LMFDB - Embedded newform 418.2.h.b.65.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(65,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("418.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.h (of order $6$, degree $2$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 41 x^{18} + 707 x^{16} + 6667 x^{14} + 37400 x^{12} + 126976 x^{10} + 253280 x^{8} + \cdots + 2304 $ x^20 + 41x^18 + 707x^16 + 6667x^14 + 37400x^12 + 126976x^10 + 253280x^8 + 273276x^6 + 137476x^4 + 30336*x^2 + 2304
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Root			$0.579050i$ of defining polynomial
Character	$\chi$	$=$	418.65
Dual form			418.2.h.b.373.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.501472 - 0.289525i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.06779 - 1.84947i) q^{5} +(-0.501472 + 0.289525i) q^{6} -0.637717i q^{7} -1.00000 q^{8} +(-1.33235 - 2.30770i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.501472 - 0.289525i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.06779 - 1.84947i) q^{5} +(-0.501472 + 0.289525i) q^{6} -0.637717i q^{7} -1.00000 q^{8} +(-1.33235 - 2.30770i) q^{9} +(-1.06779 - 1.84947i) q^{10} +(-3.03774 - 1.33121i) q^{11} +0.579050i q^{12} +(2.63347 + 4.56130i) q^{13} +(-0.552279 - 0.318859i) q^{14} +(-1.07094 + 0.618306i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.56416 - 1.48042i) q^{17} -2.66470 q^{18} +(3.92865 - 1.88830i) q^{19} -2.13558 q^{20} +(-0.184635 + 0.319798i) q^{21} +(-2.67174 + 1.96515i) q^{22} +(-3.83656 - 6.64512i) q^{23} +(0.501472 + 0.289525i) q^{24} +(0.219639 + 0.380426i) q^{25} +5.26693 q^{26} +3.28015i q^{27} +(-0.552279 + 0.318859i) q^{28} +(1.42808 + 2.47350i) q^{29} +1.23661i q^{30} -8.81822i q^{31} +(0.500000 + 0.866025i) q^{32} +(1.13792 + 1.54707i) q^{33} +(-2.56416 + 1.48042i) q^{34} +(-1.17944 - 0.680949i) q^{35} +(-1.33235 + 2.30770i) q^{36} -2.47627i q^{37} +(0.329008 - 4.34646i) q^{38} -3.04982i q^{39} +(-1.06779 + 1.84947i) q^{40} +(-4.38672 + 7.59802i) q^{41} +(0.184635 + 0.319798i) q^{42} +(-1.80603 - 1.04271i) q^{43} +(0.366005 + 3.29637i) q^{44} -5.69069 q^{45} -7.67312 q^{46} +(1.94359 + 3.36640i) q^{47} +(0.501472 - 0.289525i) q^{48} +6.59332 q^{49} +0.439278 q^{50} +(0.857237 + 1.48478i) q^{51} +(2.63347 - 4.56130i) q^{52} +(3.32586 - 1.92019i) q^{53} +(2.84069 + 1.64007i) q^{54} +(-5.70572 + 4.19675i) q^{55} +0.637717i q^{56} +(-2.51682 - 0.190512i) q^{57} +2.85615 q^{58} +(11.6633 + 6.73379i) q^{59} +(1.07094 + 0.618306i) q^{60} +(12.8719 - 7.43161i) q^{61} +(-7.63680 - 4.40911i) q^{62} +(-1.47166 + 0.849663i) q^{63} +1.00000 q^{64} +11.2480 q^{65} +(1.90876 - 0.211935i) q^{66} +(0.199470 - 0.115164i) q^{67} +2.96084i q^{68} +4.44312i q^{69} +(-1.17944 + 0.680949i) q^{70} +(-1.28095 - 0.739556i) q^{71} +(1.33235 + 2.30770i) q^{72} +(13.5966 + 7.84999i) q^{73} +(-2.14451 - 1.23813i) q^{74} -0.254364i q^{75} +(-3.59964 - 2.45816i) q^{76} +(-0.848938 + 1.93722i) q^{77} +(-2.64122 - 1.52491i) q^{78} +(1.07471 - 1.86145i) q^{79} +(1.06779 + 1.84947i) q^{80} +(-3.04737 + 5.27819i) q^{81} +(4.38672 + 7.59802i) q^{82} -8.76810i q^{83} +0.369270 q^{84} +(-5.47598 + 3.16156i) q^{85} +(-1.80603 + 1.04271i) q^{86} -1.65386i q^{87} +(3.03774 + 1.33121i) q^{88} +(3.10177 - 1.79081i) q^{89} +(-2.84535 + 4.92829i) q^{90} +(2.90882 - 1.67941i) q^{91} +(-3.83656 + 6.64512i) q^{92} +(-2.55310 + 4.42209i) q^{93} +3.88718 q^{94} +(0.702624 - 9.28224i) q^{95} -0.579050i q^{96} +(-2.77950 - 1.60474i) q^{97} +(3.29666 - 5.70998i) q^{98} +(0.975293 + 8.78383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	$ 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) $ 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.501472	−	0.289525i	−0.289525	−	0.167157i	0.348203	−	0.937419i	$-0.386792\pi$
$3$	−0.501472	−	0.289525i	−0.289525	−	0.167157i	−0.637728	+	0.770262i	$0.720125\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.06779	−	1.84947i	0.477531	−	0.827108i	−0.522137	−	0.852862i	$-0.674865\pi$
$5$	1.06779	−	1.84947i	0.477531	−	0.827108i	0.999668	+	0.0257532i	$0.00819840\pi$
$6$	−0.501472	+	0.289525i	−0.204725	+	0.118198i
$7$		−	0.637717i		−	0.241034i	−0.992711	−	0.120517i	$-0.961545\pi$
$7$		−	0.637717i		−	0.241034i	0.992711	−	0.120517i	$-0.0384553\pi$
$8$	−1.00000			−0.353553
$9$	−1.33235	−	2.30770i	−0.444117	−	0.769233i
$10$	−1.06779	−	1.84947i	−0.337666	−	0.584854i
$11$	−3.03774	−	1.33121i	−0.915913	−	0.401376i
$11$	−3.03774	−	1.33121i	−0.915913	−	0.401376i
$12$			0.579050i			0.167157i
$13$	2.63347	+	4.56130i	0.730392	+	1.26508i	0.956716	+	0.291024i	$0.0939960\pi$
$13$	2.63347	+	4.56130i	0.730392	+	1.26508i	−0.226324	+	0.974052i	$0.572671\pi$
$14$	−0.552279	−	0.318859i	−0.147603	−	0.0852185i
$15$	−1.07094	+	0.618306i	−0.276515	+	0.159646i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.56416	−	1.48042i	−0.621900	−	0.359054i	0.155708	−	0.987803i	$-0.450234\pi$
$17$	−2.56416	−	1.48042i	−0.621900	−	0.359054i	−0.777608	+	0.628749i	$0.783567\pi$
$18$	−2.66470			−0.628076
$19$	3.92865	−	1.88830i	0.901295	−	0.433207i
$19$	3.92865	−	1.88830i	0.901295	−	0.433207i
$20$	−2.13558			−0.477531
$21$	−0.184635	+	0.319798i	−0.0402907	+	0.0697855i
$22$	−2.67174	+	1.96515i	−0.569616	+	0.418972i
$23$	−3.83656	−	6.64512i	−0.799978	−	1.38560i	−0.919630	−	0.392786i	$-0.871511\pi$
$23$	−3.83656	−	6.64512i	−0.799978	−	1.38560i	0.119652	−	0.992816i	$-0.461822\pi$
$24$	0.501472	+	0.289525i	0.102363	+	0.0590991i
$25$	0.219639	+	0.380426i	0.0439278	+	0.0760852i
$26$	5.26693			1.03293
$27$			3.28015i			0.631265i
$28$	−0.552279	+	0.318859i	−0.104371	+	0.0602586i
$29$	1.42808	+	2.47350i	0.265187	+	0.459318i	0.967613	−	0.252440i	$-0.0812329\pi$
$29$	1.42808	+	2.47350i	0.265187	+	0.459318i	−0.702426	+	0.711757i	$0.747900\pi$
$30$			1.23661i			0.225773i
$31$		−	8.81822i		−	1.58380i	−0.610652	−	0.791899i	$-0.709092\pi$
$31$		−	8.81822i		−	1.58380i	0.610652	−	0.791899i	$-0.290908\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	1.13792	+	1.54707i	0.198087	+	0.269310i
$34$	−2.56416	+	1.48042i	−0.439750	+	0.253890i
$35$	−1.17944	−	0.680949i	−0.199362	−	0.115101i
$36$	−1.33235	+	2.30770i	−0.222058	+	0.384616i
$37$		−	2.47627i		−	0.407096i	−0.979065	−	0.203548i	$-0.934753\pi$
$37$		−	2.47627i		−	0.407096i	0.979065	−	0.203548i	$-0.0652473\pi$
$38$	0.329008	−	4.34646i	0.0533721	−	0.705090i
$39$		−	3.04982i		−	0.488362i
$40$	−1.06779	+	1.84947i	−0.168833	+	0.292427i
$41$	−4.38672	+	7.59802i	−0.685091	+	1.18661i	0.288318	+	0.957535i	$0.406904\pi$
$41$	−4.38672	+	7.59802i	−0.685091	+	1.18661i	−0.973408	+	0.229077i	$0.926429\pi$
$42$	0.184635	+	0.319798i	0.0284898	+	0.0493458i
$43$	−1.80603	−	1.04271i	−0.275417	−	0.159012i	0.355930	−	0.934513i	$-0.384164\pi$
$43$	−1.80603	−	1.04271i	−0.275417	−	0.159012i	−0.631347	+	0.775501i	$0.717498\pi$
$44$	0.366005	+	3.29637i	0.0551773	+	0.496946i
$45$	−5.69069			−0.848319
$46$	−7.67312			−1.13134
$47$	1.94359	+	3.36640i	0.283502	+	0.491039i	0.972245	−	0.233966i	$-0.0751705\pi$
$47$	1.94359	+	3.36640i	0.283502	+	0.491039i	−0.688743	+	0.725006i	$0.741837\pi$
$48$	0.501472	−	0.289525i	0.0723813	−	0.0417894i
$49$	6.59332			0.941902
$50$	0.439278			0.0621233
$51$	0.857237	+	1.48478i	0.120037	+	0.207910i
$52$	2.63347	−	4.56130i	0.365196	−	0.632538i
$53$	3.32586	−	1.92019i	0.456842	−	0.263758i	−0.253873	−	0.967237i	$-0.581705\pi$
$53$	3.32586	−	1.92019i	0.456842	−	0.263758i	0.710716	+	0.703480i	$0.248371\pi$
$54$	2.84069	+	1.64007i	0.386569	+	0.223186i
$55$	−5.70572	+	4.19675i	−0.769359	+	0.565890i
$56$			0.637717i			0.0852185i
$57$	−2.51682	−	0.190512i	−0.333361	−	0.0252339i
$58$	2.85615			0.375031
$59$	11.6633	+	6.73379i	1.51843	+	0.876664i	0.999765	+	0.0216851i	$0.00690314\pi$
$59$	11.6633	+	6.73379i	1.51843	+	0.876664i	0.518662	+	0.854979i	$0.326430\pi$
$60$	1.07094	+	0.618306i	0.138257	+	0.0798229i
$61$	12.8719	−	7.43161i	1.64808	−	0.951521i	0.670249	−	0.742137i	$-0.266187\pi$
$61$	12.8719	−	7.43161i	1.64808	−	0.951521i	0.977833	−	0.209384i	$-0.0671459\pi$
$62$	−7.63680	−	4.40911i	−0.969875	−	0.559957i
$63$	−1.47166	+	0.849663i	−0.185412	+	0.107047i
$64$	1.00000			0.125000
$65$	11.2480			1.39514
$66$	1.90876	−	0.211935i	0.234952	−	0.0260874i
$67$	0.199470	−	0.115164i	0.0243691	−	0.0140695i	−0.487766	−	0.872974i	$-0.662188\pi$
$67$	0.199470	−	0.115164i	0.0243691	−	0.0140695i	0.512135	+	0.858905i	$0.328855\pi$
$68$			2.96084i			0.359054i
$69$			4.44312i			0.534889i
$70$	−1.17944	+	0.680949i	−0.140970	+	0.0813890i
$71$	−1.28095	−	0.739556i	−0.152021	−	0.0877692i	0.422060	−	0.906568i	$-0.361307\pi$
$71$	−1.28095	−	0.739556i	−0.152021	−	0.0877692i	−0.574081	+	0.818799i	$0.694640\pi$
$72$	1.33235	+	2.30770i	0.157019	+	0.271965i
$73$	13.5966	+	7.84999i	1.59136	+	0.918771i	0.993074	+	0.117487i	$0.0374840\pi$
$73$	13.5966	+	7.84999i	1.59136	+	0.918771i	0.598284	+	0.801284i	$0.295849\pi$
$74$	−2.14451	−	1.23813i	−0.249294	−	0.143930i
$75$		−	0.254364i		−	0.0293714i
$76$	−3.59964	−	2.45816i	−0.412908	−	0.281970i
$77$	−0.848938	+	1.93722i	−0.0967455	+	0.220767i
$78$	−2.64122	−	1.52491i	−0.299059	−	0.172662i
$79$	1.07471	−	1.86145i	0.120914	−	0.209429i	−0.799214	−	0.601046i	$-0.794751\pi$
$79$	1.07471	−	1.86145i	0.120914	−	0.209429i	0.920128	+	0.391617i	$0.128084\pi$
$80$	1.06779	+	1.84947i	0.119383	+	0.206777i
$81$	−3.04737	+	5.27819i	−0.338596	+	0.586466i
$82$	4.38672	+	7.59802i	0.484432	+	0.839061i
$83$		−	8.76810i		−	0.962424i	−0.876604	−	0.481212i	$-0.840197\pi$
$83$		−	8.76810i		−	0.962424i	0.876604	−	0.481212i	$-0.159803\pi$
$84$	0.369270			0.0402907
$85$	−5.47598	+	3.16156i	−0.593953	+	0.342919i
$86$	−1.80603	+	1.04271i	−0.194749	+	0.112439i
$87$		−	1.65386i		−	0.177312i
$88$	3.03774	+	1.33121i	0.323824	+	0.141908i
$89$	3.10177	−	1.79081i	0.328786	−	0.189825i	−0.326516	−	0.945192i	$-0.605875\pi$
$89$	3.10177	−	1.79081i	0.328786	−	0.189825i	0.655302	+	0.755367i	$0.272541\pi$
$90$	−2.84535	+	4.92829i	−0.299926	+	0.519487i
$91$	2.90882	−	1.67941i	0.304927	−	0.176050i
$92$	−3.83656	+	6.64512i	−0.399989	+	0.692801i
$93$	−2.55310	+	4.42209i	−0.264744	+	0.458550i
$94$	3.88718			0.400932
$95$	0.702624	−	9.28224i	0.0720877	−	0.952338i
$96$		−	0.579050i		−	0.0590991i
$97$	−2.77950	−	1.60474i	−0.282215	−	0.162937i	0.352211	−	0.935921i	$-0.385430\pi$
$97$	−2.77950	−	1.60474i	−0.282215	−	0.162937i	−0.634426	+	0.772984i	$0.718763\pi$
$98$	3.29666	−	5.70998i	0.333013	−	0.576795i
$99$	0.975293	+	8.78383i	0.0980206	+	0.882808i
$100$	0.219639	−	0.380426i	0.0219639	−	0.0380426i
$101$	−8.56772	+	4.94658i	−0.852520	+	0.492203i	−0.861500	−	0.507757i	$-0.830475\pi$
$101$	−8.56772	+	4.94658i	−0.852520	+	0.492203i	0.00898036	+	0.999960i	$0.497141\pi$
$102$	1.71447			0.169758
$103$			11.5054i			1.13366i	0.823834	+	0.566830i	$0.191831\pi$
$103$			11.5054i			1.13366i	−0.823834	+	0.566830i	$0.808169\pi$
$104$	−2.63347	−	4.56130i	−0.258233	−	0.447272i
$105$	0.394304	+	0.682955i	0.0384801	+	0.0666496i
$106$		−	3.84037i		−	0.373010i
$107$	−0.742853			−0.0718143			−0.0359071	−	0.999355i	$-0.511432\pi$
$107$	−0.742853			−0.0718143			−0.0359071	+	0.999355i	$0.511432\pi$
$108$	2.84069	−	1.64007i	0.273346	−	0.157816i
$109$	2.53185	−	4.38530i	0.242508	−	0.420035i	−0.718920	−	0.695092i	$-0.755363\pi$
$109$	2.53185	−	4.38530i	0.242508	−	0.420035i	0.961428	+	0.275057i	$0.0886968\pi$
$110$	0.781634	+	7.03967i	0.0745258	+	0.671206i
$111$	−0.716942	+	1.24178i	−0.0680491	+	0.117865i
$112$	0.552279	+	0.318859i	0.0521855	+	0.0301293i
$113$		−	16.5652i		−	1.55832i	−0.626822	−	0.779162i	$-0.715645\pi$
$113$		−	16.5652i		−	1.55832i	0.626822	−	0.779162i	$-0.284355\pi$
$114$	−1.42340	+	2.08438i	−0.133314	+	0.195220i
$115$	−16.3866			−1.52806
$116$	1.42808	−	2.47350i	0.132594	−	0.229659i
$117$	7.01740	−	12.1545i	0.648759	−	1.12368i
$118$	11.6633	−	6.73379i	1.07369	−	0.619895i
$119$	−0.944088	+	1.63521i	−0.0865444	+	0.149899i
$120$	1.07094	−	0.618306i	0.0977627	−	0.0564433i
$121$	7.45573	+	8.08777i	0.677794	+	0.735252i
$122$		−	14.8632i		−	1.34565i
$123$	4.39964	−	2.54013i	0.396702	−	0.229036i
$124$	−7.63680	+	4.40911i	−0.685805	+	0.395950i
$125$	11.6160			1.03897
$126$			1.69933i			0.151388i
$127$	9.54313	+	16.5292i	0.846816	+	1.46673i	0.884035	+	0.467421i	$0.154817\pi$
$127$	9.54313	+	16.5292i	0.846816	+	1.46673i	−0.0372187	+	0.999307i	$0.511850\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.603783	+	1.04578i	0.0531602	+	0.0920761i
$130$	5.62399	−	9.74104i	0.493257	−	0.854346i
$131$	−16.2596	−	9.38748i	−1.42061	−	0.820188i	−0.424256	−	0.905542i	$-0.639464\pi$
$131$	−16.2596	−	9.38748i	−1.42061	−	0.820188i	−0.996351	+	0.0853542i	$0.972798\pi$
$132$	0.770840	−	1.75900i	0.0670930	−	0.153102i
$133$	−1.20420	−	2.50537i	−0.104418	−	0.217243i
$134$		−	0.230328i		−	0.0198973i
$135$	6.06654	+	3.50252i	0.522124	+	0.301449i
$136$	2.56416	+	1.48042i	0.219875	+	0.126945i
$137$	8.01952	+	13.8902i	0.685154	+	1.18672i	0.973388	+	0.229161i	$0.0735983\pi$
$137$	8.01952	+	13.8902i	0.685154	+	1.18672i	−0.288235	+	0.957560i	$0.593068\pi$
$138$	3.84786	+	2.22156i	0.327551	+	0.189112i
$139$	−3.40312	+	1.96479i	−0.288649	+	0.166651i	−0.637332	−	0.770589i	$-0.719962\pi$
$139$	−3.40312	+	1.96479i	−0.288649	+	0.166651i	0.348684	+	0.937240i	$0.386629\pi$
$140$			1.36190i			0.115101i
$141$		−	2.25087i		−	0.189558i
$142$	−1.28095	+	0.739556i	−0.107495	+	0.0620622i
$143$	−1.92772	−	17.3617i	−0.161204	−	1.45186i
$144$	2.66470			0.222058
$145$	6.09956			0.506541
$146$	13.5966	−	7.84999i	1.12526	−	0.649669i
$147$	−3.30637	−	1.90893i	−0.272704	−	0.157446i
$148$	−2.14451	+	1.23813i	−0.176278	+	0.101774i
$149$	−15.5815	−	8.99596i	−1.27648	−	0.736978i	−0.300283	−	0.953850i	$-0.597081\pi$
$149$	−15.5815	−	8.99596i	−1.27648	−	0.736978i	−0.976200	+	0.216873i	$0.930414\pi$
$150$	−0.220286	−	0.127182i	−0.0179863	−	0.0103844i
$151$	−17.8972			−1.45646			−0.728228	−	0.685335i	$-0.759656\pi$
$151$	−17.8972			−1.45646			−0.728228	+	0.685335i	$0.759656\pi$
$152$	−3.92865	+	1.88830i	−0.318656	+	0.153162i
$153$			7.88974i			0.637848i
$154$	1.25321	+	1.70381i	0.100987	+	0.137297i
$155$	−16.3090	−	9.41602i	−1.30997	−	0.756313i
$156$	−2.64122	+	1.52491i	−0.211467	+	0.122090i
$157$	−6.08255	+	10.5353i	−0.485440	+	0.840807i	−0.999860	−	0.0167316i	$-0.994674\pi$
$157$	−6.08255	+	10.5353i	−0.485440	+	0.840807i	0.514420	+	0.857538i	$0.328007\pi$
$158$	−1.07471	−	1.86145i	−0.0854990	−	0.148089i
$159$	−2.22377			−0.176356
$160$	2.13558			0.168833
$161$	−4.23770	+	2.44664i	−0.333978	+	0.192822i
$162$	3.04737	+	5.27819i	0.239424	+	0.414694i
$163$	−9.39151			−0.735600			−0.367800	−	0.929905i	$-0.619889\pi$
$163$	−9.39151			−0.735600			−0.367800	+	0.929905i	$0.619889\pi$
$164$	8.77344			0.685091
$165$	4.07633	−	0.452605i	0.317341	−	0.0352353i
$166$	−7.59340	−	4.38405i	−0.589362	−	0.340268i
$167$	8.74488	+	15.1466i	0.676699	+	1.17208i	0.975969	+	0.217909i	$0.0699235\pi$
$167$	8.74488	+	15.1466i	0.676699	+	1.17208i	−0.299270	+	0.954168i	$0.596743\pi$
$168$	0.184635	−	0.319798i	0.0142449	−	0.0246729i
$169$	−7.37029	+	12.7657i	−0.566945	+	0.981978i
$170$			6.32312i			0.484961i
$171$	−9.59198	−	6.55026i	−0.733517	−	0.500911i
$172$			2.08543i			0.159012i
$173$	−1.72261	+	2.98366i	−0.130968	+	0.226843i	−0.924050	−	0.382272i	$-0.875142\pi$
$173$	−1.72261	+	2.98366i	−0.130968	+	0.226843i	0.793082	+	0.609115i	$0.208475\pi$
$174$	−1.43228	−	0.826928i	−0.108581	−	0.0626893i
$175$	0.242604	−	0.140068i	0.0183391	−	0.0105881i
$176$	2.67174	−	1.96515i	0.201390	−	0.148129i
$177$	−3.89920	−	6.75362i	−0.293082	−	0.507633i
$178$		−	3.58161i		−	0.268453i
$179$		−	3.60956i		−	0.269791i	−0.990860	−	0.134896i	$-0.956930\pi$
$179$		−	3.60956i		−	0.269791i	0.990860	−	0.134896i	$-0.0430699\pi$
$180$	2.84535	+	4.92829i	0.212080	+	0.367333i
$181$	13.1744	−	7.60624i	0.979246	−	0.565368i	0.0772033	−	0.997015i	$-0.475401\pi$
$181$	13.1744	−	7.60624i	0.979246	−	0.565368i	0.902042	+	0.431648i	$0.142068\pi$
$182$		−	3.35881i		−	0.248972i
$183$	−8.60656			−0.636215
$184$	3.83656	+	6.64512i	0.282835	+	0.489884i
$185$	−4.57979	−	2.64414i	−0.336713	−	0.194401i
$186$	2.55310	+	4.42209i	0.187202	+	0.324244i
$187$	5.81850	+	7.91057i	0.425491	+	0.578478i
$188$	1.94359	−	3.36640i	0.141751	−	0.245520i
$189$	2.09181			0.152156
$190$	−7.68735	−	5.24961i	−0.557699	−	0.380847i
$191$	23.6698			1.71269			0.856344	−	0.516405i	$-0.172730\pi$
$191$	23.6698			1.71269			0.856344	+	0.516405i	$0.172730\pi$
$192$	−0.501472	−	0.289525i	−0.0361906	−	0.0208947i
$193$	−1.94997	+	3.37744i	−0.140362	+	0.243114i	−0.927633	−	0.373493i	$-0.878160\pi$
$193$	−1.94997	+	3.37744i	−0.140362	+	0.243114i	0.787271	+	0.616607i	$0.211493\pi$
$194$	−2.77950	+	1.60474i	−0.199556	+	0.115214i
$195$	−5.64055	−	3.25657i	−0.403928	−	0.233208i
$196$	−3.29666	−	5.70998i	−0.235476	−	0.407856i
$197$			0.126534i			0.00901515i	0.999990	+	0.00450757i	$0.00143481\pi$
$197$			0.126534i			0.00901515i	−0.999990	+	0.00450757i	$0.998565\pi$
$198$	8.09467	+	3.54729i	0.575263	+	0.252095i
$199$	−5.29673	−	9.17421i	−0.375476	−	0.650343i	0.614923	−	0.788588i	$-0.289187\pi$
$199$	−5.29673	−	9.17421i	−0.375476	−	0.650343i	−0.990398	+	0.138245i	$0.955854\pi$
$200$	−0.219639	−	0.380426i	−0.0155308	−	0.0269002i
$201$	−0.133371			−0.00940729
$202$			9.89315i			0.696080i
$203$	1.57739	−	0.910709i	0.110711	−	0.0639192i
$204$	0.857237	−	1.48478i	0.0600186	−	0.103955i
$205$	9.36821	+	16.2262i	0.654304	+	1.13329i
$206$	9.96397	+	5.75270i	0.694223	+	0.400810i
$207$	−10.2233	+	17.7072i	−0.710567	+	1.23074i
$208$	−5.26693			−0.365196
$209$	−14.4480	+	0.506296i	−0.999387	+	0.0350212i
$210$	0.788608			0.0544191
$211$	4.72246	−	8.17954i	0.325108	−	0.563103i	−0.656427	−	0.754390i	$-0.727933\pi$
$211$	4.72246	−	8.17954i	0.325108	−	0.563103i	0.981534	+	0.191287i	$0.0612662\pi$
$212$	−3.32586	−	1.92019i	−0.228421	−	0.131879i
$213$	0.428240	+	0.741734i	0.0293425	+	0.0508228i
$214$	−0.371426	+	0.643329i	−0.0253902	+	0.0439771i
$215$	−3.85693	+	2.22680i	−0.263041	+	0.151867i
$216$		−	3.28015i		−	0.223186i
$217$	−5.62353			−0.381750
$218$	−2.53185	−	4.38530i	−0.171479	−	0.297010i
$219$	−4.54554	−	7.87310i	−0.307159	−	0.532015i
$220$	6.48735	+	2.84292i	0.437377	+	0.191670i
$221$		−	15.5945i		−	1.04900i
$222$	0.716942	+	1.24178i	0.0481180	+	0.0833428i
$223$	−16.5914	−	9.57907i	−1.11104	−	0.641462i	−0.171945	−	0.985107i	$-0.555005\pi$
$223$	−16.5914	−	9.57907i	−1.11104	−	0.641462i	−0.939100	+	0.343645i	$0.888338\pi$
$224$	0.552279	−	0.318859i	0.0369007	−	0.0213046i
$225$	0.585272	−	1.01372i	0.0390181	−	0.0675814i
$226$	−14.3459	−	8.28261i	−0.954275	−	0.550951i
$227$	−11.9507			−0.793196			−0.396598	−	0.917992i	$-0.629809\pi$
$227$	−11.9507			−0.793196			−0.396598	+	0.917992i	$0.629809\pi$
$228$	1.09342	+	2.27489i	0.0724137	+	0.150658i
$229$	−11.9812			−0.791739			−0.395869	−	0.918307i	$-0.629557\pi$
$229$	−11.9812			−0.791739			−0.395869	+	0.918307i	$0.629557\pi$
$230$	−8.19330	+	14.1912i	−0.540250	+	0.935741i
$231$	0.986593	−	0.725673i	0.0649130	−	0.0477458i
$232$	−1.42808	−	2.47350i	−0.0937578	−	0.162393i
$233$	−10.0521	−	5.80360i	−0.658537	−	0.380207i	0.133182	−	0.991092i	$-0.457480\pi$
$233$	−10.0521	−	5.80360i	−0.658537	−	0.380207i	−0.791719	+	0.610885i	$0.790814\pi$
$234$	−7.01740	−	12.1545i	−0.458742	−	0.794564i
$235$	8.30140			0.541524
$236$		−	13.4676i		−	0.876664i
$237$	−1.07787	+	0.622309i	−0.0700152	+	0.0404233i
$238$	0.944088	+	1.63521i	0.0611961	+	0.105995i
$239$			15.3728i			0.994383i	0.867641	+	0.497191i	$0.165635\pi$
$239$			15.3728i			0.994383i	−0.867641	+	0.497191i	$0.834365\pi$
$240$		−	1.23661i		−	0.0798229i
$241$	−4.41439	−	7.64595i	−0.284356	−	0.492519i	0.688097	−	0.725619i	$-0.258446\pi$
$241$	−4.41439	−	7.64595i	−0.284356	−	0.492519i	−0.972453	+	0.233100i	$0.925113\pi$
$242$	10.7321	−	2.41297i	0.689884	−	0.155112i
$243$	11.5784	−	6.68480i	0.742755	−	0.428830i
$244$	−12.8719	−	7.43161i	−0.824041	−	0.475760i
$245$	7.04029	−	12.1941i	0.449788	−	0.779055i
$246$		−	5.08026i		−	0.323906i
$247$	18.9591	+	12.9470i	1.20634	+	0.823796i
$248$			8.81822i			0.559957i
$249$	−2.53859	+	4.39696i	−0.160876	+	0.278646i
$250$	5.80802	−	10.0598i	0.367331	−	0.636237i
$251$	−12.6547	−	21.9187i	−0.798761	−	1.38349i	−0.920424	−	0.390922i	$-0.872156\pi$
$251$	−12.6547	−	21.9187i	−0.798761	−	1.38349i	0.121663	−	0.992571i	$-0.461177\pi$
$252$	1.47166	+	0.849663i	0.0927058	+	0.0535237i
$253$	2.80840	+	25.2934i	0.176562	+	1.59018i
$254$	19.0863			1.19758
$255$	3.66140			0.229286
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.4114	+	7.74308i	−0.836581	+	0.483000i	−0.856100	−	0.516809i	$-0.827120\pi$
$257$	−13.4114	+	7.74308i	−0.836581	+	0.483000i	0.0195199	+	0.999809i	$0.493786\pi$
$258$	1.20757			0.0751798
$259$	−1.57916			−0.0981242
$260$	−5.62399	−	9.74104i	−0.348785	−	0.604114i
$261$	3.80540	−	6.59114i	0.235548	−	0.407981i
$262$	−16.2596	+	9.38748i	−1.00452	+	0.579960i
$263$	20.4305	+	11.7955i	1.25980	+	0.727344i	0.973035	−	0.230657i	$-0.0740876\pi$
$263$	20.4305	+	11.7955i	1.25980	+	0.727344i	0.286762	+	0.958002i	$0.407421\pi$
$264$	−1.13792	−	1.54707i	−0.0700343	−	0.0952156i
$265$		−	8.20144i		−	0.503811i
$266$	−2.77181	−	0.209814i	−0.169951	−	0.0128645i
$267$	−2.07393			−0.126923
$268$	−0.199470	−	0.115164i	−0.0121845	−	0.00703475i
$269$	−21.3789	−	12.3431i	−1.30349	−	0.752573i	−0.322492	−	0.946572i	$-0.604521\pi$
$269$	−21.3789	−	12.3431i	−1.30349	−	0.752573i	−0.981002	+	0.193999i	$0.937854\pi$
$270$	6.06654	−	3.50252i	0.369198	−	0.213156i
$271$	−2.97742	−	1.71901i	−0.180865	−	0.104423i	0.406834	−	0.913502i	$-0.366633\pi$
$271$	−2.97742	−	1.71901i	−0.180865	−	0.104423i	−0.587699	+	0.809080i	$0.699966\pi$
$272$	2.56416	−	1.48042i	0.155475	−	0.0897635i
$273$	−1.94492			−0.117712
$274$	16.0390			0.968954
$275$	−0.160778	−	1.44802i	−0.00969526	−	0.0873190i
$276$	3.84786	−	2.22156i	0.231614	−	0.133722i
$277$			28.0282i			1.68405i	0.539438	+	0.842026i	$0.318637\pi$
$277$			28.0282i			1.68405i	−0.539438	+	0.842026i	$0.681363\pi$
$278$			3.92958i			0.235681i
$279$	−20.3498	+	11.7490i	−1.21831	+	0.703391i
$280$	1.17944	+	0.680949i	0.0704850	+	0.0406945i
$281$	−0.401789	−	0.695919i	−0.0239687	−	0.0415151i	0.853792	−	0.520614i	$-0.174297\pi$
$281$	−0.401789	−	0.695919i	−0.0239687	−	0.0415151i	−0.877761	+	0.479099i	$0.840964\pi$
$282$	−1.94931	−	1.12544i	−0.116080	−	0.0670187i
$283$	−3.75452	−	2.16767i	−0.223183	−	0.128855i	0.384240	−	0.923233i	$-0.374463\pi$
$283$	−3.75452	−	2.16767i	−0.223183	−	0.128855i	−0.607423	+	0.794378i	$0.707797\pi$
$284$			1.47911i			0.0877692i
$285$	−3.03979	+	4.45136i	−0.180062	+	0.263676i
$286$	−15.9996	−	7.01142i	−0.946075	−	0.414594i
$287$	4.84539	+	2.79749i	0.286014	+	0.165130i
$288$	1.33235	−	2.30770i	0.0785095	−	0.135982i
$289$	−4.11672	−	7.13037i	−0.242160	−	0.419434i
$290$	3.04978	−	5.28237i	0.179089	−	0.310191i
$291$	0.929227	+	1.60947i	0.0544723	+	0.0943488i
$292$		−	15.7000i		−	0.918771i
$293$	22.2787			1.30154			0.650768	−	0.759276i	$-0.274447\pi$
$293$	22.2787			1.30154			0.650768	+	0.759276i	$0.274447\pi$
$294$	−3.30637	+	1.90893i	−0.192831	+	0.111331i
$295$	24.9079	−	14.3806i	1.45019	−	0.837269i
$296$			2.47627i			0.143930i
$297$	4.36658	−	9.96424i	0.253375	−	0.578184i
$298$	−15.5815	+	8.99596i	−0.902610	+	0.521122i
$299$	20.2069	−	34.9994i	1.16860	−	2.02407i
$300$	−0.220286	+	0.127182i	−0.0127182	+	0.00734286i
$301$	−0.664956	+	1.15174i	−0.0383274	+	0.0663850i
$302$	−8.94862	+	15.4995i	−0.514935	+	0.891894i
$303$	5.72863			0.329101
$304$	−0.329008	+	4.34646i	−0.0188699	+	0.249287i
$305$		−	31.7417i		−	1.81752i
$306$	6.83272	+	3.94487i	0.390600	+	0.225513i
$307$	7.28834	−	12.6238i	0.415968	−	0.720477i	−0.579562	−	0.814928i	$-0.696776\pi$
$307$	7.28834	−	12.6238i	0.415968	−	0.720477i	0.995530	+	0.0944510i	$0.0301096\pi$
$308$	2.10215	−	0.233407i	0.119781	−	0.0132996i
$309$	3.33110	−	5.76964i	0.189500	−	0.328223i
$310$	−16.3090	+	9.41602i	−0.926291	+	0.534794i
$311$	−1.37316			−0.0778647			−0.0389323	−	0.999242i	$-0.512396\pi$
$311$	−1.37316			−0.0778647			−0.0389323	+	0.999242i	$0.512396\pi$
$312$			3.04982i			0.172662i
$313$	11.0590	+	19.1548i	0.625093	+	1.08269i	0.988523	+	0.151071i	$0.0482722\pi$
$313$	11.0590	+	19.1548i	0.625093	+	1.08269i	−0.363430	+	0.931621i	$0.618394\pi$
$314$	6.08255	+	10.5353i	0.343258	+	0.594540i
$315$			3.62905i			0.204474i
$316$	−2.14941			−0.120914
$317$	5.09862	−	2.94369i	0.286367	−	0.165334i	−0.349935	−	0.936774i	$-0.613796\pi$
$317$	5.09862	−	2.94369i	0.286367	−	0.165334i	0.636302	+	0.771440i	$0.280463\pi$
$318$	−1.11188	+	1.92584i	−0.0623514	+	0.107996i
$319$	−1.04536	−	9.41493i	−0.0585292	−	0.527135i
$320$	1.06779	−	1.84947i	0.0596914	−	0.103389i
$321$	0.372520	+	0.215075i	0.0207920	+	0.0120043i
$322$			4.89328i			0.272692i
$323$	−12.8692	−	0.974138i	−0.716060	−	0.0542025i
$324$	6.09473			0.338596
$325$	−1.15682	+	2.00368i	−0.0641690	+	0.111144i
$326$	−4.69576	+	8.13329i	−0.260074	+	0.450461i
$327$	−2.53931	+	1.46607i	−0.140424	+	0.0810739i
$328$	4.38672	−	7.59802i	0.242216	−	0.419531i
$329$	2.14681	−	1.23946i	0.118357	−	0.0683337i
$330$	1.64619	−	3.75650i	0.0906200	−	0.206789i
$331$			7.49704i			0.412075i	0.978544	+	0.206037i	$0.0660568\pi$
$331$			7.49704i			0.412075i	−0.978544	+	0.206037i	$0.933943\pi$
$332$	−7.59340	+	4.38405i	−0.416742	+	0.240606i
$333$	−5.71448	+	3.29926i	−0.313152	+	0.180798i
$334$	17.4898			0.956997
$335$		−	0.491884i		−	0.0268745i
$336$	−0.184635	−	0.319798i	−0.0100727	−	0.0174464i
$337$	3.56137	−	6.16848i	0.194000	−	0.336019i	−0.752572	−	0.658510i	$-0.771187\pi$
$337$	3.56137	−	6.16848i	0.194000	−	0.336019i	0.946572	+	0.322491i	$0.104520\pi$
$338$	7.37029	+	12.7657i	0.400891	+	0.694364i
$339$	−4.79605	+	8.30700i	−0.260486	+	0.451174i
$340$	5.47598	+	3.16156i	0.296977	+	0.171460i
$341$	−11.7389	+	26.7875i	−0.635699	+	1.45062i
$342$	−10.4687	+	5.03176i	−0.566082	+	0.272087i
$343$		−	8.66869i		−	0.468065i
$344$	1.80603	+	1.04271i	0.0973747	+	0.0562193i
$345$	8.21742	+	4.74433i	0.442411	+	0.255426i
$346$	1.72261	+	2.98366i	0.0926084	+	0.160402i
$347$	20.4346	+	11.7979i	1.09699	+	0.633346i	0.935428	−	0.353517i	$-0.115014\pi$
$347$	20.4346	+	11.7979i	1.09699	+	0.633346i	0.161560	+	0.986863i	$0.448348\pi$
$348$	−1.43228	+	0.826928i	−0.0767783	+	0.0443280i
$349$			16.2279i			0.868659i	0.900754	+	0.434330i	$0.143015\pi$
$349$			16.2279i			0.868659i	−0.900754	+	0.434330i	$0.856985\pi$
$350$		−	0.280135i		−	0.0149738i
$351$	−14.9617	+	8.63816i	−0.798598	+	0.461071i
$352$	−0.366005	−	3.29637i	−0.0195081	−	0.175697i
$353$	4.30878			0.229333			0.114667	−	0.993404i	$-0.463420\pi$
$353$	4.30878			0.229333			0.114667	+	0.993404i	$0.463420\pi$
$354$	−7.79840			−0.414480
$355$	−2.73558	+	1.57939i	−0.145189	+	0.0838251i
$356$	−3.10177	−	1.79081i	−0.164393	−	0.0949125i
$357$	0.946868	−	0.546675i	0.0501136	−	0.0289331i
$358$	−3.12597	−	1.80478i	−0.165213	−	0.0953856i
$359$	−6.59846	−	3.80962i	−0.348254	−	0.201064i	0.315662	−	0.948872i	$-0.397773\pi$
$359$	−6.59846	−	3.80962i	−0.348254	−	0.201064i	−0.663916	+	0.747807i	$0.731107\pi$
$360$	5.69069			0.299926
$361$	11.8686	−	14.8370i	0.624664	−	0.780893i
$362$		−	15.2125i		−	0.799551i
$363$	−1.39723	−	6.21442i	−0.0733357	−	0.326172i
$364$	−2.90882	−	1.67941i	−0.152463	−	0.0880248i
$365$	29.0366	−	16.7643i	1.51985	−	0.877484i
$366$	−4.30328	+	7.45350i	−0.224936	+	0.389601i
$367$	2.19147	+	3.79574i	0.114394	+	0.198136i	0.917537	−	0.397650i	$-0.130174\pi$
$367$	2.19147	+	3.79574i	0.114394	+	0.198136i	−0.803143	+	0.595786i	$0.796841\pi$
$368$	7.67312			0.399989
$369$	23.3786			1.21704
$370$	−4.57979	+	2.64414i	−0.238092	+	0.137462i
$371$	−1.22454	−	2.12096i	−0.0635747	−	0.110115i
$372$	5.10619			0.264744
$373$	−25.2234			−1.30602			−0.653008	−	0.757351i	$-0.726493\pi$
$373$	−25.2234			−1.30602			−0.653008	+	0.757351i	$0.726493\pi$
$374$	9.76001	−	1.08368i	0.504678	−	0.0560357i
$375$	−5.82512	−	3.36314i	−0.300808	−	0.173672i
$376$	−1.94359	−	3.36640i	−0.100233	−	0.173609i
$377$	−7.52158	+	13.0278i	−0.387381	+	0.670964i
$378$	1.04590	−	1.81156i	0.0537954	−	0.0931764i
$379$			16.4811i			0.846578i	0.905995	+	0.423289i	$0.139124\pi$
$379$			16.4811i			0.846578i	−0.905995	+	0.423289i	$0.860876\pi$
$380$	−8.38997	+	4.03263i	−0.430396	+	0.206870i
$381$		−	11.0519i		−	0.566206i
$382$	11.8349	−	20.4987i	0.605527	−	1.04880i
$383$	−1.41572	−	0.817365i	−0.0723398	−	0.0417654i	0.463394	−	0.886152i	$-0.346632\pi$
$383$	−1.41572	−	0.817365i	−0.0723398	−	0.0417654i	−0.535734	+	0.844387i	$0.679965\pi$
$384$	−0.501472	+	0.289525i	−0.0255907	+	0.0147748i
$385$	2.67634	+	3.63863i	0.136399	+	0.185442i
$386$	1.94997	+	3.37744i	0.0992507	+	0.171907i
$387$			5.55704i			0.282480i
$388$			3.20949i			0.162937i
$389$	15.6366	+	27.0834i	0.792807	+	1.37318i	0.924223	+	0.381854i	$0.124714\pi$
$389$	15.6366	+	27.0834i	0.792807	+	1.37318i	−0.131416	+	0.991327i	$0.541952\pi$
$390$	−5.64055	+	3.25657i	−0.285620	+	0.164903i
$391$			22.7188i			1.14894i
$392$	−6.59332			−0.333013
$393$	5.43582	+	9.41512i	0.274201	+	0.474930i
$394$	0.109581	+	0.0632668i	0.00552063	+	0.00318734i
$395$	−2.29513	−	3.97528i	−0.115480	−	0.200018i
$396$	7.11938	−	5.23654i	0.357762	−	0.263146i
$397$	0.133064	−	0.230473i	0.00667829	−	0.0115671i	−0.862667	−	0.505772i	$-0.831208\pi$
$397$	0.133064	−	0.230473i	0.00667829	−	0.0115671i	0.869345	+	0.494205i	$0.164541\pi$
$398$	−10.5935			−0.531003
$399$	−0.121493	+	1.60502i	−0.00608224	+	0.0803515i
$400$	−0.439278			−0.0219639
$401$	6.64967	+	3.83919i	0.332069	+	0.191720i	0.656759	−	0.754100i	$-0.271927\pi$
$401$	6.64967	+	3.83919i	0.332069	+	0.191720i	−0.324690	+	0.945820i	$0.605260\pi$
$402$	−0.0666856	+	0.115503i	−0.00332598	+	0.00576076i
$403$	40.2225	−	23.2225i	2.00363	−	1.15679i
$404$	8.56772	+	4.94658i	0.426260	+	0.246101i
$405$	6.50791	+	11.2720i	0.323381	+	0.560112i
$406$		−	1.82142i		−	0.0903954i
$407$	−3.29645	+	7.52226i	−0.163399	+	0.372865i
$408$	−0.857237	−	1.48478i	−0.0424395	−	0.0735074i
$409$	5.07467	+	8.78959i	0.250926	+	0.434617i	0.963781	−	0.266694i	$-0.0859314\pi$
$409$	5.07467	+	8.78959i	0.250926	+	0.434617i	−0.712855	+	0.701312i	$0.752598\pi$
$410$	18.7364			0.925326
$411$		−	9.28741i		−	0.458114i
$412$	9.96397	−	5.75270i	0.490890	−	0.283415i
$413$	4.29425	−	7.43786i	0.211306	−	0.365993i
$414$	10.2233	+	17.7072i	0.502447	+	0.870264i
$415$	−16.2163	−	9.36251i	−0.796029	−	0.459588i
$416$	−2.63347	+	4.56130i	−0.129116	+	0.223636i
$417$	2.27543			0.111428
$418$	−6.78552	+	12.7655i	−0.331890	+	0.624379i
$419$	−9.36596			−0.457557			−0.228779	−	0.973478i	$-0.573473\pi$
$419$	−9.36596			−0.457557			−0.228779	+	0.973478i	$0.573473\pi$
$420$	0.394304	−	0.682955i	0.0192401	−	0.0333248i
$421$	0.179726	+	0.103765i	0.00875933	+	0.00505720i	0.504373	−	0.863486i	$-0.331724\pi$
$421$	0.179726	+	0.103765i	0.00875933	+	0.00505720i	−0.495614	+	0.868543i	$0.665057\pi$
$422$	−4.72246	−	8.17954i	−0.229886	−	0.398174i
$423$	5.17908	−	8.97044i	0.251816	−	0.436158i
$424$	−3.32586	+	1.92019i	−0.161518	+	0.0932525i
$425$		−	1.30063i		−	0.0630898i
$426$	0.856481			0.0414966
$427$	−4.73927	−	8.20865i	−0.229349	−	0.397245i
$428$	0.371426	+	0.643329i	0.0179536	+	0.0310965i
$429$	−4.05996	+	9.26456i	−0.196017	+	0.447297i
$430$			4.45360i			0.214772i
$431$	11.9067	+	20.6230i	0.573526	+	0.993376i	0.996200	+	0.0870942i	$0.0277581\pi$
$431$	11.9067	+	20.6230i	0.573526	+	0.993376i	−0.422674	+	0.906282i	$0.638909\pi$
$432$	−2.84069	−	1.64007i	−0.136673	−	0.0789081i
$433$	34.9099	−	20.1552i	1.67766	−	0.968598i	0.714515	−	0.699620i	$-0.246647\pi$
$433$	34.9099	−	20.1552i	1.67766	−	0.968598i	0.963146	−	0.268978i	$-0.0866860\pi$
$434$	−2.81176	+	4.87012i	−0.134969	+	0.233773i
$435$	−3.05876	−	1.76597i	−0.146656	−	0.0846720i
$436$	−5.06371			−0.242508
$437$	−27.6205	−	18.8618i	−1.32127	−	0.902280i
$438$	−9.09107			−0.434388
$439$	−13.8611	+	24.0081i	−0.661552	+	1.14584i	0.318655	+	0.947871i	$0.396769\pi$
$439$	−13.8611	+	24.0081i	−0.661552	+	1.14584i	−0.980208	+	0.197972i	$0.936565\pi$
$440$	5.70572	−	4.19675i	0.272009	−	0.200072i
$441$	−8.78461	−	15.2154i	−0.418315	−	0.724542i
$442$	−13.5053	−	7.79726i	−0.642380	−	0.370878i
$443$	7.25896	+	12.5729i	0.344883	+	0.597356i	0.985333	−	0.170645i	$-0.0545851\pi$
$443$	7.25896	+	12.5729i	0.344883	+	0.597356i	−0.640449	+	0.768001i	$0.721252\pi$
$444$	1.43388			0.0680491
$445$		−	7.64883i		−	0.362589i
$446$	−16.5914	+	9.57907i	−0.785627	+	0.453582i
$447$	5.20911	+	9.02245i	0.246383	+	0.426747i
$448$		−	0.637717i		−	0.0301293i
$449$			0.456381i			0.0215379i	0.999942	+	0.0107690i	$0.00342794\pi$
$449$			0.456381i			0.0215379i	−0.999942	+	0.0107690i	$0.996572\pi$
$450$	−0.585272	−	1.01372i	−0.0275900	−	0.0477873i
$451$	23.4403	−	17.2412i	1.10376	−	0.811854i
$452$	−14.3459	+	8.28261i	−0.674775	+	0.389581i
$453$	8.97497	+	5.18170i	0.421681	+	0.243458i
$454$	−5.97535	+	10.3496i	−0.280437	+	0.485731i
$455$		−	7.17303i		−	0.336277i
$456$	2.51682	+	0.190512i	0.117861	+	0.00892154i
$457$			18.0022i			0.842108i	0.907036	+	0.421054i	$0.138340\pi$
$457$			18.0022i			0.842108i	−0.907036	+	0.421054i	$0.861660\pi$
$458$	−5.99059	+	10.3760i	−0.279922	+	0.484839i
$459$	4.85599	−	8.41082i	0.226658	−	0.392584i
$460$	8.19330	+	14.1912i	0.382014	+	0.661668i
$461$	7.47776	+	4.31729i	0.348274	+	0.201076i	0.663925	−	0.747799i	$-0.268889\pi$
$461$	7.47776	+	4.31729i	0.348274	+	0.201076i	−0.315651	+	0.948875i	$0.602223\pi$
$462$	−0.135155	−	1.21725i	−0.00628796	−	0.0566316i
$463$	4.82881			0.224414			0.112207	−	0.993685i	$-0.464208\pi$
$463$	4.82881			0.224414			0.112207	+	0.993685i	$0.464208\pi$
$464$	−2.85615			−0.132594
$465$	5.45235	+	9.44375i	0.252847	+	0.437944i
$466$	−10.0521	+	5.80360i	−0.465656	+	0.268847i
$467$	−4.20762			−0.194705			−0.0973526	−	0.995250i	$-0.531037\pi$
$467$	−4.20762			−0.194705			−0.0973526	+	0.995250i	$0.531037\pi$
$468$	−14.0348			−0.648759
$469$	−0.0734419	−	0.127205i	−0.00339123	−	0.00587379i
$470$	4.15070	−	7.18922i	0.191458	−	0.331614i
$471$	6.10046	−	3.52210i	0.281094	−	0.162290i
$472$	−11.6633	−	6.73379i	−0.536845	−	0.309948i
$473$	4.09818	+	5.57171i	0.188435	+	0.256187i
$474$			1.24462i			0.0571672i
$475$	1.58124	+	1.07982i	0.0725525	+	0.0495453i
$476$	1.88818			0.0865444
$477$	−8.86242	−	5.11672i	−0.405783	−	0.234279i
$478$	13.3132	+	7.68639i	0.608933	+	0.351567i
$479$	−25.1298	+	14.5087i	−1.14821	+	0.662920i	−0.948451	−	0.316925i	$-0.897350\pi$
$479$	−25.1298	+	14.5087i	−1.14821	+	0.662920i	−0.199760	+	0.979845i	$0.564016\pi$
$480$	−1.07094	−	0.618306i	−0.0488813	−	0.0282217i
$481$	11.2950	−	6.52117i	0.515008	−	0.297340i
$482$	−8.82878			−0.402140
$483$	2.83346			0.128927
$484$	3.27635	−	10.5007i	0.148925	−	0.477306i
$485$	−5.93585	+	3.42707i	−0.269533	+	0.155615i
$486$		−	13.3696i		−	0.606457i
$487$			23.2276i			1.05254i	0.850317	+	0.526271i	$0.176410\pi$
$487$			23.2276i			1.05254i	−0.850317	+	0.526271i	$0.823590\pi$
$488$	−12.8719	+	7.43161i	−0.582685	+	0.336413i
$489$	4.70958	+	2.71908i	0.212975	+	0.122961i
$490$	−7.04029	−	12.1941i	−0.318048	−	0.550875i
$491$	−4.96857	−	2.86860i	−0.224228	−	0.129458i	0.383678	−	0.923467i	$-0.374657\pi$
$491$	−4.96857	−	2.86860i	−0.224228	−	0.129458i	−0.607907	+	0.794009i	$0.707991\pi$
$492$	−4.39964	−	2.54013i	−0.198351	−	0.114518i
$493$		−	8.45660i		−	0.380866i
$494$	20.6919	−	9.94557i	0.930975	−	0.447472i
$495$	17.2869	+	7.57554i	0.776986	+	0.340495i
$496$	7.63680	+	4.40911i	0.342902	+	0.197975i
$497$	−0.471628	+	0.816883i	−0.0211554	+	0.0366422i
$498$	2.53859	+	4.39696i	0.113757	+	0.197032i
$499$	−3.00551	+	5.20569i	−0.134545	+	0.233039i	−0.925424	−	0.378934i	$-0.876291\pi$
$499$	−3.00551	+	5.20569i	−0.134545	+	0.233039i	0.790879	+	0.611973i	$0.209624\pi$
$500$	−5.80802	−	10.0598i	−0.259743	−	0.449887i
$501$		−	10.1275i		−	0.452461i
$502$	−25.3095			−1.12962
$503$	9.61416	−	5.55074i	0.428674	−	0.247495i	−0.270108	−	0.962830i	$-0.587059\pi$
$503$	9.61416	−	5.55074i	0.428674	−	0.247495i	0.698782	+	0.715335i	$0.253726\pi$
$504$	1.47166	−	0.849663i	0.0655529	−	0.0378470i
$505$			21.1277i			0.940169i
$506$	23.3089	+	10.2146i	1.03621	+	0.454093i
$507$	7.39199	−	4.26777i	0.328290	−	0.189538i
$508$	9.54313	−	16.5292i	0.423408	−	0.733364i
$509$	20.0862	−	11.5968i	0.890307	−	0.514019i	0.0162640	−	0.999868i	$-0.494823\pi$
$509$	20.0862	−	11.5968i	0.890307	−	0.514019i	0.874043	+	0.485849i	$0.161489\pi$
$510$	1.83070	−	3.17087i	0.0810648	−	0.140408i
$511$	5.00607	−	8.67077i	0.221456	−	0.383572i
$512$	−1.00000			−0.0441942
$513$	6.19391	+	12.8866i	0.273468	+	0.568955i
$514$			15.4862i			0.683065i
$515$	21.2789	+	12.2854i	0.937660	+	0.541359i
$516$	0.603783	−	1.04578i	0.0265801	−	0.0460380i
$517$	−1.42273	−	12.8136i	−0.0625714	−	0.563540i
$518$	−0.789580	+	1.36759i	−0.0346921	+	0.0600885i
$519$	1.72769	−	0.997481i	0.0758371	−	0.0437846i
$520$	−11.2480			−0.493257
$521$		−	7.48388i		−	0.327875i	−0.986471	−	0.163937i	$-0.947580\pi$
$521$		−	7.48388i		−	0.327875i	0.986471	−	0.163937i	$-0.0524195\pi$
$522$	−3.80540	−	6.59114i	−0.166558	−	0.288486i
$523$	9.88392	+	17.1195i	0.432194	+	0.748582i	0.997062	−	0.0765996i	$-0.0244063\pi$
$523$	9.88392	+	17.1195i	0.432194	+	0.748582i	−0.564868	+	0.825181i	$0.691073\pi$
$524$			18.7750i			0.820188i
$525$	−0.162212			−0.00707953
$526$	20.4305	−	11.7955i	0.890811	−	0.514310i
$527$	−13.0546	+	22.6113i	−0.568669	+	0.984964i
$528$	−1.90876	+	0.211935i	−0.0830683	+	0.00922329i
$529$	−17.9384	+	31.0702i	−0.779929	+	1.35088i
$530$	−7.10266	−	4.10072i	−0.308520	−	0.178124i
$531$		−	35.8871i		−	1.55737i
$532$	−1.56761	+	2.29556i	−0.0679646	+	0.0995249i
$533$	−46.2091			−2.00154
$534$	−1.03697	+	1.79608i	−0.0448739	+	0.0777239i
$535$	−0.793212	+	1.37388i	−0.0342936	+	0.0593982i
$536$	−0.199470	+	0.115164i	−0.00861577	+	0.00497432i
$537$	−1.04506	+	1.81010i	−0.0450976	+	0.0781114i
$538$	−21.3789	+	12.3431i	−0.921710	+	0.532149i
$539$	−20.0288	−	8.77712i	−0.862701	−	0.378057i
$540$		−	7.00503i		−	0.301449i
$541$	23.1772	−	13.3813i	0.996464	−	0.575309i	0.0892636	−	0.996008i	$-0.471549\pi$
$541$	23.1772	−	13.3813i	0.996464	−	0.575309i	0.907200	+	0.420699i	$0.138215\pi$
$542$	−2.97742	+	1.71901i	−0.127891	+	0.0738379i
$543$	−8.80880			−0.378022
$544$		−	2.96084i		−	0.126945i
$545$	−5.40699	−	9.36517i	−0.231610	−	0.401160i
$546$	−0.972461	+	1.68435i	−0.0416175	+	0.0720836i
$547$	16.4934	+	28.5673i	0.705205	+	1.22145i	0.966617	+	0.256224i	$0.0824786\pi$
$547$	16.4934	+	28.5673i	0.705205	+	1.22145i	−0.261412	+	0.965227i	$0.584188\pi$
$548$	8.01952	−	13.8902i	0.342577	−	0.593360i
$549$	−34.2998	−	19.8030i	−1.46388	−	0.845173i
$550$	−1.33441	−	0.584773i	−0.0568995	−	0.0249348i
$551$	10.2811	+	7.02088i	0.437991	+	0.299100i
$552$		−	4.44312i		−	0.189112i
$553$	−1.18708	−	0.685359i	−0.0504796	−	0.0291444i
$554$	24.2731	+	14.0141i	1.03127	+	0.595402i
$555$	1.53109	+	2.65193i	0.0649912	+	0.112568i
$556$	3.40312	+	1.96479i	0.144324	+	0.0833257i
$557$	3.01517	−	1.74081i	0.127757	−	0.0737605i	−0.434759	−	0.900547i	$-0.643167\pi$
$557$	3.01517	−	1.74081i	0.127757	−	0.0737605i	0.562516	+	0.826786i	$0.309833\pi$
$558$			23.4979i			0.994746i
$559$		−	10.9838i		−	0.464565i
$560$	1.17944	−	0.680949i	0.0498404	−	0.0287754i
$561$	−0.627505	−	5.65154i	−0.0264933	−	0.238608i
$562$	−0.803578			−0.0338969
$563$	30.3621			1.27961			0.639804	−	0.768538i	$-0.279015\pi$
$563$	30.3621			1.27961			0.639804	+	0.768538i	$0.279015\pi$
$564$	−1.94931	+	1.12544i	−0.0820809	+	0.0473894i
$565$	−30.6369	−	17.6882i	−1.28890	−	0.744149i
$566$	−3.75452	+	2.16767i	−0.157814	+	0.0911140i
$567$	3.36599	+	1.94336i	0.141358	+	0.0816133i
$568$	1.28095	+	0.739556i	0.0537474	+	0.0310311i
$569$	−7.25436			−0.304119			−0.152059	−	0.988371i	$-0.548590\pi$
$569$	−7.25436			−0.304119			−0.152059	+	0.988371i	$0.548590\pi$
$570$	2.33510	+	4.85822i	0.0978065	+	0.203488i
$571$		−	4.79089i		−	0.200493i	−0.994963	−	0.100246i	$-0.968037\pi$
$571$		−	4.79089i		−	0.200493i	0.994963	−	0.100246i	$-0.0319631\pi$
$572$	−14.0719	+	10.3503i	−0.588374	+	0.432769i
$573$	−11.8698	−	6.85301i	−0.495867	−	0.286289i
$574$	4.84539	−	2.79749i	0.202243	−	0.116765i
$575$	1.68532	−	2.91905i	0.0702825	−	0.121733i
$576$	−1.33235	−	2.30770i	−0.0555146	−	0.0961541i
$577$	−36.7712			−1.53081			−0.765403	−	0.643552i	$-0.777460\pi$
$577$	−36.7712			−1.53081			−0.765403	+	0.643552i	$0.777460\pi$
$578$	−8.23345			−0.342466
$579$	1.95571	−	1.12913i	0.0812765	−	0.0469250i
$580$	−3.04978	−	5.28237i	−0.126635	−	0.219338i
$581$	−5.59157			−0.231977
$582$	1.85845			0.0770354
$583$	−12.6593	+	1.40559i	−0.524294	+	0.0582138i
$584$	−13.5966	−	7.84999i	−0.562630	−	0.324835i
$585$	−14.9863	−	25.9569i	−0.619605	−	1.07319i
$586$	11.1394	−	19.2939i	0.460163	−	0.797025i
$587$	13.8439	−	23.9783i	0.571399	−	0.989691i	−0.425024	−	0.905182i	$-0.639734\pi$
$587$	13.8439	−	23.9783i	0.571399	−	0.989691i	0.996423	−	0.0845094i	$-0.0269323\pi$
$588$			3.81786i			0.157446i
$589$	−16.6515	−	34.6437i	−0.686112	−	1.42747i
$590$		−	28.7611i		−	1.18408i
$591$	0.0366347	−	0.0634531i	0.00150695	−	0.00261011i
$592$	2.14451	+	1.23813i	0.0881389	+	0.0508870i
$593$	9.92228	−	5.72863i	0.407459	−	0.235247i	−0.282238	−	0.959344i	$-0.591077\pi$
$593$	9.92228	−	5.72863i	0.407459	−	0.235247i	0.689697	+	0.724098i	$0.257744\pi$
$594$	−6.44599	−	8.76369i	−0.264482	−	0.359578i
$595$	2.01618	+	3.49213i	0.0826553	+	0.143163i
$596$			17.9919i			0.736978i
$597$			6.13415i			0.251054i
$598$	−20.2069	−	34.9994i	−0.826322	−	1.43123i
$599$	16.0912	−	9.29029i	0.657471	−	0.379591i	−0.133842	−	0.991003i	$-0.542731\pi$
$599$	16.0912	−	9.29029i	0.657471	−	0.379591i	0.791313	+	0.611412i	$0.209398\pi$
$600$			0.254364i			0.0103844i
$601$	−41.2867			−1.68412			−0.842059	−	0.539385i	$-0.818657\pi$
$601$	−41.2867			−1.68412			−0.842059	+	0.539385i	$0.818657\pi$
$602$	0.664956	+	1.15174i	0.0271016	+	0.0469413i
$603$	−0.531527	−	0.306877i	−0.0216454	−	0.0124970i
$604$	8.94862	+	15.4995i	0.364114	+	0.630664i
$605$	22.9193	−	5.15310i	0.931801	−	0.209503i
$606$	2.86432	−	4.96114i	0.116355	−	0.201533i
$607$	0.888370			0.0360578			0.0180289	−	0.999837i	$-0.494261\pi$
$607$	0.888370			0.0360578			0.0180289	+	0.999837i	$0.494261\pi$
$608$	3.59964	+	2.45816i	0.145985	+	0.0996916i
$609$	−1.05469			−0.0427383
$610$	−27.4891	−	15.8708i	−1.11300	−	0.642592i
$611$	−10.2368	+	17.7306i	−0.414135	+	0.717302i
$612$	6.83272	−	3.94487i	0.276196	−	0.159462i
$613$	−33.6210	−	19.4111i	−1.35794	−	0.784006i	−0.368593	−	0.929591i	$-0.620160\pi$
$613$	−33.6210	−	19.4111i	−1.35794	−	0.784006i	−0.989346	+	0.145585i	$0.953494\pi$
$614$	−7.28834	−	12.6238i	−0.294134	−	0.509454i
$615$		−	10.8493i		−	0.437487i
$616$	0.848938	−	1.93722i	0.0342047	−	0.0780528i
$617$	6.79545	+	11.7701i	0.273575	+	0.473845i	0.969775	−	0.244003i	$-0.0784606\pi$
$617$	6.79545	+	11.7701i	0.273575	+	0.473845i	−0.696200	+	0.717848i	$0.745127\pi$
$618$	−3.33110	−	5.76964i	−0.133997	−	0.232089i
$619$	−28.7853			−1.15698			−0.578490	−	0.815689i	$-0.696358\pi$
$619$	−28.7853			−1.15698			−0.578490	+	0.815689i	$0.696358\pi$
$620$			18.8320i			0.756313i
$621$	21.7970	−	12.5845i	0.874682	−	0.504998i
$622$	−0.686579	+	1.18919i	−0.0275293	+	0.0476822i
$623$	−1.14203	−	1.97805i	−0.0457543	−	0.0792489i
$624$	2.64122	+	1.52491i	0.105733	+	0.0610452i
$625$	11.3053	−	19.5814i	0.452213	−	0.783256i
$626$	22.1180			0.884015
$627$	7.39184	+	3.92916i	0.295202	+	0.156915i
$628$	12.1651			0.485440
$629$	−3.66591	+	6.34955i	−0.146170	+	0.253173i
$630$	3.14285	+	1.81453i	0.125214	+	0.0722925i
$631$	−11.4590	−	19.8475i	−0.456174	−	0.790116i	0.542581	−	0.840004i	$-0.317447\pi$
$631$	−11.4590	−	19.8475i	−0.456174	−	0.790116i	−0.998755	+	0.0498872i	$0.984114\pi$
$632$	−1.07471	+	1.86145i	−0.0427495	+	0.0740443i
$633$	−4.73637	+	2.73454i	−0.188254	+	0.108688i
$634$		−	5.88738i		−	0.233818i
$635$	40.7603			1.61752
$636$	1.11188	+	1.92584i	0.0440891	+	0.0763646i
$637$	17.3633	+	30.0741i	0.687958	+	1.19158i
$638$	−8.67625	−	3.80215i	−0.343496	−	0.150529i
$639$			3.94139i			0.155919i
$640$	−1.06779	−	1.84947i	−0.0422082	−	0.0731067i
$641$	−1.02056	−	0.589223i	−0.0403099	−	0.0232729i	0.479710	−	0.877427i	$-0.340742\pi$
$641$	−1.02056	−	0.589223i	−0.0403099	−	0.0232729i	−0.520020	+	0.854154i	$0.674075\pi$
$642$	0.372520	−	0.215075i	0.0147022	−	0.00848831i
$643$	21.9099	−	37.9490i	0.864041	−	1.49656i	−0.00395560	−	0.999992i	$-0.501259\pi$
$643$	21.9099	−	37.9490i	0.864041	−	1.49656i	0.867996	−	0.496570i	$-0.165408\pi$
$644$	4.23770	+	2.44664i	0.166989	+	0.0964111i
$645$	2.57886			0.101543
$646$	−7.27821	+	10.6580i	−0.286357	+	0.419332i
$647$	4.76041			0.187151			0.0935755	−	0.995612i	$-0.470170\pi$
$647$	4.76041			0.187151			0.0935755	+	0.995612i	$0.470170\pi$
$648$	3.04737	−	5.27819i	0.119712	−	0.207347i
$649$	−26.4658	−	35.9818i	−1.03888	−	1.41241i
$650$	1.15682	+	2.00368i	0.0453744	+	0.0785907i
$651$	2.82004	+	1.62815i	0.110526	+	0.0638123i
$652$	4.69576	+	8.13329i	0.183900	+	0.318524i
$653$	−13.9841			−0.547241			−0.273621	−	0.961838i	$-0.588221\pi$
$653$	−13.9841			−0.547241			−0.273621	+	0.961838i	$0.588221\pi$
$654$			2.93214i			0.114656i
$655$	−34.7237	+	20.0478i	−1.35677	+	0.783331i
$656$	−4.38672	−	7.59802i	−0.171273	−	0.296653i
$657$		−	41.8357i		−	1.63217i
$658$		−	2.47892i		−	0.0966384i
$659$	−9.18066	−	15.9014i	−0.357628	−	0.619429i	0.629936	−	0.776647i	$-0.283081\pi$
$659$	−9.18066	−	15.9014i	−0.357628	−	0.619429i	−0.987564	+	0.157218i	$0.949748\pi$
$660$	−2.43013	−	3.30390i	−0.0945927	−	0.128604i
$661$	−12.1941	+	7.04028i	−0.474297	+	0.273835i	−0.718037	−	0.696005i	$-0.754959\pi$
$661$	−12.1941	+	7.04028i	−0.474297	+	0.273835i	0.243740	+	0.969841i	$0.421626\pi$
$662$	6.49263	+	3.74852i	0.252343	+	0.145690i
$663$	−4.51501	+	7.82022i	−0.175348	+	0.303712i
$664$			8.76810i			0.340268i
$665$	−5.91945	−	0.448075i	−0.229546	−	0.0173756i
$666$			6.59852i			0.255687i
$667$	10.9578	−	18.9795i	0.424288	−	0.734888i
$668$	8.74488	−	15.1466i	0.338350	−	0.586039i
$669$	5.54676	+	9.60728i	0.214450	+	0.371439i
$670$	−0.425984	−	0.245942i	−0.0164572	−	0.00950157i
$671$	−48.9947	+	5.44001i	−1.89142	+	0.210009i
$672$	−0.369270			−0.0142449
$673$	−42.8708			−1.65255			−0.826275	−	0.563267i	$-0.809544\pi$
$673$	−42.8708			−1.65255			−0.826275	+	0.563267i	$0.809544\pi$
$674$	−3.56137	−	6.16848i	−0.137179	−	0.237601i
$675$	−1.24785	+	0.720448i	−0.0480299	+	0.0277301i
$676$	14.7406			0.566945
$677$	34.7803			1.33671			0.668357	−	0.743841i	$-0.266998\pi$
$677$	34.7803			1.33671			0.668357	+	0.743841i	$0.266998\pi$
$678$	4.79605	+	8.30700i	0.184191	+	0.319028i
$679$	−1.02337	+	1.77253i	−0.0392734	+	0.0680236i
$680$	5.47598	−	3.16156i	0.209994	−	0.121240i
$681$	5.99294	+	3.46003i	0.229650	+	0.132589i
$682$	17.3291	+	23.5599i	0.663567	+	0.902157i
$683$			12.8439i			0.491459i	0.969338	+	0.245730i	$0.0790276\pi$
$683$			12.8439i			0.491459i	−0.969338	+	0.245730i	$0.920972\pi$
$684$	−0.876707	+	11.5820i	−0.0335217	+	0.442850i
$685$	34.2527			1.30873
$686$	−7.50731	−	4.33435i	−0.286630	−	0.165486i
$687$	6.00823	+	3.46885i	0.229228	+	0.132345i
$688$	1.80603	−	1.04271i	0.0688543	−	0.0397531i
$689$	17.5171	+	10.1135i	0.667348	+	0.385293i
$690$	8.21742	−	4.74433i	0.312832	−	0.180614i
$691$	4.30625			0.163818			0.0819088	−	0.996640i	$-0.473898\pi$
$691$	4.30625			0.163818			0.0819088	+	0.996640i	$0.473898\pi$
$692$	3.44523			0.130968
$693$	5.60160	−	0.621961i	0.212787	−	0.0236263i
$694$	20.4346	−	11.7979i	0.775688	−	0.447844i
$695$			8.39195i			0.318325i
$696$			1.65386i			0.0626893i
$697$	22.4965	−	12.9884i	0.852116	−	0.491969i
$698$	14.0538	+	8.11395i	0.531943	+	0.307117i
$699$	3.36058	+	5.82069i	0.127109	+	0.220159i
$700$	−0.242604	−	0.140068i	−0.00916957	−	0.00529405i
$701$	−22.2279	−	12.8333i	−0.839535	−	0.484706i	0.0175711	−	0.999846i	$-0.494407\pi$
$701$	−22.2279	−	12.8333i	−0.839535	−	0.484706i	−0.857106	+	0.515140i	$0.827740\pi$
$702$			17.2763i			0.652052i
$703$	−4.67595	−	9.72840i	−0.176357	−	0.366914i
$704$	−3.03774	−	1.33121i	−0.114489	−	0.0501720i
$705$	−4.16292	−	2.40346i	−0.156785	−	0.0905197i
$706$	2.15439	−	3.73151i	0.0810815	−	0.140437i
$707$	3.15452	+	5.46378i	0.118638	+	0.205487i
$708$	−3.89920	+	6.75362i	−0.146541	+	0.253816i
$709$	11.5181	+	19.9500i	0.432572	+	0.749237i	0.997094	−	0.0761810i	$-0.0242727\pi$
$709$	11.5181	+	19.9500i	0.432572	+	0.749237i	−0.564522	+	0.825418i	$0.690939\pi$
$710$			3.15877i			0.118547i
$711$	−5.72754			−0.214800
$712$	−3.10177	+	1.79081i	−0.116244	+	0.0671133i
$713$	−58.5981	+	33.8316i	−2.19452	+	1.26700i
$714$		−	1.09335i		−	0.0409176i
$715$	−34.1684	−	14.9735i	−1.27783	−	0.559976i
$716$	−3.12597	+	1.80478i	−0.116823	+	0.0674478i
$717$	4.45081	−	7.70903i	0.166219	−	0.287899i
$718$	−6.59846	+	3.80962i	−0.246252	+	0.142174i
$719$	−4.90982	+	8.50405i	−0.183105	+	0.317148i	−0.942936	−	0.332973i	$-0.891948\pi$
$719$	−4.90982	+	8.50405i	−0.183105	+	0.317148i	0.759831	+	0.650120i	$0.225282\pi$
$720$	2.84535	−	4.92829i	0.106040	−	0.183666i
$721$	7.33719			0.273251
$722$	−6.91489	−	17.6970i	−0.257345	−	0.658615i
$723$			5.11231i			0.190129i
$724$	−13.1744	−	7.60624i	−0.489623	−	0.282684i
$725$	−0.627322	+	1.08655i	−0.0232982	+	0.0403536i
$726$	−6.08046	−	1.89717i	−0.225667	−	0.0704106i
$727$	−12.6018	+	21.8269i	−0.467375	+	0.809517i	−0.999305	−	0.0372713i	$-0.988133\pi$
$727$	−12.6018	+	21.8269i	−0.467375	+	0.809517i	0.531930	+	0.846788i	$0.321467\pi$
$728$	−2.90882	+	1.67941i	−0.107808	+	0.0622429i
$729$	10.5425			0.390464
$730$		−	33.5286i		−	1.24095i
$731$	3.08730	+	5.34736i	0.114188	+	0.197779i
$732$	4.30328	+	7.45350i	0.159054	+	0.275489i
$733$		−	1.26341i		−	0.0466651i	−0.999728	−	0.0233325i	$-0.992572\pi$
$733$		−	1.26341i		−	0.0466651i	0.999728	−	0.0233325i	$-0.00742765\pi$
$734$	4.38294			0.161777
$735$	−7.06103	+	4.07668i	−0.260450	+	0.150371i
$736$	3.83656	−	6.64512i	0.141417	−	0.244942i
$737$	−0.759245	+	0.0843010i	−0.0279671	+	0.00310527i
$738$	11.6893	−	20.2465i	0.430289	−	0.745282i
$739$	14.7675	+	8.52600i	0.543230	+	0.313634i	0.746387	−	0.665512i	$-0.231787\pi$
$739$	14.7675	+	8.52600i	0.543230	+	0.313634i	−0.203157	+	0.979146i	$0.565120\pi$
$740$			5.28828i			0.194401i
$741$	−5.75898	−	11.9817i	−0.211562	−	0.440158i
$742$	−2.44907			−0.0899083
$743$	−9.11206	+	15.7825i	−0.334289	+	0.579005i	−0.983348	−	0.181733i	$-0.941829\pi$
$743$	−9.11206	+	15.7825i	−0.334289	+	0.579005i	0.649059	+	0.760738i	$0.275163\pi$
$744$	2.55310	−	4.42209i	0.0936010	−	0.162122i
$745$	−33.2755	+	19.2116i	−1.21912	+	0.703860i
$746$	−12.6117	+	21.8441i	−0.461746	+	0.799768i
$747$	−20.2341	+	11.6822i	−0.740328	+	0.427429i
$748$	3.94151	−	8.99425i	0.144116	−	0.328862i
$749$			0.473730i			0.0173097i
$750$	−5.82512	+	3.36314i	−0.212703	+	0.122804i
$751$	12.4705	−	7.19986i	0.455056	−	0.262727i	−0.254907	−	0.966965i	$-0.582045\pi$
$751$	12.4705	−	7.19986i	0.455056	−	0.262727i	0.709963	+	0.704239i	$0.248712\pi$
$752$	−3.88718			−0.141751
$753$			14.6555i			0.534075i
$754$	7.52158	+	13.0278i	0.273920	+	0.474443i
$755$	−19.1105	+	33.1004i	−0.695504	+	1.20465i
$756$	−1.04590	−	1.81156i	−0.0380391	−	0.0658857i
$757$	−2.20394	+	3.81734i	−0.0801036	+	0.138743i	−0.903294	−	0.429022i	$-0.858858\pi$
$757$	−2.20394	+	3.81734i	−0.0801036	+	0.138743i	0.823191	+	0.567765i	$0.192192\pi$
$758$	14.2731	+	8.24055i	0.518421	+	0.299310i
$759$	5.91475	−	13.4971i	0.214692	−	0.489912i
$760$	−0.702624	+	9.28224i	−0.0254868	+	0.336702i
$761$		−	37.6528i		−	1.36491i	−0.730925	−	0.682457i	$-0.760911\pi$
$761$		−	37.6528i		−	1.36491i	0.730925	−	0.682457i	$-0.239089\pi$
$762$	−9.57123	−	5.52595i	−0.346729	−	0.200184i
$763$	−2.79658	−	1.61461i	−0.101243	−	0.0584527i
$764$	−11.8349	−	20.4987i	−0.428172	−	0.741616i
$765$	14.5918	+	8.42461i	0.527569	+	0.304592i
$766$	−1.41572	+	0.817365i	−0.0511519	+	0.0295326i
$767$			70.9328i			2.56124i
$768$			0.579050i			0.0208947i
$769$	22.4248	−	12.9469i	0.808657	−	0.466879i	−0.0378320	−	0.999284i	$-0.512045\pi$
$769$	22.4248	−	12.9469i	0.808657	−	0.466879i	0.846489	+	0.532406i	$0.178712\pi$
$770$	4.48932	−	0.498461i	0.161784	−	0.0179633i
$771$	8.96727			0.322948
$772$	3.89993			0.140362
$773$	−10.0592	+	5.80767i	−0.361804	+	0.208888i	−0.669872	−	0.742477i	$-0.733651\pi$
$773$	−10.0592	+	5.80767i	−0.361804	+	0.208888i	0.308068	+	0.951364i	$0.400318\pi$
$774$	4.81253	+	2.77852i	0.172983	+	0.0998718i
$775$	3.35468	−	1.93682i	0.120504	−	0.0695728i
$776$	2.77950	+	1.60474i	0.0997782	+	0.0576069i
$777$	0.791905	+	0.457206i	0.0284094	+	0.0164022i
$778$	31.2732			1.12120
$779$	−2.88653	+	38.1334i	−0.103421	+	1.36627i
$780$			6.51315i			0.233208i
$781$	2.90668	+	3.95180i	0.104009	+	0.141406i
$782$	19.6751	+	11.3594i	0.703580	+	0.406212i
$783$	−8.11345	+	4.68430i	−0.289951	+	0.167403i
$784$	−3.29666	+	5.70998i	−0.117738	+	0.203928i
$785$	12.9898	+	22.4990i	0.463626	+	0.803023i
$786$	10.8716			0.387779
$787$	39.5474			1.40971			0.704857	−	0.709350i	$-0.251011\pi$
$787$	39.5474			1.40971			0.704857	+	0.709350i	$0.251011\pi$
$788$	0.109581	−	0.0632668i	0.00390367	−	0.00225379i
$789$	−6.83021	−	11.8303i	−0.243162	−	0.421169i
$790$	−4.59025			−0.163314
$791$	−10.5639			−0.375610
$792$	−0.975293	−	8.78383i	−0.0346555	−	0.312120i
$793$	67.7956	+	39.1418i	2.40749	+	1.38997i
$794$	−0.133064	−	0.230473i	−0.00472226	−	0.00817920i
$795$	−2.37452	+	4.11280i	−0.0842157	+	0.145866i
$796$	−5.29673	+	9.17421i	−0.187738	+	0.325171i
$797$		−	30.5017i		−	1.08043i	−0.841528	−	0.540213i	$-0.818344\pi$
$797$		−	30.5017i		−	1.08043i	0.841528	−	0.540213i	$-0.181656\pi$
$798$	1.32924	+	0.907726i	0.0470547	+	0.0321332i
$799$		−	11.5093i		−	0.407170i
$800$	−0.219639	+	0.380426i	−0.00776541	+	0.0134501i
$801$	−8.26528	−	4.77196i	−0.292039	−	0.168609i
$802$	6.64967	−	3.83919i	0.234808	−	0.135566i
$803$	−30.8528	−	41.9462i	−1.08877	−	1.48025i
$804$	0.0666856	+	0.115503i	0.00235182	+	0.00407347i
$805$			10.4500i			0.368315i
$806$		−	46.4450i		−	1.63595i
$807$	7.14728	+	12.3795i	0.251596	+	0.435777i
$808$	8.56772	−	4.94658i	0.301411	−	0.174020i
$809$		−	37.8121i		−	1.32940i	−0.747109	−	0.664702i	$-0.768559\pi$
$809$		−	37.8121i		−	1.32940i	0.747109	−	0.664702i	$-0.231441\pi$
$810$	13.0158			0.457329
$811$	9.26699	+	16.0509i	0.325408	+	0.563623i	0.981595	−	0.190975i	$-0.0611650\pi$
$811$	9.26699	+	16.0509i	0.325408	+	0.563623i	−0.656187	+	0.754599i	$0.727832\pi$
$812$	−1.57739	−	0.910709i	−0.0553557	−	0.0319596i
$813$	0.995395	+	1.72407i	0.0349100	+	0.0604659i
$814$	4.86625	+	6.61594i	0.170562	+	0.231888i
$815$	−10.0282	+	17.3693i	−0.351272	+	0.608421i
$816$	−1.71447			−0.0600186
$817$	−9.06423	−	0.686121i	−0.317117	−	0.0240043i
$818$	10.1493			0.354864
$819$	−7.75113	−	4.47512i	−0.270846	−	0.156373i
$820$	9.36821	−	16.2262i	0.327152	−	0.566644i
$821$	−0.601429	+	0.347235i	−0.0209900	+	0.0121186i	−0.510458	−	0.859903i	$-0.670524\pi$
$821$	−0.601429	+	0.347235i	−0.0209900	+	0.0121186i	0.489468	+	0.872021i	$0.337191\pi$
$822$	−8.04313	−	4.64371i	−0.280536	−	0.161968i
$823$	8.30136	+	14.3784i	0.289367	+	0.501199i	0.973659	−	0.228010i	$-0.0732218\pi$
$823$	8.30136	+	14.3784i	0.289367	+	0.501199i	−0.684292	+	0.729208i	$0.739888\pi$
$824$		−	11.5054i		−	0.400810i
$825$	−0.338613	+	0.772692i	−0.0117890	+	0.0269017i
$826$	−4.29425	−	7.43786i	−0.149416	−	0.258796i
$827$	−2.89312	−	5.01102i	−0.100604	−	0.174250i	0.811330	−	0.584588i	$-0.198744\pi$
$827$	−2.89312	−	5.01102i	−0.100604	−	0.174250i	−0.911933	+	0.410338i	$0.865411\pi$
$828$	20.4466			0.710567
$829$		−	15.1485i		−	0.526130i	−0.964778	−	0.263065i	$-0.915267\pi$
$829$		−	15.1485i		−	0.526130i	0.964778	−	0.263065i	$-0.0847334\pi$
$830$	−16.2163	+	9.36251i	−0.562878	+	0.324978i
$831$	8.11487	−	14.0554i	0.281502	−	0.487575i
$832$	2.63347	+	4.56130i	0.0912990	+	0.158135i
$833$	−16.9063	−	9.76087i	−0.585769	−	0.338194i
$834$	1.13771	−	1.97058i	0.0393958	−	0.0682355i
$835$	37.3509			1.29258
$836$	7.66245	+	12.2592i	0.265011	+	0.423992i
$837$	28.9250			0.999796
$838$	−4.68298	+	8.11116i	−0.161771	+	0.280195i
$839$	25.8600	+	14.9303i	0.892786	+	0.515450i	0.874853	−	0.484389i	$-0.160958\pi$
$839$	25.8600	+	14.9303i	0.892786	+	0.515450i	0.0179335	+	0.999839i	$0.494291\pi$
$840$	−0.394304	−	0.682955i	−0.0136048	−	0.0235642i
$841$	10.4212	−	18.0500i	0.359352	−	0.622415i
$842$	0.179726	−	0.103765i	0.00619378	−	0.00357598i
$843$			0.465312i			0.0160262i
$844$	−9.44492			−0.325108
$845$	15.7399	+	27.2623i	0.541468	+	0.937851i
$846$	−5.17908	−	8.97044i	−0.178061	−	0.308410i
$847$	5.15771	−	4.75465i	0.177221	−	0.163372i
$848$			3.84037i			0.131879i
$849$	1.25519	+	2.17405i	0.0430780	+	0.0746133i
$850$	−1.12638	−	0.650315i	−0.0386345	−	0.0223056i
$851$	−16.4551	+	9.50035i	−0.564073	+	0.325668i
$852$	0.428240	−	0.741734i	0.0146713	−	0.0254114i
$853$	−44.1590	−	25.4952i	−1.51197	−	0.872938i	−0.999902	−	0.0139958i	$-0.995545\pi$
$853$	−44.1590	−	25.4952i	−1.51197	−	0.872938i	−0.512072	−	0.858943i	$-0.671122\pi$
$854$	−9.47853			−0.324349
$855$	−22.3568	+	10.7458i	−0.764585	+	0.367497i
$856$	0.742853			0.0253902
$857$	−13.6521	+	23.6461i	−0.466347	+	0.807737i	−0.999261	−	0.0384326i	$-0.987764\pi$
$857$	−13.6521	+	23.6461i	−0.466347	+	0.807737i	0.532914	+	0.846169i	$0.321097\pi$
$858$	5.99336	+	8.14831i	0.204610	+	0.278179i
$859$	−7.16090	−	12.4031i	−0.244327	−	0.423187i	0.717615	−	0.696440i	$-0.245234\pi$
$859$	−7.16090	−	12.4031i	−0.244327	−	0.423187i	−0.961942	+	0.273253i	$0.911900\pi$
$860$	3.85693	+	2.22680i	0.131520	+	0.0759333i
$861$	−1.61989	−	2.80572i	−0.0552056	−	0.0956188i
$862$	23.8134			0.811088
$863$			52.3639i			1.78249i	0.453524	+	0.891244i	$0.350167\pi$
$863$			52.3639i			1.78249i	−0.453524	+	0.891244i	$0.649833\pi$
$864$	−2.84069	+	1.64007i	−0.0966423	+	0.0557964i
$865$	3.67879	+	6.37185i	0.125083	+	0.216649i
$866$		−	40.3104i		−	1.36980i
$867$			4.76758i			0.161916i
$868$	2.81176	+	4.87012i	0.0954375	+	0.165303i
$869$	−5.74266	+	4.22393i	−0.194807	+	0.143287i
$870$	−3.05876	+	1.76597i	−0.103702	+	0.0598722i
$871$	1.05059	+	0.606560i	0.0355980	+	0.0205525i
$872$	−2.53185	+	4.38530i	−0.0857394	+	0.148505i
$873$			8.55232i			0.289452i
$874$	−30.1450	+	14.4892i	−1.01967	+	0.490104i
$875$		−	7.40775i		−	0.250428i
$876$	−4.54554	+	7.87310i	−0.153579	+	0.266007i
$877$	−6.98396	+	12.0966i	−0.235832	+	0.408472i	−0.959514	−	0.281661i	$-0.909115\pi$
$877$	−6.98396	+	12.0966i	−0.235832	+	0.408472i	0.723682	+	0.690133i	$0.242448\pi$
$878$	13.8611	+	24.0081i	0.467788	+	0.810233i
$879$	−11.1722	−	6.45025i	−0.376828	−	0.217562i
$880$	−0.781634	−	7.03967i	−0.0263489	−	0.237307i
$881$	−5.92210			−0.199521			−0.0997603	−	0.995011i	$-0.531808\pi$
$881$	−5.92210			−0.199521			−0.0997603	+	0.995011i	$0.531808\pi$
$882$	−17.5692			−0.591586
$883$	−6.98800	−	12.1036i	−0.235165	−	0.407318i	0.724156	−	0.689637i	$-0.242230\pi$
$883$	−6.98800	−	12.1036i	−0.235165	−	0.407318i	−0.959321	+	0.282319i	$0.908896\pi$
$884$	−13.5053	+	7.79726i	−0.454231	+	0.262250i
$885$	−16.6542			−0.559823
$886$	14.5179			0.487739
$887$	7.51138	+	13.0101i	0.252207	+	0.436836i	0.964133	−	0.265419i	$-0.0855102\pi$
$887$	7.51138	+	13.0101i	0.252207	+	0.436836i	−0.711926	+	0.702255i	$0.752177\pi$
$888$	0.716942	−	1.24178i	0.0240590	−	0.0416714i
$889$	10.5409	−	6.08582i	0.353532	−	0.204112i
$890$	−6.62408	−	3.82442i	−0.222040	−	0.128195i
$891$	16.2835	−	11.9771i	0.545518	−	0.401247i
$892$			19.1581i			0.641462i
$893$	13.9925	+	9.55531i	0.468240	+	0.319756i
$894$	10.4182			0.348438
$895$	−6.67578	−	3.85426i	−0.223147	−	0.128834i
$896$	−0.552279	−	0.318859i	−0.0184504	−	0.0106523i
$897$	−20.2664	+	11.7008i	−0.676676	+	0.390679i
$898$	0.395237	+	0.228190i	0.0131892	+	0.00761481i
$899$	21.8119	−	12.5931i	0.727466	−	0.420003i
$900$	−1.17054			−0.0390181
$901$	−11.3707			−0.378814
$902$	−3.21112	−	28.9205i	−0.106919	−	0.962947i
$903$	0.666914	−	0.385043i	0.0221935	−	0.0128134i
$904$			16.5652i			0.550951i
$905$		−	32.4876i		−	1.07992i
$906$	8.97497	−	5.18170i	0.298173	−	0.172150i
$907$	−20.5925	−	11.8891i	−0.683761	−	0.394770i	0.117509	−	0.993072i	$-0.462509\pi$
$907$	−20.5925	−	11.8891i	−0.683761	−	0.394770i	−0.801271	+	0.598302i	$0.795842\pi$
$908$	5.97535	+	10.3496i	0.198299	+	0.343464i
$909$	22.8304	+	13.1811i	0.757237	+	0.437191i
$910$	−6.21203	−	3.58652i	−0.205927	−	0.118892i
$911$			52.6737i			1.74516i	0.488473	+	0.872579i	$0.337554\pi$
$911$			52.6737i			1.74516i	−0.488473	+	0.872579i	$0.662446\pi$
$912$	1.42340	−	2.08438i	0.0471335	−	0.0690206i
$913$	−11.6722	+	26.6352i	−0.386294	+	0.881497i
$914$	15.5904	+	9.00111i	0.515684	+	0.297730i
$915$	−9.19002	+	15.9176i	−0.303813	+	0.526219i
$916$	5.99059	+	10.3760i	0.197935	+	0.342833i
$917$	−5.98656	+	10.3690i	−0.197694	+	0.342415i
$918$	−4.85599	−	8.41082i	−0.160272	−	0.277598i
$919$		−	16.8304i		−	0.555184i	−0.960699	−	0.277592i	$-0.910464\pi$
$919$		−	16.8304i		−	0.555184i	0.960699	−	0.277592i	$-0.0895364\pi$
$920$	16.3866			0.540250
$921$	−7.30981	+	4.22032i	−0.240866	+	0.139064i
$922$	7.47776	−	4.31729i	0.246267	−	0.142182i
$923$		−	7.79039i		−	0.256424i
$924$	−1.12175	−	0.491578i	−0.0369028	−	0.0161717i
$925$	0.942037	−	0.543885i	0.0309740	−	0.0178828i
$926$	2.41440	−	4.18187i	0.0793422	−	0.137425i
$927$	26.5510	−	15.3292i	0.872049	−	0.503478i
$928$	−1.42808	+	2.47350i	−0.0468789	+	0.0811966i
$929$	13.6845	−	23.7022i	0.448973	−	0.777643i	−0.549347	−	0.835594i	$-0.685123\pi$
$929$	13.6845	−	23.7022i	0.448973	−	0.777643i	0.998319	+	0.0579510i	$0.0184567\pi$
$930$	10.9047			0.357579
$931$	25.9029	−	12.4502i	0.848932	−	0.408038i
$932$			11.6072i			0.380207i
$933$	0.688601	+	0.397564i	0.0225438	+	0.0130157i
$934$	−2.10381	+	3.64390i	−0.0688387	+	0.119232i
$935$	20.8433	−	2.31429i	0.681649	−	0.0756854i
$936$	−7.01740	+	12.1545i	−0.229371	+	0.397282i
$937$	9.01272	−	5.20350i	0.294433	−	0.169991i	−0.345506	−	0.938416i	$-0.612293\pi$
$937$	9.01272	−	5.20350i	0.294433	−	0.169991i	0.639939	+	0.768426i	$0.278960\pi$
$938$	−0.146884			−0.00479593
$939$		−	12.8075i		−	0.417956i
$940$	−4.15070	−	7.18922i	−0.135381	−	0.234487i
$941$	−16.9954	−	29.4369i	−0.554035	−	0.959617i	−0.997978	−	0.0635619i	$-0.979754\pi$
$941$	−16.9954	−	29.4369i	−0.554035	−	0.959617i	0.443943	−	0.896055i	$-0.353579\pi$
$942$		−	7.04420i		−	0.229512i
$943$	67.3196			2.19223
$944$	−11.6633	+	6.73379i	−0.379607	+	0.219166i
$945$	2.23361	−	3.86873i	0.0726595	−	0.125850i
$946$	6.87433	−	0.763275i	0.223504	−	0.0248162i
$947$	8.84778	−	15.3248i	0.287514	−	0.497989i	−0.685702	−	0.727883i	$-0.740504\pi$
$947$	8.84778	−	15.3248i	0.287514	−	0.497989i	0.973216	+	0.229894i	$0.0738378\pi$
$948$	1.07787	+	0.622309i	0.0350076	+	0.0202117i
$949$			82.6907i			2.68425i
$950$	1.72577	−	0.829490i	0.0559914	−	0.0269122i
$951$	−3.40909			−0.110547
$952$	0.944088	−	1.63521i	0.0305981	−	0.0529974i
$953$	−18.4400	+	31.9390i	−0.597330	+	1.03461i	0.395883	+	0.918301i	$0.370439\pi$
$953$	−18.4400	+	31.9390i	−0.597330	+	1.03461i	−0.993213	+	0.116306i	$0.962895\pi$
$954$	−8.86242	+	5.11672i	−0.286932	+	0.165660i
$955$	25.2745	−	43.7767i	0.817862	−	1.41658i
$956$	13.3132	−	7.68639i	0.430580	−	0.248596i
$957$	−2.20164	+	5.02399i	−0.0711688	+	0.162402i
$958$			29.0174i			0.937510i
$959$	8.85803	−	5.11418i	0.286041	−	0.165146i
$960$	−1.07094	+	0.618306i	−0.0345643	+	0.0199557i
$961$	−46.7609			−1.50842
$962$		−	13.0423i		−	0.420502i
$963$	0.989740	+	1.71428i	0.0318939	+	0.0552419i
$964$	−4.41439	+	7.64595i	−0.142178	+	0.246259i
$965$	4.16432	+	7.21281i	0.134054	+	0.232189i
$966$	1.41673	−	2.45384i	0.0455825	−	0.0789511i
$967$	−20.6390	−	11.9159i	−0.663705	−	0.383190i	0.129982	−	0.991516i	$-0.458508\pi$
$967$	−20.6390	−	11.9159i	−0.663705	−	0.383190i	−0.793687	+	0.608326i	$0.791841\pi$
$968$	−7.45573	−	8.08777i	−0.239636	−	0.259951i
$969$	6.17150	+	4.21445i	0.198257	+	0.135388i
$970$			6.85413i			0.220073i
$971$	4.91990	+	2.84051i	0.157887	+	0.0911561i	0.576862	−	0.816842i	$-0.304277\pi$
$971$	4.91990	+	2.84051i	0.157887	+	0.0911561i	−0.418975	+	0.907998i	$0.637610\pi$
$972$	−11.5784	−	6.68480i	−0.371378	−	0.214415i
$973$	1.25298	+	2.17023i	0.0401687	+	0.0695743i
$974$	20.1157	+	11.6138i	0.644547	+	0.372130i
$975$	1.16023	−	0.669859i	0.0371571	−	0.0214527i
$976$			14.8632i			0.475760i
$977$			49.1441i			1.57226i	0.618063	+	0.786129i	$0.287918\pi$
$977$			49.1441i			1.57226i	−0.618063	+	0.786129i	$0.712082\pi$
$978$	4.70958	−	2.71908i	0.150596	−	0.0869466i
$979$	−11.8063	+	1.31089i	−0.377331	+	0.0418961i
$980$	−14.0806			−0.449788
$981$	−13.4933			−0.430807
$982$	−4.96857	+	2.86860i	−0.158553	+	0.0915409i
$983$	−22.9440	−	13.2468i	−0.731801	−	0.422506i	0.0872794	−	0.996184i	$-0.472183\pi$
$983$	−22.9440	−	13.2468i	−0.731801	−	0.422506i	−0.819081	+	0.573678i	$0.805516\pi$
$984$	−4.39964	+	2.54013i	−0.140255	+	0.0809765i
$985$	0.234020	+	0.135112i	0.00745650	+	0.00430501i
$986$	−7.32363	−	4.22830i	−0.233232	−	0.134657i
$987$	−1.43542			−0.0456899
$988$	1.73286	−	22.8925i	0.0551296	−	0.728309i
$989$			16.0017i			0.508825i
$990$	15.2040	−	11.1831i	0.483216	−	0.355422i
$991$	53.4302	+	30.8479i	1.69727	+	0.979917i	0.948337	+	0.317266i	$0.102765\pi$
$991$	53.4302	+	30.8479i	1.69727	+	0.979917i	0.748929	+	0.662651i	$0.230569\pi$
$992$	7.63680	−	4.40911i	0.242469	−	0.139989i
$993$	2.17058	−	3.75956i	0.0688814	−	0.119306i
$994$	0.471628	+	0.816883i	0.0149591	+	0.0259100i
$995$	−22.6233			−0.717205
$996$	5.07717			0.160876
$997$	23.7888	−	13.7345i	0.753400	−	0.434976i	−0.0735213	−	0.997294i	$-0.523424\pi$
$997$	23.7888	−	13.7345i	0.753400	−	0.434976i	0.826921	+	0.562318i	$0.190090\pi$
$998$	3.00551	+	5.20569i	0.0951377	+	0.164783i
$999$	8.12253			0.256985

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.h.b.65.5	yes	20
11.10	odd	2		418.2.h.a.65.5	✓	20
19.12	odd	6		418.2.h.a.373.5	yes	20
209.164	even	6	inner	418.2.h.b.373.5	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.h.a.65.5	✓	20	11.10	odd	2
418.2.h.a.373.5	yes	20	19.12	odd	6
418.2.h.b.65.5	yes	20	1.1	even	1	trivial
418.2.h.b.373.5	yes	20	209.164	even	6	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.501472 - 0.289525i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.06779 - 1.84947i) q^{5} +(-0.501472 + 0.289525i) q^{6} -0.637717i q^{7} -1.00000 q^{8} +(-1.33235 - 2.30770i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.501472 - 0.289525i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.06779 - 1.84947i) q^{5} +(-0.501472 + 0.289525i) q^{6} -0.637717i q^{7} -1.00000 q^{8} +(-1.33235 - 2.30770i) q^{9} +(-1.06779 - 1.84947i) q^{10} +(-3.03774 - 1.33121i) q^{11} +0.579050i q^{12} +(2.63347 + 4.56130i) q^{13} +(-0.552279 - 0.318859i) q^{14} +(-1.07094 + 0.618306i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.56416 - 1.48042i) q^{17} -2.66470 q^{18} +(3.92865 - 1.88830i) q^{19} -2.13558 q^{20} +(-0.184635 + 0.319798i) q^{21} +(-2.67174 + 1.96515i) q^{22} +(-3.83656 - 6.64512i) q^{23} +(0.501472 + 0.289525i) q^{24} +(0.219639 + 0.380426i) q^{25} +5.26693 q^{26} +3.28015i q^{27} +(-0.552279 + 0.318859i) q^{28} +(1.42808 + 2.47350i) q^{29} +1.23661i q^{30} -8.81822i q^{31} +(0.500000 + 0.866025i) q^{32} +(1.13792 + 1.54707i) q^{33} +(-2.56416 + 1.48042i) q^{34} +(-1.17944 - 0.680949i) q^{35} +(-1.33235 + 2.30770i) q^{36} -2.47627i q^{37} +(0.329008 - 4.34646i) q^{38} -3.04982i q^{39} +(-1.06779 + 1.84947i) q^{40} +(-4.38672 + 7.59802i) q^{41} +(0.184635 + 0.319798i) q^{42} +(-1.80603 - 1.04271i) q^{43} +(0.366005 + 3.29637i) q^{44} -5.69069 q^{45} -7.67312 q^{46} +(1.94359 + 3.36640i) q^{47} +(0.501472 - 0.289525i) q^{48} +6.59332 q^{49} +0.439278 q^{50} +(0.857237 + 1.48478i) q^{51} +(2.63347 - 4.56130i) q^{52} +(3.32586 - 1.92019i) q^{53} +(2.84069 + 1.64007i) q^{54} +(-5.70572 + 4.19675i) q^{55} +0.637717i q^{56} +(-2.51682 - 0.190512i) q^{57} +2.85615 q^{58} +(11.6633 + 6.73379i) q^{59} +(1.07094 + 0.618306i) q^{60} +(12.8719 - 7.43161i) q^{61} +(-7.63680 - 4.40911i) q^{62} +(-1.47166 + 0.849663i) q^{63} +1.00000 q^{64} +11.2480 q^{65} +(1.90876 - 0.211935i) q^{66} +(0.199470 - 0.115164i) q^{67} +2.96084i q^{68} +4.44312i q^{69} +(-1.17944 + 0.680949i) q^{70} +(-1.28095 - 0.739556i) q^{71} +(1.33235 + 2.30770i) q^{72} +(13.5966 + 7.84999i) q^{73} +(-2.14451 - 1.23813i) q^{74} -0.254364i q^{75} +(-3.59964 - 2.45816i) q^{76} +(-0.848938 + 1.93722i) q^{77} +(-2.64122 - 1.52491i) q^{78} +(1.07471 - 1.86145i) q^{79} +(1.06779 + 1.84947i) q^{80} +(-3.04737 + 5.27819i) q^{81} +(4.38672 + 7.59802i) q^{82} -8.76810i q^{83} +0.369270 q^{84} +(-5.47598 + 3.16156i) q^{85} +(-1.80603 + 1.04271i) q^{86} -1.65386i q^{87} +(3.03774 + 1.33121i) q^{88} +(3.10177 - 1.79081i) q^{89} +(-2.84535 + 4.92829i) q^{90} +(2.90882 - 1.67941i) q^{91} +(-3.83656 + 6.64512i) q^{92} +(-2.55310 + 4.42209i) q^{93} +3.88718 q^{94} +(0.702624 - 9.28224i) q^{95} -0.579050i q^{96} +(-2.77950 - 1.60474i) q^{97} +(3.29666 - 5.70998i) q^{98} +(0.975293 + 8.78383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9}+O(q^{10}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9	\( 20 q + 10 q^{2} + 3 q^{3} - 10 q^{4} + 2 q^{5} + 3 q^{6} - 20 q^{8} + 11 q^{9} - 2 q^{10} + q^{11} + 5 q^{13} - 6 q^{14} + 12 q^{15} - 10 q^{16} + 6 q^{17} + 22 q^{18} - 18 q^{19} - 4 q^{20} - 14 q^{21} + 2 q^{22} - 4 q^{23} - 3 q^{24} - 20 q^{25} + 10 q^{26} - 6 q^{28} + 5 q^{29} + 10 q^{32} - 13 q^{33} + 6 q^{34} - 12 q^{35} + 11 q^{36} - 12 q^{38} - 2 q^{40} - q^{41} + 14 q^{42} + 3 q^{43} + q^{44} + 12 q^{45} - 8 q^{46} + q^{47} - 3 q^{48} + 8 q^{49} - 40 q^{50} - 12 q^{51} + 5 q^{52} - 24 q^{53} + 27 q^{54} - 2 q^{55} + 32 q^{57} + 10 q^{58} - 51 q^{59} - 12 q^{60} + 27 q^{61} + 12 q^{63} + 20 q^{64} - 8 q^{65} - 8 q^{66} + 27 q^{67} - 12 q^{70} + 33 q^{71} - 11 q^{72} - 9 q^{73} - 12 q^{74} + 6 q^{76} - 22 q^{77} - 24 q^{79} + 2 q^{80} + 12 q^{81} + q^{82} + 28 q^{84} - 12 q^{85} + 3 q^{86} - q^{88} + 21 q^{89} + 6 q^{90} + 12 q^{91} - 4 q^{92} - 10 q^{93} + 2 q^{94} - 24 q^{95} + 24 q^{97} + 4 q^{98} + 3 q^{99}+O(q^{100}) \) 20 * q + 10 * q^2 + 3 * q^3 - 10 * q^4 + 2 * q^5 + 3 * q^6 - 20 * q^8 + 11 * q^9 - 2 * q^10 + q^11 + 5 * q^13 - 6 * q^14 + 12 * q^15 - 10 * q^16 + 6 * q^17 + 22 * q^18 - 18 * q^19 - 4 * q^20 - 14 * q^21 + 2 * q^22 - 4 * q^23 - 3 * q^24 - 20 * q^25 + 10 * q^26 - 6 * q^28 + 5 * q^29 + 10 * q^32 - 13 * q^33 + 6 * q^34 - 12 * q^35 + 11 * q^36 - 12 * q^38 - 2 * q^40 - q^41 + 14 * q^42 + 3 * q^43 + q^44 + 12 * q^45 - 8 * q^46 + q^47 - 3 * q^48 + 8 * q^49 - 40 * q^50 - 12 * q^51 + 5 * q^52 - 24 * q^53 + 27 * q^54 - 2 * q^55 + 32 * q^57 + 10 * q^58 - 51 * q^59 - 12 * q^60 + 27 * q^61 + 12 * q^63 + 20 * q^64 - 8 * q^65 - 8 * q^66 + 27 * q^67 - 12 * q^70 + 33 * q^71 - 11 * q^72 - 9 * q^73 - 12 * q^74 + 6 * q^76 - 22 * q^77 - 24 * q^79 + 2 * q^80 + 12 * q^81 + q^82 + 28 * q^84 - 12 * q^85 + 3 * q^86 - q^88 + 21 * q^89 + 6 * q^90 + 12 * q^91 - 4 * q^92 - 10 * q^93 + 2 * q^94 - 24 * q^95 + 24 * q^97 + 4 * q^98 + 3 * q^99

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