LMFDB - Embedded newform 144.2.x.e.61.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [144,2,Mod(13,144)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(144, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("144.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	144.x (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [72,4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.14984578911$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	144.61
Dual form			144.2.x.e.85.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.35510 + 0.404605i) q^{2} +(1.51206 - 0.844796i) q^{3} +(1.67259 - 1.09656i) q^{4} +(3.32531 + 0.891015i) q^{5} +(-1.70718 + 1.75657i) q^{6} +(-3.95817 - 2.28525i) q^{7} +(-1.82285 + 2.16269i) q^{8} +(1.57264 - 2.55476i) q^{9} +(-4.86664 + 0.138025i) q^{10} +(0.568165 + 2.12042i) q^{11} +(1.60268 - 3.07106i) q^{12} +(0.0174070 - 0.0649637i) q^{13} +(6.28833 + 1.49524i) q^{14} +(5.78079 - 1.46195i) q^{15} +(1.59511 - 3.66819i) q^{16} -0.00952807 q^{17} +(-1.09741 + 4.09825i) q^{18} +(2.79059 + 2.79059i) q^{19} +(6.53893 - 2.15611i) q^{20} +(-7.91555 - 0.111584i) q^{21} +(-1.62785 - 2.64350i) q^{22} +(-4.81949 + 2.78254i) q^{23} +(-0.929225 + 4.81005i) q^{24} +(5.93367 + 3.42580i) q^{25} +(0.00269648 + 0.0950753i) q^{26} +(0.219668 - 5.19151i) q^{27} +(-9.12630 + 0.518089i) q^{28} +(-1.28304 + 0.343789i) q^{29} +(-7.24204 + 4.32002i) q^{30} +(-1.30392 - 2.25846i) q^{31} +(-0.677361 + 5.61615i) q^{32} +(2.65042 + 2.72622i) q^{33} +(0.0129115 - 0.00385511i) q^{34} +(-11.1260 - 11.1260i) q^{35} +(-0.171073 - 5.99756i) q^{36} +(-3.32550 + 3.32550i) q^{37} +(-4.91061 - 2.65244i) q^{38} +(-0.0285607 - 0.112934i) q^{39} +(-7.98853 + 5.56742i) q^{40} +(-4.34209 + 2.50691i) q^{41} +(10.7715 - 3.05146i) q^{42} +(-0.718661 - 2.68208i) q^{43} +(3.27548 + 2.92357i) q^{44} +(7.50585 - 7.09414i) q^{45} +(5.40507 - 5.72061i) q^{46} +(-2.77988 + 4.81489i) q^{47} +(-0.686977 - 6.89406i) q^{48} +(6.94473 + 12.0286i) q^{49} +(-9.42681 - 2.24151i) q^{50} +(-0.0144070 + 0.00804928i) q^{51} +(-0.0421220 - 0.127745i) q^{52} +(1.80067 - 1.80067i) q^{53} +(1.80284 + 7.12389i) q^{54} +7.55731i q^{55} +(12.1574 - 4.39461i) q^{56} +(6.57701 + 1.86205i) q^{57} +(1.59955 - 0.984992i) q^{58} +(0.221086 + 0.0592399i) q^{59} +(8.06578 - 8.78422i) q^{60} +(-10.8847 + 2.91654i) q^{61} +(2.68073 + 2.53286i) q^{62} +(-12.0630 + 6.51830i) q^{63} +(-1.35443 - 7.88451i) q^{64} +(0.115767 - 0.200515i) q^{65} +(-4.69463 - 2.62192i) q^{66} +(1.19332 - 4.45355i) q^{67} +(-0.0159365 + 0.0104481i) q^{68} +(-4.93668 + 8.27885i) q^{69} +(19.5784 + 10.5752i) q^{70} +7.21697i q^{71} +(2.65847 + 8.05807i) q^{72} -6.99151i q^{73} +(3.16086 - 5.85189i) q^{74} +(11.8662 + 0.167276i) q^{75} +(7.72756 + 1.60746i) q^{76} +(2.59680 - 9.69138i) q^{77} +(0.0843965 + 0.141481i) q^{78} +(6.86643 - 11.8930i) q^{79} +(8.57265 - 10.7766i) q^{80} +(-4.05361 - 8.03543i) q^{81} +(4.86966 - 5.15395i) q^{82} +(11.8706 - 3.18073i) q^{83} +(-13.3618 + 8.49325i) q^{84} +(-0.0316838 - 0.00848965i) q^{85} +(2.05904 + 3.34371i) q^{86} +(-1.64960 + 1.60373i) q^{87} +(-5.62149 - 2.63645i) q^{88} -2.28107i q^{89} +(-7.30084 + 12.6502i) q^{90} +(-0.217358 + 0.217358i) q^{91} +(-5.00981 + 9.93891i) q^{92} +(-3.87954 - 2.31337i) q^{93} +(1.81888 - 7.64941i) q^{94} +(6.79313 + 11.7660i) q^{95} +(3.72030 + 9.06418i) q^{96} +(-4.69078 + 8.12466i) q^{97} +(-14.2776 - 13.4901i) q^{98} +(6.31069 + 1.88313i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) $ 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8 - 20 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 20 * q^15 - 10 * q^16 - 16 * q^17 + 28 * q^19 + 12 * q^20 - 16 * q^21 - 8 * q^22 - 40 * q^24 - 4 * q^26 + 8 * q^27 - 16 * q^28 + 4 * q^29 + 18 * q^30 + 28 * q^31 - 46 * q^32 - 32 * q^33 - 14 * q^34 - 16 * q^35 + 14 * q^36 + 16 * q^37 + 2 * q^38 - 10 * q^40 + 26 * q^42 - 10 * q^43 + 60 * q^44 + 40 * q^45 + 20 * q^46 - 56 * q^47 + 2 * q^48 + 4 * q^49 - 36 * q^50 - 54 * q^51 + 6 * q^52 - 8 * q^53 + 92 * q^54 + 52 * q^56 - 14 * q^58 - 14 * q^59 + 18 * q^60 - 32 * q^61 + 16 * q^62 - 108 * q^63 - 44 * q^64 - 64 * q^65 + 26 * q^66 - 18 * q^67 + 16 * q^68 + 32 * q^69 + 14 * q^70 + 114 * q^72 + 38 * q^74 + 86 * q^75 + 10 * q^76 - 36 * q^77 + 16 * q^78 + 44 * q^79 + 144 * q^80 - 44 * q^81 - 88 * q^82 + 20 * q^83 - 58 * q^84 - 8 * q^85 + 76 * q^86 - 42 * q^88 - 80 * q^91 - 68 * q^92 - 4 * q^93 + 20 * q^94 + 48 * q^95 + 94 * q^96 + 40 * q^97 + 88 * q^98 + 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.35510	+	0.404605i	−0.958200	+	0.286099i
$2$	−1.35510	+	0.404605i	−0.958200	+	0.286099i
$3$	1.51206	−	0.844796i	0.872987	−	0.487743i
$3$	1.51206	−	0.844796i	0.872987	−	0.487743i
$4$	1.67259	−	1.09656i	0.836295	−	0.548280i
$5$	3.32531	+	0.891015i	1.48712	+	0.398474i	0.908765	−	0.417308i	$-0.137026\pi$
$5$	3.32531	+	0.891015i	1.48712	+	0.398474i	0.578360	+	0.815782i	$0.303693\pi$
$6$	−1.70718	+	1.75657i	−0.696953	+	0.717117i
$7$	−3.95817	−	2.28525i	−1.49605	−	0.863743i	−0.496057	−	0.868290i	$-0.665219\pi$
$7$	−3.95817	−	2.28525i	−1.49605	−	0.863743i	−0.999990	+	0.00454705i	$0.998553\pi$
$8$	−1.82285	+	2.16269i	−0.644475	+	0.764625i
$9$	1.57264	−	2.55476i	0.524213	−	0.851587i
$10$	−4.86664	+	0.138025i	−1.53897	+	0.0436474i
$11$	0.568165	+	2.12042i	0.171308	+	0.639331i	0.997151	+	0.0754306i	$0.0240331\pi$
$11$	0.568165	+	2.12042i	0.171308	+	0.639331i	−0.825843	+	0.563900i	$0.809300\pi$
$12$	1.60268	−	3.07106i	0.462654	−	0.886539i
$13$	0.0174070	−	0.0649637i	0.00482783	−	0.0180177i	−0.963470	−	0.267817i	$-0.913698\pi$
$13$	0.0174070	−	0.0649637i	0.00482783	−	0.0180177i	0.968298	+	0.249799i	$0.0803645\pi$
$14$	6.28833	+	1.49524i	1.68063	+	0.399621i
$15$	5.78079	−	1.46195i	1.49259	−	0.377473i
$16$	1.59511	−	3.66819i	0.398777	−	0.917048i
$17$	−0.00952807			−0.00231090			−0.00115545	−	0.999999i	$-0.500368\pi$
$17$	−0.00952807			−0.00231090			−0.00115545	+	0.999999i	$0.500368\pi$
$18$	−1.09741	+	4.09825i	−0.258662	+	0.965968i
$19$	2.79059	+	2.79059i	0.640205	+	0.640205i	0.950606	−	0.310401i	$-0.100463\pi$
$19$	2.79059	+	2.79059i	0.640205	+	0.640205i	−0.310401	+	0.950606i	$0.600463\pi$
$20$	6.53893	−	2.15611i	1.46215	−	0.482120i
$21$	−7.91555	−	0.111584i	−1.72731	−	0.0243497i
$22$	−1.62785	−	2.64350i	−0.347060	−	0.563596i
$23$	−4.81949	+	2.78254i	−1.00493	+	0.580199i	−0.909704	−	0.415256i	$-0.863692\pi$
$23$	−4.81949	+	2.78254i	−1.00493	+	0.580199i	−0.0952296	+	0.995455i	$0.530359\pi$
$24$	−0.929225	+	4.81005i	−0.189677	+	0.981846i
$25$	5.93367	+	3.42580i	1.18673	+	0.685161i
$26$	0.00269648	+	0.0950753i	0.000528823	+	0.0186458i
$27$	0.219668	−	5.19151i	0.0422752	−	0.999106i
$28$	−9.12630	+	0.518089i	−1.72471	+	0.0979096i
$29$	−1.28304	+	0.343789i	−0.238254	+	0.0638400i	−0.375970	−	0.926632i	$-0.622691\pi$
$29$	−1.28304	+	0.343789i	−0.238254	+	0.0638400i	0.137716	+	0.990472i	$0.456024\pi$
$30$	−7.24204	+	4.32002i	−1.32221	+	0.788724i
$31$	−1.30392	−	2.25846i	−0.234191	−	0.405631i	0.724846	−	0.688911i	$-0.241911\pi$
$31$	−1.30392	−	2.25846i	−0.234191	−	0.405631i	−0.959037	+	0.283280i	$0.908578\pi$
$32$	−0.677361	+	5.61615i	−0.119742	+	0.992805i
$33$	2.65042	+	2.72622i	0.461379	+	0.474573i
$34$	0.0129115	−	0.00385511i	0.00221430	−	0.000661146i
$35$	−11.1260	−	11.1260i	−1.88063	−	1.88063i
$36$	−0.171073	−	5.99756i	−0.0285121	−	0.999593i
$37$	−3.32550	+	3.32550i	−0.546708	+	0.546708i	−0.925487	−	0.378779i	$-0.876344\pi$
$37$	−3.32550	+	3.32550i	−0.546708	+	0.546708i	0.378779	+	0.925487i	$0.376344\pi$
$38$	−4.91061	−	2.65244i	−0.796607	−	0.430282i
$39$	−0.0285607	−	0.112934i	−0.00457338	−	0.0180840i
$40$	−7.98853	+	5.56742i	−1.26310	+	0.880287i
$41$	−4.34209	+	2.50691i	−0.678121	+	0.391513i	−0.799147	−	0.601136i	$-0.794715\pi$
$41$	−4.34209	+	2.50691i	−0.678121	+	0.391513i	0.121026	+	0.992649i	$0.461382\pi$
$42$	10.7715	−	3.05146i	1.66208	−	0.470851i
$43$	−0.718661	−	2.68208i	−0.109595	−	0.409013i	0.889231	−	0.457458i	$-0.151240\pi$
$43$	−0.718661	−	2.68208i	−0.109595	−	0.409013i	−0.998826	+	0.0484450i	$0.984573\pi$
$44$	3.27548	+	2.92357i	0.493797	+	0.440744i
$45$	7.50585	−	7.09414i	1.11891	−	1.05753i
$46$	5.40507	−	5.72061i	0.796933	−	0.843457i
$47$	−2.77988	+	4.81489i	−0.405487	+	0.702324i	−0.994378	−	0.105889i	$-0.966231\pi$
$47$	−2.77988	+	4.81489i	−0.405487	+	0.702324i	0.588891	+	0.808212i	$0.299565\pi$
$48$	−0.686977	−	6.89406i	−0.0991566	−	0.995072i
$49$	6.94473	+	12.0286i	0.992104	+	1.71837i
$50$	−9.42681	−	2.24151i	−1.33315	−	0.316998i
$51$	−0.0144070	+	0.00804928i	−0.00201738	+	0.00112712i
$52$	−0.0421220	−	0.127745i	−0.00584126	−	0.0177151i
$53$	1.80067	−	1.80067i	0.247341	−	0.247341i	−0.572537	−	0.819879i	$-0.694041\pi$
$53$	1.80067	−	1.80067i	0.247341	−	0.247341i	0.819879	+	0.572537i	$0.194041\pi$
$54$	1.80284	+	7.12389i	0.245335	+	0.969438i
$55$			7.55731i			1.01903i
$56$	12.1574	−	4.39461i	1.62460	−	0.587255i
$57$	6.57701	+	1.86205i	0.871147	+	0.246635i
$58$	1.59955	−	0.984992i	0.210031	−	0.129336i
$59$	0.221086	+	0.0592399i	0.0287830	+	0.00771238i	0.273182	−	0.961962i	$-0.411924\pi$
$59$	0.221086	+	0.0592399i	0.0287830	+	0.00771238i	−0.244399	+	0.969675i	$0.578591\pi$
$60$	8.06578	−	8.78422i	1.04129	−	1.13404i
$61$	−10.8847	+	2.91654i	−1.39364	+	0.373425i	−0.876057	−	0.482207i	$-0.839835\pi$
$61$	−10.8847	+	2.91654i	−1.39364	+	0.373425i	−0.517584	+	0.855632i	$0.673169\pi$
$62$	2.68073	+	2.53286i	0.340453	+	0.321674i
$63$	−12.0630	+	6.51830i	−1.51980	+	0.821229i
$64$	−1.35443	−	7.88451i	−0.169304	−	0.985564i
$65$	0.115767	−	0.200515i	0.0143592	−	0.0248708i
$66$	−4.69463	−	2.62192i	−0.577869	−	0.322736i
$67$	1.19332	−	4.45355i	0.145788	−	0.544087i	−0.853931	−	0.520386i	$-0.825788\pi$
$67$	1.19332	−	4.45355i	0.145788	−	0.544087i	0.999719	−	0.0237016i	$-0.00754517\pi$
$68$	−0.0159365	+	0.0104481i	−0.00193259	+	0.00126702i
$69$	−4.93668	+	8.27885i	−0.594306	+	0.996656i
$70$	19.5784	+	10.5752i	2.34007	+	1.26397i
$71$			7.21697i			0.856497i	0.903661	+	0.428248i	$0.140869\pi$
$71$			7.21697i			0.856497i	−0.903661	+	0.428248i	$0.859131\pi$
$72$	2.65847	+	8.05807i	0.313303	+	0.949653i
$73$		−	6.99151i		−	0.818294i	−0.912469	−	0.409147i	$-0.865826\pi$
$73$		−	6.99151i		−	0.818294i	0.912469	−	0.409147i	$-0.134174\pi$
$74$	3.16086	−	5.85189i	0.367443	−	0.680269i
$75$	11.8662	+	0.167276i	1.37019	+	0.0193153i
$76$	7.72756	+	1.60746i	0.886412	+	0.184388i
$77$	2.59680	−	9.69138i	0.295933	−	1.10444i
$78$	0.0843965	+	0.141481i	0.00955602	+	0.0160196i
$79$	6.86643	−	11.8930i	0.772534	−	1.33807i	−0.163636	−	0.986521i	$-0.552322\pi$
$79$	6.86643	−	11.8930i	0.772534	−	1.33807i	0.936170	−	0.351547i	$-0.114344\pi$
$80$	8.57265	−	10.7766i	0.958451	−	1.20486i
$81$	−4.05361	−	8.03543i	−0.450402	−	0.892826i
$82$	4.86966	−	5.15395i	0.537764	−	0.569158i
$83$	11.8706	−	3.18073i	1.30297	−	0.349130i	0.460398	−	0.887712i	$-0.347707\pi$
$83$	11.8706	−	3.18073i	1.30297	−	0.349130i	0.842573	+	0.538582i	$0.181040\pi$
$84$	−13.3618	+	8.49325i	−1.45789	+	0.926689i
$85$	−0.0316838	−	0.00848965i	−0.00343659	−	0.000920832i
$86$	2.05904	+	3.34371i	0.222032	+	0.360562i
$87$	−1.64960	+	1.60373i	−0.176855	+	0.171938i
$88$	−5.62149	−	2.63645i	−0.599253	−	0.281046i
$89$		−	2.28107i		−	0.241793i	−0.992665	−	0.120896i	$-0.961423\pi$
$89$		−	2.28107i		−	0.241793i	0.992665	−	0.120896i	$-0.0385769\pi$
$90$	−7.30084	+	12.6502i	−0.769576	+	1.33344i
$91$	−0.217358	+	0.217358i	−0.0227853	+	0.0227853i
$92$	−5.00981	+	9.93891i	−0.522309	+	1.03620i
$93$	−3.87954	−	2.31337i	−0.402290	−	0.239886i
$94$	1.81888	−	7.64941i	0.187603	−	0.788976i
$95$	6.79313	+	11.7660i	0.696960	+	1.20717i
$96$	3.72030	+	9.06418i	0.379701	+	0.925109i
$97$	−4.69078	+	8.12466i	−0.476276	+	0.824934i	−0.999631	−	0.0271807i	$-0.991347\pi$
$97$	−4.69078	+	8.12466i	−0.476276	+	0.824934i	0.523354	+	0.852115i	$0.324680\pi$
$98$	−14.2776	−	13.4901i	−1.44226	−	1.36271i
$99$	6.31069	+	1.88313i	0.634248	+	0.189262i
$100$	13.6812	−	0.776664i	1.36812	−	0.0776664i
$101$	−4.65331	−	17.3664i	−0.463022	−	1.72802i	−0.663365	−	0.748296i	$-0.730872\pi$
$101$	−4.65331	−	17.3664i	−0.463022	−	1.72802i	0.200343	−	0.979726i	$-0.435794\pi$
$102$	0.0162661	−	0.0167367i	0.00161059	−	0.00165718i
$103$	5.05311	−	2.91741i	0.497897	−	0.287461i	−0.229948	−	0.973203i	$-0.573855\pi$
$103$	5.05311	−	2.91741i	0.497897	−	0.287461i	0.727845	+	0.685742i	$0.240522\pi$
$104$	0.108766	+	0.156065i	0.0106654	+	0.0153034i
$105$	−26.2222	−	7.42392i	−2.55903	−	0.724501i
$106$	−1.71153	+	3.16865i	−0.166238	+	0.307767i
$107$	−11.3933	+	11.3933i	−1.10143	+	1.10143i	−0.107195	+	0.994238i	$0.534187\pi$
$107$	−11.3933	+	11.3933i	−1.10143	+	1.10143i	−0.994238	+	0.107195i	$0.965813\pi$
$108$	−5.32539	−	8.92414i	−0.512436	−	0.858726i
$109$	11.9264	+	11.9264i	1.14235	+	1.14235i	0.988020	+	0.154326i	$0.0493206\pi$
$109$	11.9264	+	11.9264i	1.14235	+	1.14235i	0.154326	+	0.988020i	$0.450679\pi$
$110$	−3.05773	−	10.2409i	−0.291543	−	0.976432i
$111$	−2.21898	+	7.83771i	−0.210616	+	0.743922i
$112$	−14.6964	+	10.8741i	−1.38868	+	1.02751i
$113$	−2.85638	−	4.94740i	−0.268706	−	0.465412i	0.699822	−	0.714317i	$-0.253263\pi$
$113$	−2.85638	−	4.94740i	−0.268706	−	0.465412i	−0.968528	+	0.248905i	$0.919929\pi$
$114$	−9.66590	+	0.137826i	−0.905295	+	0.0129086i
$115$	−18.5056	+	4.95856i	−1.72566	+	0.462388i
$116$	−1.76901	+	1.98195i	−0.164248	+	0.184019i
$117$	−0.138592	−	0.146635i	−0.0128128	−	0.0135564i
$118$	−0.323563	+	0.00917674i	−0.0297864	+	0.000844788i
$119$	0.0377137	+	0.0217740i	0.00345721	+	0.00199602i
$120$	−7.37579	+	15.1670i	−0.673314	+	1.38455i
$121$	5.35291	−	3.09050i	0.486628	−	0.280955i
$122$	13.5698	−	8.35621i	1.22855	−	0.756536i
$123$	−4.44767	+	7.45878i	−0.401033	+	0.672535i
$124$	−4.65747	−	2.34765i	−0.418253	−	0.210825i
$125$	4.50737	+	4.50737i	0.403151	+	0.403151i
$126$	13.7093	−	13.7137i	1.22132	−	1.22171i
$127$	9.97753			0.885363			0.442681	−	0.896679i	$-0.354027\pi$
$127$	9.97753			0.885363			0.442681	+	0.896679i	$0.354027\pi$
$128$	5.02551	+	10.1363i	0.444196	+	0.895930i
$129$	−3.35247	−	3.44834i	−0.295168	−	0.303609i
$130$	−0.0757468	+	0.318558i	−0.00664344	+	0.0279393i
$131$	−0.00265571	+	0.00991124i	−0.000232030	+	0.000865949i	−0.966042	−	0.258386i	$-0.916809\pi$
$131$	−0.00265571	+	0.00991124i	−0.000232030	+	0.000865949i	0.965810	+	0.259252i	$0.0834760\pi$
$132$	7.42253	+	1.65349i	0.646048	+	0.143918i
$133$	−4.66843	−	17.4228i	−0.404804	−	1.51075i
$134$	0.184856	+	6.51783i	0.0159691	+	0.563054i
$135$	5.35618	−	17.0677i	0.460986	−	1.46895i
$136$	0.0173682	−	0.0206062i	0.00148932	−	0.00176697i
$137$	4.04634	+	2.33615i	0.345702	+	0.199591i	0.662791	−	0.748805i	$-0.269372\pi$
$137$	4.04634	+	2.33615i	0.345702	+	0.199591i	−0.317089	+	0.948396i	$0.602705\pi$
$138$	3.34003	−	13.2161i	0.284322	−	1.12503i
$139$	5.90168	+	1.58135i	0.500574	+	0.134128i	0.500266	−	0.865872i	$-0.333235\pi$
$139$	5.90168	+	1.58135i	0.500574	+	0.134128i	0.000307450		1.00000i	$0.499902\pi$
$140$	−30.8094	−	6.40886i	−2.60387	−	0.541648i
$141$	−0.135736	+	9.62882i	−0.0114311	+	0.810893i
$142$	−2.92002	−	9.77971i	−0.245043	−	0.820695i
$143$	0.147640			0.0123463
$144$	−6.86282	−	9.84386i	−0.571902	−	0.820322i
$145$	−4.57282			−0.379752
$146$	2.82880	+	9.47419i	0.234113	+	0.784089i
$147$	20.6626	+	12.3211i	1.70422	+	1.01623i
$148$	−1.91558	+	9.20880i	−0.157460	+	0.756958i
$149$	6.74921	+	1.80845i	0.552917	+	0.148154i	0.524450	−	0.851441i	$-0.324271\pi$
$149$	6.74921	+	1.80845i	0.552917	+	0.148154i	0.0284668	+	0.999595i	$0.490938\pi$
$150$	−16.1475	+	4.57443i	−1.31844	+	0.373501i
$151$	11.7804	+	6.80144i	0.958679	+	0.553494i	0.895766	−	0.444525i	$-0.146628\pi$
$151$	11.7804	+	6.80144i	0.958679	+	0.553494i	0.0629127	+	0.998019i	$0.479961\pi$
$152$	−11.1220	+	0.948346i	−0.902113	+	0.0769210i
$153$	−0.0149842	+	0.0243420i	−0.00121140	+	0.00196793i
$154$	0.402265	+	14.1835i	0.0324154	+	1.14294i
$155$	−2.32363	−	8.67190i	−0.186638	−	0.696544i
$156$	−0.171610	−	0.157574i	−0.0137398	−	0.0126160i
$157$	4.50899	−	16.8278i	0.359857	−	1.34300i	−0.514404	−	0.857548i	$-0.671987\pi$
$157$	4.50899	−	16.8278i	0.359857	−	1.34300i	0.874261	−	0.485456i	$-0.161347\pi$
$158$	−4.49272	+	18.8944i	−0.357422	+	1.50316i
$159$	1.20152	−	4.24392i	0.0952867	−	0.336565i
$160$	−7.25651	+	18.0719i	−0.573678	+	1.42871i
$161$	25.4352			2.00457
$162$	8.74423	+	9.24870i	0.687012	+	0.726646i
$163$	−8.11902	−	8.11902i	−0.635930	−	0.635930i	0.313619	−	0.949549i	$-0.398459\pi$
$163$	−8.11902	−	8.11902i	−0.635930	−	0.635930i	−0.949549	+	0.313619i	$0.898459\pi$
$164$	−4.51356	+	8.95440i	−0.352450	+	0.699221i
$165$	6.38438	+	11.4271i	0.497024	+	0.889597i
$166$	−14.7989	+	9.11312i	−1.14862	+	0.707315i
$167$	9.28313	−	5.35962i	0.718350	−	0.414740i	−0.0957949	−	0.995401i	$-0.530539\pi$
$167$	9.28313	−	5.35962i	0.718350	−	0.414740i	0.814145	+	0.580661i	$0.197206\pi$
$168$	14.6702	−	16.9155i	1.13183	−	1.30506i
$169$	11.2544	+	6.49774i	0.865724	+	0.499826i
$170$	0.0463697	−	0.00131512i	0.00355639	−	0.000100865i
$171$	11.5179	−	2.74070i	0.880794	−	0.209587i
$172$	−4.14309	−	3.69796i	−0.315907	−	0.281967i
$173$	−5.77879	+	1.54842i	−0.439353	+	0.117724i	−0.471713	−	0.881752i	$-0.656364\pi$
$173$	−5.77879	+	1.54842i	−0.439353	+	0.117724i	0.0323603	+	0.999476i	$0.489698\pi$
$174$	1.58649	−	2.84065i	0.120271	−	0.215349i
$175$	−15.6576	−	27.1198i	−1.18361	−	2.05007i
$176$	8.68439	+	1.29816i	0.654611	+	0.0978528i
$177$	0.384341	−	0.0971988i	0.0288889	−	0.00730591i
$178$	0.922932	+	3.09108i	0.0691767	+	0.231686i
$179$	−1.39609	−	1.39609i	−0.104349	−	0.104349i	0.653005	−	0.757354i	$-0.273508\pi$
$179$	−1.39609	−	1.39609i	−0.104349	−	0.104349i	−0.757354	+	0.653005i	$0.773508\pi$
$180$	4.77504	−	20.0962i	0.355911	−	1.49788i
$181$	1.82587	−	1.82587i	0.135716	−	0.135716i	−0.635985	−	0.771701i	$-0.719406\pi$
$181$	1.82587	−	1.82587i	0.135716	−	0.135716i	0.771701	+	0.635985i	$0.219406\pi$
$182$	0.206598	−	0.382486i	0.0153140	−	0.0283517i
$183$	−13.9944	+	13.6053i	−1.03450	+	1.00573i
$184$	2.76746	−	15.4952i	0.204020	−	1.14232i
$185$	−14.0214	+	8.09525i	−1.03087	+	0.595174i
$186$	6.19317	+	1.56517i	0.454105	+	0.114764i
$187$	−0.00541352	−	0.0202035i	−0.000395876	−	0.00147743i
$188$	0.630226	+	11.1016i	0.0459640	+	0.809670i
$189$	−12.7334	+	20.0469i	−0.926216	+	1.45819i
$190$	−13.9660	−	13.1956i	−1.01320	−	0.957311i
$191$	5.22560	−	9.05100i	0.378111	−	0.654907i	−0.612676	−	0.790334i	$-0.709907\pi$
$191$	5.22560	−	9.05100i	0.378111	−	0.654907i	0.990787	+	0.135426i	$0.0432404\pi$
$192$	−8.70879	−	10.7776i	−0.628503	−	0.777808i
$193$	−12.0468	−	20.8657i	−0.867150	−	1.50195i	−0.864896	−	0.501951i	$-0.832616\pi$
$193$	−12.0468	−	20.8657i	−0.867150	−	1.50195i	−0.00225418	−	0.999997i	$-0.500718\pi$
$194$	3.06919	−	12.9076i	0.220355	−	0.926714i
$195$	0.00565270	−	0.400990i	0.000404798	−	0.0287155i
$196$	24.8058	+	12.5036i	1.77184	+	0.893116i
$197$	11.7435	−	11.7435i	0.836687	−	0.836687i	−0.151735	−	0.988421i	$-0.548486\pi$
$197$	11.7435	−	11.7435i	0.836687	−	0.836687i	0.988421	+	0.151735i	$0.0484859\pi$
$198$	−9.31353	+	0.00150949i	−0.661884	+	0.000107275i
$199$		−	8.85458i		−	0.627684i	−0.949475	−	0.313842i	$-0.898384\pi$
$199$		−	8.85458i		−	0.627684i	0.949475	−	0.313842i	$-0.101616\pi$
$200$	−18.2251	+	6.58794i	−1.28871	+	0.465838i
$201$	−1.95796	−	7.74214i	−0.138104	−	0.546088i
$202$	13.3322	+	21.6504i	0.938053	+	1.52332i
$203$	5.86412	+	1.57129i	0.411581	+	0.110283i
$204$	−0.0152705	+	0.0292613i	−0.00106915	+	0.00204870i
$205$	−16.6725	+	4.46739i	−1.16446	+	0.312016i
$206$	−5.66706	+	5.99790i	−0.394843	+	0.417893i
$207$	−0.470607	+	16.6886i	−0.0327094	+	1.15994i
$208$	−0.210533	−	0.167476i	−0.0145979	−	0.0116124i
$209$	−4.33171	+	7.50274i	−0.299631	+	0.518975i
$210$	38.5375	−	0.549505i	2.65934	−	0.0379195i
$211$	−6.17529	+	23.0465i	−0.425125	+	1.58659i	0.338526	+	0.940957i	$0.390072\pi$
$211$	−6.17529	+	23.0465i	−0.425125	+	1.58659i	−0.763651	+	0.645630i	$0.776595\pi$
$212$	1.03724	−	4.98633i	0.0712378	−	0.342463i
$213$	6.09687	+	10.9125i	0.417750	+	0.747710i
$214$	10.8293	−	20.0489i	0.740274	−	1.37051i
$215$		−	9.55909i		−	0.651924i
$216$	10.8272	+	9.93841i	0.736697	+	0.676223i
$217$			11.9191i			0.809125i
$218$	−20.9870	−	11.3360i	−1.42142	−	0.767772i
$219$	−5.90640	−	10.5716i	−0.399117	−	0.714360i
$220$	8.28704	+	12.6403i	0.558712	+	0.852207i
$221$	−0.000165855	0	0.000618979i	−1.11566e−5	0	4.16370e-5i
$222$	−0.164245	−	11.5187i	−0.0110234	−	0.773084i
$223$	−9.55369	+	16.5475i	−0.639762	+	1.10810i	0.345722	+	0.938337i	$0.387634\pi$
$223$	−9.55369	+	16.5475i	−0.639762	+	1.10810i	−0.985485	+	0.169764i	$0.945699\pi$
$224$	15.5154	−	20.6817i	1.03667	−	1.38186i
$225$	18.0836	−	9.77155i	1.20558	−	0.651437i
$226$	5.87242	+	5.54851i	0.390628	+	0.369081i
$227$	−0.0783128	+	0.0209838i	−0.00519780	+	0.00139275i	−0.261417	−	0.965226i	$-0.584190\pi$
$227$	−0.0783128	+	0.0209838i	−0.00519780	+	0.00139275i	0.256219	+	0.966619i	$0.417523\pi$
$228$	13.0425	−	4.09764i	0.863760	−	0.271373i
$229$	−3.39514	−	0.909725i	−0.224357	−	0.0601163i	0.144889	−	0.989448i	$-0.453717\pi$
$229$	−3.39514	−	0.909725i	−0.224357	−	0.0601163i	−0.369246	+	0.929332i	$0.620384\pi$
$230$	23.0707	−	14.2068i	1.52124	−	0.936769i
$231$	−4.26073	−	16.8477i	−0.280336	−	1.10850i
$232$	1.59528	−	3.40149i	0.104735	−	0.223318i
$233$			27.7645i			1.81891i	0.415798	+	0.909457i	$0.363502\pi$
$233$			27.7645i			1.81891i	−0.415798	+	0.909457i	$0.636498\pi$
$234$	0.247135	+	0.142630i	0.0161557	+	0.00932403i
$235$	−13.5341	+	13.5341i	−0.882867	+	0.882867i
$236$	0.434747	−	0.143351i	0.0282996	−	0.00933133i
$237$	0.335275	−	23.7837i	0.0217785	−	1.54491i
$238$	−0.0599157	−	0.0142468i	−0.00388376	−	0.000923483i
$239$	−2.56538	−	4.44336i	−0.165940	−	0.287417i	0.771048	−	0.636776i	$-0.219733\pi$
$239$	−2.56538	−	4.44336i	−0.165940	−	0.287417i	−0.936989	+	0.349359i	$0.886399\pi$
$240$	3.85830	−	23.5370i	0.249052	−	1.51931i
$241$	0.729827	−	1.26410i	0.0470123	−	0.0814277i	−0.841562	−	0.540161i	$-0.818363\pi$
$241$	0.729827	−	1.26410i	0.0470123	−	0.0814277i	0.888574	+	0.458733i	$0.151697\pi$
$242$	−6.00329	+	6.35375i	−0.385906	+	0.408435i
$243$	−12.9176	−	8.72557i	−0.828665	−	0.559745i
$244$	−15.0074	+	16.8139i	−0.960753	+	1.07640i
$245$	12.3757	+	46.1868i	0.790655	+	2.95076i
$246$	3.00918	−	11.9069i	0.191858	−	0.759159i
$247$	0.229863	−	0.132711i	0.0146258	−	0.00844422i
$248$	7.26120	+	1.29686i	0.461087	+	0.0823505i
$249$	15.2620	−	14.8377i	0.967191	−	0.940302i
$250$	−7.93164	−	4.28423i	−0.501641	−	0.270958i
$251$	0.191647	−	0.191647i	0.0120967	−	0.0120967i	−0.701033	−	0.713129i	$-0.747277\pi$
$251$	0.191647	−	0.191647i	0.0120967	−	0.0120967i	0.713129	+	0.701033i	$0.247277\pi$
$252$	−13.0288	+	24.1303i	−0.820736	+	1.52007i
$253$	−8.63842	−	8.63842i	−0.543093	−	0.543093i
$254$	−13.5205	+	4.03696i	−0.848355	+	0.253302i
$255$	−0.0550798	+	0.0139295i	−0.00344923	+	0.000872300i
$256$	−10.9113	−	11.7023i	−0.681954	−	0.731396i
$257$	−15.8433	−	27.4414i	−0.988278	−	1.71175i	−0.626353	−	0.779540i	$-0.715453\pi$
$257$	−15.8433	−	27.4414i	−0.988278	−	1.71175i	−0.361925	−	0.932207i	$-0.617880\pi$
$258$	5.93814	+	3.31641i	0.369693	+	0.206471i
$259$	20.7625	−	5.56328i	1.29012	−	0.345686i
$260$	−0.0262456	−	0.462325i	−0.00162768	−	0.0286722i
$261$	−1.13946	+	3.81851i	−0.0705306	+	0.236360i
$262$	−0.000411391	−	0.0145052i	−2.54158e−5	−	0.000896136i
$263$	10.2637	+	5.92574i	0.632886	+	0.365397i	0.781869	−	0.623443i	$-0.214267\pi$
$263$	10.2637	+	5.92574i	0.632886	+	0.365397i	−0.148983	+	0.988840i	$0.547600\pi$
$264$	−10.7273	+	0.762551i	−0.660218	+	0.0469318i
$265$	7.59222	−	4.38337i	0.466386	−	0.269268i
$266$	13.3755	+	21.7208i	0.820108	+	1.33179i
$267$	−1.92704	−	3.44911i	−0.117933	−	0.211082i
$268$	−2.88764	−	8.75751i	−0.176391	−	0.534950i
$269$	4.40442	+	4.40442i	0.268542	+	0.268542i	0.828513	−	0.559970i	$-0.189187\pi$
$269$	4.40442	+	4.40442i	0.268542	+	0.268542i	−0.559970	+	0.828513i	$0.689187\pi$
$270$	−0.352487	+	25.2955i	−0.0214517	+	1.53944i
$271$	−5.01359			−0.304554			−0.152277	−	0.988338i	$-0.548661\pi$
$271$	−5.01359			−0.304554			−0.152277	+	0.988338i	$0.548661\pi$
$272$	−0.0151983	+	0.0349508i	−0.000921533	+	0.00211920i
$273$	−0.145035	+	0.512281i	−0.00877790	+	0.0310047i
$274$	−6.42841	−	1.52855i	−0.388355	−	0.0923432i
$275$	−3.89285	+	14.5283i	−0.234747	+	0.876089i
$276$	0.821224	+	19.2605i	0.0494319	+	1.15934i
$277$	−1.80783	−	6.74690i	−0.108622	−	0.405382i	0.890109	−	0.455747i	$-0.150628\pi$
$277$	−1.80783	−	6.74690i	−0.108622	−	0.405382i	−0.998731	+	0.0503657i	$0.983961\pi$
$278$	−8.63718	+	0.244964i	−0.518024	+	0.0146920i
$279$	−7.82043	−	0.220531i	−0.468197	−	0.0132028i
$280$	44.3429	−	3.78101i	2.65000	−	0.225959i
$281$	−15.4222	−	8.90401i	−0.920011	−	0.531169i	−0.0363725	−	0.999338i	$-0.511580\pi$
$281$	−15.4222	−	8.90401i	−0.920011	−	0.531169i	−0.883639	+	0.468170i	$0.844914\pi$
$282$	−3.71194	−	13.1029i	−0.221043	−	0.780268i
$283$	12.2594	+	3.28490i	0.728746	+	0.195267i	0.604071	−	0.796931i	$-0.293544\pi$
$283$	12.2594	+	3.28490i	0.728746	+	0.195267i	0.124675	+	0.992198i	$0.460211\pi$
$284$	7.91384	+	12.0710i	0.469600	+	0.716283i
$285$	20.2115	+	12.0521i	1.19723	+	0.713906i
$286$	−0.200068	+	0.0597361i	−0.0118302	+	0.00353227i
$287$	22.9156			1.35267
$288$	13.2827	+	10.5627i	0.782690	+	0.622412i
$289$	−16.9999			−0.999995
$290$	6.19663	−	1.85019i	0.363879	−	0.108647i
$291$	−0.229042	+	16.2477i	−0.0134267	+	0.952457i
$292$	−7.66661	−	11.6939i	−0.448655	−	0.684335i
$293$	13.0762	+	3.50375i	0.763918	+	0.204691i	0.619683	−	0.784852i	$-0.287261\pi$
$293$	13.0762	+	3.50375i	0.763918	+	0.204691i	0.144235	+	0.989543i	$0.453928\pi$
$294$	−32.9850	−	8.33612i	−1.92372	−	0.486173i
$295$	0.682398	+	0.393983i	0.0397307	+	0.0229386i
$296$	−1.13013	−	13.2539i	−0.0656873	−	0.770367i
$297$	11.1330	−	2.48384i	0.646001	−	0.144127i
$298$	−9.87756	+	0.280143i	−0.572192	+	0.0162282i
$299$	0.0968711	+	0.361528i	0.00560220	+	0.0209077i
$300$	20.0306	−	12.7322i	1.15647	−	0.735093i
$301$	−3.28464	+	12.2584i	−0.189323	+	0.706565i
$302$	−18.7156	−	4.45020i	−1.07696	−	0.256080i
$303$	−21.7071	−	22.3279i	−1.24704	−	1.28270i
$304$	14.6877	−	5.78512i	0.842398	−	0.331800i
$305$	−38.7937			−2.22132
$306$	0.0104562	−	0.0390485i	0.000597742	−	0.00223225i
$307$	3.28894	+	3.28894i	0.187710	+	0.187710i	0.794705	−	0.606995i	$-0.207625\pi$
$307$	3.28894	+	3.28894i	0.187710	+	0.187710i	−0.606995	+	0.794705i	$0.707625\pi$
$308$	−6.28381	−	19.0572i	−0.358053	−	1.08589i
$309$	5.17597	−	8.68014i	0.294451	−	0.493796i
$310$	6.65744	+	10.8111i	0.378117	+	0.614031i
$311$	−21.8951	+	12.6412i	−1.24156	+	0.716814i	−0.969411	−	0.245442i	$-0.921067\pi$
$311$	−21.8951	+	12.6412i	−1.24156	+	0.716814i	−0.272147	+	0.962256i	$0.587734\pi$
$312$	0.296303	+	0.144094i	0.0167749	+	0.00815773i
$313$	−3.90504	−	2.25458i	−0.220726	−	0.127436i	0.385560	−	0.922683i	$-0.374008\pi$
$313$	−3.90504	−	2.25458i	−0.220726	−	0.127436i	−0.606286	+	0.795246i	$0.707341\pi$
$314$	0.698480	+	24.6277i	0.0394175	+	1.38982i
$315$	−45.9213	+	10.9271i	−2.58737	+	0.615670i
$316$	−1.55669	−	27.4216i	−0.0875706	−	1.54258i
$317$	−2.62723	+	0.703963i	−0.147560	+	0.0395385i	−0.331843	−	0.943335i	$-0.607670\pi$
$317$	−2.62723	+	0.703963i	−0.147560	+	0.0395385i	0.184283	+	0.982873i	$0.441004\pi$
$318$	0.0889343	+	6.23708i	0.00498719	+	0.349758i
$319$	−1.45795	−	2.52525i	−0.0816298	−	0.141387i
$320$	2.52130	−	27.4253i	0.140945	−	1.53312i
$321$	−7.60232	+	26.8524i	−0.424320	+	1.49875i
$322$	−34.4672	+	10.2912i	−1.92078	+	0.573506i
$323$	−0.0265889	−	0.0265889i	−0.00147945	−	0.00147945i
$324$	−15.5914	−	8.99495i	−0.866187	−	0.499719i
$325$	0.325840	−	0.325840i	0.0180744	−	0.0180744i
$326$	14.2871	+	7.71708i	0.791288	+	0.427409i
$327$	28.1089	+	7.95806i	1.55442	+	0.440082i
$328$	2.49333	−	13.9603i	0.137671	−	0.770829i
$329$	22.0064	−	12.7054i	1.21325	−	0.700473i
$330$	−13.2749	−	12.9017i	−0.730761	−	0.710214i
$331$	−8.04319	−	30.0176i	−0.442094	−	1.64992i	−0.723497	−	0.690327i	$-0.757466\pi$
$331$	−8.04319	−	30.0176i	−0.442094	−	1.64992i	0.281403	−	0.959590i	$-0.409200\pi$
$332$	16.3668	−	18.3369i	0.898247	−	1.00637i
$333$	3.26605	+	13.7257i	0.178978	+	0.752161i
$334$	−10.4110	+	11.0188i	−0.569667	+	0.602923i
$335$	7.93635	−	13.7462i	0.433609	−	0.751033i
$336$	−13.0355	+	28.8578i	−0.711143	+	1.57432i
$337$	10.2176	+	17.6974i	0.556587	+	0.964037i	0.997778	+	0.0666240i	$0.0212228\pi$
$337$	10.2176	+	17.6974i	0.556587	+	0.964037i	−0.441191	+	0.897413i	$0.645444\pi$
$338$	−17.8799	−	4.25149i	−0.972537	−	0.231250i
$339$	−8.49855	−	5.06769i	−0.461578	−	0.275239i
$340$	−0.0623034	+	0.0205435i	−0.00337888	+	0.00111413i
$341$	4.04804	−	4.04804i	0.219214	−	0.219214i
$342$	−14.4990	+	8.37412i	−0.784015	+	0.452821i
$343$		−	31.4882i		−	1.70020i
$344$	7.11051	+	3.33479i	0.383373	+	0.179800i
$345$	−23.7926	+	23.1311i	−1.28095	+	1.24534i
$346$	7.20433	−	4.43639i	0.387307	−	0.238502i
$347$	−22.8570	−	6.12452i	−1.22703	−	0.328782i	−0.413607	−	0.910455i	$-0.635731\pi$
$347$	−22.8570	−	6.12452i	−1.22703	−	0.328782i	−0.813422	+	0.581674i	$0.802398\pi$
$348$	−1.00050	+	4.49127i	−0.0536327	+	0.240757i
$349$	17.4369	−	4.67221i	0.933378	−	0.250098i	0.240083	−	0.970752i	$-0.422825\pi$
$349$	17.4369	−	4.67221i	0.933378	−	0.250098i	0.693294	+	0.720655i	$0.256159\pi$
$350$	32.1905	+	30.4149i	1.72065	+	1.62574i
$351$	−0.333436	−	0.104639i	−0.0177975	−	0.00558521i
$352$	−12.2935	+	1.75461i	−0.655244	+	0.0935211i
$353$	−12.5772	+	21.7843i	−0.669415	+	1.15946i	0.308653	+	0.951175i	$0.400122\pi$
$353$	−12.5772	+	21.7843i	−0.669415	+	1.15946i	−0.978068	+	0.208286i	$0.933212\pi$
$354$	−0.481493	+	0.287220i	−0.0255911	+	0.0152656i
$355$	−6.43043	+	23.9987i	−0.341292	+	1.27372i
$356$	−2.50133	−	3.81529i	−0.132570	−	0.202210i
$357$	0.0754199	+	0.00106318i	0.00399165	+	5.62697e-5i
$358$	2.45671	+	1.32698i	0.129841	+	0.0701331i
$359$		−	7.27780i		−	0.384108i	−0.981384	−	0.192054i	$-0.938485\pi$
$359$		−	7.27780i		−	0.384108i	0.981384	−	0.192054i	$-0.0615148\pi$
$360$	1.66037	+	29.1643i	0.0875089	+	1.53710i
$361$		−	3.42522i		−	0.180275i
$362$	−1.73548	+	3.21300i	−0.0912149	+	0.168871i
$363$	5.48306	−	9.19513i	0.287786	−	0.482619i
$364$	−0.125204	+	0.601897i	−0.00656249	+	0.0315480i
$365$	6.22954	−	23.2489i	0.326069	−	1.21691i
$366$	13.4590	−	24.0988i	0.703514	−	1.25966i
$367$	−8.64087	+	14.9664i	−0.451050	+	0.781241i	−0.998452	−	0.0556291i	$-0.982284\pi$
$367$	−8.64087	+	14.9664i	−0.451050	+	0.781241i	0.547402	+	0.836870i	$0.315617\pi$
$368$	2.51926	+	22.1173i	0.131325	+	1.15294i
$369$	−0.423991	+	15.0355i	−0.0220721	+	0.782716i
$370$	15.7250	−	16.6430i	0.817503	−	0.865228i
$371$	−11.2423	+	3.01238i	−0.583673	+	0.156395i
$372$	−9.02564	+	0.384833i	−0.467958	+	0.0199527i
$373$	4.86123	+	1.30256i	0.251705	+	0.0674441i	0.382465	−	0.923970i	$-0.375075\pi$
$373$	4.86123	+	1.30256i	0.251705	+	0.0674441i	−0.130760	+	0.991414i	$0.541742\pi$
$374$	0.0155103	+	0.0251874i	0.000802019	+	0.00130241i
$375$	10.6232	+	3.00760i	0.548580	+	0.155312i
$376$	−5.34580	−	14.7888i	−0.275689	−	0.762676i
$377$			0.0893352i			0.00460100i
$378$	9.14392	−	32.3175i	0.470312	−	1.66223i
$379$	−15.2370	+	15.2370i	−0.782672	+	0.782672i	−0.980281	−	0.197609i	$-0.936682\pi$
$379$	−15.2370	+	15.2370i	−0.782672	+	0.782672i	0.197609	+	0.980281i	$0.436682\pi$
$380$	24.2643	+	12.2307i	1.24473	+	0.627420i
$381$	15.0866	−	8.42898i	0.772910	−	0.431830i
$382$	−3.41912	+	14.3793i	−0.174938	+	0.735710i
$383$	13.3638	+	23.1468i	0.682859	+	1.18275i	0.974104	+	0.226099i	$0.0725972\pi$
$383$	13.3638	+	23.1468i	0.682859	+	1.18275i	−0.291245	+	0.956649i	$0.594069\pi$
$384$	16.1620	+	11.0811i	0.824761	+	0.565481i
$385$	17.2703	−	29.9131i	0.880177	−	1.52451i
$386$	24.7670	+	23.4009i	1.26061	+	1.19108i
$387$	−7.98227	−	2.38193i	−0.405761	−	0.121081i
$388$	1.06345	+	18.7329i	0.0539883	+	0.951021i
$389$	−5.47767	−	20.4430i	−0.277729	−	1.03650i	−0.953990	−	0.299837i	$-0.903068\pi$
$389$	−5.47767	−	20.4430i	−0.277729	−	1.03650i	0.676261	−	0.736662i	$-0.263599\pi$
$390$	0.154583	+	0.545668i	0.00782759	+	0.0276310i
$391$	0.0459205	−	0.0265122i	0.00232230	−	0.00134078i
$392$	−38.6733	−	6.90710i	−1.95330	−	0.348861i
$393$	0.00435739	+	0.0172299i	0.000219801	+	0.000869134i
$394$	−11.1621	+	20.6650i	−0.562338	+	1.04109i
$395$	33.4299	−	33.4299i	1.68204	−	1.68204i
$396$	12.6202	−	3.77035i	0.634187	−	0.189467i
$397$	18.8537	+	18.8537i	0.946242	+	0.946242i	0.998627	−	0.0523851i	$-0.0166823\pi$
$397$	18.8537	+	18.8537i	0.946242	+	0.946242i	−0.0523851	+	0.998627i	$0.516682\pi$
$398$	3.58261	+	11.9988i	0.179580	+	0.601447i
$399$	−21.7777	−	22.4004i	−1.09025	−	1.12142i
$400$	22.0314	−	16.3013i	1.10157	−	0.815065i
$401$	2.65035	+	4.59054i	0.132352	+	0.229241i	0.924583	−	0.380981i	$-0.124414\pi$
$401$	2.65035	+	4.59054i	0.132352	+	0.229241i	−0.792231	+	0.610222i	$0.791080\pi$
$402$	5.78575	+	9.69916i	0.288567	+	0.483750i
$403$	−0.169415	+	0.0453947i	−0.00843918	+	0.00226127i
$404$	−26.8264	−	23.9442i	−1.33466	−	1.19127i
$405$	−6.31984	−	30.3322i	−0.314035	−	1.50722i
$406$	−8.58222	+	0.243405i	−0.425928	+	0.0120800i
$407$	−8.94088	−	5.16202i	−0.443183	−	0.255872i
$408$	0.00885373	−	0.0458305i	0.000438325	−	0.00226895i
$409$	−22.2531	+	12.8479i	−1.10035	+	0.635285i	−0.936312	−	0.351169i	$-0.885784\pi$
$409$	−22.2531	+	12.8479i	−1.10035	+	0.635285i	−0.164035	+	0.986455i	$0.552451\pi$
$410$	20.7854	−	12.7995i	1.02652	−	0.632124i
$411$	8.09187	+	0.114070i	0.399143	+	0.00562666i
$412$	5.25265	−	10.4207i	0.258779	−	0.513390i
$413$	−0.739719	−	0.739719i	−0.0363992	−	0.0363992i
$414$	−6.11457	−	22.8051i	−0.300515	−	1.12081i
$415$	42.3076			2.07680
$416$	0.353055	+	0.141764i	0.0173100	+	0.00695056i
$417$	10.2596	−	2.59462i	0.502415	−	0.127059i
$418$	2.83425	−	11.9196i	0.138628	−	0.583006i
$419$	9.68369	−	36.1400i	0.473079	−	1.76556i	−0.155528	−	0.987832i	$-0.549708\pi$
$419$	9.68369	−	36.1400i	0.473079	−	1.76556i	0.628607	−	0.777723i	$-0.283626\pi$
$420$	−51.9998	+	16.3371i	−2.53733	+	0.797170i
$421$	4.37016	+	16.3097i	0.212989	+	0.794885i	0.986865	+	0.161548i	$0.0516486\pi$
$421$	4.37016	+	16.3097i	0.212989	+	0.794885i	−0.773876	+	0.633337i	$0.781685\pi$
$422$	−0.956602	−	33.7289i	−0.0465667	−	1.64190i
$423$	7.92915	+	14.6740i	0.385529	+	0.713475i
$424$	0.611935	+	7.17665i	0.0297182	+	0.348529i
$425$	−0.0565364	−	0.0326413i	−0.00274242	−	0.00158334i
$426$	−12.6771	−	12.3207i	−0.614208	−	0.596938i
$427$	49.7484	+	13.3301i	2.40750	+	0.645087i
$428$	−6.56287	+	31.5498i	−0.317228	+	1.52502i
$429$	0.223241	−	0.124726i	0.0107782	−	0.00602183i
$430$	3.86766	+	12.9535i	0.186515	+	0.624674i
$431$	−35.2704			−1.69891			−0.849457	−	0.527658i	$-0.823070\pi$
$431$	−35.2704			−1.69891			−0.849457	+	0.527658i	$0.823070\pi$
$432$	−18.6930	−	9.08680i	−0.899370	−	0.437189i
$433$	40.6920			1.95553			0.977766	−	0.209700i	$-0.0672488\pi$
$433$	40.6920			1.95553			0.977766	+	0.209700i	$0.0672488\pi$
$434$	−4.82255	−	16.1516i	−0.231490	−	0.775303i
$435$	−6.91437	+	3.86310i	−0.331519	+	0.185222i
$436$	33.0261	+	6.86997i	1.58166	+	0.329012i
$437$	−21.2142	−	5.68431i	−1.01481	−	0.271918i
$438$	12.2811	+	11.9358i	0.586812	+	0.570313i
$439$	11.7973	+	6.81118i	0.563055	+	0.325080i	0.754371	−	0.656449i	$-0.227942\pi$
$439$	11.7973	+	6.81118i	0.563055	+	0.325080i	−0.191316	+	0.981529i	$0.561275\pi$
$440$	−16.3441	−	13.7758i	−0.779174	−	0.656737i
$441$	41.6518	+	1.17455i	1.98342	+	0.0559311i
$442$	−2.56923e−5	0	0.000905884i	−1.22206e−6	0	4.30885e-5i
$443$	−2.61349	−	9.75367i	−0.124171	−	0.463411i	0.875638	−	0.482968i	$-0.160441\pi$
$443$	−2.61349	−	9.75367i	−0.124171	−	0.463411i	−0.999809	+	0.0195569i	$0.993774\pi$
$444$	4.88309	+	15.5425i	0.231741	+	0.737615i
$445$	2.03247	−	7.58527i	0.0963481	−	0.359576i
$446$	6.25100	−	26.2889i	0.295994	−	1.24482i
$447$	11.7330	−	2.96723i	0.554950	−	0.140345i
$448$	−12.6570	+	34.3034i	−0.597987	+	1.62068i
$449$	−5.23717			−0.247158			−0.123579	−	0.992335i	$-0.539437\pi$
$449$	−5.23717			−0.247158			−0.123579	+	0.992335i	$0.539437\pi$
$450$	−20.5515	+	20.5582i	−0.968807	+	0.969121i
$451$	−7.78273	−	7.78273i	−0.366474	−	0.366474i
$452$	−10.2027	−	5.14277i	−0.479893	−	0.241895i
$453$	23.5585	+	0.332102i	1.10688	+	0.0156035i
$454$	0.0976314	−	0.0601210i	0.00458207	−	0.00282162i
$455$	−0.916453	+	0.529114i	−0.0429640	+	0.0248053i
$456$	−16.0160	+	10.8298i	−0.750016	+	0.507151i
$457$	−3.03428	−	1.75184i	−0.141938	−	0.0819477i	0.427349	−	0.904087i	$-0.359447\pi$
$457$	−3.03428	−	1.75184i	−0.141938	−	0.0819477i	−0.569287	+	0.822139i	$0.692781\pi$
$458$	4.96883	−	0.140924i	0.232178	−	0.00658493i
$459$	−0.00209302	+	0.0494651i	−9.76936e−5	+	0.00230883i
$460$	−25.5149	+	28.5862i	−1.18964	+	1.33284i
$461$	−32.1116	+	8.60429i	−1.49559	+	0.400742i	−0.911620	−	0.411035i	$-0.865167\pi$
$461$	−32.1116	+	8.60429i	−1.49559	+	0.400742i	−0.583968	+	0.811777i	$0.698501\pi$
$462$	12.5904	+	21.1064i	0.585758	+	0.981958i
$463$	14.6805	+	25.4274i	0.682261	+	1.18171i	0.974289	+	0.225301i	$0.0723366\pi$
$463$	14.6805	+	25.4274i	0.682261	+	1.18171i	−0.292028	+	0.956410i	$0.594330\pi$
$464$	−0.785501	+	5.25481i	−0.0364660	+	0.243948i
$465$	−10.8394	−	11.1494i	−0.502667	−	0.517042i
$466$	−11.2337	−	37.6237i	−0.520390	−	1.74288i
$467$	7.90699	+	7.90699i	0.365892	+	0.365892i	0.865977	−	0.500085i	$-0.166698\pi$
$467$	7.90699	+	7.90699i	0.365892	+	0.365892i	−0.500085	+	0.865977i	$0.666698\pi$
$468$	−0.392602	−	0.0932859i	−0.0181480	−	0.00431214i
$469$	−14.9008	+	14.9008i	−0.688057	+	0.688057i
$470$	12.8641	−	23.8160i	0.593376	−	1.09855i
$471$	−7.39820	−	29.2538i	−0.340891	−	1.34794i
$472$	−0.531125	+	0.370155i	−0.0244470	+	0.0170378i
$473$	5.27882	−	3.04773i	0.242720	−	0.140135i
$474$	9.16866	+	32.3649i	0.421131	+	1.48657i
$475$	6.99842	+	26.1185i	0.321109	+	1.19840i
$476$	0.0869561	−	0.00493639i	0.00398562	−	0.000226259i
$477$	−1.76848	−	7.43209i	−0.0809732	−	0.340292i
$478$	5.27415	+	4.98323i	0.241234	+	0.227928i
$479$	5.66988	−	9.82052i	0.259064	−	0.448711i	−0.706928	−	0.707286i	$-0.749919\pi$
$479$	5.66988	−	9.82052i	0.259064	−	0.448711i	0.965991	+	0.258575i	$0.0832528\pi$
$480$	4.29482	+	33.4561i	0.196031	+	1.52705i
$481$	0.158150	+	0.273923i	0.00721101	+	0.0124898i
$482$	−0.477528	+	2.00827i	−0.0217508	+	0.0914742i
$483$	38.4594	−	21.4875i	1.74996	−	0.977716i
$484$	5.56429	−	11.0389i	0.252922	−	0.501769i
$485$	−22.8375	+	22.8375i	−1.03700	+	1.03700i
$486$	21.0350	+	6.59748i	0.954169	+	0.299268i
$487$			27.9896i			1.26833i	0.773198	+	0.634165i	$0.218656\pi$
$487$			27.9896i			1.26833i	−0.773198	+	0.634165i	$0.781344\pi$
$488$	13.5336	−	28.8566i	0.612637	−	1.30628i
$489$	−19.1353	−	5.41751i	−0.865330	−	0.244988i
$490$	−35.4577	−	57.5804i	−1.60182	−	2.60122i
$491$	12.6271	+	3.38342i	0.569853	+	0.152692i	0.532229	−	0.846600i	$-0.321354\pi$
$491$	12.6271	+	3.38342i	0.569853	+	0.152692i	0.0376238	+	0.999292i	$0.488021\pi$
$492$	0.739876	+	17.3526i	0.0333562	+	0.782316i
$493$	0.0122249	−	0.00327565i	0.000550581	−	0.000147528i
$494$	−0.257791	+	0.272841i	−0.0115986	+	0.0122757i
$495$	19.3071	+	11.8849i	0.867790	+	0.534187i
$496$	−10.3644	+	1.18055i	−0.465374	+	0.0530082i
$497$	16.4926	−	28.5660i	0.739793	−	1.28136i
$498$	−14.6781	+	26.2817i	−0.657743	+	1.17771i
$499$	3.90895	−	14.5884i	0.174989	−	0.653066i	−0.821565	−	0.570115i	$-0.806899\pi$
$499$	3.90895	−	14.5884i	0.174989	−	0.653066i	0.996554	−	0.0829515i	$-0.0264347\pi$
$500$	12.4816	+	2.59637i	0.558193	+	0.116113i
$501$	9.50885	−	15.9464i	0.424824	−	0.712433i
$502$	−0.182160	+	0.337243i	−0.00813018	+	0.0150519i
$503$			2.90879i			0.129697i	0.997895	+	0.0648483i	$0.0206564\pi$
$503$			2.90879i			0.129697i	−0.997895	+	0.0648483i	$0.979344\pi$
$504$	7.89205	−	37.9705i	0.351540	−	1.69134i
$505$		−	61.8949i		−	2.75429i
$506$	15.2011	+	8.21076i	0.675770	+	0.365013i
$507$	22.5066	+	0.317272i	0.999553	+	0.0140906i
$508$	16.6883	−	10.9410i	0.740424	−	0.485427i
$509$	−9.12406	+	34.0514i	−0.404417	+	1.50930i	0.400712	+	0.916204i	$0.368763\pi$
$509$	−9.12406	+	34.0514i	−0.404417	+	1.50930i	−0.805129	+	0.593100i	$0.797904\pi$
$510$	0.0690026	−	0.0411615i	0.00305549	−	0.00182266i
$511$	−15.9773	+	27.6736i	−0.706796	+	1.22421i
$512$	19.5207	+	11.4431i	0.862700	+	0.505717i
$513$	15.1004	−	13.8744i	0.666698	−	0.612568i
$514$	32.5722	+	30.7755i	1.43670	+	1.35745i
$515$	19.4026	−	5.19891i	0.854981	−	0.229092i
$516$	−9.38861	−	2.09147i	−0.413311	−	0.0920717i
$517$	−11.7890	−	3.15886i	−0.518481	−	0.138926i
$518$	−25.8843	+	15.9394i	−1.13729	+	0.700337i
$519$	−7.42976	+	7.22320i	−0.326130	+	0.317063i
$520$	0.222624	+	0.615877i	0.00976273	+	0.0270080i
$521$			13.7437i			0.602123i	0.953605	+	0.301061i	$0.0973409\pi$
$521$			13.7437i			0.602123i	−0.953605	+	0.301061i	$0.902659\pi$
$522$	−0.000913373	−	5.63549i	−3.99773e−5	−	0.246659i
$523$	9.11467	−	9.11467i	0.398557	−	0.398557i	−0.479167	−	0.877724i	$-0.659061\pi$
$523$	9.11467	−	9.11467i	0.398557	−	0.398557i	0.877724	+	0.479167i	$0.159061\pi$
$524$	0.00642637	+	0.0194896i	0.000280737	+	0.000851406i
$525$	−46.5860	−	27.7792i	−2.03318	−	1.21238i
$526$	−16.3059	−	3.87723i	−0.710971	−	0.169055i
$527$	0.0124239	+	0.0215188i	0.000541192	+	0.000937372i
$528$	14.2280	−	5.37364i	0.619194	−	0.233858i
$529$	3.98502	−	6.90225i	0.173262	−	0.300098i
$530$	−8.51468	+	9.01176i	−0.369854	+	0.391446i
$531$	0.499033	−	0.471660i	0.0216562	−	0.0204683i
$532$	−26.9135	−	24.0220i	−1.16685	−	1.04149i
$533$	0.0872754	+	0.325716i	0.00378032	+	0.0141083i
$534$	4.00686	+	3.89419i	0.173394	+	0.168518i
$535$	−48.0379	+	27.7347i	−2.07686	+	1.19908i
$536$	7.45638	+	10.6989i	0.322067	+	0.462124i
$537$	−3.29039	−	0.931561i	−0.141991	−	0.0401998i
$538$	−7.75048	−	4.18638i	−0.334147	−	0.180488i
$539$	−21.5600	+	21.5600i	−0.928654	+	0.928654i
$540$	−9.75704	−	34.4205i	−0.419876	−	1.48122i
$541$	−17.0782	−	17.0782i	−0.734248	−	0.734248i	0.237210	−	0.971458i	$-0.423767\pi$
$541$	−17.0782	−	17.0782i	−0.734248	−	0.734248i	−0.971458	+	0.237210i	$0.923767\pi$
$542$	6.79392	−	2.02853i	0.291824	−	0.0871326i
$543$	1.21834	−	4.30332i	0.0522838	−	0.184673i
$544$	0.00645395	−	0.0535111i	0.000276711	−	0.00229427i
$545$	29.0325	+	50.2858i	1.24362	+	2.15401i
$546$	−0.0107352	−	0.752874i	−0.000459424	−	0.0322200i
$547$	3.34927	−	0.897434i	0.143204	−	0.0383715i	−0.186505	−	0.982454i	$-0.559716\pi$
$547$	3.34927	−	0.897434i	0.143204	−	0.0383715i	0.329709	+	0.944083i	$0.393049\pi$
$548$	9.32960	−	0.529630i	0.398541	−	0.0226247i
$549$	−9.66661	+	32.3945i	−0.412561	+	1.38256i
$550$	−0.603033	−	21.2624i	−0.0257134	−	0.906630i
$551$	−4.53981	−	2.62106i	−0.193402	−	0.111661i
$552$	−8.90573	−	25.7676i	−0.379053	−	1.09674i
$553$	−54.3570	+	31.3830i	−2.31149	+	1.33454i
$554$	5.17961	+	8.41126i	0.220061	+	0.357360i
$555$	−14.3623	+	24.0857i	−0.609646	+	1.02238i
$556$	11.6051	−	3.82660i	0.492167	−	0.162284i
$557$	−6.42266	−	6.42266i	−0.272137	−	0.272137i	0.557823	−	0.829960i	$-0.311637\pi$
$557$	−6.42266	−	6.42266i	−0.272137	−	0.272137i	−0.829960	+	0.557823i	$0.811637\pi$
$558$	10.6867	−	2.86534i	0.452403	−	0.121300i
$559$	−0.186748			−0.00789858
$560$	−58.5592	+	23.0650i	−2.47458	+	0.974675i
$561$	−0.0252534	−	0.0259756i	−0.00106620	−	0.00109669i
$562$	24.5012	+	5.82592i	1.03352	+	0.245751i
$563$	−0.591735	+	2.20839i	−0.0249387	+	0.0930723i	−0.977273	−	0.211982i	$-0.932008\pi$
$563$	−0.591735	+	2.20839i	−0.0249387	+	0.0930723i	0.952335	+	0.305055i	$0.0986747\pi$
$564$	10.3316	+	16.2539i	0.435037	+	0.684413i
$565$	−5.09015	−	18.9967i	−0.214144	−	0.799198i
$566$	−17.9418	+	0.508857i	−0.754150	+	0.0213889i
$567$	−2.31809	+	41.0691i	−0.0973505	+	1.72474i
$568$	−15.6080	−	13.1555i	−0.654899	−	0.551991i
$569$	−8.94577	−	5.16484i	−0.375026	−	0.216522i	0.300626	−	0.953742i	$-0.402804\pi$
$569$	−8.94577	−	5.16484i	−0.375026	−	0.216522i	−0.675652	+	0.737221i	$0.736138\pi$
$570$	−32.2650	−	8.15415i	−1.35143	−	0.341540i
$571$	−40.8233	−	10.9386i	−1.70840	−	0.457765i	−0.733371	−	0.679828i	$-0.762054\pi$
$571$	−40.8233	−	10.9386i	−1.70840	−	0.457765i	−0.975032	+	0.222063i	$0.928721\pi$
$572$	0.246942	−	0.161897i	0.0103252	−	0.00676924i
$573$	0.255156	−	18.1002i	0.0106593	−	0.756147i
$574$	−31.0530	+	9.27179i	−1.29613	+	0.386997i
$575$	−38.1297			−1.59012
$576$	−22.2731	−	8.93923i	−0.928045	−	0.372468i
$577$	−28.0181			−1.16641			−0.583204	−	0.812326i	$-0.698201\pi$
$577$	−28.0181			−1.16641			−0.583204	+	0.812326i	$0.698201\pi$
$578$	23.0366	−	6.87825i	0.958195	−	0.286098i
$579$	−35.8428	−	21.3731i	−1.48958	−	0.888235i
$580$	−7.64845	+	5.01438i	−0.317585	+	0.208211i
$581$	−54.2547	−	14.5375i	−2.25086	−	0.603117i
$582$	−6.26353	−	22.1099i	−0.259632	−	0.916486i
$583$	4.84126	+	2.79510i	0.200505	+	0.115761i
$584$	15.1204	+	12.7445i	0.625688	+	0.527370i
$585$	−0.330207	−	0.611095i	−0.0136524	−	0.0252657i
$586$	−19.1372	+	0.542759i	−0.790549	+	0.0224212i
$587$	7.00291	+	26.1352i	0.289041	+	1.07872i	0.945835	+	0.324646i	$0.105245\pi$
$587$	7.00291	+	26.1352i	0.289041	+	1.07872i	−0.656794	+	0.754070i	$0.728088\pi$
$588$	48.0708	−	2.04963i	1.98241	−	0.0845254i
$589$	2.66372	−	9.94115i	0.109757	−	0.409618i
$590$	−1.08412	−	0.257784i	−0.0446327	−	0.0106128i
$591$	7.83596	−	27.6776i	0.322328	−	1.13850i
$592$	6.89403	+	17.5031i	0.283343	+	0.719372i
$593$	27.4816			1.12853			0.564267	−	0.825592i	$-0.309159\pi$
$593$	27.4816			1.12853			0.564267	+	0.825592i	$0.309159\pi$
$594$	−14.0813	+	7.87032i	−0.577764	+	0.322923i
$595$	0.106009	+	0.106009i	0.00434594	+	0.00434594i
$596$	13.2717	−	4.37614i	0.543631	−	0.179253i
$597$	−7.48031	−	13.3886i	−0.306149	−	0.547960i
$598$	−0.277546	−	0.450712i	−0.0113497	−	0.0184310i
$599$	23.2792	−	13.4402i	0.951162	−	0.549153i	0.0577200	−	0.998333i	$-0.481617\pi$
$599$	23.2792	−	13.4402i	0.951162	−	0.549153i	0.893442	+	0.449179i	$0.148284\pi$
$600$	−21.9920	+	25.3579i	−0.897819	+	1.03523i
$601$	33.4069	+	19.2875i	1.36269	+	0.786752i	0.989982	−	0.141195i	$-0.0450944\pi$
$601$	33.4069	+	19.2875i	1.36269	+	0.786752i	0.372713	+	0.927947i	$0.378428\pi$
$602$	−0.508817	−	17.9404i	−0.0207378	−	0.731196i
$603$	−9.50108	−	10.0525i	−0.386914	−	0.409369i
$604$	27.1620	−	1.54195i	1.10521	−	0.0627412i
$605$	20.5538	−	5.50737i	0.835630	−	0.223906i
$606$	38.4493	+	21.4737i	1.56190	+	0.872310i
$607$	−4.36643	−	7.56288i	−0.177228	−	0.306968i	0.763702	−	0.645569i	$-0.223380\pi$
$607$	−4.36643	−	7.56288i	−0.177228	−	0.306968i	−0.940930	+	0.338601i	$0.890046\pi$
$608$	−17.5626	+	13.7821i	−0.712258	+	0.558940i
$609$	10.1943	−	2.57811i	0.413094	−	0.104470i
$610$	52.5693	−	15.6961i	2.12847	−	0.635518i
$611$	0.264404	+	0.264404i	0.0106966	+	0.0106966i
$612$	0.00162999	+	0.0571452i	6.58886e−5	+	0.00230996i
$613$	22.3747	−	22.3747i	0.903705	−	0.903705i	−0.0920491	−	0.995754i	$-0.529342\pi$
$613$	22.3747	−	22.3747i	0.903705	−	0.903705i	0.995754	+	0.0920491i	$0.0293417\pi$
$614$	−5.78757	−	3.12612i	−0.233567	−	0.126160i
$615$	−21.4358	+	20.8398i	−0.864374	+	0.840343i
$616$	16.2259	+	23.2820i	0.653758	+	0.938058i
$617$	36.5935	−	21.1273i	1.47320	−	0.850552i	0.473654	−	0.880711i	$-0.342935\pi$
$617$	36.5935	−	21.1273i	1.47320	−	0.850552i	0.999545	+	0.0301587i	$0.00960127\pi$
$618$	−3.50192	+	13.8567i	−0.140868	+	0.557397i
$619$	1.95959	+	7.31328i	0.0787625	+	0.293946i	0.994060	−	0.108833i	$-0.0347113\pi$
$619$	1.95959	+	7.31328i	0.0787625	+	0.293946i	−0.915298	+	0.402778i	$0.868045\pi$
$620$	−13.3957	−	11.9565i	−0.537986	−	0.480186i
$621$	13.3869	+	25.6317i	0.537196	+	1.02856i
$622$	24.5554	−	25.9889i	0.984581	−	1.04206i
$623$	−5.21281	+	9.02885i	−0.208847	+	0.361733i
$624$	−0.459822	−	0.0753762i	−0.0184076	−	0.00301746i
$625$	−6.15675	−	10.6638i	−0.246270	−	0.426552i
$626$	6.20393	+	1.47518i	0.247959	+	0.0589599i
$627$	−0.211509	+	15.0040i	−0.00844687	+	0.599202i
$628$	−10.9110	−	33.0904i	−0.435397	−	1.32045i
$629$	0.0316856	−	0.0316856i	0.00126339	−	0.00126339i
$630$	57.8067	−	33.3872i	2.30308	−	1.33018i
$631$			9.01756i			0.358983i	0.983759	+	0.179492i	$0.0574453\pi$
$631$			9.01756i			0.358983i	−0.983759	+	0.179492i	$0.942555\pi$
$632$	13.2044	+	36.5291i	0.525242	+	1.45305i
$633$	10.1322	+	40.0645i	0.402719	+	1.59242i
$634$	3.27533	−	2.01693i	0.130080	−	0.0801025i
$635$	33.1784	+	8.89013i	1.31664	+	0.352794i
$636$	−2.64407	−	8.41588i	−0.104844	−	0.333711i
$637$	0.902311	−	0.241773i	0.0357508	−	0.00957941i
$638$	2.99740	+	2.83207i	0.118668	+	0.112123i
$639$	18.4376	+	11.3497i	0.729382	+	0.448987i
$640$	7.67980	+	38.1841i	0.303571	+	1.50936i
$641$	−16.9278	+	29.3199i	−0.668609	+	1.15807i	0.309684	+	0.950840i	$0.399777\pi$
$641$	−16.9278	+	29.3199i	−0.668609	+	1.15807i	−0.978293	+	0.207226i	$0.933557\pi$
$642$	−0.562710	−	39.4636i	−0.0222084	−	1.55750i
$643$	10.3175	−	38.5056i	0.406884	−	1.51851i	−0.393669	−	0.919252i	$-0.628794\pi$
$643$	10.3175	−	38.5056i	0.406884	−	1.51851i	0.800554	−	0.599261i	$-0.204539\pi$
$644$	42.5426	−	27.8912i	1.67641	−	1.09907i
$645$	−8.07548	−	14.4539i	−0.317972	−	0.569122i
$646$	0.0467887	+	0.0252726i	0.00184088	+	0.000994338i
$647$		−	19.8346i		−	0.779778i	−0.920862	−	0.389889i	$-0.872513\pi$
$647$		−	19.8346i		−	0.779778i	0.920862	−	0.389889i	$-0.127487\pi$
$648$	24.7673	+	5.88069i	0.972950	+	0.231016i
$649$			0.502454i			0.0197231i
$650$	−0.309709	+	0.573383i	−0.0121478	+	0.0224899i
$651$	10.0693	+	18.0224i	0.394645	+	0.706355i
$652$	−22.4828	−	4.67678i	−0.880493	−	0.183157i
$653$	1.89281	−	7.06407i	0.0740714	−	0.276438i	−0.918950	−	0.394375i	$-0.870961\pi$
$653$	1.89281	−	7.06407i	0.0740714	−	0.276438i	0.993021	+	0.117936i	$0.0376279\pi$
$654$	−41.3102	+	0.589041i	−1.61536	+	0.0230333i
$655$	−0.0176621	+	0.0305917i	−0.000690116	+	0.00119532i
$656$	2.26971	+	19.9264i	0.0886173	+	0.777996i
$657$	−17.8616	−	10.9951i	−0.696849	−	0.428960i
$658$	−24.6802	+	26.1210i	−0.962136	+	1.01830i
$659$	−29.2812	+	7.84588i	−1.14063	+	0.305632i	−0.779206	−	0.626768i	$-0.784378\pi$
$659$	−29.2812	+	7.84588i	−1.14063	+	0.305632i	−0.361429	+	0.932400i	$0.617711\pi$
$660$	23.2089	+	12.1120i	0.903407	+	0.471457i
$661$	−6.59497	−	1.76712i	−0.256515	−	0.0687329i	0.128270	−	0.991739i	$-0.459058\pi$
$661$	−6.59497	−	1.76712i	−0.256515	−	0.0687329i	−0.384785	+	0.923006i	$0.625724\pi$
$662$	23.0446	+	37.4225i	0.895654	+	1.45447i
$663$	0.000272129		0.00107605i	1.05686e−5		4.17902e-5i
$664$	−14.7595	+	31.4705i	−0.572779	+	1.22129i
$665$		−	62.0959i		−	2.40798i
$666$	−9.97929	−	17.2782i	−0.386690	−	0.669515i
$667$	5.22699	−	5.22699i	0.202390	−	0.202390i
$668$	9.64972	−	19.1440i	0.373359	−	0.740702i
$669$	−0.466489	+	33.0917i	−0.0180355	+	1.27940i
$670$	−5.19278	+	21.8385i	−0.200614	+	0.843695i
$671$	−12.3686	−	21.4230i	−0.477485	−	0.827027i
$672$	5.98836	−	44.3794i	0.231006	−	1.71197i
$673$	−15.7160	+	27.2209i	−0.605808	+	1.04929i	0.386116	+	0.922450i	$0.373817\pi$
$673$	−15.7160	+	27.2209i	−0.605808	+	1.04929i	−0.991923	+	0.126839i	$0.959517\pi$
$674$	−21.0063	−	19.8476i	−0.809132	−	0.764501i
$675$	19.0885	−	30.0521i	0.734718	−	1.15671i
$676$	25.9492	−	1.47310i	0.998045	−	0.0566578i
$677$	8.04835	+	30.0368i	0.309323	+	1.15441i	0.929160	+	0.369679i	$0.120532\pi$
$677$	8.04835	+	30.0368i	0.309323	+	1.15441i	−0.619837	+	0.784731i	$0.712801\pi$
$678$	13.5668	+	3.42867i	0.521030	+	0.131677i
$679$	37.1337	−	21.4392i	1.42506	−	0.822760i
$680$	0.0761153	−	0.0530468i	0.00291889	−	0.00203425i
$681$	−0.100686	+	0.0978871i	−0.00385831	+	0.00375104i
$682$	−3.84764	+	7.12336i	−0.147334	+	0.272768i
$683$	−4.48036	+	4.48036i	−0.171436	+	0.171436i	−0.787610	−	0.616174i	$-0.788682\pi$
$683$	−4.48036	+	4.48036i	−0.171436	+	0.171436i	0.616174	+	0.787610i	$0.288682\pi$
$684$	16.2593	−	17.2141i	0.621691	−	0.658199i
$685$	11.3738	+	11.3738i	0.434570	+	0.434570i
$686$	12.7403	+	42.6697i	0.486427	+	1.62914i
$687$	−5.90218	+	1.49264i	−0.225182	+	0.0569479i
$688$	−10.9847	−	1.64202i	−0.418789	−	0.0626015i
$689$	−0.0856341	−	0.148323i	−0.00326240	−	0.00565064i
$690$	22.8823	−	40.9715i	0.871116	−	1.55976i
$691$	31.7592	−	8.50986i	1.20818	−	0.323730i	0.402131	−	0.915582i	$-0.368270\pi$
$691$	31.7592	−	8.50986i	1.20818	−	0.323730i	0.806047	+	0.591852i	$0.201603\pi$
$692$	−7.96760	+	8.92666i	−0.302883	+	0.339341i
$693$	−20.6753	−	21.8752i	−0.785391	−	0.830972i
$694$	33.4516	−	0.948738i	1.26980	−	0.0360136i
$695$	18.2159	+	10.5170i	0.690969	+	0.398931i
$696$	−0.461409	−	6.49093i	−0.0174897	−	0.246038i
$697$	0.0413718	−	0.0238860i	0.00156707	−	0.000904747i
$698$	−21.7384	+	13.3864i	−0.822810	+	0.506682i
$699$	23.4554	+	41.9816i	0.887163	+	1.58789i
$700$	−55.9273	−	28.1908i	−2.11385	−	1.06551i
$701$	−22.5839	−	22.5839i	−0.852983	−	0.852983i	0.137517	−	0.990499i	$-0.456088\pi$
$701$	−22.5839	−	22.5839i	−0.852983	−	0.852983i	−0.990499	+	0.137517i	$0.956088\pi$
$702$	0.494176	+	0.00688623i	0.0186515	+	0.000259904i
$703$	−18.5602			−0.700011
$704$	15.9489	−	7.35167i	0.601098	−	0.277077i
$705$	−9.03079	+	31.8979i	−0.340119	+	1.20134i
$706$	8.22927	−	34.6087i	0.309713	−	1.30251i
$707$	−21.2680	+	79.3731i	−0.799864	+	2.98513i
$708$	0.536261	−	0.584027i	0.0201539	−	0.0219491i
$709$	7.70727	+	28.7639i	0.289453	+	1.08025i	0.945524	+	0.325553i	$0.105550\pi$
$709$	7.70727	+	28.7639i	0.289453	+	1.08025i	−0.656071	+	0.754699i	$0.727783\pi$
$710$	−0.996125	−	35.1224i	−0.0373839	−	1.31812i
$711$	−19.5854	−	36.2455i	−0.734509	−	1.35931i
$712$	4.93324	+	4.15805i	0.184881	+	0.155829i
$713$	12.5685	+	7.25642i	0.470694	+	0.271755i
$714$	−0.102632	+	0.0290746i	−0.00384089	+	0.00108809i
$715$	0.490951	+	0.131550i	0.0183605	+	0.00491969i
$716$	−3.86600	−	0.804190i	−0.144479	−	0.0300540i
$717$	−7.63273	−	4.55140i	−0.285050	−	0.169975i
$718$	2.94464	+	9.86215i	0.109893	+	0.368052i
$719$	39.3171			1.46628			0.733140	−	0.680078i	$-0.238054\pi$
$719$	39.3171			1.46628			0.733140	+	0.680078i	$0.238054\pi$
$720$	−14.0500	−	38.8488i	−0.523613	−	1.44781i
$721$	−26.6680			−0.993170
$722$	1.38586	+	4.64151i	0.0515764	+	0.172739i
$723$	0.0356361	−	2.52794i	0.00132532	−	0.0940153i
$724$	1.05175	−	5.05612i	0.0390882	−	0.187909i
$725$	−8.79087	−	2.35551i	−0.326485	−	0.0874814i
$726$	−3.70969	+	14.6788i	−0.137680	+	0.544781i
$727$	−26.4795	−	15.2880i	−0.982072	−	0.566999i	−0.0791766	−	0.996861i	$-0.525229\pi$
$727$	−26.4795	−	15.2880i	−0.982072	−	0.566999i	−0.902895	+	0.429861i	$0.858562\pi$
$728$	−0.0738663	−	0.866289i	−0.00273767	−	0.0321068i
$729$	−26.9035	−	2.28082i	−0.996426	−	0.0844748i
$730$	0.965005	+	34.0251i	0.0357164	+	1.25933i
$731$	0.00684745	+	0.0255550i	0.000253262	+	0.000945187i
$732$	−8.48781	+	38.1018i	−0.313718	+	1.40828i
$733$	5.26522	−	19.6501i	0.194475	−	0.725792i	−0.797927	−	0.602755i	$-0.794070\pi$
$733$	5.26522	−	19.6501i	0.194475	−	0.725792i	0.992402	−	0.123038i	$-0.0392636\pi$
$734$	5.65374	−	23.7771i	0.208683	−	0.877630i
$735$	57.7312	+	59.3821i	2.12945	+	2.19034i
$736$	−12.3626	−	28.9518i	−0.455692	−	1.06718i
$737$	10.1214			0.372827
$738$	−5.50889	−	20.5461i	−0.202785	−	0.756313i
$739$	−30.6148	−	30.6148i	−1.12618	−	1.12618i	−0.990792	−	0.135393i	$-0.956770\pi$
$739$	−30.6148	−	30.6148i	−1.12618	−	1.12618i	−0.135393	−	0.990792i	$-0.543230\pi$
$740$	−14.5751	+	28.9153i	−0.535790	+	1.06295i
$741$	0.235452	−	0.394855i	0.00864954	−	0.0145053i
$742$	14.0157	−	8.63078i	0.514531	−	0.316846i
$743$	−1.59632	+	0.921634i	−0.0585632	+	0.0338115i	−0.528996	−	0.848625i	$-0.677431\pi$
$743$	−1.59632	+	0.921634i	−0.0585632	+	0.0338115i	0.470433	+	0.882436i	$0.344098\pi$
$744$	12.0749	−	4.17331i	0.442689	−	0.153001i
$745$	20.8319	+	12.0273i	0.763221	+	0.440646i
$746$	−7.11447	+	0.201777i	−0.260479	+	0.00738759i
$747$	10.5422	−	35.3288i	0.385720	−	1.29261i
$748$	−0.0312090	−	0.0278559i	−0.00114111	−	0.00101851i
$749$	71.1332	−	19.0601i	2.59915	−	0.696440i
$750$	−15.6124	+	0.222617i	−0.570084	+	0.00812881i
$751$	−1.25078	−	2.16642i	−0.0456416	−	0.0790536i	0.842302	−	0.539006i	$-0.181200\pi$
$751$	−1.25078	−	2.16642i	−0.0456416	−	0.0790536i	−0.887944	+	0.459952i	$0.847867\pi$
$752$	13.2277	+	17.8774i	0.482366	+	0.651922i
$753$	0.127879	−	0.451685i	0.00466017	−	0.0164603i
$754$	−0.0361455	−	0.121058i	−0.00131634	−	0.00440868i
$755$	33.1135	+	33.1135i	1.20512	+	1.20512i
$756$	0.684901	+	47.4931i	0.0249096	+	1.72731i
$757$	−20.0347	+	20.0347i	−0.728173	+	0.728173i	−0.970256	−	0.242083i	$-0.922169\pi$
$757$	−20.0347	+	20.0347i	−0.728173	+	0.728173i	0.242083	+	0.970256i	$0.422169\pi$
$758$	14.4827	−	26.8126i	0.526034	−	0.973878i
$759$	−20.3595	−	5.76409i	−0.739003	−	0.209223i
$760$	−37.8291	−	6.75632i	−1.37221	−	0.245078i
$761$	−37.9914	+	21.9344i	−1.37719	+	0.795120i	−0.991820	−	0.127642i	$-0.959259\pi$
$761$	−37.9914	+	21.9344i	−1.37719	+	0.795120i	−0.385369	+	0.922763i	$0.625926\pi$
$762$	−17.0334	+	17.5262i	−0.617056	+	0.634908i
$763$	−19.9520	−	74.4617i	−0.722310	−	2.69570i
$764$	−1.18470	−	20.8688i	−0.0428608	−	0.755006i
$765$	−0.0715162	+	0.0675934i	−0.00258568	+	0.00244385i
$766$	−27.4746	−	25.9592i	−0.992699	−	0.937943i
$767$	0.00769689	−	0.0133314i	0.000277919	−	0.000481369i
$768$	−26.3845	−	8.47681i	−0.952070	−	0.305881i
$769$	16.2595	+	28.1622i	0.586331	+	1.01555i	0.994708	+	0.102742i	$0.0327615\pi$
$769$	16.2595	+	28.1622i	0.586331	+	1.01555i	−0.408377	+	0.912813i	$0.633905\pi$
$770$	−11.3000	+	47.5229i	−0.407224	+	1.71261i
$771$	−47.1384	−	28.1086i	−1.69765	−	1.01231i
$772$	−43.0300	−	21.6897i	−1.54868	−	0.780630i
$773$	−7.08821	+	7.08821i	−0.254945	+	0.254945i	−0.822995	−	0.568049i	$-0.807698\pi$
$773$	−7.08821	+	7.08821i	−0.254945	+	0.254945i	0.568049	+	0.822995i	$0.307698\pi$
$774$	11.7805	−	0.00190933i	0.423442	−	6.86293e-5i
$775$		−	17.8679i		−	0.641835i
$776$	−9.02052	−	24.9547i	−0.323818	−	0.895822i
$777$	26.6942	−	25.9521i	0.957649	−	0.931025i
$778$	15.6941	+	25.4859i	0.562661	+	0.913715i
$779$	−19.1128	−	5.12125i	−0.684786	−	0.183488i
$780$	−0.430255	−	0.676890i	−0.0154056	−	0.0242365i
$781$	−15.3030	+	4.10043i	−0.547585	+	0.146725i
$782$	−0.0514999	+	0.0545064i	−0.00184163	+	0.00194914i
$783$	1.50294	+	6.73642i	0.0537107	+	0.240740i
$784$	55.2009	−	6.28763i	1.97146	−	0.224558i
$785$	29.9876	−	51.9401i	1.07030	−	1.85382i
$786$	−0.0128760	−	0.0215852i	−0.000459272	−	0.000769919i
$787$	8.61189	−	32.1400i	0.306981	−	1.14567i	−0.624246	−	0.781228i	$-0.714594\pi$
$787$	8.61189	−	32.1400i	0.306981	−	1.14567i	0.931227	−	0.364440i	$-0.118740\pi$
$788$	6.76456	−	32.5194i	0.240978	−	1.15846i
$789$	20.5253	+	0.289343i	0.730721	+	0.0103009i
$790$	−31.7749	+	58.8267i	−1.13050	+	2.09296i
$791$			26.1102i			0.928371i
$792$	−15.5761	+	10.2154i	−0.553471	+	0.362988i
$793$			0.757878i			0.0269130i
$794$	−33.1770	−	17.9204i	−1.17741	−	0.635970i
$795$	7.77682	−	13.0418i	0.275816	−	0.462545i
$796$	−9.70958	−	14.8101i	−0.344147	−	0.524929i
$797$	−6.18597	+	23.0863i	−0.219118	+	0.817760i	0.765558	+	0.643367i	$0.222463\pi$
$797$	−6.18597	+	23.0863i	−0.219118	+	0.817760i	−0.984676	+	0.174393i	$0.944204\pi$
$798$	38.5742	+	21.5435i	1.36551	+	0.762630i
$799$	0.0264869	−	0.0458766i	0.000937038	−	0.00162300i
$800$	−23.2591	+	31.0039i	−0.822333	+	1.09615i
$801$	−5.82759	−	3.58730i	−0.205908	−	0.126751i
$802$	−5.44884	−	5.14829i	−0.192405	−	0.181792i
$803$	14.8249	−	3.97233i	0.523161	−	0.140180i
$804$	−11.7646	−	10.8024i	−0.414905	−	0.380971i
$805$	84.5798	+	22.6631i	2.98105	+	0.798769i
$806$	0.211208	−	0.130061i	0.00743947	−	0.00458119i
$807$	10.3806	+	2.93890i	0.365414	+	0.103454i
$808$	46.0404	+	21.5927i	1.61970	+	0.759628i
$809$		−	36.2540i		−	1.27462i	−0.770606	−	0.637312i	$-0.780046\pi$
$809$		−	36.2540i		−	1.27462i	0.770606	−	0.637312i	$-0.219954\pi$
$810$	20.8366	+	38.5461i	0.732122	+	1.35437i
$811$	−2.21531	+	2.21531i	−0.0777902	+	0.0777902i	−0.744931	−	0.667141i	$-0.767518\pi$
$811$	−2.21531	+	2.21531i	−0.0777902	+	0.0777902i	0.667141	+	0.744931i	$0.267518\pi$
$812$	11.5313	−	3.80225i	0.404669	−	0.133433i
$813$	−7.58084	+	4.23546i	−0.265872	+	0.148544i
$814$	14.2044	+	3.37752i	0.497863	+	0.118382i
$815$	−19.7641	−	34.2324i	−0.692306	−	1.19911i
$816$	0.00654557	+	0.0656871i	0.000229141	+	0.00229951i
$817$	5.47910	−	9.49007i	0.191689	−	0.332016i
$818$	24.9569	−	26.4139i	0.872598	−	0.923539i
$819$	0.213472	+	0.897124i	0.00745932	+	0.0313480i
$820$	−22.9875	+	25.7545i	−0.802758	+	0.899387i
$821$	−6.81787	−	25.4446i	−0.237945	−	0.888024i	−0.976799	−	0.214158i	$-0.931299\pi$
$821$	−6.81787	−	25.4446i	−0.237945	−	0.888024i	0.738854	−	0.673866i	$-0.235367\pi$
$822$	−11.0114	+	3.11944i	−0.384068	+	0.108803i
$823$	−38.4020	+	22.1714i	−1.33861	+	0.772846i	−0.986601	−	0.163152i	$-0.947834\pi$
$823$	−38.4020	+	22.1714i	−1.33861	+	0.772846i	−0.352007	+	0.935997i	$0.614501\pi$
$824$	−2.90161	+	16.2463i	−0.101082	+	0.565966i
$825$	6.38724	+	25.2563i	0.222375	+	0.879311i
$826$	1.30169	+	0.703099i	0.0452915	+	0.0244639i
$827$	4.61829	−	4.61829i	0.160594	−	0.160594i	−0.622236	−	0.782830i	$-0.713776\pi$
$827$	4.61829	−	4.61829i	0.160594	−	0.160594i	0.782830	+	0.622236i	$0.213776\pi$
$828$	17.5129	+	28.4292i	0.608616	+	0.987983i
$829$	20.8452	+	20.8452i	0.723983	+	0.723983i	0.969414	−	0.245431i	$-0.0789294\pi$
$829$	20.8452	+	20.8452i	0.723983	+	0.723983i	−0.245431	+	0.969414i	$0.578929\pi$
$830$	−57.3311	+	17.1179i	−1.98999	+	0.594171i
$831$	−8.43329	−	8.67446i	−0.292548	−	0.300914i
$832$	−0.535784	−	0.0492565i	−0.0185750	−	0.00170766i
$833$	−0.0661698	−	0.114610i	−0.00229265	−	0.00397099i
$834$	−12.8530	+	7.66706i	−0.445062	+	0.265488i
$835$	35.6448	−	9.55100i	1.23354	−	0.330526i
$836$	0.982042	+	17.2990i	0.0339646	+	0.598298i
$837$	−12.0112	+	6.27321i	−0.415169	+	0.216834i
$838$	1.50008	+	52.8914i	0.0518194	+	1.82710i
$839$	−16.4553	−	9.50046i	−0.568099	−	0.327992i	0.188291	−	0.982113i	$-0.439705\pi$
$839$	−16.4553	−	9.50046i	−0.568099	−	0.327992i	−0.756390	+	0.654121i	$0.773039\pi$
$840$	63.8549	−	43.1778i	2.20320	−	1.48978i
$841$	−23.5867	+	13.6178i	−0.813336	+	0.469580i
$842$	−12.5210	−	20.3330i	−0.431502	−	0.700723i
$843$	−30.8413	−	0.434766i	−1.06223	−	0.0149741i
$844$	14.9432	+	45.3189i	0.514365	+	1.55994i
$845$	31.6349	+	31.6349i	1.08827	+	1.08827i
$846$	−16.6820	−	16.6766i	−0.573538	−	0.573352i
$847$	−28.2503			−0.970691
$848$	−3.73294	−	9.47748i	−0.128190	−	0.325458i
$849$	21.3120	−	5.38974i	0.731426	−	0.184976i
$850$	0.0898193	+	0.0213573i	0.00308078	+	0.000732549i
$851$	6.77390	−	25.2805i	0.232206	−	0.866605i
$852$	22.1637	+	11.5665i	0.759317	+	0.396262i
$853$	1.07402	+	4.00831i	0.0367739	+	0.137242i	0.981872	−	0.189544i	$-0.0607010\pi$
$853$	1.07402	+	4.00831i	0.0367739	+	0.137242i	−0.945098	+	0.326786i	$0.894034\pi$
$854$	−72.8075	+	2.06493i	−2.49142	+	0.0706606i
$855$	40.7426	+	1.14891i	1.39337	+	0.0392920i
$856$	−3.87187	−	45.4085i	−0.132338	−	1.55203i
$857$	31.7416	+	18.3260i	1.08427	+	0.626005i	0.932046	−	0.362341i	$-0.118022\pi$
$857$	31.7416	+	18.3260i	1.08427	+	0.626005i	0.152227	+	0.988346i	$0.451356\pi$
$858$	−0.252049	+	0.259341i	−0.00860481	+	0.00885375i
$859$	−39.7072	−	10.6395i	−1.35479	−	0.363015i	−0.492890	−	0.870091i	$-0.664060\pi$
$859$	−39.7072	−	10.6395i	−1.35479	−	0.363015i	−0.861901	+	0.507076i	$0.830726\pi$
$860$	−10.4821	−	15.9884i	−0.357437	−	0.545201i
$861$	34.6498	−	19.3591i	1.18086	−	0.659755i
$862$	47.7948	−	14.2706i	1.62790	−	0.486058i
$863$	−31.7020			−1.07915			−0.539574	−	0.841938i	$-0.681415\pi$
$863$	−31.7020			−1.07915			−0.539574	+	0.841938i	$0.681415\pi$
$864$	29.0075	+	4.75022i	0.986855	+	0.161606i
$865$	−20.5959			−0.700283
$866$	−55.1417	+	16.4642i	−1.87379	+	0.559476i
$867$	−25.7048	+	14.3615i	−0.872982	+	0.487741i
$868$	13.0701	+	19.9358i	0.443627	+	0.676666i
$869$	29.1195	+	7.80253i	0.987810	+	0.264683i
$870$	7.80663	−	8.03248i	0.264670	−	0.272327i
$871$	−0.268547	−	0.155046i	−0.00909936	−	0.00525352i
$872$	−47.5333	+	4.05305i	−1.60968	+	0.137253i
$873$	13.3797	+	24.7610i	0.452833	+	0.838032i
$874$	31.0472	−	0.880546i	1.05019	−	0.0297849i
$875$	−7.54046	−	28.1414i	−0.254914	−	0.951352i
$876$	−21.4713	−	11.2052i	−0.725449	−	0.378587i
$877$	5.31917	−	19.8514i	0.179616	−	0.670335i	−0.816103	−	0.577906i	$-0.803870\pi$
$877$	5.31917	−	19.8514i	0.179616	−	0.670335i	0.995719	−	0.0924294i	$-0.0294632\pi$
$878$	−18.7424	−	4.45657i	−0.632524	−	0.150402i
$879$	22.7319	−	5.74883i	0.766728	−	0.193903i
$880$	27.7216	+	12.0547i	0.934496	+	0.406365i
$881$	36.0840			1.21570			0.607850	−	0.794052i	$-0.292032\pi$
$881$	36.0840			1.21570			0.607850	+	0.794052i	$0.292032\pi$
$882$	−56.9176	+	15.2609i	−1.91651	+	0.513861i
$883$	28.2105	+	28.2105i	0.949358	+	0.949358i	0.998778	−	0.0494198i	$-0.0157372\pi$
$883$	28.2105	+	28.2105i	0.949358	+	0.949358i	−0.0494198	+	0.998778i	$0.515737\pi$
$884$	0.000401341		0.00121717i	1.34986e−5		4.09378e-5i
$885$	1.36466	+	0.0192374i	0.0458725	+	0.000646659i
$886$	7.48792	+	12.1598i	0.251562	+	0.408515i
$887$	−13.2260	+	7.63604i	−0.444086	+	0.256393i	−0.705329	−	0.708880i	$-0.749201\pi$
$887$	−13.2260	+	7.63604i	−0.444086	+	0.256393i	0.261243	+	0.965273i	$0.415867\pi$
$888$	−12.9057	−	19.0859i	−0.433085	−	0.640482i
$889$	−39.4927	−	22.8011i	−1.32454	−	0.764726i
$890$	0.314845	+	11.1011i	0.0105536	+	0.372111i
$891$	14.7354	−	13.1608i	0.493654	−	0.440904i
$892$	2.16592	+	38.1533i	0.0725202	+	1.27747i
$893$	−21.1939	+	5.67888i	−0.709226	+	0.190037i
$894$	−14.6988	+	8.76812i	−0.491601	+	0.293250i
$895$	−3.39851	−	5.88639i	−0.113600	−	0.196760i
$896$	3.27214	−	51.6056i	0.109314	−	1.72402i
$897$	0.451892	+	0.464815i	0.0150882	+	0.0155197i
$898$	7.09689	−	2.11899i	0.236826	−	0.0707116i
$899$	2.44942	+	2.44942i	0.0816926	+	0.0816926i
$900$	19.5314	−	36.1736i	0.651046	−	1.20579i
$901$	−0.0171569	+	0.0171569i	−0.000571580	+	0.000571580i
$902$	13.6953	+	7.39744i	0.456004	+	0.246308i
$903$	5.38932	+	21.3103i	0.179345	+	0.709163i
$904$	15.9064	+	2.84090i	0.529040	+	0.0944871i
$905$	7.69848	−	4.44472i	0.255906	−	0.147747i
$906$	−32.0585	+	9.08188i	−1.06507	+	0.301725i
$907$	1.31620	+	4.91214i	0.0437038	+	0.163105i	0.984329	−	0.176342i	$-0.0564266\pi$
$907$	1.31620	+	4.91214i	0.0437038	+	0.163105i	−0.940625	+	0.339447i	$0.889760\pi$
$908$	−0.107975	+	0.120972i	−0.00358328	+	0.00401460i
$909$	−51.6850	−	15.4230i	−1.71428	−	0.511548i
$910$	1.02780	−	1.08780i	0.0340713	−	0.0360603i
$911$	−1.04628	+	1.81220i	−0.0346647	+	0.0600410i	−0.882837	−	0.469679i	$-0.844370\pi$
$911$	−1.04628	+	1.81220i	−0.0346647	+	0.0600410i	0.848173	+	0.529720i	$0.177703\pi$
$912$	17.3214	−	21.1556i	0.573570	−	0.700531i
$913$	13.4890	+	23.3636i	0.446419	+	0.773221i
$914$	4.82056	+	1.14624i	0.159450	+	0.0379141i
$915$	−58.6583	+	32.7727i	−1.93918	+	1.08343i
$916$	−6.67624	+	2.20138i	−0.220589	+	0.0727357i
$917$	0.0331614	−	0.0331614i	0.00109509	−	0.00109509i
$918$	−0.0171776	−	0.0678769i	−0.000566945	−	0.00224027i
$919$		−	11.8733i		−	0.391666i	−0.980637	−	0.195833i	$-0.937259\pi$
$919$		−	11.8733i		−	0.391666i	0.980637	−	0.195833i	$-0.0627410\pi$
$920$	23.0091	−	49.0606i	0.758589	−	1.61748i
$921$	7.75156	+	2.19459i	0.255423	+	0.0723141i
$922$	40.0331	−	24.6522i	1.31842	−	0.811877i
$923$	0.468841	+	0.125626i	0.0154321	+	0.00413502i
$924$	−25.6010	−	23.5071i	−0.842210	−	0.773327i
$925$	−31.1249	+	8.33989i	−1.02338	+	0.274214i
$926$	−30.1816	−	28.5168i	−0.991829	−	0.937121i
$927$	0.493418	−	17.4975i	0.0162060	−	0.574694i
$928$	−1.06169	−	7.43861i	−0.0348517	−	0.244184i
$929$	3.14107	−	5.44050i	0.103055	−	0.178497i	−0.809887	−	0.586586i	$-0.800471\pi$
$929$	3.14107	−	5.44050i	0.103055	−	0.178497i	0.912942	+	0.408089i	$0.133805\pi$
$930$	19.1996	+	10.7229i	0.629581	+	0.351617i
$931$	−14.1871	+	52.9468i	−0.464962	+	1.73526i
$932$	30.4455	+	46.4386i	0.997275	+	1.52115i
$933$	−22.4275	+	37.6111i	−0.734243	+	1.23133i
$934$	−13.9140	−	7.51555i	−0.455279	−	0.245916i
$935$		−	0.0720065i		−	0.00235487i
$936$	0.569758	−	0.0324371i	0.0186231	−	0.00106024i
$937$			2.77088i			0.0905208i	0.998975	+	0.0452604i	$0.0144117\pi$
$937$			2.77088i			0.0905208i	−0.998975	+	0.0452604i	$0.985588\pi$
$938$	14.1632	−	26.2211i	0.462444	−	0.856149i
$939$	−7.80931	−	0.110087i	−0.254847	−	0.00359255i
$940$	−7.79602	+	37.4779i	−0.254278	+	1.22240i
$941$	−0.268694	+	1.00278i	−0.00875919	+	0.0326897i	−0.970167	−	0.242437i	$-0.922053\pi$
$941$	−0.268694	+	1.00278i	−0.00875919	+	0.0326897i	0.961408	+	0.275127i	$0.0887199\pi$
$942$	21.8615	+	36.6484i	0.712287	+	1.19407i
$943$	13.9511	−	24.1641i	0.454311	−	0.786890i
$944$	0.569960	−	0.716493i	0.0185506	−	0.0233199i
$945$	−60.2045	+	55.3164i	−1.95845	+	1.79944i
$946$	−5.92020	+	6.26581i	−0.192482	+	0.203719i
$947$	−29.0835	+	7.79291i	−0.945088	+	0.253236i	−0.698277	−	0.715828i	$-0.746049\pi$
$947$	−29.0835	+	7.79291i	−0.945088	+	0.253236i	−0.246811	+	0.969064i	$0.579383\pi$
$948$	−25.5194	−	40.1479i	−0.828833	−	1.30394i
$949$	−0.454194	−	0.121701i	−0.0147438	−	0.00395058i
$950$	−20.0512	−	32.5615i	−0.650547	−	1.05643i
$951$	−3.37781	+	3.28390i	−0.109533	+	0.106488i
$952$	−0.115837	+	0.0418722i	−0.00375429	+	0.00135709i
$953$			29.6429i			0.960227i	0.877206	+	0.480113i	$0.159404\pi$
$953$			29.6429i			0.960227i	−0.877206	+	0.480113i	$0.840596\pi$
$954$	5.40353	+	9.35569i	0.174946	+	0.302902i
$955$	25.4413	−	25.4413i	0.823262	−	0.823262i
$956$	−9.16324	−	4.61883i	−0.296360	−	0.149384i
$957$	−4.33783	−	2.58665i	−0.140222	−	0.0836146i
$958$	−3.70982	+	15.6019i	−0.119859	+	0.504073i
$959$	−10.6774	−	18.4938i	−0.344791	−	0.597195i
$960$	−19.3564	−	43.5986i	−0.624726	−	1.40714i
$961$	12.0996	−	20.9571i	0.390309	−	0.676035i
$962$	−0.325140	−	0.307205i	−0.0104829	−	0.00990470i
$963$	11.1896	+	47.0247i	0.360581	+	1.51535i
$964$	−0.165459	−	2.91462i	−0.00532908	−	0.0938735i
$965$	−21.4678	−	80.1190i	−0.691074	−	2.57912i
$966$	−43.4224	+	44.6786i	−1.39709	+	1.43751i
$967$	−5.94486	+	3.43226i	−0.191174	+	0.110374i	−0.592532	−	0.805547i	$-0.701872\pi$
$967$	−5.94486	+	3.43226i	−0.191174	+	0.110374i	0.401358	+	0.915921i	$0.368538\pi$
$968$	−3.07376	+	17.2102i	−0.0987943	+	0.553156i
$969$	−0.0626663	−	0.0177418i	−0.00201313	−	0.000569948i
$970$	21.7069	−	40.1872i	0.696966	−	1.29033i
$971$	21.8370	−	21.8370i	0.700784	−	0.700784i	−0.263795	−	0.964579i	$-0.584974\pi$
$971$	21.8370	−	21.8370i	0.700784	−	0.700784i	0.964579	+	0.263795i	$0.0849742\pi$
$972$	−31.1740	−	0.429348i	−0.999905	−	0.0137713i
$973$	−19.7460	−	19.7460i	−0.633029	−	0.633029i
$974$	−11.3247	−	37.9287i	−0.362868	−	1.21531i
$975$	0.217421	−	0.767958i	0.00696304	−	0.0245943i
$976$	−6.66382	+	44.5793i	−0.213304	+	1.42695i
$977$	−4.93463	−	8.54704i	−0.157873	−	0.273444i	0.776228	−	0.630452i	$-0.217130\pi$
$977$	−4.93463	−	8.54704i	−0.157873	−	0.273444i	−0.934101	+	0.357008i	$0.883797\pi$
$978$	28.1222	−	0.400994i	0.899250	−	0.0128224i
$979$	4.83683	−	1.29602i	0.154586	−	0.0414211i
$980$	71.3461	+	63.6808i	2.27907	+	2.03421i
$981$	49.2252	−	11.7132i	1.57164	−	0.373975i
$982$	−18.4799	+	0.524119i	−0.589718	+	0.0167253i
$983$	31.0817	+	17.9450i	0.991351	+	0.572357i	0.905678	−	0.423967i	$-0.139363\pi$
$983$	31.0817	+	17.9450i	0.991351	+	0.572357i	0.0856731	+	0.996323i	$0.472696\pi$
$984$	−8.02356	−	23.2152i	−0.255782	−	0.740072i
$985$	49.5143	−	28.5871i	1.57766	−	0.910860i
$986$	−0.0152406	+	0.00938508i	−0.000485359	+	0.000298882i
$987$	22.5415	−	37.8023i	0.717505	−	1.20326i
$988$	0.238940	−	0.474030i	0.00760169	−	0.0150809i
$989$	10.9266	+	10.9266i	0.347445	+	0.347445i
$990$	−30.9718	−	8.29348i	−0.984347	−	0.263584i
$991$	20.3758			0.647258			0.323629	−	0.946184i	$-0.395097\pi$
$991$	20.3758			0.647258			0.323629	+	0.946184i	$0.395097\pi$
$992$	13.5671	−	5.79324i	0.430755	−	0.183935i
$993$	−37.5205	−	38.5935i	−1.19068	−	1.22473i
$994$	−10.7911	+	45.3827i	−0.342274	+	1.43945i
$995$	7.88956	−	29.4442i	0.250116	−	0.933445i
$996$	9.25664	−	41.5531i	0.293308	−	1.31666i
$997$	10.4098	+	38.8498i	0.329680	+	1.23038i	0.909522	+	0.415655i	$0.136448\pi$
$997$	10.4098	+	38.8498i	0.329680	+	1.23038i	−0.579842	+	0.814729i	$0.696886\pi$
$998$	0.605528	+	21.3503i	0.0191676	+	0.675832i
$999$	16.5338	+	17.9948i	0.523107	+	0.569332i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.2.x.e.61.3	yes	72
3.2	odd	2		432.2.y.e.397.16		72
4.3	odd	2		576.2.bb.e.529.2		72
9.4	even	3	inner	144.2.x.e.13.10	✓	72
9.5	odd	6		432.2.y.e.253.9		72
12.11	even	2		1728.2.bc.e.721.1		72
16.5	even	4	inner	144.2.x.e.133.10	yes	72
16.11	odd	4		576.2.bb.e.241.13		72
36.23	even	6		1728.2.bc.e.145.18		72
36.31	odd	6		576.2.bb.e.337.13		72
48.5	odd	4		432.2.y.e.181.9		72
48.11	even	4		1728.2.bc.e.1585.18		72
144.5	odd	12		432.2.y.e.37.16		72
144.59	even	12		1728.2.bc.e.1009.1		72
144.85	even	12	inner	144.2.x.e.85.3	yes	72
144.139	odd	12		576.2.bb.e.49.2		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.10	✓	72	9.4	even	3	inner
144.2.x.e.61.3	yes	72	1.1	even	1	trivial
144.2.x.e.85.3	yes	72	144.85	even	12	inner
144.2.x.e.133.10	yes	72	16.5	even	4	inner
432.2.y.e.37.16		72	144.5	odd	12
432.2.y.e.181.9		72	48.5	odd	4
432.2.y.e.253.9		72	9.5	odd	6
432.2.y.e.397.16		72	3.2	odd	2
576.2.bb.e.49.2		72	144.139	odd	12
576.2.bb.e.241.13		72	16.11	odd	4
576.2.bb.e.337.13		72	36.31	odd	6
576.2.bb.e.529.2		72	4.3	odd	2
1728.2.bc.e.145.18		72	36.23	even	6
1728.2.bc.e.721.1		72	12.11	even	2
1728.2.bc.e.1009.1		72	144.59	even	12
1728.2.bc.e.1585.18		72	48.11	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	144.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35510 + 0.404605i) q^{2} +(1.51206 - 0.844796i) q^{3} +(1.67259 - 1.09656i) q^{4} +(3.32531 + 0.891015i) q^{5} +(-1.70718 + 1.75657i) q^{6} +(-3.95817 - 2.28525i) q^{7} +(-1.82285 + 2.16269i) q^{8} +(1.57264 - 2.55476i) q^{9} +(-4.86664 + 0.138025i) q^{10} +(0.568165 + 2.12042i) q^{11} +(1.60268 - 3.07106i) q^{12} +(0.0174070 - 0.0649637i) q^{13} +(6.28833 + 1.49524i) q^{14} +(5.78079 - 1.46195i) q^{15} +(1.59511 - 3.66819i) q^{16} -0.00952807 q^{17} +(-1.09741 + 4.09825i) q^{18} +(2.79059 + 2.79059i) q^{19} +(6.53893 - 2.15611i) q^{20} +(-7.91555 - 0.111584i) q^{21} +(-1.62785 - 2.64350i) q^{22} +(-4.81949 + 2.78254i) q^{23} +(-0.929225 + 4.81005i) q^{24} +(5.93367 + 3.42580i) q^{25} +(0.00269648 + 0.0950753i) q^{26} +(0.219668 - 5.19151i) q^{27} +(-9.12630 + 0.518089i) q^{28} +(-1.28304 + 0.343789i) q^{29} +(-7.24204 + 4.32002i) q^{30} +(-1.30392 - 2.25846i) q^{31} +(-0.677361 + 5.61615i) q^{32} +(2.65042 + 2.72622i) q^{33} +(0.0129115 - 0.00385511i) q^{34} +(-11.1260 - 11.1260i) q^{35} +(-0.171073 - 5.99756i) q^{36} +(-3.32550 + 3.32550i) q^{37} +(-4.91061 - 2.65244i) q^{38} +(-0.0285607 - 0.112934i) q^{39} +(-7.98853 + 5.56742i) q^{40} +(-4.34209 + 2.50691i) q^{41} +(10.7715 - 3.05146i) q^{42} +(-0.718661 - 2.68208i) q^{43} +(3.27548 + 2.92357i) q^{44} +(7.50585 - 7.09414i) q^{45} +(5.40507 - 5.72061i) q^{46} +(-2.77988 + 4.81489i) q^{47} +(-0.686977 - 6.89406i) q^{48} +(6.94473 + 12.0286i) q^{49} +(-9.42681 - 2.24151i) q^{50} +(-0.0144070 + 0.00804928i) q^{51} +(-0.0421220 - 0.127745i) q^{52} +(1.80067 - 1.80067i) q^{53} +(1.80284 + 7.12389i) q^{54} +7.55731i q^{55} +(12.1574 - 4.39461i) q^{56} +(6.57701 + 1.86205i) q^{57} +(1.59955 - 0.984992i) q^{58} +(0.221086 + 0.0592399i) q^{59} +(8.06578 - 8.78422i) q^{60} +(-10.8847 + 2.91654i) q^{61} +(2.68073 + 2.53286i) q^{62} +(-12.0630 + 6.51830i) q^{63} +(-1.35443 - 7.88451i) q^{64} +(0.115767 - 0.200515i) q^{65} +(-4.69463 - 2.62192i) q^{66} +(1.19332 - 4.45355i) q^{67} +(-0.0159365 + 0.0104481i) q^{68} +(-4.93668 + 8.27885i) q^{69} +(19.5784 + 10.5752i) q^{70} +7.21697i q^{71} +(2.65847 + 8.05807i) q^{72} -6.99151i q^{73} +(3.16086 - 5.85189i) q^{74} +(11.8662 + 0.167276i) q^{75} +(7.72756 + 1.60746i) q^{76} +(2.59680 - 9.69138i) q^{77} +(0.0843965 + 0.141481i) q^{78} +(6.86643 - 11.8930i) q^{79} +(8.57265 - 10.7766i) q^{80} +(-4.05361 - 8.03543i) q^{81} +(4.86966 - 5.15395i) q^{82} +(11.8706 - 3.18073i) q^{83} +(-13.3618 + 8.49325i) q^{84} +(-0.0316838 - 0.00848965i) q^{85} +(2.05904 + 3.34371i) q^{86} +(-1.64960 + 1.60373i) q^{87} +(-5.62149 - 2.63645i) q^{88} -2.28107i q^{89} +(-7.30084 + 12.6502i) q^{90} +(-0.217358 + 0.217358i) q^{91} +(-5.00981 + 9.93891i) q^{92} +(-3.87954 - 2.31337i) q^{93} +(1.81888 - 7.64941i) q^{94} +(6.79313 + 11.7660i) q^{95} +(3.72030 + 9.06418i) q^{96} +(-4.69078 + 8.12466i) q^{97} +(-14.2776 - 13.4901i) q^{98} +(6.31069 + 1.88313i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 4 q^{2} + 2 q^{3} - 2 q^{4} + 4 q^{5} - 28 q^{6} - 8 q^{8} - 20 q^{10} - 2 q^{11} + 8 q^{12} - 16 q^{13} - 4 q^{14} - 20 q^{15} - 10 q^{16} - 16 q^{17} + 28 q^{19} + 12 q^{20} - 16 q^{21} - 8 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) \) 72 * q + 4 * q^2 + 2 * q^3 - 2 * q^4 + 4 * q^5 - 28 * q^6 - 8 * q^8 - 20 * q^10 - 2 * q^11 + 8 * q^12 - 16 * q^13 - 4 * q^14 - 20 * q^15 - 10 * q^16 - 16 * q^17 + 28 * q^19 + 12 * q^20 - 16 * q^21 - 8 * q^22 - 40 * q^24 - 4 * q^26 + 8 * q^27 - 16 * q^28 + 4 * q^29 + 18 * q^30 + 28 * q^31 - 46 * q^32 - 32 * q^33 - 14 * q^34 - 16 * q^35 + 14 * q^36 + 16 * q^37 + 2 * q^38 - 10 * q^40 + 26 * q^42 - 10 * q^43 + 60 * q^44 + 40 * q^45 + 20 * q^46 - 56 * q^47 + 2 * q^48 + 4 * q^49 - 36 * q^50 - 54 * q^51 + 6 * q^52 - 8 * q^53 + 92 * q^54 + 52 * q^56 - 14 * q^58 - 14 * q^59 + 18 * q^60 - 32 * q^61 + 16 * q^62 - 108 * q^63 - 44 * q^64 - 64 * q^65 + 26 * q^66 - 18 * q^67 + 16 * q^68 + 32 * q^69 + 14 * q^70 + 114 * q^72 + 38 * q^74 + 86 * q^75 + 10 * q^76 - 36 * q^77 + 16 * q^78 + 44 * q^79 + 144 * q^80 - 44 * q^81 - 88 * q^82 + 20 * q^83 - 58 * q^84 - 8 * q^85 + 76 * q^86 - 42 * q^88 - 80 * q^91 - 68 * q^92 - 4 * q^93 + 20 * q^94 + 48 * q^95 + 94 * q^96 + 40 * q^97 + 88 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more