LMFDB - Embedded newform 460.2.o.b.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(19,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 15]))

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

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

chi := DirichletCharacter("460.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.o (of order $22$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$64$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			19.1
Character	$\chi$	$=$	460.19
Dual form			460.2.o.b.339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41365 - 0.0397971i) q^{2} +(2.67003 - 0.783991i) q^{3} +(1.99683 + 0.112519i) q^{4} +(1.97695 + 1.04482i) q^{5} +(-3.80569 + 1.00203i) q^{6} +(0.790909 - 0.113716i) q^{7} +(-2.81835 - 0.238531i) q^{8} +(3.99064 - 2.56463i) q^{9} +O(q^{10})$	\(q+(-1.41365 - 0.0397971i) q^{2} +(2.67003 - 0.783991i) q^{3} +(1.99683 + 0.112519i) q^{4} +(1.97695 + 1.04482i) q^{5} +(-3.80569 + 1.00203i) q^{6} +(0.790909 - 0.113716i) q^{7} +(-2.81835 - 0.238531i) q^{8} +(3.99064 - 2.56463i) q^{9} +(-2.75315 - 1.55569i) q^{10} +(1.99109 - 4.35987i) q^{11} +(5.41981 - 1.26507i) q^{12} +(-5.90595 - 0.849148i) q^{13} +(-1.12260 + 0.129278i) q^{14} +(6.09765 + 1.23979i) q^{15} +(3.97468 + 0.449362i) q^{16} +(1.26656 + 1.46169i) q^{17} +(-5.74345 + 3.46668i) q^{18} +(0.618802 - 0.714136i) q^{19} +(3.83008 + 2.30878i) q^{20} +(2.02260 - 0.923689i) q^{21} +(-2.98822 + 6.08411i) q^{22} +(-2.20929 + 4.25664i) q^{23} +(-7.71208 + 1.57268i) q^{24} +(2.81670 + 4.13113i) q^{25} +(8.31518 + 1.43544i) q^{26} +(3.17754 - 3.66708i) q^{27} +(1.59211 - 0.138079i) q^{28} +(-5.41409 - 6.24819i) q^{29} +(-8.57063 - 1.99530i) q^{30} +(-1.72567 + 5.87709i) q^{31} +(-5.60094 - 0.793423i) q^{32} +(1.89816 - 13.2020i) q^{33} +(-1.73231 - 2.11673i) q^{34} +(1.68240 + 0.601548i) q^{35} +(8.25722 - 4.67212i) q^{36} +(-5.66971 + 3.64370i) q^{37} +(-0.903192 + 0.984914i) q^{38} +(-16.4348 + 2.36296i) q^{39} +(-5.32253 - 3.41624i) q^{40} +(5.17715 + 3.32716i) q^{41} +(-2.89601 + 1.22528i) q^{42} +(2.12347 + 7.23187i) q^{43} +(4.46643 - 8.48189i) q^{44} +(10.5689 - 0.900651i) q^{45} +(3.29258 - 5.92950i) q^{46} +9.15791 q^{47} +(10.9648 - 1.91630i) q^{48} +(-6.10385 + 1.79225i) q^{49} +(-3.81743 - 5.95208i) q^{50} +(4.52770 + 2.90978i) q^{51} +(-11.6977 - 2.36014i) q^{52} +(-0.828412 - 5.76174i) q^{53} +(-4.63788 + 5.05752i) q^{54} +(8.49157 - 6.53894i) q^{55} +(-2.25618 + 0.131834i) q^{56} +(1.09234 - 2.39190i) q^{57} +(7.40499 + 9.04824i) q^{58} +(1.41915 + 0.204043i) q^{59} +(12.0365 + 3.16175i) q^{60} +(1.54500 - 5.26179i) q^{61} +(2.67339 - 8.23950i) q^{62} +(2.86460 - 2.48219i) q^{63} +(7.88621 + 1.34453i) q^{64} +(-10.7886 - 7.84939i) q^{65} +(-3.20874 + 18.5875i) q^{66} +(-1.33870 + 0.611366i) q^{67} +(2.36464 + 3.06126i) q^{68} +(-2.56170 + 13.0974i) q^{69} +(-2.35440 - 0.917335i) q^{70} +(8.87792 - 4.05441i) q^{71} +(-11.8588 + 6.27614i) q^{72} +(-2.40346 - 2.08261i) q^{73} +(8.16001 - 4.92529i) q^{74} +(10.7594 + 8.82196i) q^{75} +(1.31600 - 1.35638i) q^{76} +(1.07898 - 3.67468i) q^{77} +(23.3271 - 2.68636i) q^{78} +(-1.00145 + 6.96520i) q^{79} +(7.38826 + 5.04120i) q^{80} +(-0.302627 + 0.662660i) q^{81} +(-7.18629 - 4.90948i) q^{82} +(-3.07852 - 4.79028i) q^{83} +(4.14272 - 1.61687i) q^{84} +(0.976729 + 4.21302i) q^{85} +(-2.71404 - 10.3079i) q^{86} +(-19.3543 - 12.4382i) q^{87} +(-6.65154 + 11.8127i) q^{88} +(-1.73215 - 5.89918i) q^{89} +(-14.9766 + 0.852596i) q^{90} -4.76763 q^{91} +(-4.89054 + 8.25122i) q^{92} +17.0449i q^{93} +(-12.9461 - 0.364459i) q^{94} +(1.96949 - 0.765276i) q^{95} +(-15.5767 + 2.27262i) q^{96} +(7.73828 + 4.97309i) q^{97} +(8.70005 - 2.29071i) q^{98} +(-3.23574 - 22.5051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	$ 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) $ 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{15}{22}\right)$

Coefficient data

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

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

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

$2$	−1.41365	−	0.0397971i	−0.999604	−	0.0281408i
$2$	−1.41365	−	0.0397971i	−0.999604	−	0.0281408i
$3$	2.67003	−	0.783991i	1.54154	−	0.452637i	0.602982	−	0.797755i	$-0.293979\pi$
$3$	2.67003	−	0.783991i	1.54154	−	0.452637i	0.938559	+	0.345118i	$0.112161\pi$
$4$	1.99683	+	0.112519i	0.998416	+	0.0562594i
$5$	1.97695	+	1.04482i	0.884121	+	0.467258i
$5$	1.97695	+	1.04482i	0.884121	+	0.467258i
$6$	−3.80569	+	1.00203i	−1.55367	+	0.409078i
$7$	0.790909	−	0.113716i	0.298935	−	0.0429804i	0.00878480	−	0.999961i	$-0.497204\pi$
$7$	0.790909	−	0.113716i	0.298935	−	0.0429804i	0.290151	+	0.956981i	$0.406295\pi$
$8$	−2.81835	−	0.238531i	−0.996438	−	0.0843333i
$9$	3.99064	−	2.56463i	1.33021	−	0.854877i
$10$	−2.75315	−	1.55569i	−0.870622	−	0.491953i
$11$	1.99109	−	4.35987i	0.600335	−	1.31455i	−0.328657	−	0.944449i	$-0.606596\pi$
$11$	1.99109	−	4.35987i	0.600335	−	1.31455i	0.928992	−	0.370101i	$-0.120677\pi$
$12$	5.41981	−	1.26507i	1.56456	−	0.365194i
$13$	−5.90595	−	0.849148i	−1.63802	−	0.235511i	−0.739089	−	0.673608i	$-0.764744\pi$
$13$	−5.90595	−	0.849148i	−1.63802	−	0.235511i	−0.898928	+	0.438097i	$0.855653\pi$
$14$	−1.12260	+	0.129278i	−0.300027	+	0.0345511i
$15$	6.09765	+	1.23979i	1.57441	+	0.320111i
$16$	3.97468	+	0.449362i	0.993670	+	0.112340i
$17$	1.26656	+	1.46169i	0.307186	+	0.354512i	0.888262	−	0.459338i	$-0.151913\pi$
$17$	1.26656	+	1.46169i	0.307186	+	0.354512i	−0.581075	+	0.813850i	$0.697368\pi$
$18$	−5.74345	+	3.46668i	−1.35374	+	0.817105i
$19$	0.618802	−	0.714136i	0.141963	−	0.163834i	−0.680315	−	0.732919i	$-0.738157\pi$
$19$	0.618802	−	0.714136i	0.141963	−	0.163834i	0.822278	+	0.569085i	$0.192703\pi$
$20$	3.83008	+	2.30878i	0.856433	+	0.516258i
$21$	2.02260	−	0.923689i	0.441367	−	0.201565i
$22$	−2.98822	+	6.08411i	−0.637090	+	1.29714i
$23$	−2.20929	+	4.25664i	−0.460670	+	0.887572i
$23$	−2.20929	+	4.25664i	−0.460670	+	0.887572i
$24$	−7.71208	+	1.57268i	−1.57422	+	0.321022i
$25$	2.81670	+	4.13113i	0.563340	+	0.826225i
$26$	8.31518	+	1.43544i	1.63074	+	0.281513i
$27$	3.17754	−	3.66708i	0.611518	−	0.705730i
$28$	1.59211	−	0.138079i	0.300880	−	0.0260944i
$29$	−5.41409	−	6.24819i	−1.00537	−	1.16026i	−0.987048	−	0.160428i	$-0.948713\pi$
$29$	−5.41409	−	6.24819i	−1.00537	−	1.16026i	−0.0183237	−	0.999832i	$-0.505833\pi$
$30$	−8.57063	−	1.99530i	−1.56478	−	0.364290i
$31$	−1.72567	+	5.87709i	−0.309940	+	1.05556i	0.646327	+	0.763061i	$0.276304\pi$
$31$	−1.72567	+	5.87709i	−0.309940	+	1.05556i	−0.956267	+	0.292497i	$0.905514\pi$
$32$	−5.60094	−	0.793423i	−0.990115	−	0.140259i
$33$	1.89816	−	13.2020i	0.330427	−	2.29817i
$34$	−1.73231	−	2.11673i	−0.297088	−	0.363016i
$35$	1.68240	+	0.601548i	0.284378	+	0.101680i
$36$	8.25722	−	4.67212i	1.37620	−	0.778686i
$37$	−5.66971	+	3.64370i	−0.932095	+	0.599021i	−0.916143	−	0.400852i	$-0.868714\pi$
$37$	−5.66971	+	3.64370i	−0.932095	+	0.599021i	−0.0159517	+	0.999873i	$0.505078\pi$
$38$	−0.903192	+	0.984914i	−0.146517	+	0.159774i
$39$	−16.4348	+	2.36296i	−2.63167	+	0.378377i
$40$	−5.32253	−	3.41624i	−0.841566	−	0.540154i
$41$	5.17715	+	3.32716i	0.808536	+	0.519614i	0.878391	−	0.477943i	$-0.158617\pi$
$41$	5.17715	+	3.32716i	0.808536	+	0.519614i	−0.0698552	+	0.997557i	$0.522254\pi$
$42$	−2.89601	+	1.22528i	−0.446864	+	0.189065i
$43$	2.12347	+	7.23187i	0.323826	+	1.10285i	0.947125	+	0.320866i	$0.103974\pi$
$43$	2.12347	+	7.23187i	0.323826	+	1.10285i	−0.623299	+	0.781984i	$0.714208\pi$
$44$	4.46643	−	8.48189i	0.673340	−	1.27869i
$45$	10.5689	−	0.900651i	1.57552	−	0.134261i
$46$	3.29258	−	5.92950i	0.485464	−	0.874257i
$47$	9.15791			1.33582			0.667909	−	0.744243i	$-0.267189\pi$
$47$	9.15791			1.33582			0.667909	+	0.744243i	$0.267189\pi$
$48$	10.9648	−	1.91630i	1.58263	−	0.276595i
$49$	−6.10385	+	1.79225i	−0.871978	+	0.256036i
$50$	−3.81743	−	5.95208i	−0.539866	−	0.841751i
$51$	4.52770	+	2.90978i	0.634005	+	0.407450i
$52$	−11.6977	−	2.36014i	−1.62217	−	0.327292i
$53$	−0.828412	−	5.76174i	−0.113791	−	0.791435i	−0.964174	−	0.265271i	$-0.914539\pi$
$53$	−0.828412	−	5.76174i	−0.113791	−	0.791435i	0.850383	−	0.526165i	$-0.176370\pi$
$54$	−4.63788	+	5.05752i	−0.631136	+	0.688242i
$55$	8.49157	−	6.53894i	1.14500	−	0.881710i
$56$	−2.25618	+	0.131834i	−0.301495	+	0.0176171i
$57$	1.09234	−	2.39190i	0.144684	−	0.316814i
$58$	7.40499	+	9.04824i	0.972322	+	1.18809i
$59$	1.41915	+	0.204043i	0.184758	+	0.0265642i	0.234073	−	0.972219i	$-0.424795\pi$
$59$	1.41915	+	0.204043i	0.184758	+	0.0265642i	−0.0493148	+	0.998783i	$0.515704\pi$
$60$	12.0365	+	3.16175i	1.55390	+	0.408180i
$61$	1.54500	−	5.26179i	0.197817	−	0.673703i	−0.799511	−	0.600651i	$-0.794908\pi$
$61$	1.54500	−	5.26179i	0.197817	−	0.673703i	0.997328	−	0.0730516i	$-0.0232738\pi$
$62$	2.67339	−	8.23950i	0.339521	−	1.04642i
$63$	2.86460	−	2.48219i	0.360905	−	0.312726i
$64$	7.88621	+	1.34453i	0.985776	+	0.168066i
$65$	−10.7886	−	7.84939i	−1.33816	−	0.973597i
$66$	−3.20874	+	18.5875i	−0.394968	+	2.28796i
$67$	−1.33870	+	0.611366i	−0.163549	+	0.0746902i	−0.495507	−	0.868604i	$-0.665018\pi$
$67$	−1.33870	+	0.611366i	−0.163549	+	0.0746902i	0.331959	+	0.943294i	$0.392291\pi$
$68$	2.36464	+	3.06126i	0.286755	+	0.371232i
$69$	−2.56170	+	13.0974i	−0.308393	+	1.57674i
$70$	−2.35440	−	0.917335i	−0.281404	−	0.109642i
$71$	8.87792	−	4.05441i	1.05362	−	0.481170i	0.188151	−	0.982140i	$-0.439751\pi$
$71$	8.87792	−	4.05441i	1.05362	−	0.481170i	0.865465	+	0.500970i	$0.167023\pi$
$72$	−11.8588	+	6.27614i	−1.39757	+	0.739650i
$73$	−2.40346	−	2.08261i	−0.281304	−	0.243751i	0.502768	−	0.864421i	$-0.332315\pi$
$73$	−2.40346	−	2.08261i	−0.281304	−	0.243751i	−0.784072	+	0.620670i	$0.786860\pi$
$74$	8.16001	−	4.92529i	0.948582	−	0.572554i
$75$	10.7594	+	8.82196i	1.24239	+	1.01867i
$76$	1.31600	−	1.35638i	0.150955	−	0.155588i
$77$	1.07898	−	3.67468i	0.122961	−	0.418768i
$78$	23.3271	−	2.68636i	2.64128	−	0.304170i
$79$	−1.00145	+	6.96520i	−0.112671	+	0.783647i	0.852631	+	0.522513i	$0.175005\pi$
$79$	−1.00145	+	6.96520i	−0.112671	+	0.783647i	−0.965303	+	0.261134i	$0.915904\pi$
$80$	7.38826	+	5.04120i	0.826032	+	0.563623i
$81$	−0.302627	+	0.662660i	−0.0336252	+	0.0736289i
$82$	−7.18629	−	4.90948i	−0.793593	−	0.542161i
$83$	−3.07852	−	4.79028i	−0.337912	−	0.525801i	0.630163	−	0.776463i	$-0.282988\pi$
$83$	−3.07852	−	4.79028i	−0.337912	−	0.525801i	−0.968075	+	0.250662i	$0.919352\pi$
$84$	4.14272	−	1.61687i	0.452008	−	0.176415i
$85$	0.976729	+	4.21302i	0.105941	+	0.456966i
$86$	−2.71404	−	10.3079i	−0.292662	−	1.11153i
$87$	−19.3543	−	12.4382i	−2.07500	−	1.33352i
$88$	−6.65154	+	11.8127i	−0.709057	+	1.25924i
$89$	−1.73215	−	5.89918i	−0.183608	−	0.625312i	−0.998928	−	0.0463003i	$-0.985257\pi$
$89$	−1.73215	−	5.89918i	−0.183608	−	0.625312i	0.815320	−	0.579011i	$-0.196561\pi$
$90$	−14.9766	+	0.852596i	−1.57867	+	0.0898715i
$91$	−4.76763			−0.499783
$92$	−4.89054	+	8.25122i	−0.509874	+	0.860249i
$93$			17.0449i			1.76748i
$94$	−12.9461	−	0.364459i	−1.33529	−	0.0375910i
$95$	1.96949	−	0.765276i	0.202065	−	0.0785157i
$96$	−15.5767	+	2.27262i	−1.58979	+	0.231948i
$97$	7.73828	+	4.97309i	0.785703	+	0.504941i	0.870922	−	0.491421i	$-0.163522\pi$
$97$	7.73828	+	4.97309i	0.785703	+	0.504941i	−0.0852185	+	0.996362i	$0.527159\pi$
$98$	8.70005	−	2.29071i	0.878838	−	0.231396i
$99$	−3.23574	−	22.5051i	−0.325204	−	2.26185i
$100$	5.15965	+	8.56610i	0.515965	+	0.856610i
$101$	−5.28571	+	3.39692i	−0.525948	+	0.338006i	−0.776521	−	0.630091i	$-0.783017\pi$
$101$	−5.28571	+	3.39692i	−0.525948	+	0.338006i	0.250573	+	0.968098i	$0.419381\pi$
$102$	−6.28480	−	4.29361i	−0.622288	−	0.425130i
$103$	−9.68876	−	4.42471i	−0.954662	−	0.435980i	−0.123707	−	0.992319i	$-0.539478\pi$
$103$	−9.68876	−	4.42471i	−0.954662	−	0.435980i	−0.830955	+	0.556339i	$0.812206\pi$
$104$	16.4425	+	3.80195i	1.61232	+	0.372812i
$105$	4.96367	+	0.287160i	0.484405	+	0.0280240i
$106$	0.941788	+	8.17807i	0.0914745	+	0.794324i
$107$	−0.719395	+	2.45003i	−0.0695465	+	0.236854i	−0.986930	−	0.161152i	$-0.948479\pi$
$107$	−0.719395	+	2.45003i	−0.0695465	+	0.236854i	0.917383	+	0.398005i	$0.130297\pi$
$108$	6.75764	−	6.96501i	0.650254	−	0.670209i
$109$	−15.5442	+	13.4692i	−1.48887	+	1.29011i	−0.631538	+	0.775345i	$0.717576\pi$
$109$	−15.5442	+	13.4692i	−1.48887	+	1.29011i	−0.857331	+	0.514766i	$0.827879\pi$
$110$	−12.2644	+	8.90585i	−1.16936	+	0.849139i
$111$	−12.2817	+	14.1738i	−1.16572	+	1.34532i
$112$	3.19471	−	0.0965784i	0.301872	−	0.00912580i
$113$	−6.04320	−	13.2328i	−0.568496	−	1.24483i	−0.947594	−	0.319477i	$-0.896493\pi$
$113$	−6.04320	−	13.2328i	−0.568496	−	1.24483i	0.379098	−	0.925357i	$-0.376234\pi$
$114$	−1.63938	+	3.33784i	−0.153542	+	0.312617i
$115$	−8.81510	+	6.10688i	−0.822013	+	0.569469i
$116$	−10.1080	−	13.0858i	−0.938503	−	1.21498i
$117$	−25.7463	+	11.7579i	−2.38025	+	1.08702i
$118$	−1.99807	−	0.344924i	−0.183937	−	0.0317529i
$119$	1.16795	+	1.01203i	0.107066	+	0.0927731i
$120$	−16.8896	−	4.94863i	−1.54180	−	0.451746i
$121$	−7.84057	−	9.04850i	−0.712779	−	0.822591i
$122$	−2.39350	+	7.37686i	−0.216697	+	0.667869i
$123$	16.4316	+	4.82475i	1.48159	+	0.435033i
$124$	−4.10716	+	11.5414i	−0.368834	+	1.03645i
$125$	1.25220	+	11.1100i	0.112000	+	0.993708i
$126$	−4.14833	+	3.39495i	−0.369563	+	0.302446i
$127$	5.41839	−	11.8646i	0.480805	−	1.05282i	−0.501437	−	0.865194i	$-0.667195\pi$
$127$	5.41839	−	11.8646i	0.480805	−	1.05282i	0.982241	−	0.187621i	$-0.0600777\pi$
$128$	−11.0949	−	2.21454i	−0.980656	−	0.195740i
$129$	11.3394	+	17.6445i	0.998381	+	1.55351i
$130$	14.9389	+	11.5257i	1.31023	+	1.01087i
$131$	−2.02589	+	0.291279i	−0.177003	+	0.0254491i	−0.230246	−	0.973132i	$-0.573953\pi$
$131$	−2.02589	+	0.291279i	−0.177003	+	0.0254491i	0.0532436	+	0.998582i	$0.483044\pi$
$132$	5.27577	−	26.1485i	0.459197	−	2.27594i
$133$	0.408208	−	0.635184i	0.0353961	−	0.0550774i
$134$	1.91679	−	0.810983i	0.165586	−	0.0700582i
$135$	10.1133	−	3.92969i	0.870414	−	0.338214i
$136$	−3.22095	−	4.42167i	−0.276195	−	0.379155i
$137$	7.07892			0.604793			0.302396	−	0.953182i	$-0.402213\pi$
$137$	7.07892			0.604793			0.302396	+	0.953182i	$0.402213\pi$
$138$	4.14260	−	18.4133i	0.352642	−	1.56744i
$139$		−	10.9592i		−	0.929544i	−0.885430	−	0.464772i	$-0.846136\pi$
$139$		−	10.9592i		−	0.929544i	0.885430	−	0.464772i	$-0.153864\pi$
$140$	3.29179	+	1.39049i	0.278207	+	0.117518i
$141$	24.4519	−	7.17972i	2.05922	−	0.604641i
$142$	−12.7117	+	5.37822i	−1.06674	+	0.451330i
$143$	−15.4614	+	24.0585i	−1.29295	+	2.01187i
$144$	17.0140	−	8.40034i	1.41783	−	0.700028i
$145$	−4.17517	−	18.0091i	−0.346729	−	1.49558i
$146$	3.31478	+	3.03974i	0.274333	+	0.251571i
$147$	−14.8923	+	9.57072i	−1.22830	+	0.789379i
$148$	−11.7314	+	6.63791i	−0.964319	+	0.545633i
$149$	3.33881	+	1.52478i	0.273526	+	0.124915i	0.547456	−	0.836835i	$-0.315596\pi$
$149$	3.33881	+	1.52478i	0.273526	+	0.124915i	−0.273930	+	0.961750i	$0.588324\pi$
$150$	−14.8590	−	12.8994i	−1.21323	−	1.05323i
$151$	18.6853	+	2.68654i	1.52059	+	0.218627i	0.851420	−	0.524485i	$-0.175742\pi$
$151$	18.6853	+	2.68654i	1.52059	+	0.218627i	0.669167	+	0.743112i	$0.266651\pi$
$152$	−1.91434	+	1.86508i	−0.155274	+	0.151278i
$153$	8.80308	+	2.58482i	0.711687	+	0.208970i
$154$	−1.67155	+	5.15178i	−0.134697	+	0.415142i
$155$	−9.55208	+	9.81573i	−0.767242	+	0.788419i
$156$	−33.0834	+	2.86922i	−2.64879	+	0.229722i
$157$	−8.88949	+	10.2590i	−0.709459	+	0.818759i	−0.989998	−	0.141084i	$-0.954941\pi$
$157$	−8.88949	+	10.2590i	−0.709459	+	0.818759i	0.280539	+	0.959843i	$0.409487\pi$
$158$	1.69289	−	9.80653i	0.134679	−	0.780166i
$159$	−6.72903	−	14.7345i	−0.533647	−	1.16852i
$160$	−10.2438	−	7.42054i	−0.809844	−	0.586645i
$161$	−1.26330	+	3.61785i	−0.0995622	+	0.285126i
$162$	0.454181	−	0.924728i	0.0356838	−	0.0726535i
$163$	−2.18129	−	4.77636i	−0.170852	−	0.374113i	0.804765	−	0.593593i	$-0.202291\pi$
$163$	−2.18129	−	4.77636i	−0.170852	−	0.374113i	−0.975617	+	0.219480i	$0.929564\pi$
$164$	9.96354	+	7.22630i	0.778022	+	0.564279i
$165$	17.5463	−	24.1165i	1.36597	−	1.87746i
$166$	4.16133	+	6.89431i	0.322981	+	0.535102i
$167$	0.547813	+	0.632210i	0.0423911	+	0.0489219i	0.776549	−	0.630057i	$-0.216968\pi$
$167$	0.547813	+	0.632210i	0.0423911	+	0.0489219i	−0.734158	+	0.678979i	$0.762423\pi$
$168$	−5.92071	+	2.12083i	−0.456793	+	0.163625i
$169$	21.6858	+	6.36753i	1.66814	+	0.489810i
$170$	−1.21309	−	5.99462i	−0.0930398	−	0.459767i
$171$	0.637924	−	4.43686i	0.0487833	−	0.339295i
$172$	3.42649	+	14.6798i	0.261267	+	1.11932i
$173$	−6.69369	−	3.05691i	−0.508912	−	0.232412i	0.144374	−	0.989523i	$-0.453883\pi$
$173$	−6.69369	−	3.05691i	−0.508912	−	0.232412i	−0.653287	+	0.757111i	$0.726610\pi$
$174$	26.8653	+	18.3536i	2.03665	+	1.39138i
$175$	2.69752	+	2.94704i	0.203914	+	0.222775i
$176$	9.87309	−	16.4344i	0.744212	−	1.23879i
$177$	3.94914	−	0.567801i	0.296836	−	0.0426785i
$178$	2.21390	+	8.40833i	0.165939	+	0.630231i
$179$	−0.238588	+	0.371250i	−0.0178329	+	0.0277486i	−0.850056	−	0.526693i	$-0.823432\pi$
$179$	−0.238588	+	0.371250i	−0.0178329	+	0.0277486i	0.832223	+	0.554442i	$0.187068\pi$
$180$	21.2057	−	0.609249i	1.58058	−	0.0454108i
$181$	3.23322	+	11.0113i	0.240323	+	0.818465i	0.988007	+	0.154410i	$0.0493477\pi$
$181$	3.23322	+	11.0113i	0.240323	+	0.818465i	−0.747684	+	0.664055i	$0.768834\pi$
$182$	6.73978	+	0.189738i	0.499586	+	0.0140643i
$183$		−	15.2604i		−	1.12808i
$184$	7.24190	−	11.4697i	0.533880	−	0.845560i
$185$	−15.0158	+	1.27960i	−1.10398	+	0.0940781i
$186$	0.678339	−	24.0956i	0.0497382	−	1.76678i
$187$	8.89460	−	2.61169i	0.650438	−	0.190986i
$188$	18.2868	+	1.03044i	1.33370	+	0.0751523i
$189$	2.09614	−	3.26166i	0.152472	−	0.237251i
$190$	−2.81463	+	1.00346i	−0.204195	+	0.0727983i
$191$	0.817823	+	5.68808i	0.0591756	+	0.411575i	0.997781	+	0.0665825i	$0.0212096\pi$
$191$	0.817823	+	5.68808i	0.0591756	+	0.411575i	−0.938605	+	0.344993i	$0.887881\pi$
$192$	22.1105	−	2.59279i	1.59569	−	0.187119i
$193$	3.51481	+	5.46915i	0.253001	+	0.393678i	0.944402	−	0.328794i	$-0.106642\pi$
$193$	3.51481	+	5.46915i	0.253001	+	0.393678i	−0.691400	+	0.722472i	$0.743006\pi$
$194$	−10.7413	−	7.33819i	−0.771183	−	0.526851i
$195$	−34.9597	−	12.4999i	−2.50351	−	0.895138i
$196$	−12.3900	+	2.89203i	−0.885001	+	0.206573i
$197$	7.38241	+	1.06143i	0.525975	+	0.0756238i	0.400187	−	0.916433i	$-0.368945\pi$
$197$	7.38241	+	1.06143i	0.525975	+	0.0756238i	0.125788	+	0.992057i	$0.459854\pi$
$198$	3.67858	+	31.9432i	0.261425	+	2.27010i
$199$	−6.10207	−	1.79173i	−0.432564	−	0.127012i	0.0581995	−	0.998305i	$-0.481464\pi$
$199$	−6.10207	−	1.79173i	−0.432564	−	0.127012i	−0.490764	+	0.871293i	$0.663282\pi$
$200$	−6.95304	−	12.3148i	−0.491655	−	0.870790i
$201$	−3.09507	+	2.68189i	−0.218310	+	0.189166i
$202$	7.60735	−	4.59171i	0.535252	−	0.323072i
$203$	−4.99257	−	4.32608i	−0.350410	−	0.303632i
$204$	8.71366	+	6.31979i	0.610078	+	0.442474i
$205$	6.75872	+	11.9868i	0.472049	+	0.837197i
$206$	13.5205	+	6.64059i	0.942015	+	0.462672i
$207$	2.10022	+	22.6528i	0.145975	+	1.57448i
$208$	−23.0927	−	6.02900i	−1.60119	−	0.418036i
$209$	−1.88145	−	4.11980i	−0.130143	−	0.284973i
$210$	−7.00548	−	0.603485i	−0.483424	−	0.0416444i
$211$	−1.25181	−	1.08470i	−0.0861780	−	0.0746737i	0.610706	−	0.791857i	$-0.290886\pi$
$211$	−1.25181	−	1.08470i	−0.0861780	−	0.0746737i	−0.696885	+	0.717183i	$0.745431\pi$
$212$	−1.00590	−	11.5984i	−0.0690853	−	0.796584i
$213$	20.5257	−	17.7856i	1.40640	−	1.21865i
$214$	1.11448	−	3.43487i	0.0761842	−	0.234803i
$215$	−3.35801	+	16.5157i	−0.229014	+	1.12636i
$216$	−9.83014	+	9.57718i	−0.668857	+	0.651644i
$217$	−0.696531	+	4.84448i	−0.0472836	+	0.328865i
$218$	22.5102	−	18.4221i	1.52458	−	1.24770i
$219$	−8.05005	−	3.67633i	−0.543972	−	0.248424i
$220$	17.6920	−	12.1017i	1.19279	−	0.815896i
$221$	−6.23906	−	9.70816i	−0.419684	−	0.653041i
$222$	17.9261	−	19.5480i	1.20312	−	1.31198i
$223$	−1.76280	−	12.2605i	−0.118046	−	0.821027i	−0.959703	−	0.281015i	$-0.909329\pi$
$223$	−1.76280	−	12.2605i	−0.118046	−	0.821027i	0.841657	−	0.540012i	$-0.181580\pi$
$224$	−4.52005	+	0.00938811i	−0.302009	+	0.000627269i
$225$	21.8353	+	9.26206i	1.45568	+	0.617471i
$226$	8.01636	+	18.9470i	0.533241	+	1.26034i
$227$	−6.50492	−	22.1537i	−0.431746	−	1.47039i	−0.832406	−	0.554166i	$-0.813037\pi$
$227$	−6.50492	−	22.1537i	−0.431746	−	1.47039i	0.400659	−	0.916227i	$-0.368781\pi$
$228$	2.45036	−	4.65331i	0.162279	−	0.308173i
$229$		−	2.08567i		−	0.137825i	−0.997623	−	0.0689125i	$-0.978047\pi$
$229$		−	2.08567i		−	0.137825i	0.997623	−	0.0689125i	$-0.0219529\pi$
$230$	12.7045	−	8.28219i	0.837712	−	0.546112i
$231$		−	10.6574i		−	0.701205i
$232$	13.7684	+	18.9010i	0.903941	+	1.24091i
$233$	5.47980	+	18.6625i	0.358994	+	1.22262i	0.919042	+	0.394160i	$0.128964\pi$
$233$	5.47980	+	18.6625i	0.358994	+	1.22262i	−0.560048	+	0.828460i	$0.689217\pi$
$234$	36.8643	−	15.5970i	2.40989	−	1.01961i
$235$	18.1048	+	9.56838i	1.18103	+	0.624172i
$236$	2.81085	+	0.567121i	0.182971	+	0.0369164i
$237$	2.78677	+	19.3824i	0.181020	+	1.25902i
$238$	−1.61080	−	1.47715i	−0.104413	−	0.0957493i
$239$	9.38347	+	14.6010i	0.606966	+	0.944458i	0.999692	+	0.0248025i	$0.00789568\pi$
$239$	9.38347	+	14.6010i	0.606966	+	0.944458i	−0.392726	+	0.919655i	$0.628468\pi$
$240$	23.6791	+	7.66781i	1.52848	+	0.494955i
$241$	−19.6948	−	8.99432i	−1.26865	−	0.579375i	−0.336585	−	0.941653i	$-0.609272\pi$
$241$	−19.6948	−	8.99432i	−1.26865	−	0.579375i	−0.932070	+	0.362278i	$0.881999\pi$
$242$	10.7237	+	13.1035i	0.689349	+	0.842324i
$243$	−2.36014	+	16.4151i	−0.151403	+	1.05303i
$244$	3.67716	−	10.3331i	0.235406	−	0.661507i
$245$	−13.9396	−	2.83423i	−0.890569	−	0.181072i
$246$	−23.0366	−	7.47446i	−1.46876	−	0.476554i
$247$	−4.26102	+	3.69220i	−0.271122	+	0.234929i
$248$	6.26541	−	16.1521i	0.397854	−	1.02566i
$249$	−11.9753	−	10.3766i	−0.758902	−	0.657592i
$250$	−1.32803	−	15.7555i	−0.0839918	−	0.996466i
$251$	−5.41504	−	11.8573i	−0.341794	−	0.748425i	0.658196	−	0.752847i	$-0.271320\pi$
$251$	−5.41504	−	11.8573i	−0.341794	−	0.748425i	−0.999990	+	0.00442159i	$0.998593\pi$
$252$	5.99941	−	4.63419i	0.377927	−	0.291927i
$253$	14.1595	+	18.1076i	0.890202	+	1.13841i
$254$	−8.13191	+	16.5568i	−0.510241	+	1.03887i
$255$	5.91086	+	10.4831i	0.370153	+	0.656479i
$256$	15.5961	+	3.57214i	0.974759	+	0.223259i
$257$	−6.51866	−	5.64845i	−0.406623	−	0.352341i	0.427408	−	0.904059i	$-0.359427\pi$
$257$	−6.51866	−	5.64845i	−0.406623	−	0.352341i	−0.834031	+	0.551718i	$0.813972\pi$
$258$	−15.3278	−	25.3945i	−0.954269	−	1.58099i
$259$	−4.06988	+	3.52657i	−0.252890	+	0.219130i
$260$	−20.6598	−	16.8878i	−1.28127	−	1.04734i
$261$	−37.6300	−	11.0492i	−2.32924	−	0.683926i
$262$	2.87549	−	0.331142i	0.177649	−	0.0204580i
$263$	3.65567	+	0.525606i	0.225418	+	0.0324103i	0.254098	−	0.967178i	$-0.418221\pi$
$263$	3.65567	+	0.525606i	0.225418	+	0.0324103i	−0.0286800	+	0.999589i	$0.509130\pi$
$264$	−8.49874	+	36.7550i	−0.523061	+	2.26211i
$265$	4.38225	−	12.2562i	0.269199	−	0.752894i
$266$	−0.602343	+	0.881684i	−0.0369320	+	0.0540595i
$267$	−9.24980	−	14.3930i	−0.566079	−	0.880836i
$268$	−2.74196	+	1.07017i	−0.167492	+	0.0653708i
$269$	−1.46949	−	10.2205i	−0.0895962	−	0.623156i	−0.984301	−	0.176498i	$-0.943523\pi$
$269$	−1.46949	−	10.2205i	−0.0895962	−	0.623156i	0.894705	−	0.446658i	$-0.147386\pi$
$270$	−14.4531	+	5.15274i	−0.879587	+	0.313586i
$271$	3.60874	−	5.61531i	0.219216	−	0.341106i	−0.714176	−	0.699967i	$-0.753198\pi$
$271$	3.60874	−	5.61531i	0.219216	−	0.341106i	0.933391	+	0.358860i	$0.116835\pi$
$272$	4.37734	+	6.37889i	0.265415	+	0.386777i
$273$	−12.7297	+	3.73778i	−0.770437	+	0.226221i
$274$	−10.0071	−	0.281721i	−0.604553	−	0.0170194i
$275$	23.6195	−	4.05501i	1.42431	−	0.244526i
$276$	−6.58900	+	25.8651i	−0.396611	+	1.55690i
$277$		−	30.6300i		−	1.84038i	−0.391474	−	0.920189i	$-0.628035\pi$
$277$		−	30.6300i		−	1.84038i	0.391474	−	0.920189i	$-0.371965\pi$
$278$	−0.436143	+	15.4925i	−0.0261581	+	0.929175i
$279$	8.18604	+	27.8791i	0.490086	+	1.66908i
$280$	−4.59812	−	2.09668i	−0.274790	−	0.125300i
$281$	−1.96377	+	3.05568i	−0.117148	+	0.182287i	−0.894876	−	0.446315i	$-0.852736\pi$
$281$	−1.96377	+	3.05568i	−0.117148	+	0.182287i	0.777727	+	0.628602i	$0.216372\pi$
$282$	−34.8522	+	9.17652i	−2.07542	+	0.546454i
$283$	23.9400	−	3.44205i	1.42308	−	0.204609i	0.612611	−	0.790384i	$-0.290119\pi$
$283$	23.9400	−	3.44205i	1.42308	−	0.204609i	0.810473	+	0.585776i	$0.199210\pi$
$284$	18.1839	−	7.09705i	1.07902	−	0.421132i
$285$	4.65862	−	3.58737i	0.275953	−	0.212497i
$286$	22.8146	−	33.3950i	1.34905	−	1.97469i
$287$	4.47301	+	2.04275i	0.264033	+	0.120580i
$288$	−24.3862	+	11.1981i	−1.43697	+	0.659852i
$289$	1.88699	−	13.1243i	0.111000	−	0.772019i
$290$	5.18553	+	25.6249i	0.304505	+	1.50474i
$291$	24.5603	+	7.21155i	1.43975	+	0.422748i
$292$	−4.56497	−	4.42906i	−0.267145	−	0.259191i
$293$	8.98670	+	10.3712i	0.525009	+	0.605892i	0.954878	−	0.296999i	$-0.0959858\pi$
$293$	8.98670	+	10.3712i	0.525009	+	0.605892i	−0.429869	+	0.902891i	$0.641440\pi$
$294$	21.4335	−	12.9370i	1.25003	−	0.754501i
$295$	2.59241	+	1.88614i	0.150936	+	0.109815i
$296$	16.8484	−	8.91683i	0.979291	−	0.518280i
$297$	−9.66123	−	21.1551i	−0.560602	−	1.22755i
$298$	−4.65923	−	2.28839i	−0.269902	−	0.132563i
$299$	16.6625	−	23.2635i	0.963617	−	1.34536i
$300$	20.4921	+	18.8266i	1.18311	+	1.08695i
$301$	2.50185	+	5.47828i	0.144204	+	0.315763i
$302$	−26.3076	−	4.54145i	−1.51383	−	0.261331i
$303$	−11.4498	+	13.2138i	−0.657776	+	0.759114i
$304$	2.78045	−	2.56039i	0.159469	−	0.146849i
$305$	8.55202	−	8.78806i	0.489687	−	0.503203i
$306$	−12.3416	−	4.00438i	−0.705525	−	0.228915i
$307$	16.9262	+	4.96999i	0.966032	+	0.283653i	0.726447	−	0.687223i	$-0.241170\pi$
$307$	16.9262	+	4.96999i	0.966032	+	0.283653i	0.239585	+	0.970875i	$0.422989\pi$
$308$	2.56802	−	7.21631i	0.146326	−	0.411187i
$309$	−29.3382	−	4.21820i	−1.66899	−	0.239965i
$310$	13.8940	−	13.4959i	0.789125	−	0.766516i
$311$	−0.377622	−	0.172454i	−0.0214130	−	0.00977899i	0.404680	−	0.914458i	$-0.367383\pi$
$311$	−0.377622	−	0.172454i	−0.0214130	−	0.00977899i	−0.426093	+	0.904679i	$0.640110\pi$
$312$	46.8826	−	2.73946i	2.65421	−	0.155092i
$313$	1.04181	−	0.669534i	0.0588868	−	0.0378443i	−0.510866	−	0.859660i	$-0.670675\pi$
$313$	1.04181	−	0.669534i	0.0588868	−	0.0378443i	0.569753	+	0.821816i	$0.307039\pi$
$314$	12.9749	−	14.1489i	0.732218	−	0.798470i
$315$	8.25662	−	1.91418i	0.465208	−	0.107852i
$316$	−2.78343	+	13.7957i	−0.156580	+	0.776067i
$317$	11.1420	−	17.3373i	0.625798	−	0.973761i	−0.373144	−	0.927773i	$-0.621720\pi$
$317$	11.1420	−	17.3373i	0.625798	−	0.973761i	0.998942	−	0.0459872i	$-0.0146433\pi$
$318$	8.92613	+	21.0973i	0.500552	+	1.18308i
$319$	−38.0212	+	11.1640i	−2.12878	+	0.625066i
$320$	14.1859	+	10.8977i	0.793015	+	0.609202i
$321$			7.10565i			0.396599i
$322$	1.92985	−	5.06411i	0.107546	−	0.282212i
$323$	1.82759			0.101690
$324$	−0.678856	+	1.28917i	−0.0377142	+	0.0716205i
$325$	−13.1273	−	26.7900i	−0.728174	−	1.48604i
$326$	2.89350	+	6.83893i	0.160256	+	0.378773i
$327$	−30.9438	+	48.1496i	−1.71120	+	2.66268i
$328$	−13.7974	−	10.6120i	−0.761835	−	0.585950i
$329$	7.24307	−	1.04140i	0.399324	−	0.0574141i
$330$	−25.7641	+	33.3940i	−1.41827	+	1.83828i
$331$	−5.70091	−	8.87079i	−0.313351	−	0.487583i	0.648479	−	0.761233i	$-0.275405\pi$
$331$	−5.70091	−	8.87079i	−0.313351	−	0.487583i	−0.961829	+	0.273650i	$0.911769\pi$
$332$	−5.60830	−	9.91177i	−0.307795	−	0.543979i
$333$	−13.2810	+	29.0814i	−0.727797	+	1.59365i
$334$	−0.749258	−	0.915528i	−0.0409976	−	0.0500954i
$335$	−3.28533	−	0.190064i	−0.179496	−	0.0103843i
$336$	8.45424	−	2.76249i	0.461217	−	0.150706i
$337$	−15.3029	−	4.49335i	−0.833604	−	0.244768i	−0.163039	−	0.986620i	$-0.552130\pi$
$337$	−15.3029	−	4.49335i	−0.833604	−	0.244768i	−0.670564	+	0.741851i	$0.733948\pi$
$338$	−30.4028	−	9.86451i	−1.65369	−	0.536559i
$339$	−26.5099	−	30.5940i	−1.43982	−	1.66164i
$340$	1.47632	+	8.52260i	0.0800648	+	0.462203i
$341$	22.1874	+	19.2255i	1.20152	+	1.04112i
$342$	−1.07838	+	6.24680i	−0.0583120	+	0.337788i
$343$	−9.71162	+	4.43515i	−0.524378	+	0.239475i
$344$	−4.25966	−	20.8885i	−0.229665	−	1.12623i
$345$	−18.7488	+	23.2165i	−1.00940	+	1.24993i
$346$	9.34091	+	4.58780i	0.502170	+	0.246642i
$347$	−10.1345	−	22.1914i	−0.544048	−	1.19130i	−0.959506	−	0.281687i	$-0.909106\pi$
$347$	−10.1345	−	22.1914i	−0.544048	−	1.19130i	0.415459	−	0.909612i	$-0.363621\pi$
$348$	−37.2477	−	27.0148i	−1.99669	−	1.44815i
$349$	−21.7064	+	25.0505i	−1.16192	+	1.34092i	−0.232189	+	0.972671i	$0.574589\pi$
$349$	−21.7064	+	25.0505i	−1.16192	+	1.34092i	−0.929726	+	0.368252i	$0.879957\pi$
$350$	−3.69608	−	4.27345i	−0.197564	−	0.228426i
$351$	−21.8803	+	18.9594i	−1.16788	+	1.01198i
$352$	−14.6112	+	22.8396i	−0.778778	+	1.21735i
$353$	−5.11898	+	17.4336i	−0.272456	+	0.927899i	0.703640	+	0.710557i	$0.251557\pi$
$353$	−5.11898	+	17.4336i	−0.272456	+	0.927899i	−0.976095	+	0.217342i	$0.930261\pi$
$354$	−5.60531	+	0.645509i	−0.297919	+	0.0343084i
$355$	21.7874	+	1.26045i	1.15635	+	0.0668978i
$356$	−2.79506	−	11.9746i	−0.148138	−	0.634651i
$357$	3.91189	+	1.78650i	0.207039	+	0.0945515i
$358$	0.352056	−	0.515324i	0.0186067	−	0.0272357i
$359$	−9.86059	+	6.33702i	−0.520422	+	0.334455i	−0.774339	−	0.632771i	$-0.781917\pi$
$359$	−9.86059	+	6.33702i	−0.520422	+	0.334455i	0.253917	+	0.967226i	$0.418281\pi$
$360$	−30.0017	+	0.0173431i	−1.58123	+	0.000914061i
$361$	2.57691	+	17.9228i	0.135627	+	0.943305i
$362$	−4.13243	−	15.6949i	−0.217196	−	0.824904i
$363$	−28.0285	−	18.0128i	−1.47111	−	0.945428i
$364$	−9.52016	−	0.536448i	−0.498992	−	0.0281175i
$365$	−2.57558	−	6.62841i	−0.134812	−	0.346947i
$366$	−0.607319	+	21.5729i	−0.0317451	+	1.12763i
$367$		−	24.9756i		−	1.30372i	−0.758341	−	0.651859i	$-0.773990\pi$
$367$		−	24.9756i		−	1.30372i	0.758341	−	0.651859i	$-0.226010\pi$
$368$	−10.6940	+	15.9260i	−0.557464	+	0.830201i
$369$	29.1931			1.51973
$370$	21.2780	−	1.21133i	1.10619	−	0.0629739i
$371$	−1.31040	−	4.46280i	−0.0680324	−	0.231697i
$372$	−1.91787	+	34.0358i	−0.0994370	+	1.76468i
$373$	−30.5643	−	19.6425i	−1.58256	−	1.01705i	−0.974843	−	0.222895i	$-0.928449\pi$
$373$	−30.5643	−	19.6425i	−1.58256	−	1.01705i	−0.607716	−	0.794154i	$-0.707914\pi$
$374$	−12.6778	+	3.33805i	−0.655555	+	0.172606i
$375$	12.0535	+	28.6823i	0.622442	+	1.48115i
$376$	−25.8102	−	2.18444i	−1.33106	−	0.112654i
$377$	26.6697	+	41.4989i	1.37356	+	2.13730i
$378$	−3.09302	+	4.52744i	−0.159088	+	0.232866i
$379$	−7.40996	+	16.2256i	−0.380624	+	0.833451i	0.618248	+	0.785983i	$0.287843\pi$
$379$	−7.40996	+	16.2256i	−0.380624	+	0.833451i	−0.998873	+	0.0474682i	$0.984885\pi$
$380$	4.01884	−	1.30652i	0.206162	−	0.0670233i
$381$	5.16550	−	35.9269i	0.264637	−	1.84059i
$382$	−0.929749	−	8.07353i	−0.0475701	−	0.413078i
$383$	6.83604	−	23.2814i	0.349305	−	1.18962i	−0.578225	−	0.815877i	$-0.696255\pi$
$383$	6.83604	−	23.2814i	0.349305	−	1.18962i	0.927531	−	0.373747i	$-0.121927\pi$
$384$	−31.3597	+	2.78537i	−1.60032	+	0.142141i
$385$	5.97248	−	6.13733i	0.304386	−	0.312787i
$386$	−4.75106	−	7.87136i	−0.241823	−	0.400641i
$387$	27.0211	+	23.4139i	1.37356	+	1.19020i
$388$	14.8925	+	10.8011i	0.756051	+	0.548344i
$389$	9.14350	−	4.17570i	0.463594	−	0.211716i	−0.169904	−	0.985461i	$-0.554346\pi$
$389$	9.14350	−	4.17570i	0.463594	−	0.211716i	0.633498	+	0.773744i	$0.281618\pi$
$390$	48.9234	+	19.0619i	2.47733	+	0.965235i
$391$	−9.02009	+	2.16200i	−0.456166	+	0.109337i
$392$	17.6303	−	3.59524i	0.890464	−	0.181587i
$393$	−5.18081	+	2.36600i	−0.261337	+	0.119349i
$394$	−10.3939	−	1.79429i	−0.523639	−	0.0903952i
$395$	−9.25720	+	12.7236i	−0.465780	+	0.640192i
$396$	−3.92899	−	45.3030i	−0.197439	−	2.27656i
$397$	11.0488	−	9.57388i	0.554526	−	0.480499i	−0.331936	−	0.943302i	$-0.607702\pi$
$397$	11.0488	−	9.57388i	0.554526	−	0.480499i	0.886461	+	0.462803i	$0.153156\pi$
$398$	8.55491	+	2.77573i	0.428819	+	0.139135i
$399$	0.591948	−	2.01599i	0.0296345	−	0.100926i
$400$	9.33910	+	17.6856i	0.466955	+	0.884281i
$401$	−16.5596	−	2.38091i	−0.826947	−	0.118897i	−0.284170	−	0.958774i	$-0.591718\pi$
$401$	−16.5596	−	2.38091i	−0.826947	−	0.118897i	−0.542777	+	0.839877i	$0.682627\pi$
$402$	4.48209	−	3.66810i	0.223546	−	0.182948i
$403$	15.1822	−	33.2445i	0.756282	−	1.65603i
$404$	−10.9369	+	6.18834i	−0.544131	+	0.307881i
$405$	−1.29064	+	0.993858i	−0.0641324	+	0.0493852i
$406$	6.88560	+	6.31427i	0.341726	+	0.313372i
$407$	4.59718	+	31.9741i	0.227874	+	1.58490i
$408$	−12.0666	−	9.28077i	−0.597385	−	0.459467i
$409$	7.54395	+	4.84820i	0.373024	+	0.239728i	0.713698	−	0.700453i	$-0.247019\pi$
$409$	7.54395	+	4.84820i	0.373024	+	0.239728i	−0.340674	+	0.940182i	$0.610655\pi$
$410$	−9.07744	−	17.2142i	−0.448303	−	0.850149i
$411$	18.9009	−	5.54981i	0.932313	−	0.273752i
$412$	−18.8490	−	9.92557i	−0.928622	−	0.488998i
$413$	1.14562			0.0563724
$414$	−2.06747	−	32.1068i	−0.101610	−	1.57796i
$415$	−1.08112	−	12.6867i	−0.0530701	−	0.622764i
$416$	32.4051	+	9.44194i	1.58879	+	0.462929i
$417$	−8.59188	−	29.2612i	−0.420746	−	1.43293i
$418$	2.49576	+	5.89885i	0.122072	+	0.288522i
$419$	−26.4154	−	16.9762i	−1.29048	−	0.829340i	−0.298336	−	0.954461i	$-0.596432\pi$
$419$	−26.4154	−	16.9762i	−1.29048	−	0.829340i	−0.992141	+	0.125121i	$0.960068\pi$
$420$	9.87931	+	1.13192i	0.482061	+	0.0552319i
$421$	30.1781	−	4.33895i	1.47079	−	0.211468i	0.640138	−	0.768260i	$-0.278877\pi$
$421$	30.1781	−	4.33895i	1.47079	−	0.211468i	0.830652	+	0.556793i	$0.187968\pi$
$422$	1.72646	+	1.58321i	0.0840425	+	0.0770692i
$423$	36.5460	−	23.4867i	1.77693	−	1.14196i
$424$	0.960407	+	16.4362i	0.0466415	+	0.798212i
$425$	−2.47090	+	9.34946i	−0.119856	+	0.453515i
$426$	−29.7240	+	24.3258i	−1.44013	+	1.17859i
$427$	0.623607	−	4.33728i	0.0301785	−	0.209896i
$428$	−1.71218	+	4.81136i	−0.0827616	+	0.232566i
$429$	−22.4208	+	76.3583i	−1.08249	+	3.68662i
$430$	5.40434	−	23.2139i	0.260620	−	1.11947i
$431$	11.3680	+	13.1194i	0.547577	+	0.631937i	0.960317	−	0.278912i	$-0.0899737\pi$
$431$	11.3680	+	13.1194i	0.547577	+	0.631937i	−0.412740	+	0.910849i	$0.635428\pi$
$432$	14.2776	−	13.1476i	0.686929	−	0.632564i
$433$	1.16440	−	1.34379i	0.0559574	−	0.0645783i	−0.727081	−	0.686552i	$-0.759123\pi$
$433$	1.16440	−	1.34379i	0.0559574	−	0.0645783i	0.783038	+	0.621974i	$0.213669\pi$
$434$	1.17745	−	6.82070i	0.0565194	−	0.327404i
$435$	−25.2668	−	44.8116i	−1.21145	−	2.14855i
$436$	−32.5548	+	25.1466i	−1.55909	+	1.20431i
$437$	1.67271	+	4.21176i	0.0800164	+	0.201476i
$438$	11.2337	+	5.51743i	0.536766	+	0.263633i
$439$	17.8789	−	8.16504i	0.853316	−	0.389696i	0.0597739	−	0.998212i	$-0.480962\pi$
$439$	17.8789	−	8.16504i	0.853316	−	0.389696i	0.793542	+	0.608516i	$0.208235\pi$
$440$	−25.4920	+	16.4035i	−1.21528	+	0.782007i
$441$	−19.7618	+	22.8063i	−0.941039	+	1.08602i
$442$	8.43351	+	13.9723i	0.401141	+	0.664593i
$443$	16.1359	+	18.6218i	0.766638	+	0.884748i	0.996069	−	0.0885771i	$-0.0282320\pi$
$443$	16.1359	+	18.6218i	0.766638	+	0.884748i	−0.229431	+	0.973325i	$0.573687\pi$
$444$	−26.1192	+	26.9208i	−1.23956	+	1.27760i
$445$	2.73919	−	13.4722i	0.129850	−	0.638643i
$446$	2.00405	+	17.4023i	0.0948947	+	0.824024i
$447$	10.1101	+	1.45362i	0.478192	+	0.0687537i
$448$	6.39016	+	0.166614i	0.301907	+	0.00787175i
$449$	7.54386	−	16.5188i	0.356017	−	0.779568i	−0.643879	−	0.765128i	$-0.722676\pi$
$449$	7.54386	−	16.5188i	0.356017	−	0.779568i	0.999896	−	0.0144409i	$-0.00459683\pi$
$450$	−30.4989	−	13.9623i	−1.43773	−	0.658191i
$451$	24.8141	−	15.9471i	1.16845	−	0.750918i
$452$	−10.5783	−	27.1036i	−0.497562	−	1.27484i
$453$	51.9964	−	7.47596i	2.44301	−	0.351251i
$454$	8.31404	+	31.5765i	0.390197	+	1.48196i
$455$	−9.42539	−	4.98132i	−0.441869	−	0.233528i
$456$	−3.64915	+	6.48065i	−0.170887	+	0.303484i
$457$	−3.40007	+	0.998352i	−0.159049	+	0.0467009i	−0.360288	−	0.932841i	$-0.617321\pi$
$457$	−3.40007	+	0.998352i	−0.159049	+	0.0467009i	0.201239	+	0.979542i	$0.435503\pi$
$458$	−0.0830037	+	2.94841i	−0.00387851	+	0.137770i
$459$	9.38468			0.438039
$460$	−18.2894	+	11.2025i	−0.852749	+	0.522321i
$461$	17.6569			0.822364			0.411182	−	0.911553i	$-0.365116\pi$
$461$	17.6569			0.822364			0.411182	+	0.911553i	$0.365116\pi$
$462$	−0.424134	+	15.0659i	−0.0197325	+	0.700928i
$463$	34.0670	−	10.0030i	1.58323	−	0.464877i	0.632410	−	0.774634i	$-0.282066\pi$
$463$	34.0670	−	10.0030i	1.58323	−	0.464877i	0.950816	+	0.309757i	$0.100248\pi$
$464$	−18.7116	−	27.2674i	−0.868663	−	1.26586i
$465$	−17.8089	+	33.6970i	−0.825867	+	1.56266i
$466$	−7.00383	−	26.6004i	−0.324446	−	1.23224i
$467$	−14.5349	+	2.08981i	−0.672596	+	0.0967047i	−0.470147	−	0.882588i	$-0.655799\pi$
$467$	−14.5349	+	2.08981i	−0.672596	+	0.0967047i	−0.202449	+	0.979293i	$0.564890\pi$
$468$	−52.7340	+	20.5817i	−2.43763	+	0.951389i
$469$	−0.989271	+	0.635766i	−0.0456803	+	0.0293569i
$470$	−25.2131	−	14.2469i	−1.16299	−	0.657160i
$471$	−15.6922	+	34.3612i	−0.723059	+	1.58328i
$472$	−3.95100	−	0.913576i	−0.181859	−	0.0420508i
$473$	35.7580	+	5.14123i	1.64415	+	0.236394i
$474$	−3.16816	−	27.5109i	−0.145519	−	1.26362i
$475$	4.69316	+	0.544845i	0.215337	+	0.0249992i
$476$	2.21833	+	2.15228i	0.101677	+	0.0986496i
$477$	−18.0826	−	20.8685i	−0.827946	−	0.955501i
$478$	−12.6839	−	21.0141i	−0.580148	−	0.961164i
$479$	2.37996	−	2.74662i	0.108743	−	0.125496i	−0.698769	−	0.715348i	$-0.746268\pi$
$479$	2.37996	−	2.74662i	0.108743	−	0.125496i	0.807512	+	0.589852i	$0.200814\pi$
$480$	−33.1689	−	11.7820i	−1.51395	−	0.537771i
$481$	36.5791	−	16.7051i	1.66786	−	0.761687i
$482$	27.4837	+	13.4987i	1.25185	+	0.614847i
$483$	−0.536694	+	10.6502i	−0.0244204	+	0.484600i
$484$	−14.6382	−	18.9506i	−0.665372	−	0.861389i
$485$	10.1022	+	17.9167i	0.458719	+	0.813555i
$486$	3.98970	−	23.1114i	0.180976	−	1.04835i
$487$	17.5169	−	20.2156i	0.793766	−	0.916055i	−0.204256	−	0.978917i	$-0.565478\pi$
$487$	17.5169	−	20.2156i	0.793766	−	0.916055i	0.998022	+	0.0628629i	$0.0200231\pi$
$488$	−5.60945	+	14.4610i	−0.253928	+	0.654620i
$489$	−9.56873	−	11.0429i	−0.432713	−	0.499377i
$490$	19.5930	+	4.56137i	0.885121	+	0.206062i
$491$	−2.21726	+	7.55128i	−0.100063	+	0.340784i	−0.994274	−	0.106862i	$-0.965920\pi$
$491$	−2.21726	+	7.55128i	−0.100063	+	0.340784i	0.894210	+	0.447647i	$0.147738\pi$
$492$	32.2683	+	11.4831i	1.45477	+	0.517698i
$493$	2.27564	−	15.8274i	0.102490	−	0.712831i
$494$	6.17055	−	5.04991i	0.277626	−	0.227206i
$495$	17.1169	−	47.8723i	0.769346	−	2.15170i
$496$	−9.49993	+	22.5841i	−0.426559	+	1.01406i
$497$	6.56058	−	4.21623i	0.294282	−	0.189124i
$498$	16.5159	+	15.1455i	0.740096	+	0.678688i
$499$	22.2280	−	3.19591i	0.995064	−	0.143069i	0.374502	−	0.927226i	$-0.377814\pi$
$499$	22.2280	−	3.19591i	0.995064	−	0.143069i	0.620562	+	0.784158i	$0.286905\pi$
$500$	1.25034	+	22.3257i	0.0559171	+	0.998435i
$501$	1.95832	+	1.25854i	0.0874915	+	0.0562273i
$502$	7.18310	+	16.9776i	0.320598	+	0.757747i
$503$	4.71175	+	16.0467i	0.210086	+	0.715489i	0.995350	+	0.0963268i	$0.0307094\pi$
$503$	4.71175	+	16.0467i	0.210086	+	0.715489i	−0.785263	+	0.619162i	$0.787472\pi$
$504$	−8.66552	+	6.31238i	−0.385993	+	0.281176i
$505$	−13.9988	+	1.19294i	−0.622938	+	0.0530849i
$506$	−19.2960	−	26.1613i	−0.857813	−	1.16301i
$507$	62.8938			2.79321
$508$	12.1546	−	23.0820i	0.539274	−	1.02410i
$509$	18.1281	−	5.32289i	0.803514	−	0.235933i	0.145911	−	0.989298i	$-0.453389\pi$
$509$	18.1281	−	5.32289i	0.803514	−	0.235933i	0.657603	+	0.753365i	$0.271570\pi$
$510$	−7.93871	−	15.0548i	−0.351532	−	0.666636i
$511$	−2.13774	−	1.37384i	−0.0945682	−	0.0607753i
$512$	−21.9054	−	5.67045i	−0.968091	−	0.250601i
$513$	−0.652523	−	4.53839i	−0.0288096	−	0.200375i
$514$	8.99034	+	8.24438i	0.396547	+	0.363644i
$515$	−14.5312	−	18.8705i	−0.640322	−	0.831532i
$516$	20.6576	+	36.5090i	0.909401	+	1.60722i
$517$	18.2342	−	39.9273i	0.801939	−	1.75600i
$518$	5.89375	−	4.82338i	0.258956	−	0.211927i
$519$	−20.2689	−	2.91423i	−0.889707	−	0.127921i
$520$	28.5337	+	24.6957i	1.25129	+	1.08298i
$521$	−1.60215	+	5.45643i	−0.0701916	+	0.239050i	−0.987115	−	0.160013i	$-0.948846\pi$
$521$	−1.60215	+	5.45643i	−0.0701916	+	0.239050i	0.916923	+	0.399063i	$0.130665\pi$
$522$	52.7561	+	17.1173i	2.30907	+	0.749202i
$523$	−30.9523	+	26.8203i	−1.35345	+	1.17277i	−0.385187	+	0.922839i	$0.625863\pi$
$523$	−30.9523	+	26.8203i	−1.35345	+	1.17277i	−0.968263	+	0.249932i	$0.919592\pi$
$524$	−4.07813	+	0.353684i	−0.178154	+	0.0154508i
$525$	9.51292	+	5.75385i	0.415178	+	0.251119i
$526$	−5.14694	−	0.888511i	−0.224417	−	0.0387409i
$527$	−10.7761	+	4.92130i	−0.469416	+	0.214375i
$528$	13.4770	−	51.6206i	0.586512	−	2.24650i
$529$	−13.2380	−	18.8084i	−0.575567	−	0.817754i
$530$	−6.68274	+	17.1517i	−0.290280	+	0.745021i
$531$	6.18662	−	2.82534i	0.268477	−	0.122609i
$532$	0.886592	−	1.22242i	0.0384387	−	0.0529988i
$533$	−27.7508	−	24.0462i	−1.20202	−	1.04156i
$534$	12.5032	+	20.7148i	0.541067	+	0.896417i
$535$	−3.98206	+	4.09196i	−0.172159	+	0.176911i
$536$	3.91877	−	1.40372i	0.169265	−	0.0606315i
$537$	−0.345980	+	1.17830i	−0.0149301	+	0.0508474i
$538$	1.67060	+	14.5067i	0.0720247	+	0.625430i
$539$	−4.33930	+	30.1805i	−0.186907	+	1.29997i
$540$	20.6367	−	6.70899i	0.888063	−	0.288709i
$541$	−7.94115	+	17.3887i	−0.341417	+	0.747599i	−0.999988	−	0.00491984i	$-0.998434\pi$
$541$	−7.94115	+	17.3887i	−0.341417	+	0.747599i	0.658571	+	0.752519i	$0.271161\pi$
$542$	−5.32499	+	7.79449i	−0.228728	+	0.334802i
$543$	17.2655	+	26.8657i	0.740936	+	1.15292i
$544$	−5.93419	−	9.19174i	−0.254426	−	0.394093i
$545$	−44.8031	+	10.3870i	−1.91915	+	0.444929i
$546$	18.1441	−	4.77732i	0.776498	−	0.204450i
$547$	29.0605	+	18.6760i	1.24254	+	0.798530i	0.985795	−	0.167951i	$-0.0537149\pi$
$547$	29.0605	+	18.6760i	1.24254	+	0.798530i	0.256741	+	0.966480i	$0.417351\pi$
$548$	14.1354	+	0.796511i	0.603835	+	0.0340253i
$549$	−7.32900	−	24.9603i	−0.312794	−	1.06528i
$550$	−33.5511	+	4.79239i	−1.43062	+	0.204348i
$551$	−7.81231			−0.332815
$552$	10.3439	−	36.3021i	0.440266	−	1.54512i
$553$			5.62272i			0.239102i
$554$	−1.21899	+	43.3002i	−0.0517898	+	1.83965i
$555$	−39.0893	+	15.1888i	−1.65925	+	0.644728i
$556$	1.23311	−	21.8836i	0.0522955	−	0.928071i
$557$	31.6865	+	20.3637i	1.34260	+	0.862836i	0.997138	−	0.0755977i	$-0.0240865\pi$
$557$	31.6865	+	20.3637i	1.34260	+	0.862836i	0.345460	+	0.938433i	$0.387723\pi$
$558$	−10.4627	−	39.7372i	−0.442922	−	1.68221i
$559$	−6.40018	−	44.5142i	−0.270699	−	1.88275i
$560$	6.41670	+	3.14697i	0.271155	+	0.132984i
$561$	21.7013	−	13.9466i	0.916229	−	0.588825i
$562$	2.89769	−	4.24152i	0.122232	−	0.178918i
$563$	8.55919	+	3.90885i	0.360727	+	0.164738i	0.587530	−	0.809202i	$-0.300100\pi$
$563$	8.55919	+	3.90885i	0.360727	+	0.164738i	−0.226804	+	0.973941i	$0.572828\pi$
$564$	49.6342	−	11.5854i	2.08998	−	0.487833i
$565$	1.87873	−	32.4746i	0.0790390	−	1.36622i
$566$	−33.9798	+	3.91312i	−1.42828	+	0.164481i
$567$	−0.163995	+	0.558517i	−0.00688716	+	0.0234555i
$568$	−25.9882	+	9.30910i	−1.09044	+	0.390601i
$569$	26.7298	−	23.1615i	1.12057	−	0.970980i	0.120806	−	0.992676i	$-0.461452\pi$
$569$	26.7298	−	23.1615i	1.12057	−	0.970980i	0.999765	+	0.0216966i	$0.00690677\pi$
$570$	−6.72844	+	4.88590i	−0.281823	+	0.204648i
$571$	13.5869	−	15.6801i	0.568594	−	0.656192i	−0.396519	−	0.918026i	$-0.629782\pi$
$571$	13.5869	−	15.6801i	0.568594	−	0.656192i	0.965113	+	0.261834i	$0.0843274\pi$
$572$	−33.5809	+	46.3010i	−1.40409	+	1.93594i
$573$	6.64302	+	14.5462i	0.277516	+	0.607675i
$574$	−6.24199	−	3.06576i	−0.260535	−	0.127962i
$575$	−23.8077	+	2.86281i	−0.992848	+	0.119388i
$576$	34.9193	−	14.8597i	1.45497	−	0.619153i
$577$	10.3261	−	4.71578i	0.429882	−	0.196320i	−0.188710	−	0.982033i	$-0.560431\pi$
$577$	10.3261	−	4.71578i	0.429882	−	0.196320i	0.618592	+	0.785712i	$0.287703\pi$
$578$	−3.18987	+	18.4782i	−0.132681	+	0.768590i
$579$	13.6724	+	11.8472i	0.568205	+	0.492353i
$580$	−6.31074	−	36.4310i	−0.262039	−	1.51272i
$581$	−2.97956	−	3.43860i	−0.123613	−	0.142657i
$582$	−34.4327	−	11.1721i	−1.42728	−	0.463097i
$583$	−26.7699	−	7.86034i	−1.10869	−	0.325542i
$584$	6.27703	+	6.44282i	0.259745	+	0.266606i
$585$	−63.1842	−	3.65536i	−2.61235	−	0.151130i
$586$	−12.2913	−	15.0189i	−0.507750	−	0.620426i
$587$	3.24635	−	7.10851i	0.133991	−	0.293400i	−0.830729	−	0.556677i	$-0.812076\pi$
$587$	3.24635	−	7.10851i	0.133991	−	0.293400i	0.964720	+	0.263277i	$0.0848034\pi$
$588$	−30.8144	+	17.4355i	−1.27076	+	0.719026i
$589$	3.12919	+	4.86912i	0.128936	+	0.200629i
$590$	−3.58970	−	2.76952i	−0.147786	−	0.114019i
$591$	20.5434	−	2.95369i	0.845042	−	0.121499i
$592$	−24.1726	+	11.9348i	−0.993488	+	0.490517i
$593$	−1.57572	+	2.45186i	−0.0647070	+	0.100686i	−0.872099	−	0.489329i	$-0.837242\pi$
$593$	−1.57572	+	2.45186i	−0.0647070	+	0.100686i	0.807392	+	0.590015i	$0.200878\pi$
$594$	12.8157	+	30.2905i	0.525835	+	1.24284i
$595$	1.25159	+	3.22105i	0.0513102	+	0.132050i
$596$	6.49547	+	3.42041i	0.266065	+	0.140106i
$597$	−17.6974			−0.724306
$598$	−24.4808	+	32.2234i	−1.00110	+	1.31771i
$599$			31.3309i			1.28015i	0.768314	+	0.640073i	$0.221096\pi$
$599$			31.3309i			1.28015i	−0.768314	+	0.640073i	$0.778904\pi$
$600$	−28.2195	−	27.4298i	−1.15206	−	1.11982i
$601$	−1.51172	+	0.443882i	−0.0616645	+	0.0181063i	−0.312419	−	0.949944i	$-0.601139\pi$
$601$	−1.51172	+	0.443882i	−0.0616645	+	0.0181063i	0.250755	+	0.968051i	$0.419321\pi$
$602$	−3.31872	−	7.84395i	−0.135261	−	0.319696i
$603$	−3.77436	+	5.87303i	−0.153704	+	0.239168i
$604$	37.0091	+	7.46701i	1.50588	+	0.303828i
$605$	−6.04639	−	26.0805i	−0.245821	−	1.06032i
$606$	16.7120	−	18.2241i	0.678878	−	0.740303i
$607$	−10.8691	+	6.98514i	−0.441163	+	0.283518i	−0.742306	−	0.670061i	$-0.766268\pi$
$607$	−10.8691	+	6.98514i	−0.441163	+	0.283518i	0.301144	+	0.953579i	$0.402632\pi$
$608$	−4.03248	+	3.50886i	−0.163539	+	0.142303i
$609$	−16.7219	−	7.63664i	−0.677606	−	0.309452i
$610$	−12.4393	+	12.0829i	−0.503654	+	0.489224i
$611$	−54.0862	−	7.77642i	−2.18809	−	0.314600i
$612$	17.2874	+	6.15196i	0.698803	+	0.248678i
$613$	2.55846	+	0.751231i	0.103335	+	0.0303419i	0.332991	−	0.942930i	$-0.391942\pi$
$613$	2.55846	+	0.751231i	0.103335	+	0.0303419i	−0.229656	+	0.973272i	$0.573760\pi$
$614$	−23.7301	−	7.69946i	−0.957667	−	0.310725i
$615$	27.4435	+	26.7064i	1.10663	+	1.07691i
$616$	−3.91747	+	10.0992i	−0.157840	+	0.406907i
$617$	−32.3687	+	37.3555i	−1.30312	+	1.50388i	−0.575750	+	0.817625i	$0.695290\pi$
$617$	−32.3687	+	37.3555i	−1.30312	+	1.50388i	−0.727365	+	0.686250i	$0.759255\pi$
$618$	41.3062	+	7.13064i	1.66158	+	0.286837i
$619$	16.1769	+	35.4225i	0.650205	+	1.42375i	0.891375	+	0.453267i	$0.149742\pi$
$619$	16.1769	+	35.4225i	0.650205	+	1.42375i	−0.241170	+	0.970483i	$0.577531\pi$
$620$	−20.1784	+	18.5256i	−0.810383	+	0.744005i
$621$	8.58933	+	21.6273i	0.344678	+	0.867875i
$622$	0.526964	+	0.258819i	0.0211293	+	0.0103777i
$623$	−2.04080	−	4.46874i	−0.0817631	−	0.179036i
$624$	−66.3848	+	2.00686i	−2.65752	+	0.0803387i
$625$	−9.13242	+	23.2723i	−0.365297	+	0.930891i
$626$	−1.49941	+	0.905027i	−0.0599285	+	0.0361722i
$627$	−8.25341	−	9.52494i	−0.329609	−	0.380390i
$628$	−18.9052	+	19.4853i	−0.754398	+	0.777549i
$629$	−12.5070	−	3.67238i	−0.498686	−	0.146427i
$630$	−11.7482	+	2.37740i	−0.468059	+	0.0947178i
$631$	−0.508615	+	3.53750i	−0.0202477	+	0.140826i	−0.997438	−	0.0715415i	$-0.977208\pi$
$631$	−0.508615	+	3.53750i	−0.0202477	+	0.140826i	0.977190	+	0.212367i	$0.0681173\pi$
$632$	4.48384	−	19.3915i	0.178358	−	0.771353i
$633$	−4.19276	−	1.91477i	−0.166647	−	0.0761052i
$634$	−16.4409	+	24.0655i	−0.652952	+	0.955764i
$635$	23.1083	−	17.7946i	0.917026	−	0.706156i
$636$	−11.7788	−	30.1795i	−0.467061	−	1.19670i
$637$	37.5709	−	5.40188i	1.48861	−	0.214030i
$638$	54.1931	−	14.2689i	2.14553	−	0.564913i
$639$	25.0305	−	38.9483i	0.990193	−	1.54077i
$640$	−19.6202	−	15.9702i	−0.775557	−	0.631277i
$641$	3.75294	+	12.7814i	0.148232	+	0.504833i	0.999812	−	0.0193922i	$-0.00617311\pi$
$641$	3.75294	+	12.7814i	0.148232	+	0.504833i	−0.851580	+	0.524225i	$0.824355\pi$
$642$	0.282785	−	10.0449i	0.0111606	−	0.396442i
$643$		−	18.1403i		−	0.715385i	−0.933839	−	0.357692i	$-0.883564\pi$
$643$		−	18.1403i		−	0.715385i	0.933839	−	0.357692i	$-0.116436\pi$
$644$	−2.92968	+	7.08209i	−0.115446	+	0.279074i
$645$	3.98220	+	46.7301i	0.156799	+	1.83999i
$646$	−2.58358	−	0.0727330i	−0.101650	−	0.00286164i
$647$	−32.0051	+	9.39756i	−1.25825	+	0.369456i	−0.841844	−	0.539721i	$-0.818530\pi$
$647$	−32.0051	+	9.39756i	−1.25825	+	0.369456i	−0.416409	+	0.909178i	$0.636711\pi$
$648$	1.01097	−	1.79542i	0.0397148	−	0.0705309i
$649$	3.71525	−	5.78105i	0.145836	−	0.226926i
$650$	17.4914	+	38.3942i	0.686067	+	1.50595i
$651$	1.93827	+	13.4810i	0.0759668	+	0.528361i
$652$	−3.81824	−	9.78303i	−0.149534	−	0.383133i
$653$	−14.8844	−	23.1606i	−0.582471	−	0.906343i	0.417526	−	0.908665i	$-0.362897\pi$
$653$	−14.8844	−	23.1606i	−0.582471	−	0.906343i	−0.999997	+	0.00232217i	$0.999261\pi$
$654$	45.6601	−	66.8353i	1.78545	−	2.61347i
$655$	−4.30942	−	1.54084i	−0.168383	−	0.0602058i
$656$	19.0824	+	15.5508i	0.745044	+	0.607156i
$657$	−14.9325	−	2.14697i	−0.582571	−	0.0837611i
$658$	−10.2806	+	1.18392i	−0.400781	+	0.0461540i
$659$	5.14018	+	1.50929i	0.200233	+	0.0587937i	0.380311	−	0.924859i	$-0.375817\pi$
$659$	5.14018	+	1.50929i	0.200233	+	0.0587937i	−0.180078	+	0.983652i	$0.557635\pi$
$660$	37.7505	−	46.1822i	1.46944	−	1.79764i
$661$	18.9078	−	16.3837i	0.735426	−	0.637251i	−0.204406	−	0.978886i	$-0.565526\pi$
$661$	18.9078	−	16.3837i	0.735426	−	0.637251i	0.939833	+	0.341636i	$0.110981\pi$
$662$	7.70608	+	12.7671i	0.299505	+	0.496208i
$663$	−24.2696	−	21.0297i	−0.942551	−	0.816725i
$664$	7.53373	+	14.2350i	0.292365	+	0.552425i
$665$	1.47066	−	0.829225i	0.0570298	−	0.0321560i
$666$	19.9322	−	40.5825i	0.772355	−	1.57254i
$667$	38.5576	−	9.24176i	1.49296	−	0.357843i
$668$	1.02276	+	1.32406i	0.0395716	+	0.0512293i
$669$	−14.3189	−	31.3540i	−0.553600	−	1.21221i
$670$	4.63675	+	0.399431i	0.179133	+	0.0154314i
$671$	−19.8645	−	17.2127i	−0.766860	−	0.664488i
$672$	−12.0613	+	3.56875i	−0.465275	+	0.137667i
$673$	−29.2839	+	25.3746i	−1.12881	+	0.978120i	−0.999908	−	0.0135370i	$-0.995691\pi$
$673$	−29.2839	+	25.3746i	−1.12881	+	0.978120i	−0.128903	+	0.991657i	$0.541145\pi$
$674$	21.4542	+	6.96105i	0.826386	+	0.268129i
$675$	24.0994	+	2.79778i	0.927585	+	0.107686i
$676$	42.5865	+	15.1549i	1.63794	+	0.582882i
$677$	5.03248	−	35.0017i	0.193414	−	1.34522i	−0.629474	−	0.777021i	$-0.716730\pi$
$677$	5.03248	−	35.0017i	0.193414	−	1.34522i	0.822888	−	0.568203i	$-0.192361\pi$
$678$	36.2582	+	44.3044i	1.39249	+	1.70150i
$679$	6.68579	+	3.05330i	0.256577	+	0.117175i
$680$	−1.74783	−	12.1068i	−0.0670263	−	0.464273i
$681$	−34.7366	−	54.0512i	−1.33111	−	2.07125i
$682$	−30.6002	−	28.0612i	−1.17174	−	1.07452i
$683$	0.0179088	+	0.124558i	0.000685261	+	0.00476609i	0.990161	−	0.139931i	$-0.0446882\pi$
$683$	0.0179088	+	0.124558i	0.000685261	+	0.00476609i	−0.989476	+	0.144697i	$0.953779\pi$
$684$	1.77306	−	8.78789i	0.0677945	−	0.336013i
$685$	13.9947	+	7.39620i	0.534710	+	0.282594i
$686$	13.9054	−	5.88327i	0.530909	−	0.224624i
$687$	−1.63515	−	5.56880i	−0.0623847	−	0.212463i
$688$	5.19038	+	29.6986i	0.197881	+	1.13225i
$689$			34.7320i			1.32318i
$690$	27.4283	−	32.0739i	1.04418	−	1.22103i
$691$			7.66411i			0.291556i	0.989317	+	0.145778i	$0.0465686\pi$
$691$			7.66411i			0.291556i	−0.989317	+	0.145778i	$0.953431\pi$
$692$	−13.0222	−	6.85730i	−0.495031	−	0.260675i
$693$	−5.11836	−	17.4315i	−0.194430	−	0.662169i
$694$	13.4435	+	31.7743i	0.510308	+	1.20614i
$695$	11.4504	−	21.6658i	0.434337	−	0.821829i
$696$	51.5803	+	39.6719i	1.95515	+	1.50376i
$697$	1.69391	+	11.7814i	0.0641616	+	0.446254i
$698$	31.6822	−	34.5489i	1.19919	−	1.30769i
$699$	29.2624	+	45.5332i	1.10681	+	1.72223i
$700$	5.05491	+	6.18827i	0.191058	+	0.233895i
$701$	−22.3062	−	10.1869i	−0.842492	−	0.384753i	−0.0530599	−	0.998591i	$-0.516897\pi$
$701$	−22.3062	−	10.1869i	−0.842492	−	0.384753i	−0.789432	+	0.613838i	$0.789625\pi$
$702$	31.6857	−	25.9312i	1.19590	−	0.978712i
$703$	−0.906331	+	6.30367i	−0.0341829	+	0.237747i
$704$	21.5641	−	31.7058i	0.812727	−	1.19496i
$705$	55.8418	+	11.3539i	2.10312	+	0.427611i
$706$	7.93027	−	24.4414i	0.298460	−	0.919865i
$707$	−3.79423	+	3.28772i	−0.142697	+	0.123648i
$708$	7.94966	−	0.689451i	0.298767	−	0.0259111i
$709$	−29.1085	−	25.2226i	−1.09319	−	0.947255i	−0.0943572	−	0.995538i	$-0.530080\pi$
$709$	−29.1085	−	25.2226i	−1.09319	−	0.947255i	−0.998834	+	0.0482831i	$0.984625\pi$
$710$	−30.7496	−	2.64892i	−1.15401	−	0.0994121i
$711$	13.8668	+	30.3640i	0.520044	+	1.13874i
$712$	3.47469	+	17.0391i	0.130219	+	0.638568i
$713$	−21.2042	−	20.3298i	−0.794103	−	0.761357i
$714$	−5.45895	−	2.68117i	−0.204296	−	0.100340i
$715$	−55.7033	+	31.4080i	−2.08319	+	1.17459i
$716$	−0.518193	+	0.714479i	−0.0193658	+	0.0267013i
$717$	36.5011	+	31.6284i	1.36316	+	1.18119i
$718$	14.1916	−	8.56592i	0.529628	−	0.319677i
$719$	3.24241	−	2.80956i	0.120921	−	0.104779i	−0.592301	−	0.805717i	$-0.701780\pi$
$719$	3.24241	−	2.80956i	0.120921	−	0.104779i	0.713222	+	0.700938i	$0.247235\pi$
$720$	42.4127	+	1.16946i	1.58063	+	0.0435834i
$721$	−8.16609	−	2.39778i	−0.304121	−	0.0892980i
$722$	−2.92958	−	25.4392i	−0.109028	−	0.946748i
$723$	−59.6372	−	8.57453i	−2.21793	−	0.318890i
$724$	5.21721	+	22.3516i	0.193896	+	0.830689i
$725$	10.5622	−	39.9656i	0.392271	−	1.48428i
$726$	38.9057	+	26.5793i	1.44393	+	0.986452i
$727$	11.4983	+	17.8918i	0.426450	+	0.663569i	0.986288	−	0.165033i	$-0.0527731\pi$
$727$	11.4983	+	17.8918i	0.426450	+	0.663569i	−0.559838	+	0.828602i	$0.689137\pi$
$728$	13.4369	+	1.13723i	0.498003	+	0.0421484i
$729$	6.25665	+	43.5160i	0.231728	+	1.61170i
$730$	3.37718	+	9.47277i	0.124995	+	0.350603i
$731$	−7.88124	+	12.2634i	−0.291498	+	0.453580i
$732$	1.71708	−	30.4724i	0.0634650	−	1.12629i
$733$	−26.6741	+	7.83223i	−0.985232	+	0.289290i	−0.734382	−	0.678736i	$-0.762528\pi$
$733$	−26.6741	+	7.83223i	−0.985232	+	0.289290i	−0.250849	+	0.968026i	$0.580710\pi$
$734$	−0.993958	+	35.3069i	−0.0366877	+	1.30320i
$735$	−39.4411	+	3.36106i	−1.45481	+	0.123974i
$736$	15.7514	−	22.0883i	0.580605	−	0.814185i
$737$			7.05386i			0.259832i
$738$	−41.2689	−	1.16180i	−1.51913	−	0.0427665i
$739$	−12.4295	−	42.3310i	−0.457226	−	1.55717i	−0.789355	−	0.613936i	$-0.789585\pi$
$739$	−12.4295	−	42.3310i	−0.457226	−	1.55717i	0.332129	−	0.943234i	$-0.392233\pi$
$740$	−30.1280	+	0.865592i	−1.10753	+	0.0318198i
$741$	−8.48240	+	13.1989i	−0.311609	+	0.484872i
$742$	1.67484	+	6.36101i	0.0614854	+	0.233520i
$743$	51.0270	−	7.33658i	1.87200	−	0.269153i	0.889711	−	0.456523i	$-0.150905\pi$
$743$	51.0270	−	7.33658i	1.87200	−	0.269153i	0.982289	+	0.187370i	$0.0599964\pi$
$744$	4.06573	−	48.0386i	0.149057	−	1.76118i
$745$	5.00755	+	6.50288i	0.183462	+	0.238247i
$746$	42.4256	+	28.9840i	1.55331	+	1.06118i
$747$	−24.5706	−	11.2210i	−0.898990	−	0.410555i
$748$	18.0549	−	4.21430i	0.660152	−	0.154090i
$749$	−0.290369	+	2.01956i	−0.0106098	+	0.0737931i
$750$	−15.8980	−	41.0265i	−0.580515	−	1.49808i
$751$	32.3860	+	9.50939i	1.18178	+	0.347003i	0.812861	−	0.582458i	$-0.197909\pi$
$751$	32.3860	+	9.50939i	1.18178	+	0.347003i	0.368921	+	0.929461i	$0.379727\pi$
$752$	36.3998	+	4.11522i	1.32736	+	0.150067i
$753$	−23.7543	−	27.4139i	−0.865655	−	0.999019i
$754$	−36.0502	−	59.7264i	−1.31287	−	2.17511i
$755$	34.1330	+	24.8339i	1.24223	+	0.903799i
$756$	4.55264	−	6.27714i	0.165578	−	0.228297i
$757$	4.67997	+	10.2477i	0.170096	+	0.372459i	0.975413	−	0.220386i	$-0.0707318\pi$
$757$	4.67997	+	10.2477i	0.170096	+	0.372459i	−0.805316	+	0.592845i	$0.798005\pi$
$758$	11.1209	−	22.6424i	0.403928	−	0.822410i
$759$	52.0025	+	37.2468i	1.88757	+	1.35197i
$760$	−5.73325	+	1.68703i	−0.207967	+	0.0611952i
$761$	18.7583	+	41.0748i	0.679986	+	1.48896i	0.862658	+	0.505788i	$0.168798\pi$
$761$	18.7583	+	41.0748i	0.679986	+	1.48896i	−0.182672	+	0.983174i	$0.558474\pi$
$762$	−8.73201	+	50.5825i	−0.316328	+	1.83241i
$763$	−10.7624	+	12.4205i	−0.389626	+	0.449652i
$764$	0.993040	+	11.4502i	0.0359269	+	0.414253i
$765$	14.7026	+	14.3077i	0.531574	+	0.517297i
$766$	−10.5903	+	32.6398i	−0.382644	+	1.17932i
$767$	−8.20818	−	2.41014i	−0.296380	−	0.0870250i
$768$	44.4427	−	2.68953i	1.60369	−	0.0970499i
$769$	34.7536	+	4.99681i	1.25325	+	0.180190i	0.736788	−	0.676123i	$-0.236341\pi$
$769$	34.7536	+	4.99681i	1.25325	+	0.180190i	0.516457	+	0.856313i	$0.327250\pi$
$770$	−8.68726	+	8.43836i	−0.313067	+	0.304098i
$771$	−21.8333	−	9.97095i	−0.786309	−	0.359095i
$772$	6.40310	+	11.3164i	0.230453	+	0.407288i
$773$	−2.76060	+	1.77413i	−0.0992918	+	0.0638110i	−0.589344	−	0.807882i	$-0.700614\pi$
$773$	−2.76060	+	1.77413i	−0.0992918	+	0.0638110i	0.490053	+	0.871693i	$0.336978\pi$
$774$	−37.2666	−	34.1745i	−1.33952	−	1.22838i
$775$	−29.1397	+	9.42504i	−1.04673	+	0.338557i
$776$	−20.6230	−	15.8617i	−0.740321	−	0.569403i
$777$	−8.10189	+	12.6068i	−0.290654	+	0.452266i
$778$	−13.0919	+	5.53910i	−0.469368	+	0.198587i
$779$	5.57967	−	1.63834i	0.199913	−	0.0586996i
$780$	−68.4021	−	28.8939i	−2.44919	−	1.03457i
$781$		−	46.7793i		−	1.67389i
$782$	12.8373	−	2.69734i	0.459062	−	0.0964568i
$783$	−40.1161			−1.43363
$784$	−25.0662	+	4.38079i	−0.895221	+	0.156457i
$785$	−28.2930	+	10.9937i	−1.00982	+	0.392382i
$786$	7.41803	−	3.13852i	0.264593	−	0.111947i
$787$	−18.7829	+	29.2267i	−0.669537	+	1.04182i	0.325807	+	0.945436i	$0.394364\pi$
$787$	−18.7829	+	29.2267i	−0.669537	+	1.04182i	−0.995344	+	0.0963839i	$0.969272\pi$
$788$	14.6220	+	2.95016i	0.520888	+	0.105095i
$789$	10.1728	−	1.46263i	0.362162	−	0.0520710i
$790$	13.5928	−	17.6183i	0.483612	−	0.626831i
$791$	−6.28439	−	9.77870i	−0.223447	−	0.347691i
$792$	3.75131	+	64.1991i	0.133297	+	2.28121i
$793$	−13.5927	+	29.7639i	−0.482692	+	1.05695i
$794$	−16.0003	+	13.0944i	−0.567828	+	0.464704i
$795$	2.09195	−	36.1601i	0.0741938	−	1.28247i
$796$	−11.9832	−	4.26438i	−0.424734	−	0.151147i
$797$	−3.09392	−	0.908457i	−0.109592	−	0.0321792i	0.226477	−	0.974017i	$-0.427279\pi$
$797$	−3.09392	−	0.908457i	−0.109592	−	0.0321792i	−0.336069	+	0.941837i	$0.609097\pi$
$798$	−0.917039	+	2.82635i	−0.0324628	+	0.100052i
$799$	11.5991	+	13.3860i	0.410345	+	0.473563i
$800$	−12.4984	−	25.3730i	−0.441886	−	0.897071i
$801$	−22.0416	−	19.0992i	−0.778803	−	0.674836i
$802$	23.3148	+	4.02481i	0.823273	+	0.142121i
$803$	−13.8654	+	6.33212i	−0.489299	+	0.223456i
$804$	−6.48210	+	5.00704i	−0.228606	+	0.176585i
$805$	−6.27750	+	5.83240i	−0.221253	+	0.205565i
$806$	−22.7855	+	46.3920i	−0.802584	+	1.63409i
$807$	−11.9364	−	26.1370i	−0.420180	−	0.920065i
$808$	15.7073	−	8.31291i	0.552580	−	0.292447i
$809$	−9.04785	+	10.4418i	−0.318105	+	0.367113i	−0.892172	−	0.451695i	$-0.850819\pi$
$809$	−9.04785	+	10.4418i	−0.318105	+	0.367113i	0.574067	+	0.818808i	$0.305365\pi$
$810$	1.86407	−	1.35361i	0.0654968	−	0.0475609i
$811$	−1.19538	+	1.03580i	−0.0419754	+	0.0363719i	−0.675596	−	0.737272i	$-0.736114\pi$
$811$	−1.19538	+	1.03580i	−0.0419754	+	0.0363719i	0.633620	+	0.773644i	$0.281568\pi$
$812$	−9.48256	−	9.20022i	−0.332772	−	0.322865i
$813$	5.23309	−	17.8223i	0.183532	−	0.625054i
$814$	−5.22635	−	45.3833i	−0.183183	−	1.59068i
$815$	0.678129	−	11.7217i	0.0237538	−	0.410593i
$816$	16.6886	+	13.6000i	0.584218	+	0.476095i
$817$	6.47854	+	2.95865i	0.226655	+	0.103510i
$818$	−10.4716	−	7.15391i	−0.366130	−	0.250130i
$819$	−19.0259	+	12.2272i	−0.664819	+	0.427253i
$820$	12.1473	+	24.6962i	0.424202	+	0.862428i
$821$	1.28828	+	8.96019i	0.0449613	+	0.312713i	0.999875	+	0.0158283i	$0.00503853\pi$
$821$	1.28828	+	8.96019i	0.0449613	+	0.312713i	−0.954913	+	0.296884i	$0.904052\pi$
$822$	−26.9402	+	7.09330i	−0.939647	+	0.247407i
$823$	−7.58851	−	4.87684i	−0.264519	−	0.169996i	0.401658	−	0.915790i	$-0.368434\pi$
$823$	−7.58851	−	4.87684i	−0.264519	−	0.169996i	−0.666177	+	0.745794i	$0.732070\pi$
$824$	26.2509	+	14.7815i	0.914494	+	0.514936i
$825$	59.8855	−	29.3444i	2.08495	−	1.02164i
$826$	−1.61951	−	0.0455925i	−0.0563501	−	0.00158637i
$827$		−	3.92448i		−	0.136468i	−0.997669	−	0.0682338i	$-0.978264\pi$
$827$		−	3.92448i		−	0.136468i	0.997669	−	0.0682338i	$-0.0217364\pi$
$828$	1.64493	+	45.4701i	0.0571651	+	1.58020i
$829$	−3.62949			−0.126057			−0.0630287	−	0.998012i	$-0.520076\pi$
$829$	−3.62949			−0.126057			−0.0630287	+	0.998012i	$0.520076\pi$
$830$	1.02344	+	17.9776i	0.0355240	+	0.624011i
$831$	−24.0136	−	81.7829i	−0.833024	−	2.83702i
$832$	−45.4339	−	14.6373i	−1.57514	−	0.507456i
$833$	−10.3506	−	6.65193i	−0.358627	−	0.230476i
$834$	10.9814	+	41.7072i	0.380256	+	1.44420i
$835$	0.422456	+	1.82222i	0.0146197	+	0.0630605i
$836$	−3.29339	−	8.43825i	−0.113904	−	0.291843i
$837$	16.0684	+	25.0029i	0.555405	+	0.864227i
$838$	36.6666	+	25.0497i	1.26663	+	0.865326i
$839$	22.8431	−	50.0195i	0.788633	−	1.72687i	0.108109	−	0.994139i	$-0.465520\pi$
$839$	22.8431	−	50.0195i	0.788633	−	1.72687i	0.680524	−	0.732726i	$-0.261752\pi$
$840$	−13.9209	−	1.99331i	−0.480316	−	0.0687756i
$841$	−5.60041	+	38.9517i	−0.193118	+	1.34316i
$842$	−42.8340	+	4.93277i	−1.47616	+	0.169995i
$843$	−2.84768	+	9.69832i	−0.0980795	+	0.334028i
$844$	−2.37760	−	2.30681i	−0.0818404	−	0.0794037i
$845$	36.2189	+	35.2461i	1.24597	+	1.21250i
$846$	−52.5980	+	31.7476i	−1.80836	+	1.09150i
$847$	−7.23013	−	6.26495i	−0.248430	−	0.215266i
$848$	−0.703569	−	23.2733i	−0.0241607	−	0.799209i
$849$	61.2219	−	27.9591i	2.10113	−	0.959554i
$850$	3.86508	−	13.1186i	0.132571	−	0.449963i
$851$	−2.98389	−	32.1839i	−0.102286	−	1.10325i
$852$	42.9875	−	33.2053i	1.47273	−	1.13760i
$853$	−18.5807	+	8.48552i	−0.636191	+	0.290539i	−0.707282	−	0.706931i	$-0.750079\pi$
$853$	−18.5807	+	8.48552i	−0.636191	+	0.290539i	0.0710917	+	0.997470i	$0.477352\pi$
$854$	−1.05418	+	6.10660i	−0.0360732	+	0.208964i
$855$	5.89687	−	8.10495i	0.201669	−	0.277184i
$856$	2.61191	−	6.73345i	0.0892734	−	0.230145i
$857$	−11.9612	+	10.3644i	−0.408587	+	0.354042i	−0.834774	−	0.550593i	$-0.814402\pi$
$857$	−11.9612	+	10.3644i	−0.408587	+	0.354042i	0.426188	+	0.904635i	$0.359856\pi$
$858$	34.7341	−	107.052i	1.18580	−	3.65469i
$859$	−9.25301	+	31.5128i	−0.315708	+	1.07520i	0.636885	+	0.770959i	$0.280223\pi$
$859$	−9.25301	+	31.5128i	−0.315708	+	1.07520i	−0.952594	+	0.304246i	$0.901596\pi$
$860$	−8.56370	+	32.6013i	−0.292020	+	1.11169i
$861$	13.5446	+	1.94741i	0.461597	+	0.0663676i
$862$	−15.5483	−	18.9986i	−0.529577	−	0.647096i
$863$	−12.8331	+	28.1005i	−0.436843	+	0.956553i	0.555324	+	0.831634i	$0.312594\pi$
$863$	−12.8331	+	28.1005i	−0.436843	+	0.956553i	−0.992167	+	0.124919i	$0.960133\pi$
$864$	−20.7068	+	18.0179i	−0.704458	+	0.612983i
$865$	−10.0392	−	13.0371i	−0.341343	−	0.443274i
$866$	−1.69953	+	1.85331i	−0.0577525	+	0.0629780i
$867$	−5.25103	−	36.5217i	−0.178334	−	1.24034i
$868$	−1.93595	+	9.59525i	−0.0657105	+	0.325684i
$869$	28.3734	+	18.2345i	0.962502	+	0.618563i
$870$	33.9351	+	64.3537i	1.15051	+	2.18179i
$871$	8.42546	−	2.47394i	0.285486	−	0.0838262i
$872$	47.0219	−	34.2530i	1.59236	−	1.15995i
$873$	43.6349			1.47682
$874$	−2.19701	−	6.02053i	−0.0743150	−	0.203648i
$875$	2.25375	+	8.64460i	0.0761907	+	0.292241i
$876$	−15.6609	−	8.24680i	−0.529134	−	0.278634i
$877$	5.10974	+	17.4022i	0.172544	+	0.587630i	0.999672	+	0.0256165i	$0.00815489\pi$
$877$	5.10974	+	17.4022i	0.172544	+	0.587630i	−0.827128	+	0.562013i	$0.810027\pi$
$878$	−25.5996	+	10.8310i	−0.863944	+	0.365529i
$879$	32.1257	+	20.6459i	1.08357	+	0.696369i
$880$	36.6896	−	22.1744i	1.23681	−	0.747498i
$881$	−0.832286	+	0.119665i	−0.0280404	+	0.00403160i	−0.156321	−	0.987706i	$-0.549963\pi$
$881$	−0.832286	+	0.119665i	−0.0280404	+	0.00403160i	0.128280	+	0.991738i	$0.459054\pi$
$882$	28.8440	−	31.4538i	0.971227	−	1.05910i
$883$	4.85771	−	3.12186i	0.163475	−	0.105059i	−0.456345	−	0.889803i	$-0.650842\pi$
$883$	4.85771	−	3.12186i	0.163475	−	0.105059i	0.619820	+	0.784744i	$0.287205\pi$
$884$	−11.3660	−	20.0876i	−0.382280	−	0.675618i
$885$	8.40052	+	3.00363i	0.282380	+	0.100966i
$886$	−22.0694	−	26.9669i	−0.741437	−	0.905971i
$887$	−2.02245	+	14.0665i	−0.0679073	+	0.472306i	0.927284	+	0.374358i	$0.122137\pi$
$887$	−2.02245	+	14.0665i	−0.0679073	+	0.472306i	−0.995192	+	0.0979478i	$0.968772\pi$
$888$	37.9949	−	37.0171i	1.27503	−	1.24221i
$889$	2.93626	−	9.99999i	0.0984791	−	0.335389i
$890$	−4.40842	+	18.9360i	−0.147771	+	0.634736i
$891$	2.28656	+	2.63883i	0.0766025	+	0.0884040i
$892$	−2.14048	−	24.6806i	−0.0716685	−	0.826368i
$893$	5.66694	−	6.53999i	0.189637	−	0.218853i
$894$	−14.2344	−	2.45726i	−0.476068	−	0.0821832i
$895$	−0.859568	+	0.484663i	−0.0287322	+	0.0162005i
$896$	−9.02685	−	0.489844i	−0.301566	−	0.0163645i
$897$	26.2509	−	75.1775i	0.876494	−	2.51010i
$898$	−11.3218	+	23.0516i	−0.377814	+	0.769241i
$899$	46.0642	−	21.0368i	1.53633	−	0.701616i
$900$	42.5592	+	20.9517i	1.41864	+	0.698389i
$901$	7.37263	−	8.50847i	0.245618	−	0.283458i
$902$	−35.7132	+	21.5561i	−1.18912	+	0.717740i
$903$	10.9749	+	12.6657i	0.365222	+	0.421489i
$904$	13.8754	+	38.7360i	0.461490	+	1.28834i
$905$	−5.11294	+	25.1470i	−0.169960	+	0.835915i
$906$	−73.8025	+	8.49910i	−2.45192	+	0.282364i
$907$	−11.7968	−	1.69613i	−0.391708	−	0.0563191i	−0.0563528	−	0.998411i	$-0.517947\pi$
$907$	−11.7968	−	1.69613i	−0.391708	−	0.0563191i	−0.335355	+	0.942092i	$0.608856\pi$
$908$	−10.4965	−	44.9692i	−0.348339	−	1.49235i
$909$	−12.3815	+	27.1118i	−0.410670	+	0.899242i
$910$	13.1260	+	7.41696i	0.435122	+	0.245870i
$911$	−37.4617	+	24.0752i	−1.24116	+	0.797646i	−0.985591	−	0.169144i	$-0.945900\pi$
$911$	−37.4617	+	24.0752i	−1.24116	+	0.797646i	−0.255571	+	0.966790i	$0.582263\pi$
$912$	5.41654	−	9.01616i	0.179360	−	0.298555i
$913$	−27.0146	+	3.88411i	−0.894052	+	0.128545i
$914$	4.84626	−	1.27601i	0.160300	−	0.0422067i
$915$	15.9444	−	30.1691i	0.527104	−	0.997359i
$916$	0.234677	−	4.16473i	0.00775394	−	0.137607i
$917$	−1.56917	+	0.460750i	−0.0518185	+	0.0152153i
$918$	−13.2667	−	0.373483i	−0.437866	−	0.0123268i
$919$	46.2043			1.52414			0.762070	−	0.647495i	$-0.224183\pi$
$919$	46.2043			1.52414			0.762070	+	0.647495i	$0.224183\pi$
$920$	26.3007	−	15.1087i	0.867110	−	0.498117i
$921$	49.0900			1.61757
$922$	−24.9607	−	0.702694i	−0.822038	−	0.0231420i
$923$	−55.8754	+	16.4065i	−1.83916	+	0.540026i
$924$	1.19916	−	21.2810i	0.0394494	−	0.700095i
$925$	−31.0225	−	13.1591i	−1.02001	−	0.432668i
$926$	−48.5570	+	12.7850i	−1.59568	+	0.420140i
$927$	−50.0122	+	7.19066i	−1.64261	+	0.236172i
$928$	25.3665	+	39.2914i	0.832696	+	1.28980i
$929$	45.0323	−	28.9405i	1.47746	−	0.949506i	0.480076	−	0.877227i	$-0.340609\pi$
$929$	45.0323	−	28.9405i	1.47746	−	0.949506i	0.997384	−	0.0722794i	$-0.0230273\pi$
$930$	26.5166	−	46.9272i	0.869515	−	1.53880i
$931$	−2.49716	+	5.46802i	−0.0818412	+	0.179207i
$932$	8.84236	+	37.8824i	0.289641	+	1.24088i
$933$	−1.14346	−	0.164405i	−0.0374353	−	0.00538239i
$934$	20.6305	−	2.37581i	0.675051	−	0.0777390i
$935$	20.3130	+	4.13007i	0.664305	+	0.135068i
$936$	75.3667	−	26.9967i	2.46344	−	0.882416i
$937$	24.2039	+	27.9328i	0.790708	+	0.912525i	0.997834	−	0.0657890i	$-0.0209564\pi$
$937$	24.2039	+	27.9328i	0.790708	+	0.912525i	−0.207126	+	0.978314i	$0.566411\pi$
$938$	1.42379	−	0.859383i	0.0464883	−	0.0280598i
$939$	2.25677	−	2.60445i	0.0736468	−	0.0849929i
$940$	35.0756	+	21.1436i	1.14404	+	0.689627i
$941$	−31.2428	+	14.2681i	−1.01849	+	0.465128i	−0.853458	−	0.521161i	$-0.825499\pi$
$941$	−31.2428	+	14.2681i	−1.01849	+	0.465128i	−0.165029	+	0.986289i	$0.552772\pi$
$942$	23.5508	−	47.9503i	0.767327	−	1.56230i
$943$	−25.6004	+	14.6866i	−0.833663	+	0.478263i
$944$	5.54898	+	1.44872i	0.180604	+	0.0471518i
$945$	7.55183	−	4.25806i	0.245661	−	0.138515i
$946$	−50.3448	−	8.69098i	−1.63685	−	0.282568i
$947$	−6.25578	+	7.21955i	−0.203285	+	0.234604i	−0.848233	−	0.529623i	$-0.822334\pi$
$947$	−6.25578	+	7.21955i	−0.203285	+	0.234604i	0.644948	+	0.764227i	$0.276879\pi$
$948$	3.38383	+	39.0170i	0.109902	+	1.26721i
$949$	12.4263	+	14.3407i	0.403374	+	0.465518i
$950$	−6.61282	−	0.956997i	−0.214548	−	0.0310491i
$951$	16.1572	−	55.0263i	0.523933	−	1.78435i
$952$	−3.05029	−	3.13086i	−0.0988606	−	0.101472i
$953$	5.95621	−	41.4263i	0.192940	−	1.34193i	−0.631233	−	0.775593i	$-0.717451\pi$
$953$	5.95621	−	41.4263i	0.192940	−	1.34193i	0.824174	−	0.566337i	$-0.191640\pi$
$954$	24.7321	+	30.2204i	0.800730	+	0.978422i
$955$	−4.32623	+	12.0996i	−0.139994	+	0.391533i
$956$	17.0943	+	30.2115i	0.552870	+	0.977110i
$957$	−92.7652	+	59.6166i	−2.99867	+	1.92713i
$958$	−3.47374	+	3.78805i	−0.112231	+	0.122386i
$959$	5.59878	−	0.804983i	0.180794	−	0.0259943i
$960$	46.4204	+	17.9757i	1.49821	+	0.580162i
$961$	−5.48344	−	3.52399i	−0.176885	−	0.113677i
$962$	−52.3749	+	22.1595i	−1.68864	+	0.714450i
$963$	3.41258	+	11.6222i	0.109969	+	0.374520i
$964$	−38.3152	−	20.1762i	−1.23405	−	0.649831i
$965$	1.23433	+	14.4846i	0.0397346	+	0.466276i
$966$	1.18255	−	15.0343i	0.0380478	−	0.483721i
$967$	−10.2680			−0.330195			−0.165098	−	0.986277i	$-0.552794\pi$
$967$	−10.2680			−0.330195			−0.165098	+	0.986277i	$0.552794\pi$
$968$	19.9391	+	27.3721i	0.640868	+	0.879772i
$969$	4.87973	−	1.43282i	0.156759	−	0.0460287i
$970$	−13.5680	−	25.7300i	−0.435643	−	0.826142i
$971$	−21.1780	−	13.6103i	−0.679635	−	0.436775i	0.154752	−	0.987953i	$-0.450542\pi$
$971$	−21.1780	−	13.6103i	−0.679635	−	0.436775i	−0.834388	+	0.551178i	$0.814178\pi$
$972$	−6.55982	+	32.5127i	−0.210406	+	1.04285i
$973$	−1.24623	−	8.66769i	−0.0399522	−	0.277874i
$974$	−25.5673	+	27.8807i	−0.819230	+	0.893355i
$975$	−56.0535	−	61.2384i	−1.79515	−	1.96120i
$976$	8.50533	−	20.2196i	0.272249	−	0.647215i
$977$	3.53978	−	7.75105i	0.113248	−	0.247978i	−0.844518	−	0.535527i	$-0.820113\pi$
$977$	3.53978	−	7.75105i	0.113248	−	0.247978i	0.957766	+	0.287549i	$0.0928404\pi$
$978$	13.0874	+	15.9916i	0.418489	+	0.511356i
$979$	−29.1685	−	4.19380i	−0.932230	−	0.134034i
$980$	−27.5162	−	7.22794i	−0.878971	−	0.230888i
$981$	−27.4881	+	93.6159i	−0.877627	+	2.98892i
$982$	3.43495	−	10.5867i	0.109614	−	0.337834i
$983$	25.9268	−	22.4657i	0.826935	−	0.716543i	−0.134697	−	0.990887i	$-0.543006\pi$
$983$	25.9268	−	22.4657i	0.826935	−	0.716543i	0.961632	+	0.274344i	$0.0884605\pi$
$984$	−45.1592	−	17.5173i	−1.43962	−	0.558431i
$985$	13.4857	+	9.81170i	0.429690	+	0.312627i
$986$	−3.84685	+	22.2839i	−0.122509	+	0.709665i
$987$	18.5228	−	8.45906i	0.589586	−	0.269255i
$988$	−8.92399	+	6.89325i	−0.283910	+	0.219304i
$989$	−35.4749	−	6.93847i	−1.12803	−	0.220630i
$990$	−26.1025	+	66.9937i	−0.829592	+	2.12920i
$991$	−6.25675	+	2.85736i	−0.198752	+	0.0907671i	−0.512305	−	0.858804i	$-0.671208\pi$
$991$	−6.25675	+	2.85736i	−0.198752	+	0.0907671i	0.313552	+	0.949571i	$0.398481\pi$
$992$	14.3284	−	31.5480i	0.454927	−	1.00165i
$993$	−22.1762	−	19.2158i	−0.703741	−	0.609795i
$994$	−9.44217	+	5.69919i	−0.299488	+	0.180767i
$995$	−10.1915	−	9.91774i	−0.323092	−	0.314413i
$996$	−22.7450	−	22.0678i	−0.720704	−	0.699246i
$997$	4.05963	−	13.8258i	0.128570	−	0.437868i	−0.869896	−	0.493234i	$-0.835814\pi$
$997$	4.05963	−	13.8258i	0.128570	−	0.437868i	0.998466	+	0.0553664i	$0.0176327\pi$
$998$	−31.5499	+	3.63330i	−0.998696	+	0.115010i
$999$	−4.65400	+	32.3693i	−0.147246	+	1.02412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.o.b.19.1	✓	640
4.3	odd	2	inner	460.2.o.b.19.21	yes	640
5.4	even	2	inner	460.2.o.b.19.64	yes	640
20.19	odd	2	inner	460.2.o.b.19.44	yes	640
23.17	odd	22	inner	460.2.o.b.339.44	yes	640
92.63	even	22	inner	460.2.o.b.339.64	yes	640
115.109	odd	22	inner	460.2.o.b.339.21	yes	640
460.339	even	22	inner	460.2.o.b.339.1	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.o.b.19.1	✓	640	1.1	even	1	trivial
460.2.o.b.19.21	yes	640	4.3	odd	2	inner
460.2.o.b.19.44	yes	640	20.19	odd	2	inner
460.2.o.b.19.64	yes	640	5.4	even	2	inner
460.2.o.b.339.1	yes	640	460.339	even	22	inner
460.2.o.b.339.21	yes	640	115.109	odd	22	inner
460.2.o.b.339.44	yes	640	23.17	odd	22	inner
460.2.o.b.339.64	yes	640	92.63	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41365 - 0.0397971i) q^{2} +(2.67003 - 0.783991i) q^{3} +(1.99683 + 0.112519i) q^{4} +(1.97695 + 1.04482i) q^{5} +(-3.80569 + 1.00203i) q^{6} +(0.790909 - 0.113716i) q^{7} +(-2.81835 - 0.238531i) q^{8} +(3.99064 - 2.56463i) q^{9} +O(q^{10})\)	\(q+(-1.41365 - 0.0397971i) q^{2} +(2.67003 - 0.783991i) q^{3} +(1.99683 + 0.112519i) q^{4} +(1.97695 + 1.04482i) q^{5} +(-3.80569 + 1.00203i) q^{6} +(0.790909 - 0.113716i) q^{7} +(-2.81835 - 0.238531i) q^{8} +(3.99064 - 2.56463i) q^{9} +(-2.75315 - 1.55569i) q^{10} +(1.99109 - 4.35987i) q^{11} +(5.41981 - 1.26507i) q^{12} +(-5.90595 - 0.849148i) q^{13} +(-1.12260 + 0.129278i) q^{14} +(6.09765 + 1.23979i) q^{15} +(3.97468 + 0.449362i) q^{16} +(1.26656 + 1.46169i) q^{17} +(-5.74345 + 3.46668i) q^{18} +(0.618802 - 0.714136i) q^{19} +(3.83008 + 2.30878i) q^{20} +(2.02260 - 0.923689i) q^{21} +(-2.98822 + 6.08411i) q^{22} +(-2.20929 + 4.25664i) q^{23} +(-7.71208 + 1.57268i) q^{24} +(2.81670 + 4.13113i) q^{25} +(8.31518 + 1.43544i) q^{26} +(3.17754 - 3.66708i) q^{27} +(1.59211 - 0.138079i) q^{28} +(-5.41409 - 6.24819i) q^{29} +(-8.57063 - 1.99530i) q^{30} +(-1.72567 + 5.87709i) q^{31} +(-5.60094 - 0.793423i) q^{32} +(1.89816 - 13.2020i) q^{33} +(-1.73231 - 2.11673i) q^{34} +(1.68240 + 0.601548i) q^{35} +(8.25722 - 4.67212i) q^{36} +(-5.66971 + 3.64370i) q^{37} +(-0.903192 + 0.984914i) q^{38} +(-16.4348 + 2.36296i) q^{39} +(-5.32253 - 3.41624i) q^{40} +(5.17715 + 3.32716i) q^{41} +(-2.89601 + 1.22528i) q^{42} +(2.12347 + 7.23187i) q^{43} +(4.46643 - 8.48189i) q^{44} +(10.5689 - 0.900651i) q^{45} +(3.29258 - 5.92950i) q^{46} +9.15791 q^{47} +(10.9648 - 1.91630i) q^{48} +(-6.10385 + 1.79225i) q^{49} +(-3.81743 - 5.95208i) q^{50} +(4.52770 + 2.90978i) q^{51} +(-11.6977 - 2.36014i) q^{52} +(-0.828412 - 5.76174i) q^{53} +(-4.63788 + 5.05752i) q^{54} +(8.49157 - 6.53894i) q^{55} +(-2.25618 + 0.131834i) q^{56} +(1.09234 - 2.39190i) q^{57} +(7.40499 + 9.04824i) q^{58} +(1.41915 + 0.204043i) q^{59} +(12.0365 + 3.16175i) q^{60} +(1.54500 - 5.26179i) q^{61} +(2.67339 - 8.23950i) q^{62} +(2.86460 - 2.48219i) q^{63} +(7.88621 + 1.34453i) q^{64} +(-10.7886 - 7.84939i) q^{65} +(-3.20874 + 18.5875i) q^{66} +(-1.33870 + 0.611366i) q^{67} +(2.36464 + 3.06126i) q^{68} +(-2.56170 + 13.0974i) q^{69} +(-2.35440 - 0.917335i) q^{70} +(8.87792 - 4.05441i) q^{71} +(-11.8588 + 6.27614i) q^{72} +(-2.40346 - 2.08261i) q^{73} +(8.16001 - 4.92529i) q^{74} +(10.7594 + 8.82196i) q^{75} +(1.31600 - 1.35638i) q^{76} +(1.07898 - 3.67468i) q^{77} +(23.3271 - 2.68636i) q^{78} +(-1.00145 + 6.96520i) q^{79} +(7.38826 + 5.04120i) q^{80} +(-0.302627 + 0.662660i) q^{81} +(-7.18629 - 4.90948i) q^{82} +(-3.07852 - 4.79028i) q^{83} +(4.14272 - 1.61687i) q^{84} +(0.976729 + 4.21302i) q^{85} +(-2.71404 - 10.3079i) q^{86} +(-19.3543 - 12.4382i) q^{87} +(-6.65154 + 11.8127i) q^{88} +(-1.73215 - 5.89918i) q^{89} +(-14.9766 + 0.852596i) q^{90} -4.76763 q^{91} +(-4.89054 + 8.25122i) q^{92} +17.0449i q^{93} +(-12.9461 - 0.364459i) q^{94} +(1.96949 - 0.765276i) q^{95} +(-15.5767 + 2.27262i) q^{96} +(7.73828 + 4.97309i) q^{97} +(8.70005 - 2.29071i) q^{98} +(-3.23574 - 22.5051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9}+O(q^{10}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9	\( 640 q - 6 q^{4} - 22 q^{5} + 2 q^{6} - 100 q^{9} - 11 q^{10} - 22 q^{14} + 2 q^{16} - 11 q^{20} - 44 q^{21} - 8 q^{24} - 38 q^{25} - 46 q^{26} - 52 q^{29} - 11 q^{30} - 44 q^{34} + 18 q^{36} - 11 q^{40} - 76 q^{41} - 154 q^{44} - 30 q^{46} - 100 q^{49} + 21 q^{50} + 178 q^{54} + 242 q^{56} - 11 q^{60} - 44 q^{61} + 6 q^{64} - 22 q^{65} + 44 q^{66} - 12 q^{69} + 22 q^{70} - 22 q^{74} + 88 q^{76} - 110 q^{80} - 252 q^{81} - 374 q^{84} + 94 q^{85} - 198 q^{86} - 44 q^{89} - 242 q^{90} - 62 q^{94} + 372 q^{96}+O(q^{100}) \) 640 * q - 6 * q^4 - 22 * q^5 + 2 * q^6 - 100 * q^9 - 11 * q^10 - 22 * q^14 + 2 * q^16 - 11 * q^20 - 44 * q^21 - 8 * q^24 - 38 * q^25 - 46 * q^26 - 52 * q^29 - 11 * q^30 - 44 * q^34 + 18 * q^36 - 11 * q^40 - 76 * q^41 - 154 * q^44 - 30 * q^46 - 100 * q^49 + 21 * q^50 + 178 * q^54 + 242 * q^56 - 11 * q^60 - 44 * q^61 + 6 * q^64 - 22 * q^65 + 44 * q^66 - 12 * q^69 + 22 * q^70 - 22 * q^74 + 88 * q^76 - 110 * q^80 - 252 * q^81 - 374 * q^84 + 94 * q^85 - 198 * q^86 - 44 * q^89 - 242 * q^90 - 62 * q^94 + 372 * q^96

Introduction

L-functions

Modular forms

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