6016i	−3.18319	+	1.41836i
$946$	1.61114	+	1.51296i	0.0523827	+	0.0491906i
$947$	39.7033	+	18.6830i	1.29018	+	0.607115i	0.943657	−	0.330925i	$-0.107361\pi$
$947$	39.7033	+	18.6830i	1.29018	+	0.607115i	0.346528	+	0.938040i	$0.387361\pi$
$948$	−12.4786	−	10.3232i	−0.405286	−	0.335281i
$949$	−7.44803	+	22.9227i	−0.241773	+	0.744102i
$950$	−1.39332	+	2.30368i	−0.0452053	+	0.0747413i
$951$	25.1828	+	77.5047i	0.816608	+	2.51326i
$952$	6.73425	−	17.0088i	0.218258	−	0.551257i
$953$	−4.72385	+	5.03039i	−0.153021	+	0.162950i	−0.800911	−	0.598783i	$-0.795651\pi$
$953$	−4.72385	+	5.03039i	−0.153021	+	0.162950i	0.647891	+	0.761733i	$0.275651\pi$
$954$	−4.61034	−	24.1682i	−0.149265	−	0.782476i
$955$	−2.87506	+	6.84509i	−0.0930348	+	0.221502i
$956$	24.9161	−	23.3978i	0.805846	−	0.756740i
$957$	9.36767	−	3.04374i	0.302814	−	0.0983902i
$958$	−13.7197	−	2.61717i	−0.443263	−	0.0845569i
$959$	−6.04640	−	96.1048i	−0.195249	−	3.10339i
$960$	−2.73286	+	1.90057i	−0.0882027	+	0.0613407i
$961$	−3.93249	−	6.19662i	−0.126855	−	0.199891i
$962$	2.34138	−	0.147307i	0.0754891	−	0.00474937i
$963$	−95.7232	−	60.7478i	−3.08464	−	1.95757i
$964$	2.21445	−	2.67682i	0.0713228	−	0.0862144i
$965$	12.9325	−	6.76577i	0.416313	−	0.217798i
$966$	34.5038	+	8.85908i	1.11014	+	0.285036i
$967$	−0.412614	+	0.194162i	−0.0132688	+	0.00624382i	−0.432402	−	0.901681i	$-0.642334\pi$
$967$	−0.412614	+	0.194162i	−0.0132688	+	0.00624382i	0.419133	+	0.907925i	$0.362334\pi$
$968$	22.0925	+	7.17830i	0.710081	+	0.230719i
$969$	3.86230	+	2.12332i	0.124075	+	0.0682108i
$970$	−13.0989	−	18.8351i	−0.420581	−	0.604759i
$971$	−19.3987	−	2.45063i	−0.622534	−	0.0786444i	−0.192262	−	0.981344i	$-0.561582\pi$
$971$	−19.3987	−	2.45063i	−0.622534	−	0.0786444i	−0.430272	+	0.902699i	$0.641582\pi$
$972$	−0.490409	+	3.88199i	−0.0157299	+	0.124515i
$973$	−71.1922	+	45.1799i	−2.28232	+	1.44840i
$974$	−2.11033	+	1.53325i	−0.0676194	+	0.0491284i
$975$	26.3124	+	1.08742i	0.842670	+	0.0348252i
$976$	12.3950	+	9.00553i	0.396756	+	0.288260i
$977$	51.8752	+	3.26371i	1.65963	+	0.104415i	0.864703	−	0.502284i	$-0.167507\pi$
$977$	51.8752	+	3.26371i	1.65963	+	0.104415i	0.794931	+	0.606700i	$0.207507\pi$
$978$	8.08169	+	14.7005i	0.258424	+	0.470071i
$979$	−0.577961	+	1.22823i	−0.0184717	+	0.0392544i
$980$	18.3196	−	65.6876i	0.585199	−	2.09831i
$981$	−2.53635	+	13.2960i	−0.0809793	+	0.424509i
$982$	3.54084	+	4.87355i	0.112993	+	0.155521i
$983$	−7.73305	+	14.0664i	−0.246646	+	0.448647i	−0.970431	−	0.241378i	$-0.922401\pi$
$983$	−7.73305	+	14.0664i	−0.246646	+	0.448647i	0.723785	+	0.690025i	$0.242401\pi$
$984$	−3.13830	+	4.94517i	−0.100045	+	0.157646i
$985$	−1.10508	−	26.1837i	−0.0352109	−	0.834282i
$986$	−4.52399	−	1.79118i	−0.144073	−	0.0570427i
$987$	−33.0322	−	83.4298i	−1.05143	−	2.65560i
$988$	−1.95022	+	1.61336i	−0.0620448	+	0.0513279i
$989$	−20.3968	+	5.23701i	−0.648581	+	0.166527i
$990$	1.14743	−	5.40602i	0.0364679	−	0.171815i
$991$	−54.8553	+	21.7188i	−1.74254	+	0.689919i	−0.742744	+	0.669576i	$0.766476\pi$
$991$	−54.8553	+	21.7188i	−1.74254	+	0.689919i	−0.999793	+	0.0203436i	$0.993524\pi$
$992$	18.5537	+	19.7577i	0.589081	+	0.627307i
$993$	5.35248	−	7.36705i	0.169856	−	0.233786i
$994$	−1.74115	−	3.70013i	−0.0552259	−	0.117361i
$995$	−0.401934	+	0.0681029i	−0.0127422	+	0.00215901i
$996$	52.7241	−	28.9853i	1.67063	−	0.918435i
$997$	−16.8400	+	3.21239i	−0.533327	+	0.101738i	−0.447008	−	0.894530i	$-0.647510\pi$
$997$	−16.8400	+	3.21239i	−0.533327	+	0.101738i	−0.0863190	+	0.996268i	$0.527510\pi$
$998$	−4.56209	−	17.7682i	−0.144411	−	0.562442i
$999$	−21.0110			−0.664757

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.h.a.104.6	✓	240
5.2	odd	4		625.2.g.b.351.15		480
5.3	odd	4		625.2.g.b.351.10		480
5.4	even	2		625.2.h.a.274.7		240
125.6	even	25		625.2.h.a.349.7		240
125.33	odd	100		625.2.g.b.276.10		480
125.92	odd	100		625.2.g.b.276.15		480
125.119	even	50	inner	125.2.h.a.119.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.104.6	✓	240	1.1	even	1	trivial
125.2.h.a.119.6	yes	240	125.119	even	50	inner
625.2.g.b.276.10		480	125.33	odd	100
625.2.g.b.276.15		480	125.92	odd	100
625.2.g.b.351.10		480	5.3	odd	4
625.2.g.b.351.15		480	5.2	odd	4
625.2.h.a.274.7		240	5.4	even	2
625.2.h.a.349.7		240	125.6	even	25

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.h (of order \(50\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.150619 - 0.586621i) q^{2} +(-2.96797 + 0.566170i) q^{3} +(1.43117 - 0.786795i) q^{4} +(1.03654 + 1.98131i) q^{5} +(0.779158 + 1.65580i) q^{6} +(2.97825 - 4.09921i) q^{7} +(-1.50630 - 1.60405i) q^{8} +(5.69894 - 2.25637i) q^{9} +O(q^{10})\)	\(q+(-0.150619 - 0.586621i) q^{2} +(-2.96797 + 0.566170i) q^{3} +(1.43117 - 0.786795i) q^{4} +(1.03654 + 1.98131i) q^{5} +(0.779158 + 1.65580i) q^{6} +(2.97825 - 4.09921i) q^{7} +(-1.50630 - 1.60405i) q^{8} +(5.69894 - 2.25637i) q^{9} +(1.00616 - 0.906479i) q^{10} +(0.644855 - 0.165571i) q^{11} +(-3.80222 + 3.14547i) q^{12} +(0.641704 + 1.62076i) q^{13} +(-2.85327 - 1.12969i) q^{14} +(-4.19817 - 5.29360i) q^{15} +(1.03612 - 1.63267i) q^{16} +(-0.790438 + 1.43780i) q^{17} +(-2.18200 - 3.00327i) q^{18} +(-0.166592 + 0.873305i) q^{19} +(3.04235 + 2.02005i) q^{20} +(-6.51850 + 13.8525i) q^{21} +(-0.194254 - 0.353347i) q^{22} +(3.83432 + 0.241235i) q^{23} +(5.37882 + 3.90794i) q^{24} +(-2.85117 + 4.10741i) q^{25} +(0.854119 - 0.620554i) q^{26} +(-7.98340 + 5.06642i) q^{27} +(1.03716 - 8.20997i) q^{28} +(-4.85783 - 0.613686i) q^{29} +(-2.47301 + 3.26005i) q^{30} +(-4.26257 - 2.34337i) q^{31} +(-5.29930 - 1.72185i) q^{32} +(-1.82017 + 0.856505i) q^{33} +(0.962499 + 0.247128i) q^{34} +(11.2089 + 1.65184i) q^{35} +(6.38088 - 7.71316i) q^{36} +(1.87620 + 1.19068i) q^{37} +(0.537391 - 0.0338098i) q^{38} +(-2.82218 - 4.44704i) q^{39} +(1.61677 - 4.64711i) q^{40} +(0.0553140 + 0.879191i) q^{41} +(9.10799 + 1.73744i) q^{42} +(-5.21297 + 1.69380i) q^{43} +(0.792630 - 0.744329i) q^{44} +(10.3777 + 8.95254i) q^{45} +(-0.436007 - 2.28563i) q^{46} +(-4.01220 + 4.27256i) q^{47} +(-2.15081 + 5.43232i) q^{48} +(-5.77044 - 17.7596i) q^{49} +(2.83893 + 1.05390i) q^{50} +(1.53195 - 4.71486i) q^{51} +(2.19360 + 1.81470i) q^{52} +(5.99702 + 2.82199i) q^{53} +(4.17452 + 3.92013i) q^{54} +(0.996464 + 1.10604i) q^{55} +(-11.0615 + 1.39739i) q^{56} -2.68626i q^{57} +(0.371678 + 2.94214i) q^{58} +(2.85719 + 3.45375i) q^{59} +(-10.1733 - 4.27296i) q^{60} +(-0.497506 + 7.90763i) q^{61} +(-0.732646 + 2.85347i) q^{62} +(7.72354 - 30.0812i) q^{63} +(0.0309366 - 0.491723i) q^{64} +(-2.54607 + 2.95140i) q^{65} +(0.776595 + 0.938742i) q^{66} +(0.307262 + 2.43223i) q^{67} +2.67966i q^{68} +(-11.5167 + 1.45490i) q^{69} +(-0.719264 - 6.82417i) q^{70} +(0.971397 + 0.912203i) q^{71} +(-12.2037 - 5.74261i) q^{72} +(10.6537 + 8.81348i) q^{73} +(0.415884 - 1.27996i) q^{74} +(6.13668 - 13.8049i) q^{75} +(0.448690 + 1.38093i) q^{76} +(1.24183 - 3.13651i) q^{77} +(-2.18366 + 2.32536i) q^{78} +(0.614971 + 3.22379i) q^{79} +(4.30880 + 0.360552i) q^{80} +(7.42165 - 6.96939i) q^{81} +(0.507421 - 0.164871i) q^{82} +(-11.9766 - 2.28466i) q^{83} +(1.56998 + 24.9541i) q^{84} +(-3.66805 - 0.0757628i) q^{85} +(1.77879 + 2.80292i) q^{86} +(14.7653 - 0.928955i) q^{87} +(-1.23693 - 0.784979i) q^{88} +(-1.29962 + 1.57097i) q^{89} +(3.68867 - 7.43623i) q^{90} +(8.55500 + 2.19655i) q^{91} +(5.67739 - 2.67158i) q^{92} +(13.9779 + 4.54170i) q^{93} +(3.11069 + 1.71011i) q^{94} +(-1.90296 + 0.575146i) q^{95} +(16.7030 + 2.11008i) q^{96} +(2.12322 - 16.8070i) q^{97} +(-9.54902 + 6.05999i) q^{98} +(3.30140 - 2.39861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9	\( 240 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 25 q^{5} - 20 q^{6} - 25 q^{7} - 35 q^{8} - 20 q^{9} - 20 q^{10} - 25 q^{11} + 60 q^{12} - 20 q^{13} - 30 q^{14} - 40 q^{15} - 40 q^{16} - 15 q^{17} - 25 q^{18} - 10 q^{19} - 10 q^{20} - 35 q^{21} - 25 q^{22} + 70 q^{23} + 15 q^{24} + 35 q^{25} - 45 q^{26} - 20 q^{27} - 10 q^{28} - 10 q^{29} - 40 q^{30} - 30 q^{31} - 25 q^{32} - 35 q^{33} - 20 q^{34} - 40 q^{35} + 170 q^{36} - 55 q^{37} - 40 q^{38} - 35 q^{40} - 35 q^{41} - 10 q^{42} - 25 q^{43} + 15 q^{44} + 140 q^{45} - 40 q^{46} + 100 q^{47} + 5 q^{48} + 35 q^{49} - 10 q^{50} - 55 q^{51} - 15 q^{52} - 15 q^{53} + 30 q^{54} - 15 q^{55} + 65 q^{56} + 255 q^{58} + 5 q^{59} + 135 q^{60} - 40 q^{61} + 5 q^{62} - 35 q^{63} + 25 q^{64} - 30 q^{65} - 95 q^{66} + 105 q^{67} - 10 q^{69} - 55 q^{70} + 45 q^{71} - 30 q^{72} - 40 q^{73} + 35 q^{74} - 15 q^{75} - 65 q^{76} - 35 q^{77} + 100 q^{78} + 430 q^{80} - 95 q^{81} + 175 q^{82} + 20 q^{83} + 45 q^{84} - 10 q^{85} - 80 q^{86} - 5 q^{87} - 5 q^{88} + 30 q^{89} + 65 q^{91} - 55 q^{92} + 275 q^{93} + 60 q^{94} + 10 q^{95} - 135 q^{96} + 35 q^{97} - 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 25 * q^5 - 20 * q^6 - 25 * q^7 - 35 * q^8 - 20 * q^9 - 20 * q^10 - 25 * q^11 + 60 * q^12 - 20 * q^13 - 30 * q^14 - 40 * q^15 - 40 * q^16 - 15 * q^17 - 25 * q^18 - 10 * q^19 - 10 * q^20 - 35 * q^21 - 25 * q^22 + 70 * q^23 + 15 * q^24 + 35 * q^25 - 45 * q^26 - 20 * q^27 - 10 * q^28 - 10 * q^29 - 40 * q^30 - 30 * q^31 - 25 * q^32 - 35 * q^33 - 20 * q^34 - 40 * q^35 + 170 * q^36 - 55 * q^37 - 40 * q^38 - 35 * q^40 - 35 * q^41 - 10 * q^42 - 25 * q^43 + 15 * q^44 + 140 * q^45 - 40 * q^46 + 100 * q^47 + 5 * q^48 + 35 * q^49 - 10 * q^50 - 55 * q^51 - 15 * q^52 - 15 * q^53 + 30 * q^54 - 15 * q^55 + 65 * q^56 + 255 * q^58 + 5 * q^59 + 135 * q^60 - 40 * q^61 + 5 * q^62 - 35 * q^63 + 25 * q^64 - 30 * q^65 - 95 * q^66 + 105 * q^67 - 10 * q^69 - 55 * q^70 + 45 * q^71 - 30 * q^72 - 40 * q^73 + 35 * q^74 - 15 * q^75 - 65 * q^76 - 35 * q^77 + 100 * q^78 + 430 * q^80 - 95 * q^81 + 175 * q^82 + 20 * q^83 + 45 * q^84 - 10 * q^85 - 80 * q^86 - 5 * q^87 - 5 * q^88 + 30 * q^89 + 65 * q^91 - 55 * q^92 + 275 * q^93 + 60 * q^94 + 10 * q^95 - 135 * q^96 + 35 * q^97 - 15 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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