LMFDB - Embedded newform 354.4.c.a.353.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.3
Character	$\chi$	$=$	354.353
Dual form			354.4.c.a.353.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +(-4.86384 - 1.82840i) q^{3} +4.00000 q^{4} -6.14441i q^{5} +(9.72768 + 3.65680i) q^{6} -15.5071 q^{7} -8.00000 q^{8} +(20.3139 + 17.7861i) q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +(-4.86384 - 1.82840i) q^{3} +4.00000 q^{4} -6.14441i q^{5} +(9.72768 + 3.65680i) q^{6} -15.5071 q^{7} -8.00000 q^{8} +(20.3139 + 17.7861i) q^{9} +12.2888i q^{10} +37.5894 q^{11} +(-19.4554 - 7.31361i) q^{12} -29.6619i q^{13} +31.0142 q^{14} +(-11.2345 + 29.8854i) q^{15} +16.0000 q^{16} +47.7975i q^{17} +(-40.6278 - 35.5722i) q^{18} +69.7384 q^{19} -24.5776i q^{20} +(75.4242 + 28.3533i) q^{21} -75.1789 q^{22} -3.79881 q^{23} +(38.9107 + 14.6272i) q^{24} +87.2462 q^{25} +59.3238i q^{26} +(-66.2833 - 123.651i) q^{27} -62.0285 q^{28} +129.732i q^{29} +(22.4689 - 59.7709i) q^{30} -12.3439i q^{31} -32.0000 q^{32} +(-182.829 - 68.7286i) q^{33} -95.5951i q^{34} +95.2821i q^{35} +(81.2556 + 71.1445i) q^{36} -237.899i q^{37} -139.477 q^{38} +(-54.2339 + 144.271i) q^{39} +49.1553i q^{40} +336.548i q^{41} +(-150.848 - 56.7065i) q^{42} -347.768i q^{43} +150.358 q^{44} +(109.285 - 124.817i) q^{45} +7.59763 q^{46} -173.622 q^{47} +(-77.8214 - 29.2544i) q^{48} -102.529 q^{49} -174.492 q^{50} +(87.3931 - 232.480i) q^{51} -118.648i q^{52} -99.3130i q^{53} +(132.567 + 247.302i) q^{54} -230.965i q^{55} +124.057 q^{56} +(-339.197 - 127.510i) q^{57} -259.465i q^{58} +(25.0425 - 452.495i) q^{59} +(-44.9378 + 119.542i) q^{60} -764.593i q^{61} +24.6878i q^{62} +(-315.010 - 275.811i) q^{63} +64.0000 q^{64} -182.255 q^{65} +(365.658 + 137.457i) q^{66} -596.820i q^{67} +191.190i q^{68} +(18.4768 + 6.94576i) q^{69} -190.564i q^{70} -755.397i q^{71} +(-162.511 - 142.289i) q^{72} -360.437i q^{73} +475.798i q^{74} +(-424.352 - 159.521i) q^{75} +278.954 q^{76} -582.904 q^{77} +(108.468 - 288.542i) q^{78} -963.297 q^{79} -98.3106i q^{80} +(96.3082 + 722.610i) q^{81} -673.096i q^{82} -669.330 q^{83} +(301.697 + 113.413i) q^{84} +293.688 q^{85} +695.536i q^{86} +(237.203 - 630.998i) q^{87} -300.715 q^{88} +337.882 q^{89} +(-218.570 + 249.634i) q^{90} +459.971i q^{91} -15.1953 q^{92} +(-22.5696 + 60.0387i) q^{93} +347.244 q^{94} -428.502i q^{95} +(155.643 + 58.5089i) q^{96} +765.179i q^{97} +205.058 q^{98} +(763.588 + 668.570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	$ 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) $ 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$	−4.86384	−	1.82840i	−0.936047	−	0.351876i
$3$	−4.86384	−	1.82840i	−0.936047	−	0.351876i
$4$	4.00000			0.500000
$5$		−	6.14441i		−	0.549573i	−0.961505	−	0.274786i	$-0.911393\pi$
$5$		−	6.14441i		−	0.549573i	0.961505	−	0.274786i	$-0.0886071\pi$
$6$	9.72768	+	3.65680i	0.661885	+	0.248814i
$7$	−15.5071			−0.837306			−0.418653	−	0.908146i	$-0.637498\pi$
$7$	−15.5071			−0.837306			−0.418653	+	0.908146i	$0.637498\pi$
$8$	−8.00000			−0.353553
$9$	20.3139	+	17.7861i	0.752366	+	0.658745i
$10$			12.2888i			0.388607i
$11$	37.5894			1.03033			0.515165	−	0.857091i	$-0.327730\pi$
$11$	37.5894			1.03033			0.515165	+	0.857091i	$0.327730\pi$
$12$	−19.4554	−	7.31361i	−0.468023	−	0.175938i
$13$		−	29.6619i		−	0.632826i	−0.948622	−	0.316413i	$-0.897522\pi$
$13$		−	29.6619i		−	0.632826i	0.948622	−	0.316413i	$-0.102478\pi$
$14$	31.0142			0.592065
$15$	−11.2345	+	29.8854i	−0.193382	+	0.514426i
$16$	16.0000			0.250000
$17$			47.7975i			0.681918i	0.940078	+	0.340959i	$0.110752\pi$
$17$			47.7975i			0.681918i	−0.940078	+	0.340959i	$0.889248\pi$
$18$	−40.6278	−	35.5722i	−0.532003	−	0.465803i
$19$	69.7384			0.842057			0.421029	−	0.907047i	$-0.361669\pi$
$19$	69.7384			0.842057			0.421029	+	0.907047i	$0.361669\pi$
$20$		−	24.5776i		−	0.274786i
$21$	75.4242	+	28.3533i	0.783757	+	0.294628i
$22$	−75.1789			−0.728554
$23$	−3.79881			−0.0344394			−0.0172197	−	0.999852i	$-0.505481\pi$
$23$	−3.79881			−0.0344394			−0.0172197	+	0.999852i	$0.505481\pi$
$24$	38.9107	+	14.6272i	0.330942	+	0.124407i
$25$	87.2462			0.697970
$26$			59.3238i			0.447475i
$27$	−66.2833	−	123.651i	−0.472453	−	0.881356i
$28$	−62.0285			−0.418653
$29$			129.732i			0.830714i	0.909659	+	0.415357i	$0.136343\pi$
$29$			129.732i			0.830714i	−0.909659	+	0.415357i	$0.863657\pi$
$30$	22.4689	−	59.7709i	0.136741	−	0.363754i
$31$		−	12.3439i		−	0.0715170i	−0.999360	−	0.0357585i	$-0.988615\pi$
$31$		−	12.3439i		−	0.0715170i	0.999360	−	0.0357585i	$-0.0113847\pi$
$32$	−32.0000			−0.176777
$33$	−182.829	−	68.7286i	−0.964438	−	0.362549i
$34$		−	95.5951i		−	0.482189i
$35$			95.2821i			0.460161i
$36$	81.2556	+	71.1445i	0.376183	+	0.329373i
$37$		−	237.899i		−	1.05704i	−0.848922	−	0.528519i	$-0.822748\pi$
$37$		−	237.899i		−	1.05704i	0.848922	−	0.528519i	$-0.177252\pi$
$38$	−139.477			−0.595424
$39$	−54.2339	+	144.271i	−0.222676	+	0.592354i
$40$			49.1553i			0.194303i
$41$			336.548i			1.28195i	0.767562	+	0.640975i	$0.221470\pi$
$41$			336.548i			1.28195i	−0.767562	+	0.640975i	$0.778530\pi$
$42$	−150.848	−	56.7065i	−0.554200	−	0.208333i
$43$		−	347.768i		−	1.23335i	−0.787217	−	0.616676i	$-0.788479\pi$
$43$		−	347.768i		−	1.23335i	0.787217	−	0.616676i	$-0.211521\pi$
$44$	150.358			0.515165
$45$	109.285	−	124.817i	0.362028	−	0.413480i
$46$	7.59763			0.0243524
$47$	−173.622			−0.538837			−0.269419	−	0.963023i	$-0.586832\pi$
$47$	−173.622			−0.538837			−0.269419	+	0.963023i	$0.586832\pi$
$48$	−77.8214	−	29.2544i	−0.234012	−	0.0879690i
$49$	−102.529			−0.298919
$50$	−174.492			−0.493539
$51$	87.3931	−	232.480i	0.239951	−	0.638307i
$52$		−	118.648i		−	0.316413i
$53$		−	99.3130i		−	0.257390i	−0.991684	−	0.128695i	$-0.958921\pi$
$53$		−	99.3130i		−	0.257390i	0.991684	−	0.128695i	$-0.0410789\pi$
$54$	132.567	+	247.302i	0.334075	+	0.623213i
$55$		−	230.965i		−	0.566242i
$56$	124.057			0.296032
$57$	−339.197	−	127.510i	−0.788205	−	0.296300i
$58$		−	259.465i		−	0.587403i
$59$	25.0425	−	452.495i	0.0552585	−	0.998472i
$59$	25.0425	−	452.495i	0.0552585	−	0.998472i
$60$	−44.9378	+	119.542i	−0.0966908	+	0.257213i
$61$		−	764.593i		−	1.60485i	−0.596750	−	0.802427i	$-0.703542\pi$
$61$		−	764.593i		−	1.60485i	0.596750	−	0.802427i	$-0.296458\pi$
$62$			24.6878i			0.0505702i
$63$	−315.010	−	275.811i	−0.629961	−	0.551571i
$64$	64.0000			0.125000
$65$	−182.255			−0.347784
$66$	365.658	+	137.457i	0.681960	+	0.256361i
$67$		−	596.820i		−	1.08826i	−0.839002	−	0.544129i	$-0.816860\pi$
$67$		−	596.820i		−	1.08826i	0.839002	−	0.544129i	$-0.183140\pi$
$68$			191.190i			0.340959i
$69$	18.4768	+	6.94576i	0.0322369	+	0.0121184i
$70$		−	190.564i		−	0.325383i
$71$		−	755.397i		−	1.26266i	−0.775513	−	0.631332i	$-0.782509\pi$
$71$		−	755.397i		−	1.26266i	0.775513	−	0.631332i	$-0.217491\pi$
$72$	−162.511	−	142.289i	−0.266002	−	0.232902i
$73$		−	360.437i		−	0.577890i	−0.957346	−	0.288945i	$-0.906696\pi$
$73$		−	360.437i		−	0.577890i	0.957346	−	0.288945i	$-0.0933045\pi$
$74$			475.798i			0.747438i
$75$	−424.352	−	159.521i	−0.653332	−	0.245599i
$76$	278.954			0.421029
$77$	−582.904			−0.862702
$78$	108.468	−	288.542i	0.157456	−	0.418858i
$79$	−963.297			−1.37189			−0.685946	−	0.727653i	$-0.740611\pi$
$79$	−963.297			−1.37189			−0.685946	+	0.727653i	$0.740611\pi$
$80$		−	98.3106i		−	0.137393i
$81$	96.3082	+	722.610i	0.132110	+	0.991235i
$82$		−	673.096i		−	0.906476i
$83$	−669.330			−0.885163			−0.442582	−	0.896728i	$-0.645937\pi$
$83$	−669.330			−0.885163			−0.442582	+	0.896728i	$0.645937\pi$
$84$	301.697	+	113.413i	0.391879	+	0.147314i
$85$	293.688			0.374764
$86$			695.536i			0.872111i
$87$	237.203	−	630.998i	0.292308	−	0.777587i
$88$	−300.715			−0.364277
$89$	337.882			0.402421			0.201210	−	0.979548i	$-0.435512\pi$
$89$	337.882			0.402421			0.201210	+	0.979548i	$0.435512\pi$
$90$	−218.570	+	249.634i	−0.255993	+	0.292375i
$91$			459.971i			0.529868i
$92$	−15.1953			−0.0172197
$93$	−22.5696	+	60.0387i	−0.0251651	+	0.0669433i
$94$	347.244			0.381015
$95$		−	428.502i		−	0.462772i
$96$	155.643	+	58.5089i	0.165471	+	0.0622035i
$97$			765.179i			0.800950i	0.916308	+	0.400475i	$0.131155\pi$
$97$			765.179i			0.800950i	−0.916308	+	0.400475i	$0.868845\pi$
$98$	205.058			0.211368
$99$	763.588	+	668.570i	0.775186	+	0.678725i
$100$	348.985			0.348985
$101$	190.129			0.187312			0.0936559	−	0.995605i	$-0.470145\pi$
$101$	190.129			0.187312			0.0936559	+	0.995605i	$0.470145\pi$
$102$	−174.786	+	464.959i	−0.169671	+	0.451351i
$103$		−	710.629i		−	0.679809i	−0.940460	−	0.339904i	$-0.889605\pi$
$103$		−	710.629i		−	0.679809i	0.940460	−	0.339904i	$-0.110395\pi$
$104$			237.295i			0.223738i
$105$	174.214	−	463.437i	0.161920	−	0.430732i
$106$			198.626i			0.182003i
$107$		−	231.311i		−	0.208987i	−0.994526	−	0.104494i	$-0.966678\pi$
$107$		−	231.311i		−	0.208987i	0.994526	−	0.104494i	$-0.0333222\pi$
$108$	−265.133	−	494.603i	−0.236227	−	0.440678i
$109$			1801.78i			1.58329i	0.610980	+	0.791646i	$0.290776\pi$
$109$			1801.78i			1.58329i	−0.610980	+	0.791646i	$0.709224\pi$
$110$			461.930i			0.400393i
$111$	−434.975	+	1157.10i	−0.371946	+	0.989436i
$112$	−248.114			−0.209326
$113$	2168.40			1.80519			0.902593	−	0.430496i	$-0.141661\pi$
$113$	2168.40			1.80519			0.902593	+	0.430496i	$0.141661\pi$
$114$	678.393	+	255.020i	0.557345	+	0.209516i
$115$			23.3415i			0.0189270i
$116$			518.930i			0.415357i
$117$	527.570	−	602.549i	0.416871	−	0.476117i
$118$	−50.0849	+	904.990i	−0.0390737	+	0.706026i
$119$		−	741.202i		−	0.570974i
$120$	89.8756	−	239.083i	0.0683707	−	0.181877i
$121$	81.9653			0.0615817
$122$			1529.19i			1.13480i
$123$	615.345	−	1636.92i	0.451088	−	1.19997i
$124$		−	49.3755i		−	0.0357585i
$125$		−	1304.13i		−	0.933158i
$126$	630.020	+	551.623i	0.445449	+	0.390020i
$127$	−595.402			−0.416011			−0.208005	−	0.978128i	$-0.566697\pi$
$127$	−595.402			−0.416011			−0.208005	+	0.978128i	$0.566697\pi$
$128$	−128.000			−0.0883883
$129$	−635.860	+	1691.49i	−0.433987	+	1.15447i
$130$	364.510			0.245920
$131$	−310.086			−0.206812			−0.103406	−	0.994639i	$-0.532974\pi$
$131$	−310.086			−0.206812			−0.103406	+	0.994639i	$0.532974\pi$
$132$	−731.316	−	274.914i	−0.482219	−	0.181274i
$133$	−1081.44			−0.705059
$134$			1193.64i			0.769514i
$135$	−759.761	+	407.272i	−0.484369	+	0.259647i
$136$		−	382.380i		−	0.241094i
$137$			781.948i			0.487638i	0.969821	+	0.243819i	$0.0784002\pi$
$137$			781.948i			0.487638i	−0.969821	+	0.243819i	$0.921600\pi$
$138$	−36.9536	−	13.8915i	−0.0227949	−	0.00856902i
$139$	−746.843			−0.455730			−0.227865	−	0.973693i	$-0.573174\pi$
$139$	−746.843			−0.455730			−0.227865	+	0.973693i	$0.573174\pi$
$140$			381.128i			0.230080i
$141$	844.469	+	317.451i	0.504377	+	0.189604i
$142$			1510.79i			0.892838i
$143$		−	1114.97i		−	0.652020i
$144$	325.022	+	284.578i	0.188092	+	0.164686i
$145$	797.129			0.456538
$146$			720.874i			0.408630i
$147$	498.686	+	187.465i	0.279802	+	0.105183i
$148$		−	951.597i		−	0.528519i
$149$	−1760.53			−0.967974			−0.483987	−	0.875075i	$-0.660812\pi$
$149$	−1760.53			−0.967974			−0.483987	+	0.875075i	$0.660812\pi$
$150$	848.703	+	319.042i	0.461976	+	0.173665i
$151$		−	1096.98i		−	0.591199i	−0.955312	−	0.295599i	$-0.904481\pi$
$151$		−	1096.98i		−	0.591199i	0.955312	−	0.295599i	$-0.0955193\pi$
$152$	−557.907			−0.297712
$153$	−850.132	+	970.954i	−0.449210	+	0.513052i
$154$	1165.81			0.610022
$155$	−75.8459			−0.0393038
$156$	−216.936	+	577.083i	−0.111338	+	0.296177i
$157$		−	1749.55i		−	0.889360i	−0.895690	−	0.444680i	$-0.853317\pi$
$157$		−	1749.55i		−	0.889360i	0.895690	−	0.444680i	$-0.146683\pi$
$158$	1926.59			0.970074
$159$	−181.584	+	483.043i	−0.0905696	+	0.240929i
$160$			196.621i			0.0971517i
$161$	58.9086			0.0288363
$162$	−192.616	−	1445.22i	−0.0934159	−	0.700909i
$163$	2202.40			1.05831			0.529157	−	0.848524i	$-0.322508\pi$
$163$	2202.40			1.05831			0.529157	+	0.848524i	$0.322508\pi$
$164$			1346.19i			0.640975i
$165$	−422.297	+	1123.38i	−0.199247	+	0.530029i
$166$	1338.66			0.625905
$167$			818.846i			0.379426i	0.981840	+	0.189713i	$0.0607558\pi$
$167$			818.846i			0.379426i	−0.981840	+	0.189713i	$0.939244\pi$
$168$	−603.393	−	226.826i	−0.277100	−	0.104167i
$169$	1317.17			0.599532
$170$	−587.375			−0.264998
$171$	1416.66	+	1240.38i	0.633536	+	0.554701i
$172$		−	1391.07i		−	0.616676i
$173$	−132.319			−0.0581505			−0.0290753	−	0.999577i	$-0.509256\pi$
$173$	−132.319			−0.0581505			−0.0290753	+	0.999577i	$0.509256\pi$
$174$	−474.406	+	1262.00i	−0.206693	+	0.549837i
$175$	−1352.94			−0.584414
$176$	601.431			0.257583
$177$	−949.146	+	2155.08i	−0.403063	+	0.915172i
$178$	−675.765			−0.284555
$179$	3983.35			1.66329			0.831646	−	0.555306i	$-0.187399\pi$
$179$	3983.35			1.66329			0.831646	+	0.555306i	$0.187399\pi$
$180$	437.141	−	499.268i	0.181014	−	0.206740i
$181$	1090.88			0.447983			0.223991	−	0.974591i	$-0.428091\pi$
$181$	1090.88			0.447983			0.223991	+	0.974591i	$0.428091\pi$
$182$		−	919.941i		−	0.374674i
$183$	−1397.98	+	3718.86i	−0.564710	+	1.50222i
$184$	30.3905			0.0121762
$185$	−1461.75			−0.580919
$186$	45.1392	−	120.077i	0.0177944	−	0.0473360i
$187$			1796.68i			0.702601i
$188$	−694.487			−0.269419
$189$	1027.86	+	1917.47i	0.395588	+	0.737964i
$190$			857.003i			0.327229i
$191$	1315.20			0.498245			0.249122	−	0.968472i	$-0.419858\pi$
$191$	1315.20			0.498245			0.249122	+	0.968472i	$0.419858\pi$
$192$	−311.286	−	117.018i	−0.117006	−	0.0439845i
$193$	−1466.27			−0.546863			−0.273431	−	0.961892i	$-0.588159\pi$
$193$	−1466.27			−0.546863			−0.273431	+	0.961892i	$0.588159\pi$
$194$		−	1530.36i		−	0.566357i
$195$	886.459	+	333.235i	0.325542	+	0.122377i
$196$	−410.117			−0.149460
$197$		−	2618.27i		−	0.946925i	−0.880814	−	0.473463i	$-0.843004\pi$
$197$		−	2618.27i		−	0.946925i	0.880814	−	0.473463i	$-0.156996\pi$
$198$	−1527.18	−	1337.14i	−0.548139	−	0.479931i
$199$	−2161.41			−0.769942			−0.384971	−	0.922929i	$-0.625789\pi$
$199$	−2161.41			−0.769942			−0.384971	+	0.922929i	$0.625789\pi$
$200$	−697.970			−0.246770
$201$	−1091.23	+	2902.84i	−0.382932	+	1.01866i
$202$	−380.257			−0.132449
$203$		−	2011.78i		−	0.695562i
$204$	349.572	−	929.918i	0.119975	−	0.319153i
$205$	2067.89			0.704525
$206$			1421.26i			0.480697i
$207$	−77.1687	−	67.5661i	−0.0259111	−	0.0226868i
$208$		−	474.590i		−	0.158206i
$209$	2621.43			0.867598
$210$	−348.428	+	926.874i	−0.114494	+	0.304573i
$211$		−	3484.29i		−	1.13682i	−0.822746	−	0.568409i	$-0.807559\pi$
$211$		−	3484.29i		−	1.13682i	0.822746	−	0.568409i	$-0.192441\pi$
$212$		−	397.252i		−	0.128695i
$213$	−1381.17	+	3674.13i	−0.444301	+	1.18191i
$214$			462.621i			0.147776i
$215$	−2136.83			−0.677817
$216$	530.267	+	989.206i	0.167037	+	0.311606i
$217$			191.418i			0.0598816i
$218$		−	3603.55i		−	1.11956i
$219$	−659.024	+	1753.11i	−0.203346	+	0.540932i
$220$		−	923.860i		−	0.283121i
$221$	1417.77			0.431535
$222$	869.951	−	2314.21i	0.263006	−	0.699637i
$223$	−3500.59			−1.05120			−0.525599	−	0.850733i	$-0.676159\pi$
$223$	−3500.59			−1.05120			−0.525599	+	0.850733i	$0.676159\pi$
$224$	496.228			0.148016
$225$	1772.31	+	1551.77i	0.525129	+	0.459784i
$226$	−4336.80			−1.27646
$227$	−3747.45			−1.09571			−0.547857	−	0.836572i	$-0.684556\pi$
$227$	−3747.45			−1.09571			−0.547857	+	0.836572i	$0.684556\pi$
$228$	−1356.79	−	510.040i	−0.394102	−	0.148150i
$229$		−	6066.58i		−	1.75062i	−0.483566	−	0.875308i	$-0.660659\pi$
$229$		−	6066.58i		−	1.75062i	0.483566	−	0.875308i	$-0.339341\pi$
$230$		−	46.6829i		−	0.0133834i
$231$	2835.15	+	1065.78i	0.807529	+	0.303564i
$232$		−	1037.86i		−	0.293702i
$233$	−1799.94			−0.506085			−0.253042	−	0.967455i	$-0.581431\pi$
$233$	−1799.94			−0.506085			−0.253042	+	0.967455i	$0.581431\pi$
$234$	−1055.14	+	1205.10i	−0.294772	+	0.336665i
$235$			1066.80i			0.296130i
$236$	100.170	−	1809.98i	0.0276293	−	0.499236i
$237$	4685.32	+	1761.30i	1.28415	+	0.482736i
$238$			1482.40i			0.403739i
$239$		−	4577.45i		−	1.23887i	−0.785047	−	0.619436i	$-0.787361\pi$
$239$		−	4577.45i		−	1.23887i	0.785047	−	0.619436i	$-0.212639\pi$
$240$	−179.751	+	478.167i	−0.0483454	+	0.128606i
$241$	4953.06			1.32388			0.661938	−	0.749558i	$-0.269734\pi$
$241$	4953.06			1.32388			0.661938	+	0.749558i	$0.269734\pi$
$242$	−163.931			−0.0435449
$243$	852.795	−	3690.75i	0.225131	−	0.974329i
$244$		−	3058.37i		−	0.802427i
$245$			629.982i			0.164278i
$246$	−1230.69	+	3273.83i	−0.318967	+	0.848503i
$247$		−	2068.57i		−	0.532875i
$248$			98.7511i			0.0252851i
$249$	3255.52	+	1223.81i	0.828554	+	0.311468i
$250$			2608.26i			0.659842i
$251$			1877.08i			0.472032i	0.971749	+	0.236016i	$0.0758418\pi$
$251$			1877.08i			0.472032i	−0.971749	+	0.236016i	$0.924158\pi$
$252$	−1260.04	−	1103.25i	−0.314980	−	0.275785i
$253$	−142.795			−0.0354840
$254$	1190.80			0.294164
$255$	−1428.45	−	536.979i	−0.350796	−	0.131870i
$256$	256.000			0.0625000
$257$			2724.72i			0.661337i	0.943747	+	0.330669i	$0.107274\pi$
$257$			2724.72i			0.661337i	−0.943747	+	0.330669i	$0.892726\pi$
$258$	1271.72	−	3382.98i	0.306875	−	0.816337i
$259$			3689.13i			0.885063i
$260$	−729.020			−0.173892
$261$	−2307.44	+	2635.37i	−0.547229	+	0.625001i
$262$	620.172			0.146238
$263$			2455.44i			0.575700i	0.957676	+	0.287850i	$0.0929404\pi$
$263$			2455.44i			0.575700i	−0.957676	+	0.287850i	$0.907060\pi$
$264$	1462.63	+	549.829i	0.340980	+	0.128180i
$265$	−610.220			−0.141455
$266$	2162.88			0.498552
$267$	−1643.41	−	617.785i	−0.376685	−	0.141602i
$268$		−	2387.28i		−	0.544129i
$269$	18.3589			0.00416119			0.00208060	−	0.999998i	$-0.499338\pi$
$269$	18.3589			0.00416119			0.00208060	+	0.999998i	$0.499338\pi$
$270$	1519.52	−	814.544i	0.342501	−	0.183598i
$271$	−5236.26			−1.17373			−0.586864	−	0.809685i	$-0.699638\pi$
$271$	−5236.26			−1.17373			−0.586864	+	0.809685i	$0.699638\pi$
$272$			764.760i			0.170479i
$273$	841.011	−	2237.22i	0.186448	−	0.495982i
$274$		−	1563.90i		−	0.344812i
$275$	3279.54			0.719140
$276$	73.9073	+	27.7830i	0.0161185	+	0.00605921i
$277$	2112.01			0.458116			0.229058	−	0.973413i	$-0.426435\pi$
$277$	2112.01			0.458116			0.229058	+	0.973413i	$0.426435\pi$
$278$	1493.69			0.322249
$279$	219.550	−	250.752i	0.0471115	−	0.0538070i
$280$		−	762.257i		−	0.162691i
$281$		−	4807.27i		−	1.02056i	−0.860008	−	0.510281i	$-0.829541\pi$
$281$		−	4807.27i		−	1.02056i	0.860008	−	0.510281i	$-0.170459\pi$
$282$	−1688.94	−	634.901i	−0.356648	−	0.134070i
$283$		−	4686.74i		−	0.984445i	−0.870469	−	0.492222i	$-0.836185\pi$
$283$		−	4686.74i		−	0.984445i	0.870469	−	0.492222i	$-0.163815\pi$
$284$		−	3021.59i		−	0.631332i
$285$	−783.473	+	2084.16i	−0.162838	+	0.433176i
$286$			2229.95i			0.461048i
$287$		−	5218.89i		−	1.07338i
$288$	−650.044	−	569.156i	−0.133001	−	0.116451i
$289$	2628.40			0.534988
$290$	−1594.26			−0.322821
$291$	1399.06	−	3721.71i	0.281835	−	0.749727i
$292$		−	1441.75i		−	0.288945i
$293$			1618.62i			0.322733i	0.986895	+	0.161367i	$0.0515902\pi$
$293$			1618.62i			0.322733i	−0.986895	+	0.161367i	$0.948410\pi$
$294$	−997.372	−	374.929i	−0.197850	−	0.0743753i
$295$	−2780.32	−	153.871i	−0.548733	−	0.0303686i
$296$			1903.19i			0.373719i
$297$	−2491.55	−	4647.96i	−0.486783	−	0.908088i
$298$	3521.06			0.684461
$299$			112.680i			0.0217942i
$300$	−1697.41	−	638.085i	−0.326666	−	0.122799i
$301$			5392.88i			1.03269i
$302$			2193.96i			0.418040i
$303$	−924.755	−	347.631i	−0.175333	−	0.0659106i
$304$	1115.81			0.210514
$305$	−4697.97			−0.881984
$306$	1700.26	−	1941.91i	0.317639	−	0.362783i
$307$	2818.93			0.524054			0.262027	−	0.965060i	$-0.415609\pi$
$307$	2818.93			0.524054			0.262027	+	0.965060i	$0.415609\pi$
$308$	−2331.62			−0.431351
$309$	−1299.31	+	3456.38i	−0.239209	+	0.636333i
$310$	151.692			0.0277920
$311$		−	5769.41i		−	1.05194i	−0.850503	−	0.525970i	$-0.823703\pi$
$311$		−	5769.41i		−	1.05194i	0.850503	−	0.525970i	$-0.176297\pi$
$312$	433.871	−	1154.17i	0.0787279	−	0.209429i
$313$		−	3407.55i		−	0.615354i	−0.951491	−	0.307677i	$-0.900448\pi$
$313$		−	3407.55i		−	0.615354i	0.951491	−	0.307677i	$-0.0995517\pi$
$314$			3499.10i			0.628872i
$315$	−1694.70	+	1935.55i	−0.303128	+	0.346209i
$316$	−3853.19			−0.685946
$317$			5400.51i			0.956854i	0.878127	+	0.478427i	$0.158793\pi$
$317$			5400.51i			0.956854i	−0.878127	+	0.478427i	$0.841207\pi$
$318$	363.168	−	966.086i	0.0640424	−	0.170363i
$319$			4876.57i			0.855910i
$320$		−	393.242i		−	0.0686966i
$321$	−422.929	+	1125.06i	−0.0735376	+	0.195622i
$322$	−117.817			−0.0203904
$323$			3333.32i			0.574214i
$324$	385.233	+	2890.44i	0.0660550	+	0.495618i
$325$		−	2587.89i		−	0.441693i
$326$	−4404.80			−0.748341
$327$	3294.37	−	8763.55i	0.557123	−	1.48204i
$328$		−	2692.38i		−	0.453238i
$329$	2692.37			0.451172
$330$	844.594	−	2246.75i	0.140889	−	0.374787i
$331$	1280.16			0.212580			0.106290	−	0.994335i	$-0.466103\pi$
$331$	1280.16			0.212580			0.106290	+	0.994335i	$0.466103\pi$
$332$	−2677.32			−0.442582
$333$	4231.30	−	4832.66i	0.696318	−	0.795279i
$334$		−	1637.69i		−	0.268295i
$335$	−3667.11			−0.598077
$336$	1206.79	+	453.652i	0.195939	+	0.0736570i
$337$		−	3980.72i		−	0.643454i	−0.946833	−	0.321727i	$-0.895737\pi$
$337$		−	3980.72i		−	0.643454i	0.946833	−	0.321727i	$-0.104263\pi$
$338$	−2634.34			−0.423933
$339$	−10546.8	−	3964.71i	−1.68974	−	0.635202i
$340$	1174.75			0.187382
$341$		−	464.000i		−	0.0736862i
$342$	−2833.32	−	2480.75i	−0.447977	−	0.392233i
$343$	6908.88			1.08759
$344$			2782.14i			0.436056i
$345$	42.6776	−	113.529i	0.00665996	−	0.0177165i
$346$	264.638			0.0411186
$347$	−4527.75			−0.700467			−0.350234	−	0.936662i	$-0.613898\pi$
$347$	−4527.75			−0.700467			−0.350234	+	0.936662i	$0.613898\pi$
$348$	948.812	−	2523.99i	0.146154	−	0.388793i
$349$		−	7946.74i		−	1.21885i	−0.792843	−	0.609426i	$-0.791400\pi$
$349$		−	7946.74i		−	1.21885i	0.792843	−	0.609426i	$-0.208600\pi$
$350$	2705.87			0.413243
$351$	−3667.72	+	1966.09i	−0.557744	+	0.298980i
$352$	−1202.86			−0.182138
$353$	−10596.7			−1.59775			−0.798873	−	0.601500i	$-0.794570\pi$
$353$	−10596.7			−1.59775			−0.798873	+	0.601500i	$0.794570\pi$
$354$	1898.29	−	4310.15i	0.285009	−	0.647124i
$355$	−4641.47			−0.693925
$356$	1351.53			0.201210
$357$	−1355.22	+	3605.09i	−0.200912	+	0.534458i
$358$	−7966.69			−1.17613
$359$		−	145.320i		−	0.0213640i	−0.999943	−	0.0106820i	$-0.996600\pi$
$359$		−	145.320i		−	0.0213640i	0.999943	−	0.0106820i	$-0.00340026\pi$
$360$	−874.282	+	998.535i	−0.127996	+	0.146187i
$361$	−1995.55			−0.290939
$362$	−2181.77			−0.316771
$363$	−398.666	−	149.866i	−0.0576434	−	0.0216691i
$364$			1839.88i			0.264934i
$365$	−2214.67			−0.317593
$366$	2795.97	−	7437.72i	0.399310	−	1.06223i
$367$		−	7466.74i		−	1.06202i	−0.847366	−	0.531009i	$-0.821813\pi$
$367$		−	7466.74i		−	1.06202i	0.847366	−	0.531009i	$-0.178187\pi$
$368$	−60.7810			−0.00860986
$369$	−5985.88	+	6836.60i	−0.844478	+	0.964496i
$370$	2923.50			0.410772
$371$			1540.06i			0.215515i
$372$	−90.2784	+	240.155i	−0.0125826	+	0.0334716i
$373$	8681.86			1.20517			0.602586	−	0.798054i	$-0.294137\pi$
$373$	8681.86			1.20517			0.602586	+	0.798054i	$0.294137\pi$
$374$		−	3593.36i		−	0.496814i
$375$	−2384.47	+	6343.07i	−0.328356	+	0.873479i
$376$	1388.97			0.190508
$377$	3848.11			0.525697
$378$	−2055.73	−	3834.94i	−0.279723	−	0.521820i
$379$	−3340.84			−0.452790			−0.226395	−	0.974036i	$-0.572694\pi$
$379$	−3340.84			−0.452790			−0.226395	+	0.974036i	$0.572694\pi$
$380$		−	1714.01i		−	0.231386i
$381$	2895.94	+	1088.63i	0.389405	+	0.146384i
$382$	−2630.41			−0.352312
$383$		−	3014.17i		−	0.402133i	−0.979578	−	0.201067i	$-0.935559\pi$
$383$		−	3014.17i		−	0.402133i	0.979578	−	0.201067i	$-0.0644408\pi$
$384$	622.572	+	234.036i	0.0827356	+	0.0311018i
$385$			3581.60i			0.474118i
$386$	2932.54			0.386690
$387$	6185.44	−	7064.52i	0.812464	−	0.927932i
$388$			3060.72i			0.400475i
$389$			5660.70i			0.737812i	0.929467	+	0.368906i	$0.120268\pi$
$389$			5660.70i			0.737812i	−0.929467	+	0.368906i	$0.879732\pi$
$390$	−1772.92	−	666.471i	−0.230193	−	0.0865335i
$391$		−	181.574i		−	0.0234849i
$392$	820.234			0.105684
$393$	1508.21	+	566.962i	0.193586	+	0.0727722i
$394$			5236.55i			0.669577i
$395$			5918.89i			0.753954i
$396$	3054.35	+	2674.28i	0.387593	+	0.339363i
$397$			10235.7i			1.29400i	0.762491	+	0.646998i	$0.223976\pi$
$397$			10235.7i			1.29400i	−0.762491	+	0.646998i	$0.776024\pi$
$398$	4322.83			0.544431
$399$	5259.96	+	1977.31i	0.659968	+	0.248094i
$400$	1395.94			0.174492
$401$	13337.0			1.66090			0.830449	−	0.557095i	$-0.188084\pi$
$401$	13337.0			1.66090			0.830449	+	0.557095i	$0.188084\pi$
$402$	2182.46	−	5805.68i	0.270774	−	0.720301i
$403$	−366.143			−0.0452578
$404$	760.514			0.0936559
$405$	4440.02	−	591.757i	0.544756	−	0.0726041i
$406$			4023.55i			0.491836i
$407$		−	8942.49i		−	1.08910i
$408$	−699.145	+	1859.84i	−0.0848354	+	0.225676i
$409$		−	2319.85i		−	0.280462i	−0.990119	−	0.140231i	$-0.955215\pi$
$409$		−	2319.85i		−	0.280462i	0.990119	−	0.140231i	$-0.0447846\pi$
$410$	−4135.78			−0.498174
$411$	1429.72	−	3803.27i	0.171588	−	0.456452i
$412$		−	2842.51i		−	0.339904i
$413$	−388.337	+	7016.90i	−0.0462683	+	0.836026i
$414$	154.337	+	135.132i	0.0183219	+	0.0160420i
$415$			4112.64i			0.486462i
$416$			949.181i			0.111869i
$417$	3632.53	+	1365.53i	0.426584	+	0.160360i
$418$	−5242.85			−0.613484
$419$	−10284.6			−1.19913			−0.599567	−	0.800325i	$-0.704660\pi$
$419$	−10284.6			−1.19913			−0.599567	+	0.800325i	$0.704660\pi$
$420$	696.856	−	1853.75i	0.0809598	−	0.215366i
$421$			10593.3i			1.22633i	0.789954	+	0.613166i	$0.210104\pi$
$421$			10593.3i			1.22633i	−0.789954	+	0.613166i	$0.789896\pi$
$422$			6968.59i			0.803852i
$423$	−3526.94	−	3088.06i	−0.405403	−	0.354956i
$424$			794.504i			0.0910013i
$425$			4170.15i			0.475958i
$426$	2762.34	−	7348.26i	0.314168	−	0.835738i
$427$			11856.6i			1.34375i
$428$		−	925.242i		−	0.104494i
$429$	−2038.62	+	5423.06i	−0.229430	+	0.610321i
$430$	4273.66			0.479289
$431$	11615.8			1.29817			0.649085	−	0.760716i	$-0.275152\pi$
$431$	11615.8			1.29817			0.649085	+	0.760716i	$0.275152\pi$
$432$	−1060.53	−	1978.41i	−0.118113	−	0.220339i
$433$	−10373.3			−1.15130			−0.575648	−	0.817697i	$-0.695250\pi$
$433$	−10373.3			−1.15130			−0.575648	+	0.817697i	$0.695250\pi$
$434$		−	382.836i		−	0.0423427i
$435$	−3877.11	−	1457.47i	−0.427341	−	0.160645i
$436$			7207.11i			0.791646i
$437$	−264.923			−0.0290000
$438$	1318.05	−	3506.22i	0.143787	−	0.382497i
$439$	13515.0			1.46933			0.734667	−	0.678428i	$-0.237338\pi$
$439$	13515.0			1.46933			0.734667	+	0.678428i	$0.237338\pi$
$440$			1847.72i			0.200197i
$441$	−2082.77	−	1823.60i	−0.224897	−	0.196911i
$442$	−2835.53			−0.305141
$443$	17605.6			1.88819			0.944093	−	0.329681i	$-0.106941\pi$
$443$	17605.6			1.88819			0.944093	+	0.329681i	$0.106941\pi$
$444$	−1739.90	+	4628.41i	−0.185973	+	0.494718i
$445$		−	2076.09i		−	0.221160i
$446$	7001.19			0.743309
$447$	8562.93	+	3218.95i	0.906068	+	0.340607i
$448$	−992.456			−0.104663
$449$			4355.32i			0.457773i	0.973453	+	0.228886i	$0.0735085\pi$
$449$			4355.32i			0.457773i	−0.973453	+	0.228886i	$0.926492\pi$
$450$	−3544.62	−	3103.54i	−0.371322	−	0.325116i
$451$			12650.6i			1.32083i
$452$	8673.60			0.902593
$453$	−2005.72	+	5335.54i	−0.208029	+	0.553389i
$454$	7494.91			0.774787
$455$	2826.25			0.291201
$456$	2713.57	+	1020.08i	0.278673	+	0.104758i
$457$			8005.35i			0.819419i	0.912216	+	0.409709i	$0.134370\pi$
$457$			8005.35i			0.819419i	−0.912216	+	0.409709i	$0.865630\pi$
$458$			12133.2i			1.23787i
$459$	5910.20	−	3168.18i	0.601012	−	0.322174i
$460$			93.3659i			0.00946349i
$461$		−	678.360i		−	0.0685345i	−0.999413	−	0.0342672i	$-0.989090\pi$
$461$		−	678.360i		−	0.0685345i	0.999413	−	0.0342672i	$-0.0109097\pi$
$462$	−5670.30	−	2131.57i	−0.571009	−	0.214652i
$463$			601.819i			0.0604080i	0.999544	+	0.0302040i	$0.00961569\pi$
$463$			601.819i			0.0604080i	−0.999544	+	0.0302040i	$0.990384\pi$
$464$			2075.72i			0.207678i
$465$	368.902	+	138.677i	0.0367902	+	0.0138301i
$466$	3599.87			0.357856
$467$	2683.13			0.265868			0.132934	−	0.991125i	$-0.457560\pi$
$467$	2683.13			0.265868			0.132934	+	0.991125i	$0.457560\pi$
$468$	2110.28	−	2410.19i	0.208435	−	0.238058i
$469$			9254.97i			0.911204i
$470$		−	2133.61i		−	0.209396i
$471$	−3198.89	+	8509.54i	−0.312944	+	0.832482i
$472$	−200.340	+	3619.96i	−0.0195368	+	0.353013i
$473$		−	13072.4i		−	1.27076i
$474$	−9370.65	−	3522.59i	−0.908034	−	0.341346i
$475$	6084.41			0.587731
$476$		−	2964.81i		−	0.285487i
$477$	1766.39	−	2017.43i	0.169555	−	0.193652i
$478$			9154.90i			0.876015i
$479$		−	2056.10i		−	0.196129i	−0.995180	−	0.0980643i	$-0.968735\pi$
$479$		−	2056.10i		−	0.196129i	0.995180	−	0.0980643i	$-0.0312651\pi$
$480$	359.503	−	956.334i	0.0341854	−	0.0909385i
$481$	−7056.54			−0.668920
$482$	−9906.11			−0.936122
$483$	−286.522	−	107.709i	−0.0269922	−	0.0101468i
$484$	327.861			0.0307909
$485$	4701.58			0.440181
$486$	−1705.59	+	7381.50i	−0.159192	+	0.688954i
$487$	−2175.49			−0.202425			−0.101212	−	0.994865i	$-0.532272\pi$
$487$	−2175.49			−0.202425			−0.101212	+	0.994865i	$0.532272\pi$
$488$			6116.74i			0.567402i
$489$	−10712.1	−	4026.87i	−0.990631	−	0.372395i
$490$		−	1259.96i		−	0.116162i
$491$		−	16386.0i		−	1.50609i	−0.657969	−	0.753045i	$-0.728584\pi$
$491$		−	16386.0i		−	1.50609i	0.657969	−	0.753045i	$-0.271416\pi$
$492$	2461.38	−	6547.66i	0.225544	−	0.599983i
$493$	−6200.89			−0.566479
$494$			4137.15i			0.376800i
$495$	4107.97	−	4691.80i	0.373009	−	0.426021i
$496$		−	197.502i		−	0.0178793i
$497$			11714.0i			1.05724i
$498$	−6511.03	−	2447.61i	−0.585876	−	0.220241i
$499$	1232.49			0.110569			0.0552843	−	0.998471i	$-0.482393\pi$
$499$	1232.49			0.110569			0.0552843	+	0.998471i	$0.482393\pi$
$500$		−	5216.51i		−	0.466579i
$501$	1497.18	−	3982.73i	0.133511	−	0.355161i
$502$		−	3754.15i		−	0.333777i
$503$	−8495.67			−0.753088			−0.376544	−	0.926399i	$-0.622888\pi$
$503$	−8495.67			−0.753088			−0.376544	+	0.926399i	$0.622888\pi$
$504$	2520.08	+	2206.49i	0.222725	+	0.195010i
$505$		−	1168.23i		−	0.102941i
$506$	285.590			0.0250910
$507$	−6406.51	−	2408.32i	−0.561190	−	0.210961i
$508$	−2381.61			−0.208005
$509$	−13693.4			−1.19244			−0.596218	−	0.802822i	$-0.703331\pi$
$509$	−13693.4			−1.19244			−0.596218	+	0.802822i	$0.703331\pi$
$510$	2856.90	+	1073.96i	0.248050	+	0.0932464i
$511$			5589.34i			0.483871i
$512$	−512.000			−0.0441942
$513$	−4622.50	−	8623.21i	−0.397833	−	0.742152i
$514$		−	5449.45i		−	0.467636i
$515$	−4366.39			−0.373604
$516$	−2543.44	+	6765.95i	−0.216994	+	0.577237i
$517$	−6526.35			−0.555181
$518$		−	7378.26i		−	0.625834i
$519$	643.579	+	241.933i	0.0544316	+	0.0204618i
$520$	1458.04			0.122960
$521$		−	9385.64i		−	0.789237i	−0.918845	−	0.394618i	$-0.870877\pi$
$521$		−	9385.64i		−	0.789237i	0.918845	−	0.394618i	$-0.129123\pi$
$522$	4614.87	−	5270.74i	0.386949	−	0.441943i
$523$	23536.3			1.96782			0.983912	−	0.178653i	$-0.0571740\pi$
$523$	23536.3			1.96782			0.983912	+	0.178653i	$0.0571740\pi$
$524$	−1240.34			−0.103406
$525$	6580.47	+	2473.71i	0.547039	+	0.205641i
$526$		−	4910.88i		−	0.407081i
$527$	590.007			0.0487687
$528$	−2925.26	−	1099.66i	−0.241109	−	0.0906372i
$529$	−12152.6			−0.998814
$530$	1220.44			0.100024
$531$	8556.84	−	8746.53i	0.699313	−	0.714815i
$532$	−4325.77			−0.352530
$533$	9982.65			0.811251
$534$	3286.81	+	1235.57i	0.266356	+	0.100128i
$535$	−1421.27			−0.114854
$536$			4774.56i			0.384757i
$537$	−19374.4	−	7283.16i	−1.55692	−	0.585273i
$538$	−36.7178			−0.00294241
$539$	−3854.02			−0.307986
$540$	−3039.05	+	1629.09i	−0.242185	+	0.129824i
$541$			16276.9i			1.29352i	0.762692	+	0.646762i	$0.223877\pi$
$541$			16276.9i			1.29352i	−0.762692	+	0.646762i	$0.776123\pi$
$542$	10472.5			0.829951
$543$	−5305.89	−	1994.58i	−0.419332	−	0.157634i
$544$		−	1529.52i		−	0.120547i
$545$	11070.9			0.870135
$546$	−1682.02	+	4474.45i	−0.131839	+	0.350712i
$547$	−7876.39			−0.615667			−0.307834	−	0.951440i	$-0.599604\pi$
$547$	−7876.39			−0.615667			−0.307834	+	0.951440i	$0.599604\pi$
$548$			3127.79i			0.243819i
$549$	13599.1	−	15531.9i	1.05719	−	1.20744i
$550$	−6559.07			−0.508509
$551$			9047.33i			0.699509i
$552$	−147.815	−	55.5661i	−0.0113975	−	0.00428451i
$553$	14938.0			1.14869
$554$	−4224.02			−0.323937
$555$	7109.72	+	2672.67i	0.543767	+	0.204412i
$556$	−2987.37			−0.227865
$557$		−	2242.95i		−	0.170623i	−0.996354	−	0.0853113i	$-0.972812\pi$
$557$		−	2242.95i		−	0.170623i	0.996354	−	0.0853113i	$-0.0271885\pi$
$558$	−439.100	+	501.505i	−0.0333128	+	0.0380473i
$559$	−10315.5			−0.780497
$560$			1524.51i			0.115040i
$561$	3285.06	−	8738.77i	0.247229	−	0.657667i
$562$			9614.55i			0.721646i
$563$	−6388.13			−0.478202			−0.239101	−	0.970995i	$-0.576853\pi$
$563$	−6388.13			−0.478202			−0.239101	+	0.970995i	$0.576853\pi$
$564$	3377.88	+	1269.80i	0.252188	+	0.0948020i
$565$		−	13323.5i		−	0.992081i
$566$			9373.48i			0.696108i
$567$	−1493.46	−	11205.6i	−0.110616	−	0.829967i
$568$			6043.17i			0.446419i
$569$	−18713.5			−1.37875			−0.689377	−	0.724403i	$-0.742115\pi$
$569$	−18713.5			−1.37875			−0.689377	+	0.724403i	$0.742115\pi$
$570$	1566.95	−	4168.33i	0.115144	−	0.306302i
$571$			19015.3i			1.39363i	0.717250	+	0.696816i	$0.245401\pi$
$571$			19015.3i			1.39363i	−0.717250	+	0.696816i	$0.754599\pi$
$572$		−	4459.90i		−	0.326010i
$573$	−6396.94	−	2404.72i	−0.466380	−	0.175320i
$574$			10437.8i			0.758997i
$575$	−331.432			−0.0240377
$576$	1300.09	+	1138.31i	0.0940458	+	0.0823431i
$577$	17500.1			1.26263			0.631317	−	0.775525i	$-0.282515\pi$
$577$	17500.1			1.26263			0.631317	+	0.775525i	$0.282515\pi$
$578$	−5256.79			−0.378294
$579$	7131.71	+	2680.93i	0.511889	+	0.192428i
$580$	3188.52			0.228269
$581$	10379.4			0.741152
$582$	−2798.11	+	7443.42i	−0.199288	+	0.530137i
$583$		−	3733.12i		−	0.265197i
$584$			2883.50i			0.204315i
$585$	−3702.31	−	3241.61i	−0.261661	−	0.229101i
$586$		−	3237.24i		−	0.228207i
$587$	−11173.2			−0.785631			−0.392816	−	0.919617i	$-0.628499\pi$
$587$	−11173.2			−0.785631			−0.392816	+	0.919617i	$0.628499\pi$
$588$	1994.74	+	749.859i	0.139901	+	0.0525913i
$589$		−	860.843i		−	0.0602214i
$590$	5560.63	+	307.742i	0.388013	+	0.0214738i
$591$	−4787.26	+	12734.9i	−0.333200	+	0.886366i
$592$		−	3806.39i		−	0.264259i
$593$		−	3188.44i		−	0.220799i	−0.993887	−	0.110399i	$-0.964787\pi$
$593$		−	3188.44i		−	0.220799i	0.993887	−	0.110399i	$-0.0352130\pi$
$594$	4983.11	+	9295.93i	0.344208	+	0.642115i
$595$	−4554.25			−0.313792
$596$	−7042.11			−0.483987
$597$	10512.8	+	3951.93i	0.720702	+	0.270924i
$598$		−	225.360i		−	0.0154108i
$599$			1071.46i			0.0730864i	0.999332	+	0.0365432i	$0.0116347\pi$
$599$			1071.46i			0.0730864i	−0.999332	+	0.0365432i	$0.988365\pi$
$600$	3394.81	+	1276.17i	0.230988	+	0.0868323i
$601$			15946.0i			1.08228i	0.840932	+	0.541141i	$0.182008\pi$
$601$			15946.0i			1.08228i	−0.840932	+	0.541141i	$0.817992\pi$
$602$		−	10785.8i		−	0.730224i
$603$	10615.1	−	12123.7i	0.716884	−	0.818768i
$604$		−	4387.92i		−	0.295599i
$605$		−	503.628i		−	0.0338436i
$606$	1849.51	+	695.263i	0.123979	+	0.0466058i
$607$	667.595			0.0446406			0.0223203	−	0.999751i	$-0.492895\pi$
$607$	667.595			0.0446406			0.0223203	+	0.999751i	$0.492895\pi$
$608$	−2231.63			−0.148856
$609$	−3678.34	+	9784.96i	−0.244752	+	0.651078i
$610$	9395.95			0.623657
$611$			5149.95i			0.340990i
$612$	−3400.53	+	3883.82i	−0.224605	+	0.256526i
$613$		−	2135.23i		−	0.140687i	−0.997523	−	0.0703435i	$-0.977590\pi$
$613$		−	2135.23i		−	0.140687i	0.997523	−	0.0703435i	$-0.0224095\pi$
$614$	−5637.85			−0.370562
$615$	−10057.9	−	3780.93i	−0.659468	−	0.247906i
$616$	4663.23			0.305011
$617$		−	7976.64i		−	0.520466i	−0.965546	−	0.260233i	$-0.916201\pi$
$617$		−	7976.64i		−	0.520466i	0.965546	−	0.260233i	$-0.0837993\pi$
$618$	2598.63	−	6912.77i	0.169146	−	0.449955i
$619$	−8112.80			−0.526787			−0.263393	−	0.964689i	$-0.584842\pi$
$619$	−8112.80			−0.526787			−0.263393	+	0.964689i	$0.584842\pi$
$620$	−303.384			−0.0196519
$621$	251.798	+	469.726i	0.0162710	+	0.0303534i
$622$			11538.8i			0.743833i
$623$	−5239.58			−0.336949
$624$	−867.742	+	2308.33i	−0.0556691	+	0.148089i
$625$	2892.68			0.185131
$626$			6815.09i			0.435121i
$627$	−12750.2	−	4793.02i	−0.812112	−	0.305287i
$628$		−	6998.21i		−	0.444680i
$629$	11371.0			0.720813
$630$	3389.40	−	3871.10i	0.214344	−	0.244807i
$631$	−12330.0			−0.777893			−0.388947	−	0.921260i	$-0.627161\pi$
$631$	−12330.0			−0.777893			−0.388947	+	0.921260i	$0.627161\pi$
$632$	7706.38			0.485037
$633$	−6370.69	+	16947.0i	−0.400019	+	1.06411i
$634$		−	10801.0i		−	0.676598i
$635$			3658.39i			0.228628i
$636$	−726.337	+	1932.17i	−0.0452848	+	0.120465i
$637$			3041.21i			0.189164i
$638$		−	9753.13i		−	0.605220i
$639$	13435.6	−	15345.0i	0.831773	−	0.949985i
$640$			786.485i			0.0485758i
$641$		−	30333.8i		−	1.86913i	−0.355789	−	0.934566i	$-0.615788\pi$
$641$		−	30333.8i		−	1.86913i	0.355789	−	0.934566i	$-0.384212\pi$
$642$	845.857	−	2250.12i	0.0519990	−	0.138325i
$643$	−18397.3			−1.12834			−0.564168	−	0.825660i	$-0.690803\pi$
$643$	−18397.3			−1.12834			−0.564168	+	0.825660i	$0.690803\pi$
$644$	235.635			0.0144182
$645$	10393.2	+	3906.98i	0.634468	+	0.238508i
$646$		−	6666.65i		−	0.406031i
$647$			7409.51i			0.450229i	0.974332	+	0.225114i	$0.0722756\pi$
$647$			7409.51i			0.450229i	−0.974332	+	0.225114i	$0.927724\pi$
$648$	−770.466	−	5780.88i	−0.0467080	−	0.350455i
$649$	941.332	−	17009.0i	0.0569345	−	1.02876i
$650$			5175.78i			0.312324i
$651$	349.989	−	931.027i	0.0210709	−	0.0560520i
$652$	8809.59			0.529157
$653$			1033.77i			0.0619518i	0.999520	+	0.0309759i	$0.00986151\pi$
$653$			1033.77i			0.0619518i	−0.999520	+	0.0309759i	$0.990138\pi$
$654$	−6588.74	+	17527.1i	−0.393945	+	1.04796i
$655$			1905.30i			0.113658i
$656$			5384.77i			0.320488i
$657$	6410.78	−	7321.88i	0.380682	−	0.434785i
$658$	−5384.75			−0.319026
$659$	19878.1			1.17503			0.587513	−	0.809214i	$-0.300107\pi$
$659$	19878.1			1.17503			0.587513	+	0.809214i	$0.300107\pi$
$660$	−1689.19	+	4493.51i	−0.0996235	+	0.265014i
$661$	1751.78			0.103081			0.0515404	−	0.998671i	$-0.483587\pi$
$661$	1751.78			0.103081			0.0515404	+	0.998671i	$0.483587\pi$
$662$	−2560.32			−0.150317
$663$	−6895.79	−	2592.25i	−0.403937	−	0.151847i
$664$	5354.64			0.312952
$665$			6644.82i			0.387482i
$666$	−8462.60	+	9665.31i	−0.492371	+	0.562347i
$667$		−	492.829i		−	0.0286093i
$668$			3275.38i			0.189713i
$669$	17026.3	+	6400.49i	0.983970	+	0.369891i
$670$	7334.22			0.422904
$671$		−	28740.6i		−	1.65353i
$672$	−2413.57	−	907.304i	−0.138550	−	0.0520834i
$673$			38.4471i			0.00220212i	0.999999	+	0.00110106i	$0.000350478\pi$
$673$			38.4471i			0.00220212i	−0.999999	+	0.00110106i	$0.999650\pi$
$674$			7961.45i			0.454990i
$675$	−5782.97	−	10788.1i	−0.329758	−	0.615160i
$676$	5268.69			0.299766
$677$			25987.7i			1.47531i	0.675176	+	0.737656i	$0.264068\pi$
$677$			25987.7i			1.47531i	−0.675176	+	0.737656i	$0.735932\pi$
$678$	21093.5	+	7929.42i	1.19482	+	0.449155i
$679$		−	11865.7i		−	0.670640i
$680$	−2349.50			−0.132499
$681$	18227.0	+	6851.85i	1.02564	+	0.385556i
$682$			927.999i			0.0521040i
$683$	712.696			0.0399276			0.0199638	−	0.999801i	$-0.493645\pi$
$683$	712.696			0.0399276			0.0199638	+	0.999801i	$0.493645\pi$
$684$	5666.63	+	4961.50i	0.316768	+	0.277351i
$685$	4804.61			0.267992
$686$	−13817.8			−0.769044
$687$	−11092.2	+	29506.9i	−0.616000	+	1.63866i
$688$		−	5564.29i		−	0.308338i
$689$	−2945.81			−0.162883
$690$	−85.3552	+	227.058i	−0.00470930	+	0.0125275i
$691$		−	19443.2i		−	1.07041i	−0.844722	−	0.535205i	$-0.820234\pi$
$691$		−	19443.2i		−	1.07041i	0.844722	−	0.535205i	$-0.179766\pi$
$692$	−529.277			−0.0290753
$693$	−11841.0	−	10367.6i	−0.649068	−	0.568301i
$694$	9055.49			0.495305
$695$			4588.91i			0.250457i
$696$	−1897.62	+	5047.98i	−0.103347	+	0.274918i
$697$	−16086.2			−0.874185
$698$			15893.5i			0.861858i
$699$	8754.61	+	3291.01i	0.473719	+	0.178079i
$700$	−5411.75			−0.292207
$701$	−20895.4			−1.12583			−0.562916	−	0.826514i	$-0.690321\pi$
$701$	−20895.4			−1.12583			−0.562916	+	0.826514i	$0.690321\pi$
$702$	7335.44	−	3932.18i	0.394385	−	0.211411i
$703$		−	16590.7i		−	0.890086i
$704$	2405.72			0.128791
$705$	1950.55	−	5188.76i	0.104201	−	0.277192i
$706$	21193.4			1.12978
$707$	−2948.35			−0.156837
$708$	−3796.58	+	8620.31i	−0.201532	+	0.457586i
$709$	−15357.9			−0.813509			−0.406754	−	0.913538i	$-0.633340\pi$
$709$	−15357.9			−0.813509			−0.406754	+	0.913538i	$0.633340\pi$
$710$	9282.94			0.490679
$711$	−19568.3	−	17133.3i	−1.03216	−	0.903727i
$712$	−2703.06			−0.142277
$713$			46.8921i			0.00246301i
$714$	2710.43	−	7210.18i	0.142066	−	0.377919i
$715$	−6850.86			−0.358332
$716$	15933.4			0.831646
$717$	−8369.42	+	22264.0i	−0.435930	+	1.15964i
$718$			290.640i			0.0151067i
$719$	6866.22			0.356143			0.178071	−	0.984018i	$-0.443014\pi$
$719$	6866.22			0.356143			0.178071	+	0.984018i	$0.443014\pi$
$720$	1748.56	−	1997.07i	0.0905071	−	0.103370i
$721$			11019.8i			0.569208i
$722$	3991.11			0.205725
$723$	−24090.9	−	9056.18i	−1.23921	−	0.465841i
$724$	4363.54			0.223991
$725$			11318.7i			0.579813i
$726$	797.332	+	299.731i	0.0407600	+	0.0153224i
$727$	8402.93			0.428676			0.214338	−	0.976760i	$-0.431241\pi$
$727$	8402.93			0.428676			0.214338	+	0.976760i	$0.431241\pi$
$728$		−	3679.77i		−	0.187337i
$729$	−10896.0	+	16392.0i	−0.553576	+	0.832799i
$730$	4429.35			0.224572
$731$	16622.5			0.841045
$732$	−5591.94	+	14875.4i	−0.282355	+	0.751109i
$733$	1474.16			0.0742827			0.0371414	−	0.999310i	$-0.488175\pi$
$733$	1474.16			0.0742827			0.0371414	+	0.999310i	$0.488175\pi$
$734$			14933.5i			0.750961i
$735$	1151.86	−	3064.13i	0.0578054	−	0.153772i
$736$	121.562			0.00608809
$737$		−	22434.1i		−	1.12126i
$738$	11971.8	−	13673.2i	0.597136	−	0.682002i
$739$		−	17998.9i		−	0.895940i	−0.894049	−	0.447970i	$-0.852147\pi$
$739$		−	17998.9i		−	0.895940i	0.894049	−	0.447970i	$-0.147853\pi$
$740$	−5847.00			−0.290459
$741$	−3782.19	+	10061.2i	−0.187506	+	0.498796i
$742$		−	3080.12i		−	0.152392i
$743$		−	32770.1i		−	1.61806i	−0.587767	−	0.809030i	$-0.699993\pi$
$743$		−	32770.1i		−	1.61806i	0.587767	−	0.809030i	$-0.300007\pi$
$744$	180.557	−	480.310i	0.00889722	−	0.0236680i
$745$			10817.4i			0.531972i
$746$	−17363.7			−0.852186
$747$	−13596.7	−	11904.8i	−0.665967	−	0.583097i
$748$			7186.73i			0.351301i
$749$			3586.96i			0.174986i
$750$	4768.94	−	12686.1i	0.232183	−	0.617643i
$751$			25490.1i			1.23855i	0.785176	+	0.619273i	$0.212573\pi$
$751$			25490.1i			1.23855i	−0.785176	+	0.619273i	$0.787427\pi$
$752$	−2777.95			−0.134709
$753$	3432.05	−	9129.80i	0.166097	−	0.441844i
$754$	−7696.22			−0.371724
$755$	−6740.30			−0.324907
$756$	4111.46	+	7669.87i	0.197794	+	0.368982i
$757$	24617.7			1.18196			0.590982	−	0.806685i	$-0.298741\pi$
$757$	24617.7			1.18196			0.590982	+	0.806685i	$0.298741\pi$
$758$	6681.68			0.320171
$759$	694.533	+	261.087i	0.0332147	+	0.0124860i
$760$			3428.01i			0.163615i
$761$			8444.94i			0.402272i	0.979563	+	0.201136i	$0.0644633\pi$
$761$			8444.94i			0.402272i	−0.979563	+	0.201136i	$0.935537\pi$
$762$	−5791.88	−	2177.27i	−0.275351	−	0.103509i
$763$		−	27940.4i		−	1.32570i
$764$	5260.81			0.249122
$765$	5965.94	+	5223.56i	0.281959	+	0.246874i
$766$			6028.35i			0.284351i
$767$	−13421.9	−	742.807i	−0.631859	−	0.0349690i
$768$	−1245.14	−	468.071i	−0.0585029	−	0.0219923i
$769$		−	18427.2i		−	0.864113i	−0.901847	−	0.432056i	$-0.857788\pi$
$769$		−	18427.2i		−	0.864113i	0.901847	−	0.432056i	$-0.142212\pi$
$770$		−	7163.20i		−	0.335252i
$771$	4981.89	−	13252.6i	0.232709	−	0.619042i
$772$	−5865.08			−0.273431
$773$	−33235.5			−1.54644			−0.773221	−	0.634137i	$-0.781356\pi$
$773$	−33235.5			−1.54644			−0.773221	+	0.634137i	$0.781356\pi$
$774$	−12370.9	+	14129.0i	−0.574499	+	0.656147i
$775$		−	1076.96i		−	0.0499167i
$776$		−	6121.43i		−	0.283179i
$777$	6745.21	−	17943.3i	0.311433	−	0.828461i
$778$		−	11321.4i		−	0.521712i
$779$			23470.3i			1.07948i
$780$	3545.84	+	1332.94i	0.162771	+	0.0611884i
$781$		−	28394.9i		−	1.30096i
$782$			363.148i			0.0166063i
$783$	16041.5	−	8599.10i	0.732154	−	0.392473i
$784$	−1640.47			−0.0747298
$785$	−10750.0			−0.488768
$786$	−3016.42	−	1133.92i	−0.136886	−	0.0514577i
$787$	−344.799			−0.0156172			−0.00780861	−	0.999970i	$-0.502486\pi$
$787$	−344.799			−0.0156172			−0.00780861	+	0.999970i	$0.502486\pi$
$788$		−	10473.1i		−	0.473463i
$789$	4489.54	−	11942.9i	0.202575	−	0.538882i
$790$		−	11837.8i		−	0.533126i
$791$	−33625.6			−1.51149
$792$	−6108.70	−	5348.56i	−0.274070	−	0.239966i
$793$	−22679.3			−1.01559
$794$		−	20471.5i		−	0.914994i
$795$	2968.01	+	1115.73i	0.132408	+	0.0497746i
$796$	−8645.65			−0.384971
$797$	8986.88			0.399412			0.199706	−	0.979856i	$-0.436001\pi$
$797$	8986.88			0.399412			0.199706	+	0.979856i	$0.436001\pi$
$798$	−10519.9	−	3954.62i	−0.466668	−	0.175429i
$799$		−	8298.70i		−	0.367443i
$800$	−2791.88			−0.123385
$801$	6863.70	+	6009.61i	0.302768	+	0.265093i
$802$	−26674.1			−1.17443
$803$		−	13548.6i		−	0.595418i
$804$	−4364.91	+	11611.4i	−0.191466	+	0.509330i
$805$		−	361.959i		−	0.0158477i
$806$	732.286			0.0320021
$807$	−89.2947	−	33.5674i	−0.00389507	−	0.00146422i
$808$	−1521.03			−0.0662247
$809$	29592.4			1.28605			0.643024	−	0.765846i	$-0.277679\pi$
$809$	29592.4			1.28605			0.643024	+	0.765846i	$0.277679\pi$
$810$	−8880.03	+	1183.51i	−0.385201	+	0.0513388i
$811$			879.011i			0.0380595i	0.999819	+	0.0190298i	$0.00605772\pi$
$811$			879.011i			0.0380595i	−0.999819	+	0.0190298i	$0.993942\pi$
$812$		−	8047.10i		−	0.347781i
$813$	25468.3	+	9574.00i	1.09866	+	0.413007i
$814$			17885.0i			0.770109i
$815$		−	13532.4i		−	0.581620i
$816$	1398.29	−	3719.67i	0.0599877	−	0.159577i
$817$		−	24252.8i		−	1.03855i
$818$			4639.70i			0.198317i
$819$	−8181.09	+	9343.79i	−0.349048	+	0.398655i
$820$	8271.56			0.352263
$821$	31034.5			1.31926			0.659629	−	0.751592i	$-0.270714\pi$
$821$	31034.5			1.31926			0.659629	+	0.751592i	$0.270714\pi$
$822$	−2859.43	+	7606.54i	−0.121331	+	0.322760i
$823$		−	38201.9i		−	1.61803i	−0.587791	−	0.809013i	$-0.700002\pi$
$823$		−	38201.9i		−	1.61803i	0.587791	−	0.809013i	$-0.299998\pi$
$824$			5685.03i			0.240349i
$825$	−15951.1	−	5996.31i	−0.673148	−	0.253048i
$826$	776.673	−	14033.8i	0.0327166	−	0.591160i
$827$			42456.2i			1.78518i	0.450866	+	0.892592i	$0.351115\pi$
$827$			42456.2i			1.78518i	−0.450866	+	0.892592i	$0.648885\pi$
$828$	−308.675	−	270.265i	−0.0129555	−	0.0113434i
$829$	43638.8			1.82827			0.914137	−	0.405405i	$-0.132870\pi$
$829$	43638.8			1.82827			0.914137	+	0.405405i	$0.132870\pi$
$830$		−	8225.28i		−	0.343980i
$831$	−10272.5	−	3861.60i	−0.428818	−	0.161200i
$832$		−	1898.36i		−	0.0791032i
$833$		−	4900.64i		−	0.203838i
$834$	−7265.05	−	2731.06i	−0.301641	−	0.113392i
$835$	5031.32			0.208522
$836$	10485.7			0.433799
$837$	−1526.33	+	818.194i	−0.0630319	+	0.0337884i
$838$	20569.3			0.847915
$839$	18074.2			0.743730			0.371865	−	0.928287i	$-0.378718\pi$
$839$	18074.2			0.743730			0.371865	+	0.928287i	$0.378718\pi$
$840$	−1393.71	+	3707.50i	−0.0572472	+	0.152287i
$841$	7558.50			0.309914
$842$		−	21186.6i		−	0.867148i
$843$	−8789.63	+	23381.8i	−0.359111	+	0.955293i
$844$		−	13937.2i		−	0.568409i
$845$		−	8093.24i		−	0.329486i
$846$	7053.87	+	6176.12i	0.286663	+	0.250992i
$847$	−1271.05			−0.0515627
$848$		−	1589.01i		−	0.0643476i
$849$	−8569.25	+	22795.6i	−0.346403	+	0.921486i
$850$		−	8340.31i		−	0.336553i
$851$			903.734i			0.0364038i
$852$	−5524.68	+	14696.5i	−0.222151	+	0.590956i
$853$	−19883.0			−0.798103			−0.399051	−	0.916929i	$-0.630661\pi$
$853$	−19883.0			−0.798103			−0.399051	+	0.916929i	$0.630661\pi$
$854$		−	23713.3i		−	0.950177i
$855$	7621.38	−	8704.53i	0.304849	−	0.348174i
$856$			1850.48i			0.0738881i
$857$	12149.2			0.484256			0.242128	−	0.970244i	$-0.422155\pi$
$857$	12149.2			0.484256			0.242128	+	0.970244i	$0.422155\pi$
$858$	4077.24	−	10846.1i	0.162232	−	0.431562i
$859$			18310.8i			0.727308i	0.931534	+	0.363654i	$0.118471\pi$
$859$			18310.8i			0.727308i	−0.931534	+	0.363654i	$0.881529\pi$
$860$	−8547.32			−0.338908
$861$	−9542.23	+	25383.8i	−0.377698	+	1.00474i
$862$	−23231.5			−0.917945
$863$	−9127.33			−0.360021			−0.180010	−	0.983665i	$-0.557613\pi$
$863$	−9127.33			−0.360021			−0.180010	+	0.983665i	$0.557613\pi$
$864$	2121.07	+	3956.83i	0.0835187	+	0.155803i
$865$			813.023i			0.0319579i
$866$	20746.7			0.814089
$867$	−12784.1	−	4805.77i	−0.500774	−	0.188250i
$868$			765.672i			0.0299408i
$869$	−36209.8			−1.41350
$870$	7754.22	+	2914.95i	0.302175	+	0.113593i
$871$	−17702.8			−0.688677
$872$		−	14414.2i		−	0.559778i
$873$	−13609.6	+	15543.8i	−0.527622	+	0.602608i
$874$	529.846			0.0205061
$875$			20223.3i			0.781339i
$876$	−2636.10	+	7012.43i	−0.101673	+	0.270466i
$877$	32363.5			1.24611			0.623054	−	0.782179i	$-0.285892\pi$
$877$	32363.5			1.24611			0.623054	+	0.782179i	$0.285892\pi$
$878$	−27030.1			−1.03898
$879$	2959.49	−	7872.72i	0.113562	−	0.302093i
$880$		−	3695.44i		−	0.141560i
$881$	7944.01			0.303792			0.151896	−	0.988397i	$-0.451462\pi$
$881$	7944.01			0.303792			0.151896	+	0.988397i	$0.451462\pi$
$882$	4165.54	+	3647.19i	0.159026	+	0.139237i
$883$	−29059.0			−1.10749			−0.553744	−	0.832687i	$-0.686801\pi$
$883$	−29059.0			−1.10749			−0.553744	+	0.832687i	$0.686801\pi$
$884$	5671.06			0.215768
$885$	13241.7	+	5831.94i	0.502954	+	0.221513i
$886$	−35211.1			−1.33515
$887$	36893.4			1.39657			0.698286	−	0.715819i	$-0.253946\pi$
$887$	36893.4			1.39657			0.698286	+	0.715819i	$0.253946\pi$
$888$	3479.80	−	9256.83i	0.131503	−	0.349818i
$889$	9232.97			0.348328
$890$			4152.18i			0.156383i
$891$	3620.17	+	27162.5i	0.136117	+	1.02130i
$892$	−14002.4			−0.525599
$893$	−12108.1			−0.453732
$894$	−17125.9	−	6437.91i	−0.640687	−	0.240845i
$895$		−	24475.3i		−	0.914100i
$896$	1984.91			0.0740081
$897$	206.024	−	548.058i	0.00766885	−	0.0204003i
$898$		−	8710.63i		−	0.323694i
$899$	1601.40			0.0594102
$900$	7089.24	+	6207.08i	0.262564	+	0.229892i
$901$	4746.92			0.175519
$902$		−	25301.3i		−	0.933970i
$903$	9860.36	−	26230.1i	0.363380	−	0.966648i
$904$	−17347.2			−0.638229
$905$		−	6702.85i		−	0.246199i
$906$	4011.44	−	10671.1i	0.147098	−	0.391305i
$907$	50872.9			1.86241			0.931205	−	0.364495i	$-0.118758\pi$
$907$	50872.9			1.86241			0.931205	+	0.364495i	$0.118758\pi$
$908$	−14989.8			−0.547857
$909$	3862.25	+	3381.65i	0.140927	+	0.123391i
$910$	−5652.50			−0.205910
$911$			12668.6i			0.460735i	0.973104	+	0.230368i	$0.0739928\pi$
$911$			12668.6i			0.460735i	−0.973104	+	0.230368i	$0.926007\pi$
$912$	−5427.14	−	2040.16i	−0.197051	−	0.0740750i
$913$	−25159.7			−0.912011
$914$		−	16010.7i		−	0.579417i
$915$	22850.2	+	8589.79i	0.825578	+	0.310349i
$916$		−	24266.3i		−	0.875308i
$917$	4808.54			0.173165
$918$	−11820.4	+	6336.36i	−0.424980	+	0.227812i
$919$			22751.1i			0.816637i	0.912840	+	0.408318i	$0.133885\pi$
$919$			22751.1i			0.816637i	−0.912840	+	0.408318i	$0.866115\pi$
$920$		−	186.732i		−	0.00669170i
$921$	−13710.8	−	5154.13i	−0.490539	−	0.184402i
$922$			1356.72i			0.0484612i
$923$	−22406.5			−0.799046
$924$	11340.6	+	4263.13i	0.403765	+	0.151782i
$925$		−	20755.8i		−	0.737780i
$926$		−	1203.64i		−	0.0427149i
$927$	12639.3	−	14435.6i	0.447821	−	0.511465i
$928$		−	4151.44i		−	0.146851i
$929$	−2768.28			−0.0977658			−0.0488829	−	0.998805i	$-0.515566\pi$
$929$	−2768.28			−0.0977658			−0.0488829	+	0.998805i	$0.515566\pi$
$930$	−737.805	−	277.354i	−0.0260146	−	0.00977934i
$931$	−7150.23			−0.251707
$932$	−7199.75			−0.253042
$933$	−10548.8	+	28061.5i	−0.370152	+	0.984664i
$934$	−5366.26			−0.187997
$935$	11039.6			0.386130
$936$	−4220.56	+	4820.39i	−0.147386	+	0.168333i
$937$			37493.3i			1.30721i	0.756837	+	0.653604i	$0.226744\pi$
$937$			37493.3i			1.30721i	−0.756837	+	0.653604i	$0.773256\pi$
$938$		−	18509.9i		−	0.644318i
$939$	−6230.37	+	16573.8i	−0.216529	+	0.576000i
$940$			4267.22i			0.148065i
$941$	4852.62			0.168109			0.0840547	−	0.996461i	$-0.473213\pi$
$941$	4852.62			0.168109			0.0840547	+	0.996461i	$0.473213\pi$
$942$	6397.77	−	17019.1i	0.221285	−	0.588654i
$943$		−	1278.48i		−	0.0441497i
$944$	400.679	−	7239.92i	0.0138146	−	0.249618i
$945$	11781.7	−	6315.62i	0.405565	−	0.217404i
$946$			26144.8i			0.898563i
$947$			32735.3i			1.12329i	0.827378	+	0.561645i	$0.189831\pi$
$947$			32735.3i			1.12329i	−0.827378	+	0.561645i	$0.810169\pi$
$948$	18741.3	+	7045.18i	0.642077	+	0.241368i
$949$	−10691.3			−0.365704
$950$	−12168.8			−0.415588
$951$	9874.30	−	26267.2i	0.336694	−	0.895660i
$952$			5929.62i			0.201870i
$953$		−	40998.1i		−	1.39356i	−0.717287	−	0.696778i	$-0.754616\pi$
$953$		−	40998.1i		−	1.39356i	0.717287	−	0.696778i	$-0.245384\pi$
$954$	−3532.79	+	4034.87i	−0.119893	+	0.136933i
$955$		−	8081.15i		−	0.273822i
$956$		−	18309.8i		−	0.619436i
$957$	8916.33	−	23718.8i	0.301174	−	0.801172i
$958$			4112.20i			0.138684i
$959$		−	12125.8i		−	0.408302i
$960$	−719.005	+	1912.67i	−0.0241727	+	0.0643032i
$961$	29638.6			0.994885
$962$	14113.1			0.472998
$963$	4114.12	−	4698.82i	0.137669	−	0.157235i
$964$	19812.2			0.661938
$965$			9009.37i			0.300541i
$966$	573.045	+	215.417i	0.0190863	+	0.00717489i
$967$			35548.6i			1.18218i	0.806606	+	0.591089i	$0.201302\pi$
$967$			35548.6i			1.18218i	−0.806606	+	0.591089i	$0.798698\pi$
$968$	−655.722			−0.0217724
$969$	6094.66	−	16212.8i	0.202052	−	0.537491i
$970$	−9403.15			−0.311255
$971$			57383.4i			1.89652i	0.317496	+	0.948260i	$0.397158\pi$
$971$			57383.4i			1.89652i	−0.317496	+	0.948260i	$0.602842\pi$
$972$	3411.18	−	14763.0i	0.112565	−	0.487164i
$973$	11581.4			0.381585
$974$	4350.98			0.143136
$975$	−4731.70	+	12587.1i	−0.155421	+	0.413445i
$976$		−	12233.5i		−	0.401214i
$977$	−57340.6			−1.87767			−0.938837	−	0.344361i	$-0.888096\pi$
$977$	−57340.6			−1.87767			−0.938837	+	0.344361i	$0.888096\pi$
$978$	21424.2	+	8053.74i	0.700482	+	0.263323i
$979$	12700.8			0.414627
$980$			2519.93i			0.0821389i
$981$	−32046.6	+	36601.1i	−1.04299	+	1.19122i
$982$			32772.0i			1.06497i
$983$	17876.4			0.580028			0.290014	−	0.957022i	$-0.406340\pi$
$983$	17876.4			0.580028			0.290014	+	0.957022i	$0.406340\pi$
$984$	−4922.76	+	13095.3i	−0.159484	+	0.424252i
$985$	−16087.8			−0.520404
$986$	12401.8			0.400561
$987$	−13095.3	−	4922.74i	−0.422318	−	0.158757i
$988$		−	8274.30i		−	0.266438i
$989$			1321.11i			0.0424760i
$990$	−8215.94	+	9383.59i	−0.263757	+	0.301243i
$991$			32366.4i			1.03749i	0.854929	+	0.518745i	$0.173601\pi$
$991$			32366.4i			1.03749i	−0.854929	+	0.518745i	$0.826399\pi$
$992$			395.004i			0.0126425i
$993$	−6226.49	−	2340.65i	−0.198985	−	0.0748018i
$994$		−	23428.1i		−	0.747578i
$995$			13280.6i			0.423139i
$996$	13022.1	+	4895.22i	0.414277	+	0.155734i
$997$	−36919.3			−1.17276			−0.586382	−	0.810035i	$-0.699448\pi$
$997$	−36919.3			−1.17276			−0.586382	+	0.810035i	$0.699448\pi$
$998$	−2464.98			−0.0781838
$999$	−29416.4	+	15768.8i	−0.931626	+	0.499401i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.a.353.3	✓	30
3.2	odd	2		354.4.c.b.353.4	yes	30
59.58	odd	2		354.4.c.b.353.3	yes	30
177.176	even	2	inner	354.4.c.a.353.4	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.3	✓	30	1.1	even	1	trivial
354.4.c.a.353.4	yes	30	177.176	even	2	inner
354.4.c.b.353.3	yes	30	59.58	odd	2
354.4.c.b.353.4	yes	30	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +(-4.86384 - 1.82840i) q^{3} +4.00000 q^{4} -6.14441i q^{5} +(9.72768 + 3.65680i) q^{6} -15.5071 q^{7} -8.00000 q^{8} +(20.3139 + 17.7861i) q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +(-4.86384 - 1.82840i) q^{3} +4.00000 q^{4} -6.14441i q^{5} +(9.72768 + 3.65680i) q^{6} -15.5071 q^{7} -8.00000 q^{8} +(20.3139 + 17.7861i) q^{9} +12.2888i q^{10} +37.5894 q^{11} +(-19.4554 - 7.31361i) q^{12} -29.6619i q^{13} +31.0142 q^{14} +(-11.2345 + 29.8854i) q^{15} +16.0000 q^{16} +47.7975i q^{17} +(-40.6278 - 35.5722i) q^{18} +69.7384 q^{19} -24.5776i q^{20} +(75.4242 + 28.3533i) q^{21} -75.1789 q^{22} -3.79881 q^{23} +(38.9107 + 14.6272i) q^{24} +87.2462 q^{25} +59.3238i q^{26} +(-66.2833 - 123.651i) q^{27} -62.0285 q^{28} +129.732i q^{29} +(22.4689 - 59.7709i) q^{30} -12.3439i q^{31} -32.0000 q^{32} +(-182.829 - 68.7286i) q^{33} -95.5951i q^{34} +95.2821i q^{35} +(81.2556 + 71.1445i) q^{36} -237.899i q^{37} -139.477 q^{38} +(-54.2339 + 144.271i) q^{39} +49.1553i q^{40} +336.548i q^{41} +(-150.848 - 56.7065i) q^{42} -347.768i q^{43} +150.358 q^{44} +(109.285 - 124.817i) q^{45} +7.59763 q^{46} -173.622 q^{47} +(-77.8214 - 29.2544i) q^{48} -102.529 q^{49} -174.492 q^{50} +(87.3931 - 232.480i) q^{51} -118.648i q^{52} -99.3130i q^{53} +(132.567 + 247.302i) q^{54} -230.965i q^{55} +124.057 q^{56} +(-339.197 - 127.510i) q^{57} -259.465i q^{58} +(25.0425 - 452.495i) q^{59} +(-44.9378 + 119.542i) q^{60} -764.593i q^{61} +24.6878i q^{62} +(-315.010 - 275.811i) q^{63} +64.0000 q^{64} -182.255 q^{65} +(365.658 + 137.457i) q^{66} -596.820i q^{67} +191.190i q^{68} +(18.4768 + 6.94576i) q^{69} -190.564i q^{70} -755.397i q^{71} +(-162.511 - 142.289i) q^{72} -360.437i q^{73} +475.798i q^{74} +(-424.352 - 159.521i) q^{75} +278.954 q^{76} -582.904 q^{77} +(108.468 - 288.542i) q^{78} -963.297 q^{79} -98.3106i q^{80} +(96.3082 + 722.610i) q^{81} -673.096i q^{82} -669.330 q^{83} +(301.697 + 113.413i) q^{84} +293.688 q^{85} +695.536i q^{86} +(237.203 - 630.998i) q^{87} -300.715 q^{88} +337.882 q^{89} +(-218.570 + 249.634i) q^{90} +459.971i q^{91} -15.1953 q^{92} +(-22.5696 + 60.0387i) q^{93} +347.244 q^{94} -428.502i q^{95} +(155.643 + 58.5089i) q^{96} +765.179i q^{97} +205.058 q^{98} +(763.588 + 668.570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9}+O(q^{10}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9	\( 30 q - 60 q^{2} + 5 q^{3} + 120 q^{4} - 10 q^{6} + 6 q^{7} - 240 q^{8} + 27 q^{9} - 60 q^{11} + 20 q^{12} - 12 q^{14} + 20 q^{15} + 480 q^{16} - 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} + 24 q^{23} - 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} - 40 q^{30} - 960 q^{32} + 336 q^{33} + 108 q^{36} - 180 q^{38} + 652 q^{39} - 264 q^{42} - 240 q^{44} - 878 q^{45} - 48 q^{46} + 792 q^{47} + 80 q^{48} + 2016 q^{49} + 2160 q^{50} + 650 q^{51} + 110 q^{54} - 48 q^{56} + 846 q^{57} - 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} - 1416 q^{65} - 672 q^{66} - 590 q^{69} - 216 q^{72} - 952 q^{75} + 360 q^{76} + 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} + 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} - 300 q^{89} + 1756 q^{90} + 96 q^{92} + 1684 q^{93} - 1584 q^{94} - 160 q^{96} - 4032 q^{98} + 730 q^{99}+O(q^{100}) \) 30 * q - 60 * q^2 + 5 * q^3 + 120 * q^4 - 10 * q^6 + 6 * q^7 - 240 * q^8 + 27 * q^9 - 60 * q^11 + 20 * q^12 - 12 * q^14 + 20 * q^15 + 480 * q^16 - 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 + 24 * q^23 - 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 - 40 * q^30 - 960 * q^32 + 336 * q^33 + 108 * q^36 - 180 * q^38 + 652 * q^39 - 264 * q^42 - 240 * q^44 - 878 * q^45 - 48 * q^46 + 792 * q^47 + 80 * q^48 + 2016 * q^49 + 2160 * q^50 + 650 * q^51 + 110 * q^54 - 48 * q^56 + 846 * q^57 - 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 - 1416 * q^65 - 672 * q^66 - 590 * q^69 - 216 * q^72 - 952 * q^75 + 360 * q^76 + 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 + 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 - 300 * q^89 + 1756 * q^90 + 96 * q^92 + 1684 * q^93 - 1584 * q^94 - 160 * q^96 - 4032 * q^98 + 730 * q^99

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