LMFDB - Embedded newform 354.4.c.b.353.10

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			353.10
Character	$\chi$	$=$	354.353
Dual form			354.4.c.b.353.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-3.04040 + 4.21378i) q^{3} +4.00000 q^{4} -12.5447i q^{5} +(-6.08081 + 8.42756i) q^{6} -33.4405 q^{7} +8.00000 q^{8} +(-8.51188 - 25.6232i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-3.04040 + 4.21378i) q^{3} +4.00000 q^{4} -12.5447i q^{5} +(-6.08081 + 8.42756i) q^{6} -33.4405 q^{7} +8.00000 q^{8} +(-8.51188 - 25.6232i) q^{9} -25.0894i q^{10} +55.6576 q^{11} +(-12.1616 + 16.8551i) q^{12} +53.4865i q^{13} -66.8811 q^{14} +(52.8606 + 38.1410i) q^{15} +16.0000 q^{16} +114.641i q^{17} +(-17.0238 - 51.2464i) q^{18} +78.3915 q^{19} -50.1788i q^{20} +(101.673 - 140.911i) q^{21} +111.315 q^{22} +163.867 q^{23} +(-24.3232 + 33.7102i) q^{24} -32.3697 q^{25} +106.973i q^{26} +(133.850 + 42.0377i) q^{27} -133.762 q^{28} -76.0732i q^{29} +(105.721 + 76.2820i) q^{30} +160.914i q^{31} +32.0000 q^{32} +(-169.222 + 234.529i) q^{33} +229.283i q^{34} +419.502i q^{35} +(-34.0475 - 102.493i) q^{36} +83.0925i q^{37} +156.783 q^{38} +(-225.380 - 162.621i) q^{39} -100.358i q^{40} -70.9020i q^{41} +(203.346 - 281.822i) q^{42} -257.980i q^{43} +222.631 q^{44} +(-321.435 + 106.779i) q^{45} +327.733 q^{46} -497.485 q^{47} +(-48.6465 + 67.4205i) q^{48} +775.270 q^{49} -64.7393 q^{50} +(-483.073 - 348.556i) q^{51} +213.946i q^{52} +500.411i q^{53} +(267.700 + 84.0753i) q^{54} -698.209i q^{55} -267.524 q^{56} +(-238.342 + 330.324i) q^{57} -152.146i q^{58} +(453.067 + 10.4364i) q^{59} +(211.443 + 152.564i) q^{60} -32.9911i q^{61} +321.828i q^{62} +(284.642 + 856.853i) q^{63} +64.0000 q^{64} +670.972 q^{65} +(-338.443 + 469.058i) q^{66} -1052.72i q^{67} +458.565i q^{68} +(-498.221 + 690.498i) q^{69} +839.004i q^{70} +470.752i q^{71} +(-68.0951 - 204.986i) q^{72} +912.066i q^{73} +166.185i q^{74} +(98.4169 - 136.399i) q^{75} +313.566 q^{76} -1861.22 q^{77} +(-450.761 - 325.241i) q^{78} +674.923 q^{79} -200.715i q^{80} +(-584.096 + 436.203i) q^{81} -141.804i q^{82} +483.590 q^{83} +(406.691 - 563.644i) q^{84} +1438.14 q^{85} -515.960i q^{86} +(320.556 + 231.293i) q^{87} +445.261 q^{88} +70.2848 q^{89} +(-642.871 + 213.558i) q^{90} -1788.62i q^{91} +655.467 q^{92} +(-678.055 - 489.243i) q^{93} -994.970 q^{94} -983.398i q^{95} +(-97.2929 + 134.841i) q^{96} +549.167i q^{97} +1550.54 q^{98} +(-473.751 - 1426.13i) 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
$3$	−3.04040	+	4.21378i	−0.585126	+	0.810942i
$3$	−3.04040	+	4.21378i	−0.585126	+	0.810942i
$4$	4.00000			0.500000
$5$		−	12.5447i		−	1.12203i	−0.827805	−	0.561016i	$-0.810410\pi$
$5$		−	12.5447i		−	1.12203i	0.827805	−	0.561016i	$-0.189590\pi$
$6$	−6.08081	+	8.42756i	−0.413747	+	0.573423i
$7$	−33.4405			−1.80562			−0.902810	−	0.430040i	$-0.858499\pi$
$7$	−33.4405			−1.80562			−0.902810	+	0.430040i	$0.858499\pi$
$8$	8.00000			0.353553
$9$	−8.51188	−	25.6232i	−0.315255	−	0.949007i
$10$		−	25.0894i		−	0.793397i
$11$	55.6576			1.52558			0.762791	−	0.646645i	$-0.223828\pi$
$11$	55.6576			1.52558			0.762791	+	0.646645i	$0.223828\pi$
$12$	−12.1616	+	16.8551i	−0.292563	+	0.405471i
$13$			53.4865i			1.14111i	0.821258	+	0.570557i	$0.193273\pi$
$13$			53.4865i			1.14111i	−0.821258	+	0.570557i	$0.806727\pi$
$14$	−66.8811			−1.27677
$15$	52.8606	+	38.1410i	0.909904	+	0.656531i
$16$	16.0000			0.250000
$17$			114.641i			1.63556i	0.575528	+	0.817782i	$0.304797\pi$
$17$			114.641i			1.63556i	−0.575528	+	0.817782i	$0.695203\pi$
$18$	−17.0238	−	51.2464i	−0.222919	−	0.671049i
$19$	78.3915			0.946539			0.473269	−	0.880918i	$-0.343074\pi$
$19$	78.3915			0.946539			0.473269	+	0.880918i	$0.343074\pi$
$20$		−	50.1788i		−	0.561016i
$21$	101.673	−	140.911i	1.05652	−	1.46425i
$22$	111.315			1.07875
$23$	163.867			1.48559			0.742795	−	0.669519i	$-0.233500\pi$
$23$	163.867			1.48559			0.742795	+	0.669519i	$0.233500\pi$
$24$	−24.3232	+	33.7102i	−0.206873	+	0.286711i
$25$	−32.3697			−0.258957
$26$			106.973i			0.806889i
$27$	133.850	+	42.0377i	0.954054	+	0.299635i
$28$	−133.762			−0.902810
$29$		−	76.0732i		−	0.487119i	−0.969886	−	0.243559i	$-0.921685\pi$
$29$		−	76.0732i		−	0.487119i	0.969886	−	0.243559i	$-0.0783151\pi$
$30$	105.721	+	76.2820i	0.643399	+	0.464237i
$31$			160.914i			0.932289i	0.884708	+	0.466145i	$0.154357\pi$
$31$			160.914i			0.932289i	−0.884708	+	0.466145i	$0.845643\pi$
$32$	32.0000			0.176777
$33$	−169.222	+	234.529i	−0.892658	+	1.23716i
$34$			229.283i			1.15652i
$35$			419.502i			2.02596i
$36$	−34.0475	−	102.493i	−0.157627	−	0.474504i
$37$			83.0925i			0.369198i	0.982814	+	0.184599i	$0.0590986\pi$
$37$			83.0925i			0.369198i	−0.982814	+	0.184599i	$0.940901\pi$
$38$	156.783			0.669304
$39$	−225.380	−	162.621i	−0.925378	−	0.667696i
$40$		−	100.358i		−	0.396698i
$41$		−	70.9020i		−	0.270074i	−0.990841	−	0.135037i	$-0.956885\pi$
$41$		−	70.9020i		−	0.270074i	0.990841	−	0.135037i	$-0.0431153\pi$
$42$	203.346	−	281.822i	0.747069	−	1.03538i
$43$		−	257.980i		−	0.914920i	−0.889230	−	0.457460i	$-0.848759\pi$
$43$		−	257.980i		−	0.914920i	0.889230	−	0.457460i	$-0.151241\pi$
$44$	222.631			0.762791
$45$	−321.435	+	106.779i	−1.06482	+	0.353726i
$46$	327.733			1.05047
$47$	−497.485			−1.54395			−0.771975	−	0.635653i	$-0.780731\pi$
$47$	−497.485			−1.54395			−0.771975	+	0.635653i	$0.780731\pi$
$48$	−48.6465	+	67.4205i	−0.146282	+	0.202736i
$49$	775.270			2.26026
$50$	−64.7393			−0.183110
$51$	−483.073	−	348.556i	−1.32635	−	0.957012i
$52$			213.946i			0.570557i
$53$			500.411i			1.29692i	0.761249	+	0.648459i	$0.224586\pi$
$53$			500.411i			1.29692i	−0.761249	+	0.648459i	$0.775414\pi$
$54$	267.700	+	84.0753i	0.674618	+	0.211874i
$55$		−	698.209i		−	1.71175i
$56$	−267.524			−0.638383
$57$	−238.342	+	330.324i	−0.553844	+	0.767588i
$58$		−	152.146i		−	0.344445i
$59$	453.067	+	10.4364i	0.999735	+	0.0230290i
$59$	453.067	+	10.4364i	0.999735	+	0.0230290i
$60$	211.443	+	152.564i	0.454952	+	0.328265i
$61$		−	32.9911i		−	0.0692472i	−0.999400	−	0.0346236i	$-0.988977\pi$
$61$		−	32.9911i		−	0.0692472i	0.999400	−	0.0346236i	$-0.0110232\pi$
$62$			321.828i			0.659228i
$63$	284.642	+	856.853i	0.569230	+	1.71355i
$64$	64.0000			0.125000
$65$	670.972			1.28037
$66$	−338.443	+	469.058i	−0.631205	+	0.874804i
$67$		−	1052.72i		−	1.91956i	−0.280760	−	0.959778i	$-0.590586\pi$
$67$		−	1052.72i		−	1.91956i	0.280760	−	0.959778i	$-0.409414\pi$
$68$			458.565i			0.817782i
$69$	−498.221	+	690.498i	−0.869257	+	1.20473i
$70$			839.004i			1.43257i
$71$			470.752i			0.786873i	0.919352	+	0.393437i	$0.128714\pi$
$71$			470.752i			0.786873i	−0.919352	+	0.393437i	$0.871286\pi$
$72$	−68.0951	−	204.986i	−0.111459	−	0.335525i
$73$			912.066i			1.46232i	0.682207	+	0.731159i	$0.261020\pi$
$73$			912.066i			1.46232i	−0.682207	+	0.731159i	$0.738980\pi$
$74$			166.185i			0.261062i
$75$	98.4169	−	136.399i	0.151523	−	0.209999i
$76$	313.566			0.473269
$77$	−1861.22			−2.75462
$78$	−450.761	−	325.241i	−0.654341	−	0.472132i
$79$	674.923			0.961199			0.480600	−	0.876940i	$-0.340419\pi$
$79$	674.923			0.961199			0.480600	+	0.876940i	$0.340419\pi$
$80$		−	200.715i		−	0.280508i
$81$	−584.096	+	436.203i	−0.801229	+	0.598358i
$82$		−	141.804i		−	0.190971i
$83$	483.590			0.639528			0.319764	−	0.947497i	$-0.396396\pi$
$83$	483.590			0.639528			0.319764	+	0.947497i	$0.396396\pi$
$84$	406.691	−	563.644i	0.528258	−	0.732127i
$85$	1438.14			1.83516
$86$		−	515.960i		−	0.646946i
$87$	320.556	+	231.293i	0.395025	+	0.285026i
$88$	445.261			0.539375
$89$	70.2848			0.0837098			0.0418549	−	0.999124i	$-0.486673\pi$
$89$	70.2848			0.0837098			0.0418549	+	0.999124i	$0.486673\pi$
$90$	−642.871	+	213.558i	−0.752939	+	0.250122i
$91$		−	1788.62i		−	2.06042i
$92$	655.467			0.742795
$93$	−678.055	−	489.243i	−0.756033	−	0.545507i
$94$	−994.970			−1.09174
$95$		−	983.398i		−	1.06205i
$96$	−97.2929	+	134.841i	−0.103437	+	0.143356i
$97$			549.167i			0.574840i	0.957805	+	0.287420i	$0.0927975\pi$
$97$			549.167i			0.574840i	−0.957805	+	0.287420i	$0.907203\pi$
$98$	1550.54			1.59825
$99$	−473.751	−	1426.13i	−0.480947	−	1.44779i
$100$	−129.479			−0.129479
$101$	1282.30			1.26330			0.631652	−	0.775252i	$-0.282377\pi$
$101$	1282.30			1.26330			0.631652	+	0.775252i	$0.282377\pi$
$102$	−966.146	−	697.112i	−0.937870	−	0.676709i
$103$			1210.94i			1.15842i	0.815177	+	0.579212i	$0.196640\pi$
$103$			1210.94i			1.15842i	−0.815177	+	0.579212i	$0.803360\pi$
$104$			427.892i			0.403445i
$105$	−1767.69	−	1275.46i	−1.64294	−	1.18544i
$106$			1000.82i			0.917060i
$107$		−	618.091i		−	0.558440i	−0.960227	−	0.279220i	$-0.909924\pi$
$107$		−	618.091i		−	0.558440i	0.960227	−	0.279220i	$-0.0900759\pi$
$108$	535.400	+	168.151i	0.477027	+	0.149818i
$109$			14.7828i			0.0129902i	0.999979	+	0.00649512i	$0.00206748\pi$
$109$			14.7828i			0.0129902i	−0.999979	+	0.00649512i	$0.997933\pi$
$110$		−	1396.42i		−	1.21039i
$111$	−350.133	−	252.635i	−0.299398	−	0.216027i
$112$	−535.049			−0.451405
$113$	−759.245			−0.632068			−0.316034	−	0.948748i	$-0.602351\pi$
$113$	−759.245			−0.632068			−0.316034	+	0.948748i	$0.602351\pi$
$114$	−476.683	+	660.649i	−0.391627	+	0.542767i
$115$		−	2055.66i		−	1.66688i
$116$		−	304.293i		−	0.243559i
$117$	1370.49	−	455.271i	1.08293	−	0.359742i
$118$	906.135	+	20.8729i	0.706919	+	0.0162839i
$119$		−	3833.67i		−	2.95321i
$120$	422.885	+	305.128i	0.321700	+	0.232119i
$121$	1766.77			1.32740
$122$		−	65.9823i		−	0.0489652i
$123$	298.765	+	215.571i	0.219014	+	0.158027i
$124$			643.655i			0.466145i
$125$		−	1162.02i		−	0.831474i
$126$	569.284	+	1713.71i	0.402507	+	1.21166i
$127$	−1634.61			−1.14211			−0.571055	−	0.820912i	$-0.693466\pi$
$127$	−1634.61			−1.14211			−0.571055	+	0.820912i	$0.693466\pi$
$128$	128.000			0.0883883
$129$	1087.07	+	784.363i	0.741947	+	0.535344i
$130$	1341.94			0.905356
$131$	−1341.04			−0.894403			−0.447201	−	0.894433i	$-0.647579\pi$
$131$	−1341.04			−0.894403			−0.447201	+	0.894433i	$0.647579\pi$
$132$	−676.887	+	938.116i	−0.446329	+	0.618580i
$133$	−2621.45			−1.70909
$134$		−	2105.44i		−	1.35733i
$135$	527.350	−	1679.11i	0.336201	−	1.07048i
$136$			917.130i			0.578259i
$137$			2577.02i			1.60708i	0.595251	+	0.803540i	$0.297053\pi$
$137$			2577.02i			1.60708i	−0.595251	+	0.803540i	$0.702947\pi$
$138$	−996.442	+	1381.00i	−0.614658	+	0.851871i
$139$	−280.345			−0.171069			−0.0855344	−	0.996335i	$-0.527260\pi$
$139$	−280.345			−0.171069			−0.0855344	+	0.996335i	$0.527260\pi$
$140$			1678.01i			1.01298i
$141$	1512.56	−	2096.29i	0.903406	−	1.25205i
$142$			941.504i			0.556403i
$143$			2976.93i			1.74086i
$144$	−136.190	−	409.971i	−0.0788137	−	0.237252i
$145$	−954.316			−0.546563
$146$			1824.13i			1.03402i
$147$	−2357.13	+	3266.82i	−1.32254	+	1.83294i
$148$			332.370i			0.184599i
$149$	−2428.29			−1.33512			−0.667562	−	0.744554i	$-0.732662\pi$
$149$	−2428.29			−1.33512			−0.667562	+	0.744554i	$0.732662\pi$
$150$	196.834	−	272.797i	0.107143	−	0.148492i
$151$		−	477.528i		−	0.257355i	−0.991686	−	0.128678i	$-0.958927\pi$
$151$		−	477.528i		−	0.257355i	0.991686	−	0.128678i	$-0.0410733\pi$
$152$	627.132			0.334652
$153$	2937.48	−	975.813i	1.55216	−	0.515620i
$154$	−3722.44			−1.94781
$155$	2018.62			1.04606
$156$	−901.521	−	650.482i	−0.462689	−	0.333848i
$157$		−	1193.03i		−	0.606460i	−0.952917	−	0.303230i	$-0.901935\pi$
$157$		−	1193.03i		−	0.606460i	0.952917	−	0.303230i	$-0.0980650\pi$
$158$	1349.85			0.679671
$159$	−2108.62	−	1521.45i	−1.05173	−	0.758861i
$160$		−	401.431i		−	0.198349i
$161$	−5479.79			−2.68241
$162$	−1168.19	+	872.406i	−0.566554	+	0.423103i
$163$	−325.353			−0.156341			−0.0781707	−	0.996940i	$-0.524908\pi$
$163$	−325.353			−0.156341			−0.0781707	+	0.996940i	$0.524908\pi$
$164$		−	283.608i		−	0.135037i
$165$	2942.10	+	2122.84i	1.38813	+	1.00159i
$166$	967.179			0.452215
$167$		−	266.183i		−	0.123340i	−0.998097	−	0.0616701i	$-0.980357\pi$
$167$		−	266.183i		−	0.123340i	0.998097	−	0.0616701i	$-0.0196427\pi$
$168$	813.382	−	1127.29i	0.373535	−	0.517692i
$169$	−663.804			−0.302141
$170$	2876.28			1.29765
$171$	−667.259	−	2008.64i	−0.298401	−	0.898272i
$172$		−	1031.92i		−	0.457460i
$173$	−286.319			−0.125829			−0.0629144	−	0.998019i	$-0.520040\pi$
$173$	−286.319			−0.125829			−0.0629144	+	0.998019i	$0.520040\pi$
$174$	641.112	+	462.587i	0.279325	+	0.201544i
$175$	1082.46			0.467578
$176$	890.522			0.381396
$177$	−1421.49	+	1877.40i	−0.603646	+	0.797252i
$178$	140.570			0.0591918
$179$	2828.27			1.18098			0.590489	−	0.807046i	$-0.298935\pi$
$179$	2828.27			1.18098			0.590489	+	0.807046i	$0.298935\pi$
$180$	−1285.74	+	427.116i	−0.532408	+	0.176863i
$181$	746.946			0.306741			0.153370	−	0.988169i	$-0.450987\pi$
$181$	746.946			0.306741			0.153370	+	0.988169i	$0.450987\pi$
$182$		−	3577.23i		−	1.45694i
$183$	139.017	+	100.306i	0.0561555	+	0.0405184i
$184$	1310.93			0.525235
$185$	1042.37			0.414252
$186$	−1356.11	−	978.486i	−0.534596	−	0.385732i
$187$			6380.66i			2.49519i
$188$	−1989.94			−0.771975
$189$	−4476.02	−	1405.76i	−1.72266	−	0.541027i
$190$		−	1966.80i		−	0.750981i
$191$	−769.440			−0.291491			−0.145745	−	0.989322i	$-0.546558\pi$
$191$	−769.440			−0.291491			−0.145745	+	0.989322i	$0.546558\pi$
$192$	−194.586	+	269.682i	−0.0731408	+	0.101368i
$193$	4249.52			1.58491			0.792453	−	0.609933i	$-0.208804\pi$
$193$	4249.52			1.58491			0.792453	+	0.609933i	$0.208804\pi$
$194$			1098.33i			0.406473i
$195$	−2040.03	+	2827.33i	−0.749176	+	1.03830i
$196$	3101.08			1.13013
$197$		−	2929.88i		−	1.05962i	−0.848116	−	0.529810i	$-0.822263\pi$
$197$		−	2929.88i		−	1.05962i	0.848116	−	0.529810i	$-0.177737\pi$
$198$	−947.502	−	2852.25i	−0.340081	−	1.02374i
$199$	1773.01			0.631583			0.315792	−	0.948829i	$-0.397730\pi$
$199$	1773.01			0.631583			0.315792	+	0.948829i	$0.397730\pi$
$200$	−258.957			−0.0915552
$201$	4435.93	+	3200.70i	1.55665	+	1.12318i
$202$	2564.60			0.893291
$203$			2543.93i			0.879551i
$204$	−1932.29	−	1394.22i	−0.663174	−	0.478506i
$205$	−889.445			−0.303032
$206$			2421.88i			0.819129i
$207$	−1394.81	−	4198.79i	−0.468339	−	1.40984i
$208$			855.784i			0.285278i
$209$	4363.08			1.44402
$210$	−3535.38	−	2550.91i	−1.16173	−	0.838236i
$211$			796.189i			0.259772i	0.991529	+	0.129886i	$0.0414611\pi$
$211$			796.189i			0.259772i	−0.991529	+	0.129886i	$0.958539\pi$
$212$			2001.64i			0.648459i
$213$	−1983.65	−	1431.28i	−0.638109	−	0.460420i
$214$		−	1236.18i		−	0.394877i
$215$	−3236.28			−1.02657
$216$	1070.80	+	336.301i	0.337309	+	0.105937i
$217$		−	5381.05i		−	1.68336i
$218$			29.5656i			0.00918549i
$219$	−3843.25	−	2773.05i	−1.18586	−	0.855641i
$220$		−	2792.83i		−	0.855877i
$221$	−6131.76			−1.86637
$222$	−700.267	−	505.269i	−0.211706	−	0.152754i
$223$	4107.19			1.23335			0.616677	−	0.787217i	$-0.288479\pi$
$223$	4107.19			1.23335			0.616677	+	0.787217i	$0.288479\pi$
$224$	−1070.10			−0.319191
$225$	275.527	+	829.414i	0.0816376	+	0.245752i
$226$	−1518.49			−0.446940
$227$	−1090.69			−0.318907			−0.159454	−	0.987205i	$-0.550973\pi$
$227$	−1090.69			−0.318907			−0.159454	+	0.987205i	$0.550973\pi$
$228$	−953.367	+	1321.30i	−0.276922	+	0.383794i
$229$			4974.89i			1.43559i	0.696254	+	0.717795i	$0.254849\pi$
$229$			4974.89i			1.43559i	−0.696254	+	0.717795i	$0.745151\pi$
$230$		−	4111.32i		−	1.17866i
$231$	5658.87	−	7842.78i	1.61180	−	2.23384i
$232$		−	608.586i		−	0.172222i
$233$	−434.162			−0.122072			−0.0610362	−	0.998136i	$-0.519441\pi$
$233$	−434.162			−0.122072			−0.0610362	+	0.998136i	$0.519441\pi$
$234$	2740.99	−	910.541i	0.765744	−	0.254376i
$235$			6240.81i			1.73236i
$236$	1812.27	+	41.7457i	0.499867	+	0.0115145i
$237$	−2052.04	+	2843.98i	−0.562423	+	0.779477i
$238$		−	7667.33i		−	2.08823i
$239$			2563.30i			0.693748i	0.937912	+	0.346874i	$0.112757\pi$
$239$			2563.30i			0.693748i	−0.937912	+	0.346874i	$0.887243\pi$
$240$	845.770	+	610.256i	0.227476	+	0.164133i
$241$	−3436.16			−0.918434			−0.459217	−	0.888324i	$-0.651870\pi$
$241$	−3436.16			−0.918434			−0.459217	+	0.888324i	$0.651870\pi$
$242$	3533.54			0.938615
$243$	−62.1768	−	3787.48i	−0.0164142	−	0.999865i
$244$		−	131.965i		−	0.0346236i
$245$		−	9725.54i		−	2.53609i
$246$	597.531	+	431.141i	0.154867	+	0.111742i
$247$			4192.88i			1.08011i
$248$			1287.31i			0.329614i
$249$	−1470.31	+	2037.74i	−0.374205	+	0.518621i
$250$		−	2324.04i		−	0.587941i
$251$		−	4517.63i		−	1.13606i	−0.823009	−	0.568029i	$-0.807706\pi$
$251$		−	4517.63i		−	1.13606i	0.823009	−	0.568029i	$-0.192294\pi$
$252$	1138.57	+	3427.41i	0.284615	+	0.856773i
$253$	9120.43			2.26639
$254$	−3269.21			−0.807594
$255$	−4372.53	+	6060.01i	−1.07380	+	1.48821i
$256$	256.000			0.0625000
$257$			6867.44i			1.66685i	0.552636	+	0.833423i	$0.313622\pi$
$257$			6867.44i			1.66685i	−0.552636	+	0.833423i	$0.686378\pi$
$258$	2174.14	+	1568.73i	0.524636	+	0.378545i
$259$		−	2778.66i		−	0.666631i
$260$	2683.89			0.640184
$261$	−1949.24	+	647.526i	−0.462279	+	0.153567i
$262$	−2682.07			−0.632438
$263$		−	2.40574i		−	0.000564048i	−1.00000		0.000282024i	$-0.999910\pi$
$263$		−	2.40574i		−	0.000564048i	1.00000		0.000282024i	$-8.97710e-5\pi$
$264$	−1353.77	+	1876.23i	−0.315602	+	0.437402i
$265$	6277.50			1.45518
$266$	−5242.91			−1.20851
$267$	−213.694	+	296.165i	−0.0489808	+	0.0678838i
$268$		−	4210.88i		−	0.959778i
$269$	−827.485			−0.187556			−0.0937781	−	0.995593i	$-0.529894\pi$
$269$	−827.485			−0.187556			−0.0937781	+	0.995593i	$0.529894\pi$
$270$	1054.70	−	3358.22i	0.237730	−	0.756943i
$271$	2974.52			0.666750			0.333375	−	0.942794i	$-0.391812\pi$
$271$	2974.52			0.666750			0.333375	+	0.942794i	$0.391812\pi$
$272$			1834.26i			0.408891i
$273$	7536.84	+	5438.12i	1.67088	+	1.20560i
$274$			5154.04i			1.13638i
$275$	−1801.62			−0.395061
$276$	−1992.88	+	2761.99i	−0.434629	+	0.602364i
$277$	−5038.87			−1.09298			−0.546491	−	0.837465i	$-0.684037\pi$
$277$	−5038.87			−1.09298			−0.546491	+	0.837465i	$0.684037\pi$
$278$	−560.690			−0.120964
$279$	4123.13	−	1369.68i	0.884749	−	0.293909i
$280$			3356.01i			0.716287i
$281$		−	2614.62i		−	0.555073i	−0.960715	−	0.277536i	$-0.910482\pi$
$281$		−	2614.62i		−	0.555073i	0.960715	−	0.277536i	$-0.0895179\pi$
$282$	3025.11	−	4192.59i	0.638804	−	0.885336i
$283$		−	8910.03i		−	1.87154i	−0.352610	−	0.935770i	$-0.614706\pi$
$283$		−	8910.03i		−	1.87154i	0.352610	−	0.935770i	$-0.385294\pi$
$284$			1883.01i			0.393437i
$285$	4143.82	+	2989.93i	0.861259	+	0.621432i
$286$			5953.86i			1.23098i
$287$			2371.00i			0.487651i
$288$	−272.380	−	819.942i	−0.0557297	−	0.167762i
$289$	−8229.63			−1.67507
$290$	−1908.63			−0.386478
$291$	−2314.07	−	1669.69i	−0.466162	−	0.336354i
$292$			3648.26i			0.731159i
$293$		−	1455.27i		−	0.290162i	−0.989420	−	0.145081i	$-0.953656\pi$
$293$		−	1455.27i		−	0.290162i	0.989420	−	0.145081i	$-0.0463443\pi$
$294$	−4714.27	+	6533.63i	−0.935176	+	1.29609i
$295$	130.922	−	5683.60i	0.0258392	−	1.12174i
$296$			664.740i			0.130531i
$297$	7449.78	+	2339.72i	1.45549	+	0.457118i
$298$	−4856.58			−0.944075
$299$			8764.65i			1.69523i
$300$	393.667	−	545.595i	0.0757613	−	0.105000i
$301$			8626.99i			1.65200i
$302$		−	955.056i		−	0.181978i
$303$	−3898.71	+	5403.33i	−0.739192	+	1.02447i
$304$	1254.26			0.236635
$305$	−413.864			−0.0776977
$306$	5874.95	−	1951.63i	1.09754	−	0.364598i
$307$	4945.35			0.919369			0.459684	−	0.888082i	$-0.347963\pi$
$307$	4945.35			0.919369			0.459684	+	0.888082i	$0.347963\pi$
$308$	−7444.89			−1.37731
$309$	−5102.64	−	3681.75i	−0.939414	−	0.677824i
$310$	4037.23			0.739676
$311$		−	6782.57i		−	1.23667i	−0.785915	−	0.618335i	$-0.787808\pi$
$311$		−	6782.57i		−	1.23667i	0.785915	−	0.618335i	$-0.212192\pi$
$312$	−1803.04	−	1300.96i	−0.327170	−	0.236066i
$313$		−	10189.2i		−	1.84002i	−0.391891	−	0.920012i	$-0.628179\pi$
$313$		−	10189.2i		−	1.84002i	0.391891	−	0.920012i	$-0.371821\pi$
$314$		−	2386.06i		−	0.428832i
$315$	10749.0	−	3570.75i	1.92265	−	0.638695i
$316$	2699.69			0.480600
$317$			7339.51i			1.30040i	0.759762	+	0.650202i	$0.225316\pi$
$317$			7339.51i			1.30040i	−0.759762	+	0.650202i	$0.774684\pi$
$318$	−4217.24	−	3042.90i	−0.743683	−	0.536596i
$319$		−	4234.06i		−	0.743140i
$320$		−	802.861i		−	0.140254i
$321$	2604.50	+	1879.25i	0.452863	+	0.326758i
$322$	−10959.6			−1.89675
$323$			8986.90i			1.54813i
$324$	−2336.38	+	1744.81i	−0.400614	+	0.299179i
$325$		−	1731.34i		−	0.295500i
$326$	−650.707			−0.110550
$327$	−62.2915	−	44.9457i	−0.0105343	−	0.00760093i
$328$		−	567.216i		−	0.0954855i
$329$	16636.2			2.78779
$330$	5884.20	+	4245.67i	0.981558	+	0.708232i
$331$	−1887.25			−0.313391			−0.156696	−	0.987647i	$-0.550084\pi$
$331$	−1887.25			−0.313391			−0.156696	+	0.987647i	$0.550084\pi$
$332$	1934.36			0.319764
$333$	2129.09	−	707.273i	0.350371	−	0.116391i
$334$		−	532.365i		−	0.0872147i
$335$	−13206.1			−2.15380
$336$	1626.76	−	2254.58i	0.264129	−	0.366063i
$337$			2949.58i			0.476778i	0.971170	+	0.238389i	$0.0766193\pi$
$337$			2949.58i			0.476778i	−0.971170	+	0.238389i	$0.923381\pi$
$338$	−1327.61			−0.213646
$339$	2308.41	−	3199.29i	0.369840	−	0.512571i
$340$	5752.57			0.917578
$341$			8956.08i			1.42228i
$342$	−1334.52	−	4017.28i	−0.211001	−	0.635174i
$343$	−14455.3			−2.27556
$344$		−	2063.84i		−	0.323473i
$345$	8662.10	+	6250.04i	1.35174	+	0.975335i
$346$	−572.637			−0.0889744
$347$	4174.20			0.645771			0.322886	−	0.946438i	$-0.395347\pi$
$347$	4174.20			0.645771			0.322886	+	0.946438i	$0.395347\pi$
$348$	1282.22	+	925.173i	0.197513	+	0.142513i
$349$			5532.72i			0.848595i	0.905523	+	0.424297i	$0.139479\pi$
$349$			5532.72i			0.848595i	−0.905523	+	0.424297i	$0.860521\pi$
$350$	2164.92			0.330628
$351$	−2248.45	+	7159.17i	−0.341918	+	1.08868i
$352$	1781.04			0.269687
$353$	−1343.96			−0.202640			−0.101320	−	0.994854i	$-0.532307\pi$
$353$	−1343.96			−0.202640			−0.101320	+	0.994854i	$0.532307\pi$
$354$	−2842.97	+	3754.79i	−0.426842	+	0.563743i
$355$	5905.45			0.882897
$356$	281.139			0.0418549
$357$	16154.2	+	11655.9i	2.39488	+	1.72800i
$358$	5656.54			0.835077
$359$			1042.10i			0.153204i	0.997062	+	0.0766019i	$0.0244071\pi$
$359$			1042.10i			0.153204i	−0.997062	+	0.0766019i	$0.975593\pi$
$360$	−2571.48	+	854.232i	−0.376470	+	0.125061i
$361$	−713.780			−0.104065
$362$	1493.89			0.216898
$363$	−5371.70	+	7444.79i	−0.776698	+	1.07645i
$364$		−	7154.47i		−	1.03021i
$365$	11441.6			1.64077
$366$	278.035	+	200.613i	0.0397079	+	0.0286508i
$367$		−	3839.73i		−	0.546137i	−0.961995	−	0.273069i	$-0.911961\pi$
$367$		−	3839.73i		−	0.546137i	0.961995	−	0.273069i	$-0.0880386\pi$
$368$	2621.87			0.371397
$369$	−1816.73	+	603.509i	−0.256302	+	0.0851421i
$370$	2084.74			0.292920
$371$		−	16734.0i		−	2.34174i
$372$	−2712.22	−	1956.97i	−0.378016	−	0.272753i
$373$	−4156.50			−0.576985			−0.288492	−	0.957482i	$-0.593154\pi$
$373$	−4156.50			−0.576985			−0.288492	+	0.957482i	$0.593154\pi$
$374$			12761.3i			1.76436i
$375$	4896.50	+	3533.01i	0.674278	+	0.486517i
$376$	−3979.88			−0.545869
$377$	4068.89			0.555858
$378$	−8952.04	−	2811.52i	−1.21810	−	0.382564i
$379$	4195.10			0.568570			0.284285	−	0.958740i	$-0.408244\pi$
$379$	4195.10			0.568570			0.284285	+	0.958740i	$0.408244\pi$
$380$		−	3933.59i		−	0.531024i
$381$	4969.87	−	6887.87i	0.668278	−	0.926185i
$382$	−1538.88			−0.206115
$383$			7774.39i			1.03721i	0.855013	+	0.518607i	$0.173549\pi$
$383$			7774.39i			1.03721i	−0.855013	+	0.518607i	$0.826451\pi$
$384$	−389.172	+	539.364i	−0.0517183	+	0.0716779i
$385$			23348.5i			3.09078i
$386$	8499.03			1.12070
$387$	−6610.27	+	2195.89i	−0.868266	+	0.288433i
$388$			2196.67i			0.287420i
$389$			4113.36i			0.536133i	0.963400	+	0.268066i	$0.0863846\pi$
$389$			4113.36i			0.536133i	−0.963400	+	0.268066i	$0.913615\pi$
$390$	−4080.05	+	5654.66i	−0.529748	+	0.734192i
$391$			18785.9i			2.42978i
$392$	6202.16			0.799124
$393$	4077.29	−	5650.83i	0.523338	−	0.725309i
$394$		−	5859.76i		−	0.749265i
$395$		−	8466.71i		−	1.07850i
$396$	−1895.00	−	5704.50i	−0.240474	−	0.723894i
$397$			856.145i			0.108233i	0.998535	+	0.0541167i	$0.0172343\pi$
$397$			856.145i			0.108233i	−0.998535	+	0.0541167i	$0.982766\pi$
$398$	3546.01			0.446597
$399$	7970.28	−	11046.2i	1.00003	−	1.38597i
$400$	−517.915			−0.0647393
$401$	−7604.09			−0.946958			−0.473479	−	0.880805i	$-0.657002\pi$
$401$	−7604.09			−0.946958			−0.473479	+	0.880805i	$0.657002\pi$
$402$	8871.86	+	6401.39i	1.10072	+	0.794210i
$403$	−8606.71			−1.06385
$404$	5129.20			0.631652
$405$	5472.04	+	7327.31i	0.671377	+	0.899005i
$406$			5087.86i			0.621937i
$407$			4624.73i			0.563242i
$408$	−3864.59	−	2788.45i	−0.468935	−	0.338355i
$409$		−	8859.06i		−	1.07103i	−0.844525	−	0.535516i	$-0.820117\pi$
$409$		−	8859.06i		−	1.07103i	0.844525	−	0.535516i	$-0.179883\pi$
$410$	−1778.89			−0.214276
$411$	−10859.0	−	7835.19i	−1.30325	−	0.940344i
$412$			4843.77i			0.579212i
$413$	−15150.8	−	349.000i	−1.80514	−	0.0415815i
$414$	−2789.63	−	8397.58i	−0.331166	−	0.996904i
$415$		−	6066.49i		−	0.717572i
$416$			1711.57i			0.201722i
$417$	852.362	−	1181.31i	0.100097	−	0.138727i
$418$	8726.17			1.02108
$419$	5885.62			0.686232			0.343116	−	0.939293i	$-0.388518\pi$
$419$	5885.62			0.686232			0.343116	+	0.939293i	$0.388518\pi$
$420$	−7070.75	−	5101.82i	−0.821470	−	0.592722i
$421$		−	9980.94i		−	1.15544i	−0.816234	−	0.577721i	$-0.803942\pi$
$421$		−	9980.94i		−	1.15544i	0.816234	−	0.577721i	$-0.196058\pi$
$422$			1592.38i			0.183687i
$423$	4234.53	+	12747.2i	0.486738	+	1.46522i
$424$			4003.28i			0.458530i
$425$		−	3710.90i		−	0.423541i
$426$	−3967.29	−	2862.55i	−0.451211	−	0.325566i
$427$			1103.24i			0.125034i
$428$		−	2472.36i		−	0.279220i
$429$	−12544.1	−	9051.07i	−1.41174	−	1.01862i
$430$	−6472.56			−0.725895
$431$	−9150.70			−1.02268			−0.511339	−	0.859379i	$-0.670850\pi$
$431$	−9150.70			−1.02268			−0.511339	+	0.859379i	$0.670850\pi$
$432$	2141.60	+	672.603i	0.238513	+	0.0749088i
$433$	−7782.99			−0.863803			−0.431902	−	0.901921i	$-0.642157\pi$
$433$	−7782.99			−0.863803			−0.431902	+	0.901921i	$0.642157\pi$
$434$		−	10762.1i		−	1.19032i
$435$	2901.51	−	4021.28i	0.319808	−	0.443231i
$436$			59.1312i			0.00649512i
$437$	12845.7			1.40617
$438$	−7686.49	−	5546.10i	−0.838527	−	0.605030i
$439$	−6307.27			−0.685717			−0.342858	−	0.939387i	$-0.611395\pi$
$439$	−6307.27			−0.685717			−0.342858	+	0.939387i	$0.611395\pi$
$440$		−	5585.67i		−	0.605196i
$441$	−6599.01	−	19864.9i	−0.712559	−	2.14501i
$442$	−12263.5			−1.31972
$443$	2388.29			0.256142			0.128071	−	0.991765i	$-0.459121\pi$
$443$	2388.29			0.256142			0.128071	+	0.991765i	$0.459121\pi$
$444$	−1400.53	−	1010.54i	−0.149699	−	0.108014i
$445$		−	881.702i		−	0.0939251i
$446$	8214.38			0.872112
$447$	7382.99	−	10232.3i	0.781216	−	1.08271i
$448$	−2140.19			−0.225702
$449$		−	804.443i		−	0.0845523i	−0.999106	−	0.0422762i	$-0.986539\pi$
$449$		−	804.443i		−	0.0845523i	0.999106	−	0.0422762i	$-0.0134609\pi$
$450$	551.053	+	1658.83i	0.0577265	+	0.173773i
$451$		−	3946.24i		−	0.412020i
$452$	−3036.98			−0.316034
$453$	2012.20	+	1451.88i	0.208700	+	0.150585i
$454$	−2181.39			−0.225501
$455$	−22437.7			−2.31186
$456$	−1906.73	+	2642.59i	−0.195814	+	0.271383i
$457$		−	7628.94i		−	0.780890i	−0.920626	−	0.390445i	$-0.872321\pi$
$457$		−	7628.94i		−	0.780890i	0.920626	−	0.390445i	$-0.127679\pi$
$458$			9949.79i			1.01512i
$459$	−4819.25	+	15344.7i	−0.490073	+	1.56042i
$460$		−	8222.64i		−	0.833440i
$461$		−	1278.14i		−	0.129130i	−0.997913	−	0.0645651i	$-0.979434\pi$
$461$		−	1278.14i		−	0.129130i	0.997913	−	0.0645651i	$-0.0205660\pi$
$462$	11317.7	−	15685.6i	1.13972	−	1.57956i
$463$		−	7402.48i		−	0.743029i	−0.928427	−	0.371514i	$-0.878839\pi$
$463$		−	7402.48i		−	0.743029i	0.928427	−	0.371514i	$-0.121161\pi$
$464$		−	1217.17i		−	0.121780i
$465$	−6137.41	+	8506.01i	−0.612077	+	0.848294i
$466$	−868.323			−0.0863182
$467$	−12702.0			−1.25862			−0.629312	−	0.777153i	$-0.716663\pi$
$467$	−12702.0			−1.25862			−0.629312	+	0.777153i	$0.716663\pi$
$468$	5481.98	−	1821.08i	0.541463	−	0.179871i
$469$			35203.5i			3.46599i
$470$			12481.6i			1.22497i
$471$	5027.17	+	3627.29i	0.491804	+	0.354855i
$472$	3624.54	+	83.4915i	0.353460	+	0.00814197i
$473$		−	14358.6i		−	1.39579i
$474$	−4104.08	+	5687.95i	−0.397693	+	0.551174i
$475$	−2537.50			−0.245113
$476$		−	15334.7i		−	1.47660i
$477$	12822.1	−	4259.44i	1.23078	−	0.408860i
$478$			5126.59i			0.490554i
$479$		−	2126.89i		−	0.202881i	−0.994842	−	0.101441i	$-0.967655\pi$
$479$		−	2126.89i		−	0.202881i	0.994842	−	0.101441i	$-0.0323452\pi$
$480$	1691.54	+	1220.51i	0.160850	+	0.116059i
$481$	−4444.32			−0.421297
$482$	−6872.32			−0.649431
$483$	16660.8	−	23090.6i	1.56955	−	2.17528i
$484$	7067.09			0.663701
$485$	6889.14			0.644989
$486$	−124.354	−	7574.97i	−0.0116066	−	0.707012i
$487$	−15234.4			−1.41753			−0.708764	−	0.705446i	$-0.750747\pi$
$487$	−15234.4			−1.41753			−0.708764	+	0.705446i	$0.750747\pi$
$488$		−	263.929i		−	0.0244826i
$489$	989.206	−	1370.97i	0.0914794	−	0.126784i
$490$		−	19451.1i		−	1.79329i
$491$			1651.33i			0.151779i	0.997116	+	0.0758895i	$0.0241796\pi$
$491$			1651.33i			0.151779i	−0.997116	+	0.0758895i	$0.975820\pi$
$492$	1195.06	+	862.283i	0.109507	+	0.0790136i
$493$	8721.13			0.796714
$494$			8385.77i			0.763752i
$495$	−17890.3	+	5943.07i	−1.62447	+	0.539639i
$496$			2574.62i			0.233072i
$497$		−	15742.2i		−	1.42079i
$498$	−2940.62	+	4075.48i	−0.264603	+	0.366720i
$499$	4317.55			0.387335			0.193667	−	0.981067i	$-0.437962\pi$
$499$	4317.55			0.387335			0.193667	+	0.981067i	$0.437962\pi$
$500$		−	4648.08i		−	0.415737i
$501$	1121.63	+	809.303i	0.100022	+	0.0721696i
$502$		−	9035.27i		−	0.803314i
$503$	−8677.03			−0.769164			−0.384582	−	0.923091i	$-0.625654\pi$
$503$	−8677.03			−0.769164			−0.384582	+	0.923091i	$0.625654\pi$
$504$	2277.14	+	6854.83i	0.201253	+	0.605830i
$505$		−	16086.1i		−	1.41747i
$506$	18240.9			1.60258
$507$	2018.23	−	2797.12i	0.176791	−	0.245019i
$508$	−6538.43			−0.571055
$509$	−12695.8			−1.10557			−0.552783	−	0.833325i	$-0.686434\pi$
$509$	−12695.8			−1.10557			−0.552783	+	0.833325i	$0.686434\pi$
$510$	−8745.06	+	12120.0i	−0.759290	+	1.05232i
$511$		−	30500.0i		−	2.64039i
$512$	512.000			0.0441942
$513$	10492.7	+	3295.39i	0.903049	+	0.283616i
$514$			13734.9i			1.17864i
$515$	15190.9			1.29979
$516$	4348.28	+	3137.45i	0.370974	+	0.267672i
$517$	−27688.8			−2.35542
$518$		−	5557.31i		−	0.471379i
$519$	870.524	−	1206.48i	0.0736258	−	0.102040i
$520$	5367.78			0.452678
$521$			12284.8i			1.03303i	0.856279	+	0.516513i	$0.172770\pi$
$521$			12284.8i			1.03303i	−0.856279	+	0.516513i	$0.827230\pi$
$522$	−3898.48	+	1295.05i	−0.326881	+	0.108588i
$523$	17854.6			1.49279			0.746395	−	0.665503i	$-0.231783\pi$
$523$	17854.6			1.49279			0.746395	+	0.665503i	$0.231783\pi$
$524$	−5364.14			−0.447201
$525$	−3291.11	+	4561.24i	−0.273592	+	0.379179i
$526$		−	4.81149i		−	0.000398842i
$527$	−18447.4			−1.52482
$528$	−2707.55	+	3752.46i	−0.223165	+	0.309290i
$529$	14685.3			1.20698
$530$	12555.0			1.02897
$531$	−3589.04	−	11697.9i	−0.293317	−	0.956015i
$532$	−10485.8			−0.854544
$533$	3792.30			0.308185
$534$	−427.388	+	592.329i	−0.0346347	+	0.0480011i
$535$	−7753.77			−0.626588
$536$		−	8421.76i		−	0.678666i
$537$	−8599.09	+	11917.7i	−0.691021	+	0.957704i
$538$	−1654.97			−0.132622
$539$	43149.7			3.44822
$540$	2109.40	−	6716.44i	0.168100	−	0.535240i
$541$		−	6201.21i		−	0.492811i	−0.969167	−	0.246405i	$-0.920751\pi$
$541$		−	6201.21i		−	0.492811i	0.969167	−	0.246405i	$-0.0792495\pi$
$542$	5949.04			0.471463
$543$	−2271.02	+	3147.47i	−0.179482	+	0.248749i
$544$			3668.52i			0.289130i
$545$	185.446			0.0145755
$546$	15073.7	+	10876.2i	1.18149	+	0.852491i
$547$	17428.0			1.36228			0.681142	−	0.732151i	$-0.261484\pi$
$547$	17428.0			1.36228			0.681142	+	0.732151i	$0.261484\pi$
$548$			10308.1i			0.803540i
$549$	−845.338	+	280.817i	−0.0657161	+	0.0218305i
$550$	−3603.24			−0.279350
$551$		−	5963.49i		−	0.461077i
$552$	−3985.77	+	5523.99i	−0.307329	+	0.425936i
$553$	−22569.8			−1.73556
$554$	−10077.7			−0.772856
$555$	−3169.23	+	4392.32i	−0.242390	+	0.335934i
$556$	−1121.38			−0.0855344
$557$			5117.71i			0.389308i	0.980872	+	0.194654i	$0.0623584\pi$
$557$			5117.71i			0.389308i	−0.980872	+	0.194654i	$0.937642\pi$
$558$	8246.25	−	2739.36i	0.625612	−	0.207825i
$559$	13798.4			1.04403
$560$			6712.03i			0.506491i
$561$	−26886.7	−	19399.8i	−2.02345	−	1.46000i
$562$		−	5229.25i		−	0.392496i
$563$	−5851.37			−0.438021			−0.219010	−	0.975723i	$-0.570283\pi$
$563$	−5851.37			−0.438021			−0.219010	+	0.975723i	$0.570283\pi$
$564$	6050.22	−	8385.17i	0.451703	−	0.626027i
$565$			9524.50i			0.709201i
$566$		−	17820.1i		−	1.32338i
$567$	19532.5	−	14586.9i	1.44671	−	1.08041i
$568$			3766.02i			0.278202i
$569$	19207.5			1.41515			0.707576	−	0.706637i	$-0.249789\pi$
$569$	19207.5			1.41515			0.707576	+	0.706637i	$0.249789\pi$
$570$	8287.64	+	5979.85i	0.609002	+	0.439418i
$571$		−	449.899i		−	0.0329732i	−0.999864	−	0.0164866i	$-0.994752\pi$
$571$		−	449.899i		−	0.0329732i	0.999864	−	0.0164866i	$-0.00524808\pi$
$572$			11907.7i			0.870432i
$573$	2339.41	−	3242.25i	0.170559	−	0.236382i
$574$			4742.00i			0.344821i
$575$	−5304.31			−0.384704
$576$	−544.760	−	1639.88i	−0.0394069	−	0.118626i
$577$	−4649.13			−0.335435			−0.167717	−	0.985835i	$-0.553640\pi$
$577$	−4649.13			−0.335435			−0.167717	+	0.985835i	$0.553640\pi$
$578$	−16459.3			−1.18445
$579$	−12920.2	+	17906.5i	−0.927370	+	1.28527i
$580$	−3817.26			−0.273282
$581$	−16171.5			−1.15475
$582$	−4628.14	−	3339.38i	−0.329626	−	0.237838i
$583$			27851.7i			1.97856i
$584$			7296.53i			0.517008i
$585$	−5711.24	−	17192.4i	−0.403642	−	1.21508i
$586$		−	2910.53i		−	0.205176i
$587$	13192.8			0.927641			0.463820	−	0.885929i	$-0.346478\pi$
$587$	13192.8			0.927641			0.463820	+	0.885929i	$0.346478\pi$
$588$	−9428.54	+	13067.3i	−0.661269	+	0.916471i
$589$			12614.3i			0.882448i
$590$	261.844	−	11367.2i	0.0182711	−	0.793186i
$591$	12345.9	+	8908.02i	0.859291	+	0.620012i
$592$			1329.48i			0.0922994i
$593$		−	9442.45i		−	0.653887i	−0.945044	−	0.326944i	$-0.893981\pi$
$593$		−	9442.45i		−	0.653887i	0.945044	−	0.326944i	$-0.106019\pi$
$594$	14899.6	+	4679.43i	1.02919	+	0.323231i
$595$	−48092.2			−3.31360
$596$	−9713.17			−0.667562
$597$	−5390.66	+	7471.06i	−0.369556	+	0.512178i
$598$			17529.3i			1.19871i
$599$			2266.84i			0.154625i	0.997007	+	0.0773127i	$0.0246340\pi$
$599$			2266.84i			0.154625i	−0.997007	+	0.0773127i	$0.975366\pi$
$600$	787.335	−	1091.19i	0.0535714	−	0.0742460i
$601$		−	28113.0i		−	1.90807i	−0.299689	−	0.954037i	$-0.596883\pi$
$601$		−	28113.0i		−	1.90807i	0.299689	−	0.954037i	$-0.403117\pi$
$602$			17254.0i			1.16814i
$603$	−26974.1	+	8960.63i	−1.82167	+	0.605149i
$604$		−	1910.11i		−	0.128678i
$605$		−	22163.6i		−	1.48939i
$606$	−7797.42	+	10806.7i	−0.522688	+	0.724407i
$607$	−22442.7			−1.50069			−0.750345	−	0.661046i	$-0.770113\pi$
$607$	−22442.7			−1.50069			−0.750345	+	0.661046i	$0.770113\pi$
$608$	2508.53			0.167326
$609$	−10719.6	−	7734.58i	−0.713265	−	0.514648i
$610$	−827.728			−0.0549405
$611$		−	26608.7i		−	1.76182i
$612$	11749.9	−	3903.25i	0.776081	−	0.257810i
$613$		−	22313.5i		−	1.47020i	−0.677958	−	0.735100i	$-0.737135\pi$
$613$		−	22313.5i		−	1.47020i	0.677958	−	0.735100i	$-0.262865\pi$
$614$	9890.70			0.650092
$615$	2704.27	−	3747.92i	0.177312	−	0.245741i
$616$	−14889.8			−0.973906
$617$			13469.4i			0.878861i	0.898277	+	0.439431i	$0.144820\pi$
$617$			13469.4i			0.878861i	−0.898277	+	0.439431i	$0.855180\pi$
$618$	−10205.3	−	7363.50i	−0.664266	−	0.479294i
$619$	2388.74			0.155108			0.0775538	−	0.996988i	$-0.475289\pi$
$619$	2388.74			0.155108			0.0775538	+	0.996988i	$0.475289\pi$
$620$	8074.47			0.523030
$621$	21933.6	+	6888.57i	1.41733	+	0.445135i
$622$		−	13565.1i		−	0.874457i
$623$	−2350.36			−0.151148
$624$	−3606.08	−	2601.93i	−0.231344	−	0.166924i
$625$	−18623.4			−1.19190
$626$		−	20378.4i		−	1.30109i
$627$	−13265.5	+	18385.1i	−0.844935	+	1.17102i
$628$		−	4772.12i		−	0.303230i
$629$	−9525.83			−0.603847
$630$	21498.0	−	7141.50i	1.35952	−	0.451626i
$631$	−17418.9			−1.09895			−0.549474	−	0.835511i	$-0.685172\pi$
$631$	−17418.9			−1.09895			−0.549474	+	0.835511i	$0.685172\pi$
$632$	5399.38			0.339835
$633$	−3354.96	−	2420.74i	−0.210660	−	0.151999i
$634$			14679.0i			0.919524i
$635$			20505.7i			1.28148i
$636$	−8434.48	−	6085.80i	−0.525863	−	0.379430i
$637$			41466.5i			2.57922i
$638$		−	8468.11i		−	0.525479i
$639$	12062.2	−	4006.99i	0.746748	−	0.248066i
$640$		−	1605.72i		−	0.0991746i
$641$			21873.3i			1.34780i	0.738821	+	0.673902i	$0.235383\pi$
$641$			21873.3i			1.34780i	−0.738821	+	0.673902i	$0.764617\pi$
$642$	5209.00	+	3758.49i	0.320222	+	0.231053i
$643$	19302.9			1.18388			0.591939	−	0.805983i	$-0.298363\pi$
$643$	19302.9			1.18388			0.591939	+	0.805983i	$0.298363\pi$
$644$	−21919.2			−1.34121
$645$	9839.61	−	13637.0i	0.600673	−	0.832489i
$646$			17973.8i			1.09469i
$647$			5086.48i			0.309073i	0.987987	+	0.154537i	$0.0493884\pi$
$647$			5086.48i			0.309073i	−0.987987	+	0.154537i	$0.950612\pi$
$648$	−4672.77	+	3489.63i	−0.283277	+	0.211552i
$649$	25216.7	+	580.867i	1.52518	+	0.0351326i
$650$		−	3462.68i		−	0.208950i
$651$	22674.5	+	16360.6i	1.36511	+	0.984978i
$652$	−1301.41			−0.0781707
$653$		−	8037.99i		−	0.481701i	−0.970562	−	0.240851i	$-0.922574\pi$
$653$		−	8037.99i		−	0.481701i	0.970562	−	0.240851i	$-0.0774264\pi$
$654$	−124.583	−	89.8914i	−0.00744890	−	0.00537467i
$655$			16822.9i			1.00355i
$656$		−	1134.43i		−	0.0675185i
$657$	23370.0	−	7763.40i	1.38775	−	0.461003i
$658$	33272.3			1.97126
$659$	10316.1			0.609798			0.304899	−	0.952385i	$-0.401377\pi$
$659$	10316.1			0.609798			0.304899	+	0.952385i	$0.401377\pi$
$660$	11768.4	+	8491.35i	0.694067	+	0.500796i
$661$	18597.1			1.09432			0.547160	−	0.837028i	$-0.315709\pi$
$661$	18597.1			1.09432			0.547160	+	0.837028i	$0.315709\pi$
$662$	−3774.50			−0.221601
$663$	18643.0	−	25837.9i	1.09206	−	1.51351i
$664$	3868.72			0.226107
$665$			32885.4i			1.91765i
$666$	4258.19	−	1414.55i	0.247750	−	0.0823011i
$667$		−	12465.9i		−	0.723659i
$668$		−	1064.73i		−	0.0616701i
$669$	−12487.5	+	17306.8i	−0.721667	+	1.00018i
$670$	−26412.1			−1.52297
$671$		−	1836.21i		−	0.105642i
$672$	3253.53	−	4509.16i	0.186767	−	0.258846i
$673$			8336.73i			0.477500i	0.971081	+	0.238750i	$0.0767376\pi$
$673$			8336.73i			0.477500i	−0.971081	+	0.238750i	$0.923262\pi$
$674$			5899.17i			0.337133i
$675$	−4332.68	−	1360.74i	−0.247059	−	0.0775927i
$676$	−2655.22			−0.151071
$677$		−	324.448i		−	0.0184188i	−0.999958	−	0.00920942i	$-0.997069\pi$
$677$		−	324.448i		−	0.0184188i	0.999958	−	0.00920942i	$-0.00293149\pi$
$678$	4616.82	−	6398.58i	0.261516	−	0.362442i
$679$		−	18364.4i		−	1.03794i
$680$	11505.1			0.648826
$681$	3316.15	−	4595.95i	0.186601	−	0.258615i
$682$			17912.2i			1.00571i
$683$	21486.8			1.20376			0.601882	−	0.798585i	$-0.294418\pi$
$683$	21486.8			1.20376			0.601882	+	0.798585i	$0.294418\pi$
$684$	−2669.04	−	8034.56i	−0.149200	−	0.449136i
$685$	32328.0			1.80320
$686$	−28910.7			−1.60906
$687$	−20963.1	−	15125.7i	−1.16418	−	0.840002i
$688$		−	4127.68i		−	0.228730i
$689$	−26765.2			−1.47993
$690$	17324.2	+	12500.1i	0.955827	+	0.689666i
$691$		−	23522.7i		−	1.29500i	−0.762064	−	0.647501i	$-0.775814\pi$
$691$		−	23522.7i		−	1.29500i	0.762064	−	0.647501i	$-0.224186\pi$
$692$	−1145.27			−0.0629144
$693$	15842.5	+	47690.4i	0.868408	+	2.61416i
$694$	8348.39			0.456629
$695$			3516.85i			0.191945i
$696$	2564.45	+	1850.35i	0.139662	+	0.100772i
$697$	8128.29			0.441723
$698$			11065.4i			0.600047i
$699$	1320.03	−	1829.46i	0.0714278	−	0.0989937i
$700$	4329.84			0.233789
$701$	4275.19			0.230345			0.115172	−	0.993346i	$-0.463258\pi$
$701$	4275.19			0.230345			0.115172	+	0.993346i	$0.463258\pi$
$702$	−4496.89	+	14318.3i	−0.241773	+	0.769816i
$703$			6513.74i			0.349460i
$704$	3562.09			0.190698
$705$	−26297.4	−	18974.6i	−1.40485	−	1.01365i
$706$	−2687.92			−0.143288
$707$	−42880.8			−2.28105
$708$	−5685.94	+	7509.58i	−0.301823	+	0.398626i
$709$	−3259.59			−0.172661			−0.0863305	−	0.996267i	$-0.527514\pi$
$709$	−3259.59			−0.172661			−0.0863305	+	0.996267i	$0.527514\pi$
$710$	11810.9			0.624303
$711$	−5744.86	−	17293.7i	−0.303023	−	0.912185i
$712$	562.278			0.0295959
$713$			26368.4i			1.38500i
$714$	32308.5	+	23311.8i	1.69344	+	1.22188i
$715$	37344.7			1.95331
$716$	11313.1			0.590489
$717$	−10801.2	−	7793.45i	−0.562590	−	0.405930i
$718$			2084.21i			0.108332i
$719$	−14322.0			−0.742865			−0.371433	−	0.928460i	$-0.621133\pi$
$719$	−14322.0			−0.742865			−0.371433	+	0.928460i	$0.621133\pi$
$720$	−5142.97	+	1708.46i	−0.266204	+	0.0884316i
$721$		−	40494.5i		−	2.09167i
$722$	−1427.56			−0.0735848
$723$	10447.3	−	14479.2i	0.537400	−	0.744797i
$724$	2987.78			0.153370
$725$			2462.46i			0.126143i
$726$	−10743.4	+	14889.6i	−0.549208	+	0.761163i
$727$	27243.3			1.38982			0.694909	−	0.719098i	$-0.255445\pi$
$727$	27243.3			1.38982			0.694909	+	0.719098i	$0.255445\pi$
$728$		−	14308.9i		−	0.728468i
$729$	16148.7	+	11253.5i	0.820437	+	0.571736i
$730$	22883.2			1.16020
$731$	29575.1			1.49641
$732$	556.070	+	401.226i	0.0280778	+	0.0202592i
$733$	20545.8			1.03530			0.517652	−	0.855591i	$-0.326806\pi$
$733$	20545.8			1.03530			0.517652	+	0.855591i	$0.326806\pi$
$734$		−	7679.47i		−	0.386178i
$735$	40981.3	+	29569.6i	2.05662	+	1.48393i
$736$	5243.73			0.262618
$737$		−	58591.9i		−	2.92844i
$738$	−3633.47	+	1207.02i	−0.181233	+	0.0602046i
$739$			3615.91i			0.179991i	0.995942	+	0.0899956i	$0.0286853\pi$
$739$			3615.91i			0.179991i	−0.995942	+	0.0899956i	$0.971315\pi$
$740$	4169.48			0.207126
$741$	−17667.9	−	12748.1i	−0.875906	−	0.632000i
$742$		−	33468.0i		−	1.65586i
$743$		−	36180.7i		−	1.78646i	−0.449600	−	0.893230i	$-0.648434\pi$
$743$		−	36180.7i		−	1.78646i	0.449600	−	0.893230i	$-0.351566\pi$
$744$	−5424.44	−	3913.94i	−0.267298	−	0.192866i
$745$			30462.2i			1.49805i
$746$	−8313.00			−0.407990
$747$	−4116.26	−	12391.1i	−0.201614	−	0.606917i
$748$			25522.7i			1.24759i
$749$			20669.3i			1.00833i
$750$	9793.00	+	7066.02i	0.476786	+	0.344020i
$751$		−	13254.4i		−	0.644019i	−0.946736	−	0.322009i	$-0.895642\pi$
$751$		−	13254.4i		−	0.644019i	0.946736	−	0.322009i	$-0.104358\pi$
$752$	−7959.76			−0.385988
$753$	19036.3	+	13735.4i	0.921277	+	0.664737i
$754$	8137.78			0.393051
$755$	−5990.45			−0.288761
$756$	−17904.1	−	5623.05i	−0.861329	−	0.270514i
$757$	−19347.1			−0.928904			−0.464452	−	0.885598i	$-0.653749\pi$
$757$	−19347.1			−0.928904			−0.464452	+	0.885598i	$0.653749\pi$
$758$	8390.20			0.402039
$759$	−27729.8	+	38431.5i	−1.32612	+	1.83791i
$760$		−	7867.18i		−	0.375490i
$761$		−	24236.4i		−	1.15449i	−0.816570	−	0.577247i	$-0.804127\pi$
$761$		−	24236.4i		−	1.15449i	0.816570	−	0.577247i	$-0.195873\pi$
$762$	9939.73	−	13775.7i	0.472544	−	0.654912i
$763$		−	494.345i		−	0.0234554i
$764$	−3077.76			−0.145745
$765$	−12241.3	−	36849.8i	−0.578542	−	1.74158i
$766$			15548.8i			0.733421i
$767$	−558.208	+	24233.0i	−0.0262787	+	1.14081i
$768$	−778.344	+	1078.73i	−0.0365704	+	0.0506839i
$769$		−	23437.6i		−	1.09907i	−0.835472	−	0.549533i	$-0.814805\pi$
$769$		−	23437.6i		−	1.09907i	0.835472	−	0.549533i	$-0.185195\pi$
$770$			46697.0i			2.18551i
$771$	−28937.9	−	20879.8i	−1.35172	−	0.975315i
$772$	16998.1			0.792453
$773$	2034.21			0.0946514			0.0473257	−	0.998880i	$-0.484930\pi$
$773$	2034.21			0.0946514			0.0473257	+	0.998880i	$0.484930\pi$
$774$	−13220.5	+	4391.79i	−0.613957	+	0.203953i
$775$		−	5208.73i		−	0.241423i
$776$			4393.33i			0.203236i
$777$	11708.6	+	8448.24i	0.540599	+	0.390063i
$778$			8226.72i			0.379103i
$779$		−	5558.11i		−	0.255635i
$780$	−8160.11	+	11309.3i	−0.374588	+	0.519152i
$781$			26200.9i			1.20044i
$782$			37571.8i			1.71811i
$783$	3197.94	−	10182.4i	0.145958	−	0.464737i
$784$	12404.3			0.565066
$785$	−14966.2			−0.680468
$786$	8154.58	−	11301.7i	0.370056	−	0.512871i
$787$	−23012.9			−1.04234			−0.521170	−	0.853453i	$-0.674504\pi$
$787$	−23012.9			−1.04234			−0.521170	+	0.853453i	$0.674504\pi$
$788$		−	11719.5i		−	0.529810i
$789$	10.1373	+	7.31443i	0.000457410	+	0.000330039i
$790$		−	16933.4i		−	0.762613i
$791$	25389.6			1.14128
$792$	−3790.01	−	11409.0i	−0.170041	−	0.511871i
$793$	1764.58			0.0790190
$794$			1712.29i			0.0765326i
$795$	−19086.1	+	26452.0i	−0.851467	+	1.18007i
$796$	7092.03			0.315792
$797$	8204.42			0.364637			0.182318	−	0.983240i	$-0.441640\pi$
$797$	8204.42			0.364637			0.182318	+	0.983240i	$0.441640\pi$
$798$	15940.6	−	22092.5i	0.707130	−	0.980030i
$799$		−	57032.3i		−	2.52523i
$800$	−1035.83			−0.0457776
$801$	−598.256	−	1800.92i	−0.0263899	−	0.0794412i
$802$	−15208.2			−0.669600
$803$			50763.4i			2.23089i
$804$	17743.7	+	12802.8i	0.778325	+	0.561591i
$805$			68742.4i			3.00975i
$806$	−17213.4			−0.752254
$807$	2515.89	−	3486.84i	0.109744	−	0.152097i
$808$	10258.4			0.446645
$809$	−17732.7			−0.770640			−0.385320	−	0.922783i	$-0.625909\pi$
$809$	−17732.7			−0.770640			−0.385320	+	0.922783i	$0.625909\pi$
$810$	10944.1	+	14654.6i	0.474736	+	0.635692i
$811$			13848.3i			0.599604i	0.954001	+	0.299802i	$0.0969206\pi$
$811$			13848.3i			0.599604i	−0.954001	+	0.299802i	$0.903079\pi$
$812$			10175.7i			0.439776i
$813$	−9043.74	+	12534.0i	−0.390133	+	0.540696i
$814$			9249.46i			0.398272i
$815$			4081.46i			0.175420i
$816$	−7729.17	−	5576.89i	−0.331587	−	0.239253i
$817$		−	20223.4i		−	0.866007i
$818$		−	17718.1i		−	0.757335i
$819$	−45830.1	+	15224.5i	−1.95535	+	0.649557i
$820$	−3557.78			−0.151516
$821$	16741.1			0.711653			0.355827	−	0.934552i	$-0.384199\pi$
$821$	16741.1			0.711653			0.355827	+	0.934552i	$0.384199\pi$
$822$	−21718.0	−	15670.4i	−0.921536	−	0.664924i
$823$		−	25986.4i		−	1.10064i	−0.834953	−	0.550322i	$-0.814505\pi$
$823$		−	25986.4i		−	1.10064i	0.834953	−	0.550322i	$-0.185495\pi$
$824$			9687.53i			0.409564i
$825$	5477.65	−	7591.62i	0.231160	−	0.320371i
$826$	−30301.6	−	698.000i	−1.27643	−	0.0294026i
$827$		−	36797.3i		−	1.54724i	−0.633649	−	0.773620i	$-0.718444\pi$
$827$		−	36797.3i		−	1.54724i	0.633649	−	0.773620i	$-0.281556\pi$
$828$	−5579.26	−	16795.2i	−0.234170	−	0.704918i
$829$	−4459.84			−0.186848			−0.0934238	−	0.995626i	$-0.529781\pi$
$829$	−4459.84			−0.186848			−0.0934238	+	0.995626i	$0.529781\pi$
$830$		−	12133.0i		−	0.507400i
$831$	15320.2	−	21232.7i	0.639533	−	0.886346i
$832$			3423.14i			0.142639i
$833$			88878.0i			3.69681i
$834$	1704.72	−	2362.62i	0.0707791	−	0.0980947i
$835$	−3339.18			−0.138392
$836$	17452.3			0.722011
$837$	−6764.44	+	21538.3i	−0.279347	+	0.889454i
$838$	11771.2			0.485240
$839$	−236.762			−0.00974249			−0.00487124	−	0.999988i	$-0.501551\pi$
$839$	−236.762			−0.00974249			−0.00487124	+	0.999988i	$0.501551\pi$
$840$	−14141.5	−	10203.6i	−0.580867	−	0.419118i
$841$	18601.9			0.762715
$842$		−	19961.9i		−	0.817021i
$843$	11017.5	+	7949.52i	0.450132	+	0.324788i
$844$			3184.76i			0.129886i
$845$			8327.23i			0.339012i
$846$	8469.07	+	25494.3i	0.344176	+	1.03607i
$847$	−59081.8			−2.39678
$848$			8006.57i			0.324230i
$849$	37544.9	+	27090.1i	1.51771	+	1.09509i
$850$		−	7421.80i		−	0.299489i
$851$			13616.1i			0.548476i
$852$	−7934.58	−	5725.11i	−0.319054	−	0.230210i
$853$	23034.2			0.924590			0.462295	−	0.886726i	$-0.347026\pi$
$853$	23034.2			0.924590			0.462295	+	0.886726i	$0.347026\pi$
$854$			2206.48i			0.0884125i
$855$	−25197.8	+	8370.57i	−1.00789	+	0.334816i
$856$		−	4944.73i		−	0.197438i
$857$	31941.4			1.27316			0.636579	−	0.771211i	$-0.280349\pi$
$857$	31941.4			1.27316			0.636579	+	0.771211i	$0.280349\pi$
$858$	−25088.3	−	18102.1i	−0.998251	−	0.720276i
$859$			48871.3i			1.94117i	0.240757	+	0.970585i	$0.422604\pi$
$859$			48871.3i			1.94117i	−0.240757	+	0.970585i	$0.577396\pi$
$860$	−12945.1			−0.513285
$861$	−9990.88	−	7208.80i	−0.395457	−	0.285337i
$862$	−18301.4			−0.723142
$863$	−5868.09			−0.231463			−0.115731	−	0.993281i	$-0.536921\pi$
$863$	−5868.09			−0.231463			−0.115731	+	0.993281i	$0.536921\pi$
$864$	4283.20	+	1345.21i	0.168654	+	0.0529685i
$865$			3591.78i			0.141184i
$866$	−15566.0			−0.610801
$867$	25021.4	−	34677.8i	0.980128	−	1.35839i
$868$		−	21524.2i		−	0.841680i
$869$	37564.6			1.46639
$870$	5803.01	−	8042.56i	0.226139	−	0.313412i
$871$	56306.3			2.19043
$872$			118.262i			0.00459274i
$873$	14071.4	−	4674.44i	0.545527	−	0.181221i
$874$	25691.5			0.994311
$875$			38858.6i			1.50133i
$876$	−15373.0	−	11092.2i	−0.592928	−	0.427820i
$877$	17315.4			0.666705			0.333353	−	0.942802i	$-0.391820\pi$
$877$	17315.4			0.666705			0.333353	+	0.942802i	$0.391820\pi$
$878$	−12614.5			−0.484875
$879$	6132.17	+	4424.60i	0.235305	+	0.169782i
$880$		−	11171.3i		−	0.427938i
$881$	−31653.0			−1.21046			−0.605231	−	0.796050i	$-0.706919\pi$
$881$	−31653.0			−1.21046			−0.605231	+	0.796050i	$0.706919\pi$
$882$	−13198.0	−	39729.8i	−0.503855	−	1.51675i
$883$	−32748.3			−1.24810			−0.624048	−	0.781386i	$-0.714513\pi$
$883$	−32748.3			−1.24810			−0.624048	+	0.781386i	$0.714513\pi$
$884$	−24527.0			−0.933183
$885$	23551.4	+	17832.1i	0.894543	+	0.677311i
$886$	4776.58			0.181120
$887$	−24272.6			−0.918823			−0.459411	−	0.888224i	$-0.651940\pi$
$887$	−24272.6			−0.918823			−0.459411	+	0.888224i	$0.651940\pi$
$888$	−2801.07	−	2021.08i	−0.105853	−	0.0763772i
$889$	54662.2			2.06222
$890$		−	1763.40i		−	0.0664151i
$891$	−32509.4	+	24278.0i	−1.22234	+	0.912845i
$892$	16428.8			0.616677
$893$	−38998.6			−1.46141
$894$	14766.0	−	20464.6i	0.552403	−	0.765590i
$895$		−	35479.8i		−	1.32510i
$896$	−4280.39			−0.159596
$897$	−36932.3	−	26648.1i	−1.37473	−	0.991922i
$898$		−	1608.89i		−	0.0597875i
$899$	12241.2			0.454136
$900$	1102.11	+	3317.66i	0.0408188	+	0.122876i
$901$	−57367.7			−2.12119
$902$		−	7892.47i		−	0.291342i
$903$	−36352.2	−	26229.5i	−1.33967	−	0.966627i
$904$	−6073.96			−0.223470
$905$		−	9370.22i		−	0.344173i
$906$	4024.40	+	2903.76i	0.147573	+	0.106480i
$907$	−24434.5			−0.894524			−0.447262	−	0.894403i	$-0.647601\pi$
$907$	−24434.5			−0.894524			−0.447262	+	0.894403i	$0.647601\pi$
$908$	−4362.78			−0.159454
$909$	−10914.8	−	32856.6i	−0.398263	−	1.19888i
$910$	−44875.4			−1.63473
$911$			27512.4i			1.00058i	0.865859	+	0.500289i	$0.166773\pi$
$911$			27512.4i			1.00058i	−0.865859	+	0.500289i	$0.833227\pi$
$912$	−3813.47	+	5285.19i	−0.138461	+	0.191897i
$913$	26915.5			0.975653
$914$		−	15257.9i		−	0.552173i
$915$	1258.31	−	1743.93i	0.0454629	−	0.0630083i
$916$			19899.6i			0.717795i
$917$	44844.9			1.61495
$918$	−9638.50	+	30689.5i	−0.346534	+	1.10338i
$919$		−	6767.64i		−	0.242920i	−0.992596	−	0.121460i	$-0.961242\pi$
$919$		−	6767.64i		−	0.242920i	0.992596	−	0.121460i	$-0.0387577\pi$
$920$		−	16445.3i		−	0.589331i
$921$	−15035.9	+	20838.6i	−0.537947	+	0.745555i
$922$		−	2556.29i		−	0.0913089i
$923$	−25178.9			−0.897912
$924$	22635.5	−	31371.1i	0.805901	−	1.11692i
$925$		−	2689.67i		−	0.0956064i
$926$		−	14805.0i		−	0.525401i
$927$	31028.2	−	10307.4i	1.09935	−	0.365199i
$928$		−	2434.34i		−	0.0861112i
$929$	−47152.2			−1.66525			−0.832623	−	0.553841i	$-0.813162\pi$
$929$	−47152.2			−1.66525			−0.832623	+	0.553841i	$0.813162\pi$
$930$	−12274.8	+	17012.0i	−0.432803	+	0.599834i
$931$	60774.6			2.13943
$932$	−1736.65			−0.0610362
$933$	28580.2	+	20621.7i	1.00287	+	0.723607i
$934$	−25403.9			−0.889981
$935$	80043.5			2.79968
$936$	10964.0	−	3642.17i	0.382872	−	0.127188i
$937$			21544.1i			0.751136i	0.926795	+	0.375568i	$0.122552\pi$
$937$			21544.1i			0.751136i	−0.926795	+	0.375568i	$0.877448\pi$
$938$			70407.1i			2.45082i
$939$	42935.0	+	30979.3i	1.49215	+	1.07665i
$940$			24963.2i			0.866181i
$941$	3628.62			0.125706			0.0628532	−	0.998023i	$-0.479980\pi$
$941$	3628.62			0.125706			0.0628532	+	0.998023i	$0.479980\pi$
$942$	10054.3	+	7254.59i	0.347758	+	0.250921i
$943$		−	11618.5i		−	0.401219i
$944$	7249.08	+	166.983i	0.249934	+	0.00575724i
$945$	−17634.9	+	56150.3i	−0.607050	+	1.93288i
$946$		−	28717.1i		−	0.986970i
$947$		−	34650.5i		−	1.18901i	−0.804093	−	0.594503i	$-0.797349\pi$
$947$		−	34650.5i		−	1.18901i	0.804093	−	0.594503i	$-0.202651\pi$
$948$	−8208.15	+	11375.9i	−0.281211	+	0.389739i
$949$	−48783.2			−1.66867
$950$	−5075.01			−0.173321
$951$	−30927.1	−	22315.1i	−1.05455	−	0.760900i
$952$		−	30669.3i		−	1.04412i
$953$		−	29717.0i		−	1.01010i	−0.863089	−	0.505052i	$-0.831473\pi$
$953$		−	29717.0i		−	1.01010i	0.863089	−	0.505052i	$-0.168527\pi$
$954$	25644.2	−	8518.87i	0.870296	−	0.289108i
$955$			9652.40i			0.327062i
$956$			10253.2i			0.346874i
$957$	17841.4	+	12873.2i	0.602643	+	0.434830i
$958$		−	4253.78i		−	0.143459i
$959$		−	86177.0i		−	2.90177i
$960$	3383.08	+	2441.02i	0.113738	+	0.0820663i
$961$	3897.75			0.130836
$962$	−8888.65			−0.297902
$963$	−15837.5	+	5261.12i	−0.529964	+	0.176051i
$964$	−13744.6			−0.459217
$965$		−	53308.9i		−	1.77832i
$966$	33321.6	−	46181.3i	1.10984	−	1.53816i
$967$			4345.44i			0.144509i	0.997386	+	0.0722544i	$0.0230193\pi$
$967$			4345.44i			0.144509i	−0.997386	+	0.0722544i	$0.976981\pi$
$968$	14134.2			0.469308
$969$	−37868.8	−	27323.8i	−1.25544	−	0.905848i
$970$	13778.3			0.456076
$971$			46728.5i			1.54438i	0.635394	+	0.772188i	$0.280838\pi$
$971$			46728.5i			1.54438i	−0.635394	+	0.772188i	$0.719162\pi$
$972$	−248.707	−	15149.9i	−0.00820708	−	0.499933i
$973$	9374.89			0.308885
$974$	−30468.8			−1.00234
$975$	7295.48	+	5263.97i	0.239633	+	0.172905i
$976$		−	527.858i		−	0.0173118i
$977$	23068.5			0.755399			0.377700	−	0.925928i	$-0.376715\pi$
$977$	23068.5			0.755399			0.377700	+	0.925928i	$0.376715\pi$
$978$	1978.41	−	2741.93i	0.0646857	−	0.0896497i
$979$	3911.89			0.127706
$980$		−	38902.1i		−	1.26804i
$981$	378.783	−	125.830i	0.0123278	−	0.00409524i
$982$			3302.66i			0.107324i
$983$	9487.51			0.307838			0.153919	−	0.988083i	$-0.450811\pi$
$983$	9487.51			0.307838			0.153919	+	0.988083i	$0.450811\pi$
$984$	2390.12	+	1724.57i	0.0774333	+	0.0558711i
$985$	−36754.5			−1.18893
$986$	17442.3			0.563362
$987$	−50580.7	+	70101.2i	−1.63121	+	2.26073i
$988$			16771.5i			0.540054i
$989$		−	42274.3i		−	1.35920i
$990$	−35780.7	+	11886.1i	−1.14867	+	0.381582i
$991$			24894.2i			0.797973i	0.916957	+	0.398987i	$0.130638\pi$
$991$			24894.2i			0.797973i	−0.916957	+	0.398987i	$0.869362\pi$
$992$			5149.24i			0.164807i
$993$	5738.00	−	7952.45i	0.183373	−	0.254142i
$994$		−	31484.4i		−	1.00465i
$995$		−	22241.8i		−	0.708657i
$996$	−5881.23	+	8150.96i	−0.187102	+	0.259310i
$997$	43927.8			1.39540			0.697698	−	0.716392i	$-0.254208\pi$
$997$	43927.8			1.39540			0.697698	+	0.716392i	$0.254208\pi$
$998$	8635.09			0.273887
$999$	−3493.01	+	11121.9i	−0.110625	+	0.352234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.b.353.10	yes	30
3.2	odd	2		354.4.c.a.353.9	✓	30
59.58	odd	2		354.4.c.a.353.10	yes	30
177.176	even	2	inner	354.4.c.b.353.9	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.9	✓	30	3.2	odd	2
354.4.c.a.353.10	yes	30	59.58	odd	2
354.4.c.b.353.9	yes	30	177.176	even	2	inner
354.4.c.b.353.10	yes	30	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-3.04040 + 4.21378i) q^{3} +4.00000 q^{4} -12.5447i q^{5} +(-6.08081 + 8.42756i) q^{6} -33.4405 q^{7} +8.00000 q^{8} +(-8.51188 - 25.6232i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-3.04040 + 4.21378i) q^{3} +4.00000 q^{4} -12.5447i q^{5} +(-6.08081 + 8.42756i) q^{6} -33.4405 q^{7} +8.00000 q^{8} +(-8.51188 - 25.6232i) q^{9} -25.0894i q^{10} +55.6576 q^{11} +(-12.1616 + 16.8551i) q^{12} +53.4865i q^{13} -66.8811 q^{14} +(52.8606 + 38.1410i) q^{15} +16.0000 q^{16} +114.641i q^{17} +(-17.0238 - 51.2464i) q^{18} +78.3915 q^{19} -50.1788i q^{20} +(101.673 - 140.911i) q^{21} +111.315 q^{22} +163.867 q^{23} +(-24.3232 + 33.7102i) q^{24} -32.3697 q^{25} +106.973i q^{26} +(133.850 + 42.0377i) q^{27} -133.762 q^{28} -76.0732i q^{29} +(105.721 + 76.2820i) q^{30} +160.914i q^{31} +32.0000 q^{32} +(-169.222 + 234.529i) q^{33} +229.283i q^{34} +419.502i q^{35} +(-34.0475 - 102.493i) q^{36} +83.0925i q^{37} +156.783 q^{38} +(-225.380 - 162.621i) q^{39} -100.358i q^{40} -70.9020i q^{41} +(203.346 - 281.822i) q^{42} -257.980i q^{43} +222.631 q^{44} +(-321.435 + 106.779i) q^{45} +327.733 q^{46} -497.485 q^{47} +(-48.6465 + 67.4205i) q^{48} +775.270 q^{49} -64.7393 q^{50} +(-483.073 - 348.556i) q^{51} +213.946i q^{52} +500.411i q^{53} +(267.700 + 84.0753i) q^{54} -698.209i q^{55} -267.524 q^{56} +(-238.342 + 330.324i) q^{57} -152.146i q^{58} +(453.067 + 10.4364i) q^{59} +(211.443 + 152.564i) q^{60} -32.9911i q^{61} +321.828i q^{62} +(284.642 + 856.853i) q^{63} +64.0000 q^{64} +670.972 q^{65} +(-338.443 + 469.058i) q^{66} -1052.72i q^{67} +458.565i q^{68} +(-498.221 + 690.498i) q^{69} +839.004i q^{70} +470.752i q^{71} +(-68.0951 - 204.986i) q^{72} +912.066i q^{73} +166.185i q^{74} +(98.4169 - 136.399i) q^{75} +313.566 q^{76} -1861.22 q^{77} +(-450.761 - 325.241i) q^{78} +674.923 q^{79} -200.715i q^{80} +(-584.096 + 436.203i) q^{81} -141.804i q^{82} +483.590 q^{83} +(406.691 - 563.644i) q^{84} +1438.14 q^{85} -515.960i q^{86} +(320.556 + 231.293i) q^{87} +445.261 q^{88} +70.2848 q^{89} +(-642.871 + 213.558i) q^{90} -1788.62i q^{91} +655.467 q^{92} +(-678.055 - 489.243i) q^{93} -994.970 q^{94} -983.398i q^{95} +(-97.2929 + 134.841i) q^{96} +549.167i q^{97} +1550.54 q^{98} +(-473.751 - 1426.13i) 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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