LMFDB - Embedded newform 507.2.q.b.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			55.1
Character	$\chi$	$=$	507.55
Dual form			507.2.q.b.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.73567 + 2.12581i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-1.10646 - 5.41982i) q^{4} +(0.355841 + 2.93061i) q^{5} +(1.90110 - 1.97925i) q^{6} +(0.0396979 - 0.0251034i) q^{7} +(8.58190 + 4.50413i) q^{8} +(0.987050 + 0.160411i) q^{9} +(-6.84755 - 4.33013i) q^{10} +(-2.29870 + 0.373576i) q^{11} +(0.666762 + 5.49128i) q^{12} +(-0.627698 - 3.55049i) q^{13} +(-0.0155373 + 0.127961i) q^{14} +(-0.118871 - 2.94975i) q^{15} +(-14.2923 + 6.08938i) q^{16} +(-5.18980 + 3.28183i) q^{17} +(-2.05420 + 1.81986i) q^{18} +(-2.75493 + 4.77168i) q^{19} +(15.4897 - 5.17121i) q^{20} +(-0.0415891 + 0.0218277i) q^{21} +(3.19564 - 5.53501i) q^{22} +(-4.02443 - 6.97052i) q^{23} +(-8.19164 - 5.18008i) q^{24} +(-3.60717 + 0.889088i) q^{25} +(8.63714 + 4.82811i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.179980 - 0.187379i) q^{28} +(1.22510 - 1.50048i) q^{29} +(6.47691 + 4.86708i) q^{30} +(5.75851 + 1.41935i) q^{31} +(6.46885 - 22.3331i) q^{32} +(2.32131 - 0.187396i) q^{33} +(2.03123 - 16.7287i) q^{34} +(0.0876946 + 0.107406i) q^{35} +(-0.222735 - 5.52712i) q^{36} +(-1.86333 - 6.43296i) q^{37} +(-5.36203 - 14.1385i) q^{38} +(0.339967 + 3.58949i) q^{39} +(-10.1461 + 26.7530i) q^{40} +(3.15489 + 0.254689i) q^{41} +(0.0257835 - 0.126296i) q^{42} +(2.79259 - 9.64115i) q^{43} +(4.56815 + 12.0452i) q^{44} +(-0.118871 + 2.94975i) q^{45} +(21.8031 + 3.54334i) q^{46} +(-4.30586 - 3.81466i) q^{47} +(14.7360 - 4.91958i) q^{48} +(-2.99990 + 6.32216i) q^{49} +(4.37083 - 9.21132i) q^{50} +(5.43705 - 2.85358i) q^{51} +(-18.5485 + 7.33050i) q^{52} +(0.749879 + 0.393567i) q^{53} +(2.19397 - 1.64866i) q^{54} +(-1.91278 - 6.60368i) q^{55} +(0.453752 - 0.0366306i) q^{56} +(3.12996 - 4.53453i) q^{57} +(1.06336 + 5.20867i) q^{58} +(-2.12317 - 0.904600i) q^{59} +(-15.8556 + 3.90804i) q^{60} +(-0.325075 + 8.06666i) q^{61} +(-13.0121 + 9.77797i) q^{62} +(0.0432107 - 0.0184103i) q^{63} +(18.5977 + 26.9435i) q^{64} +(10.1818 - 3.10295i) q^{65} +(-3.63066 + 5.25992i) q^{66} +(0.184770 - 0.905062i) q^{67} +(23.5292 + 24.4965i) q^{68} +(3.45049 + 7.27175i) q^{69} -0.380534 q^{70} +(-5.58231 - 11.7645i) q^{71} +(7.74825 + 5.82243i) q^{72} +(-0.449993 + 1.18653i) q^{73} +(16.9094 + 7.20441i) q^{74} +(3.66702 - 0.595948i) q^{75} +(28.9099 + 9.65153i) q^{76} +(-0.0818756 + 0.0725355i) q^{77} +(-8.22063 - 5.50746i) q^{78} +(-11.3774 - 10.0795i) q^{79} +(-22.9314 - 39.7184i) q^{80} +(0.948536 + 0.316668i) q^{81} +(-6.01727 + 6.26464i) q^{82} +(0.164037 + 0.237649i) q^{83} +(0.164319 + 0.201254i) q^{84} +(-11.4645 - 14.0415i) q^{85} +(15.6482 + 22.6704i) q^{86} +(-1.34187 + 1.39703i) q^{87} +(-21.4099 - 7.14767i) q^{88} +(2.11193 + 3.65797i) q^{89} +(-6.06427 - 5.37248i) q^{90} +(-0.114048 - 0.125190i) q^{91} +(-33.3261 + 29.5243i) q^{92} +(-5.62563 - 1.87811i) q^{93} +(15.5828 - 2.53245i) q^{94} +(-14.9643 - 6.37568i) q^{95} +(-8.24494 + 21.7401i) q^{96} +(-10.8746 - 8.17176i) q^{97} +(-8.23286 - 17.3504i) q^{98} -2.32886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{28}{39}\right)$

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 $

$2$	−1.73567	+	2.12581i	−1.22730	+	1.50317i	−0.426221	+	0.904619i	$0.640155\pi$
$2$	−1.73567	+	2.12581i	−1.22730	+	1.50317i	−0.801082	+	0.598554i	$0.795742\pi$
$3$	−0.996757	−	0.0804666i	−0.575478	−	0.0464574i
$3$	−0.996757	−	0.0804666i	−0.575478	−	0.0464574i
$4$	−1.10646	−	5.41982i	−0.553232	−	2.70991i
$5$	0.355841	+	2.93061i	0.159137	+	1.31061i	0.825253	+	0.564763i	$0.191032\pi$
$5$	0.355841	+	2.93061i	0.159137	+	1.31061i	−0.666116	+	0.745848i	$0.732045\pi$
$6$	1.90110	−	1.97925i	0.776120	−	0.808026i
$7$	0.0396979	−	0.0251034i	0.0150044	−	0.00948820i	−0.526943	−	0.849901i	$-0.676662\pi$
$7$	0.0396979	−	0.0251034i	0.0150044	−	0.00948820i	0.541947	+	0.840413i	$0.317687\pi$
$8$	8.58190	+	4.50413i	3.03416	+	1.59245i
$9$	0.987050	+	0.160411i	0.329017	+	0.0534704i
$10$	−6.84755	−	4.33013i	−2.16538	−	1.36931i
$11$	−2.29870	+	0.373576i	−0.693086	+	0.112637i	−0.496743	−	0.867898i	$-0.665471\pi$
$11$	−2.29870	+	0.373576i	−0.693086	+	0.112637i	−0.196343	+	0.980535i	$0.562907\pi$
$12$	0.666762	+	5.49128i	0.192477	+	1.58519i
$13$	−0.627698	−	3.55049i	−0.174092	−	0.984729i
$13$	−0.627698	−	3.55049i	−0.174092	−	0.984729i
$14$	−0.0155373	+	0.127961i	−0.00415252	+	0.0341991i
$15$	−0.118871	−	2.94975i	−0.0306923	−	0.761621i
$16$	−14.2923	+	6.08938i	−3.57308	+	1.52235i
$17$	−5.18980	+	3.28183i	−1.25871	+	0.795960i	−0.986098	−	0.166164i	$-0.946862\pi$
$17$	−5.18980	+	3.28183i	−1.25871	+	0.795960i	−0.272612	+	0.962124i	$0.587888\pi$
$18$	−2.05420	+	1.81986i	−0.484179	+	0.428945i
$19$	−2.75493	+	4.77168i	−0.632025	+	1.09470i	0.355113	+	0.934823i	$0.384442\pi$
$19$	−2.75493	+	4.77168i	−0.632025	+	1.09470i	−0.987137	+	0.159875i	$0.948891\pi$
$20$	15.4897	−	5.17121i	3.46360	−	1.15632i
$21$	−0.0415891	+	0.0218277i	−0.00907549	+	0.00476319i
$22$	3.19564	−	5.53501i	0.681313	−	1.18007i
$23$	−4.02443	−	6.97052i	−0.839152	−	1.45345i	−0.890605	−	0.454778i	$-0.849719\pi$
$23$	−4.02443	−	6.97052i	−0.839152	−	1.45345i	0.0514529	−	0.998675i	$-0.483615\pi$
$24$	−8.19164	−	5.18008i	−1.67211	−	1.05738i
$25$	−3.60717	+	0.889088i	−0.721434	+	0.177818i
$26$	8.63714	+	4.82811i	1.69388	+	0.946871i
$27$	−0.970942	−	0.239316i	−0.186858	−	0.0460563i
$28$	−0.179980	−	0.187379i	−0.0340131	−	0.0354113i
$29$	1.22510	−	1.50048i	0.227496	−	0.278632i	−0.648226	−	0.761448i	$-0.724489\pi$
$29$	1.22510	−	1.50048i	0.227496	−	0.278632i	0.875722	+	0.482816i	$0.160386\pi$
$30$	6.47691	+	4.86708i	1.18252	+	0.888604i
$31$	5.75851	+	1.41935i	1.03426	+	0.254922i	0.719677	−	0.694309i	$-0.244290\pi$
$31$	5.75851	+	1.41935i	1.03426	+	0.254922i	0.314581	+	0.949230i	$0.398136\pi$
$32$	6.46885	−	22.3331i	1.14354	−	3.94796i
$33$	2.32131	−	0.187396i	0.404088	−	0.0326214i
$34$	2.03123	−	16.7287i	0.348353	−	2.86895i
$35$	0.0876946	+	0.107406i	0.0148231	+	0.0181550i
$36$	−0.222735	−	5.52712i	−0.0371226	−	0.921187i
$37$	−1.86333	−	6.43296i	−0.306330	−	1.05757i	−0.955025	−	0.296524i	$-0.904172\pi$
$37$	−1.86333	−	6.43296i	−0.306330	−	1.05757i	0.648696	−	0.761048i	$-0.275315\pi$
$38$	−5.36203	−	14.1385i	−0.869836	−	2.29357i
$39$	0.339967	+	3.58949i	0.0544383	+	0.574778i
$40$	−10.1461	+	26.7530i	−1.60423	+	4.23002i
$41$	3.15489	+	0.254689i	0.492711	+	0.0397758i	0.324326	−	0.945945i	$-0.394863\pi$
$41$	3.15489	+	0.254689i	0.492711	+	0.0397758i	0.168385	+	0.985721i	$0.446145\pi$
$42$	0.0257835	−	0.126296i	0.00397849	−	0.0194879i
$43$	2.79259	−	9.64115i	0.425867	−	1.47026i	−0.405272	−	0.914196i	$-0.632823\pi$
$43$	2.79259	−	9.64115i	0.425867	−	1.47026i	0.831138	−	0.556066i	$-0.187690\pi$
$44$	4.56815	+	12.0452i	0.688674	+	1.81588i
$45$	−0.118871	+	2.94975i	−0.0177202	+	0.439722i
$46$	21.8031	+	3.54334i	3.21469	+	0.522437i
$47$	−4.30586	−	3.81466i	−0.628074	−	0.556425i	0.287901	−	0.957660i	$-0.407042\pi$
$47$	−4.30586	−	3.81466i	−0.628074	−	0.556425i	−0.915975	+	0.401235i	$0.868581\pi$
$48$	14.7360	−	4.91958i	2.12695	−	0.710081i
$49$	−2.99990	+	6.32216i	−0.428557	+	0.903166i
$50$	4.37083	−	9.21132i	0.618128	−	1.30268i
$51$	5.43705	−	2.85358i	0.761339	−	0.399581i
$52$	−18.5485	+	7.33050i	−2.57221	+	1.01656i
$53$	0.749879	+	0.393567i	0.103004	+	0.0540605i	0.515438	−	0.856927i	$-0.327629\pi$
$53$	0.749879	+	0.393567i	0.103004	+	0.0540605i	−0.412435	+	0.910987i	$0.635321\pi$
$54$	2.19397	−	1.64866i	0.298562	−	0.224355i
$55$	−1.91278	−	6.60368i	−0.257919	−	0.890441i
$56$	0.453752	−	0.0366306i	0.0606352	−	0.00489498i
$57$	3.12996	−	4.53453i	0.414573	−	0.600613i
$58$	1.06336	+	5.20867i	0.139626	+	0.683932i
$59$	−2.12317	−	0.904600i	−0.276414	−	0.117769i	0.249311	−	0.968423i	$-0.419796\pi$
$59$	−2.12317	−	0.904600i	−0.276414	−	0.117769i	−0.525725	+	0.850654i	$0.676206\pi$
$60$	−15.8556	+	3.90804i	−2.04694	+	0.504526i
$61$	−0.325075	+	8.06666i	−0.0416216	+	1.03283i	0.834581	+	0.550886i	$0.185710\pi$
$61$	−0.325075	+	8.06666i	−0.0416216	+	1.03283i	−0.876202	+	0.481944i	$0.839931\pi$
$62$	−13.0121	+	9.77797i	−1.65254	+	1.24180i
$63$	0.0432107	−	0.0184103i	0.00544403	−	0.00231949i
$64$	18.5977	+	26.9435i	2.32472	+	3.36793i
$65$	10.1818	−	3.10295i	1.26289	−	0.384874i
$66$	−3.63066	+	5.25992i	−0.446903	+	0.647451i
$67$	0.184770	−	0.905062i	0.0225732	−	0.110571i	−0.966943	−	0.254992i	$-0.917927\pi$
$67$	0.184770	−	0.905062i	0.0225732	−	0.110571i	0.989516	+	0.144422i	$0.0461321\pi$
$68$	23.5292	+	24.4965i	2.85334	+	2.97064i
$69$	3.45049	+	7.27175i	0.415390	+	0.875416i
$70$	−0.380534			−0.0454825
$71$	−5.58231	−	11.7645i	−0.662498	−	1.39618i	−0.904738	−	0.425968i	$-0.859933\pi$
$71$	−5.58231	−	11.7645i	−0.662498	−	1.39618i	0.242240	−	0.970216i	$-0.422118\pi$
$72$	7.74825	+	5.82243i	0.913140	+	0.686180i
$73$	−0.449993	+	1.18653i	−0.0526677	+	0.138873i	−0.958768	−	0.284189i	$-0.908276\pi$
$73$	−0.449993	+	1.18653i	−0.0526677	+	0.138873i	0.906101	+	0.423062i	$0.139045\pi$
$74$	16.9094	+	7.20441i	1.96567	+	0.837495i
$75$	3.66702	−	0.595948i	0.423431	−	0.0688142i
$76$	28.9099	+	9.65153i	3.31619	+	1.10711i
$77$	−0.0818756	+	0.0725355i	−0.00933060	+	0.00826619i
$78$	−8.22063	−	5.50746i	−0.930803	−	0.623597i
$79$	−11.3774	−	10.0795i	−1.28005	−	1.13403i	−0.983867	−	0.178899i	$-0.942746\pi$
$79$	−11.3774	−	10.0795i	−1.28005	−	1.13403i	−0.296187	−	0.955130i	$-0.595715\pi$
$80$	−22.9314	−	39.7184i	−2.56381	−	4.44065i
$81$	0.948536	+	0.316668i	0.105393	+	0.0351853i
$82$	−6.01727	+	6.26464i	−0.664496	+	0.691813i
$83$	0.164037	+	0.237649i	0.0180054	+	0.0260853i	0.831883	−	0.554951i	$-0.187263\pi$
$83$	0.164037	+	0.237649i	0.0180054	+	0.0260853i	−0.813878	+	0.581036i	$0.802648\pi$
$84$	0.164319	+	0.201254i	0.0179286	+	0.0219586i
$85$	−11.4645	−	14.0415i	−1.24350	−	1.52301i
$86$	15.6482	+	22.6704i	1.68739	+	2.44461i
$87$	−1.34187	+	1.39703i	−0.143863	+	0.149778i
$88$	−21.4099	−	7.14767i	−2.28230	−	0.761944i
$89$	2.11193	+	3.65797i	0.223864	+	0.387744i	0.955978	−	0.293438i	$-0.0947995\pi$
$89$	2.11193	+	3.65797i	0.223864	+	0.387744i	−0.732114	+	0.681182i	$0.761466\pi$
$90$	−6.06427	−	5.37248i	−0.639230	−	0.566309i
$91$	−0.114048	−	0.125190i	−0.0119555	−	0.0131234i
$92$	−33.3261	+	29.5243i	−3.47448	+	3.07812i
$93$	−5.62563	−	1.87811i	−0.583350	−	0.194751i
$94$	15.5828	−	2.53245i	1.60724	−	0.261202i
$95$	−14.9643	−	6.37568i	−1.53530	−	0.654131i
$96$	−8.24494	+	21.7401i	−0.841495	+	2.21884i
$97$	−10.8746	−	8.17176i	−1.10415	−	0.829716i	−0.117583	−	0.993063i	$-0.537515\pi$
$97$	−10.8746	−	8.17176i	−1.10415	−	0.829716i	−0.986569	+	0.163347i	$0.947771\pi$
$98$	−8.23286	−	17.3504i	−0.831645	−	1.75265i
$99$	−2.32886			−0.234060
$100$	8.80990	+	18.5665i	0.880990	+	1.85665i
$101$	−2.24613	−	2.33847i	−0.223498	−	0.232686i	0.600007	−	0.799994i	$-0.295164\pi$
$101$	−2.24613	−	2.33847i	−0.223498	−	0.232686i	−0.823506	+	0.567308i	$0.807985\pi$
$102$	−3.37074	+	16.5110i	−0.333753	+	1.63483i
$103$	3.99480	−	5.78747i	0.393620	−	0.570256i	−0.575203	−	0.818010i	$-0.695077\pi$
$103$	3.99480	−	5.78747i	0.393620	−	0.570256i	0.968823	+	0.247754i	$0.0796925\pi$
$104$	10.6050	−	33.2972i	1.03991	−	3.26506i
$105$	−0.0787676	−	0.114115i	−0.00768693	−	0.0111364i
$106$	−2.13819	+	0.910997i	−0.207679	+	0.0884838i
$107$	−8.42977	+	6.33456i	−0.814936	+	0.612385i	−0.924322	−	0.381614i	$-0.875368\pi$
$107$	−8.42977	+	6.33456i	−0.814936	+	0.612385i	0.109385	+	0.993999i	$0.465112\pi$
$108$	−0.222735	+	5.52712i	−0.0214327	+	0.531847i
$109$	8.27736	−	2.04019i	0.792828	−	0.195414i	0.177953	−	0.984039i	$-0.443053\pi$
$109$	8.27736	−	2.04019i	0.792828	−	0.195414i	0.614875	+	0.788625i	$0.289206\pi$
$110$	17.3581	+	7.39560i	1.65503	+	0.705143i
$111$	1.33965	+	6.56204i	0.127154	+	0.622841i
$112$	−0.414510	+	0.600521i	−0.0391675	+	0.0567439i
$113$	5.37826	−	0.434178i	0.505944	−	0.0408440i	0.175140	−	0.984544i	$-0.443962\pi$
$113$	5.37826	−	0.434178i	0.505944	−	0.0408440i	0.330804	+	0.943699i	$0.392680\pi$
$114$	4.20697	+	14.5241i	0.394018	+	1.36031i
$115$	18.9958	−	14.2745i	1.77137	−	1.33110i
$116$	−9.48785	−	4.97961i	−0.880925	−	0.462345i
$117$	−0.0500308	−	3.60520i	−0.00462535	−	0.333301i
$118$	5.60813	−	2.94338i	0.516271	−	0.270960i
$119$	−0.123639	+	0.260563i	−0.0113339	+	0.0238858i
$120$	12.2659	−	25.8498i	1.11972	−	2.35975i
$121$	−5.28942	+	1.76587i	−0.480856	+	0.160533i
$122$	−16.5839	−	14.6921i	−1.50144	−	1.33016i
$123$	−3.12417	−	0.507727i	−0.281697	−	0.0457802i
$124$	1.32101	−	32.7805i	0.118630	−	2.94378i
$125$	1.34506	+	3.54663i	0.120306	+	0.317220i
$126$	−0.0358625	+	0.123812i	−0.00319489	+	0.0110300i
$127$	1.51406	−	7.41636i	0.134351	−	0.658096i	−0.855710	−	0.517456i	$-0.826879\pi$
$127$	1.51406	−	7.41636i	0.134351	−	0.658096i	0.990061	−	0.140640i	$-0.0449159\pi$
$128$	−43.2048	−	3.48785i	−3.81880	−	0.308285i
$129$	−3.55933	+	9.38518i	−0.313382	+	0.826319i
$130$	−11.0759	+	27.0302i	−0.971420	+	2.37070i
$131$	−1.36320	−	3.59447i	−0.119104	−	0.314050i	0.862185	−	0.506594i	$-0.169096\pi$
$131$	−1.36320	−	3.59447i	−0.119104	−	0.314050i	−0.981288	+	0.192543i	$0.938326\pi$
$132$	−3.58410	−	12.3737i	−0.311956	−	1.07700i
$133$	0.0104206	+	0.258584i	0.000903578	+	0.0224221i
$134$	1.60329	+	1.96367i	0.138503	+	0.169636i
$135$	0.355841	−	2.93061i	0.0306259	−	0.252227i
$136$	−59.3201	+	4.78881i	−5.08665	+	0.410637i
$137$	−4.43906	+	15.3254i	−0.379254	+	1.30934i	0.513227	+	0.858253i	$0.328450\pi$
$137$	−4.43906	+	15.3254i	−0.379254	+	1.30934i	−0.892481	+	0.451085i	$0.851037\pi$
$138$	−21.4472	−	5.28627i	−1.82571	−	0.449997i
$139$	8.75278	+	6.57729i	0.742402	+	0.557879i	0.903257	−	0.429099i	$-0.141169\pi$
$139$	8.75278	+	6.57729i	0.742402	+	0.557879i	−0.160856	+	0.986978i	$0.551425\pi$
$140$	0.485092	−	0.594130i	0.0409977	−	0.0502131i
$141$	3.98494	+	4.14876i	0.335593	+	0.349389i
$142$	34.6980	+	8.55230i	2.91179	+	0.717693i
$143$	2.76927	+	7.92704i	0.231578	+	0.662892i
$144$	−15.0840	+	3.71788i	−1.25700	+	0.309823i
$145$	4.83327	+	3.05637i	0.401381	+	0.253818i
$146$	−1.74130	−	3.01603i	−0.144111	−	0.249608i
$147$	3.49890	−	6.06027i	0.288584	−	0.499842i
$148$	−32.8038	+	17.2167i	−2.69645	+	1.41521i
$149$	−15.9952	+	5.33998i	−1.31038	+	0.437468i	−0.884173	−	0.467159i	$-0.845277\pi$
$149$	−15.9952	+	5.33998i	−1.31038	+	0.437468i	−0.426204	+	0.904627i	$0.640149\pi$
$150$	−5.09786	+	8.82974i	−0.416238	+	0.720946i
$151$	−9.90371	+	8.77392i	−0.805953	+	0.714012i	−0.961795	−	0.273770i	$-0.911729\pi$
$151$	−9.90371	+	8.77392i	−0.805953	+	0.714012i	0.155842	+	0.987782i	$0.450191\pi$
$152$	−45.1348	+	28.5415i	−3.66091	+	2.31502i
$153$	−5.64903	+	2.40683i	−0.456697	+	0.194580i
$154$	−0.0120876	−	0.299950i	−0.000974043	−	0.0241706i
$155$	−2.11044	+	17.3810i	−0.169515	+	1.39608i
$156$	19.0782	−	5.81420i	1.52748	−	0.465508i
$157$	−1.21797	−	10.0309i	−0.0972046	−	0.800552i	−0.957035	−	0.289972i	$-0.906354\pi$
$157$	−1.21797	−	10.0309i	−0.0972046	−	0.800552i	0.859831	−	0.510580i	$-0.170569\pi$
$158$	41.1744	−	6.69149i	3.27566	−	0.532346i
$159$	−0.715778	−	0.452631i	−0.0567649	−	0.0358959i
$160$	67.7515	+	11.0107i	5.35622	+	0.870471i
$161$	−0.334745	−	0.175688i	−0.0263816	−	0.0138461i
$162$	−2.31952	+	1.46678i	−0.182239	+	0.115241i
$163$	−8.86006	+	9.22430i	−0.693974	+	0.722503i	−0.971191	−	0.238304i	$-0.923408\pi$
$163$	−8.86006	+	9.22430i	−0.693974	+	0.722503i	0.277217	+	0.960807i	$0.410588\pi$
$164$	−2.11040	−	17.3807i	−0.164795	−	1.35721i
$165$	1.37520	+	6.73619i	0.107059	+	0.524411i
$166$	−0.789909	−	0.0637681i	−0.0613088	−	0.00494936i
$167$	0.138430	−	0.169545i	0.0107120	−	0.0131198i	−0.769221	−	0.638983i	$-0.779356\pi$
$167$	0.138430	−	0.169545i	0.0107120	−	0.0131198i	0.779933	+	0.625863i	$0.215253\pi$
$168$	−0.455228			−0.0351216
$169$	−12.2120	+	4.45728i	−0.939384	+	0.342867i
$170$	49.7481			3.81551
$171$	−3.48469	+	4.26797i	−0.266481	+	0.326380i
$172$	−55.3432	−	4.46777i	−4.21988	−	0.340664i
$173$	0.685013	+	3.35542i	0.0520806	+	0.255108i	0.997493	−	0.0707696i	$-0.0225455\pi$
$173$	0.685013	+	3.35542i	0.0520806	+	0.255108i	−0.945412	+	0.325877i	$0.894340\pi$
$174$	−0.640786	−	5.27734i	−0.0485778	−	0.400074i
$175$	−0.120878	+	0.125847i	−0.00913751	+	0.00951316i
$176$	30.5789	−	19.3370i	2.30498	−	1.45758i
$177$	2.04350	+	1.07251i	0.153599	+	0.0806149i
$178$	−11.4418	−	1.85947i	−0.857595	−	0.139373i
$179$	−1.20434	−	0.761580i	−0.0900167	−	0.0569231i	0.488699	−	0.872452i	$-0.337472\pi$
$179$	−1.20434	−	0.761580i	−0.0900167	−	0.0569231i	−0.578716	+	0.815529i	$0.696446\pi$
$180$	16.1186	−	2.61953i	1.20141	−	0.195248i
$181$	2.94138	+	24.2245i	0.218631	+	1.80059i	0.527574	+	0.849509i	$0.323102\pi$
$181$	2.94138	+	24.2245i	0.218631	+	1.80059i	−0.308943	+	0.951080i	$0.599975\pi$
$182$	0.464078	−	0.0251560i	0.0343998	−	0.00186468i
$183$	0.973117	−	8.01434i	0.0719349	−	0.592437i
$184$	−3.14115	−	77.9468i	−0.231569	−	5.74632i
$185$	18.1895	−	7.74981i	1.33732	−	0.569778i
$186$	13.7567	−	8.69923i	1.00869	−	0.637858i
$187$	10.7038	−	9.48274i	0.782739	−	0.693446i
$188$	−15.9105	+	27.5577i	−1.16039	+	2.00985i
$189$	−0.0445520	+	0.0148736i	−0.00324068	+	0.00108190i
$190$	39.5265	−	20.7451i	2.86755	−	1.50501i
$191$	4.93608	−	8.54954i	0.357162	−	0.618623i	−0.630323	−	0.776333i	$-0.717078\pi$
$191$	4.93608	−	8.54954i	0.357162	−	0.618623i	0.987486	+	0.157710i	$0.0504110\pi$
$192$	−16.3694	−	28.3526i	−1.18136	−	2.04617i
$193$	18.9326	+	11.9723i	1.36280	+	0.861784i	0.997606	−	0.0691474i	$-0.0220279\pi$
$193$	18.9326	+	11.9723i	1.36280	+	0.861784i	0.365195	+	0.930931i	$0.381002\pi$
$194$	36.2464	−	8.93393i	2.60234	−	0.641418i
$195$	−10.3984	+	2.27360i	−0.744647	+	0.162816i
$196$	37.5842	+	9.26368i	2.68459	+	0.661692i
$197$	3.75490	+	3.90927i	0.267526	+	0.278524i	0.841392	−	0.540425i	$-0.181737\pi$
$197$	3.75490	+	3.90927i	0.267526	+	0.278524i	−0.573866	+	0.818949i	$0.694557\pi$
$198$	4.04213	−	4.95072i	0.287262	−	0.351832i
$199$	−11.4973	−	8.63968i	−0.815024	−	0.612451i	0.109322	−	0.994006i	$-0.465132\pi$
$199$	−11.4973	−	8.63968i	−0.815024	−	0.612451i	−0.924346	+	0.381556i	$0.875388\pi$
$200$	−34.9609	−	8.61710i	−2.47211	−	0.609321i
$201$	−0.256998	+	0.887260i	−0.0181272	+	0.0625825i
$202$	8.86967	−	0.716034i	0.624068	−	0.0503800i
$203$	0.0109668	−	0.0903201i	0.000769722	−	0.00633923i
$204$	−21.4818	−	26.3104i	−1.50403	−	1.84210i
$205$	0.376244	+	9.33640i	0.0262780	+	0.652082i
$206$	5.36940	+	18.5373i	0.374104	+	1.29156i
$207$	−2.85417	−	7.52582i	−0.198378	−	0.523080i
$208$	30.5916	+	46.9224i	2.12114	+	3.25349i
$209$	4.55019	−	11.9979i	0.314743	−	0.829909i
$210$	0.379300	+	0.0306203i	0.0261742	+	0.00211300i
$211$	−0.444377	+	2.17670i	−0.0305921	+	0.149850i	−0.992218	−	0.124515i	$-0.960263\pi$
$211$	−0.444377	+	2.17670i	−0.0305921	+	0.149850i	0.961626	+	0.274365i	$0.0884677\pi$
$212$	1.30335	−	4.49967i	0.0895142	−	0.309039i
$213$	4.61756	+	12.1755i	0.316390	+	0.834252i
$214$	1.16523	−	28.9148i	0.0796532	−	1.97657i
$215$	29.2482	+	4.75330i	1.99471	+	0.324172i
$216$	−7.25461	−	6.42703i	−0.493614	−	0.437304i
$217$	0.264231	−	0.0882133i	0.0179372	−	0.00598831i
$218$	−10.0297	+	21.1372i	−0.679298	+	1.43159i
$219$	0.544010	−	1.14648i	0.0367608	−	0.0774717i
$220$	−33.6743	+	17.6737i	−2.27032	+	1.19156i
$221$	14.9097	+	16.3663i	1.00294	+	1.10092i
$222$	−16.2748	−	8.54168i	−1.09229	−	0.573280i
$223$	−10.5388	+	7.91937i	−0.705728	+	0.530321i	−0.891920	−	0.452193i	$-0.850642\pi$
$223$	−10.5388	+	7.91937i	−0.705728	+	0.530321i	0.186192	+	0.982513i	$0.440385\pi$
$224$	−0.303836	−	1.04896i	−0.0203009	−	0.0700869i
$225$	−3.70308	+	0.298944i	−0.246872	+	0.0199296i
$226$	−8.41190	+	12.1867i	−0.559551	+	0.810650i
$227$	3.49226	+	17.1062i	0.231789	+	1.13538i	0.914467	+	0.404660i	$0.132610\pi$
$227$	3.49226	+	17.1062i	0.231789	+	1.13538i	−0.682678	+	0.730720i	$0.739185\pi$
$228$	−28.0395	−	11.9465i	−1.85696	−	0.791177i
$229$	11.9461	−	2.94446i	0.789423	−	0.194575i	0.176063	−	0.984379i	$-0.443664\pi$
$229$	11.9461	−	2.94446i	0.789423	−	0.194575i	0.613360	+	0.789803i	$0.289817\pi$
$230$	−2.62575	+	65.1573i	−0.173137	+	4.29634i
$231$	0.0874468	−	0.0657120i	0.00575358	−	0.00432353i
$232$	17.2721	−	7.35893i	1.13397	−	0.483138i
$233$	−9.05936	−	13.1247i	−0.593498	−	0.859831i	0.405017	−	0.914309i	$-0.367266\pi$
$233$	−9.05936	−	13.1247i	−0.593498	−	0.859831i	−0.998515	+	0.0544787i	$0.982650\pi$
$234$	7.75081	+	6.15108i	0.506686	+	0.402109i
$235$	9.64709	−	13.9762i	0.629307	−	0.911708i
$236$	−2.55355	+	12.5081i	−0.166222	+	0.814209i
$237$	10.5294	+	10.9623i	0.683959	+	0.712077i
$238$	−0.339311	−	0.715084i	−0.0219943	−	0.0463520i
$239$	−10.7308			−0.694116			−0.347058	−	0.937844i	$-0.612819\pi$
$239$	−10.7308			−0.694116			−0.347058	+	0.937844i	$0.612819\pi$
$240$	19.6611	+	41.4348i	1.26912	+	2.67461i
$241$	−22.3964	−	16.8298i	−1.44268	−	1.08411i	−0.980320	−	0.197414i	$-0.936746\pi$
$241$	−22.3964	−	16.8298i	−1.44268	−	1.08411i	−0.462362	−	0.886691i	$-0.652998\pi$
$242$	5.42678	−	14.3092i	0.348847	−	0.919833i
$243$	−0.919979	−	0.391967i	−0.0590167	−	0.0251447i
$244$	44.0795	−	7.16362i	2.82190	−	0.458603i
$245$	−19.5953	−	6.54187i	−1.25190	−	0.417945i
$246$	6.50185	−	5.76013i	0.414543	−	0.367253i
$247$	18.6711	+	6.78619i	1.18801	+	0.431795i
$248$	43.0260	+	38.1177i	2.73216	+	2.42048i
$249$	−0.144382	−	0.250077i	−0.00914985	−	0.0158480i
$250$	−9.87404	−	3.29644i	−0.624489	−	0.208485i
$251$	5.37069	−	5.59148i	0.338995	−	0.352931i	−0.529783	−	0.848133i	$-0.677727\pi$
$251$	5.37069	−	5.59148i	0.338995	−	0.352931i	0.868778	+	0.495202i	$0.164906\pi$
$252$	−0.147592	−	0.213824i	−0.00929740	−	0.0134696i
$253$	11.8550	+	14.5197i	0.745317	+	0.912848i
$254$	13.1379	+	16.0910i	0.824343	+	1.00964i
$255$	10.2975	+	14.9185i	0.644853	+	0.934231i
$256$	37.0459	−	38.5688i	2.31537	−	2.41055i
$257$	−27.3218	−	9.12136i	−1.70429	−	0.568975i	−0.713056	−	0.701107i	$-0.752689\pi$
$257$	−27.3218	−	9.12136i	−1.70429	−	0.568975i	−0.991232	+	0.132132i	$0.957818\pi$
$258$	−13.7733	−	23.8560i	−0.857487	−	1.48521i
$259$	−0.235459	−	0.208599i	−0.0146307	−	0.0129617i
$260$	−28.0832	−	51.7500i	−1.74165	−	3.20940i
$261$	1.44993	−	1.28453i	0.0897485	−	0.0795103i
$262$	10.0072	+	3.34090i	0.618248	+	0.206402i
$263$	−16.9834	+	2.76007i	−1.04724	+	0.170193i	−0.659600	−	0.751617i	$-0.729274\pi$
$263$	−16.9834	+	2.76007i	−1.04724	+	0.170193i	−0.387642	+	0.921810i	$0.626710\pi$
$264$	20.7653	+	8.84727i	1.27802	+	0.544512i
$265$	−0.886555	+	2.33765i	−0.0544606	+	0.143601i
$266$	−0.567786	−	0.426664i	−0.0348132	−	0.0261604i
$267$	−1.81074	−	3.81605i	−0.110815	−	0.233538i
$268$	−5.10971			−0.312125
$269$	2.74696	+	5.78909i	0.167485	+	0.352967i	0.969788	−	0.243950i	$-0.0784433\pi$
$269$	2.74696	+	5.78909i	0.167485	+	0.352967i	−0.802303	+	0.596917i	$0.796392\pi$
$270$	5.61230	+	5.84303i	0.341554	+	0.355595i
$271$	−0.320449	+	1.56967i	−0.0194659	+	0.0953504i	−0.988363	−	0.152114i	$-0.951392\pi$
$271$	−0.320449	+	1.56967i	−0.0194659	+	0.0953504i	0.968897	+	0.247464i	$0.0795972\pi$
$272$	54.1899	−	78.5076i	3.28574	−	4.76022i
$273$	0.103604	+	0.133961i	0.00627042	+	0.00810767i
$274$	−24.8741	−	36.0364i	−1.50270	−	2.17704i
$275$	7.95968	−	3.39130i	0.479987	−	0.204503i
$276$	35.5937	−	26.7469i	2.14249	−	1.60998i
$277$	−0.186416	+	4.62587i	−0.0112007	+	0.277942i	0.983877	+	0.178845i	$0.0572362\pi$
$277$	−0.186416	+	4.62587i	−0.0112007	+	0.277942i	−0.995078	+	0.0990962i	$0.968405\pi$
$278$	−29.1740	+	7.19074i	−1.74974	+	0.431272i
$279$	5.45626	+	2.32469i	0.326658	+	0.139176i
$280$	0.268814	+	1.31674i	0.0160647	+	0.0786901i
$281$	−15.6352	+	22.6516i	−0.932721	+	1.35128i	0.00354779	+	0.999994i	$0.498871\pi$
$281$	−15.6352	+	22.6516i	−0.932721	+	1.35128i	−0.936268	+	0.351285i	$0.885745\pi$
$282$	−15.7360	+	1.27034i	−0.937066	+	0.0756478i
$283$	3.05060	+	10.5319i	0.181339	+	0.626056i	0.998749	+	0.0499994i	$0.0159220\pi$
$283$	3.05060	+	10.5319i	0.181339	+	0.626056i	−0.817410	+	0.576056i	$0.804591\pi$
$284$	−57.5846	+	43.2720i	−3.41702	+	2.56772i
$285$	14.4027	+	7.55913i	0.853144	+	0.447764i
$286$	−21.6579	−	7.87178i	−1.28066	−	0.465468i
$287$	0.131636	−	0.0690879i	0.00777023	−	0.00407813i
$288$	9.96755	−	21.0062i	0.587344	−	1.23780i
$289$	8.87582	−	18.7054i	0.522107	−	1.10032i
$290$	−14.8862	+	4.96975i	−0.874149	+	0.291834i
$291$	10.1818	+	9.02031i	0.596869	+	0.528780i
$292$	6.92870	+	1.12602i	0.405471	+	0.0658955i
$293$	−0.201990	+	5.01234i	−0.0118004	+	0.292824i	0.982504	+	0.186243i	$0.0596312\pi$
$293$	−0.201990	+	5.01234i	−0.0118004	+	0.292824i	−0.994304	+	0.106581i	$0.966010\pi$
$294$	6.81004	+	17.9566i	0.397170	+	1.04725i
$295$	1.89552	−	6.54410i	0.110362	−	0.381012i
$296$	12.9840	−	63.5997i	0.754678	−	3.69666i
$297$	2.32131	+	0.187396i	0.134696	+	0.0108738i
$298$	16.4106	−	43.2711i	0.950639	−	2.50663i
$299$	−22.2226	+	18.6641i	−1.28517	+	1.07937i
$300$	−7.28735	−	19.2152i	−0.420735	−	1.10939i
$301$	−0.131166	−	0.452837i	−0.00756027	−	0.0261011i
$302$	−1.46212	−	36.2820i	−0.0841353	−	2.08780i
$303$	2.05068	+	2.51162i	0.117808	+	0.144289i
$304$	10.3177	−	84.9742i	0.591763	−	4.87360i
$305$	−23.7559	+	1.91778i	−1.36026	+	0.109812i
$306$	4.68839	−	16.1862i	0.268018	−	0.925304i
$307$	−19.6345	−	4.83946i	−1.12060	−	0.276203i	−0.364851	−	0.931066i	$-0.618880\pi$
$307$	−19.6345	−	4.83946i	−1.12060	−	0.276203i	−0.755747	+	0.654863i	$0.772726\pi$
$308$	0.483722	+	0.363493i	0.0275626	+	0.0207119i
$309$	−4.44755	+	5.44726i	−0.253012	+	0.309884i
$310$	−33.2857	−	34.6541i	−1.89050	−	1.96822i
$311$	11.1738	+	2.75408i	0.633606	+	0.156170i	0.543021	−	0.839719i	$-0.317280\pi$
$311$	11.1738	+	2.75408i	0.633606	+	0.156170i	0.0905846	+	0.995889i	$0.471126\pi$
$312$	−13.2499	+	32.3359i	−0.750130	+	1.83066i
$313$	−24.1139	+	5.94353i	−1.36300	+	0.335948i	−0.851958	−	0.523610i	$-0.824585\pi$
$313$	−24.1139	+	5.94353i	−1.36300	+	0.335948i	−0.511038	+	0.859558i	$0.670739\pi$
$314$	23.4377	+	14.8211i	1.32267	+	0.836404i
$315$	0.0693298	+	0.120083i	0.00390629	+	0.00676589i
$316$	−42.0402	+	72.8158i	−2.36495	+	4.09621i
$317$	3.68479	−	1.93393i	0.206959	−	0.108620i	−0.358059	−	0.933699i	$-0.616561\pi$
$317$	3.68479	−	1.93393i	0.206959	−	0.108620i	0.565018	+	0.825079i	$0.308869\pi$
$318$	2.20456	−	0.735990i	0.123626	−	0.0412723i
$319$	−2.25561	+	3.90683i	−0.126290	+	0.218740i
$320$	−72.3430	+	64.0903i	−4.04410	+	3.58276i
$321$	8.91215	−	5.63570i	0.497428	−	0.314554i
$322$	0.954485	−	0.406668i	0.0531914	−	0.0226627i
$323$	−1.36231	−	33.8053i	−0.0758007	−	1.88098i
$324$	0.666762	−	5.49128i	0.0370423	−	0.305071i
$325$	5.42092	+	12.2492i	0.300698	+	0.679461i
$326$	−4.23096	−	34.8451i	−0.234331	−	1.92989i
$327$	−8.41469	+	1.36752i	−0.465333	+	0.0756240i
$328$	25.9278	+	16.3957i	1.43162	+	0.905304i
$329$	−0.266694	−	0.0433420i	−0.0147033	−	0.00238952i
$330$	−16.7067	−	8.76837i	−0.919676	−	0.482683i
$331$	21.4956	−	13.5930i	1.18151	−	0.747139i	0.208523	−	0.978017i	$-0.433134\pi$
$331$	21.4956	−	13.5930i	1.18151	−	0.747139i	0.972983	+	0.230879i	$0.0741600\pi$
$332$	1.10651	−	1.15200i	0.0607277	−	0.0632242i
$333$	−0.807281	−	6.64855i	−0.0442387	−	0.364339i
$334$	0.120153	+	0.588550i	0.00657449	+	0.0322040i
$335$	2.71814	+	0.219431i	0.148508	+	0.0119888i
$336$	0.461488	−	0.565220i	0.0251762	−	0.0308353i
$337$	32.5268			1.77185			0.885924	−	0.463831i	$-0.153526\pi$
$337$	32.5268			1.77185			0.885924	+	0.463831i	$0.153526\pi$
$338$	11.7207	−	33.6967i	0.637520	−	1.83286i
$339$	−5.39576			−0.293057
$340$	−63.4172	+	77.6720i	−3.43928	+	4.21236i
$341$	−13.7673	−	1.11142i	−0.745544	−	0.0601865i
$342$	−3.02462	−	14.8156i	−0.163553	−	0.801133i
$343$	0.0792486	+	0.652671i	0.00427902	+	0.0352409i
$344$	67.3907	−	70.1612i	3.63347	−	3.78284i
$345$	−20.0829	+	12.6996i	−1.08123	+	0.683725i
$346$	−8.32193	−	4.36769i	−0.447390	−	0.234808i
$347$	9.25335	+	1.50382i	0.496746	+	0.0807290i	0.403623	−	0.914926i	$-0.367751\pi$
$347$	9.25335	+	1.50382i	0.496746	+	0.0807290i	0.0931231	+	0.995655i	$0.470315\pi$
$348$	9.05640	+	5.72692i	0.485474	+	0.306995i
$349$	−5.91380	+	0.961086i	−0.316558	+	0.0514457i	−0.316615	−	0.948554i	$-0.602546\pi$
$349$	−5.91380	+	0.961086i	−0.316558	+	0.0514457i	5.62591e−5		1.00000i	$0.499982\pi$
$350$	−0.0577231	−	0.475392i	−0.00308543	−	0.0254108i
$351$	−0.240230	+	3.59754i	−0.0128225	+	0.192022i
$352$	−6.52688	+	53.7537i	−0.347884	+	2.86508i
$353$	−0.709442	−	17.6046i	−0.0377598	−	0.937000i	−0.901425	−	0.432934i	$-0.857478\pi$
$353$	−0.709442	−	17.6046i	−0.0377598	−	0.937000i	0.863666	−	0.504065i	$-0.168163\pi$
$354$	−5.82679	+	2.48256i	−0.309690	+	0.131947i
$355$	32.4907	−	20.5459i	1.72443	−	1.09046i
$356$	17.4888	−	15.4937i	0.926902	−	0.821163i
$357$	0.144204	−	0.249769i	0.00763211	−	0.0132192i
$358$	3.70931	−	1.23835i	0.196043	−	0.0654488i
$359$	31.1859	−	16.3676i	1.64593	−	0.863850i	0.651477	−	0.758669i	$-0.274150\pi$
$359$	31.1859	−	16.3676i	1.64593	−	0.863850i	0.994453	−	0.105182i	$-0.0335424\pi$
$360$	−14.3062	+	24.7790i	−0.754001	+	1.30597i
$361$	−5.67929	−	9.83682i	−0.298910	−	0.517727i
$362$	−56.6018	−	35.7928i	−2.97492	−	1.88123i
$363$	5.41436	−	1.33452i	0.284180	−	0.0700441i
$364$	−0.552315	+	0.756636i	−0.0289492	+	0.0396585i
$365$	−3.63740	−	0.896538i	−0.190390	−	0.0469270i
$366$	15.3479	+	15.9789i	0.802250	+	0.835231i
$367$	−23.7703	+	29.1134i	−1.24080	+	1.51971i	−0.469944	+	0.882696i	$0.655726\pi$
$367$	−23.7703	+	29.1134i	−1.24080	+	1.51971i	−0.770856	+	0.637009i	$0.780171\pi$
$368$	99.9646	+	75.1185i	5.21101	+	3.91582i
$369$	3.07318	+	0.757471i	0.159983	+	0.0394324i
$370$	−15.0963	+	52.1185i	−0.784819	+	2.70951i
$371$	0.0396485	−	0.00320075i	0.00205845	−	0.000166175i
$372$	−3.95446	+	32.5679i	−0.205029	+	1.68857i
$373$	−2.84802	−	3.48819i	−0.147465	−	0.180612i	0.695590	−	0.718439i	$-0.255143\pi$
$373$	−2.84802	−	3.48819i	−0.147465	−	0.180612i	−0.843055	+	0.537827i	$0.819245\pi$
$374$	1.58023	+	39.2131i	0.0817120	+	2.02766i
$375$	−1.05531	−	3.64336i	−0.0544961	−	0.188143i
$376$	−19.7707	−	52.1311i	−1.01960	−	2.68846i
$377$	−6.09643	−	3.40787i	−0.313982	−	0.175514i
$378$	0.0457090	−	0.120525i	0.00235102	−	0.00619912i
$379$	21.7949	+	1.75947i	1.11953	+	0.0903779i	0.626345	−	0.779546i	$-0.284550\pi$
$379$	21.7949	+	1.75947i	1.11953	+	0.0903779i	0.493186	+	0.869924i	$0.335832\pi$
$380$	−17.9976	+	88.1581i	−0.923258	+	4.52242i
$381$	−2.10592	+	7.27048i	−0.107890	+	0.372478i
$382$	9.60729	+	25.3323i	0.491552	+	1.29611i
$383$	−0.624766	+	15.5034i	−0.0319241	+	0.792187i	0.901365	+	0.433061i	$0.142566\pi$
$383$	−0.624766	+	15.5034i	−0.0319241	+	0.792187i	−0.933289	+	0.359127i	$0.883075\pi$
$384$	42.7840	+	6.95308i	2.18331	+	0.354823i
$385$	−0.241708	−	0.214135i	−0.0123186	−	0.0109133i
$386$	−58.3116	+	19.4673i	−2.96798	+	0.990858i
$387$	4.30298	−	9.06834i	0.218733	−	0.460970i
$388$	−32.2571	+	67.9803i	−1.63760	+	3.45118i
$389$	−16.0528	+	8.42515i	−0.813909	+	0.427172i	−0.819687	−	0.572811i	$-0.805853\pi$
$389$	−16.0528	+	8.42515i	−0.813909	+	0.427172i	0.00577876	+	0.999983i	$0.498161\pi$
$390$	13.2150	−	26.0513i	0.669167	−	1.31916i
$391$	43.7620	+	22.9681i	2.21314	+	1.16155i
$392$	−54.2207	+	40.7442i	−2.73856	+	2.05789i
$393$	1.06955	+	3.69251i	0.0539515	+	0.186262i
$394$	−14.8276	+	1.19701i	−0.747005	+	0.0603045i
$395$	25.4905	−	36.9294i	1.28257	−	1.85812i
$396$	2.57680	+	12.6220i	0.129489	+	0.634280i
$397$	−6.70975	−	2.85876i	−0.336753	−	0.143477i	0.216970	−	0.976178i	$-0.430383\pi$
$397$	−6.70975	−	2.85876i	−0.336753	−	0.143477i	−0.553722	+	0.832702i	$0.686793\pi$
$398$	38.3219	−	9.44549i	1.92090	−	0.473460i
$399$	0.0104206	−	0.258584i	0.000521681	−	0.0129454i
$400$	46.1408	−	34.6726i	2.30704	−	1.73363i
$401$	−3.96302	+	1.68848i	−0.197904	+	0.0843189i	−0.488645	−	0.872483i	$-0.662509\pi$
$401$	−3.96302	+	1.68848i	−0.197904	+	0.0843189i	0.290741	+	0.956802i	$0.406098\pi$
$402$	−1.44008	−	2.08632i	−0.0718247	−	0.104056i
$403$	1.42477	−	21.3365i	0.0709727	−	1.06284i
$404$	−10.1888	+	14.7610i	−0.506912	+	0.734389i
$405$	−0.590504	+	2.89248i	−0.0293424	+	0.143728i
$406$	0.172968	+	0.180079i	0.00858428	+	0.00893718i
$407$	6.68644	+	14.0914i	0.331435	+	0.698484i
$408$	59.5131			2.94634
$409$	5.62092	+	11.8458i	0.277937	+	0.585739i	0.993632	−	0.112673i	$-0.0359414\pi$
$409$	5.62092	+	11.8458i	0.277937	+	0.585739i	−0.715695	+	0.698413i	$0.753890\pi$
$410$	−20.5004	−	15.4051i	−1.01244	−	0.760802i
$411$	5.65785	−	14.9185i	0.279081	−	0.735876i
$412$	−35.7871	−	15.2475i	−1.76311	−	0.751189i
$413$	−0.106994	+	0.0173882i	−0.00526483	+	0.000855619i
$414$	20.9523	+	6.99492i	1.02975	+	0.343781i
$415$	−0.638085	+	0.565294i	−0.0313224	+	0.0277492i
$416$	−83.3538	−	8.94918i	−4.08676	−	0.438769i
$417$	−8.19515	−	7.26027i	−0.401318	−	0.355537i
$418$	17.6075	+	30.4971i	0.861213	+	1.49166i
$419$	−21.0143	−	7.01560i	−1.02662	−	0.342735i	−0.247015	−	0.969012i	$-0.579450\pi$
$419$	−21.0143	−	7.01560i	−1.02662	−	0.342735i	−0.779600	+	0.626277i	$0.784578\pi$
$420$	−0.531326	+	0.553169i	−0.0259261	+	0.0269919i
$421$	7.87751	+	11.4125i	0.383926	+	0.556214i	0.966533	−	0.256540i	$-0.0825827\pi$
$421$	7.87751	+	11.4125i	0.383926	+	0.556214i	−0.582607	+	0.812754i	$0.697967\pi$
$422$	−3.85596	−	4.72269i	−0.187705	−	0.229897i
$423$	−3.63818	−	4.45597i	−0.176895	−	0.216656i
$424$	4.66271	+	6.75510i	0.226441	+	0.328057i
$425$	15.8027	−	16.4523i	0.766541	−	0.798054i
$426$	−33.8973	−	11.3166i	−1.64233	−	0.548291i
$427$	0.189596	+	0.328390i	0.00917519	+	0.0158919i
$428$	43.6594	+	38.6788i	2.11036	+	1.86961i
$429$	−2.12243	−	8.12417i	−0.102472	−	0.392239i
$430$	−60.8699	+	53.9260i	−2.93540	+	2.60054i
$431$	−17.7471	−	5.92486i	−0.854849	−	0.285390i	−0.144729	−	0.989471i	$-0.546231\pi$
$431$	−17.7471	−	5.92486i	−0.854849	−	0.285390i	−0.710120	+	0.704081i	$0.751359\pi$
$432$	15.3343	−	2.49206i	0.737771	−	0.119899i
$433$	−12.9967	−	5.53736i	−0.624580	−	0.266109i	0.0564028	−	0.998408i	$-0.482037\pi$
$433$	−12.9967	−	5.53736i	−0.624580	−	0.266109i	−0.680983	+	0.732299i	$0.738447\pi$
$434$	−0.271093	+	0.714813i	−0.0130129	+	0.0343121i
$435$	−4.57166	−	3.43538i	−0.219194	−	0.164714i
$436$	−20.2160	−	42.6044i	−0.968173	−	2.04038i
$437$	44.3481			2.12146
$438$	1.49297	+	3.14636i	0.0713368	+	0.150339i
$439$	15.4331	+	16.0676i	0.736582	+	0.766863i	0.979121	−	0.203279i	$-0.0651598\pi$
$439$	15.4331	+	16.0676i	0.736582	+	0.766863i	−0.242539	+	0.970142i	$0.577980\pi$
$440$	13.3285	−	65.2875i	0.635414	−	3.11246i
$441$	−3.97520	+	5.75907i	−0.189295	+	0.274241i
$442$	−60.6701	+	3.28870i	−2.88578	+	0.156428i
$443$	−2.61474	−	3.78810i	−0.124230	−	0.179978i	0.755934	−	0.654648i	$-0.227183\pi$
$443$	−2.61474	−	3.78810i	−0.124230	−	0.179978i	−0.880164	+	0.474670i	$0.842568\pi$
$444$	34.0828	−	14.5213i	1.61750	−	0.689151i
$445$	−9.96859	+	7.49091i	−0.472556	+	0.355103i
$446$	1.45675	−	36.1488i	0.0689790	−	1.71170i
$447$	16.3730	−	4.03558i	0.774417	−	0.190877i
$448$	1.41466	+	0.602731i	0.0668365	+	0.0284764i
$449$	−1.52256	−	7.45801i	−0.0718542	−	0.351965i	0.927930	−	0.372755i	$-0.121587\pi$
$449$	−1.52256	−	7.45801i	−0.0718542	−	0.351965i	−0.999784	+	0.0207902i	$0.993382\pi$
$450$	5.79182	−	8.39091i	0.273029	−	0.395551i
$451$	−7.34731	+	0.593136i	−0.345971	+	0.0279297i
$452$	−8.30401	−	28.6688i	−0.390588	−	1.34847i
$453$	10.5776	−	7.94856i	0.496979	−	0.373456i
$454$	−42.4260	−	22.2669i	−1.99115	−	1.04504i
$455$	0.326300	−	0.378778i	0.0152972	−	0.0177574i
$456$	47.2851	−	24.8171i	2.21433	−	1.16217i
$457$	7.02589	−	14.8067i	0.328657	−	0.692630i	−0.670111	−	0.742261i	$-0.733753\pi$
$457$	7.02589	−	14.8067i	0.328657	−	0.692630i	0.998768	+	0.0496312i	$0.0158046\pi$
$458$	−14.4752	+	30.5058i	−0.676381	+	1.42544i
$459$	5.82438	−	1.94446i	0.271859	−	0.0907599i
$460$	−98.3831	−	87.1599i	−4.58714	−	4.06385i
$461$	29.4216	+	4.78148i	1.37030	+	0.222696i	0.800622	−	0.599170i	$-0.204503\pi$
$461$	29.4216	+	4.78148i	1.37030	+	0.222696i	0.569681	+	0.821866i	$0.307067\pi$
$462$	−0.0120876	+	0.299950i	−0.000562364	+	0.0139549i
$463$	−11.6116	−	30.6173i	−0.539637	−	1.42291i	−0.876523	−	0.481361i	$-0.840143\pi$
$463$	−11.6116	−	30.6173i	−0.539637	−	1.42291i	0.336885	−	0.941546i	$-0.390627\pi$
$464$	−8.37256	+	28.9054i	−0.388686	+	1.34190i
$465$	3.50219	−	17.1549i	0.162410	−	0.795537i
$466$	43.6247	+	3.52175i	2.02088	+	0.163142i
$467$	−0.396915	+	1.04658i	−0.0183670	+	0.0484298i	−0.943886	−	0.330271i	$-0.892860\pi$
$467$	−0.396915	+	1.04658i	−0.0183670	+	0.0484298i	0.925519	+	0.378701i	$0.123629\pi$
$468$	−19.4842	+	4.26018i	−0.900657	+	0.196927i
$469$	−0.0153852	−	0.0405674i	−0.000710422	−	0.00187323i
$470$	12.9666	+	44.7659i	0.598105	+	2.06490i
$471$	0.406869	+	10.0964i	0.0187476	+	0.465216i
$472$	−14.1464	−	17.3262i	−0.651142	−	0.797504i
$473$	−2.81765	+	23.2054i	−0.129556	+	1.06699i
$474$	−41.5793	+	3.35663i	−1.90980	+	0.154175i
$475$	5.69507	−	19.6617i	0.261308	−	0.902138i
$476$	1.54901	+	0.381796i	0.0709986	+	0.0174996i
$477$	0.677035	+	0.508759i	0.0309993	+	0.0232945i
$478$	18.6251	−	22.8116i	0.851890	−	1.04338i
$479$	3.22495	+	3.35753i	0.147352	+	0.153409i	0.790788	−	0.612091i	$-0.209671\pi$
$479$	3.22495	+	3.35753i	0.147352	+	0.153409i	−0.643436	+	0.765500i	$0.722492\pi$
$480$	−66.6458	−	16.4267i	−3.04195	−	0.749773i
$481$	−21.6706	+	10.6537i	−0.988093	+	0.485767i
$482$	74.6498	−	18.3995i	3.40021	−	0.838076i
$483$	0.319523	+	0.202054i	0.0145388	+	0.00919377i
$484$	15.4232	+	26.7138i	0.701056	+	1.21426i
$485$	20.0786	−	34.7772i	0.911724	−	1.57915i
$486$	2.43003	−	1.27538i	0.110228	−	0.0578522i
$487$	0.106991	−	0.0357188i	0.00484822	−	0.00161857i	−0.314243	−	0.949343i	$-0.601751\pi$
$487$	0.106991	−	0.0357188i	0.00484822	−	0.00161857i	0.319091	+	0.947724i	$0.396622\pi$
$488$	−39.1230	+	67.7630i	−1.77102	+	3.06749i
$489$	9.57358	−	8.48145i	0.432932	−	0.383545i
$490$	47.9177	−	30.3013i	2.16470	−	1.36887i
$491$	−16.3710	+	6.97502i	−0.738812	+	0.314778i	−0.728386	−	0.685167i	$-0.759729\pi$
$491$	−16.3710	+	6.97502i	−0.738812	+	0.314778i	−0.0104261	+	0.999946i	$0.503319\pi$
$492$	0.704992	+	17.4942i	0.0317835	+	0.788699i
$493$	−1.43372	+	11.8078i	−0.0645716	+	0.531795i
$494$	−46.8329	+	27.9126i	−2.10711	+	1.25585i
$495$	−0.828705	−	6.82500i	−0.0372475	−	0.306761i
$496$	−90.9453	+	14.7801i	−4.08357	+	0.663644i
$497$	−0.516934	−	0.326889i	−0.0231876	−	0.0146630i
$498$	0.782216	+	0.127123i	0.0350520	+	0.00569650i
$499$	−4.08565	−	2.14432i	−0.182899	−	0.0959928i	0.370789	−	0.928717i	$-0.379087\pi$
$499$	−4.08565	−	2.14432i	−0.182899	−	0.0959928i	−0.553687	+	0.832725i	$0.686780\pi$
$500$	17.7338	−	11.2142i	0.793081	−	0.501514i
$501$	−0.151623	+	0.157857i	−0.00677404	+	0.00705252i
$502$	2.56468	+	21.1220i	0.114467	+	0.942722i
$503$	−4.31281	−	21.1255i	−0.192299	−	0.941941i	−0.955321	−	0.295569i	$-0.904491\pi$
$503$	−4.31281	−	21.1255i	−0.192299	−	0.941941i	0.763023	−	0.646372i	$-0.223714\pi$
$504$	0.453752	+	0.0366306i	0.0202117	+	0.00163166i
$505$	6.05388	−	7.41466i	0.269394	−	0.329948i
$506$	−51.4425			−2.28690
$507$	12.5311	−	3.46017i	0.556524	−	0.153671i
$508$	−41.8706			−1.85771
$509$	−4.39332	+	5.38084i	−0.194731	+	0.238502i	−0.862736	−	0.505655i	$-0.831251\pi$
$509$	−4.39332	+	5.38084i	−0.194731	+	0.238502i	0.668005	+	0.744157i	$0.267148\pi$
$510$	−49.5868	−	4.00306i	−2.19574	−	0.177258i
$511$	0.0119223	+	0.0583992i	0.000527411	+	0.00258343i
$512$	7.24118	+	59.6365i	0.320018	+	2.63559i
$513$	3.81682	−	3.97373i	0.168517	−	0.175444i
$514$	66.8119	−	42.2493i	2.94695	−	1.86354i
$515$	18.3824	+	9.64781i	0.810024	+	0.425133i
$516$	54.8042	+	8.90655i	2.41262	+	0.392089i
$517$	11.3230	+	7.16020i	0.497983	+	0.314905i
$518$	0.852121	−	0.138483i	0.0374400	−	0.00608460i
$519$	−0.412793	−	3.39966i	−0.0181196	−	0.149228i
$520$	101.355	+	19.2307i	4.44471	+	0.843324i
$521$	2.90853	−	23.9539i	0.127425	−	1.04944i	−0.778985	−	0.627042i	$-0.784265\pi$
$521$	2.90853	−	23.9539i	0.127425	−	1.04944i	0.906410	−	0.422398i	$-0.138812\pi$
$522$	0.214058	+	5.31179i	0.00936906	+	0.232491i
$523$	27.2700	−	11.6187i	1.19243	−	0.508048i	0.297704	−	0.954658i	$-0.403779\pi$
$523$	27.2700	−	11.6187i	1.19243	−	0.508048i	0.894729	+	0.446610i	$0.147369\pi$
$524$	−17.9730	+	11.3655i	−0.785156	+	0.496502i
$525$	0.130612	−	0.115713i	0.00570039	−	0.00505011i
$526$	23.6102	−	40.8940i	1.02945	−	1.78307i
$527$	−34.5435	+	11.5323i	−1.50474	+	0.502356i
$528$	−32.0358	+	16.8137i	−1.39418	+	0.731721i
$529$	−20.8921	+	36.1862i	−0.908352	+	1.57331i
$530$	−3.43064	−	5.94204i	−0.149017	−	0.258106i
$531$	−1.95057	−	1.23347i	−0.0846476	−	0.0535279i
$532$	1.38995	−	0.342591i	0.0602618	−	0.0148532i
$533$	−1.07605	−	11.3613i	−0.0466088	−	0.492112i
$534$	11.2550	+	2.77411i	0.487053	+	0.120048i
$535$	−21.5638	−	22.4503i	−0.932285	−	0.970611i
$536$	5.66219	−	6.93492i	0.244569	−	0.299543i
$537$	1.13915	+	0.856019i	0.0491582	+	0.0369400i
$538$	−17.0743	−	4.20844i	−0.736126	−	0.181439i
$539$	4.53408	−	15.6535i	0.195297	−	0.674243i
$540$	−16.2771	+	1.31403i	−0.700456	+	0.0565466i
$541$	−2.18268	+	17.9760i	−0.0938409	+	0.772849i	0.867490	+	0.497454i	$0.165732\pi$
$541$	−2.18268	+	17.9760i	−0.0938409	+	0.772849i	−0.961331	+	0.275395i	$0.911191\pi$
$542$	−2.78061	−	3.40563i	−0.119438	−	0.146284i
$543$	−0.982584	−	24.3826i	−0.0421667	−	1.04636i
$544$	39.7213	+	137.134i	1.70303	+	5.87956i
$545$	8.92443	+	23.5318i	0.382280	+	1.00799i
$546$	−0.464598	−	0.0122684i	−0.0198829	−	0.000525038i
$547$	−14.4090	+	37.9934i	−0.616085	+	1.62448i	0.155120	+	0.987896i	$0.450424\pi$
$547$	−14.4090	+	37.9934i	−0.616085	+	1.62448i	−0.771205	+	0.636587i	$0.780346\pi$
$548$	87.9725	+	7.10188i	3.75800	+	0.303377i
$549$	−1.61485	+	7.91005i	−0.0689201	+	0.337593i
$550$	−6.60611	+	22.8069i	−0.281685	+	0.972491i
$551$	3.78473	+	9.97952i	0.161235	+	0.425142i
$552$	−3.14115	+	77.9468i	−0.133696	+	3.31764i
$553$	−0.704687	−	0.114523i	−0.0299663	−	0.00487000i
$554$	−9.51016	−	8.42527i	−0.404048	−	0.357955i
$555$	−18.7541	+	6.26104i	−0.796067	+	0.265766i
$556$	25.9631	−	54.7160i	1.10108	−	2.32048i
$557$	7.10455	−	14.9725i	0.301029	−	0.634406i	−0.695420	−	0.718604i	$-0.744782\pi$
$557$	7.10455	−	14.9725i	0.301029	−	0.634406i	0.996449	+	0.0841979i	$0.0268328\pi$
$558$	−14.4121	+	7.56406i	−0.610113	+	0.320212i
$559$	−35.9838	−	3.86335i	−1.52195	−	0.163402i
$560$	−1.90740	−	1.00108i	−0.0806022	−	0.0423033i
$561$	−11.4321	+	8.59069i	−0.482665	+	0.362699i
$562$	−21.0153	−	72.5532i	−0.886476	−	3.06047i
$563$	−18.2862	+	1.47621i	−0.770672	+	0.0622150i	−0.459546	−	0.888154i	$-0.651988\pi$
$563$	−18.2862	+	1.47621i	−0.770672	+	0.0622150i	−0.311125	+	0.950369i	$0.600706\pi$
$564$	18.0763	−	26.1881i	0.761152	−	1.10272i
$565$	3.18621	+	15.6071i	0.134045	+	0.656596i
$566$	−27.6836	−	11.7949i	−1.16363	−	0.495776i
$567$	0.0456043	−	0.0112405i	0.00191520	−	0.000472055i
$568$	5.08185	−	126.105i	0.213230	−	5.29124i
$569$	−11.3232	+	8.50883i	−0.474693	+	0.356709i	−0.811002	−	0.585043i	$-0.801078\pi$
$569$	−11.3232	+	8.50883i	−0.474693	+	0.356709i	0.336309	+	0.941752i	$0.390821\pi$
$570$	−41.0676	+	17.4973i	−1.72013	+	0.732880i
$571$	14.8669	+	21.5384i	0.622161	+	0.901356i	0.999696	−	0.0246395i	$-0.00784379\pi$
$571$	14.8669	+	21.5384i	0.622161	+	0.901356i	−0.377536	+	0.925995i	$0.623228\pi$
$572$	39.8990	−	23.7799i	1.66826	−	0.994289i
$573$	−5.60803	+	8.12463i	−0.234279	+	0.339411i
$574$	−0.0816089	+	0.399747i	−0.00340629	+	0.0166851i
$575$	20.7142	+	21.5658i	0.863843	+	0.899356i
$576$	14.0349	+	29.5778i	0.584786	+	1.23241i
$577$	1.91923			0.0798986			0.0399493	−	0.999202i	$-0.487280\pi$
$577$	1.91923			0.0798986			0.0399493	+	0.999202i	$0.487280\pi$
$578$	24.3586	+	51.3346i	1.01318	+	2.13524i
$579$	−17.9079	−	13.4569i	−0.744226	−	0.559250i
$580$	11.2172	−	29.5772i	0.465767	−	1.22813i
$581$	0.0124777	+	0.00531625i	0.000517662	+	0.000220555i
$582$	−36.8477	+	5.98834i	−1.52739	+	0.248224i
$583$	−1.87078	−	0.624557i	−0.0774797	−	0.0258665i
$584$	−9.20609	+	8.15588i	−0.380951	+	0.337493i
$585$	10.5477	−	1.42950i	0.436092	−	0.0591026i
$586$	−10.3047	−	9.12915i	−0.425682	−	0.377122i
$587$	0.595445	+	1.03134i	0.0245766	+	0.0425680i	0.878052	−	0.478565i	$-0.158843\pi$
$587$	0.595445	+	1.03134i	0.0245766	+	0.0425680i	−0.853475	+	0.521133i	$0.825510\pi$
$588$	−36.7169	−	12.2579i	−1.51418	−	0.505508i
$589$	−22.6370	+	23.5676i	−0.932740	+	0.971085i
$590$	10.6215	+	15.3879i	0.437280	+	0.633510i
$591$	−3.42816	−	4.19874i	−0.141016	−	0.172713i
$592$	65.8041	+	80.5953i	2.70453	+	3.31245i
$593$	−6.77155	−	9.81028i	−0.278074	−	0.402860i	0.658916	−	0.752217i	$-0.271015\pi$
$593$	−6.77155	−	9.81028i	−0.278074	−	0.402860i	−0.936990	+	0.349357i	$0.886400\pi$
$594$	−4.42739	+	4.60941i	−0.181658	+	0.189126i
$595$	−0.807606	−	0.269619i	−0.0331086	−	0.0110533i
$596$	46.6398	+	80.7825i	1.91044	+	3.30898i
$597$	10.7648	+	9.53682i	0.440576	+	0.390316i
$598$	−1.10514	−	79.6358i	−0.0451924	−	3.25655i
$599$	14.9571	−	13.2508i	0.611130	−	0.541414i	−0.299785	−	0.954007i	$-0.596915\pi$
$599$	14.9571	−	13.2508i	0.611130	−	0.541414i	0.910916	+	0.412592i	$0.135377\pi$
$600$	34.1542	+	11.4023i	1.39434	+	0.465499i
$601$	−2.61979	+	0.425757i	−0.106863	+	0.0173670i	−0.213608	−	0.976920i	$-0.568521\pi$
$601$	−2.61979	+	0.425757i	−0.106863	+	0.0173670i	0.106744	+	0.994286i	$0.465957\pi$
$602$	1.19030	+	0.507142i	0.0485132	+	0.0206695i
$603$	0.327559	−	0.863703i	0.0133392	−	0.0351727i
$604$	58.5112	+	43.9683i	2.38079	+	1.78904i
$605$	−7.05727	−	14.8729i	−0.286919	−	0.604668i
$606$	−8.89853			−0.361478
$607$	4.55596	+	9.60148i	0.184921	+	0.389712i	0.974647	−	0.223747i	$-0.0718289\pi$
$607$	4.55596	+	9.60148i	0.184921	+	0.389712i	−0.789727	+	0.613459i	$0.789778\pi$
$608$	88.7450	+	92.3933i	3.59908	+	3.74704i
$609$	−0.0181990	+	0.0891447i	−0.000737462	+	0.00361233i
$610$	37.1556	−	53.8292i	1.50439	−	2.17948i
$611$	−10.8411	+	17.6824i	−0.438585	+	0.715352i
$612$	19.2950	+	27.9537i	0.779955	+	1.12996i
$613$	31.8811	−	13.5833i	1.28766	−	0.548622i	0.363848	−	0.931458i	$-0.381463\pi$
$613$	31.8811	−	13.5833i	1.28766	−	0.548622i	0.923816	+	0.382836i	$0.125053\pi$
$614$	44.3667	−	33.3394i	1.79049	−	1.34547i
$615$	0.376244	−	9.33640i	0.0151716	−	0.376480i
$616$	−1.02936	+	0.253714i	−0.0414740	+	0.0102224i
$617$	16.1961	+	6.90051i	0.652030	+	0.277804i	0.692545	−	0.721375i	$-0.256489\pi$
$617$	16.1961	+	6.90051i	0.652030	+	0.277804i	−0.0405146	+	0.999179i	$0.512900\pi$
$618$	−3.86035	−	18.9093i	−0.155286	−	0.760642i
$619$	26.2207	−	37.9873i	1.05390	−	1.52684i	0.219549	−	0.975601i	$-0.429541\pi$
$619$	26.2207	−	37.9873i	1.05390	−	1.52684i	0.834350	−	0.551235i	$-0.185843\pi$
$620$	96.5372	−	7.79329i	3.87703	−	0.312986i
$621$	2.23933	+	7.73108i	0.0898614	+	0.310237i
$622$	−25.2486	+	18.9731i	−1.01238	+	0.760752i
$623$	0.175667	+	0.0921969i	0.00703793	+	0.00369379i
$624$	−26.7167	−	49.2319i	−1.06952	−	1.97085i
$625$	−26.3631	+	13.8364i	−1.05452	+	0.553457i
$626$	29.2189	−	61.5775i	1.16782	−	2.46113i
$627$	−5.50086	+	11.5928i	−0.219683	+	0.462972i
$628$	−53.0179	+	17.7000i	−2.11565	+	0.706306i
$629$	30.7822	+	27.2706i	1.22737	+	1.08735i
$630$	−0.375606	−	0.0610419i	−0.0149645	−	0.00243197i
$631$	−1.38067	+	34.2611i	−0.0549638	+	1.36391i	0.702802	+	0.711386i	$0.251932\pi$
$631$	−1.38067	+	34.2611i	−0.0549638	+	1.36391i	−0.757766	+	0.652527i	$0.773709\pi$
$632$	−52.2402	−	137.746i	−2.07800	−	5.47925i
$633$	0.618087	−	2.13388i	0.0245668	−	0.0848143i
$634$	−2.28442	+	11.1898i	−0.0907259	+	0.444405i
$635$	22.2733	+	1.79808i	0.883888	+	0.0713548i
$636$	−1.66119	+	4.38021i	−0.0658706	+	0.173686i
$637$	24.3298	+	6.68272i	0.963982	+	0.264779i
$638$	−4.39018	−	11.5759i	−0.173809	−	0.458296i
$639$	−3.62286	−	12.5076i	−0.143318	−	0.494792i
$640$	−5.15249	−	127.858i	−0.203670	−	5.05402i
$641$	−29.0388	−	35.5661i	−1.14696	−	1.40477i	−0.900077	−	0.435730i	$-0.856490\pi$
$641$	−29.0388	−	35.5661i	−1.14696	−	1.40477i	−0.246886	−	0.969045i	$-0.579407\pi$
$642$	−3.48812	+	28.7272i	−0.137665	+	1.13377i
$643$	−41.0667	+	3.31524i	−1.61951	+	0.130740i	−0.856677	−	0.515854i	$-0.827475\pi$
$643$	−41.0667	+	3.31524i	−1.61951	+	0.130740i	−0.762834	+	0.646594i	$0.776193\pi$
$644$	−0.581812	+	2.00865i	−0.0229266	+	0.0791519i
$645$	−28.7709	−	7.09139i	−1.13285	−	0.279223i
$646$	74.2280	+	55.7787i	2.92046	+	2.19459i
$647$	22.7422	−	27.8542i	0.894090	−	1.09506i	−0.100881	−	0.994898i	$-0.532166\pi$
$647$	22.7422	−	27.8542i	0.894090	−	1.09506i	0.994971	−	0.100163i	$-0.0319364\pi$
$648$	6.71393	+	6.98994i	0.263748	+	0.274591i
$649$	5.21849	+	1.28624i	0.204844	+	0.0504894i
$650$	−35.4483	−	9.73665i	−1.39040	−	0.381903i
$651$	−0.270472	+	0.0666654i	−0.0106006	+	0.00261282i
$652$	59.7974	+	37.8136i	2.34185	+	1.48089i
$653$	−21.9271	−	37.9789i	−0.858074	−	1.48623i	−0.873764	−	0.486350i	$-0.838328\pi$
$653$	−21.9271	−	37.9789i	−0.858074	−	1.48623i	0.0156902	−	0.999877i	$-0.495005\pi$
$654$	11.6980	−	20.2616i	0.457429	−	0.792290i
$655$	10.0489	−	5.27408i	0.392644	−	0.206075i
$656$	−46.6416	+	15.5712i	−1.82105	+	0.607955i
$657$	−0.634499	+	1.09898i	−0.0247542	+	0.0428755i
$658$	0.555030	−	0.491713i	0.0216373	−	0.0191690i
$659$	−15.1296	+	9.56739i	−0.589366	+	0.372692i	−0.795611	−	0.605808i	$-0.792850\pi$
$659$	−15.1296	+	9.56739i	−0.589366	+	0.372692i	0.206245	+	0.978500i	$0.433876\pi$
$660$	34.9873	−	14.9067i	1.36188	−	0.580242i
$661$	−0.669389	−	16.6107i	−0.0260362	−	0.646082i	−0.958546	−	0.284938i	$-0.908027\pi$
$661$	−0.669389	−	16.6107i	−0.0260362	−	0.646082i	0.932510	−	0.361145i	$-0.117614\pi$
$662$	−8.41315	+	69.2885i	−0.326986	+	2.69297i
$663$	−13.5444	−	17.5130i	−0.526023	−	0.680149i
$664$	0.337349	+	2.77832i	0.0130917	+	0.107820i
$665$	−0.754101	+	0.122553i	−0.0292428	+	0.00475242i
$666$	15.5347	+	9.82356i	0.601958	+	0.380655i
$667$	−15.3895	−	2.50103i	−0.595882	−	0.0968403i
$668$	−1.07207	−	0.562667i	−0.0414797	−	0.0217702i
$669$	11.1418	−	7.04568i	0.430769	−	0.272402i
$670$	−5.18425	+	5.39738i	−0.200285	+	0.208519i
$671$	−2.26626	−	18.6643i	−0.0874879	−	0.720527i
$672$	0.218445	+	1.07001i	0.00842668	+	0.0412766i
$673$	29.9464	+	2.41752i	1.15435	+	0.0931886i	0.642778	−	0.766053i	$-0.277782\pi$
$673$	29.9464	+	2.41752i	1.15435	+	0.0931886i	0.511570	+	0.859241i	$0.329064\pi$
$674$	−56.4557	+	69.1457i	−2.17459	+	2.66339i
$675$	3.71513			0.142995
$676$	37.6697	+	61.2549i	1.44884	+	2.35596i
$677$	−22.6584			−0.870832			−0.435416	−	0.900229i	$-0.643399\pi$
$677$	−22.6584			−0.870832			−0.435416	+	0.900229i	$0.643399\pi$
$678$	9.36525	−	11.4703i	0.359670	−	0.440516i
$679$	−0.636839	−	0.0514110i	−0.0244396	−	0.00197297i
$680$	−35.1427	−	172.140i	−1.34766	−	6.60128i
$681$	−2.10446	−	17.3318i	−0.0806430	−	0.664155i
$682$	26.2582	−	27.3377i	1.00548	−	1.04681i
$683$	−20.0984	+	12.7094i	−0.769043	+	0.486313i	−0.860472	−	0.509498i	$-0.829831\pi$
$683$	−20.0984	+	12.7094i	−0.769043	+	0.486313i	0.0914286	+	0.995812i	$0.470857\pi$
$684$	26.9873	+	14.1640i	1.03188	+	0.541575i
$685$	−46.4925	−	7.55576i	−1.77639	−	0.288691i
$686$	−1.52500	−	0.964353i	−0.0582249	−	0.0368192i
$687$	−12.1443	+	1.97365i	−0.463335	+	0.0752993i
$688$	18.7961	+	154.800i	0.716593	+	5.90168i
$689$	0.926658	−	2.90948i	0.0353029	−	0.110842i
$690$	7.86021	−	64.7347i	0.299233	−	2.46441i
$691$	−0.505938	−	12.5547i	−0.0192468	−	0.477605i	−0.979856	−	0.199703i	$-0.936002\pi$
$691$	−0.505938	−	12.5547i	−0.0192468	−	0.477605i	0.960610	−	0.277901i	$-0.0896388\pi$
$692$	17.4278	−	7.42529i	0.662506	−	0.282267i
$693$	−0.0924509	+	0.0584624i	−0.00351192	+	0.00222080i
$694$	−19.2576	+	17.0607i	−0.731007	+	0.647616i
$695$	−16.1609	+	27.9915i	−0.613018	+	1.06178i
$696$	−17.8082	+	5.94525i	−0.675018	+	0.225354i
$697$	−17.2091	+	9.03203i	−0.651841	+	0.342112i
$698$	8.22131	−	14.2397i	0.311181	−	0.538982i
$699$	7.97388	+	13.8112i	0.301600	+	0.522386i
$700$	0.815816	+	0.515891i	0.0308349	+	0.0194988i
$701$	18.1689	−	4.47823i	0.686230	−	0.169140i	0.119240	−	0.992865i	$-0.461954\pi$
$701$	18.1689	−	4.47823i	0.686230	−	0.169140i	0.566990	+	0.823725i	$0.308108\pi$
$702$	−7.23072	−	6.75482i	−0.272906	−	0.254944i
$703$	35.8294	+	8.83115i	1.35133	+	0.333073i
$704$	−52.8161	−	54.9874i	−1.99058	−	2.07241i
$705$	−10.7404	+	13.1546i	−0.404508	+	0.495432i
$706$	38.6554	+	29.0477i	1.45482	+	1.09322i
$707$	−0.147870	−	0.0364467i	−0.00556123	−	0.00137072i
$708$	3.55176	−	12.2621i	0.133483	−	0.460837i
$709$	−15.3103	+	1.23597i	−0.574989	+	0.0464179i	−0.364541	−	0.931187i	$-0.618774\pi$
$709$	−15.3103	+	1.23597i	−0.574989	+	0.0464179i	−0.210448	+	0.977605i	$0.567492\pi$
$710$	−12.7165	+	104.730i	−0.477242	+	3.93044i
$711$	−9.61318	−	11.7740i	−0.360522	−	0.441560i
$712$	1.64840	+	40.9047i	0.0617765	+	1.53297i
$713$	−13.2812	−	45.8519i	−0.497383	−	1.71717i
$714$	0.280671	+	0.740068i	0.0105038	+	0.0276964i
$715$	−22.2457	+	10.9364i	−0.831941	+	0.408999i
$716$	−2.79506	+	7.36997i	−0.104456	+	0.275429i
$717$	10.6960	+	0.863468i	0.399448	+	0.0322468i
$718$	−19.3340	+	94.7041i	−0.721537	+	3.53432i
$719$	2.72856	−	9.42010i	0.101758	−	0.351310i	−0.893441	−	0.449181i	$-0.851716\pi$
$719$	2.72856	−	9.42010i	0.101758	−	0.351310i	0.995199	+	0.0978705i	$0.0312031\pi$
$720$	−16.2632	−	42.8825i	−0.606093	−	1.59814i
$721$	0.0132999	−	0.330033i	0.000495314	−	0.0122911i
$722$	30.7686	+	5.00038i	1.14509	+	0.186095i
$723$	20.9696	+	18.5774i	0.779867	+	0.690902i
$724$	128.038	−	42.7452i	4.75848	−	1.58861i
$725$	−3.08510	+	6.50171i	−0.114578	+	0.241467i
$726$	−6.56060	+	13.8262i	−0.243487	+	0.513137i
$727$	−17.7777	+	9.33047i	−0.659340	+	0.346048i	−0.760982	−	0.648773i	$-0.775283\pi$
$727$	−17.7777	+	9.33047i	−0.659340	+	0.346048i	0.101643	+	0.994821i	$0.467590\pi$
$728$	−0.414876	−	1.58805i	−0.0153763	−	0.0588570i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	8.21919	−	6.17632i	0.304206	−	0.228596i
$731$	17.1476	+	59.2005i	0.634228	+	2.18961i
$732$	−44.5130	+	3.59346i	−1.64525	+	0.132818i
$733$	−17.3462	+	25.1303i	−0.640697	+	0.928210i	−0.999987	−	0.00501608i	$-0.998403\pi$
$733$	−17.3462	+	25.1303i	−0.640697	+	0.928210i	0.359291	+	0.933226i	$0.383019\pi$
$734$	−20.6320	−	101.062i	−0.761542	−	3.73028i
$735$	19.0054	+	8.09743i	0.701023	+	0.298678i
$736$	−181.706	+	44.7866i	−6.69779	+	1.65086i
$737$	−0.0866217	+	2.14950i	−0.00319075	+	0.0791777i
$738$	−6.94426	+	5.21827i	−0.255622	+	0.192087i
$739$	28.5064	−	12.1454i	1.04863	−	0.446778i	0.202233	−	0.979337i	$-0.435180\pi$
$739$	28.5064	−	12.1454i	1.04863	−	0.446778i	0.846392	+	0.532560i	$0.178770\pi$
$740$	−62.1286	−	90.0088i	−2.28389	−	3.30879i
$741$	−18.0645	−	8.26658i	−0.663615	−	0.303680i
$742$	−0.0620124	+	0.0898405i	−0.00227655	+	0.00329815i
$743$	3.39281	−	16.6191i	0.124470	−	0.609695i	−0.868924	−	0.494945i	$-0.835188\pi$
$743$	3.39281	−	16.6191i	0.124470	−	0.609695i	0.993394	−	0.114750i	$-0.0366067\pi$
$744$	−39.8193	−	41.4563i	−1.45985	−	1.51986i
$745$	−21.3412	−	44.9756i	−0.781880	−	1.64778i
$746$	12.3585			0.452475
$747$	0.123791	+	0.260884i	0.00452928	+	0.00954526i
$748$	−63.2381	−	47.5203i	−2.31221	−	1.73752i
$749$	−0.175625	+	0.463084i	−0.00641719	+	0.0169207i
$750$	9.57677	+	4.08028i	0.349694	+	0.148991i
$751$	−36.9839	+	6.01047i	−1.34956	+	0.219325i	−0.791853	−	0.610711i	$-0.790884\pi$
$751$	−36.9839	+	6.01047i	−1.34956	+	0.219325i	−0.557709	+	0.830037i	$0.688319\pi$
$752$	84.7695	+	28.3002i	3.09123	+	1.03200i
$753$	−5.80321	+	5.14119i	−0.211481	+	0.187355i
$754$	17.8259	−	7.04491i	0.649180	−	0.256561i
$755$	−29.2371	−	25.9018i	−1.06405	−	0.942665i
$756$	0.129907	+	0.225006i	0.00472469	+	0.00818340i
$757$	19.3683	+	6.46609i	0.703953	+	0.235014i	0.646036	−	0.763307i	$-0.276426\pi$
$757$	19.3683	+	6.46609i	0.703953	+	0.235014i	0.0579176	+	0.998321i	$0.481554\pi$
$758$	−41.5691	+	43.2780i	−1.50986	+	1.57193i
$759$	−10.6482	−	15.4266i	−0.386505	−	0.559949i
$760$	−99.7050	−	122.116i	−3.61668	−	4.42963i
$761$	5.02922	+	6.15968i	0.182309	+	0.223288i	0.857672	−	0.514198i	$-0.171910\pi$
$761$	5.02922	+	6.15968i	0.182309	+	0.223288i	−0.675363	+	0.737486i	$0.736013\pi$
$762$	−11.8005	−	17.0959i	−0.427486	−	0.619320i
$763$	0.277378	−	0.288781i	0.0100418	−	0.0104546i
$764$	−51.7985	−	17.2929i	−1.87401	−	0.625635i
$765$	−9.06364	−	15.6987i	−0.327697	−	0.567587i
$766$	−31.8729	−	28.2369i	−1.15161	−	1.02024i
$767$	−1.87906	+	8.10613i	−0.0678490	+	0.292695i
$768$	−40.0292	+	35.4628i	−1.44443	+	1.27965i
$769$	31.3871	+	10.4786i	1.13185	+	0.377866i	0.820056	−	0.572284i	$-0.193942\pi$
$769$	31.3871	+	10.4786i	1.13185	+	0.377866i	0.311793	+	0.950150i	$0.399071\pi$
$770$	0.874735	−	0.142158i	0.0315233	−	0.00512303i
$771$	26.4993	+	11.2903i	0.954347	+	0.406609i
$772$	43.9393	−	115.858i	1.58141	−	4.16983i
$773$	−3.80950	−	2.86265i	−0.137018	−	0.102963i	0.530023	−	0.847983i	$-0.322183\pi$
$773$	−3.80950	−	2.86265i	−0.137018	−	0.102963i	−0.667041	+	0.745021i	$0.732440\pi$
$774$	11.8090	+	24.8869i	0.424466	+	0.894543i
$775$	−22.0339			−0.791480
$776$	−56.5184	−	119.110i	−2.02889	−	4.27580i
$777$	0.217911	+	0.226869i	0.00781750	+	0.00813888i
$778$	9.95206	−	48.7484i	0.356799	−	1.74772i
$779$	−9.90680	+	14.3525i	−0.354948	+	0.514231i
$780$	23.8280	+	53.8419i	0.853179	+	1.92785i
$781$	17.2270	+	24.9576i	0.616430	+	0.893053i
$782$	−124.782	+	53.1647i	−4.46220	+	1.90117i
$783$	−1.54859	+	1.16369i	−0.0553422	+	0.0415869i
$784$	4.37747	−	108.626i	0.156338	−	3.87949i
$785$	28.9633	−	7.13880i	1.03374	−	0.254795i
$786$	−9.70594	−	4.13531i	−0.346199	−	0.147502i
$787$	4.61028	+	22.5826i	0.164339	+	0.804984i	0.975472	+	0.220123i	$0.0706459\pi$
$787$	4.61028	+	22.5826i	0.164339	+	0.804984i	−0.811133	+	0.584861i	$0.801149\pi$
$788$	17.0329	−	24.6763i	0.606770	−	0.879058i
$789$	17.1504	−	1.38453i	0.610572	−	0.0492904i
$790$	34.2617	+	118.285i	1.21898	+	4.20840i
$791$	0.202606	−	0.152249i	0.00720384	−	0.00541334i
$792$	−19.9861	−	10.4895i	−0.710174	−	0.372728i
$793$	28.8447	−	3.90925i	1.02430	−	0.138822i
$794$	17.7231	−	9.30178i	0.628968	−	0.330108i
$795$	1.07178	−	2.25873i	0.0380122	−	0.0801091i
$796$	−34.1041	+	71.8729i	−1.20879	+	2.54747i
$797$	47.4327	−	15.8353i	1.68015	−	0.560917i	0.693032	−	0.720906i	$-0.256274\pi$
$797$	47.4327	−	15.8353i	1.68015	−	0.560917i	0.987119	+	0.159990i	$0.0511461\pi$
$798$	0.531613	+	0.470968i	0.0188189	+	0.0166721i
$799$	34.8656	+	5.66621i	1.23346	+	0.200456i
$800$	−3.47820	+	86.3106i	−0.122973	+	3.05154i
$801$	1.49780	+	3.94938i	0.0529222	+	0.139544i
$802$	3.28909	−	11.3553i	0.116142	−	0.400969i
$803$	0.591140	−	2.89560i	0.0208609	−	0.102183i
$804$	5.09314	+	0.411161i	0.179621	+	0.0145005i
$805$	0.395757	−	1.04353i	0.0139486	−	0.0367795i
$806$	42.8843	+	40.0618i	1.51054	+	1.41112i
$807$	−2.27222	−	5.99136i	−0.0799860	−	0.210906i
$808$	−8.74329	−	30.1853i	−0.307588	−	1.06192i
$809$	−1.54910	−	38.4405i	−0.0544634	−	1.35149i	−0.763264	−	0.646086i	$-0.776405\pi$
$809$	−1.54910	−	38.4405i	−0.0544634	−	1.35149i	0.708801	−	0.705408i	$-0.249236\pi$
$810$	−5.12394	−	6.27568i	−0.180037	−	0.220505i
$811$	1.49911	−	12.3463i	0.0526410	−	0.433538i	−0.942432	−	0.334397i	$-0.891467\pi$
$811$	1.49911	−	12.3463i	0.0526410	−	0.433538i	0.995073	−	0.0991410i	$-0.0316095\pi$
$812$	−0.501653	+	0.0404976i	−0.0176046	+	0.00142119i
$813$	0.445716	−	1.53879i	0.0156319	−	0.0539677i
$814$	−41.5610	−	10.2439i	−1.45671	−	0.359048i
$815$	−30.1857	−	22.6830i	−1.05736	−	0.794553i
$816$	−60.3314	+	73.8925i	−2.11202	+	2.58676i
$817$	38.3111	+	39.8861i	1.34034	+	1.39544i
$818$	−34.9380	−	8.61145i	−1.22158	−	0.301092i
$819$	−0.0924890	−	0.141863i	−0.00323183	−	0.00495709i
$820$	50.1853	−	12.3696i	1.75255	−	0.431964i
$821$	41.6812	+	26.3576i	1.45468	+	0.919886i	0.999566	+	0.0294537i	$0.00937677\pi$
$821$	41.6812	+	26.3576i	1.45468	+	0.919886i	0.455117	+	0.890432i	$0.349598\pi$
$822$	21.8938	+	37.9211i	0.763632	+	1.32265i
$823$	13.4105	−	23.2277i	0.467461	−	0.809666i	−0.531848	−	0.846840i	$-0.678502\pi$
$823$	13.4105	−	23.2277i	0.467461	−	0.809666i	0.999309	+	0.0371738i	$0.0118355\pi$
$824$	60.3505	−	31.6744i	2.10241	−	1.10343i
$825$	−8.20676	+	2.73982i	−0.285723	+	0.0953882i
$826$	0.148742	−	0.257629i	0.00517540	−	0.00896406i
$827$	−24.2628	+	21.4950i	−0.843701	+	0.747454i	−0.969628	−	0.244585i	$-0.921348\pi$
$827$	−24.2628	+	21.4950i	−0.843701	+	0.747454i	0.125926	+	0.992040i	$0.459810\pi$
$828$	−37.6305	+	23.7961i	−1.30775	+	0.826972i
$829$	−6.76997	+	2.88442i	−0.235131	+	0.100180i	−0.506318	−	0.862347i	$-0.668994\pi$
$829$	−6.76997	+	2.88442i	−0.235131	+	0.100180i	0.271187	+	0.962527i	$0.412584\pi$
$830$	−0.0942025	−	2.33761i	−0.00326982	−	0.0811397i
$831$	0.558040	−	4.59587i	0.0193582	−	0.159429i
$832$	83.9888	−	82.9434i	2.91179	−	2.87555i
$833$	−5.17936	−	42.6559i	−0.179454	−	1.47794i
$834$	29.6580	−	4.81990i	1.02697	−	0.166899i
$835$	0.546131	+	0.345353i	0.0188997	+	0.0119514i
$836$	−70.0608	−	11.3860i	−2.42310	−	0.393793i
$837$	−5.25151	−	2.75620i	−0.181519	−	0.0952683i
$838$	51.3877	−	32.4956i	1.77516	−	1.12254i
$839$	−1.70743	+	1.77762i	−0.0589470	+	0.0613703i	−0.750023	−	0.661412i	$-0.769958\pi$
$839$	−1.70743	+	1.77762i	−0.0589470	+	0.0613703i	0.691076	+	0.722782i	$0.257137\pi$
$840$	−0.161989	−	1.33410i	−0.00558915	−	0.0460308i
$841$	5.05019	+	24.7374i	0.174144	+	0.853015i
$842$	−37.9336	−	3.06232i	−1.30728	−	0.105535i
$843$	17.4072	−	21.3200i	0.599537	−	0.734300i
$844$	12.2890			0.423005
$845$	−17.4081	−	34.2026i	−0.598856	−	1.17660i
$846$	15.7872			0.542775
$847$	−0.165649	+	0.202884i	−0.00569178	+	0.00697116i
$848$	−13.1141	−	1.05868i	−0.450339	−	0.0363551i
$849$	−2.19324	−	10.7432i	−0.0752719	−	0.368706i
$850$	7.54628	+	62.1492i	0.258835	+	2.13170i
$851$	−37.3422	+	38.8774i	−1.28008	+	1.33270i
$852$	60.8798	−	38.4981i	2.08571	−	1.31892i
$853$	−6.55745	−	3.44162i	−0.224523	−	0.117839i	0.348712	−	0.937230i	$-0.386619\pi$
$853$	−6.55745	−	3.44162i	−0.224523	−	0.117839i	−0.573235	+	0.819391i	$0.694312\pi$
$854$	−1.02717	−	0.166931i	−0.0351490	−	0.00571227i
$855$	−13.7478	−	8.69356i	−0.470164	−	0.297313i
$856$	−100.875	+	16.3938i	−3.44784	+	0.560328i
$857$	4.63310	+	38.1570i	0.158264	+	1.30342i	0.827962	+	0.560785i	$0.189500\pi$
$857$	4.63310	+	38.1570i	0.158264	+	1.30342i	−0.669698	+	0.742633i	$0.733577\pi$
$858$	20.9543	+	9.58899i	0.715367	+	0.327363i
$859$	−2.74862	+	22.6369i	−0.0937817	+	0.772362i	0.867623	+	0.497223i	$0.165647\pi$
$859$	−2.74862	+	22.6369i	−0.0937817	+	0.772362i	−0.961404	+	0.275139i	$0.911276\pi$
$860$	−6.60009	−	163.779i	−0.225061	−	5.58483i
$861$	−0.136768	+	0.0582716i	−0.00466106	+	0.00198589i
$862$	43.3982	−	27.4434i	1.47815	−	0.934725i
$863$	−29.8104	+	26.4097i	−1.01476	+	0.898996i	−0.994906	−	0.100807i	$-0.967858\pi$
$863$	−29.8104	+	26.4097i	−1.01476	+	0.898996i	−0.0198509	+	0.999803i	$0.506319\pi$
$864$	−11.6255	+	20.1360i	−0.395508	+	0.685041i
$865$	−9.58968	+	3.20151i	−0.326059	+	0.108854i
$866$	34.3293	−	18.0174i	1.16656	−	0.612256i
$867$	−10.3522	+	17.9305i	−0.351579	+	0.608953i
$868$	−0.770462	−	1.33448i	−0.0261512	−	0.0452952i
$869$	29.9187	+	18.9194i	1.01492	+	0.641797i
$870$	15.2378	−	3.75579i	0.516611	−	0.127333i
$871$	−3.32940	−	0.0879176i	−0.112812	−	0.00297897i
$872$	80.2247	+	19.7736i	2.71675	+	0.669619i
$873$	−9.42297	−	9.81035i	−0.318919	−	0.332030i
$874$	−76.9736	+	94.2756i	−2.60367	+	3.18892i
$875$	0.142429	+	0.107028i	0.00481497	+	0.00361821i
$876$	−6.81562	−	1.67990i	−0.230279	−	0.0567586i
$877$	−2.15092	+	7.42585i	−0.0726316	+	0.250753i	−0.988616	−	0.150460i	$-0.951924\pi$
$877$	−2.15092	+	7.42585i	−0.0726316	+	0.250753i	0.915984	+	0.401214i	$0.131412\pi$
$878$	−60.9433	+	4.91985i	−2.05674	+	0.166037i
$879$	0.604661	−	4.97983i	0.0203947	−	0.167966i
$880$	67.5504	+	82.7342i	2.27712	+	2.78897i
$881$	0.389438	+	9.66380i	0.0131205	+	0.325582i	0.992399	+	0.123063i	$0.0392717\pi$
$881$	0.389438	+	9.66380i	0.0131205	+	0.325582i	−0.979278	+	0.202519i	$0.935087\pi$
$882$	−5.34305	−	18.4464i	−0.179910	−	0.621121i
$883$	−13.0307	−	34.3591i	−0.438518	−	1.15628i	−0.954114	−	0.299444i	$-0.903199\pi$
$883$	−13.0307	−	34.3591i	−0.438518	−	1.15628i	0.515596	−	0.856832i	$-0.327570\pi$
$884$	72.2055	−	98.9168i	2.42853	−	3.32693i
$885$	−2.41596	+	6.37035i	−0.0812115	+	0.214137i
$886$	12.5911	+	1.01646i	0.423006	+	0.0341486i
$887$	2.76120	−	13.5253i	0.0927121	−	0.454134i	−0.906760	−	0.421647i	$-0.861452\pi$
$887$	2.76120	−	13.5253i	0.0927121	−	0.454134i	0.999472	−	0.0324870i	$-0.0103428\pi$
$888$	−18.0595	+	62.3487i	−0.606037	+	2.09228i
$889$	−0.126071	−	0.332422i	−0.00422829	−	0.0111491i
$890$	1.37793	−	34.1930i	0.0461884	−	1.14615i
$891$	−2.29870	−	0.373576i	−0.0770095	−	0.0125153i
$892$	54.5823	+	48.3557i	1.82755	+	1.61907i
$893$	30.0647	−	10.0371i	1.00608	−	0.335877i
$894$	−19.8392	+	41.8103i	−0.663524	+	1.39835i
$895$	1.80334	−	3.80046i	0.0602791	−	0.127035i
$896$	−1.80269	+	0.946127i	−0.0602238	+	0.0316079i
$897$	23.6524	−	16.8154i	0.789731	−	0.561450i
$898$	18.4970	+	9.70795i	0.617251	+	0.323959i
$899$	9.18447	−	6.90168i	0.306319	−	0.230184i
$900$	5.71754	+	19.7392i	0.190585	+	0.657975i
$901$	−5.18334	+	0.418442i	−0.172682	+	0.0139403i
$902$	11.4916	−	16.6485i	0.382628	−	0.554333i
$903$	0.0943023	+	0.461923i	0.00313818	+	0.0153718i
$904$	48.1113	+	20.4983i	1.60016	+	0.681763i
$905$	−69.9459	+	17.2401i	−2.32508	+	0.573081i
$906$	−1.46212	+	36.2820i	−0.0485755	+	1.20539i
$907$	1.22831	−	0.923012i	0.0407852	−	0.0306481i	−0.580154	−	0.814507i	$-0.697008\pi$
$907$	1.22831	−	0.923012i	0.0407852	−	0.0306481i	0.620939	+	0.783859i	$0.286751\pi$
$908$	88.8485	−	37.8548i	2.94854	−	1.25626i
$909$	−1.84193	−	2.66849i	−0.0610928	−	0.0885082i
$910$	0.238861	+	1.35108i	0.00791815	+	0.0447880i
$911$	−10.8544	+	15.7253i	−0.359621	+	0.521001i	−0.960478	−	0.278355i	$-0.910211\pi$
$911$	−10.8544	+	15.7253i	−0.359621	+	0.521001i	0.600857	+	0.799356i	$0.294826\pi$
$912$	−17.1219	+	83.8684i	−0.566961	+	2.77716i
$913$	−0.465852	−	0.485004i	−0.0154175	−	0.0160513i
$914$	19.2817	+	40.6353i	0.637781	+	1.34410i
$915$	23.8332			0.787902
$916$	−29.1764	−	61.4880i	−0.964016	−	2.03162i
$917$	−0.144350	−	0.108472i	−0.00476685	−	0.00358205i
$918$	−5.97564	+	15.7565i	−0.197226	+	0.520041i
$919$	5.21528	+	2.22202i	0.172036	+	0.0732978i	0.476268	−	0.879300i	$-0.341989\pi$
$919$	5.21528	+	2.22202i	0.172036	+	0.0732978i	−0.304231	+	0.952598i	$0.598400\pi$
$920$	227.314	−	36.9422i	7.49433	−	1.21795i
$921$	19.1814	+	6.40369i	0.632048	+	0.211009i
$922$	−61.2307	+	54.2457i	−2.01653	+	1.78649i
$923$	−38.2656	+	27.2045i	−1.25953	+	0.895446i
$924$	−0.452904	−	0.401238i	−0.0148994	−	0.0131998i
$925$	12.4408	+	21.5481i	0.409052	+	0.708498i
$926$	85.2404	+	28.4574i	2.80117	+	0.935169i
$927$	4.87145	−	5.07171i	0.159999	−	0.166577i
$928$	−25.5853	−	37.0667i	−0.839878	−	1.21677i
$929$	24.1112	+	29.5309i	0.791063	+	0.968877i	0.999959	−	0.00906115i	$-0.00288429\pi$
$929$	24.1112	+	29.5309i	0.791063	+	0.968877i	−0.208896	+	0.977938i	$0.566987\pi$
$930$	30.3893	+	37.2201i	0.996504	+	1.22050i
$931$	−21.9028	−	31.7317i	−0.717835	−	1.03996i
$932$	−61.1099	+	63.6221i	−2.00172	+	2.08401i
$933$	−10.9159	−	3.64427i	−0.357371	−	0.119308i
$934$	−1.53591	−	2.66028i	−0.0502566	−	0.0870469i
$935$	31.5991	+	27.9944i	1.03340	+	0.915514i
$936$	15.8089	−	31.1648i	0.516731	−	1.01865i
$937$	39.0325	−	34.5798i	1.27514	−	1.12967i	0.290160	−	0.956978i	$-0.406291\pi$
$937$	39.0325	−	34.5798i	1.27514	−	1.12967i	0.984976	−	0.172694i	$-0.0552470\pi$
$938$	0.112942	+	0.0377056i	0.00368769	+	0.00123113i
$939$	24.5139	−	3.98390i	0.799982	−	0.130010i
$940$	−86.4227	−	36.8213i	−2.81880	−	1.20098i
$941$	19.2861	−	50.8532i	0.628708	−	1.65777i	−0.118320	−	0.992976i	$-0.537751\pi$
$941$	19.2861	−	50.8532i	0.628708	−	1.65777i	0.747028	−	0.664792i	$-0.231480\pi$
$942$	−22.1691	−	16.6590i	−0.722309	−	0.542780i
$943$	−10.9213	−	23.0162i	−0.355647	−	0.749511i
$944$	35.8535			1.16693
$945$	−0.0594423	−	0.125272i	−0.00193366	−	0.00407510i
$946$	−44.4398	−	46.2667i	−1.44486	−	1.50426i
$947$	−4.11639	+	20.1634i	−0.133765	+	0.655222i	0.856514	+	0.516124i	$0.172626\pi$
$947$	−4.11639	+	20.1634i	−0.133765	+	0.655222i	−0.990279	+	0.139099i	$0.955580\pi$
$948$	47.7632	−	69.1969i	1.55128	−	2.24741i
$949$	4.49524	+	0.852911i	0.145922	+	0.0276867i
$950$	31.9122	+	46.2327i	1.03537	+	1.49999i
$951$	−3.82846	+	1.63115i	−0.124146	+	0.0528938i
$952$	−2.23466	+	1.67924i	−0.0724259	+	0.0544245i
$953$	−0.386249	+	9.58467i	−0.0125118	+	0.310478i	0.980800	+	0.195016i	$0.0624758\pi$
$953$	−0.386249	+	9.58467i	−0.0125118	+	0.310478i	−0.993312	+	0.115462i	$0.963165\pi$
$954$	−2.25663	+	0.556210i	−0.0730612	+	0.0180080i
$955$	26.8119	+	11.4235i	0.867612	+	0.369655i
$956$	11.8732	+	58.1588i	0.384007	+	1.88099i
$957$	2.56266	−	3.71266i	0.0828391	−	0.120013i
$958$	−12.7349	+	1.02807i	−0.411446	+	0.0332154i
$959$	0.208499	+	0.719821i	0.00673278	+	0.0232442i
$960$	77.2656	−	58.0613i	2.49374	−	1.87392i
$961$	3.69676	+	1.94021i	0.119250	+	0.0625873i
$962$	14.9652	−	64.5588i	0.482498	−	2.08146i
$963$	−9.33674	+	4.90030i	−0.300872	+	0.157910i
$964$	−66.4338	+	140.006i	−2.13969	+	4.50930i
$965$	−28.3491	+	59.7445i	−0.912591	+	1.92324i
$966$	−0.984113	+	0.328545i	−0.0316633	+	0.0105708i
$967$	39.5282	+	35.0189i	1.27114	+	1.12613i	0.985839	+	0.167696i	$0.0536327\pi$
$967$	39.5282	+	35.0189i	1.27114	+	1.12613i	0.285303	+	0.958437i	$0.407906\pi$
$968$	−53.3469	−	8.66972i	−1.71463	−	0.278655i
$969$	−1.36231	+	33.8053i	−0.0437636	+	1.08598i
$970$	39.0798	+	103.045i	1.25478	+	3.30858i
$971$	−5.25404	+	18.1390i	−0.168610	+	0.582110i	0.831054	+	0.556192i	$0.187738\pi$
$971$	−5.25404	+	18.1390i	−0.168610	+	0.582110i	−0.999664	+	0.0259178i	$0.991749\pi$
$972$	−1.10646	+	5.41982i	−0.0354898	+	0.173841i
$973$	0.512579	+	0.0413797i	0.0164325	+	0.00132657i
$974$	−0.109769	+	0.289438i	−0.00351724	+	0.00927420i
$975$	−4.41769	−	12.6456i	−0.141479	−	0.404985i
$976$	−44.4749	−	117.271i	−1.42361	−	3.75374i
$977$	10.5740	+	36.5057i	0.338292	+	1.16792i	0.931764	+	0.363065i	$0.118270\pi$
$977$	10.5740	+	36.5057i	0.338292	+	1.16792i	−0.593472	+	0.804855i	$0.702243\pi$
$978$	1.41338	+	35.0726i	0.0451948	+	1.12150i
$979$	−6.22123	−	7.61962i	−0.198831	−	0.243524i
$980$	−13.7743	+	113.441i	−0.440003	+	3.62375i
$981$	8.49744	−	0.685984i	0.271302	−	0.0219018i
$982$	13.5870	−	46.9079i	0.433580	−	1.49689i
$983$	36.6520	+	9.03391i	1.16902	+	0.288137i	0.775601	−	0.631223i	$-0.217447\pi$
$983$	36.6520	+	9.03391i	1.16902	+	0.288137i	0.393417	+	0.919360i	$0.371293\pi$
$984$	−24.5244	−	18.4289i	−0.781810	−	0.587492i
$985$	−10.1204	+	12.3953i	−0.322463	+	0.394946i
$986$	−22.6126	−	23.5422i	−0.720131	−	0.749736i
$987$	0.262342	+	0.0646614i	0.00835043	+	0.00205820i
$988$	16.1210	−	108.703i	0.512878	−	3.45829i
$989$	−78.4425	+	19.3343i	−2.49432	+	0.614796i
$990$	15.9470	+	10.0843i	0.506829	+	0.320499i
$991$	−20.4345	−	35.3935i	−0.649122	−	1.12431i	−0.983333	−	0.181815i	$-0.941803\pi$
$991$	−20.4345	−	35.3935i	−0.649122	−	1.12431i	0.334210	−	0.942498i	$-0.391530\pi$
$992$	68.9492	−	119.424i	2.18914	−	3.79170i
$993$	−22.5197	+	11.8192i	−0.714641	+	0.375072i
$994$	1.59213	−	0.531531i	0.0504993	−	0.0168591i
$995$	21.2284	−	36.7686i	0.672984	−	1.16564i
$996$	−1.19562	+	1.05923i	−0.0378847	+	0.0335629i
$997$	3.87417	−	2.44987i	0.122696	−	0.0775883i	−0.471708	−	0.881755i	$-0.656362\pi$
$997$	3.87417	−	2.44987i	0.122696	−	0.0775883i	0.594404	+	0.804167i	$0.297388\pi$
$998$	11.6497	−	4.96349i	0.368766	−	0.157117i
$999$	0.269677	+	6.69195i	0.00853219	+	0.211724i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.55.1	✓	384
169.126	even	39	inner	507.2.q.b.295.1	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.55.1	✓	384	1.1	even	1	trivial
507.2.q.b.295.1	yes	384	169.126	even	39	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73567 + 2.12581i) q^{2} +(-0.996757 - 0.0804666i) q^{3} +(-1.10646 - 5.41982i) q^{4} +(0.355841 + 2.93061i) q^{5} +(1.90110 - 1.97925i) q^{6} +(0.0396979 - 0.0251034i) q^{7} +(8.58190 + 4.50413i) q^{8} +(0.987050 + 0.160411i) q^{9} +(-6.84755 - 4.33013i) q^{10} +(-2.29870 + 0.373576i) q^{11} +(0.666762 + 5.49128i) q^{12} +(-0.627698 - 3.55049i) q^{13} +(-0.0155373 + 0.127961i) q^{14} +(-0.118871 - 2.94975i) q^{15} +(-14.2923 + 6.08938i) q^{16} +(-5.18980 + 3.28183i) q^{17} +(-2.05420 + 1.81986i) q^{18} +(-2.75493 + 4.77168i) q^{19} +(15.4897 - 5.17121i) q^{20} +(-0.0415891 + 0.0218277i) q^{21} +(3.19564 - 5.53501i) q^{22} +(-4.02443 - 6.97052i) q^{23} +(-8.19164 - 5.18008i) q^{24} +(-3.60717 + 0.889088i) q^{25} +(8.63714 + 4.82811i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(-0.179980 - 0.187379i) q^{28} +(1.22510 - 1.50048i) q^{29} +(6.47691 + 4.86708i) q^{30} +(5.75851 + 1.41935i) q^{31} +(6.46885 - 22.3331i) q^{32} +(2.32131 - 0.187396i) q^{33} +(2.03123 - 16.7287i) q^{34} +(0.0876946 + 0.107406i) q^{35} +(-0.222735 - 5.52712i) q^{36} +(-1.86333 - 6.43296i) q^{37} +(-5.36203 - 14.1385i) q^{38} +(0.339967 + 3.58949i) q^{39} +(-10.1461 + 26.7530i) q^{40} +(3.15489 + 0.254689i) q^{41} +(0.0257835 - 0.126296i) q^{42} +(2.79259 - 9.64115i) q^{43} +(4.56815 + 12.0452i) q^{44} +(-0.118871 + 2.94975i) q^{45} +(21.8031 + 3.54334i) q^{46} +(-4.30586 - 3.81466i) q^{47} +(14.7360 - 4.91958i) q^{48} +(-2.99990 + 6.32216i) q^{49} +(4.37083 - 9.21132i) q^{50} +(5.43705 - 2.85358i) q^{51} +(-18.5485 + 7.33050i) q^{52} +(0.749879 + 0.393567i) q^{53} +(2.19397 - 1.64866i) q^{54} +(-1.91278 - 6.60368i) q^{55} +(0.453752 - 0.0366306i) q^{56} +(3.12996 - 4.53453i) q^{57} +(1.06336 + 5.20867i) q^{58} +(-2.12317 - 0.904600i) q^{59} +(-15.8556 + 3.90804i) q^{60} +(-0.325075 + 8.06666i) q^{61} +(-13.0121 + 9.77797i) q^{62} +(0.0432107 - 0.0184103i) q^{63} +(18.5977 + 26.9435i) q^{64} +(10.1818 - 3.10295i) q^{65} +(-3.63066 + 5.25992i) q^{66} +(0.184770 - 0.905062i) q^{67} +(23.5292 + 24.4965i) q^{68} +(3.45049 + 7.27175i) q^{69} -0.380534 q^{70} +(-5.58231 - 11.7645i) q^{71} +(7.74825 + 5.82243i) q^{72} +(-0.449993 + 1.18653i) q^{73} +(16.9094 + 7.20441i) q^{74} +(3.66702 - 0.595948i) q^{75} +(28.9099 + 9.65153i) q^{76} +(-0.0818756 + 0.0725355i) q^{77} +(-8.22063 - 5.50746i) q^{78} +(-11.3774 - 10.0795i) q^{79} +(-22.9314 - 39.7184i) q^{80} +(0.948536 + 0.316668i) q^{81} +(-6.01727 + 6.26464i) q^{82} +(0.164037 + 0.237649i) q^{83} +(0.164319 + 0.201254i) q^{84} +(-11.4645 - 14.0415i) q^{85} +(15.6482 + 22.6704i) q^{86} +(-1.34187 + 1.39703i) q^{87} +(-21.4099 - 7.14767i) q^{88} +(2.11193 + 3.65797i) q^{89} +(-6.06427 - 5.37248i) q^{90} +(-0.114048 - 0.125190i) q^{91} +(-33.3261 + 29.5243i) q^{92} +(-5.62563 - 1.87811i) q^{93} +(15.5828 - 2.53245i) q^{94} +(-14.9643 - 6.37568i) q^{95} +(-8.24494 + 21.7401i) q^{96} +(-10.8746 - 8.17176i) q^{97} +(-8.23286 - 17.3504i) q^{98} -2.32886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19}+ \cdots - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

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Database

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