LMFDB - Embedded newform 728.2.h.b.27.47

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [728,2,Mod(27,728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(728, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("728.27");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 728 = 2^{3} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	728.h (of order $2$, degree $1$, 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:	$5.81310926715$
Analytic rank:	$0$
Dimension:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			27.47
Character	$\chi$	$=$	728.27
Dual form			728.2.h.b.27.48

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41227 - 0.0740988i) q^{2} -1.48862i q^{3} +(1.98902 - 0.209295i) q^{4} -1.02997 q^{5} +(-0.110305 - 2.10234i) q^{6} +(1.70779 + 2.02076i) q^{7} +(2.79352 - 0.442965i) q^{8} +0.784007 q^{9} +(-1.45459 + 0.0763194i) q^{10} +0.608038 q^{11} +(-0.311561 - 2.96090i) q^{12} +1.00000 q^{13} +(2.56160 + 2.72731i) q^{14} +1.53323i q^{15} +(3.91239 - 0.832584i) q^{16} +0.526406i q^{17} +(1.10723 - 0.0580940i) q^{18} -1.94810i q^{19} +(-2.04863 + 0.215567i) q^{20} +(3.00814 - 2.54225i) q^{21} +(0.858714 - 0.0450549i) q^{22} -0.0153141i q^{23} +(-0.659408 - 4.15850i) q^{24} -3.93917 q^{25} +(1.41227 - 0.0740988i) q^{26} -5.63295i q^{27} +(3.81976 + 3.66189i) q^{28} -4.64455i q^{29} +(0.113611 + 2.16534i) q^{30} -4.57506 q^{31} +(5.46366 - 1.46574i) q^{32} -0.905138i q^{33} +(0.0390061 + 0.743428i) q^{34} +(-1.75897 - 2.08131i) q^{35} +(1.55940 - 0.164089i) q^{36} +2.15479i q^{37} +(-0.144352 - 2.75125i) q^{38} -1.48862i q^{39} +(-2.87724 + 0.456240i) q^{40} +6.24596i q^{41} +(4.05993 - 3.81325i) q^{42} -3.29851 q^{43} +(1.20940 - 0.127259i) q^{44} -0.807502 q^{45} +(-0.00113476 - 0.0216276i) q^{46} +2.60155 q^{47} +(-1.23940 - 5.82407i) q^{48} +(-1.16691 + 6.90205i) q^{49} +(-5.56317 + 0.291887i) q^{50} +0.783619 q^{51} +(1.98902 - 0.209295i) q^{52} +1.16935i q^{53} +(-0.417395 - 7.95526i) q^{54} -0.626260 q^{55} +(5.66588 + 4.88854i) q^{56} -2.89999 q^{57} +(-0.344155 - 6.55936i) q^{58} -0.783099i q^{59} +(0.320898 + 3.04963i) q^{60} -5.32371 q^{61} +(-6.46122 + 0.339006i) q^{62} +(1.33892 + 1.58429i) q^{63} +(7.60756 - 2.47487i) q^{64} -1.02997 q^{65} +(-0.0670696 - 1.27830i) q^{66} -4.18167 q^{67} +(0.110174 + 1.04703i) q^{68} -0.0227969 q^{69} +(-2.63836 - 2.80904i) q^{70} -14.9594i q^{71} +(2.19014 - 0.347288i) q^{72} +9.18228i q^{73} +(0.159668 + 3.04315i) q^{74} +5.86392i q^{75} +(-0.407729 - 3.87482i) q^{76} +(1.03840 + 1.22870i) q^{77} +(-0.110305 - 2.10234i) q^{78} +9.29066i q^{79} +(-4.02964 + 0.857535i) q^{80} -6.03331 q^{81} +(0.462818 + 8.82099i) q^{82} -1.45140i q^{83} +(5.45117 - 5.68618i) q^{84} -0.542182i q^{85} +(-4.65839 + 0.244416i) q^{86} -6.91397 q^{87} +(1.69857 - 0.269340i) q^{88} +12.0597i q^{89} +(-1.14041 + 0.0598349i) q^{90} +(1.70779 + 2.02076i) q^{91} +(-0.00320517 - 0.0304600i) q^{92} +6.81053i q^{93} +(3.67409 - 0.192772i) q^{94} +2.00649i q^{95} +(-2.18193 - 8.13332i) q^{96} +8.46670i q^{97} +(-1.13655 + 9.83403i) q^{98} +0.476706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) $ 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * q^42 - 4 * q^43 - 30 * q^44 - 24 * q^45 + 2 * q^46 - 48 * q^48 + 11 * q^50 - 40 * q^51 + q^52 - 62 * q^54 - 14 * q^56 + 2 * q^58 + 18 * q^60 + 36 * q^62 - 20 * q^63 - 11 * q^64 - 32 * q^66 - 4 * q^67 - 62 * q^68 - 37 * q^70 + 13 * q^72 - 44 * q^74 + 48 * q^76 + 20 * q^77 + 10 * q^78 - 32 * q^80 + 64 * q^81 + 50 * q^82 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * q^98 + 20 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/728\mathbb{Z}\right)^\times$.

$n$	$183$	$365$	$521$	$561$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

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 $

$2$	1.41227	−	0.0740988i	0.998626	−	0.0523958i
$2$	1.41227	−	0.0740988i	0.998626	−	0.0523958i
$3$		−	1.48862i		−	0.859456i	−0.902958	−	0.429728i	$-0.858609\pi$
$3$		−	1.48862i		−	0.859456i	0.902958	−	0.429728i	$-0.141391\pi$
$4$	1.98902	−	0.209295i	0.994509	−	0.104648i
$5$	−1.02997			−0.460616			−0.230308	−	0.973118i	$-0.573973\pi$
$5$	−1.02997			−0.460616			−0.230308	+	0.973118i	$0.573973\pi$
$6$	−0.110305	−	2.10234i	−0.0450318	−	0.858275i
$7$	1.70779	+	2.02076i	0.645484	+	0.763774i
$7$	1.70779	+	2.02076i	0.645484	+	0.763774i
$8$	2.79352	−	0.442965i	0.987660	−	0.156612i
$9$	0.784007			0.261336
$10$	−1.45459	+	0.0763194i	−0.459983	+	0.0241343i
$11$	0.608038			0.183330			0.0916651	−	0.995790i	$-0.470781\pi$
$11$	0.608038			0.183330			0.0916651	+	0.995790i	$0.470781\pi$
$12$	−0.311561	−	2.96090i	−0.0899400	−	0.854737i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$	2.56160	+	2.72731i	0.684616	+	0.728904i
$15$			1.53323i			0.395879i
$16$	3.91239	−	0.832584i	0.978098	−	0.208146i
$17$			0.526406i			0.127672i	0.997960	+	0.0638361i	$0.0203335\pi$
$17$			0.526406i			0.127672i	−0.997960	+	0.0638361i	$0.979667\pi$
$18$	1.10723	−	0.0580940i	0.260977	−	0.0136929i
$19$		−	1.94810i		−	0.446926i	−0.974712	−	0.223463i	$-0.928264\pi$
$19$		−	1.94810i		−	0.446926i	0.974712	−	0.223463i	$-0.0717361\pi$
$20$	−2.04863	+	0.215567i	−0.458087	+	0.0482023i
$21$	3.00814	−	2.54225i	0.656430	−	0.554765i
$22$	0.858714	−	0.0450549i	0.183078	−	0.00960573i
$23$		−	0.0153141i		−	0.00319321i	−0.999999	−	0.00159660i	$-0.999492\pi$
$23$		−	0.0153141i		−	0.00319321i	0.999999	−	0.00159660i	$-0.000508215\pi$
$24$	−0.659408	−	4.15850i	−0.134601	−	0.848850i
$25$	−3.93917			−0.787833
$26$	1.41227	−	0.0740988i	0.276969	−	0.0145320i
$27$		−	5.63295i		−	1.08406i
$28$	3.81976	+	3.66189i	0.721867	+	0.692032i
$29$		−	4.64455i		−	0.862471i	−0.902239	−	0.431236i	$-0.858078\pi$
$29$		−	4.64455i		−	0.862471i	0.902239	−	0.431236i	$-0.141922\pi$
$30$	0.113611	+	2.16534i	0.0207424	+	0.395335i
$31$	−4.57506			−0.821705			−0.410852	−	0.911702i	$-0.634769\pi$
$31$	−4.57506			−0.821705			−0.410852	+	0.911702i	$0.634769\pi$
$32$	5.46366	−	1.46574i	0.965848	−	0.259108i
$33$		−	0.905138i		−	0.157564i
$34$	0.0390061	+	0.743428i	0.00668948	+	0.127497i
$35$	−1.75897	−	2.08131i	−0.297320	−	0.351806i
$36$	1.55940	−	0.164089i	0.259901	−	0.0273481i
$37$			2.15479i			0.354246i	0.984189	+	0.177123i	$0.0566790\pi$
$37$			2.15479i			0.354246i	−0.984189	+	0.177123i	$0.943321\pi$
$38$	−0.144352	−	2.75125i	−0.0234170	−	0.446312i
$39$		−	1.48862i		−	0.238370i
$40$	−2.87724	+	0.456240i	−0.454932	+	0.0721379i
$41$			6.24596i			0.975455i	0.872996	+	0.487727i	$0.162174\pi$
$41$			6.24596i			0.975455i	−0.872996	+	0.487727i	$0.837826\pi$
$42$	4.05993	−	3.81325i	0.626461	−	0.588397i
$43$	−3.29851			−0.503019			−0.251509	−	0.967855i	$-0.580927\pi$
$43$	−3.29851			−0.503019			−0.251509	+	0.967855i	$0.580927\pi$
$44$	1.20940	−	0.127259i	0.182324	−	0.0191851i
$45$	−0.807502			−0.120375
$46$	−0.00113476	−	0.0216276i	−0.000167311	−	0.00318882i
$47$	2.60155			0.379475			0.189737	−	0.981835i	$-0.439236\pi$
$47$	2.60155			0.379475			0.189737	+	0.981835i	$0.439236\pi$
$48$	−1.23940	−	5.82407i	−0.178892	−	0.840632i
$49$	−1.16691	+	6.90205i	−0.166701	+	0.986008i
$50$	−5.56317	+	0.291887i	−0.786751	+	0.0412791i
$51$	0.783619			0.109729
$52$	1.98902	−	0.209295i	0.275827	−	0.0290240i
$53$			1.16935i			0.160622i	0.996770	+	0.0803111i	$0.0255914\pi$
$53$			1.16935i			0.160622i	−0.996770	+	0.0803111i	$0.974409\pi$
$54$	−0.417395	−	7.95526i	−0.0568003	−	1.08257i
$55$	−0.626260			−0.0844448
$56$	5.66588	+	4.88854i	0.757135	+	0.653259i
$57$	−2.89999			−0.384113
$58$	−0.344155	−	6.55936i	−0.0451898	−	0.861286i
$59$		−	0.783099i		−	0.101951i	−0.998700	−	0.0509754i	$-0.983767\pi$
$59$		−	0.783099i		−	0.101951i	0.998700	−	0.0509754i	$-0.0162330\pi$
$60$	0.320898	+	3.04963i	0.0414278	+	0.393705i
$61$	−5.32371			−0.681631			−0.340815	−	0.940130i	$-0.610703\pi$
$61$	−5.32371			−0.681631			−0.340815	+	0.940130i	$0.610703\pi$
$62$	−6.46122	+	0.339006i	−0.820576	+	0.0430538i
$63$	1.33892	+	1.58429i	0.168688	+	0.199601i
$64$	7.60756	−	2.47487i	0.950945	−	0.309359i
$65$	−1.02997			−0.127752
$66$	−0.0670696	−	1.27830i	−0.00825570	−	0.157348i
$67$	−4.18167			−0.510872			−0.255436	−	0.966826i	$-0.582219\pi$
$67$	−4.18167			−0.510872			−0.255436	+	0.966826i	$0.582219\pi$
$68$	0.110174	+	1.04703i	0.0133606	+	0.126971i
$69$	−0.0227969			−0.00274442
$70$	−2.63836	−	2.80904i	−0.315345	−	0.335745i
$71$		−	14.9594i		−	1.77535i	−0.460470	−	0.887675i	$-0.652319\pi$
$71$		−	14.9594i		−	1.77535i	0.460470	−	0.887675i	$-0.347681\pi$
$72$	2.19014	−	0.347288i	0.258111	−	0.0409283i
$73$			9.18228i			1.07470i	0.843358	+	0.537352i	$0.180575\pi$
$73$			9.18228i			1.07470i	−0.843358	+	0.537352i	$0.819425\pi$
$74$	0.159668	+	3.04315i	0.0185610	+	0.353759i
$75$			5.86392i			0.677108i
$76$	−0.407729	−	3.87482i	−0.0467697	−	0.444472i
$77$	1.03840	+	1.22870i	0.118337	+	0.140023i
$78$	−0.110305	−	2.10234i	−0.0124896	−	0.238043i
$79$			9.29066i			1.04528i	0.852553	+	0.522641i	$0.175053\pi$
$79$			9.29066i			1.04528i	−0.852553	+	0.522641i	$0.824947\pi$
$80$	−4.02964	+	0.857535i	−0.450527	+	0.0958753i
$81$	−6.03331			−0.670368
$82$	0.462818	+	8.82099i	0.0511097	+	0.974115i
$83$		−	1.45140i		−	0.159311i	−0.996822	−	0.0796557i	$-0.974618\pi$
$83$		−	1.45140i		−	0.159311i	0.996822	−	0.0796557i	$-0.0253821\pi$
$84$	5.45117	−	5.68618i	0.594771	−	0.620413i
$85$		−	0.542182i		−	0.0588078i
$86$	−4.65839	+	0.244416i	−0.502328	+	0.0263560i
$87$	−6.91397			−0.741256
$88$	1.69857	−	0.269340i	0.181068	−	0.0287117i
$89$			12.0597i			1.27832i	0.769073	+	0.639162i	$0.220718\pi$
$89$			12.0597i			1.27832i	−0.769073	+	0.639162i	$0.779282\pi$
$90$	−1.14041	+	0.0598349i	−0.120210	+	0.00630716i
$91$	1.70779	+	2.02076i	0.179025	+	0.211833i
$92$	−0.00320517	−	0.0304600i	−0.000334162	−	0.00317568i
$93$			6.81053i			0.706219i
$94$	3.67409	−	0.192772i	0.378954	−	0.0198829i
$95$			2.00649i			0.205861i
$96$	−2.18193	−	8.13332i	−0.222692	−	0.830104i
$97$			8.46670i			0.859663i	0.902909	+	0.429831i	$0.141427\pi$
$97$			8.46670i			0.859663i	−0.902909	+	0.429831i	$0.858573\pi$
$98$	−1.13655	+	9.83403i	−0.114809	+	0.993388i
$99$	0.476706			0.0479107
$100$	−7.83507	+	0.824448i	−0.783507	+	0.0824448i
$101$	−7.70127			−0.766305			−0.383153	−	0.923685i	$-0.625162\pi$
$101$	−7.70127			−0.766305			−0.383153	+	0.923685i	$0.625162\pi$
$102$	1.10668	−	0.0580652i	0.109578	−	0.00574932i
$103$	4.43728			0.437218			0.218609	−	0.975813i	$-0.429848\pi$
$103$	4.43728			0.437218			0.218609	+	0.975813i	$0.429848\pi$
$104$	2.79352	−	0.442965i	0.273928	−	0.0434363i
$105$	−3.09829	+	2.61844i	−0.302362	+	0.255534i
$106$	0.0866472	+	1.65143i	0.00841592	+	0.160402i
$107$	6.18159			0.597597			0.298798	−	0.954316i	$-0.403414\pi$
$107$	6.18159			0.597597			0.298798	+	0.954316i	$0.403414\pi$
$108$	−1.17895	−	11.2040i	−0.113444	−	1.07811i
$109$			16.1401i			1.54594i	0.634441	+	0.772971i	$0.281230\pi$
$109$			16.1401i			1.54594i	−0.634441	+	0.772971i	$0.718770\pi$
$110$	−0.884448	+	0.0464051i	−0.0843288	+	0.00442455i
$111$	3.20767			0.304459
$112$	8.36399	+	6.48411i	0.790323	+	0.612691i
$113$	−2.76655			−0.260255			−0.130128	−	0.991497i	$-0.541539\pi$
$113$	−2.76655			−0.260255			−0.130128	+	0.991497i	$0.541539\pi$
$114$	−4.09557	+	0.214886i	−0.383585	+	0.0201259i
$115$			0.0157730i			0.00147084i
$116$	−0.972082	−	9.23809i	−0.0902555	−	0.857736i
$117$	0.784007			0.0724815
$118$	−0.0580267	−	1.10595i	−0.00534179	−	0.101811i
$119$	−1.06374	+	0.898991i	−0.0975127	+	0.0824104i
$120$	0.679169	+	4.28312i	0.0619994	+	0.390994i
$121$	−10.6303			−0.966390
$122$	−7.51851	+	0.394480i	−0.680694	+	0.0357146i
$123$	9.29787			0.838360
$124$	−9.09988	+	0.957538i	−0.817193	+	0.0859894i
$125$	9.20706			0.823504
$126$	2.00831	+	2.13823i	0.178915	+	0.190489i
$127$		−	11.5046i		−	1.02087i	−0.859917	−	0.510434i	$-0.829485\pi$
$127$		−	11.5046i		−	1.02087i	0.859917	−	0.510434i	$-0.170515\pi$
$128$	10.5606	−	4.05890i	0.933430	−	0.358759i
$129$			4.91024i			0.432322i
$130$	−1.45459	+	0.0763194i	−0.127576	+	0.00669366i
$131$		−	10.8481i		−	0.947800i	−0.880579	−	0.473900i	$-0.842846\pi$
$131$		−	10.8481i		−	0.947800i	0.880579	−	0.473900i	$-0.157154\pi$
$132$	−0.189441	−	1.80034i	−0.0164887	−	0.156699i
$133$	3.93664	−	3.32695i	0.341350	−	0.288483i
$134$	−5.90565	+	0.309857i	−0.510170	+	0.0267675i
$135$			5.80176i			0.499336i
$136$	0.233180	+	1.47053i	0.0199950	+	0.126097i
$137$	−3.67475			−0.313955			−0.156977	−	0.987602i	$-0.550175\pi$
$137$	−3.67475			−0.313955			−0.156977	+	0.987602i	$0.550175\pi$
$138$	−0.0321954	+	0.00168922i	−0.00274065	+	0.000143796i
$139$			14.5439i			1.23360i	0.787121	+	0.616798i	$0.211571\pi$
$139$			14.5439i			1.23360i	−0.787121	+	0.616798i	$0.788429\pi$
$140$	−3.93423	−	3.77163i	−0.332503	−	0.318761i
$141$		−	3.87272i		−	0.326142i
$142$	−1.10847	−	21.1267i	−0.0930209	−	1.77291i
$143$	0.608038			0.0508467
$144$	3.06734	−	0.652752i	0.255612	−	0.0543960i
$145$			4.78374i			0.397268i
$146$	0.680396	+	12.9679i	0.0563100	+	1.07323i
$147$	10.2745	+	1.73708i	0.847430	+	0.143272i
$148$	0.450988	+	4.28592i	0.0370710	+	0.352301i
$149$		−	15.7637i		−	1.29142i	−0.763584	−	0.645708i	$-0.776562\pi$
$149$		−	15.7637i		−	1.29142i	0.763584	−	0.645708i	$-0.223438\pi$
$150$	0.434510	+	8.28145i	0.0354776	+	0.676178i
$151$		−	8.76049i		−	0.712919i	−0.934311	−	0.356459i	$-0.883984\pi$
$151$		−	8.76049i		−	0.712919i	0.934311	−	0.356459i	$-0.116016\pi$
$152$	−0.862943	−	5.44208i	−0.0699939	−	0.441411i
$153$			0.412706i			0.0333653i
$154$	1.55755	+	1.65831i	0.125511	+	0.133630i
$155$	4.71216			0.378490
$156$	−0.311561	−	2.96090i	−0.0249449	−	0.237061i
$157$	−13.6353			−1.08821			−0.544106	−	0.839016i	$-0.683131\pi$
$157$	−13.6353			−1.08821			−0.544106	+	0.839016i	$0.683131\pi$
$158$	0.688427	+	13.1209i	0.0547683	+	1.04385i
$159$	1.74071			0.138048
$160$	−5.62740	+	1.50966i	−0.444885	+	0.119349i
$161$	0.0309460	−	0.0261533i	0.00243889	−	0.00206117i
$162$	−8.52067	+	0.447061i	−0.669447	+	0.0351244i
$163$	−5.71060			−0.447288			−0.223644	−	0.974671i	$-0.571795\pi$
$163$	−5.71060			−0.447288			−0.223644	+	0.974671i	$0.571795\pi$
$164$	1.30725	+	12.4233i	0.102079	+	0.970099i
$165$			0.932263i			0.0725766i
$166$	−0.107547	−	2.04976i	−0.00834724	−	0.159092i
$167$	16.0117			1.23902			0.619512	−	0.784987i	$-0.287331\pi$
$167$	16.0117			1.23902			0.619512	+	0.784987i	$0.287331\pi$
$168$	7.27718	−	8.43435i	0.561447	−	0.650724i
$169$	1.00000			0.0769231
$170$	−0.0401750	−	0.765707i	−0.00308128	−	0.0587271i
$171$		−	1.52733i		−	0.116798i
$172$	−6.56080	+	0.690363i	−0.500257	+	0.0526397i
$173$	−13.1654			−1.00095			−0.500475	−	0.865751i	$-0.666841\pi$
$173$	−13.1654			−1.00095			−0.500475	+	0.865751i	$0.666841\pi$
$174$	−9.76440	+	0.512317i	−0.740238	+	0.0388387i
$175$	−6.72727	−	7.96009i	−0.508534	−	0.601726i
$176$	2.37888	−	0.506243i	0.179315	−	0.0381595i
$177$	−1.16574			−0.0876223
$178$	0.893607	+	17.0315i	0.0669787	+	1.27657i
$179$	3.27796			0.245006			0.122503	−	0.992468i	$-0.460908\pi$
$179$	3.27796			0.245006			0.122503	+	0.992468i	$0.460908\pi$
$180$	−1.60614	+	0.169006i	−0.119714	+	0.0125970i
$181$	13.4214			0.997606			0.498803	−	0.866715i	$-0.333773\pi$
$181$	13.4214			0.997606			0.498803	+	0.866715i	$0.333773\pi$
$182$	2.56160	+	2.72731i	0.189878	+	0.202162i
$183$			7.92498i			0.585831i
$184$	−0.00678361	−	0.0427803i	−0.000500095	−	0.00315381i
$185$		−	2.21937i		−	0.163171i
$186$	0.504652	+	9.61831i	0.0370029	+	0.705249i
$187$			0.320075i			0.0234062i
$188$	5.17453	−	0.544492i	0.377391	−	0.0397111i
$189$	11.3828	−	9.61990i	0.827978	−	0.699745i
$190$	0.148678	+	2.83370i	0.0107862	+	0.205578i
$191$			13.3702i			0.967437i	0.875224	+	0.483719i	$0.160714\pi$
$191$			13.3702i			0.967437i	−0.875224	+	0.483719i	$0.839286\pi$
$192$	−3.68414	−	11.3248i	−0.265880	−	0.817296i
$193$	−14.0635			−1.01231			−0.506157	−	0.862441i	$-0.668934\pi$
$193$	−14.0635			−1.01231			−0.506157	+	0.862441i	$0.668934\pi$
$194$	0.627372	+	11.9573i	0.0450427	+	0.858482i
$195$			1.53323i			0.109797i
$196$	−0.876432	+	13.9725i	−0.0626023	+	0.998039i
$197$			7.40334i			0.527466i	0.964596	+	0.263733i	$0.0849538\pi$
$197$			7.40334i			0.527466i	−0.964596	+	0.263733i	$0.915046\pi$
$198$	0.673238	−	0.0353233i	0.0478449	−	0.00251032i
$199$	−21.2213			−1.50434			−0.752170	−	0.658969i	$-0.770993\pi$
$199$	−21.2213			−1.50434			−0.752170	+	0.658969i	$0.770993\pi$
$200$	−11.0042	+	1.74491i	−0.778111	+	0.123384i
$201$			6.22492i			0.439072i
$202$	−10.8763	+	0.570655i	−0.765253	+	0.0401512i
$203$	9.38550	−	7.93191i	0.658733	−	0.556711i
$204$	1.55863	−	0.164008i	0.109126	−	0.0114828i
$205$		−	6.43314i		−	0.449310i
$206$	6.26664	−	0.328797i	0.436617	−	0.0229084i
$207$		−	0.0120064i		−	0.000834499i
$208$	3.91239	−	0.832584i	0.271276	−	0.0577293i
$209$		−	1.18452i		−	0.0819350i
$210$	−4.18160	+	3.92753i	−0.288558	+	0.271025i
$211$	−9.27855			−0.638762			−0.319381	−	0.947626i	$-0.603475\pi$
$211$	−9.27855			−0.638762			−0.319381	+	0.947626i	$0.603475\pi$
$212$	0.244739	+	2.32585i	0.0168087	+	0.159740i
$213$	−22.2688			−1.52584
$214$	8.73008	−	0.458048i	0.596776	−	0.0313115i
$215$	3.39736			0.231698
$216$	−2.49520	−	15.7358i	−0.169777	−	1.07069i
$217$	−7.81324	−	9.24507i	−0.530397	−	0.627597i
$218$	1.19596	+	22.7942i	0.0810009	+	1.54382i
$219$	13.6689			0.923661
$220$	−1.24564	+	0.131073i	−0.0839812	+	0.00883695i
$221$			0.526406i			0.0354099i
$222$	4.53010	−	0.237684i	0.304040	−	0.0159523i
$223$	0.650804			0.0435811			0.0217905	−	0.999763i	$-0.493063\pi$
$223$	0.650804			0.0435811			0.0217905	+	0.999763i	$0.493063\pi$
$224$	12.2927	+	8.53756i	0.821340	+	0.570439i
$225$	−3.08833			−0.205889
$226$	−3.90712	+	0.204998i	−0.259898	+	0.0136363i
$227$		−	22.9227i		−	1.52143i	−0.649084	−	0.760717i	$-0.724848\pi$
$227$		−	22.9227i		−	1.52143i	0.649084	−	0.760717i	$-0.275152\pi$
$228$	−5.76813	+	0.606954i	−0.382004	+	0.0401965i
$229$	9.33589			0.616933			0.308467	−	0.951235i	$-0.400184\pi$
$229$	9.33589			0.616933			0.308467	+	0.951235i	$0.400184\pi$
$230$	0.00116876	+	0.0222758i	7.70659e−5	+	0.00146882i
$231$	1.82906	−	1.54579i	0.120343	−	0.101705i
$232$	−2.05737	−	12.9747i	−0.135073	−	0.851828i
$233$	−9.56308			−0.626498			−0.313249	−	0.949671i	$-0.601417\pi$
$233$	−9.56308			−0.626498			−0.313249	+	0.949671i	$0.601417\pi$
$234$	1.10723	−	0.0580940i	0.0723819	−	0.00379772i
$235$	−2.67951			−0.174792
$236$	−0.163899	−	1.55760i	−0.0106689	−	0.101391i
$237$	13.8303			0.898373
$238$	−1.43567	+	1.34844i	−0.0930608	+	0.0874064i
$239$			16.2651i			1.05210i	0.850453	+	0.526051i	$0.176328\pi$
$239$			16.2651i			1.05210i	−0.850453	+	0.526051i	$0.823672\pi$
$240$	1.27655	+	5.99861i	0.0824006	+	0.387208i
$241$		−	17.9771i		−	1.15800i	−0.815326	−	0.579002i	$-0.803442\pi$
$241$		−	17.9771i		−	1.15800i	0.815326	−	0.579002i	$-0.196558\pi$
$242$	−15.0129	+	0.787692i	−0.965063	+	0.0506347i
$243$		−	7.91754i		−	0.507911i
$244$	−10.5889	+	1.11423i	−0.677888	+	0.0713310i
$245$	1.20188	−	7.10890i	0.0767851	−	0.454171i
$246$	13.1311	−	0.688961i	0.837209	−	0.0439265i
$247$		−	1.94810i		−	0.123955i
$248$	−12.7805	+	2.02659i	−0.811565	+	0.128689i
$249$	−2.16058			−0.136921
$250$	13.0029	−	0.682232i	0.822373	−	0.0431481i
$251$		−	16.3892i		−	1.03447i	−0.855842	−	0.517237i	$-0.826961\pi$
$251$		−	16.3892i		−	1.03447i	0.855842	−	0.517237i	$-0.173039\pi$
$252$	2.99472	+	2.87095i	0.188650	+	0.180853i
$253$		−	0.00931155i		−	0.000585412i
$254$	−0.852477	−	16.2476i	−0.0534892	−	1.01947i
$255$	−0.807103			−0.0505428
$256$	14.6136	−	6.51479i	0.913350	−	0.407174i
$257$		−	27.4462i		−	1.71205i	−0.516937	−	0.856023i	$-0.672928\pi$
$257$		−	27.4462i		−	1.71205i	0.516937	−	0.856023i	$-0.327072\pi$
$258$	0.363843	+	6.93459i	0.0226519	+	0.431728i
$259$	−4.35431	+	3.67993i	−0.270564	+	0.228660i
$260$	−2.04863	+	0.215567i	−0.127050	+	0.0133689i
$261$		−	3.64136i		−	0.225394i
$262$	−0.803829	−	15.3204i	−0.0496607	−	0.946498i
$263$		−	4.35567i		−	0.268582i	−0.990942	−	0.134291i	$-0.957124\pi$
$263$		−	4.35567i		−	0.268582i	0.990942	−	0.134291i	$-0.0428757\pi$
$264$	−0.400945	−	2.52853i	−0.0246764	−	0.155620i
$265$		−	1.20439i		−	0.0739851i
$266$	5.31308	−	4.99026i	0.325766	−	0.305972i
$267$	17.9523			1.09866
$268$	−8.31742	+	0.875203i	−0.508067	+	0.0534615i
$269$	−20.3914			−1.24328			−0.621642	−	0.783302i	$-0.713534\pi$
$269$	−20.3914			−1.24328			−0.621642	+	0.783302i	$0.713534\pi$
$270$	0.429904	+	8.19366i	0.0261631	+	0.498650i
$271$	31.3447			1.90405			0.952027	−	0.306015i	$-0.0989957\pi$
$271$	31.3447			1.90405			0.952027	+	0.306015i	$0.0989957\pi$
$272$	0.438277	+	2.05951i	0.0265745	+	0.124876i
$273$	3.00814	−	2.54225i	0.182061	−	0.153864i
$274$	−5.18974	+	0.272294i	−0.313524	+	0.0164499i
$275$	−2.39516			−0.144434
$276$	−0.0453434	+	0.00477128i	−0.00272935	+	0.000287197i
$277$			5.40265i			0.324614i	0.986740	+	0.162307i	$0.0518934\pi$
$277$			5.40265i			0.324614i	−0.986740	+	0.162307i	$0.948107\pi$
$278$	1.07768	+	20.5399i	0.0646352	+	1.23190i
$279$	−3.58688			−0.214741
$280$	−5.83568	−	5.03504i	−0.348748	−	0.300901i
$281$	0.635876			0.0379332			0.0189666	−	0.999820i	$-0.493962\pi$
$281$	0.635876			0.0379332			0.0189666	+	0.999820i	$0.493962\pi$
$282$	−0.286964	−	5.46933i	−0.0170885	−	0.325694i
$283$			6.06925i			0.360779i	0.983595	+	0.180390i	$0.0577359\pi$
$283$			6.06925i			0.360779i	−0.983595	+	0.180390i	$0.942264\pi$
$284$	−3.13092	−	29.7545i	−0.185786	−	1.76560i
$285$	2.98690			0.176928
$286$	0.858714	−	0.0450549i	0.0507768	−	0.00266415i
$287$	−12.6216	+	10.6668i	−0.745027	+	0.629640i
$288$	4.28355	−	1.14915i	0.252411	−	0.0677142i
$289$	16.7229			0.983700
$290$	0.354469	+	6.75593i	0.0208152	+	0.396722i
$291$	12.6037			0.738842
$292$	1.92181	+	18.2637i	0.112465	+	1.06880i
$293$	29.8751			1.74532			0.872660	−	0.488328i	$-0.162393\pi$
$293$	29.8751			1.74532			0.872660	+	0.488328i	$0.162393\pi$
$294$	14.6392	+	1.69190i	0.853773	+	0.0986735i
$295$			0.806568i			0.0469602i
$296$	0.954498	+	6.01947i	0.0554791	+	0.349874i
$297$		−	3.42505i		−	0.198741i
$298$	−1.16807	−	22.2627i	−0.0676647	−	1.28964i
$299$		−	0.0153141i		−	0.000885637i
$300$	1.22729	+	11.6635i	0.0708577	+	0.673390i
$301$	−5.63317	−	6.66549i	−0.324690	−	0.384192i
$302$	−0.649142	−	12.3722i	−0.0373539	−	0.711940i
$303$			11.4643i			0.658606i
$304$	−1.62196	−	7.62174i	−0.0930258	−	0.437137i
$305$	5.48325			0.313970
$306$	0.0305810	+	0.582853i	0.00174820	+	0.0333195i
$307$		−	22.3570i		−	1.27598i	−0.770044	−	0.637991i	$-0.779766\pi$
$307$		−	22.3570i		−	1.27598i	0.770044	−	0.637991i	$-0.220234\pi$
$308$	2.32256	+	2.22657i	0.132340	+	0.126870i
$309$		−	6.60543i		−	0.375770i
$310$	6.65485	−	0.349166i	0.377970	−	0.0198313i
$311$	−21.5289			−1.22079			−0.610396	−	0.792096i	$-0.708990\pi$
$311$	−21.5289			−1.22079			−0.610396	+	0.792096i	$0.708990\pi$
$312$	−0.659408	−	4.15850i	−0.0373316	−	0.235429i
$313$			2.06304i			0.116610i	0.998299	+	0.0583050i	$0.0185696\pi$
$313$			2.06304i			0.116610i	−0.998299	+	0.0583050i	$0.981430\pi$
$314$	−19.2567	+	1.01036i	−1.08672	+	0.0570177i
$315$	−1.37904	−	1.63176i	−0.0777003	−	0.0919395i
$316$	1.94449	+	18.4793i	0.109386	+	1.03954i
$317$			32.5712i			1.82938i	0.404156	+	0.914690i	$0.367565\pi$
$317$			32.5712i			1.82938i	−0.404156	+	0.914690i	$0.632435\pi$
$318$	2.45836	−	0.128985i	0.137858	−	0.00723311i
$319$		−	2.82406i		−	0.158117i
$320$	−7.83555	+	2.54904i	−0.438021	+	0.142496i
$321$		−	9.20205i		−	0.513608i
$322$	0.0417663	−	0.0392285i	0.00232754	−	0.00218612i
$323$	1.02549			0.0570600
$324$	−12.0004	+	1.26274i	−0.666687	+	0.0701524i
$325$	−3.93917			−0.218506
$326$	−8.06491	+	0.423148i	−0.446674	+	0.0234360i
$327$	24.0265			1.32867
$328$	2.76674	+	17.4482i	0.152768	+	0.963418i
$329$	4.44290	+	5.25709i	0.244945	+	0.289833i
$330$	0.0690796	+	1.31661i	0.00380271	+	0.0724769i
$331$	−14.1674			−0.778710			−0.389355	−	0.921088i	$-0.627302\pi$
$331$	−14.1674			−0.778710			−0.389355	+	0.921088i	$0.627302\pi$
$332$	−0.303770	−	2.88685i	−0.0166715	−	0.158437i
$333$			1.68937i			0.0925770i
$334$	22.6129	−	1.18645i	1.23732	−	0.0649196i
$335$	4.30699			0.235316
$336$	9.65238	−	12.4508i	0.526581	−	0.679248i
$337$	23.0042			1.25312			0.626561	−	0.779373i	$-0.284462\pi$
$337$	23.0042			1.25312			0.626561	+	0.779373i	$0.284462\pi$
$338$	1.41227	−	0.0740988i	0.0768174	−	0.00403044i
$339$			4.11834i			0.223678i
$340$	−0.113476	−	1.07841i	−0.00615410	−	0.0584850i
$341$	−2.78181			−0.150643
$342$	−0.113173	−	2.15700i	−0.00611970	−	0.116637i
$343$	−15.9402	+	9.42922i	−0.860689	+	0.509130i
$344$	−9.21448	+	1.46113i	−0.496811	+	0.0787787i
$345$	0.0234801			0.00126412
$346$	−18.5932	+	0.975544i	−0.999576	+	0.0524456i
$347$	17.8224			0.956756			0.478378	−	0.878154i	$-0.341225\pi$
$347$	17.8224			0.956756			0.478378	+	0.878154i	$0.341225\pi$
$348$	−13.7520	+	1.44706i	−0.737186	+	0.0775706i
$349$	−0.0209269			−0.00112019			−0.000560096	−	1.00000i	$-0.500178\pi$
$349$	−0.0209269			−0.00112019			−0.000560096		1.00000i	$0.500178\pi$
$350$	−10.0906	−	10.7433i	−0.539363	−	0.574255i
$351$		−	5.63295i		−	0.300665i
$352$	3.32211	−	0.891224i	0.177069	−	0.0475024i
$353$		−	8.02237i		−	0.426988i	−0.976944	−	0.213494i	$-0.931516\pi$
$353$		−	8.02237i		−	0.426988i	0.976944	−	0.213494i	$-0.0684844\pi$
$354$	−1.64634	+	0.0863798i	−0.0875019	+	0.00459104i
$355$			15.4077i			0.817755i
$356$	2.52403	+	23.9869i	0.133773	+	1.27130i
$357$	1.33826	+	1.58350i	0.0708281	+	0.0838079i
$358$	4.62937	−	0.242893i	0.244670	−	0.0128373i
$359$		−	14.8589i		−	0.784223i	−0.919918	−	0.392112i	$-0.871745\pi$
$359$		−	14.8589i		−	0.784223i	0.919918	−	0.392112i	$-0.128255\pi$
$360$	−2.25578	+	0.357696i	−0.118890	+	0.0188522i
$361$	15.2049			0.800257
$362$	18.9547	−	0.994511i	0.996236	−	0.0522703i
$363$			15.8245i			0.830570i
$364$	3.81976	+	3.66189i	0.200210	+	0.191935i
$365$		−	9.45746i		−	0.495026i
$366$	0.587232	+	11.1922i	0.0306951	+	0.585027i
$367$	−20.8036			−1.08594			−0.542970	−	0.839752i	$-0.682700\pi$
$367$	−20.8036			−1.08594			−0.542970	+	0.839752i	$0.682700\pi$
$368$	−0.0127503	−	0.0599147i	−0.000664654	−	0.00312327i
$369$			4.89687i			0.254921i
$370$	−0.164452	−	3.13435i	−0.00854948	−	0.162947i
$371$	−2.36296	+	1.99700i	−0.122679	+	0.103679i
$372$	1.42541	+	13.5463i	0.0739041	+	0.702341i
$373$		−	19.1563i		−	0.991875i	−0.868358	−	0.495937i	$-0.834825\pi$
$373$		−	19.1563i		−	0.991875i	0.868358	−	0.495937i	$-0.165175\pi$
$374$	0.0237172	+	0.452032i	0.00122638	+	0.0233740i
$375$		−	13.7058i		−	0.707766i
$376$	7.26749	−	1.15240i	0.374792	−	0.0594303i
$377$		−	4.64455i		−	0.239206i
$378$	15.3628	−	14.4294i	0.790177	−	0.742166i
$379$	1.31524			0.0675596			0.0337798	−	0.999429i	$-0.489246\pi$
$379$	1.31524			0.0675596			0.0337798	+	0.999429i	$0.489246\pi$
$380$	0.419948	+	3.99094i	0.0215429	+	0.204731i
$381$	−17.1260			−0.877392
$382$	0.990719	+	18.8824i	0.0506896	+	0.966108i
$383$	8.37026			0.427700			0.213850	−	0.976866i	$-0.431400\pi$
$383$	8.37026			0.427700			0.213850	+	0.976866i	$0.431400\pi$
$384$	−6.04216	−	15.7207i	−0.308338	−	0.802242i
$385$	−1.06952	−	1.26552i	−0.0545078	−	0.0644968i
$386$	−19.8615	+	1.04209i	−1.01092	+	0.0530410i
$387$	−2.58606			−0.131457
$388$	1.77204	+	16.8404i	0.0899616	+	0.854943i
$389$			29.5123i			1.49634i	0.663510	+	0.748168i	$0.269066\pi$
$389$			29.5123i			1.49634i	−0.663510	+	0.748168i	$0.730934\pi$
$390$	0.113611	+	2.16534i	0.00575290	+	0.109646i
$391$	0.00806143			0.000407684
$392$	−0.202412	+	19.7980i	−0.0102233	+	0.999948i
$393$	−16.1487			−0.814592
$394$	0.548578	+	10.4555i	0.0276370	+	0.526741i
$395$		−	9.56909i		−	0.481473i
$396$	0.948177	−	0.0997722i	0.0476477	−	0.00501374i
$397$	18.5170			0.929339			0.464670	−	0.885484i	$-0.346173\pi$
$397$	18.5170			0.929339			0.464670	+	0.885484i	$0.346173\pi$
$398$	−29.9703	+	1.57247i	−1.50227	+	0.0788210i
$399$	−4.95257	−	5.86017i	−0.247939	−	0.293375i
$400$	−15.4116	+	3.27969i	−0.770578	+	0.163984i
$401$	23.4394			1.17051			0.585253	−	0.810850i	$-0.300995\pi$
$401$	23.4394			1.17051			0.585253	+	0.810850i	$0.300995\pi$
$402$	0.461259	+	8.79128i	0.0230055	+	0.438469i
$403$	−4.57506			−0.227900
$404$	−15.3180	+	1.61184i	−0.762098	+	0.0801920i
$405$	6.21412			0.308782
$406$	12.6671	−	11.8975i	0.628659	−	0.590461i
$407$			1.31019i			0.0649440i
$408$	2.18906	−	0.347116i	0.108375	−	0.0171848i
$409$			1.04236i			0.0515414i	0.999668	+	0.0257707i	$0.00820398\pi$
$409$			1.04236i			0.0515414i	−0.999668	+	0.0257707i	$0.991796\pi$
$410$	−0.476688	−	9.08534i	−0.0235419	−	0.448693i
$411$			5.47031i			0.269830i
$412$	8.82583	−	0.928701i	0.434817	−	0.0457538i
$413$	1.58245	−	1.33737i	0.0778674	−	0.0658076i
$414$	−0.000889656	−	0.0169562i	−4.37242e−5	−	0.000833353i
$415$			1.49489i			0.0733813i
$416$	5.46366	−	1.46574i	0.267878	−	0.0718637i
$417$	21.6503			1.06022
$418$	−0.0877716	−	1.67286i	−0.00429305	−	0.0818225i
$419$			5.33068i			0.260421i	0.991486	+	0.130210i	$0.0415653\pi$
$419$			5.33068i			0.260421i	−0.991486	+	0.130210i	$0.958435\pi$
$420$	−5.61453	+	5.85658i	−0.273961	+	0.285772i
$421$			35.9690i			1.75302i	0.481381	+	0.876511i	$0.340135\pi$
$421$			35.9690i			1.75302i	−0.481381	+	0.876511i	$0.659865\pi$
$422$	−13.1038	+	0.687530i	−0.637884	+	0.0334684i
$423$	2.03963			0.0991703
$424$	0.517980	+	3.26660i	0.0251553	+	0.158640i
$425$		−	2.07360i		−	0.100584i
$426$	−31.4496	+	1.65009i	−1.52374	+	0.0799473i
$427$	−9.09177	−	10.7579i	−0.439982	−	0.520612i
$428$	12.2953	−	1.29378i	0.594316	−	0.0625371i
$429$		−	0.905138i		−	0.0437005i
$430$	4.79800	−	0.251741i	0.231380	−	0.0121400i
$431$		−	22.1177i		−	1.06537i	−0.846312	−	0.532687i	$-0.821182\pi$
$431$		−	22.1177i		−	1.06537i	0.846312	−	0.532687i	$-0.178818\pi$
$432$	−4.68991	−	22.0383i	−0.225643	−	1.06032i
$433$		−	11.5805i		−	0.556523i	−0.960505	−	0.278261i	$-0.910242\pi$
$433$		−	11.5805i		−	0.556523i	0.960505	−	0.278261i	$-0.0897581\pi$
$434$	−11.7195	−	12.4776i	−0.562552	−	0.598944i
$435$	7.12117			0.341434
$436$	3.37805	+	32.1030i	0.161779	+	1.53745i
$437$	−0.0298334			−0.00142713
$438$	19.3042	−	1.01285i	0.922393	−	0.0483959i
$439$	38.2244			1.82435			0.912175	−	0.409801i	$-0.134402\pi$
$439$	38.2244			1.82435			0.912175	+	0.409801i	$0.134402\pi$
$440$	−1.74947	+	0.277411i	−0.0834028	+	0.0132251i
$441$	−0.914863	+	5.41126i	−0.0435649	+	0.257679i
$442$	0.0390061	+	0.743428i	0.00185533	+	0.0353613i
$443$	15.3359			0.728629			0.364315	−	0.931276i	$-0.381303\pi$
$443$	15.3359			0.728629			0.364315	+	0.931276i	$0.381303\pi$
$444$	6.38011	−	0.671350i	0.302787	−	0.0318608i
$445$		−	12.4211i		−	0.588816i
$446$	0.919111	−	0.0482238i	0.0435212	−	0.00228346i
$447$	−23.4662			−1.10992
$448$	17.9932	+	11.1465i	0.850100	+	0.526621i
$449$	23.3025			1.09971			0.549857	−	0.835259i	$-0.314682\pi$
$449$	23.3025			1.09971			0.549857	+	0.835259i	$0.314682\pi$
$450$	−4.36156	+	0.228842i	−0.205606	+	0.0107877i
$451$			3.79778i			0.178830i
$452$	−5.50272	+	0.579025i	−0.258826	+	0.0272351i
$453$	−13.0411			−0.612722
$454$	−1.69854	−	32.3731i	−0.0797167	−	1.51934i
$455$	−1.75897	−	2.08131i	−0.0824618	−	0.0975735i
$456$	−8.10119	+	1.28459i	−0.379373	+	0.0601567i
$457$	7.74554			0.362321			0.181161	−	0.983454i	$-0.442015\pi$
$457$	7.74554			0.362321			0.181161	+	0.983454i	$0.442015\pi$
$458$	13.1848	−	0.691778i	0.616086	−	0.0323247i
$459$	2.96522			0.138405
$460$	0.00330122	+	0.0313729i	0.000153920	+	0.00146277i
$461$	22.6982			1.05716			0.528581	−	0.848883i	$-0.322724\pi$
$461$	22.6982			1.05716			0.528581	+	0.848883i	$0.322724\pi$
$462$	2.46859	−	2.31860i	0.114849	−	0.107871i
$463$		−	15.2556i		−	0.708988i	−0.935058	−	0.354494i	$-0.884653\pi$
$463$		−	15.2556i		−	0.708988i	0.935058	−	0.354494i	$-0.115347\pi$
$464$	−3.86698	−	18.1713i	−0.179520	−	0.843581i
$465$		−	7.01463i		−	0.325296i
$466$	−13.5057	+	0.708613i	−0.625637	+	0.0328258i
$467$		−	33.7119i		−	1.56000i	−0.625779	−	0.780000i	$-0.715219\pi$
$467$		−	33.7119i		−	1.56000i	0.625779	−	0.780000i	$-0.284781\pi$
$468$	1.55940	−	0.164089i	0.0720835	−	0.00758501i
$469$	−7.14141	−	8.45013i	−0.329760	−	0.390191i
$470$	−3.78420	+	0.198549i	−0.174552	+	0.00915837i
$471$			20.2977i			0.935271i
$472$	−0.346886	−	2.18761i	−0.0159667	−	0.100693i
$473$	−2.00562			−0.0922185
$474$	19.5321	−	1.02481i	0.897139	−	0.0470709i
$475$			7.67390i			0.352103i
$476$	−1.92764	+	2.01075i	−0.0883533	+	0.0921624i
$477$			0.916776i			0.0419763i
$478$	1.20522	+	22.9707i	0.0551257	+	1.05066i
$479$	27.5473			1.25867			0.629333	−	0.777136i	$-0.283328\pi$
$479$	27.5473			1.25867			0.629333	+	0.777136i	$0.283328\pi$
$480$	2.24732	+	8.37707i	0.102576	+	0.382359i
$481$			2.15479i			0.0982501i
$482$	−1.33208	−	25.3885i	−0.0606745	−	1.15641i
$483$	−0.0389323	−	0.0460669i	−0.00177148	−	0.00209612i
$484$	−21.1438	+	2.22487i	−0.961084	+	0.101130i
$485$		−	8.72043i		−	0.395974i
$486$	−0.586680	−	11.1817i	−0.0266124	−	0.507213i
$487$		−	13.1983i		−	0.598073i	−0.954242	−	0.299037i	$-0.903335\pi$
$487$		−	13.1983i		−	0.598073i	0.954242	−	0.299037i	$-0.0966653\pi$
$488$	−14.8719	+	2.35822i	−0.673219	+	0.106751i
$489$			8.50091i			0.384425i
$490$	1.17061	−	10.1287i	0.0528830	−	0.457570i
$491$	−8.07921			−0.364609			−0.182305	−	0.983242i	$-0.558356\pi$
$491$	−8.07921			−0.364609			−0.182305	+	0.983242i	$0.558356\pi$
$492$	18.4936	−	1.94600i	0.833757	−	0.0877324i
$493$	2.44492			0.110114
$494$	−0.144352	−	2.75125i	−0.00649471	−	0.123785i
$495$	−0.490992			−0.0220684
$496$	−17.8994	+	3.80912i	−0.803707	+	0.171035i
$497$	30.2292	−	25.5475i	1.35597	−	1.14596i
$498$	−3.05132	+	0.160096i	−0.136733	+	0.00717408i
$499$	−26.0339			−1.16544			−0.582720	−	0.812673i	$-0.698011\pi$
$499$	−26.0339			−1.16544			−0.582720	+	0.812673i	$0.698011\pi$
$500$	18.3130	−	1.92699i	0.818983	−	0.0861777i
$501$		−	23.8354i		−	1.06489i
$502$	−1.21442	−	23.1459i	−0.0542021	−	1.03305i
$503$	5.46230			0.243552			0.121776	−	0.992558i	$-0.461141\pi$
$503$	5.46230			0.243552			0.121776	+	0.992558i	$0.461141\pi$
$504$	4.44209	+	3.83265i	0.197866	+	0.170720i
$505$	7.93207			0.352972
$506$	−0.000689974	−	0.0131504i	−3.06731e−5	−	0.000584608i
$507$		−	1.48862i		−	0.0661120i
$508$	−2.40786	−	22.8829i	−0.106831	−	1.01526i
$509$	−18.6505			−0.826670			−0.413335	−	0.910579i	$-0.635636\pi$
$509$	−18.6505			−0.826670			−0.413335	+	0.910579i	$0.635636\pi$
$510$	−1.13985	+	0.0598054i	−0.0504733	+	0.00264823i
$511$	−18.5551	+	15.6814i	−0.820831	+	0.693705i
$512$	20.1556	−	10.2835i	0.890762	−	0.454471i
$513$	−10.9736			−0.484495
$514$	−2.03373	−	38.7615i	−0.0897040	−	1.70970i
$515$	−4.57026			−0.201390
$516$	1.02769	+	9.76655i	0.0452415	+	0.429949i
$517$	1.58184			0.0695692
$518$	−5.87678	+	5.51971i	−0.258211	+	0.242522i
$519$			19.5984i			0.860273i
$520$	−2.87724	+	0.456240i	−0.126175	+	0.0200075i
$521$			16.3034i			0.714267i	0.934053	+	0.357134i	$0.116246\pi$
$521$			16.3034i			0.714267i	−0.934053	+	0.357134i	$0.883754\pi$
$522$	−0.269820	−	5.14258i	−0.0118097	−	0.225085i
$523$			19.4624i			0.851031i	0.904951	+	0.425516i	$0.139907\pi$
$523$			19.4624i			0.851031i	−0.904951	+	0.425516i	$0.860093\pi$
$524$	−2.27045	−	21.5770i	−0.0991850	−	0.942596i
$525$	−11.8496	+	10.0144i	−0.517157	+	0.437062i
$526$	−0.322750	−	6.15139i	−0.0140726	−	0.268213i
$527$		−	2.40834i		−	0.104909i
$528$	−0.753603	−	3.54125i	−0.0327964	−	0.154113i
$529$	22.9998			0.999990
$530$	−0.0892439	−	1.70093i	−0.00387651	−	0.0738835i
$531$		−	0.613955i		−	0.0266434i
$532$	7.13374	−	7.44129i	0.309287	−	0.322621i
$533$			6.24596i			0.270543i
$534$	25.3535	−	1.33024i	1.09715	−	0.0575652i
$535$	−6.36684			−0.275263
$536$	−11.6816	+	1.85233i	−0.504568	+	0.0800087i
$537$		−	4.87964i		−	0.210572i
$538$	−28.7981	+	1.51098i	−1.24158	+	0.0651428i
$539$	−0.709523	+	4.19671i	−0.0305613	+	0.180765i
$540$	1.21428	+	11.5398i	0.0522543	+	0.496595i
$541$		−	10.8033i		−	0.464471i	−0.972660	−	0.232236i	$-0.925396\pi$
$541$		−	10.8033i		−	0.464471i	0.972660	−	0.232236i	$-0.0746040\pi$
$542$	44.2672	−	2.32260i	1.90144	−	0.0997643i
$543$		−	19.9794i		−	0.857398i
$544$	0.771573	+	2.87611i	0.0330809	+	0.123312i
$545$		−	16.6238i		−	0.712086i
$546$	4.05993	−	3.81325i	0.173749	−	0.163192i
$547$	−32.4266			−1.38646			−0.693230	−	0.720717i	$-0.743813\pi$
$547$	−32.4266			−1.38646			−0.693230	+	0.720717i	$0.743813\pi$
$548$	−7.30914	+	0.769107i	−0.312231	+	0.0328546i
$549$	−4.17382			−0.178134
$550$	−3.38262	+	0.177479i	−0.144235	+	0.00756771i
$551$	−9.04806			−0.385460
$552$	−0.0636837	+	0.0100982i	−0.00271056	+	0.000429809i
$553$	−18.7742	+	15.8665i	−0.798358	+	0.674712i
$554$	0.400330	+	7.63000i	0.0170084	+	0.324168i
$555$	−3.30380			−0.140238
$556$	3.04397	+	28.9281i	0.129093	+	1.22682i
$557$		−	4.44482i		−	0.188333i	−0.995556	−	0.0941666i	$-0.969981\pi$
$557$		−	4.44482i		−	0.188333i	0.995556	−	0.0941666i	$-0.0300186\pi$
$558$	−5.06564	+	0.265783i	−0.214446	+	0.0112515i
$559$	−3.29851			−0.139512
$560$	−8.61465	−	6.67843i	−0.364035	−	0.282215i
$561$	0.476470			0.0201166
$562$	0.898030	−	0.0471177i	0.0378811	−	0.00198754i
$563$		−	9.65256i		−	0.406807i	−0.979095	−	0.203403i	$-0.934800\pi$
$563$		−	9.65256i		−	0.406807i	0.979095	−	0.203403i	$-0.0652003\pi$
$564$	−0.810542	−	7.70291i	−0.0341300	−	0.324351i
$565$	2.84946			0.119878
$566$	0.449724	+	8.57142i	0.0189033	+	0.360284i
$567$	−10.3036	−	12.1919i	−0.432712	−	0.512010i
$568$	−6.62648	−	41.7894i	−0.278041	−	1.75344i
$569$	12.1247			0.508296			0.254148	−	0.967165i	$-0.418205\pi$
$569$	12.1247			0.508296			0.254148	+	0.967165i	$0.418205\pi$
$570$	4.21831	−	0.221325i	0.176685	−	0.00927030i
$571$	−33.2882			−1.39307			−0.696534	−	0.717524i	$-0.745276\pi$
$571$	−33.2882			−1.39307			−0.696534	+	0.717524i	$0.745276\pi$
$572$	1.20940	−	0.127259i	0.0505675	−	0.00532098i
$573$	19.9032			0.831469
$574$	−17.0347	+	15.9996i	−0.711013	+	0.667812i
$575$			0.0603247i			0.00251572i
$576$	5.96438	−	1.94031i	0.248516	−	0.0808465i
$577$		−	27.7175i		−	1.15390i	−0.816781	−	0.576948i	$-0.804243\pi$
$577$		−	27.7175i		−	1.15390i	0.816781	−	0.576948i	$-0.195757\pi$
$578$	23.6173	−	1.23915i	0.982349	−	0.0515417i
$579$			20.9353i			0.870039i
$580$	1.00121	+	9.51494i	0.0415731	+	0.395087i
$581$	2.93291	−	2.47868i	0.121678	−	0.102833i
$582$	17.7998	−	0.933919i	0.737827	−	0.0387122i
$583$			0.711007i			0.0294469i
$584$	4.06743	+	25.6509i	0.168312	+	1.06144i
$585$	−0.807502			−0.0333861
$586$	42.1917	−	2.21371i	1.74292	−	0.0914474i
$587$		−	21.9684i		−	0.906732i	−0.891324	−	0.453366i	$-0.850223\pi$
$587$		−	21.9684i		−	0.906732i	0.891324	−	0.453366i	$-0.149777\pi$
$588$	20.7998	+	1.30468i	0.857770	+	0.0538039i
$589$			8.91269i			0.367241i
$590$	0.0597657	+	1.13909i	0.00246051	+	0.0468957i
$591$	11.0208			0.453334
$592$	1.79405	+	8.43039i	0.0737348	+	0.346487i
$593$		−	16.3479i		−	0.671327i	−0.941982	−	0.335663i	$-0.891040\pi$
$593$		−	16.3479i		−	0.671327i	0.941982	−	0.335663i	$-0.108960\pi$
$594$	−0.253792	−	4.83710i	−0.0104132	−	0.198468i
$595$	1.09562	−	0.925932i	0.0449159	−	0.0379595i
$596$	−3.29928	−	31.3544i	−0.135144	−	1.28433i
$597$			31.5905i			1.29291i
$598$	−0.00113476	−	0.0216276i	−4.64036e−5	−	0.000884420i
$599$			36.2459i			1.48097i	0.672075	+	0.740483i	$0.265403\pi$
$599$			36.2459i			1.48097i	−0.672075	+	0.740483i	$0.734597\pi$
$600$	2.59752	+	16.3810i	0.106043	+	0.668752i
$601$			31.2461i			1.27455i	0.770635	+	0.637277i	$0.219939\pi$
$601$			31.2461i			1.27455i	−0.770635	+	0.637277i	$0.780061\pi$
$602$	−8.44946	−	8.99607i	−0.344374	−	0.366652i
$603$	−3.27846			−0.133509
$604$	−1.83353	−	17.4248i	−0.0746052	−	0.709004i
$605$	10.9489			0.445135
$606$	0.849489	+	16.1907i	0.0345081	+	0.657701i
$607$	41.8217			1.69749			0.848745	−	0.528803i	$-0.177359\pi$
$607$	41.8217			1.69749			0.848745	+	0.528803i	$0.177359\pi$
$608$	−2.85541	−	10.6438i	−0.115802	−	0.431662i
$609$	−11.8076	−	13.9715i	−0.478469	−	0.566152i
$610$	7.74383	−	0.406302i	0.313539	−	0.0164507i
$611$	2.60155			0.105247
$612$	0.0863774	+	0.820880i	0.00349160	+	0.0331821i
$613$			4.71554i			0.190459i	0.995455	+	0.0952293i	$0.0303584\pi$
$613$			4.71554i			0.190459i	−0.995455	+	0.0952293i	$0.969642\pi$
$614$	−1.65663	−	31.5741i	−0.0668560	−	1.27423i
$615$	−9.57651			−0.386162
$616$	3.44507	+	2.97242i	0.138806	+	0.119762i
$617$	7.74058			0.311624			0.155812	−	0.987787i	$-0.450201\pi$
$617$	7.74058			0.311624			0.155812	+	0.987787i	$0.450201\pi$
$618$	−0.489454	−	9.32865i	−0.0196887	−	0.375253i
$619$			44.8288i			1.80182i	0.434004	+	0.900911i	$0.357100\pi$
$619$			44.8288i			1.80182i	−0.434004	+	0.900911i	$0.642900\pi$
$620$	9.37258	−	0.986233i	0.376412	−	0.0396081i
$621$	−0.0862636			−0.00346164
$622$	−30.4046	+	1.59527i	−1.21912	+	0.0639643i
$623$	−24.3697	+	20.5954i	−0.976350	+	0.825137i
$624$	−1.23940	−	5.82407i	−0.0496158	−	0.233149i
$625$	10.2128			0.408514
$626$	0.152869	+	2.91357i	0.00610987	+	0.116450i
$627$	−1.76330			−0.0704195
$628$	−27.1208	+	2.85379i	−1.08224	+	0.113879i
$629$	−1.13430			−0.0452273
$630$	−2.06850	−	2.20231i	−0.0824109	−	0.0877421i
$631$			17.8015i			0.708666i	0.935119	+	0.354333i	$0.115292\pi$
$631$			17.8015i			0.708666i	−0.935119	+	0.354333i	$0.884708\pi$
$632$	4.11544	+	25.9537i	0.163703	+	1.03238i
$633$			13.8122i			0.548988i
$634$	2.41349	+	45.9994i	0.0958518	+	1.82687i
$635$			11.8494i			0.470228i
$636$	3.46231	−	0.364323i	0.137290	−	0.0144464i
$637$	−1.16691	+	6.90205i	−0.0462345	+	0.273469i
$638$	−0.209260	−	3.98834i	−0.00828466	−	0.157900i
$639$		−	11.7282i		−	0.463962i
$640$	−10.8770	+	4.18054i	−0.429953	+	0.165250i
$641$	13.9549			0.551187			0.275594	−	0.961274i	$-0.411126\pi$
$641$	13.9549			0.551187			0.275594	+	0.961274i	$0.411126\pi$
$642$	−0.681861	−	12.9958i	−0.0269109	−	0.512903i
$643$			42.3514i			1.67017i	0.550117	+	0.835087i	$0.314583\pi$
$643$			42.3514i			1.67017i	−0.550117	+	0.835087i	$0.685417\pi$
$644$	0.0560785	−	0.0584962i	0.00220980	−	0.00230507i
$645$		−	5.05739i		−	0.199134i
$646$	1.44828	−	0.0759879i	0.0569816	−	0.00298970i
$647$	28.5451			1.12222			0.561111	−	0.827741i	$-0.310374\pi$
$647$	28.5451			1.12222			0.561111	+	0.827741i	$0.310374\pi$
$648$	−16.8542	+	2.67255i	−0.662096	+	0.104988i
$649$		−	0.476154i		−	0.0186907i
$650$	−5.56317	+	0.291887i	−0.218205	+	0.0114488i
$651$	−13.7624	+	11.6310i	−0.539392	+	0.455853i
$652$	−11.3585	+	1.19520i	−0.444832	+	0.0468076i
$653$		−	35.7866i		−	1.40044i	−0.713927	−	0.700220i	$-0.753085\pi$
$653$		−	35.7866i		−	1.40044i	0.713927	−	0.700220i	$-0.246915\pi$
$654$	33.9320	−	1.78034i	1.32684	−	0.0696167i
$655$			11.1732i			0.436572i
$656$	5.20029	+	24.4366i	0.203037	+	0.954090i
$657$			7.19897i			0.280859i
$658$	6.66412	+	7.09523i	0.259795	+	0.276601i
$659$	−9.09685			−0.354363			−0.177182	−	0.984178i	$-0.556698\pi$
$659$	−9.09685			−0.354363			−0.177182	+	0.984178i	$0.556698\pi$
$660$	0.195118	+	1.85429i	0.00759497	+	0.0721781i
$661$	−31.3058			−1.21765			−0.608827	−	0.793303i	$-0.708360\pi$
$661$	−31.3058			−1.21765			−0.608827	+	0.793303i	$0.708360\pi$
$662$	−20.0082	+	1.04979i	−0.777640	+	0.0408011i
$663$	0.783619			0.0304332
$664$	−0.642918	−	4.05451i	−0.0249500	−	0.157345i
$665$	−4.05462	+	3.42666i	−0.157231	+	0.132880i
$666$	0.125180	+	2.38585i	0.00485064	+	0.0924498i
$667$	−0.0711270			−0.00275405
$668$	31.8476	−	3.35117i	1.23222	−	0.129661i
$669$		−	0.968800i		−	0.0374560i
$670$	6.08263	−	0.319143i	0.234993	−	0.0123296i
$671$	−3.23701			−0.124964
$672$	12.7092	−	18.2992i	0.490267	−	0.705905i
$673$	−35.1110			−1.35343			−0.676715	−	0.736245i	$-0.736597\pi$
$673$	−35.1110			−1.35343			−0.676715	+	0.736245i	$0.736597\pi$
$674$	32.4882	−	1.70459i	1.25140	−	0.0656582i
$675$			22.1891i			0.854060i
$676$	1.98902	−	0.209295i	0.0765007	−	0.00804981i
$677$	−37.3515			−1.43554			−0.717768	−	0.696283i	$-0.754836\pi$
$677$	−37.3515			−1.43554			−0.717768	+	0.696283i	$0.754836\pi$
$678$	0.305164	+	5.81622i	0.0117198	+	0.223370i
$679$	−17.1091	+	14.4593i	−0.656588	+	0.554899i
$680$	−0.240168	−	1.51460i	−0.00921001	−	0.0580822i
$681$	−34.1232			−1.30760
$682$	−3.92867	+	0.206129i	−0.150436	+	0.00789307i
$683$	−18.2389			−0.697893			−0.348947	−	0.937143i	$-0.613461\pi$
$683$	−18.2389			−0.697893			−0.348947	+	0.937143i	$0.613461\pi$
$684$	−0.319662	−	3.03788i	−0.0122226	−	0.116156i
$685$	3.78487			0.144613
$686$	−21.8132	+	14.4978i	−0.832831	+	0.553527i
$687$		−	13.8976i		−	0.530227i
$688$	−12.9051	+	2.74629i	−0.492001	+	0.104701i
$689$			1.16935i			0.0445486i
$690$	0.0331602	−	0.00173984i	0.00126239	−	6.62348e-5i
$691$			30.2469i			1.15065i	0.817926	+	0.575323i	$0.195124\pi$
$691$			30.2469i			1.15065i	−0.817926	+	0.575323i	$0.804876\pi$
$692$	−26.1863	+	2.75546i	−0.995455	+	0.104747i
$693$	0.814113	+	0.963306i	0.0309256	+	0.0365930i
$694$	25.1700	−	1.32062i	0.955442	−	0.0501300i
$695$		−	14.9797i		−	0.568214i
$696$	−19.3144	+	3.06265i	−0.732109	+	0.116089i
$697$	−3.28791			−0.124538
$698$	−0.0295545	+	0.00155066i	−0.00111865	+	5.86933e-5i
$699$			14.2358i			0.538447i
$700$	−15.0467	−	14.4248i	−0.568711	−	0.545206i
$701$			34.8391i			1.31586i	0.753081	+	0.657928i	$0.228567\pi$
$701$			34.8391i			1.31586i	−0.753081	+	0.657928i	$0.771433\pi$
$702$	−0.417395	−	7.95526i	−0.0157536	−	0.300252i
$703$	4.19776			0.158321
$704$	4.62569	−	1.50481i	0.174337	−	0.0567148i
$705$			3.98878i			0.150226i
$706$	−0.594448	−	11.3298i	−0.0223724	−	0.426401i
$707$	−13.1522	−	15.5624i	−0.494638	−	0.585284i
$708$	−2.31868	+	0.243983i	−0.0871412	+	0.00916946i
$709$		−	39.3740i		−	1.47872i	−0.673309	−	0.739361i	$-0.735128\pi$
$709$		−	39.3740i		−	1.47872i	0.673309	−	0.739361i	$-0.264872\pi$
$710$	1.14169	+	21.7598i	0.0428469	+	0.816631i
$711$			7.28394i			0.273169i
$712$	5.34202	+	33.6890i	0.200201	+	1.26255i
$713$			0.0700629i			0.00262387i
$714$	2.00732	+	2.13717i	0.0751220	+	0.0799817i
$715$	−0.626260			−0.0234208
$716$	6.51993	−	0.686061i	0.243661	−	0.0256393i
$717$	24.2126			0.904235
$718$	−1.10103	−	20.9848i	−0.0410900	−	0.783146i
$719$	4.48168			0.167139			0.0835693	−	0.996502i	$-0.473368\pi$
$719$	4.48168			0.167139			0.0835693	+	0.996502i	$0.473368\pi$
$720$	−3.15926	+	0.672313i	−0.117739	+	0.0250556i
$721$	7.57794	+	8.96665i	0.282217	+	0.333936i
$722$	21.4734	−	1.12666i	0.799158	−	0.0419301i
$723$	−26.7610			−0.995253
$724$	26.6954	−	2.80904i	0.992128	−	0.104397i
$725$			18.2956i			0.679483i
$726$	1.17257	+	22.3484i	0.0435183	+	0.829429i
$727$	−16.5368			−0.613315			−0.306657	−	0.951820i	$-0.599211\pi$
$727$	−16.5368			−0.613315			−0.306657	+	0.951820i	$0.599211\pi$
$728$	5.66588	+	4.88854i	0.209991	+	0.181181i
$729$	−29.8862			−1.10689
$730$	−0.700786	−	13.3565i	−0.0259373	−	0.494346i
$731$		−	1.73636i		−	0.0642215i
$732$	1.65866	+	15.7629i	0.0613058	+	0.582615i
$733$	−30.2572			−1.11757			−0.558787	−	0.829311i	$-0.688733\pi$
$733$	−30.2572			−1.11757			−0.558787	+	0.829311i	$0.688733\pi$
$734$	−29.3803	+	1.54152i	−1.08445	+	0.0568986i
$735$	−10.5825	−	1.78914i	−0.390340	−	0.0659934i
$736$	−0.0224464	−	0.0836710i	−0.000827387	−	0.00308416i
$737$	−2.54261			−0.0936583
$738$	0.362853	+	6.91571i	0.0133568	+	0.254571i
$739$	−32.9352			−1.21154			−0.605771	−	0.795639i	$-0.707135\pi$
$739$	−32.9352			−1.21154			−0.605771	+	0.795639i	$0.707135\pi$
$740$	−0.464503	−	4.41436i	−0.0170755	−	0.162275i
$741$	−2.89999			−0.106534
$742$	−3.18917	+	2.99540i	−0.117078	+	0.109964i
$743$		−	26.2593i		−	0.963360i	−0.876347	−	0.481680i	$-0.840027\pi$
$743$		−	26.2593i		−	0.963360i	0.876347	−	0.481680i	$-0.159973\pi$
$744$	3.01683	+	19.0254i	0.110602	+	0.697504i
$745$			16.2362i			0.594847i
$746$	−1.41946	−	27.0539i	−0.0519700	−	0.990512i
$747$		−	1.13790i		−	0.0416337i
$748$	0.0669901	+	0.636635i	0.00244940	+	0.0232777i
$749$	10.5569	+	12.4915i	0.385739	+	0.456429i
$750$	−1.01558	−	19.3563i	−0.0370839	−	0.706793i
$751$		−	43.7992i		−	1.59826i	−0.601161	−	0.799128i	$-0.705295\pi$
$751$		−	43.7992i		−	1.59826i	0.601161	−	0.799128i	$-0.294705\pi$
$752$	10.1783	−	2.16601i	0.371164	−	0.0789862i
$753$	−24.3972			−0.889085
$754$	−0.344155	−	6.55936i	−0.0125334	−	0.238878i
$755$			9.02303i			0.328382i
$756$	20.6272	−	21.5165i	0.750206	−	0.782549i
$757$		−	18.1033i		−	0.657974i	−0.944334	−	0.328987i	$-0.893293\pi$
$757$		−	18.1033i		−	0.657974i	0.944334	−	0.328987i	$-0.106707\pi$
$758$	1.85748	−	0.0974580i	0.0674668	−	0.00353983i
$759$	−0.0138614			−0.000503136
$760$	0.888804	+	5.60517i	0.0322403	+	0.203321i
$761$			23.9490i			0.868152i	0.900876	+	0.434076i	$0.142925\pi$
$761$			23.9490i			0.868152i	−0.900876	+	0.434076i	$0.857075\pi$
$762$	−24.1866	+	1.26902i	−0.876186	+	0.0459716i
$763$	−32.6152	+	27.5639i	−1.18075	+	0.997881i
$764$	2.79833	+	26.5937i	0.101240	+	0.962125i
$765$		−	0.425074i		−	0.0153686i
$766$	11.8211	−	0.620226i	0.427113	−	0.0224097i
$767$		−	0.783099i		−	0.0282761i
$768$	−9.69805	−	21.7541i	−0.349948	−	0.784984i
$769$		−	39.8803i		−	1.43812i	−0.694948	−	0.719060i	$-0.744573\pi$
$769$		−	39.8803i		−	1.43812i	0.694948	−	0.719060i	$-0.255427\pi$
$770$	−1.60423	−	1.70800i	−0.0578123	−	0.0615522i
$771$	−40.8570			−1.47143
$772$	−27.9726	+	2.94343i	−1.00676	+	0.105936i
$773$	17.7022			0.636704			0.318352	−	0.947973i	$-0.396871\pi$
$773$	17.7022			0.636704			0.318352	+	0.947973i	$0.396871\pi$
$774$	−3.65221	+	0.191624i	−0.131276	+	0.00688777i
$775$	18.0219			0.647366
$776$	3.75045	+	23.6519i	0.134633	+	0.849055i
$777$	5.47803	+	6.48192i	0.196523	+	0.232537i
$778$	2.18683	+	41.6794i	0.0784016	+	1.49428i
$779$	12.1678			0.435956
$780$	0.320898	+	3.04963i	0.0114900	+	0.109194i
$781$		−	9.09586i		−	0.325476i
$782$	0.0113849		0.000597342i	0.000407124		2.13609e-5i
$783$	−26.1625			−0.934972
$784$	1.18114	+	27.9751i	0.0421837	+	0.999110i
$785$	14.0439			0.501248
$786$	−22.8063	+	1.19660i	−0.813473	+	0.0426812i
$787$			20.7451i			0.739482i	0.929135	+	0.369741i	$0.120554\pi$
$787$			20.7451i			0.739482i	−0.929135	+	0.369741i	$0.879446\pi$
$788$	1.54948	+	14.7254i	0.0551980	+	0.524570i
$789$	−6.48394			−0.230835
$790$	−0.709058	−	13.5141i	−0.0252271	−	0.480812i
$791$	−4.72468	−	5.59052i	−0.167990	−	0.198776i
$792$	1.33169	−	0.211164i	0.0473195	−	0.00750339i
$793$	−5.32371			−0.189050
$794$	26.1510	−	1.37208i	0.928063	−	0.0486934i
$795$	−1.79288			−0.0635869
$796$	−42.2096	+	4.44152i	−1.49608	+	0.157426i
$797$	11.6215			0.411654			0.205827	−	0.978588i	$-0.434012\pi$
$797$	11.6215			0.411654			0.205827	+	0.978588i	$0.434012\pi$
$798$	−7.42861	−	7.90917i	−0.262970	−	0.279981i
$799$			1.36947i			0.0484484i
$800$	−21.5223	+	5.77378i	−0.760927	+	0.204134i
$801$			9.45487i			0.334071i
$802$	33.1028	−	1.73683i	1.16890	−	0.0613296i
$803$			5.58317i			0.197026i
$804$	1.30285	+	12.3815i	0.0459478	+	0.436661i
$805$	−0.0318734	+	0.0269370i	−0.00112339	+	0.000949405i
$806$	−6.46122	+	0.339006i	−0.227587	+	0.0119410i
$807$			30.3550i			1.06855i
$808$	−21.5137	+	3.41140i	−0.756849	+	0.120013i
$809$	−26.3459			−0.926271			−0.463136	−	0.886287i	$-0.653276\pi$
$809$	−26.3459			−0.926271			−0.463136	+	0.886287i	$0.653276\pi$
$810$	8.77602	−	0.460459i	0.308358	−	0.0161789i
$811$			31.7543i			1.11504i	0.830163	+	0.557521i	$0.188248\pi$
$811$			31.7543i			1.11504i	−0.830163	+	0.557521i	$0.811752\pi$
$812$	17.0078	−	17.7411i	0.596857	−	0.622589i
$813$		−	46.6604i		−	1.63645i
$814$	0.0970839	+	1.85035i	0.00340279	+	0.0648547i
$815$	5.88173			0.206028
$816$	3.06582	−	0.652429i	0.107325	−	0.0228396i
$817$			6.42585i			0.224812i
$818$	0.0772377	+	1.47210i	0.00270055	+	0.0514706i
$819$	1.33892	+	1.58429i	0.0467856	+	0.0553594i
$820$	−1.34643	−	12.7956i	−0.0470192	−	0.446843i
$821$		−	32.1508i		−	1.12207i	−0.827791	−	0.561036i	$-0.810403\pi$
$821$		−	32.1508i		−	1.12207i	0.827791	−	0.561036i	$-0.189597\pi$
$822$	0.405343	+	7.72556i	0.0141380	+	0.269460i
$823$			26.3374i			0.918065i	0.888419	+	0.459033i	$0.151804\pi$
$823$			26.3374i			0.918065i	−0.888419	+	0.459033i	$0.848196\pi$
$824$	12.3956	−	1.96556i	0.431823	−	0.0684735i
$825$			3.56549i			0.124134i
$826$	2.13575	−	2.00599i	0.0743124	−	0.0697972i
$827$	28.2351			0.981832			0.490916	−	0.871207i	$-0.336662\pi$
$827$	28.2351			0.981832			0.490916	+	0.871207i	$0.336662\pi$
$828$	−0.00251287	−	0.0238809i	−8.73283e−5	−	0.000829917i
$829$	−7.20127			−0.250110			−0.125055	−	0.992150i	$-0.539911\pi$
$829$	−7.20127			−0.250110			−0.125055	+	0.992150i	$0.539911\pi$
$830$	0.110770	+	2.11119i	0.00384487	+	0.0732805i
$831$	8.04249			0.278991
$832$	7.60756	−	2.47487i	0.263745	−	0.0858007i
$833$	−3.63328	−	0.614267i	−0.125886	−	0.0212831i
$834$	30.5762	−	1.60426i	1.05877	−	0.0555511i
$835$	−16.4916			−0.570714
$836$	−0.247914	−	2.35603i	−0.00857430	−	0.0814851i
$837$			25.7711i			0.890779i
$838$	0.394997	+	7.52836i	0.0136449	+	0.260063i
$839$	−14.9034			−0.514524			−0.257262	−	0.966342i	$-0.582820\pi$
$839$	−14.9034			−0.514524			−0.257262	+	0.966342i	$0.582820\pi$
$840$	−7.49527	+	8.68711i	−0.258611	+	0.299734i
$841$	7.42817			0.256144
$842$	2.66526	+	50.7980i	0.0918510	+	1.75062i
$843$		−	0.946579i		−	0.0326019i
$844$	−18.4552	+	1.94196i	−0.635255	+	0.0668449i
$845$	−1.02997			−0.0354320
$846$	2.88051	−	0.151134i	0.0990341	−	0.00519610i
$847$	−18.1543	−	21.4812i	−0.623789	−	0.738103i
$848$	0.973580	+	4.57494i	0.0334329	+	0.157104i
$849$	9.03481			0.310074
$850$	−0.153651	−	2.92849i	−0.00527020	−	0.100446i
$851$	0.0329987			0.00113118
$852$	−44.2931	+	4.66076i	−1.51746	+	0.159675i
$853$	49.1718			1.68361			0.841804	−	0.539783i	$-0.181494\pi$
$853$	49.1718			1.68361			0.841804	+	0.539783i	$0.181494\pi$
$854$	−13.6372	−	14.5194i	−0.466655	−	0.496843i
$855$			1.57310i			0.0537988i
$856$	17.2684	−	2.73823i	0.590223	−	0.0935908i
$857$		−	20.6632i		−	0.705843i	−0.935653	−	0.352922i	$-0.885188\pi$
$857$		−	20.6632i		−	0.705843i	0.935653	−	0.352922i	$-0.114812\pi$
$858$	−0.0670696	−	1.27830i	−0.00228972	−	0.0436404i
$859$			20.8182i			0.710309i	0.934808	+	0.355154i	$0.115572\pi$
$859$			20.8182i			0.710309i	−0.934808	+	0.355154i	$0.884428\pi$
$860$	6.75742	−	0.711052i	0.230426	−	0.0242467i
$861$	15.8788	+	18.7887i	0.541148	+	0.640318i
$862$	−1.63890	−	31.2362i	−0.0558211	−	1.06391i
$863$		−	30.4131i		−	1.03527i	−0.855601	−	0.517637i	$-0.826812\pi$
$863$		−	30.4131i		−	1.03527i	0.855601	−	0.517637i	$-0.173188\pi$
$864$	−8.25643	−	30.7766i	−0.280890	−	1.04704i
$865$	13.5600			0.461054
$866$	−0.858100	−	16.3548i	−0.0291594	−	0.555758i
$867$		−	24.8941i		−	0.845447i
$868$	−17.4756	−	16.7534i	−0.593161	−	0.568646i
$869$			5.64907i			0.191632i
$870$	10.0570	−	0.527670i	0.340965	−	0.0178897i
$871$	−4.18167			−0.141690
$872$	7.14951	+	45.0878i	0.242113	+	1.52687i
$873$			6.63795i			0.224661i
$874$	−0.0421329	+	0.00221062i	−0.00142517	+	7.47754e-5i
$875$	15.7237	+	18.6052i	0.531559	+	0.628971i
$876$	27.1878	−	2.86084i	0.918590	−	0.0966589i
$877$			8.60597i			0.290603i	0.989387	+	0.145301i	$0.0464152\pi$
$877$			8.60597i			0.290603i	−0.989387	+	0.145301i	$0.953585\pi$
$878$	53.9832	−	2.83238i	1.82184	−	0.0955882i
$879$		−	44.4727i		−	1.50003i
$880$	−2.45017	+	0.521414i	−0.0825953	+	0.0175769i
$881$			22.7259i			0.765657i	0.923820	+	0.382828i	$0.125050\pi$
$881$			22.7259i			0.765657i	−0.923820	+	0.382828i	$0.874950\pi$
$882$	−0.891066	+	7.70995i	−0.0300038	+	0.259608i
$883$	26.0737			0.877449			0.438724	−	0.898622i	$-0.355430\pi$
$883$	26.0737			0.877449			0.438724	+	0.898622i	$0.355430\pi$
$884$	0.110174	+	1.04703i	0.00370556	+	0.0352155i
$885$	1.20067			0.0403602
$886$	21.6584	−	1.13637i	0.727628	−	0.0381771i
$887$	−18.7828			−0.630664			−0.315332	−	0.948981i	$-0.602116\pi$
$887$	−18.7828			−0.630664			−0.315332	+	0.948981i	$0.602116\pi$
$888$	8.96070	−	1.42089i	0.300702	−	0.0476818i
$889$	23.2480	−	19.6475i	0.779713	−	0.658954i
$890$	−0.920387	−	17.5419i	−0.0308515	−	0.588007i
$891$	−3.66848			−0.122899
$892$	1.29446	−	0.136210i	0.0433418	−	0.00456065i
$893$		−	5.06809i		−	0.169597i
$894$	−33.1407	+	1.73882i	−1.10839	+	0.0581549i
$895$	−3.37620			−0.112854
$896$	26.2373	+	14.4086i	0.876525	+	0.481356i
$897$	−0.0227969			−0.000761166
$898$	32.9095	−	1.72669i	1.09820	−	0.0576204i
$899$			21.2491i			0.708696i
$900$	−6.14275	+	0.646373i	−0.204758	+	0.0215458i
$901$	−0.615551			−0.0205070
$902$	0.281411	+	5.36349i	0.00936996	+	0.178585i
$903$	−9.92239	+	8.38565i	−0.330196	+	0.279057i
$904$	−7.72842	+	1.22549i	−0.257044	+	0.0407590i
$905$	−13.8236			−0.459513
$906$	−18.4175	+	0.966327i	−0.611881	+	0.0321041i
$907$	−2.93997			−0.0976201			−0.0488101	−	0.998808i	$-0.515543\pi$
$907$	−2.93997			−0.0976201			−0.0488101	+	0.998808i	$0.515543\pi$
$908$	−4.79761	−	45.5937i	−0.159214	−	1.51308i
$909$	−6.03785			−0.200263
$910$	−2.63836	−	2.80904i	−0.0874609	−	0.0931188i
$911$			37.3247i			1.23662i	0.785934	+	0.618311i	$0.212183\pi$
$911$			37.3247i			1.23662i	−0.785934	+	0.618311i	$0.787817\pi$
$912$	−11.3459	+	2.41448i	−0.375700	+	0.0799516i
$913$		−	0.882503i		−	0.0292066i
$914$	10.9388	−	0.573935i	0.361824	−	0.0189841i
$915$		−	8.16248i		−	0.269843i
$916$	18.5693	−	1.95396i	0.613546	−	0.0645606i
$917$	21.9213	−	18.5262i	0.723905	−	0.611790i
$918$	4.18770	−	0.219719i	0.138215	−	0.00725182i
$919$		−	8.61037i		−	0.284030i	−0.989865	−	0.142015i	$-0.954642\pi$
$919$		−	8.61037i		−	0.284030i	0.989865	−	0.142015i	$-0.0453581\pi$
$920$	0.00698691	+	0.0440624i	0.000230351	+	0.00145269i
$921$	−33.2811			−1.09665
$922$	32.0561	−	1.68191i	1.05571	−	0.0553908i
$923$		−	14.9594i		−	0.492394i
$924$	3.31451	−	3.45741i	0.109040	−	0.113740i
$925$		−	8.48808i		−	0.279086i
$926$	−1.13042	−	21.5451i	−0.0371480	−	0.708015i
$927$	3.47886			0.114261
$928$	−6.80769	−	25.3762i	−0.223473	−	0.833016i
$929$		−	55.5422i		−	1.82228i	−0.412096	−	0.911140i	$-0.635203\pi$
$929$		−	55.5422i		−	1.82228i	0.412096	−	0.911140i	$-0.364797\pi$
$930$	−0.519776	−	9.90656i	−0.0170441	−	0.324849i
$931$	13.4459	+	2.27326i	0.440672	+	0.0745029i
$932$	−19.0211	+	2.00151i	−0.623058	+	0.0655615i
$933$			32.0484i			1.04922i
$934$	−2.49801	−	47.6103i	−0.0817374	−	1.55786i
$935$		−	0.329667i		−	0.0107813i
$936$	2.19014	−	0.347288i	0.0715871	−	0.0113515i
$937$		−	29.4465i		−	0.961974i	−0.876728	−	0.480987i	$-0.840278\pi$
$937$		−	29.4465i		−	0.961974i	0.876728	−	0.480987i	$-0.159722\pi$
$938$	−10.7118	−	11.4047i	−0.349751	−	0.372377i
$939$	3.07109			0.100221
$940$	−5.32960	+	0.560809i	−0.173832	+	0.0182916i
$941$	−14.0302			−0.457371			−0.228686	−	0.973500i	$-0.573443\pi$
$941$	−14.0302			−0.457371			−0.228686	+	0.973500i	$0.573443\pi$
$942$	1.50404	+	28.6659i	0.0490042	+	0.933986i
$943$	0.0956512			0.00311483
$944$	−0.651996	−	3.06379i	−0.0212207	−	0.0997179i
$945$	−11.7239	+	9.90819i	−0.381380	+	0.322314i
$946$	−2.83248	+	0.148614i	−0.0920919	+	0.00483186i
$947$	46.5895			1.51396			0.756978	−	0.653440i	$-0.226675\pi$
$947$	46.5895			1.51396			0.756978	+	0.653440i	$0.226675\pi$
$948$	27.5087	−	2.89461i	0.893440	−	0.0940126i
$949$			9.18228i			0.298069i
$950$	0.568627	+	10.8376i	0.0184487	+	0.351619i
$951$	48.4862			1.57227
$952$	−2.57336	+	2.98255i	−0.0834030	+	0.0966651i
$953$	−42.9548			−1.39144			−0.695721	−	0.718312i	$-0.744915\pi$
$953$	−42.9548			−1.39144			−0.695721	+	0.718312i	$0.744915\pi$
$954$	0.0679320	+	1.29474i	0.00219938	+	0.0419186i
$955$		−	13.7709i		−	0.445617i
$956$	3.40421	+	32.3516i	0.110100	+	1.04633i
$957$	−4.20396			−0.135895
$958$	38.9042	−	2.04122i	1.25694	−	0.0659488i
$959$	−6.27570	−	7.42577i	−0.202653	−	0.239790i
$960$	3.79455	+	11.6642i	0.122469	+	0.376459i
$961$	−10.0688			−0.324801
$962$	0.159668	+	3.04315i	0.00514789	+	0.0981151i
$963$	4.84641			0.156173
$964$	−3.76251	−	35.7567i	−0.121182	−	1.15165i
$965$	14.4850			0.466288
$966$	−0.0583964	−	0.0621741i	−0.00187887	−	0.00200042i
$967$		−	13.9605i		−	0.448940i	−0.974481	−	0.224470i	$-0.927935\pi$
$967$		−	13.9605i		−	0.448940i	0.974481	−	0.224470i	$-0.0720652\pi$
$968$	−29.6960	+	4.70885i	−0.954465	+	0.151348i
$969$		−	1.52657i		−	0.0490406i
$970$	−0.646173	−	12.3156i	−0.0207474	−	0.395430i
$971$		−	12.7064i		−	0.407767i	−0.978995	−	0.203884i	$-0.934644\pi$
$971$		−	12.7064i		−	0.407767i	0.978995	−	0.203884i	$-0.0653564\pi$
$972$	−1.65710	−	15.7481i	−0.0531516	−	0.505122i
$973$	−29.3896	+	24.8379i	−0.942189	+	0.796267i
$974$	−0.977980	−	18.6396i	−0.0313365	−	0.597252i
$975$			5.86392i			0.187796i
$976$	−20.8284	+	4.43243i	−0.666701	+	0.141879i
$977$	45.8920			1.46821			0.734107	−	0.679034i	$-0.237601\pi$
$977$	45.8920			1.46821			0.734107	+	0.679034i	$0.237601\pi$
$978$	0.629907	+	12.0056i	0.0201422	+	0.383897i
$979$			7.33274i			0.234355i
$980$	0.902698	−	14.3913i	0.0288356	−	0.459712i
$981$			12.6540i			0.404010i
$982$	−11.4100	+	0.598659i	−0.364109	+	0.0191040i
$983$	34.2113			1.09117			0.545586	−	0.838055i	$-0.316307\pi$
$983$	34.2113			1.09117			0.545586	+	0.838055i	$0.316307\pi$
$984$	25.9738	−	4.11863i	0.828015	−	0.131297i
$985$		−	7.62520i		−	0.242959i
$986$	3.45289	−	0.181166i	0.109962	−	0.00576949i
$987$	7.82582	−	6.61379i	0.249099	−	0.210519i
$988$	−0.407729	−	3.87482i	−0.0129716	−	0.123274i
$989$			0.0505137i			0.00160624i
$990$	−0.693414	+	0.0363819i	−0.0220381	+	0.00115629i
$991$			51.9670i			1.65079i	0.564559	+	0.825393i	$0.309046\pi$
$991$			51.9670i			1.65079i	−0.564559	+	0.825393i	$0.690954\pi$
$992$	−24.9966	+	6.70584i	−0.793642	+	0.212910i
$993$			21.0899i			0.669266i
$994$	40.7988	−	38.3199i	1.29406	−	1.21543i
$995$	21.8573			0.692923
$996$	−4.29743	+	0.452198i	−0.136169	+	0.0143285i
$997$	−6.95041			−0.220122			−0.110061	−	0.993925i	$-0.535105\pi$
$997$	−6.95041			−0.220122			−0.110061	+	0.993925i	$0.535105\pi$
$998$	−36.7670	+	1.92908i	−1.16384	+	0.0610641i
$999$	12.1378			0.384024

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	728.2.h.b.27.47	yes	48
4.3	odd	2		2912.2.h.b.2575.35		48
7.6	odd	2		728.2.h.a.27.47	✓	48
8.3	odd	2		728.2.h.a.27.48	yes	48
8.5	even	2		2912.2.h.a.2575.35		48
28.27	even	2		2912.2.h.a.2575.14		48
56.13	odd	2		2912.2.h.b.2575.14		48
56.27	even	2	inner	728.2.h.b.27.48	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
728.2.h.a.27.47	✓	48	7.6	odd	2
728.2.h.a.27.48	yes	48	8.3	odd	2
728.2.h.b.27.47	yes	48	1.1	even	1	trivial
728.2.h.b.27.48	yes	48	56.27	even	2	inner
2912.2.h.a.2575.14		48	28.27	even	2
2912.2.h.a.2575.35		48	8.5	even	2
2912.2.h.b.2575.14		48	56.13	odd	2
2912.2.h.b.2575.35		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 728 = 2^{3} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	728.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41227 - 0.0740988i) q^{2} -1.48862i q^{3} +(1.98902 - 0.209295i) q^{4} -1.02997 q^{5} +(-0.110305 - 2.10234i) q^{6} +(1.70779 + 2.02076i) q^{7} +(2.79352 - 0.442965i) q^{8} +0.784007 q^{9} +(-1.45459 + 0.0763194i) q^{10} +0.608038 q^{11} +(-0.311561 - 2.96090i) q^{12} +1.00000 q^{13} +(2.56160 + 2.72731i) q^{14} +1.53323i q^{15} +(3.91239 - 0.832584i) q^{16} +0.526406i q^{17} +(1.10723 - 0.0580940i) q^{18} -1.94810i q^{19} +(-2.04863 + 0.215567i) q^{20} +(3.00814 - 2.54225i) q^{21} +(0.858714 - 0.0450549i) q^{22} -0.0153141i q^{23} +(-0.659408 - 4.15850i) q^{24} -3.93917 q^{25} +(1.41227 - 0.0740988i) q^{26} -5.63295i q^{27} +(3.81976 + 3.66189i) q^{28} -4.64455i q^{29} +(0.113611 + 2.16534i) q^{30} -4.57506 q^{31} +(5.46366 - 1.46574i) q^{32} -0.905138i q^{33} +(0.0390061 + 0.743428i) q^{34} +(-1.75897 - 2.08131i) q^{35} +(1.55940 - 0.164089i) q^{36} +2.15479i q^{37} +(-0.144352 - 2.75125i) q^{38} -1.48862i q^{39} +(-2.87724 + 0.456240i) q^{40} +6.24596i q^{41} +(4.05993 - 3.81325i) q^{42} -3.29851 q^{43} +(1.20940 - 0.127259i) q^{44} -0.807502 q^{45} +(-0.00113476 - 0.0216276i) q^{46} +2.60155 q^{47} +(-1.23940 - 5.82407i) q^{48} +(-1.16691 + 6.90205i) q^{49} +(-5.56317 + 0.291887i) q^{50} +0.783619 q^{51} +(1.98902 - 0.209295i) q^{52} +1.16935i q^{53} +(-0.417395 - 7.95526i) q^{54} -0.626260 q^{55} +(5.66588 + 4.88854i) q^{56} -2.89999 q^{57} +(-0.344155 - 6.55936i) q^{58} -0.783099i q^{59} +(0.320898 + 3.04963i) q^{60} -5.32371 q^{61} +(-6.46122 + 0.339006i) q^{62} +(1.33892 + 1.58429i) q^{63} +(7.60756 - 2.47487i) q^{64} -1.02997 q^{65} +(-0.0670696 - 1.27830i) q^{66} -4.18167 q^{67} +(0.110174 + 1.04703i) q^{68} -0.0227969 q^{69} +(-2.63836 - 2.80904i) q^{70} -14.9594i q^{71} +(2.19014 - 0.347288i) q^{72} +9.18228i q^{73} +(0.159668 + 3.04315i) q^{74} +5.86392i q^{75} +(-0.407729 - 3.87482i) q^{76} +(1.03840 + 1.22870i) q^{77} +(-0.110305 - 2.10234i) q^{78} +9.29066i q^{79} +(-4.02964 + 0.857535i) q^{80} -6.03331 q^{81} +(0.462818 + 8.82099i) q^{82} -1.45140i q^{83} +(5.45117 - 5.68618i) q^{84} -0.542182i q^{85} +(-4.65839 + 0.244416i) q^{86} -6.91397 q^{87} +(1.69857 - 0.269340i) q^{88} +12.0597i q^{89} +(-1.14041 + 0.0598349i) q^{90} +(1.70779 + 2.02076i) q^{91} +(-0.00320517 - 0.0304600i) q^{92} +6.81053i q^{93} +(3.67409 - 0.192772i) q^{94} +2.00649i q^{95} +(-2.18193 - 8.13332i) q^{96} +8.46670i q^{97} +(-1.13655 + 9.83403i) q^{98} +0.476706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} + q^{4} + 10 q^{6} - 5 q^{8} - 48 q^{9} - 4 q^{11} - 10 q^{12} + 48 q^{13} - 6 q^{14} + 5 q^{16} - 15 q^{18} + 22 q^{20} - 6 q^{22} + 48 q^{25} + q^{26} - 26 q^{28} - 26 q^{30} - 19 q^{32}+ \cdots + 20 q^{99}+O(q^{100}) \) 48 * q + q^2 + q^4 + 10 * q^6 - 5 * q^8 - 48 * q^9 - 4 * q^11 - 10 * q^12 + 48 * q^13 - 6 * q^14 + 5 * q^16 - 15 * q^18 + 22 * q^20 - 6 * q^22 + 48 * q^25 + q^26 - 26 * q^28 - 26 * q^30 - 19 * q^32 - 36 * q^34 + 12 * q^35 - 5 * q^36 + 10 * q^38 + 48 * q^40 + 39 * q^42 - 4 * q^43 - 30 * q^44 - 24 * q^45 + 2 * q^46 - 48 * q^48 + 11 * q^50 - 40 * q^51 + q^52 - 62 * q^54 - 14 * q^56 + 2 * q^58 + 18 * q^60 + 36 * q^62 - 20 * q^63 - 11 * q^64 - 32 * q^66 - 4 * q^67 - 62 * q^68 - 37 * q^70 + 13 * q^72 - 44 * q^74 + 48 * q^76 + 20 * q^77 + 10 * q^78 - 32 * q^80 + 64 * q^81 + 50 * q^82 - 45 * q^84 + 2 * q^86 + 40 * q^87 - 66 * q^88 - 74 * q^90 - 24 * q^92 + 26 * q^94 + 84 * q^96 - 20 * q^98 + 20 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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