LMFDB - Embedded newform 483.2.i.h.277.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(277,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("483.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.i (of order $3$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
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} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 $ x^20 - 3x^19 + 22x^18 - 43x^17 + 245x^16 - 416x^15 + 1707x^14 - 2021x^13 + 7135x^12 - 6640x^11 + 20315x^10 - 10565x^9 + 29358x^8 - 9009x^7 + 30661x^6 - 4026x^5 + 15786x^4 - 84x^3 + 5800x^2 + 152*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.10
Root			$-1.37000 + 2.37290i$ of defining polynomial
Character	$\chi$	$=$	483.277
Dual form			483.2.i.h.415.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37000 + 2.37290i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.75378 + 4.76968i) q^{4} +(1.69091 + 2.92874i) q^{5} +2.73999 q^{6} +(-2.19620 - 1.47537i) q^{7} -9.61066 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(1.37000 + 2.37290i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.75378 + 4.76968i) q^{4} +(1.69091 + 2.92874i) q^{5} +2.73999 q^{6} +(-2.19620 - 1.47537i) q^{7} -9.61066 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.63307 + 8.02471i) q^{10} +(-0.941706 + 1.63108i) q^{11} +(2.75378 + 4.76968i) q^{12} +1.76938 q^{13} +(0.492131 - 7.23261i) q^{14} +3.38181 q^{15} +(-7.65901 - 13.2658i) q^{16} +(2.94798 - 5.10605i) q^{17} +(1.37000 - 2.37290i) q^{18} +(3.31330 + 5.73881i) q^{19} -18.6255 q^{20} +(-2.37581 + 1.16428i) q^{21} -5.16053 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-4.80533 + 8.32307i) q^{24} +(-3.21833 + 5.57432i) q^{25} +(2.42404 + 4.19855i) q^{26} -1.00000 q^{27} +(13.0849 - 6.41231i) q^{28} +8.24468 q^{29} +(4.63307 + 8.02471i) q^{30} +(-1.47179 + 2.54922i) q^{31} +(11.3749 - 19.7020i) q^{32} +(0.941706 + 1.63108i) q^{33} +16.1549 q^{34} +(0.607409 - 8.92680i) q^{35} +5.50755 q^{36} +(2.21781 + 3.84136i) q^{37} +(-9.07841 + 15.7243i) q^{38} +(0.884688 - 1.53232i) q^{39} +(-16.2507 - 28.1471i) q^{40} -5.90495 q^{41} +(-6.01756 - 4.04250i) q^{42} +0.669028 q^{43} +(-5.18649 - 8.98327i) q^{44} +(1.69091 - 2.92874i) q^{45} +(1.37000 - 2.37290i) q^{46} +(-0.897583 - 1.55466i) q^{47} -15.3180 q^{48} +(2.64656 + 6.48041i) q^{49} -17.6364 q^{50} +(-2.94798 - 5.10605i) q^{51} +(-4.87246 + 8.43935i) q^{52} +(4.84250 - 8.38746i) q^{53} +(-1.37000 - 2.37290i) q^{54} -6.36935 q^{55} +(21.1069 + 14.1793i) q^{56} +6.62660 q^{57} +(11.2952 + 19.5638i) q^{58} +(-0.683613 + 1.18405i) q^{59} +(-9.31276 + 16.1302i) q^{60} +(-4.68170 - 8.10894i) q^{61} -8.06540 q^{62} +(-0.179610 + 2.63965i) q^{63} +31.6985 q^{64} +(2.99185 + 5.18203i) q^{65} +(-2.58027 + 4.46915i) q^{66} +(4.08947 - 7.08317i) q^{67} +(16.2361 + 28.1218i) q^{68} -1.00000 q^{69} +(22.0146 - 10.7884i) q^{70} -0.295052 q^{71} +(4.80533 + 8.32307i) q^{72} +(2.22875 - 3.86031i) q^{73} +(-6.07678 + 10.5253i) q^{74} +(3.21833 + 5.57432i) q^{75} -36.4963 q^{76} +(4.47462 - 2.19281i) q^{77} +4.84807 q^{78} +(1.51384 + 2.62205i) q^{79} +(25.9013 - 44.8624i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.08975 - 14.0119i) q^{82} -10.5300 q^{83} +(0.989213 - 14.5380i) q^{84} +19.9390 q^{85} +(0.916565 + 1.58754i) q^{86} +(4.12234 - 7.14010i) q^{87} +(9.05041 - 15.6758i) q^{88} +(5.35981 + 9.28346i) q^{89} +9.26614 q^{90} +(-3.88590 - 2.61048i) q^{91} +5.50755 q^{92} +(1.47179 + 2.54922i) q^{93} +(2.45937 - 4.25975i) q^{94} +(-11.2050 + 19.4076i) q^{95} +(-11.3749 - 19.7020i) q^{96} +15.6290 q^{97} +(-11.7516 + 15.1582i) q^{98} +1.88341 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.37000	+	2.37290i	0.968733	+	1.67789i	0.699232	+	0.714895i	$0.253525\pi$
$2$	1.37000	+	2.37290i	0.968733	+	1.67789i	0.269501	+	0.963000i	$0.413141\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.75378	+	4.76968i	−1.37689	+	2.38484i
$5$	1.69091	+	2.92874i	0.756197	+	1.30977i	0.944777	+	0.327713i	$0.106278\pi$
$5$	1.69091	+	2.92874i	0.756197	+	1.30977i	−0.188581	+	0.982058i	$0.560389\pi$
$6$	2.73999			1.11860
$7$	−2.19620	−	1.47537i	−0.830084	−	0.557638i
$7$	−2.19620	−	1.47537i	−0.830084	−	0.557638i
$8$	−9.61066			−3.39788
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−4.63307	+	8.02471i	−1.46511	+	2.53764i
$11$	−0.941706	+	1.63108i	−0.283935	+	0.491790i	−0.972350	−	0.233527i	$-0.924973\pi$
$11$	−0.941706	+	1.63108i	−0.283935	+	0.491790i	0.688415	+	0.725317i	$0.258307\pi$
$12$	2.75378	+	4.76968i	0.794946	+	1.37689i
$13$	1.76938			0.490736			0.245368	−	0.969430i	$-0.421091\pi$
$13$	1.76938			0.490736			0.245368	+	0.969430i	$0.421091\pi$
$14$	0.492131	−	7.23261i	0.131527	−	1.93300i
$15$	3.38181			0.873181
$16$	−7.65901	−	13.2658i	−1.91475	−	3.31645i
$17$	2.94798	−	5.10605i	0.714989	−	1.23840i	−0.247974	−	0.968767i	$-0.579765\pi$
$17$	2.94798	−	5.10605i	0.714989	−	1.23840i	0.962964	−	0.269631i	$-0.0869019\pi$
$18$	1.37000	−	2.37290i	0.322911	−	0.559298i
$19$	3.31330	+	5.73881i	0.760123	+	1.31657i	0.942787	+	0.333397i	$0.108195\pi$
$19$	3.31330	+	5.73881i	0.760123	+	1.31657i	−0.182663	+	0.983176i	$0.558472\pi$
$20$	−18.6255			−4.16479
$21$	−2.37581	+	1.16428i	−0.518444	+	0.254066i
$22$	−5.16053			−1.10023
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−4.80533	+	8.32307i	−0.980884	+	1.69894i
$25$	−3.21833	+	5.57432i	−0.643667	+	1.11486i
$26$	2.42404	+	4.19855i	0.475393	+	0.823404i
$27$	−1.00000			−0.192450
$28$	13.0849	−	6.41231i	2.47281	−	1.21181i
$29$	8.24468			1.53100			0.765500	−	0.643436i	$-0.222492\pi$
$29$	8.24468			1.53100			0.765500	+	0.643436i	$0.222492\pi$
$30$	4.63307	+	8.02471i	0.845879	+	1.46511i
$31$	−1.47179	+	2.54922i	−0.264342	+	0.457854i	−0.967391	−	0.253288i	$-0.918488\pi$
$31$	−1.47179	+	2.54922i	−0.264342	+	0.457854i	0.703049	+	0.711141i	$0.251821\pi$
$32$	11.3749	−	19.7020i	2.01083	−	3.48285i
$33$	0.941706	+	1.63108i	0.163930	+	0.283935i
$34$	16.1549			2.77054
$35$	0.607409	−	8.92680i	0.102671	−	1.50890i
$36$	5.50755			0.917925
$37$	2.21781	+	3.84136i	0.364606	+	0.631516i	0.988713	−	0.149823i	$-0.0478704\pi$
$37$	2.21781	+	3.84136i	0.364606	+	0.631516i	−0.624107	+	0.781339i	$0.714537\pi$
$38$	−9.07841	+	15.7243i	−1.47271	+	2.55081i
$39$	0.884688	−	1.53232i	0.141663	−	0.245368i
$40$	−16.2507	−	28.1471i	−2.56947	−	4.45044i
$41$	−5.90495			−0.922198			−0.461099	−	0.887349i	$-0.652545\pi$
$41$	−5.90495			−0.922198			−0.461099	+	0.887349i	$0.652545\pi$
$42$	−6.01756	−	4.04250i	−0.928530	−	0.623772i
$43$	0.669028			0.102026			0.0510129	−	0.998698i	$-0.483755\pi$
$43$	0.669028			0.102026			0.0510129	+	0.998698i	$0.483755\pi$
$44$	−5.18649	−	8.98327i	−0.781893	−	1.35428i
$45$	1.69091	−	2.92874i	0.252066	−	0.436590i
$46$	1.37000	−	2.37290i	0.201995	−	0.349865i
$47$	−0.897583	−	1.55466i	−0.130926	−	0.226770i	0.793108	−	0.609081i	$-0.208462\pi$
$47$	−0.897583	−	1.55466i	−0.130926	−	0.226770i	−0.924034	+	0.382311i	$0.875128\pi$
$48$	−15.3180			−2.21096
$49$	2.64656	+	6.48041i	0.378080	+	0.925773i
$50$	−17.6364			−2.49416
$51$	−2.94798	−	5.10605i	−0.412799	−	0.714989i
$52$	−4.87246	+	8.43935i	−0.675689	+	1.17033i
$53$	4.84250	−	8.38746i	0.665169	−	1.15211i	−0.314071	−	0.949400i	$-0.601693\pi$
$53$	4.84250	−	8.38746i	0.665169	−	1.15211i	0.979240	−	0.202706i	$-0.0649737\pi$
$54$	−1.37000	−	2.37290i	−0.186433	−	0.322911i
$55$	−6.36935			−0.858843
$56$	21.1069	+	14.1793i	2.82053	+	1.89479i
$57$	6.62660			0.877715
$58$	11.2952	+	19.5638i	1.48313	+	2.56886i
$59$	−0.683613	+	1.18405i	−0.0889988	+	0.154150i	−0.907088	−	0.420941i	$-0.861700\pi$
$59$	−0.683613	+	1.18405i	−0.0889988	+	0.154150i	0.818089	+	0.575091i	$0.195033\pi$
$60$	−9.31276	+	16.1302i	−1.20227	+	2.08240i
$61$	−4.68170	−	8.10894i	−0.599430	−	1.03824i	−0.992905	−	0.118908i	$-0.962061\pi$
$61$	−4.68170	−	8.10894i	−0.599430	−	1.03824i	0.393475	−	0.919335i	$-0.371273\pi$
$62$	−8.06540			−1.02431
$63$	−0.179610	+	2.63965i	−0.0226288	+	0.332564i
$64$	31.6985			3.96231
$65$	2.99185	+	5.18203i	0.371093	+	0.642752i
$66$	−2.58027	+	4.46915i	−0.317609	+	0.550115i
$67$	4.08947	−	7.08317i	0.499608	−	0.865347i	−0.500392	−	0.865799i	$-0.666811\pi$
$67$	4.08947	−	7.08317i	0.499608	−	0.865347i	1.00000		0.000452542i	$0.000144049\pi$
$68$	16.2361	+	28.1218i	1.96892	+	3.41027i
$69$	−1.00000			−0.120386
$70$	22.0146	−	10.7884i	2.63124	−	1.28945i
$71$	−0.295052			−0.0350162			−0.0175081	−	0.999847i	$-0.505573\pi$
$71$	−0.295052			−0.0350162			−0.0175081	+	0.999847i	$0.505573\pi$
$72$	4.80533	+	8.32307i	0.566313	+	0.980884i
$73$	2.22875	−	3.86031i	0.260856	−	0.451815i	−0.705614	−	0.708597i	$-0.749329\pi$
$73$	2.22875	−	3.86031i	0.260856	−	0.451815i	0.966470	+	0.256781i	$0.0826620\pi$
$74$	−6.07678	+	10.5253i	−0.706411	+	1.22354i
$75$	3.21833	+	5.57432i	0.371621	+	0.643667i
$76$	−36.4963			−4.18642
$77$	4.47462	−	2.19281i	0.509931	−	0.249894i
$78$	4.84807			0.548936
$79$	1.51384	+	2.62205i	0.170320	+	0.295004i	0.938532	−	0.345192i	$-0.112186\pi$
$79$	1.51384	+	2.62205i	0.170320	+	0.295004i	−0.768211	+	0.640196i	$0.778853\pi$
$80$	25.9013	−	44.8624i	2.89586	−	5.01577i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−8.08975	−	14.0119i	−0.893363	−	1.54735i
$83$	−10.5300			−1.15582			−0.577910	−	0.816100i	$-0.696132\pi$
$83$	−10.5300			−1.15582			−0.577910	+	0.816100i	$0.696132\pi$
$84$	0.989213	−	14.5380i	0.107932	−	1.58623i
$85$	19.9390			2.16269
$86$	0.916565	+	1.58754i	0.0988358	+	0.171189i
$87$	4.12234	−	7.14010i	0.441961	−	0.765500i
$88$	9.05041	−	15.6758i	0.964777	−	1.67104i
$89$	5.35981	+	9.28346i	0.568138	+	0.984044i	0.996750	+	0.0805556i	$0.0256695\pi$
$89$	5.35981	+	9.28346i	0.568138	+	0.984044i	−0.428612	+	0.903489i	$0.640997\pi$
$90$	9.26614			0.976737
$91$	−3.88590	−	2.61048i	−0.407353	−	0.273653i
$92$	5.50755			0.574202
$93$	1.47179	+	2.54922i	0.152618	+	0.264342i
$94$	2.45937	−	4.25975i	0.253664	−	0.439360i
$95$	−11.2050	+	19.4076i	−1.14961	+	1.99117i
$96$	−11.3749	−	19.7020i	−1.16095	−	2.01083i
$97$	15.6290			1.58688			0.793441	−	0.608648i	$-0.208288\pi$
$97$	15.6290			1.58688			0.793441	+	0.608648i	$0.208288\pi$
$98$	−11.7516	+	15.1582i	−1.18709	+	1.53121i
$99$	1.88341			0.189290
$100$	−17.7251	−	30.7008i	−1.77251	−	3.07008i
$101$	−3.78458	+	6.55508i	−0.376580	+	0.652255i	−0.990562	−	0.137065i	$-0.956233\pi$
$101$	−3.78458	+	6.55508i	−0.376580	+	0.652255i	0.613983	+	0.789320i	$0.289567\pi$
$102$	8.07743	−	13.9905i	0.799785	−	1.38527i
$103$	1.31063	+	2.27008i	0.129141	+	0.223678i	0.923344	−	0.383974i	$-0.125445\pi$
$103$	1.31063	+	2.27008i	0.129141	+	0.223678i	−0.794203	+	0.607652i	$0.792111\pi$
$104$	−17.0049			−1.66746
$105$	−7.42713	−	4.98943i	−0.724814	−	0.486919i
$106$	26.5368			2.57748
$107$	−8.66609	−	15.0101i	−0.837783	−	1.45108i	−0.891745	−	0.452539i	$-0.850518\pi$
$107$	−8.66609	−	15.0101i	−0.837783	−	1.45108i	0.0539619	−	0.998543i	$-0.482815\pi$
$108$	2.75378	−	4.76968i	0.264982	−	0.458963i
$109$	6.68403	−	11.5771i	0.640214	−	1.10888i	−0.345171	−	0.938540i	$-0.612179\pi$
$109$	6.68403	−	11.5771i	0.640214	−	1.10888i	0.985385	−	0.170343i	$-0.0544876\pi$
$110$	−8.72598	−	15.1138i	−0.831990	−	1.44105i
$111$	4.43562			0.421011
$112$	−2.75127	+	40.4342i	−0.259971	+	3.82067i
$113$	−1.18709			−0.111672			−0.0558360	−	0.998440i	$-0.517782\pi$
$113$	−1.18709			−0.111672			−0.0558360	+	0.998440i	$0.517782\pi$
$114$	9.07841	+	15.7243i	0.850271	+	1.47271i
$115$	1.69091	−	2.92874i	0.157678	−	0.273106i
$116$	−22.7040	+	39.3245i	−2.10801	+	3.65119i
$117$	−0.884688	−	1.53232i	−0.0817894	−	0.141663i
$118$	−3.74618			−0.344864
$119$	−14.0076	+	6.86452i	−1.28408	+	0.629270i
$120$	−32.5015			−2.96696
$121$	3.72638	+	6.45428i	0.338762	+	0.586753i
$122$	12.8278	−	22.2184i	1.16138	−	2.01156i
$123$	−2.95247	+	5.11383i	−0.266216	+	0.461099i
$124$	−8.10598	−	14.0400i	−0.727938	−	1.26083i
$125$	−4.85853			−0.434560
$126$	−6.50969	+	3.19011i	−0.579929	+	0.284197i
$127$	−12.2311			−1.08533			−0.542667	−	0.839948i	$-0.682585\pi$
$127$	−12.2311			−1.08533			−0.542667	+	0.839948i	$0.682585\pi$
$128$	20.6769	+	35.8134i	1.82760	+	3.16549i
$129$	0.334514	−	0.579395i	0.0294523	−	0.0510129i
$130$	−8.19764	+	14.1987i	−0.718981	+	1.24531i
$131$	3.02835	+	5.24526i	0.264588	+	0.458280i	0.967456	−	0.253041i	$-0.0814307\pi$
$131$	3.02835	+	5.24526i	0.264588	+	0.458280i	−0.702868	+	0.711321i	$0.748097\pi$
$132$	−10.3730			−0.902853
$133$	1.19021	−	17.4919i	0.103204	−	1.51674i
$134$	22.4102			1.93595
$135$	−1.69091	−	2.92874i	−0.145530	−	0.252066i
$136$	−28.3320	+	49.0725i	−2.42945	+	4.20793i
$137$	7.14630	−	12.3778i	0.610550	−	1.05750i	−0.380598	−	0.924741i	$-0.624282\pi$
$137$	7.14630	−	12.3778i	0.610550	−	1.05750i	0.991148	−	0.132763i	$-0.0423848\pi$
$138$	−1.37000	−	2.37290i	−0.116622	−	0.201995i
$139$	−16.4290			−1.39349			−0.696743	−	0.717321i	$-0.745368\pi$
$139$	−16.4290			−1.39349			−0.696743	+	0.717321i	$0.745368\pi$
$140$	40.9053	+	27.4795i	3.45713	+	2.32244i
$141$	−1.79517			−0.151180
$142$	−0.404220	−	0.700129i	−0.0339214	−	0.0587535i
$143$	−1.66623	+	2.88600i	−0.139337	+	0.241339i
$144$	−7.65901	+	13.2658i	−0.638250	+	1.10548i
$145$	13.9410	+	24.1465i	1.15774	+	2.00526i
$146$	12.2135			1.01080
$147$	6.93548	+	0.948216i	0.572029	+	0.0782075i
$148$	−24.4294			−2.00809
$149$	−6.90181	−	11.9543i	−0.565418	−	0.979333i	−0.997011	−	0.0772640i	$-0.975382\pi$
$149$	−6.90181	−	11.9543i	−0.565418	−	0.979333i	0.431593	−	0.902069i	$-0.357952\pi$
$150$	−8.81820	+	15.2736i	−0.720003	+	1.24708i
$151$	2.12357	−	3.67813i	0.172814	−	0.299322i	−0.766589	−	0.642138i	$-0.778047\pi$
$151$	2.12357	−	3.67813i	0.172814	−	0.299322i	0.939403	+	0.342816i	$0.111381\pi$
$152$	−31.8430	−	55.1537i	−2.58281	−	4.47355i
$153$	−5.89595			−0.476660
$154$	11.3335	+	7.61370i	0.913283	+	0.613529i
$155$	−9.95467			−0.799578
$156$	4.87246	+	8.43935i	0.390109	+	0.675689i
$157$	0.333896	−	0.578325i	0.0266478	−	0.0461554i	−0.852394	−	0.522900i	$-0.824850\pi$
$157$	0.333896	−	0.578325i	0.0266478	−	0.0461554i	0.879042	+	0.476745i	$0.158183\pi$
$158$	−4.14791	+	7.18440i	−0.329990	+	0.571560i
$159$	−4.84250	−	8.38746i	−0.384035	−	0.665169i
$160$	76.9359			6.08232
$161$	−0.179610	+	2.63965i	−0.0141553	+	0.208033i
$162$	−2.73999			−0.215274
$163$	0.363590	+	0.629757i	0.0284786	+	0.0493263i	0.879913	−	0.475134i	$-0.157600\pi$
$163$	0.363590	+	0.629757i	0.0284786	+	0.0493263i	−0.851435	+	0.524460i	$0.824267\pi$
$164$	16.2609	−	28.1647i	1.26976	−	2.19929i
$165$	−3.18467	+	5.51602i	−0.247927	+	0.429421i
$166$	−14.4261	−	24.9867i	−1.11968	−	1.93935i
$167$	9.42526			0.729349			0.364674	−	0.931135i	$-0.381180\pi$
$167$	9.42526			0.729349			0.364674	+	0.931135i	$0.381180\pi$
$168$	22.8331	−	11.1895i	1.76161	−	0.863286i
$169$	−9.86931			−0.759178
$170$	27.3164	+	47.3133i	2.09507	+	3.62877i
$171$	3.31330	−	5.73881i	0.253374	−	0.438857i
$172$	−1.84235	+	3.19105i	−0.140478	+	0.243315i
$173$	−5.42568	−	9.39756i	−0.412507	−	0.714483i	0.582656	−	0.812719i	$-0.302013\pi$
$173$	−5.42568	−	9.39756i	−0.412507	−	0.714483i	−0.995163	+	0.0982357i	$0.968680\pi$
$174$	22.5904			1.71257
$175$	15.2923	−	7.49406i	1.15599	−	0.566498i
$176$	28.8501			2.17466
$177$	0.683613	+	1.18405i	0.0513835	+	0.0889988i
$178$	−14.6858	+	25.4366i	−1.10075	+	1.90655i
$179$	4.97180	−	8.61141i	0.371610	−	0.643647i	−0.618204	−	0.786018i	$-0.712139\pi$
$179$	4.97180	−	8.61141i	0.371610	−	0.643647i	0.989813	+	0.142371i	$0.0454726\pi$
$180$	9.31276	+	16.1302i	0.694132	+	1.20227i
$181$	−0.975614			−0.0725168			−0.0362584	−	0.999342i	$-0.511544\pi$
$181$	−0.975614			−0.0725168			−0.0362584	+	0.999342i	$0.511544\pi$
$182$	0.870764	−	12.7972i	0.0645453	−	0.948592i
$183$	−9.36339			−0.692162
$184$	4.80533	+	8.32307i	0.354254	+	0.613585i
$185$	−7.50022	+	12.9908i	−0.551427	+	0.955100i
$186$	−4.03270	+	6.98484i	−0.295692	+	0.512154i
$187$	5.55226	+	9.61679i	0.406021	+	0.703249i
$188$	9.88696			0.721081
$189$	2.19620	+	1.47537i	0.159750	+	0.107317i
$190$	−61.4030			−4.45464
$191$	−3.50335	−	6.06798i	−0.253494	−	0.439064i	0.710992	−	0.703200i	$-0.248246\pi$
$191$	−3.50335	−	6.06798i	−0.253494	−	0.439064i	−0.964485	+	0.264137i	$0.914913\pi$
$192$	15.8492	−	27.4517i	1.14382	−	1.98116i
$193$	−6.26011	+	10.8428i	−0.450613	+	0.780484i	−0.998424	−	0.0561178i	$-0.982128\pi$
$193$	−6.26011	+	10.8428i	−0.450613	+	0.780484i	0.547812	+	0.836602i	$0.315461\pi$
$194$	21.4116	+	37.0860i	1.53726	+	2.66262i
$195$	5.98370			0.428502
$196$	−38.1975	−	5.22235i	−2.72839	−	0.373025i
$197$	−25.3287			−1.80459			−0.902296	−	0.431116i	$-0.858120\pi$
$197$	−25.3287			−1.80459			−0.902296	+	0.431116i	$0.858120\pi$
$198$	2.58027	+	4.46915i	0.183372	+	0.317609i
$199$	−0.324280	+	0.561669i	−0.0229876	+	0.0398156i	−0.877290	−	0.479960i	$-0.840651\pi$
$199$	−0.324280	+	0.561669i	−0.0229876	+	0.0398156i	0.854303	+	0.519776i	$0.173984\pi$
$200$	30.9303	−	53.5728i	2.18710	−	3.78817i
$201$	−4.08947	−	7.08317i	−0.288449	−	0.499608i
$202$	−20.7394			−1.45922
$203$	−18.1069	−	12.1640i	−1.27086	−	0.853743i
$204$	32.4723			2.27351
$205$	−9.98471	−	17.2940i	−0.697363	−	1.20787i
$206$	−3.59113	+	6.22001i	−0.250206	+	0.433369i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	−13.5517	−	23.4722i	−0.939638	−	1.62750i
$209$	−12.4806			−0.863303
$210$	1.66429	−	24.4593i	0.114847	−	1.68786i
$211$	14.4647			0.995790			0.497895	−	0.867237i	$-0.334106\pi$
$211$	14.4647			0.995790			0.497895	+	0.867237i	$0.334106\pi$
$212$	26.6703	+	46.1944i	1.83173	+	3.17264i
$213$	−0.147526	+	0.255522i	−0.0101083	+	0.0175081i
$214$	23.7450	−	41.1276i	1.62318	−	2.81142i
$215$	1.13126	+	1.95941i	0.0771516	+	0.133630i
$216$	9.61066			0.653922
$217$	6.99340	−	3.42715i	0.474743	−	0.232650i
$218$	36.6284			2.48079
$219$	−2.22875	−	3.86031i	−0.150605	−	0.260856i
$220$	17.5398	−	30.3798i	1.18253	−	2.04820i
$221$	5.21608	−	9.03451i	0.350871	−	0.607727i
$222$	6.07678	+	10.5253i	0.407847	+	0.706411i
$223$	−29.7327			−1.99105			−0.995525	−	0.0945015i	$-0.969874\pi$
$223$	−29.7327			−1.99105			−0.995525	+	0.0945015i	$0.969874\pi$
$224$	−54.0494	+	26.4872i	−3.61133	+	1.76975i
$225$	6.43667			0.429111
$226$	−1.62631	−	2.81685i	−0.108180	−	0.187374i
$227$	3.24510	−	5.62067i	0.215385	−	0.373057i	−0.738007	−	0.674793i	$-0.764233\pi$
$227$	3.24510	−	5.62067i	0.215385	−	0.373057i	0.953391	+	0.301736i	$0.0975662\pi$
$228$	−18.2482	+	31.6068i	−1.20851	+	2.09321i
$229$	0.618039	+	1.07048i	0.0408412	+	0.0707390i	0.885723	−	0.464213i	$-0.153663\pi$
$229$	0.618039	+	1.07048i	0.0408412	+	0.0707390i	−0.844882	+	0.534952i	$0.820330\pi$
$230$	9.26614			0.610991
$231$	0.338280	−	4.97154i	0.0222572	−	0.327104i
$232$	−79.2368			−5.20215
$233$	−12.1781	−	21.0931i	−0.797814	−	1.38185i	−0.921037	−	0.389475i	$-0.872656\pi$
$233$	−12.1781	−	21.0931i	−0.797814	−	1.38185i	0.123223	−	0.992379i	$-0.460677\pi$
$234$	2.42404	−	4.19855i	0.158464	−	0.274468i
$235$	3.03546	−	5.25757i	0.198011	−	0.342966i
$236$	−3.76503	−	6.52123i	−0.245083	−	0.424496i
$237$	3.02768			0.196669
$238$	−35.4793	−	23.8344i	−2.29978	−	1.54496i
$239$	15.2471			0.986251			0.493126	−	0.869958i	$-0.335854\pi$
$239$	15.2471			0.986251			0.493126	+	0.869958i	$0.335854\pi$
$240$	−25.9013	−	44.8624i	−1.67192	−	2.89586i
$241$	−2.06351	+	3.57411i	−0.132923	+	0.230229i	−0.924802	−	0.380449i	$-0.875769\pi$
$241$	−2.06351	+	3.57411i	−0.132923	+	0.230229i	0.791879	+	0.610678i	$0.209103\pi$
$242$	−10.2102	+	17.6847i	−0.656339	+	1.13681i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	51.5694			3.30139
$245$	−14.5043	+	18.7089i	−0.926647	+	1.19526i
$246$	−16.1795			−1.03157
$247$	5.86247	+	10.1541i	0.373020	+	0.646090i
$248$	14.1449	−	24.4997i	0.898202	−	1.55573i
$249$	−5.26501	+	9.11927i	−0.333657	+	0.577910i
$250$	−6.65617	−	11.5288i	−0.420973	−	0.729147i
$251$	4.82682			0.304666			0.152333	−	0.988329i	$-0.451321\pi$
$251$	4.82682			0.304666			0.152333	+	0.988329i	$0.451321\pi$
$252$	−12.0957	−	8.12568i	−0.761955	−	0.511870i
$253$	1.88341			0.118409
$254$	−16.7565	−	29.0232i	−1.05140	−	1.82108i
$255$	9.96951	−	17.2677i	0.624315	−	1.08135i
$256$	−24.9560	+	43.2251i	−1.55975	+	2.70157i
$257$	2.37570	+	4.11483i	0.148192	+	0.256676i	0.930559	−	0.366141i	$-0.119321\pi$
$257$	2.37570	+	4.11483i	0.148192	+	0.256676i	−0.782367	+	0.622817i	$0.785988\pi$
$258$	1.83313			0.114126
$259$	0.796683	−	11.7085i	0.0495035	−	0.727529i
$260$	−32.9555			−2.04381
$261$	−4.12234	−	7.14010i	−0.255167	−	0.441961i
$262$	−8.29765	+	14.3720i	−0.512631	+	0.887902i
$263$	8.07074	−	13.9789i	0.497663	−	0.861978i	−0.502333	−	0.864674i	$-0.667525\pi$
$263$	8.07074	−	13.9789i	0.497663	−	0.861978i	0.999996	+	0.00269631i	$0.000858265\pi$
$264$	−9.05041	−	15.6758i	−0.557014	−	0.964777i
$265$	32.7529			2.01199
$266$	43.1371	−	21.1396i	2.64491	−	1.29615i
$267$	10.7196			0.656030
$268$	22.5230	+	39.0109i	1.37581	+	2.38297i
$269$	−4.79781	+	8.31006i	−0.292528	+	0.506673i	−0.974407	−	0.224792i	$-0.927830\pi$
$269$	−4.79781	+	8.31006i	−0.292528	+	0.506673i	0.681879	+	0.731465i	$0.261163\pi$
$270$	4.63307	−	8.02471i	0.281960	−	0.488368i
$271$	−10.4810	−	18.1537i	−0.636677	−	1.10276i	−0.986157	−	0.165813i	$-0.946975\pi$
$271$	−10.4810	−	18.1537i	−0.636677	−	1.10276i	0.349480	−	0.936944i	$-0.386358\pi$
$272$	−90.3143			−5.47611
$273$	−4.20369	+	2.06004i	−0.254419	+	0.124679i
$274$	39.1616			2.36584
$275$	−6.06145	−	10.4987i	−0.365519	−	0.633097i
$276$	2.75378	−	4.76968i	0.165758	−	0.287101i
$277$	−7.29118	+	12.6287i	−0.438085	+	0.758785i	−0.997542	−	0.0700746i	$-0.977676\pi$
$277$	−7.29118	+	12.6287i	−0.438085	+	0.758785i	0.559457	+	0.828859i	$0.311010\pi$
$278$	−22.5076	−	38.9843i	−1.34992	−	2.33812i
$279$	2.94359			0.176228
$280$	−5.83760	+	85.7924i	−0.348863	+	5.12708i
$281$	−10.2706			−0.612694			−0.306347	−	0.951920i	$-0.599107\pi$
$281$	−10.2706			−0.612694			−0.306347	+	0.951920i	$0.599107\pi$
$282$	−2.45937	−	4.25975i	−0.146453	−	0.253664i
$283$	−8.54651	+	14.8030i	−0.508037	+	0.879946i	0.491920	+	0.870641i	$0.336295\pi$
$283$	−8.54651	+	14.8030i	−0.508037	+	0.879946i	−0.999957	+	0.00930538i	$0.997038\pi$
$284$	0.812507	−	1.40730i	0.0482134	−	0.0835081i
$285$	11.2050	+	19.4076i	0.663725	+	1.14961i
$286$	−9.13092			−0.539923
$287$	12.9684	+	8.71199i	0.765502	+	0.514252i
$288$	−22.7499			−1.34055
$289$	−8.88114	−	15.3826i	−0.522420	−	0.904858i
$290$	−38.1982	+	66.1612i	−2.24307	+	3.88512i
$291$	7.81449	−	13.5351i	0.458093	−	0.793441i
$292$	12.2750	+	21.2609i	0.718338	+	1.24420i
$293$	10.9029			0.636955			0.318478	−	0.947930i	$-0.396828\pi$
$293$	10.9029			0.636955			0.318478	+	0.947930i	$0.396828\pi$
$294$	7.25155	+	17.7563i	0.422919	+	1.03557i
$295$	−4.62370			−0.269202
$296$	−21.3146	−	36.9180i	−1.23889	−	2.14582i
$297$	0.941706	−	1.63108i	0.0546433	−	0.0946450i
$298$	18.9109	−	32.7546i	1.09548	−	1.89742i
$299$	−0.884688	−	1.53232i	−0.0511628	−	0.0886166i
$300$	−35.4503			−2.04672
$301$	−1.46932	−	0.987064i	−0.0846900	−	0.0568934i
$302$	11.6371			0.669642
$303$	3.78458	+	6.55508i	0.217418	+	0.376580i
$304$	50.7532	−	87.9071i	2.91089	−	5.04182i
$305$	15.8326	−	27.4229i	0.906574	−	1.57023i
$306$	−8.07743	−	13.9905i	−0.461756	−	0.799785i
$307$	26.7973			1.52940			0.764700	−	0.644386i	$-0.222887\pi$
$307$	26.7973			1.52940			0.764700	+	0.644386i	$0.222887\pi$
$308$	−1.86310	+	27.3810i	−0.106160	+	1.56018i
$309$	2.62127			0.149119
$310$	−13.6378	−	23.6214i	−0.774578	−	1.34161i
$311$	−8.93077	+	15.4685i	−0.506417	+	0.877141i	0.493555	+	0.869715i	$0.335697\pi$
$311$	−8.93077	+	15.4685i	−0.506417	+	0.877141i	−0.999972	+	0.00742604i	$0.997636\pi$
$312$	−8.50243	+	14.7266i	−0.481355	+	0.833732i
$313$	14.5650	+	25.2272i	0.823260	+	1.42593i	0.903242	+	0.429132i	$0.141180\pi$
$313$	14.5650	+	25.2272i	0.823260	+	1.42593i	−0.0799820	+	0.996796i	$0.525486\pi$
$314$	1.82975			0.103258
$315$	−8.03454	+	3.93737i	−0.452695	+	0.221846i
$316$	−16.6751			−0.938049
$317$	−10.9687	−	18.9983i	−0.616062	−	1.06705i	−0.990197	−	0.139676i	$-0.955394\pi$
$317$	−10.9687	−	18.9983i	−0.616062	−	1.06705i	0.374135	−	0.927374i	$-0.377940\pi$
$318$	13.2684	−	22.9816i	0.744056	−	1.28874i
$319$	−7.76407	+	13.4478i	−0.434704	+	0.752930i
$320$	53.5992	+	92.8365i	2.99629	+	5.18972i
$321$	−17.3322			−0.967388
$322$	−6.50969	+	3.19011i	−0.362771	+	0.177778i
$323$	39.0701			2.17392
$324$	−2.75378	−	4.76968i	−0.152988	−	0.264982i
$325$	−5.69444	+	9.86306i	−0.315871	+	0.547104i
$326$	−0.996234	+	1.72553i	−0.0551763	+	0.0955681i
$327$	−6.68403	−	11.5771i	−0.369628	−	0.640214i
$328$	56.7504			3.13352
$329$	−0.322430	+	4.73860i	−0.0177762	+	0.261248i
$330$	−17.4520			−0.960699
$331$	2.81522	+	4.87611i	0.154739	+	0.268015i	0.932964	−	0.359970i	$-0.117213\pi$
$331$	2.81522	+	4.87611i	0.154739	+	0.268015i	−0.778225	+	0.627985i	$0.783880\pi$
$332$	28.9973	−	50.2249i	1.59144	−	2.75645i
$333$	2.21781	−	3.84136i	0.121535	−	0.210505i
$334$	12.9126	+	22.3652i	0.706544	+	1.22377i
$335$	27.6596			1.51121
$336$	33.6414	+	22.5997i	1.83529	+	1.23292i
$337$	21.7330			1.18387			0.591936	−	0.805985i	$-0.298364\pi$
$337$	21.7330			1.18387			0.591936	+	0.805985i	$0.298364\pi$
$338$	−13.5209	−	23.4189i	−0.735441	−	1.27382i
$339$	−0.593544	+	1.02805i	−0.0322369	+	0.0558360i
$340$	−54.9076	+	95.1027i	−2.97778	+	5.15767i
$341$	−2.77199	−	4.80124i	−0.150112	−	0.260001i
$342$	18.1568			0.981809
$343$	3.74864	−	18.1369i	0.202408	−	0.979301i
$344$	−6.42980			−0.346671
$345$	−1.69091	−	2.92874i	−0.0910354	−	0.157678i
$346$	14.8663	−	25.7492i	0.799218	−	1.38429i
$347$	−16.2403	+	28.1289i	−0.871822	+	1.51004i	−0.0117127	+	0.999931i	$0.503728\pi$
$347$	−16.2403	+	28.1289i	−0.871822	+	1.51004i	−0.860110	+	0.510109i	$0.829605\pi$
$348$	22.7040	+	39.3245i	1.21706	+	2.10801i
$349$	0.230635			0.0123456			0.00617281	−	0.999981i	$-0.498035\pi$
$349$	0.230635			0.0123456			0.00617281	+	0.999981i	$0.498035\pi$
$350$	38.7330	+	26.0202i	2.07037	+	1.39084i
$351$	−1.76938			−0.0944423
$352$	21.4237	+	37.1070i	1.14189	+	1.97781i
$353$	−13.9482	+	24.1590i	−0.742388	+	1.28585i	0.209017	+	0.977912i	$0.432974\pi$
$353$	−13.9482	+	24.1590i	−0.742388	+	1.28585i	−0.951405	+	0.307942i	$0.900360\pi$
$354$	−1.87309	+	3.24429i	−0.0995537	+	0.172432i
$355$	−0.498905	−	0.864129i	−0.0264791	−	0.0458632i
$356$	−59.0388			−3.12905
$357$	−1.05897	+	15.5632i	−0.0560469	+	0.823694i
$358$	27.2454			1.43996
$359$	−8.18126	−	14.1704i	−0.431790	−	0.747883i	0.565237	−	0.824928i	$-0.308785\pi$
$359$	−8.18126	−	14.1704i	−0.431790	−	0.747883i	−0.997028	+	0.0770455i	$0.975451\pi$
$360$	−16.2507	+	28.1471i	−0.856488	+	1.48348i
$361$	−12.4559	+	21.5743i	−0.655575	+	1.13549i
$362$	−1.33659	−	2.31504i	−0.0702494	−	0.121676i
$363$	7.45276			0.391168
$364$	23.1521	−	11.3458i	1.21350	−	0.594681i
$365$	15.0745			0.789033
$366$	−12.8278	−	22.2184i	−0.670520	−	1.16138i
$367$	−7.73982	+	13.4058i	−0.404016	+	0.699775i	−0.994206	−	0.107488i	$-0.965719\pi$
$367$	−7.73982	+	13.4058i	−0.404016	+	0.699775i	0.590191	+	0.807264i	$0.299053\pi$
$368$	−7.65901	+	13.2658i	−0.399253	+	0.691527i
$369$	2.95247	+	5.11383i	0.153700	+	0.266216i
$370$	−41.1011			−2.13674
$371$	−23.0097	+	11.2760i	−1.19460	+	0.585422i
$372$	−16.2120			−0.840551
$373$	14.7036	+	25.4674i	0.761325	+	1.31865i	0.942168	+	0.335141i	$0.108784\pi$
$373$	14.7036	+	25.4674i	0.761325	+	1.31865i	−0.180843	+	0.983512i	$0.557883\pi$
$374$	−15.2131	+	26.3499i	−0.786652	+	1.36252i
$375$	−2.42927	+	4.20761i	−0.125447	+	0.217280i
$376$	8.62636	+	14.9413i	0.444870	+	0.770538i
$377$	14.5879			0.751317
$378$	−0.492131	+	7.23261i	−0.0253125	+	0.372005i
$379$	23.7449			1.21969			0.609846	−	0.792520i	$-0.291231\pi$
$379$	23.7449			1.21969			0.609846	+	0.792520i	$0.291231\pi$
$380$	−61.7119	−	106.888i	−3.16575	−	5.48325i
$381$	−6.11554	+	10.5924i	−0.313309	+	0.542667i
$382$	9.59915	−	16.6262i	0.491135	−	0.850671i
$383$	−2.39500	−	4.14826i	−0.122379	−	0.211966i	0.798327	−	0.602225i	$-0.205719\pi$
$383$	−2.39500	−	4.14826i	−0.122379	−	0.211966i	−0.920705	+	0.390259i	$0.872386\pi$
$384$	41.3538			2.11033
$385$	13.9883	+	9.39715i	0.712912	+	0.478923i
$386$	−34.3053			−1.74609
$387$	−0.334514	−	0.579395i	−0.0170043	−	0.0294523i
$388$	−43.0387	+	74.5452i	−2.18496	+	3.78446i
$389$	−11.2776	+	19.5334i	−0.571798	+	0.990384i	0.424583	+	0.905389i	$0.360421\pi$
$389$	−11.2776	+	19.5334i	−0.571798	+	0.990384i	−0.996381	+	0.0849949i	$0.972913\pi$
$390$	8.19764	+	14.1987i	0.415104	+	0.718981i
$391$	−5.89595			−0.298171
$392$	−25.4352	−	62.2810i	−1.28467	−	3.14567i
$393$	6.05670			0.305520
$394$	−34.7002	−	60.1024i	−1.74817	−	3.02792i
$395$	−5.11953	+	8.86729i	−0.257592	+	0.446162i
$396$	−5.18649	+	8.98327i	−0.260631	+	0.451426i
$397$	−1.79437	−	3.10794i	−0.0900570	−	0.155983i	0.817478	−	0.575960i	$-0.195372\pi$
$397$	−1.79437	−	3.10794i	−0.0900570	−	0.155983i	−0.907535	+	0.419977i	$0.862038\pi$
$398$	−1.77705			−0.0890753
$399$	−14.5533	−	9.77670i	−0.728577	−	0.489447i
$400$	98.5969			4.92985
$401$	−5.31679	−	9.20895i	−0.265508	−	0.459873i	0.702189	−	0.711991i	$-0.252206\pi$
$401$	−5.31679	−	9.20895i	−0.265508	−	0.459873i	−0.967697	+	0.252118i	$0.918873\pi$
$402$	11.2051	−	19.4078i	0.558860	−	0.967974i
$403$	−2.60416	+	4.51053i	−0.129722	+	0.224685i
$404$	−20.8438	−	36.1024i	−1.03702	−	1.79616i
$405$	−3.38181			−0.168044
$406$	4.05746	−	59.6306i	0.201368	−	2.95942i
$407$	−8.35410			−0.414098
$408$	28.3320	+	49.0725i	1.40264	+	2.42945i
$409$	−7.26614	+	12.5853i	−0.359288	+	0.622304i	−0.987842	−	0.155461i	$-0.950314\pi$
$409$	−7.26614	+	12.5853i	−0.359288	+	0.622304i	0.628554	+	0.777766i	$0.283647\pi$
$410$	27.3580	−	47.3855i	1.35112	−	2.34020i
$411$	−7.14630	−	12.3778i	−0.352501	−	0.610550i
$412$	−14.4368			−0.711248
$413$	3.24826	−	1.59183i	0.159837	−	0.0783288i
$414$	−2.73999			−0.134663
$415$	−17.8053	−	30.8397i	−0.874028	−	1.51386i
$416$	20.1266	−	34.8602i	0.986786	−	1.70916i
$417$	−8.21448	+	14.2279i	−0.402265	+	0.696743i
$418$	−17.0984	−	29.6153i	−0.836310	−	1.44853i
$419$	−28.8287			−1.40837			−0.704187	−	0.710015i	$-0.748688\pi$
$419$	−28.8287			−1.40837			−0.704187	+	0.710015i	$0.748688\pi$
$420$	44.2506	−	21.6852i	2.15921	−	1.05813i
$421$	25.2897			1.23254			0.616271	−	0.787534i	$-0.288643\pi$
$421$	25.2897			1.23254			0.616271	+	0.787534i	$0.288643\pi$
$422$	19.8166	+	34.3233i	0.964655	+	1.67083i
$423$	−0.897583	+	1.55466i	−0.0436420	+	0.0755901i
$424$	−46.5396	+	80.6090i	−2.26016	+	3.91472i
$425$	18.9751	+	32.8659i	0.920430	+	1.59423i
$426$	−0.808440			−0.0391690
$427$	−1.68176	+	24.7161i	−0.0813862	+	1.19609i
$428$	95.4579			4.61413
$429$	1.66623	+	2.88600i	0.0804464	+	0.139337i
$430$	−3.09965	+	5.36876i	−0.149479	+	0.258904i
$431$	0.666648	−	1.15467i	0.0321113	−	0.0556184i	−0.849523	−	0.527551i	$-0.823110\pi$
$431$	0.666648	−	1.15467i	0.0321113	−	0.0556184i	0.881634	+	0.471933i	$0.156444\pi$
$432$	7.65901	+	13.2658i	0.368494	+	0.638250i
$433$	−12.4620			−0.598887			−0.299444	−	0.954114i	$-0.596801\pi$
$433$	−12.4620			−0.598887			−0.299444	+	0.954114i	$0.596801\pi$
$434$	17.7132	+	11.8995i	0.850261	+	0.571192i
$435$	27.8820			1.33684
$436$	36.8126	+	63.7613i	1.76301	+	3.05361i
$437$	3.31330	−	5.73881i	0.158497	−	0.274524i
$438$	6.10676	−	10.5772i	0.291792	−	0.505399i
$439$	−6.88278	−	11.9213i	−0.328497	−	0.568974i	0.653717	−	0.756739i	$-0.273209\pi$
$439$	−6.88278	−	11.9213i	−0.328497	−	0.568974i	−0.982214	+	0.187766i	$0.939875\pi$
$440$	61.2136			2.91825
$441$	4.28892	−	5.53219i	0.204234	−	0.263438i
$442$	28.5840			1.35960
$443$	3.53406	+	6.12117i	0.167908	+	0.290826i	0.937684	−	0.347489i	$-0.112965\pi$
$443$	3.53406	+	6.12117i	0.167908	+	0.290826i	−0.769776	+	0.638314i	$0.779632\pi$
$444$	−12.2147	+	21.1565i	−0.579684	+	1.00404i
$445$	−18.1259	+	31.3949i	−0.859248	+	1.48826i
$446$	−40.7337	−	70.5528i	−1.92880	−	3.34077i
$447$	−13.8036			−0.652888
$448$	−69.6161	−	46.7670i	−3.28905	−	2.20953i
$449$	−22.4140			−1.05778			−0.528892	−	0.848689i	$-0.677392\pi$
$449$	−22.4140			−1.05778			−0.528892	+	0.848689i	$0.677392\pi$
$450$	8.81820	+	15.2736i	0.415694	+	0.720003i
$451$	5.56072	−	9.63146i	0.261844	−	0.453528i
$452$	3.26898	−	5.66203i	0.153760	−	0.266320i
$453$	−2.12357	−	3.67813i	−0.0997741	−	0.172814i
$454$	17.7831			0.834601
$455$	1.07473	−	15.7949i	0.0503843	−	0.740474i
$456$	−63.6860			−2.98237
$457$	1.34517	+	2.32990i	0.0629244	+	0.108988i	0.895771	−	0.444515i	$-0.146624\pi$
$457$	1.34517	+	2.32990i	0.0629244	+	0.108988i	−0.832847	+	0.553503i	$0.813291\pi$
$458$	−1.69342	+	2.93309i	−0.0791284	+	0.137054i
$459$	−2.94798	+	5.10605i	−0.137600	+	0.238330i
$460$	9.31276	+	16.1302i	0.434209	+	0.752073i
$461$	30.1064			1.40220			0.701098	−	0.713065i	$-0.252693\pi$
$461$	30.1064			1.40220			0.701098	+	0.713065i	$0.252693\pi$
$462$	12.2604	−	6.00829i	0.570407	−	0.279531i
$463$	−14.0463			−0.652787			−0.326394	−	0.945234i	$-0.605834\pi$
$463$	−14.0463			−0.652787			−0.326394	+	0.945234i	$0.605834\pi$
$464$	−63.1461	−	109.372i	−2.93148	−	5.07748i
$465$	−4.97733	+	8.62099i	−0.230818	+	0.399789i
$466$	33.3679	−	57.7949i	1.54574	−	2.67730i
$467$	5.30205	+	9.18342i	0.245350	+	0.424958i	0.962230	−	0.272238i	$-0.0877639\pi$
$467$	5.30205	+	9.18342i	0.245350	+	0.424958i	−0.716880	+	0.697196i	$0.754431\pi$
$468$	9.74492			0.450459
$469$	−19.4316	+	9.52255i	−0.897267	+	0.439710i
$470$	16.6343			0.767281
$471$	−0.333896	−	0.578325i	−0.0153851	−	0.0266478i
$472$	6.56997	−	11.3795i	0.302407	−	0.523785i
$473$	−0.630028	+	1.09124i	−0.0289687	+	0.0501753i
$474$	4.14791	+	7.18440i	0.190520	+	0.329990i
$475$	−42.6532			−1.95706
$476$	5.83235	−	85.7153i	0.267326	−	3.92876i
$477$	−9.68500			−0.443446
$478$	20.8884	+	36.1798i	0.955414	+	1.65483i
$479$	5.63196	−	9.75483i	0.257331	−	0.445710i	−0.708195	−	0.706017i	$-0.750490\pi$
$479$	5.63196	−	9.75483i	0.257331	−	0.445710i	0.965526	+	0.260307i	$0.0838237\pi$
$480$	38.4680	−	66.6285i	1.75581	−	3.04116i
$481$	3.92414	+	6.79681i	0.178925	+	0.309908i
$482$	−11.3080			−0.515066
$483$	2.19620	+	1.47537i	0.0999304	+	0.0671317i
$484$	−41.0464			−1.86575
$485$	26.4271	+	45.7731i	1.19999	+	2.07845i
$486$	−1.37000	+	2.37290i	−0.0621443	+	0.107637i
$487$	−0.951673	+	1.64835i	−0.0431244	+	0.0746937i	−0.886782	−	0.462188i	$-0.847065\pi$
$487$	−0.951673	+	1.64835i	−0.0431244	+	0.0746937i	0.843658	+	0.536882i	$0.180398\pi$
$488$	44.9942	+	77.9322i	2.03679	+	3.52783i
$489$	0.727180			0.0328842
$490$	−64.2651	−	8.78630i	−2.90320	−	0.396925i
$491$	20.8742			0.942040			0.471020	−	0.882123i	$-0.343886\pi$
$491$	20.8742			0.942040			0.471020	+	0.882123i	$0.343886\pi$
$492$	−16.2609	−	28.1647i	−0.733098	−	1.26976i
$493$	24.3051	−	42.0977i	1.09465	−	1.89599i
$494$	−16.0631	+	27.8221i	−0.722714	+	1.25178i
$495$	3.18467	+	5.51602i	0.143140	+	0.247927i
$496$	45.0899			2.02460
$497$	0.647992	+	0.435311i	0.0290664	+	0.0195264i
$498$	−28.8522			−1.29290
$499$	18.5467	+	32.1239i	0.830266	+	1.43806i	0.897828	+	0.440347i	$0.145145\pi$
$499$	18.5467	+	32.1239i	0.830266	+	1.43806i	−0.0675618	+	0.997715i	$0.521522\pi$
$500$	13.3793	−	23.1736i	0.598341	−	1.03636i
$501$	4.71263	−	8.16252i	0.210545	−	0.364674i
$502$	6.61272	+	11.4536i	0.295140	+	0.511198i
$503$	0.702967			0.0313437			0.0156719	−	0.999877i	$-0.495011\pi$
$503$	0.702967			0.0313437			0.0156719	+	0.999877i	$0.495011\pi$
$504$	1.72617	−	25.3687i	0.0768899	−	1.13001i
$505$	−25.5975			−1.13907
$506$	2.58027	+	4.46915i	0.114707	+	0.198678i
$507$	−4.93466	+	8.54707i	−0.219156	+	0.379589i
$508$	33.6817	−	58.3384i	1.49438	−	2.58835i
$509$	−9.46193	−	16.3885i	−0.419393	−	0.726409i	0.576486	−	0.817107i	$-0.304424\pi$
$509$	−9.46193	−	16.3885i	−0.419393	−	0.726409i	−0.995878	+	0.0906978i	$0.971090\pi$
$510$	54.6327			2.41918
$511$	−10.5902	+	5.18977i	−0.468482	+	0.229582i
$512$	−54.0509			−2.38874
$513$	−3.31330	−	5.73881i	−0.146286	−	0.253374i
$514$	−6.50939	+	11.2746i	−0.287117	+	0.497301i
$515$	−4.43232	+	7.67700i	−0.195311	+	0.338289i
$516$	1.84235	+	3.19105i	0.0811050	+	0.140478i
$517$	3.38104			0.148698
$518$	28.8745	−	14.1501i	1.26867	−	0.621720i
$519$	−10.8514			−0.476322
$520$	−28.7536	−	49.8028i	−1.26093	−	2.18400i
$521$	−9.57227	+	16.5797i	−0.419369	+	0.726368i	−0.995876	−	0.0907240i	$-0.971082\pi$
$521$	−9.57227	+	16.5797i	−0.419369	+	0.726368i	0.576507	+	0.817092i	$0.304415\pi$
$522$	11.2952	−	19.5638i	0.494376	−	0.856285i
$523$	−6.95888	−	12.0531i	−0.304291	−	0.527047i	0.672813	−	0.739813i	$-0.265086\pi$
$523$	−6.95888	−	12.0531i	−0.304291	−	0.527047i	−0.977103	+	0.212766i	$0.931753\pi$
$524$	−33.3576			−1.45723
$525$	1.15609	−	16.9905i	0.0504560	−	0.741527i
$526$	44.2275			1.92841
$527$	8.67763	+	15.0301i	0.378003	+	0.654721i
$528$	14.4251	−	24.9849i	0.627770	−	1.08733i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	44.8713	+	77.7194i	1.94908	+	3.37591i
$531$	1.36723			0.0593325
$532$	80.1532	+	53.8456i	3.47508	+	2.33450i
$533$	−10.4481			−0.452556
$534$	14.6858	+	25.4366i	0.635518	+	1.10075i
$535$	29.3071	−	50.7614i	1.26706	−	2.19461i
$536$	−39.3025	+	68.0739i	−1.69761	+	2.94034i
$537$	−4.97180	−	8.61141i	−0.214549	−	0.371610i
$538$	−26.2919			−1.13353
$539$	−13.0624	−	1.78588i	−0.562636	−	0.0769234i
$540$	18.6255			0.801514
$541$	−14.3756	−	24.8992i	−0.618053	−	1.07050i	−0.989841	−	0.142182i	$-0.954588\pi$
$541$	−14.3756	−	24.8992i	−0.618053	−	1.07050i	0.371787	−	0.928318i	$-0.378745\pi$
$542$	28.7179	−	49.7409i	1.23354	−	2.13656i
$543$	−0.487807	+	0.844906i	−0.0209338	+	0.0362584i
$544$	−67.0662	−	116.162i	−2.87544	−	4.98041i
$545$	45.2083			1.93651
$546$	−10.6473	−	7.15271i	−0.455663	−	0.306108i
$547$	25.9067			1.10769			0.553845	−	0.832620i	$-0.313160\pi$
$547$	25.9067			1.10769			0.553845	+	0.832620i	$0.313160\pi$
$548$	39.3586	+	68.1711i	1.68132	+	2.91213i
$549$	−4.68170	+	8.10894i	−0.199810	+	0.346081i
$550$	16.6083	−	28.7664i	0.708181	−	1.22660i
$551$	27.3171	+	47.3146i	1.16375	+	2.01567i
$552$	9.61066			0.409057
$553$	0.543803	−	7.99202i	0.0231249	−	0.339855i
$554$	−39.9555			−1.69755
$555$	7.50022	+	12.9908i	0.318367	+	0.551427i
$556$	45.2416	−	78.3608i	1.91867	−	3.32324i
$557$	2.31799	−	4.01488i	0.0982164	−	0.170116i	−0.812730	−	0.582640i	$-0.802020\pi$
$557$	2.31799	−	4.01488i	0.0982164	−	0.170116i	0.910946	+	0.412525i	$0.135353\pi$
$558$	4.03270	+	6.98484i	0.170718	+	0.295692i
$559$	1.18376			0.0500678
$560$	−123.073	+	60.3126i	−5.20079	+	2.54867i
$561$	11.1045			0.468833
$562$	−14.0707	−	24.3712i	−0.593537	−	1.02804i
$563$	−2.61558	+	4.53031i	−0.110233	+	0.190930i	−0.915864	−	0.401488i	$-0.868493\pi$
$563$	−2.61558	+	4.53031i	−0.110233	+	0.190930i	0.805631	+	0.592418i	$0.201827\pi$
$564$	4.94348	−	8.56236i	0.208158	−	0.360540i
$565$	−2.00726	−	3.47667i	−0.0844459	−	0.146265i
$566$	−46.8347			−1.96861
$567$	2.37581	−	1.16428i	0.0997745	−	0.0488950i
$568$	2.83564			0.118981
$569$	−3.85568	−	6.67823i	−0.161638	−	0.279966i	0.773818	−	0.633408i	$-0.218344\pi$
$569$	−3.85568	−	6.67823i	−0.161638	−	0.279966i	−0.935456	+	0.353442i	$0.885011\pi$
$570$	−30.7015	+	53.1766i	−1.28594	+	2.22732i
$571$	−8.77576	+	15.2001i	−0.367254	+	0.636103i	−0.989135	−	0.147009i	$-0.953035\pi$
$571$	−8.77576	+	15.2001i	−0.367254	+	0.636103i	0.621881	+	0.783112i	$0.286369\pi$
$572$	−9.17685	−	15.8948i	−0.383704	−	0.664594i
$573$	−7.00670			−0.292709
$574$	−2.90601	+	42.7082i	−0.121294	+	1.78260i
$575$	6.43667			0.268427
$576$	−15.8492	−	27.4517i	−0.660385	−	1.14382i
$577$	−7.82632	+	13.5556i	−0.325814	+	0.564327i	−0.981677	−	0.190554i	$-0.938972\pi$
$577$	−7.82632	+	13.5556i	−0.325814	+	0.564327i	0.655863	+	0.754880i	$0.272305\pi$
$578$	24.3342	−	42.1481i	1.01217	−	1.75313i
$579$	6.26011	+	10.8428i	0.260161	+	0.450613i
$580$	−153.561			−6.37629
$581$	23.1260	+	15.5357i	0.959429	+	0.644529i
$582$	42.8232			1.77508
$583$	9.12043	+	15.7970i	0.377729	+	0.654247i
$584$	−21.4198	+	37.1001i	−0.886357	+	1.53521i
$585$	2.99185	−	5.18203i	0.123698	−	0.214251i
$586$	14.9369	+	25.8715i	0.617039	+	1.06874i
$587$	29.3900			1.21305			0.606527	−	0.795063i	$-0.292562\pi$
$587$	29.3900			1.21305			0.606527	+	0.795063i	$0.292562\pi$
$588$	−23.6214	+	30.4688i	−0.974132	+	1.25651i
$589$	−19.5060			−0.803730
$590$	−6.33445	−	10.9716i	−0.260785	−	0.451693i
$591$	−12.6643	+	21.9353i	−0.520941	+	0.902296i
$592$	33.9724	−	58.8420i	1.39626	−	2.41839i
$593$	9.00362	+	15.5947i	0.369734	+	0.640399i	0.989524	−	0.144369i	$-0.0461154\pi$
$593$	9.00362	+	15.5947i	0.369734	+	0.640399i	−0.619789	+	0.784768i	$0.712782\pi$
$594$	5.16053			0.211739
$595$	−43.7900	−	29.4175i	−1.79522	−	1.20600i
$596$	76.0241			3.11407
$597$	0.324280	+	0.561669i	0.0132719	+	0.0229876i
$598$	2.42404	−	4.19855i	0.0991262	−	0.171692i
$599$	6.16954	−	10.6860i	0.252081	−	0.436617i	−0.712018	−	0.702161i	$-0.752218\pi$
$599$	6.16954	−	10.6860i	0.252081	−	0.436617i	0.964099	+	0.265545i	$0.0855518\pi$
$600$	−30.9303	−	53.5728i	−1.26272	−	2.18710i
$601$	0.594459			0.0242485			0.0121243	−	0.999926i	$-0.496141\pi$
$601$	0.594459			0.0242485			0.0121243	+	0.999926i	$0.496141\pi$
$602$	0.329249	−	4.83882i	0.0134192	−	0.197216i
$603$	−8.17894			−0.333072
$604$	11.6957	+	20.2575i	0.475890	+	0.824266i
$605$	−12.6019	+	21.8272i	−0.512341	+	0.887401i
$606$	−10.3697	+	17.9609i	−0.421241	+	0.729610i
$607$	0.0338873	+	0.0586945i	0.00137544	+	0.00238233i	0.866712	−	0.498808i	$-0.166229\pi$
$607$	0.0338873	+	0.0586945i	0.00137544	+	0.00238233i	−0.865337	+	0.501191i	$0.832896\pi$
$608$	150.755			6.11390
$609$	−19.5878	+	9.59909i	−0.793737	+	0.388975i
$610$	86.7625			3.51291
$611$	−1.58816	−	2.75077i	−0.0642501	−	0.111284i
$612$	16.2361	−	28.1218i	0.656307	−	1.13676i
$613$	−10.7516	+	18.6224i	−0.434254	+	0.752150i	−0.997234	−	0.0743201i	$-0.976321\pi$
$613$	−10.7516	+	18.6224i	−0.434254	+	0.752150i	0.562980	+	0.826470i	$0.309655\pi$
$614$	36.7121	+	63.5873i	1.48158	+	2.56617i
$615$	−19.9694			−0.805245
$616$	−43.0041	+	21.0744i	−1.73268	+	0.849111i
$617$	10.0024			0.402683			0.201341	−	0.979521i	$-0.435470\pi$
$617$	10.0024			0.402683			0.201341	+	0.979521i	$0.435470\pi$
$618$	3.59113	+	6.22001i	0.144456	+	0.250206i
$619$	6.57468	−	11.3877i	0.264259	−	0.457710i	−0.703110	−	0.711081i	$-0.748206\pi$
$619$	6.57468	−	11.3877i	0.264259	−	0.457710i	0.967369	+	0.253371i	$0.0815394\pi$
$620$	27.4129	−	47.4806i	1.10093	−	1.90686i
$621$	0.500000	+	0.866025i	0.0200643	+	0.0347524i
$622$	−48.9404			−1.96233
$623$	1.92535	−	28.2960i	0.0771376	−	1.13366i
$624$	−27.1033			−1.08500
$625$	7.87633	+	13.6422i	0.315053	+	0.545688i
$626$	−39.9078	+	69.1224i	−1.59504	+	2.76269i
$627$	−6.24031	+	10.8085i	−0.249214	+	0.431651i
$628$	1.83895	+	3.18516i	0.0733821	+	0.127102i
$629$	26.1522			1.04276
$630$	−20.3503	−	13.6710i	−0.810774	−	0.544665i
$631$	27.0831			1.07816			0.539081	−	0.842254i	$-0.318772\pi$
$631$	27.0831			1.07816			0.539081	+	0.842254i	$0.318772\pi$
$632$	−14.5490	−	25.1996i	−0.578729	−	1.00239i
$633$	7.23235	−	12.5268i	0.287460	−	0.497895i
$634$	30.0541	−	52.0552i	1.19360	−	2.06737i
$635$	−20.6816	−	35.8216i	−0.820725	−	1.42154i
$636$	53.3406			2.11509
$637$	4.68276	+	11.4663i	0.185538	+	0.454310i
$638$	−42.5469			−1.68445
$639$	0.147526	+	0.255522i	0.00583604	+	0.0101083i
$640$	−69.9254	+	121.114i	−2.76404	+	4.78747i
$641$	18.8298	−	32.6142i	0.743733	−	1.28818i	−0.207051	−	0.978330i	$-0.566387\pi$
$641$	18.8298	−	32.6142i	0.743733	−	1.28818i	0.950784	−	0.309854i	$-0.100280\pi$
$642$	−23.7450	−	41.1276i	−0.937141	−	1.62318i
$643$	0.584100			0.0230347			0.0115173	−	0.999934i	$-0.496334\pi$
$643$	0.584100			0.0230347			0.0115173	+	0.999934i	$0.496334\pi$
$644$	−12.0957	−	8.12568i	−0.476636	−	0.320197i
$645$	2.26253			0.0890869
$646$	53.5259	+	92.7096i	2.10595	+	3.64761i
$647$	−2.90401	+	5.02990i	−0.114169	+	0.197746i	−0.917447	−	0.397858i	$-0.869754\pi$
$647$	−2.90401	+	5.02990i	−0.114169	+	0.197746i	0.803279	+	0.595604i	$0.203087\pi$
$648$	4.80533	−	8.32307i	0.188771	−	0.326961i
$649$	−1.28752	−	2.23006i	−0.0505398	−	0.0875374i
$650$	−31.2054			−1.22398
$651$	0.528699	−	7.77003i	0.0207213	−	0.304532i
$652$	−4.00498			−0.156847
$653$	−12.3522	−	21.3946i	−0.483378	−	0.837235i	0.516440	−	0.856323i	$-0.327257\pi$
$653$	−12.3522	−	21.3946i	−0.483378	−	0.837235i	−0.999818	+	0.0190884i	$0.993924\pi$
$654$	18.3142	−	31.7211i	0.716141	−	1.24039i
$655$	−10.2413	+	17.7385i	−0.400161	+	0.693100i
$656$	45.2260	+	78.3338i	1.76578	+	3.05842i
$657$	−4.45751			−0.173904
$658$	−11.6860	+	5.72677i	−0.455567	+	0.223253i
$659$	24.0716			0.937697			0.468848	−	0.883279i	$-0.344669\pi$
$659$	24.0716			0.937697			0.468848	+	0.883279i	$0.344669\pi$
$660$	−17.5398	−	30.3798i	−0.682734	−	1.18253i
$661$	−5.08195	+	8.80219i	−0.197665	+	0.342366i	−0.947771	−	0.318952i	$-0.896669\pi$
$661$	−5.08195	+	8.80219i	−0.197665	+	0.342366i	0.750106	+	0.661318i	$0.230002\pi$
$662$	−7.71369	+	13.3605i	−0.299801	+	0.519271i
$663$	−5.21608	−	9.03451i	−0.202576	−	0.350871i
$664$	101.200			3.92734
$665$	53.2417	−	26.0914i	2.06462	−	1.01178i
$666$	12.1536			0.470941
$667$	−4.12234	−	7.14010i	−0.159618	−	0.276466i
$668$	−25.9550	+	44.9555i	−1.00423	+	1.73938i
$669$	−14.8664	+	25.7493i	−0.574766	+	0.995525i
$670$	37.8936	+	65.6336i	1.46396	+	2.53565i
$671$	17.6351			0.680797
$672$	−4.08612	+	60.0517i	−0.157625	+	2.31655i
$673$	21.4374			0.826350			0.413175	−	0.910652i	$-0.364420\pi$
$673$	21.4374			0.826350			0.413175	+	0.910652i	$0.364420\pi$
$674$	29.7741	+	51.5703i	1.14686	+	1.98641i
$675$	3.21833	−	5.57432i	0.123874	−	0.214556i
$676$	27.1779	−	47.0734i	1.04530	−	1.81052i
$677$	−14.5934	−	25.2765i	−0.560869	−	0.971454i	−0.997421	−	0.0717746i	$-0.977134\pi$
$677$	−14.5934	−	25.2765i	−0.560869	−	0.971454i	0.436552	−	0.899679i	$-0.356200\pi$
$678$	−3.25261			−0.124916
$679$	−34.3243	−	23.0585i	−1.31725	−	0.884905i
$680$	−191.627			−7.34856
$681$	−3.24510	−	5.62067i	−0.124352	−	0.215385i
$682$	7.59524	−	13.1553i	0.290837	−	0.503744i
$683$	24.8388	−	43.0221i	0.950432	−	1.64620i	0.205940	−	0.978565i	$-0.433975\pi$
$683$	24.8388	−	43.0221i	0.950432	−	1.64620i	0.744492	−	0.667631i	$-0.232692\pi$
$684$	18.2482	+	31.6068i	0.697736	+	1.20851i
$685$	48.3349			1.84678
$686$	48.1727	−	15.9523i	1.83924	−	0.609063i
$687$	1.23608			0.0471593
$688$	−5.12409	−	8.87518i	−0.195354	−	0.338363i
$689$	8.56820	−	14.8406i	0.326423	−	0.565380i
$690$	4.63307	−	8.02471i	0.176378	−	0.305496i
$691$	−3.61070	−	6.25391i	−0.137357	−	0.237910i	0.789138	−	0.614216i	$-0.210528\pi$
$691$	−3.61070	−	6.25391i	−0.137357	−	0.237910i	−0.926496	+	0.376306i	$0.877194\pi$
$692$	59.7644			2.27190
$693$	−4.13634	−	2.77873i	−0.157127	−	0.105555i
$694$	−88.9963			−3.37825
$695$	−27.7798	−	48.1161i	−1.05375	−	1.82515i
$696$	−39.6184	+	68.6211i	−1.50173	+	2.60108i
$697$	−17.4076	+	30.1509i	−0.659362	+	1.14205i
$698$	0.315969	+	0.547274i	0.0119596	+	0.0207146i
$699$	−24.3562			−0.921236
$700$	−6.36723	+	93.5762i	−0.240659	+	3.53685i
$701$	−43.4759			−1.64206			−0.821031	−	0.570884i	$-0.806601\pi$
$701$	−43.4759			−1.64206			−0.821031	+	0.570884i	$0.806601\pi$
$702$	−2.42404	−	4.19855i	−0.0914894	−	0.158464i
$703$	−14.6965	+	25.4552i	−0.554291	+	0.960060i
$704$	−29.8507	+	51.7029i	−1.12504	+	1.94863i
$705$	−3.03546	−	5.25757i	−0.114322	−	0.198011i
$706$	−76.4359			−2.87670
$707$	17.9829	−	8.81259i	0.676315	−	0.331432i
$708$	−7.53006			−0.282997
$709$	−11.6132	−	20.1146i	−0.436143	−	0.755421i	0.561245	−	0.827649i	$-0.310322\pi$
$709$	−11.6132	−	20.1146i	−0.436143	−	0.755421i	−0.997388	+	0.0722280i	$0.976989\pi$
$710$	1.36700	−	2.36771i	0.0513024	−	0.0888584i
$711$	1.51384	−	2.62205i	0.0567735	−	0.0983346i
$712$	−51.5112	−	89.2201i	−1.93047	−	3.34366i
$713$	2.94359			0.110238
$714$	−38.3808	+	18.8087i	−1.43637	+	0.703899i
$715$	−11.2698			−0.421466
$716$	27.3824	+	47.4278i	1.02333	+	1.77246i
$717$	7.62354	−	13.2044i	0.284706	−	0.493126i
$718$	22.4166	−	38.8267i	0.836579	−	1.44900i
$719$	−19.9020	−	34.4712i	−0.742218	−	1.28556i	−0.951483	−	0.307701i	$-0.900440\pi$
$719$	−19.9020	−	34.4712i	−0.742218	−	1.28556i	0.209265	−	0.977859i	$-0.432893\pi$
$720$	−51.8027			−1.93057
$721$	0.470807	−	6.91922i	0.0175338	−	0.257685i
$722$	−68.2582			−2.54031
$723$	2.06351	+	3.57411i	0.0767429	+	0.132923i
$724$	2.68662	−	4.65336i	0.0998475	−	0.172941i
$725$	−26.5341	+	45.9585i	−0.985453	+	1.70685i
$726$	10.2102	+	17.6847i	0.378938	+	0.656339i
$727$	−22.3786			−0.829978			−0.414989	−	0.909826i	$-0.636215\pi$
$727$	−22.3786			−0.829978			−0.414989	+	0.909826i	$0.636215\pi$
$728$	37.3460	+	25.0885i	1.38414	+	0.929841i
$729$	1.00000			0.0370370
$730$	20.6519	+	35.7702i	0.764362	+	1.32391i
$731$	1.97228	−	3.41609i	0.0729474	−	0.126349i
$732$	25.7847	−	44.6604i	0.953029	−	1.65070i
$733$	15.6130	+	27.0426i	0.576681	+	0.998840i	0.995857	+	0.0909352i	$0.0289856\pi$
$733$	15.6130	+	27.0426i	0.576681	+	0.998840i	−0.419176	+	0.907905i	$0.637681\pi$
$734$	−42.4141			−1.56553
$735$	8.95018	+	21.9155i	0.330132	+	0.808367i
$736$	−22.7499			−0.838572
$737$	7.70215	+	13.3405i	0.283712	+	0.491404i
$738$	−8.08975	+	14.0119i	−0.297788	+	0.515784i
$739$	−17.3219	+	30.0024i	−0.637197	+	1.10366i	0.348848	+	0.937179i	$0.386573\pi$
$739$	−17.3219	+	30.0024i	−0.637197	+	1.10366i	−0.986045	+	0.166478i	$0.946760\pi$
$740$	−41.3079	−	71.5473i	−1.51851	−	2.63013i
$741$	11.7249			0.430727
$742$	−58.2801	−	39.1517i	−2.13953	−	1.43730i
$743$	−23.7961			−0.872996			−0.436498	−	0.899705i	$-0.643781\pi$
$743$	−23.7961			−0.872996			−0.436498	+	0.899705i	$0.643781\pi$
$744$	−14.1449	−	24.4997i	−0.518577	−	0.898202i
$745$	23.3406	−	40.4271i	0.855134	−	1.48114i
$746$	−40.2878	+	69.7805i	−1.47504	+	2.55485i
$747$	5.26501	+	9.11927i	0.192637	+	0.333657i
$748$	−61.1587			−2.23618
$749$	−3.11304	+	45.7509i	−0.113748	+	1.67170i
$750$	−13.3123			−0.486098
$751$	1.27430	+	2.20715i	0.0464999	+	0.0805401i	0.888339	−	0.459189i	$-0.151860\pi$
$751$	1.27430	+	2.20715i	0.0464999	+	0.0805401i	−0.841839	+	0.539729i	$0.818527\pi$
$752$	−13.7492	+	23.8143i	−0.501381	+	0.868417i
$753$	2.41341	−	4.18015i	0.0879495	−	0.152333i
$754$	19.9854	+	34.6157i	0.727826	+	1.26063i
$755$	14.3630			0.522725
$756$	−13.0849	+	6.41231i	−0.475892	+	0.233214i
$757$	−35.5043			−1.29042			−0.645212	−	0.764004i	$-0.723231\pi$
$757$	−35.5043			−1.29042			−0.645212	+	0.764004i	$0.723231\pi$
$758$	32.5303	+	56.3442i	1.18156	+	2.04651i
$759$	0.941706	−	1.63108i	0.0341818	−	0.0592046i
$760$	107.687	−	186.520i	3.90622	−	6.76577i
$761$	15.0000	+	25.9808i	0.543749	+	0.941802i	0.998684	+	0.0512770i	$0.0163291\pi$
$761$	15.0000	+	25.9808i	0.543749	+	0.941802i	−0.454935	+	0.890525i	$0.650338\pi$
$762$	−33.5131			−1.21405
$763$	−31.7599	+	15.5641i	−1.14979	+	0.563459i
$764$	38.5898			1.39613
$765$	−9.96951	−	17.2677i	−0.360448	−	0.624315i
$766$	6.56228	−	11.3662i	0.237105	−	0.410677i
$767$	−1.20957	+	2.09503i	−0.0436749	+	0.0756472i
$768$	24.9560	+	43.2251i	0.900523	+	1.55975i
$769$	39.7222			1.43242			0.716210	−	0.697885i	$-0.245875\pi$
$769$	39.7222			1.43242			0.716210	+	0.697885i	$0.245875\pi$
$770$	−3.13455	+	46.0670i	−0.112961	+	1.66014i
$771$	4.75140			0.171117
$772$	−34.4779	−	59.7174i	−1.24089	−	2.14928i
$773$	−5.99665	+	10.3865i	−0.215684	+	0.373576i	−0.953484	−	0.301443i	$-0.902532\pi$
$773$	−5.99665	+	10.3865i	−0.215684	+	0.373576i	0.737800	+	0.675020i	$0.235865\pi$
$774$	0.916565	−	1.58754i	0.0329453	−	0.0570629i
$775$	−9.47344	−	16.4085i	−0.340296	−	0.589410i
$776$	−150.205			−5.39203
$777$	−9.74150	−	6.54419i	−0.349474	−	0.234771i
$778$	−61.8012			−2.21568
$779$	−19.5649	−	33.8873i	−0.700984	−	1.21414i
$780$	−16.4778	+	28.5403i	−0.589998	+	1.02191i
$781$	0.277852	−	0.481254i	0.00994233	−	0.0172206i
$782$	−8.07743	−	13.9905i	−0.288848	−	0.500300i
$783$	−8.24468			−0.294641
$784$	65.6977	−	84.7422i	2.34635	−	3.02651i
$785$	2.25835			0.0806040
$786$	8.29765	+	14.3720i	0.295967	+	0.512631i
$787$	4.02056	−	6.96382i	0.143318	−	0.248233i	−0.785426	−	0.618955i	$-0.787556\pi$
$787$	4.02056	−	6.96382i	0.143318	−	0.248233i	0.928744	+	0.370722i	$0.120890\pi$
$788$	69.7495	−	120.810i	2.48472	−	4.30366i
$789$	−8.07074	−	13.9789i	−0.287326	−	0.497663i
$790$	−28.0549			−0.998150
$791$	2.60708	+	1.75140i	0.0926971	+	0.0622725i
$792$	−18.1008			−0.643185
$793$	−8.28368	−	14.3478i	−0.294162	−	0.509504i
$794$	4.91656	−	8.51574i	0.174482	−	0.302212i
$795$	16.3764	−	28.3648i	0.580812	−	1.00600i
$796$	−1.78599	−	3.09342i	−0.0633026	−	0.109643i
$797$	−27.9672			−0.990651			−0.495325	−	0.868708i	$-0.664951\pi$
$797$	−27.9672			−0.990651			−0.495325	+	0.868708i	$0.664951\pi$
$798$	3.26115	−	47.9276i	0.115444	−	1.69662i
$799$	−10.5842			−0.374443
$800$	73.2167	+	126.815i	2.58860	+	4.48359i
$801$	5.35981	−	9.28346i	0.189379	−	0.328015i
$802$	14.5680	−	25.2324i	0.514412	−	0.890988i
$803$	4.19766	+	7.27056i	0.148132	+	0.256573i
$804$	45.0459			1.58865
$805$	−8.03454	+	3.93737i	−0.283180	+	0.138774i
$806$	−14.2707			−0.502665
$807$	4.79781	+	8.31006i	0.168891	+	0.292528i
$808$	36.3723	−	62.9986i	1.27957	−	2.21628i
$809$	−4.65850	+	8.06876i	−0.163784	+	0.283682i	−0.936223	−	0.351407i	$-0.885703\pi$
$809$	−4.65850	+	8.06876i	−0.163784	+	0.283682i	0.772439	+	0.635089i	$0.219037\pi$
$810$	−4.63307	−	8.02471i	−0.162789	−	0.281960i
$811$	−18.5550			−0.651553			−0.325776	−	0.945447i	$-0.605626\pi$
$811$	−18.5550			−0.651553			−0.325776	+	0.945447i	$0.605626\pi$
$812$	107.881	−	52.8675i	3.78587	−	1.85528i
$813$	−20.9621			−0.735172
$814$	−11.4451	−	19.8235i	−0.401150	−	0.694812i
$815$	−1.22959	+	2.12972i	−0.0430708	+	0.0746008i
$816$	−45.1571	+	78.2145i	−1.58082	+	2.73805i
$817$	2.21669	+	3.83942i	0.0775522	+	0.134324i
$818$	−39.8183			−1.39222
$819$	−0.317798	+	4.67053i	−0.0111048	+	0.163201i
$820$	109.983			3.84076
$821$	10.8387	+	18.7733i	0.378275	+	0.655191i	0.990811	−	0.135251i	$-0.0431841\pi$
$821$	10.8387	+	18.7733i	0.378275	+	0.655191i	−0.612537	+	0.790442i	$0.709851\pi$
$822$	19.5808	−	33.9150i	0.682959	−	1.18292i
$823$	−1.61481	+	2.79694i	−0.0562888	+	0.0974951i	−0.892797	−	0.450460i	$-0.851260\pi$
$823$	−1.61481	+	2.79694i	−0.0562888	+	0.0974951i	0.836508	+	0.547955i	$0.184593\pi$
$824$	−12.5961	−	21.8170i	−0.438804	−	0.760031i
$825$	−12.1229			−0.422065
$826$	8.22736	+	5.52701i	0.286266	+	0.192309i
$827$	34.5890			1.20278			0.601388	−	0.798957i	$-0.294614\pi$
$827$	34.5890			1.20278			0.601388	+	0.798957i	$0.294614\pi$
$828$	−2.75378	−	4.76968i	−0.0957003	−	0.165758i
$829$	−8.55391	+	14.8158i	−0.297090	+	0.514574i	−0.975469	−	0.220138i	$-0.929349\pi$
$829$	−8.55391	+	14.8158i	−0.297090	+	0.514574i	0.678379	+	0.734712i	$0.262683\pi$
$830$	48.7864	−	84.5005i	1.69340	−	2.93305i
$831$	7.29118	+	12.6287i	0.252928	+	0.438085i
$832$	56.0865			1.94445
$833$	40.8913	+	5.59064i	1.41680	+	0.193704i
$834$	−45.0152			−1.55875
$835$	15.9372	+	27.6041i	0.551531	+	0.955280i
$836$	34.3688	−	59.5286i	1.18867	−	2.05884i
$837$	1.47179	−	2.54922i	0.0508726	−	0.0881140i
$838$	−39.4952	−	68.4077i	−1.36434	−	2.36310i
$839$	−16.7696			−0.578951			−0.289476	−	0.957185i	$-0.593481\pi$
$839$	−16.7696			−0.578951			−0.289476	+	0.957185i	$0.593481\pi$
$840$	71.3796	+	47.9517i	2.46283	+	1.65449i
$841$	38.9748			1.34396
$842$	34.6467	+	60.0099i	1.19400	+	2.06808i
$843$	−5.13531	+	8.89462i	−0.176870	+	0.306347i
$844$	−39.8325	+	68.9919i	−1.37109	+	2.37480i
$845$	−16.6881	−	28.9046i	−0.574088	−	0.994349i
$846$	−4.91874			−0.169110
$847$	1.33859	−	19.6727i	0.0459946	−	0.675960i
$848$	−148.355			−5.09453
$849$	8.54651	+	14.8030i	0.293315	+	0.508037i
$850$	−51.9917	+	90.0523i	−1.78330	+	3.08877i
$851$	2.21781	−	3.84136i	0.0760256	−	0.131680i
$852$	−0.812507	−	1.40730i	−0.0278360	−	0.0482134i
$853$	51.7879			1.77318			0.886591	−	0.462554i	$-0.153067\pi$
$853$	51.7879			1.77318			0.886591	+	0.462554i	$0.153067\pi$
$854$	−60.9528	+	29.8702i	−2.08576	+	1.02214i
$855$	22.4099			0.766404
$856$	83.2868	+	144.257i	2.84669	+	4.93060i
$857$	21.5998	−	37.4119i	0.737835	−	1.27797i	−0.215634	−	0.976474i	$-0.569182\pi$
$857$	21.5998	−	37.4119i	0.737835	−	1.27797i	0.953469	−	0.301493i	$-0.0974849\pi$
$858$	−4.56546	+	7.90761i	−0.155862	+	0.269961i
$859$	1.15276	+	1.99665i	0.0393318	+	0.0681247i	0.885021	−	0.465551i	$-0.154144\pi$
$859$	1.15276	+	1.99665i	0.0393318	+	0.0681247i	−0.845689	+	0.533675i	$0.820810\pi$
$860$	−12.4610			−0.424916
$861$	14.0290	−	6.87499i	0.478107	−	0.234299i
$862$	3.65322			0.124429
$863$	12.7359	+	22.0592i	0.433535	+	0.750904i	0.997175	−	0.0751164i	$-0.0239328\pi$
$863$	12.7359	+	22.0592i	0.433535	+	0.750904i	−0.563640	+	0.826020i	$0.690600\pi$
$864$	−11.3749	+	19.7020i	−0.386984	+	0.670275i
$865$	18.3486	−	31.7808i	0.623873	−	1.08058i
$866$	−17.0729	−	29.5712i	−0.580162	−	1.00487i
$867$	−17.7623			−0.603238
$868$	−2.91184	+	42.7939i	−0.0988341	+	1.45252i
$869$	−5.70238			−0.193440
$870$	38.1982	+	66.1612i	1.29504	+	2.24307i
$871$	7.23580	−	12.5328i	0.245176	−	0.424657i
$872$	−64.2379	+	111.263i	−2.17537	+	3.76785i
$873$	−7.81449	−	13.5351i	−0.264480	−	0.458093i
$874$	18.1568			0.614164
$875$	10.6703	+	7.16814i	0.360722	+	0.242327i
$876$	24.5499			0.829465
$877$	3.55031	+	6.14931i	0.119885	+	0.207647i	0.919722	−	0.392570i	$-0.128414\pi$
$877$	3.55031	+	6.14931i	0.119885	+	0.207647i	−0.799837	+	0.600218i	$0.795081\pi$
$878$	18.8588	−	32.6643i	0.636452	−	1.10237i
$879$	5.45146	−	9.44220i	0.183873	−	0.318478i
$880$	48.7829	+	84.4944i	1.64447	+	2.84831i
$881$	−29.0434			−0.978497			−0.489249	−	0.872144i	$-0.662729\pi$
$881$	−29.0434			−0.978497			−0.489249	+	0.872144i	$0.662729\pi$
$882$	19.0032	+	2.59810i	0.639869	+	0.0874827i
$883$	−30.2662			−1.01854			−0.509269	−	0.860608i	$-0.670084\pi$
$883$	−30.2662			−1.01854			−0.509269	+	0.860608i	$0.670084\pi$
$884$	28.7278	+	49.7580i	0.966221	+	1.67354i
$885$	−2.31185	+	4.00424i	−0.0777120	+	0.134601i
$886$	−9.68329	+	16.7720i	−0.325316	+	0.563465i
$887$	15.6878	+	27.1721i	0.526746	+	0.912350i	0.999514	+	0.0311636i	$0.00992130\pi$
$887$	15.6878	+	27.1721i	0.526746	+	0.912350i	−0.472769	+	0.881187i	$0.656745\pi$
$888$	−42.6292			−1.43054
$889$	26.8619	+	18.0454i	0.900918	+	0.605223i
$890$	−99.3294			−3.32953
$891$	−0.941706	−	1.63108i	−0.0315483	−	0.0546433i
$892$	81.8772	−	141.815i	2.74145	−	4.74833i
$893$	5.94792	−	10.3021i	0.199040	−	0.344747i
$894$	−18.9109	−	32.7546i	−0.632475	−	1.09548i
$895$	33.6274			1.12404
$896$	7.42757	−	109.159i	0.248138	−	3.64676i
$897$	−1.76938			−0.0590777
$898$	−30.7071	−	53.1863i	−1.02471	−	1.77485i
$899$	−12.1345	+	21.0175i	−0.404707	+	0.700974i
$900$	−17.7251	+	30.7008i	−0.590838	+	1.02336i
$901$	−28.5512	−	49.4521i	−0.951177	−	1.64749i
$902$	30.4727			1.01463
$903$	−1.58948	+	0.778934i	−0.0528946	+	0.0259213i
$904$	11.4087			0.379448
$905$	−1.64967	−	2.85732i	−0.0548370	−	0.0949804i
$906$	5.81857	−	10.0781i	0.193309	−	0.334821i
$907$	−11.2817	+	19.5405i	−0.374604	+	0.648833i	−0.990268	−	0.139176i	$-0.955555\pi$
$907$	−11.2817	+	19.5405i	−0.374604	+	0.648833i	0.615664	+	0.788009i	$0.288888\pi$
$908$	17.8725	+	30.9561i	0.593121	+	1.02732i
$909$	7.56916			0.251053
$910$	38.9520	−	19.0886i	1.29125	−	0.632782i
$911$	55.2986			1.83212			0.916062	−	0.401038i	$-0.131350\pi$
$911$	55.2986			1.83212			0.916062	+	0.401038i	$0.131350\pi$
$912$	−50.7532	−	87.9071i	−1.68061	−	2.91089i
$913$	9.91619	−	17.1754i	0.328178	−	0.568421i
$914$	−3.68576	+	6.38392i	−0.121914	+	0.211161i
$915$	−15.8326	−	27.4229i	−0.523411	−	0.906574i
$916$	−6.80776			−0.224935
$917$	1.08785	−	15.9876i	0.0359238	−	0.527955i
$918$	−16.1549			−0.533190
$919$	−12.7123	−	22.0184i	−0.419341	−	0.726320i	0.576532	−	0.817074i	$-0.304405\pi$
$919$	−12.7123	−	22.0184i	−0.419341	−	0.726320i	−0.995873	+	0.0907546i	$0.971072\pi$
$920$	−16.2507	+	28.1471i	−0.535771	+	0.927982i
$921$	13.3986	−	23.2071i	0.441500	−	0.764700i
$922$	41.2457	+	71.4396i	1.35835	+	2.35274i
$923$	−0.522058			−0.0171837
$924$	22.7811	+	15.3040i	0.749444	+	0.503465i
$925$	−28.5506			−0.938738
$926$	−19.2434	−	33.3305i	−0.632377	−	1.09531i
$927$	1.31063	−	2.27008i	0.0430469	−	0.0745594i
$928$	93.7828	−	162.437i	3.07857	−	5.33224i
$929$	17.1281	+	29.6668i	0.561956	+	0.973337i	0.997326	+	0.0730848i	$0.0232844\pi$
$929$	17.1281	+	29.6668i	0.561956	+	0.973337i	−0.435370	+	0.900252i	$0.643382\pi$
$930$	−27.2757			−0.894405
$931$	−28.4210	+	36.6596i	−0.931459	+	1.20147i
$932$	134.143			4.39400
$933$	8.93077	+	15.4685i	0.292380	+	0.506417i
$934$	−14.5276	+	25.1625i	−0.475357	+	0.823342i
$935$	−18.7767	+	32.5222i	−0.614064	+	1.06359i
$936$	8.50243	+	14.7266i	0.277911	+	0.481355i
$937$	54.0699			1.76639			0.883193	−	0.469010i	$-0.155389\pi$
$937$	54.0699			1.76639			0.883193	+	0.469010i	$0.155389\pi$
$938$	−49.2172	−	33.0634i	−1.60700	−	1.07956i
$939$	29.1299			0.950619
$940$	16.7179	+	28.9563i	0.545279	+	0.944451i
$941$	8.52884	−	14.7724i	0.278032	−	0.481566i	−0.692863	−	0.721069i	$-0.743651\pi$
$941$	8.52884	−	14.7724i	0.278032	−	0.481566i	0.970896	+	0.239503i	$0.0769845\pi$
$942$	0.914873	−	1.58461i	0.0298082	−	0.0516292i
$943$	2.95247	+	5.11383i	0.0961457	+	0.166529i
$944$	20.9432			0.681642
$945$	−0.607409	+	8.92680i	−0.0197590	+	0.290389i
$946$	−3.45254			−0.112252
$947$	−16.9738	−	29.3995i	−0.551575	−	0.955356i	−0.998161	−	0.0606156i	$-0.980694\pi$
$947$	−16.9738	−	29.3995i	−0.551575	−	0.955356i	0.446586	−	0.894741i	$-0.352640\pi$
$948$	−8.33756	+	14.4411i	−0.270791	+	0.469024i
$949$	3.94350	−	6.83034i	0.128011	−	0.221722i
$950$	−58.4347	−	101.212i	−1.89587	−	3.28375i
$951$	−21.9373			−0.711367
$952$	134.623	−	65.9726i	4.36315	−	2.13818i
$953$	−22.1762			−0.718358			−0.359179	−	0.933269i	$-0.616943\pi$
$953$	−22.1762			−0.718358			−0.359179	+	0.933269i	$0.616943\pi$
$954$	−13.2684	−	22.9816i	−0.429581	−	0.744056i
$955$	11.8477	−	20.5208i	0.383382	−	0.664037i
$956$	−41.9870	+	72.7236i	−1.35796	+	2.35205i
$957$	7.76407	+	13.4478i	0.250977	+	0.434704i
$958$	30.8630			0.997139
$959$	−33.9565	+	16.6405i	−1.09651	+	0.537351i
$960$	107.198			3.45981
$961$	11.1676	+	19.3429i	0.360247	+	0.623965i
$962$	−10.7521	+	18.6232i	−0.346662	+	0.600436i
$963$	−8.66609	+	15.0101i	−0.279261	+	0.483694i
$964$	−11.3649	−	19.6846i	−0.366039	−	0.633998i
$965$	−42.3411			−1.36301
$966$	−0.492131	+	7.23261i	−0.0158340	+	0.232705i
$967$	15.9540			0.513045			0.256523	−	0.966538i	$-0.417423\pi$
$967$	15.9540			0.513045			0.256523	+	0.966538i	$0.417423\pi$
$968$	−35.8130	−	62.0298i	−1.15107	−	1.99371i
$969$	19.5351	−	33.8357i	0.627557	−	1.08696i
$970$	−72.4101	+	125.418i	−2.32495	+	4.02693i
$971$	−18.6549	−	32.3113i	−0.598665	−	1.03692i	−0.993018	−	0.117960i	$-0.962365\pi$
$971$	−18.6549	−	32.3113i	−0.598665	−	1.03692i	0.394353	−	0.918959i	$-0.370969\pi$
$972$	−5.50755			−0.176655
$973$	36.0812	+	24.2388i	1.15671	+	0.777060i
$974$	−5.21515			−0.167104
$975$	5.69444	+	9.86306i	0.182368	+	0.315871i
$976$	−71.7143	+	124.213i	−2.29552	+	3.97595i
$977$	18.5645	−	32.1546i	0.593930	−	1.02872i	−0.399767	−	0.916617i	$-0.630909\pi$
$977$	18.5645	−	32.1546i	0.593930	−	1.02872i	0.993697	−	0.112100i	$-0.0357576\pi$
$978$	0.996234	+	1.72553i	0.0318560	+	0.0551763i
$979$	−20.1894			−0.645258
$980$	−49.2935	−	120.701i	−1.57462	−	3.85565i
$981$	−13.3681			−0.426809
$982$	28.5976	+	49.5324i	0.912585	+	1.58064i
$983$	10.0202	−	17.3554i	0.319594	−	0.553553i	−0.660809	−	0.750554i	$-0.729787\pi$
$983$	10.0202	−	17.3554i	0.319594	−	0.553553i	0.980403	+	0.197001i	$0.0631202\pi$
$984$	28.3752	−	49.1473i	0.904568	−	1.56676i
$985$	−42.8284	−	74.1810i	−1.36463	−	2.36360i
$986$	133.192			4.24169
$987$	3.94254	+	2.64853i	0.125492	+	0.0843038i
$988$	−64.5757			−2.05443
$989$	−0.334514	−	0.579395i	−0.0106369	−	0.0184237i
$990$	−8.72598	+	15.1138i	−0.277330	+	0.480349i
$991$	−20.1728	+	34.9403i	−0.640810	+	1.10992i	0.344442	+	0.938808i	$0.388068\pi$
$991$	−20.1728	+	34.9403i	−0.640810	+	1.10992i	−0.985252	+	0.171108i	$0.945265\pi$
$992$	33.4832	+	57.9945i	1.06309	+	1.84133i
$993$	5.63045			0.178677
$994$	−0.145204	+	2.13400i	−0.00460559	+	0.0676862i
$995$	−2.19331			−0.0695325
$996$	−28.9973	−	50.2249i	−0.918816	−	1.59144i
$997$	−2.28550	+	3.95861i	−0.0723826	+	0.125370i	−0.899945	−	0.436003i	$-0.856394\pi$
$997$	−2.28550	+	3.95861i	−0.0723826	+	0.125370i	0.827562	+	0.561374i	$0.189727\pi$
$998$	−50.8179	+	88.0191i	−1.60861	+	2.78620i
$999$	−2.21781	−	3.84136i	−0.0701684	−	0.121535i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.i.h.277.10	✓	20
7.2	even	3	inner	483.2.i.h.415.10	yes	20
7.3	odd	6		3381.2.a.bj.1.1		10
7.4	even	3		3381.2.a.bi.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.h.277.10	✓	20	1.1	even	1	trivial
483.2.i.h.415.10	yes	20	7.2	even	3	inner
3381.2.a.bi.1.1		10	7.4	even	3
3381.2.a.bj.1.1		10	7.3	odd	6

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37000 + 2.37290i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.75378 + 4.76968i) q^{4} +(1.69091 + 2.92874i) q^{5} +2.73999 q^{6} +(-2.19620 - 1.47537i) q^{7} -9.61066 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.37000 + 2.37290i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.75378 + 4.76968i) q^{4} +(1.69091 + 2.92874i) q^{5} +2.73999 q^{6} +(-2.19620 - 1.47537i) q^{7} -9.61066 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.63307 + 8.02471i) q^{10} +(-0.941706 + 1.63108i) q^{11} +(2.75378 + 4.76968i) q^{12} +1.76938 q^{13} +(0.492131 - 7.23261i) q^{14} +3.38181 q^{15} +(-7.65901 - 13.2658i) q^{16} +(2.94798 - 5.10605i) q^{17} +(1.37000 - 2.37290i) q^{18} +(3.31330 + 5.73881i) q^{19} -18.6255 q^{20} +(-2.37581 + 1.16428i) q^{21} -5.16053 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-4.80533 + 8.32307i) q^{24} +(-3.21833 + 5.57432i) q^{25} +(2.42404 + 4.19855i) q^{26} -1.00000 q^{27} +(13.0849 - 6.41231i) q^{28} +8.24468 q^{29} +(4.63307 + 8.02471i) q^{30} +(-1.47179 + 2.54922i) q^{31} +(11.3749 - 19.7020i) q^{32} +(0.941706 + 1.63108i) q^{33} +16.1549 q^{34} +(0.607409 - 8.92680i) q^{35} +5.50755 q^{36} +(2.21781 + 3.84136i) q^{37} +(-9.07841 + 15.7243i) q^{38} +(0.884688 - 1.53232i) q^{39} +(-16.2507 - 28.1471i) q^{40} -5.90495 q^{41} +(-6.01756 - 4.04250i) q^{42} +0.669028 q^{43} +(-5.18649 - 8.98327i) q^{44} +(1.69091 - 2.92874i) q^{45} +(1.37000 - 2.37290i) q^{46} +(-0.897583 - 1.55466i) q^{47} -15.3180 q^{48} +(2.64656 + 6.48041i) q^{49} -17.6364 q^{50} +(-2.94798 - 5.10605i) q^{51} +(-4.87246 + 8.43935i) q^{52} +(4.84250 - 8.38746i) q^{53} +(-1.37000 - 2.37290i) q^{54} -6.36935 q^{55} +(21.1069 + 14.1793i) q^{56} +6.62660 q^{57} +(11.2952 + 19.5638i) q^{58} +(-0.683613 + 1.18405i) q^{59} +(-9.31276 + 16.1302i) q^{60} +(-4.68170 - 8.10894i) q^{61} -8.06540 q^{62} +(-0.179610 + 2.63965i) q^{63} +31.6985 q^{64} +(2.99185 + 5.18203i) q^{65} +(-2.58027 + 4.46915i) q^{66} +(4.08947 - 7.08317i) q^{67} +(16.2361 + 28.1218i) q^{68} -1.00000 q^{69} +(22.0146 - 10.7884i) q^{70} -0.295052 q^{71} +(4.80533 + 8.32307i) q^{72} +(2.22875 - 3.86031i) q^{73} +(-6.07678 + 10.5253i) q^{74} +(3.21833 + 5.57432i) q^{75} -36.4963 q^{76} +(4.47462 - 2.19281i) q^{77} +4.84807 q^{78} +(1.51384 + 2.62205i) q^{79} +(25.9013 - 44.8624i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-8.08975 - 14.0119i) q^{82} -10.5300 q^{83} +(0.989213 - 14.5380i) q^{84} +19.9390 q^{85} +(0.916565 + 1.58754i) q^{86} +(4.12234 - 7.14010i) q^{87} +(9.05041 - 15.6758i) q^{88} +(5.35981 + 9.28346i) q^{89} +9.26614 q^{90} +(-3.88590 - 2.61048i) q^{91} +5.50755 q^{92} +(1.47179 + 2.54922i) q^{93} +(2.45937 - 4.25975i) q^{94} +(-11.2050 + 19.4076i) q^{95} +(-11.3749 - 19.7020i) q^{96} +15.6290 q^{97} +(-11.7516 + 15.1582i) q^{98} +1.88341 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9	\( 20 q - 3 q^{2} + 10 q^{3} - 15 q^{4} + 5 q^{5} - 6 q^{6} + 18 q^{8} - 10 q^{9} - 11 q^{10} - 8 q^{11} + 15 q^{12} + 11 q^{14} + 10 q^{15} - 37 q^{16} + 11 q^{17} - 3 q^{18} - q^{19} - 30 q^{20} + 12 q^{22} - 10 q^{23} + 9 q^{24} - 21 q^{25} - q^{26} - 20 q^{27} + 44 q^{28} + 44 q^{29} + 11 q^{30} + 3 q^{31} - 11 q^{32} + 8 q^{33} - 6 q^{34} - 9 q^{35} + 30 q^{36} + 3 q^{37} - 16 q^{38} - 39 q^{40} - 52 q^{41} + 7 q^{42} + 54 q^{43} - 16 q^{44} + 5 q^{45} - 3 q^{46} - 11 q^{47} - 74 q^{48} + 22 q^{49} + 4 q^{50} - 11 q^{51} - 29 q^{52} - 5 q^{53} + 3 q^{54} - 36 q^{55} + 43 q^{56} - 2 q^{57} - 16 q^{58} + 10 q^{59} - 15 q^{60} - 22 q^{61} - 64 q^{62} + 138 q^{64} + 11 q^{65} + 6 q^{66} + 2 q^{67} + 21 q^{68} - 20 q^{69} + 84 q^{70} + 54 q^{71} - 9 q^{72} + 8 q^{73} - 14 q^{74} + 21 q^{75} - 44 q^{76} + 8 q^{77} - 2 q^{78} - 21 q^{79} + 53 q^{80} - 10 q^{81} - 36 q^{82} - 24 q^{83} + 25 q^{84} + 46 q^{85} - 18 q^{86} + 22 q^{87} + 10 q^{88} - 6 q^{89} + 22 q^{90} - 62 q^{91} + 30 q^{92} - 3 q^{93} - 35 q^{94} - 44 q^{95} + 11 q^{96} + 12 q^{97} + 2 q^{98} + 16 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 + 10 * q^3 - 15 * q^4 + 5 * q^5 - 6 * q^6 + 18 * q^8 - 10 * q^9 - 11 * q^10 - 8 * q^11 + 15 * q^12 + 11 * q^14 + 10 * q^15 - 37 * q^16 + 11 * q^17 - 3 * q^18 - q^19 - 30 * q^20 + 12 * q^22 - 10 * q^23 + 9 * q^24 - 21 * q^25 - q^26 - 20 * q^27 + 44 * q^28 + 44 * q^29 + 11 * q^30 + 3 * q^31 - 11 * q^32 + 8 * q^33 - 6 * q^34 - 9 * q^35 + 30 * q^36 + 3 * q^37 - 16 * q^38 - 39 * q^40 - 52 * q^41 + 7 * q^42 + 54 * q^43 - 16 * q^44 + 5 * q^45 - 3 * q^46 - 11 * q^47 - 74 * q^48 + 22 * q^49 + 4 * q^50 - 11 * q^51 - 29 * q^52 - 5 * q^53 + 3 * q^54 - 36 * q^55 + 43 * q^56 - 2 * q^57 - 16 * q^58 + 10 * q^59 - 15 * q^60 - 22 * q^61 - 64 * q^62 + 138 * q^64 + 11 * q^65 + 6 * q^66 + 2 * q^67 + 21 * q^68 - 20 * q^69 + 84 * q^70 + 54 * q^71 - 9 * q^72 + 8 * q^73 - 14 * q^74 + 21 * q^75 - 44 * q^76 + 8 * q^77 - 2 * q^78 - 21 * q^79 + 53 * q^80 - 10 * q^81 - 36 * q^82 - 24 * q^83 + 25 * q^84 + 46 * q^85 - 18 * q^86 + 22 * q^87 + 10 * q^88 - 6 * q^89 + 22 * q^90 - 62 * q^91 + 30 * q^92 - 3 * q^93 - 35 * q^94 - 44 * q^95 + 11 * q^96 + 12 * q^97 + 2 * q^98 + 16 * q^99

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