LMFDB - Embedded newform 117.4.r.a.43.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,4,Mod(43,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 1]))

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

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

chi := DirichletCharacter("117.43");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.90322347067$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			43.2
Character	$\chi$	$=$	117.43
Dual form			117.4.r.a.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.65052 + 2.68498i) q^{2} +(1.15725 + 5.06565i) q^{3} +(10.4182 - 18.0449i) q^{4} +(10.1662 - 5.86946i) q^{5} +(-18.9830 - 20.4507i) q^{6} -8.42000i q^{7} +68.9311i q^{8} +(-24.3215 + 11.7244i) q^{9} +(-31.5187 + 54.5920i) q^{10} +(-55.4777 + 32.0300i) q^{11} +(103.465 + 31.8926i) q^{12} +(-38.7239 - 26.4094i) q^{13} +(22.6075 + 39.1574i) q^{14} +(41.4974 + 44.7059i) q^{15} +(-101.733 - 176.206i) q^{16} +(30.6034 + 53.0066i) q^{17} +(81.6280 - 119.828i) q^{18} +(-86.4378 + 49.9049i) q^{19} -244.597i q^{20} +(42.6528 - 9.74404i) q^{21} +(172.000 - 297.913i) q^{22} -106.185 q^{23} +(-349.181 + 79.7704i) q^{24} +(6.40106 - 11.0870i) q^{25} +(250.995 + 18.8446i) q^{26} +(-87.5379 - 109.636i) q^{27} +(-151.938 - 87.7214i) q^{28} +(72.3061 + 125.238i) q^{29} +(-313.019 - 96.4862i) q^{30} +(-94.2187 + 54.3972i) q^{31} +(468.651 + 270.576i) q^{32} +(-226.454 - 243.963i) q^{33} +(-284.643 - 164.339i) q^{34} +(-49.4208 - 85.5994i) q^{35} +(-41.8213 + 561.027i) q^{36} +(-4.75786 - 2.74695i) q^{37} +(267.987 - 464.167i) q^{38} +(88.9676 - 226.724i) q^{39} +(404.588 + 700.767i) q^{40} +66.6556i q^{41} +(-172.195 + 159.837i) q^{42} +331.425 q^{43} +1334.78i q^{44} +(-178.442 + 261.947i) q^{45} +(493.815 - 285.104i) q^{46} +(-181.062 - 104.536i) q^{47} +(774.869 - 719.257i) q^{48} +272.104 q^{49} +68.7468i q^{50} +(-233.097 + 216.368i) q^{51} +(-879.989 + 423.629i) q^{52} -303.187 q^{53} +(701.468 + 274.828i) q^{54} +(-375.998 + 651.247i) q^{55} +580.400 q^{56} +(-352.831 - 380.111i) q^{57} +(-672.522 - 388.281i) q^{58} +(-576.049 - 332.582i) q^{59} +(1239.04 - 283.060i) q^{60} +636.308 q^{61} +(292.110 - 505.950i) q^{62} +(98.7197 + 204.788i) q^{63} -1278.24 q^{64} +(-548.684 - 41.1950i) q^{65} +(1708.17 + 526.532i) q^{66} +138.922i q^{67} +1275.33 q^{68} +(-122.882 - 537.895i) q^{69} +(459.665 + 265.388i) q^{70} +(-303.653 + 175.314i) q^{71} +(-808.178 - 1676.51i) q^{72} -497.163i q^{73} +29.5021 q^{74} +(63.5702 + 19.5951i) q^{75} +2079.68i q^{76} +(269.693 + 467.122i) q^{77} +(195.003 + 1293.26i) q^{78} +(-1.08336 + 1.87643i) q^{79} +(-2068.47 - 1194.23i) q^{80} +(454.076 - 570.313i) q^{81} +(-178.969 - 309.983i) q^{82} +(122.776 + 70.8847i) q^{83} +(268.536 - 871.179i) q^{84} +(622.240 + 359.250i) q^{85} +(-1541.30 + 889.869i) q^{86} +(-550.735 + 511.209i) q^{87} +(-2207.87 - 3824.14i) q^{88} +(-71.9677 - 41.5506i) q^{89} +(126.524 - 1697.30i) q^{90} +(-222.367 + 326.056i) q^{91} +(-1106.26 + 1916.09i) q^{92} +(-384.591 - 414.327i) q^{93} +1122.71 q^{94} +(-585.829 + 1014.69i) q^{95} +(-828.296 + 2687.15i) q^{96} +510.426i q^{97} +(-1265.42 + 730.592i) q^{98} +(973.769 - 1429.46i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} - 10 q^{10} - 3 q^{11} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 84 q^{15} - 551 q^{16} - 138 q^{17} + 168 q^{18} - 96 q^{19} + 249 q^{21} - 31 q^{22}+ \cdots + 2331 q^{99}+O(q^{100}) $ 80 * q - 3 * q^2 - q^3 + 153 * q^4 - 3 * q^6 - 17 * q^9 - 10 * q^10 - 3 * q^11 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 84 * q^15 - 551 * q^16 - 138 * q^17 + 168 * q^18 - 96 * q^19 + 249 * q^21 - 31 * q^22 + 654 * q^23 - 834 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 + 201 * q^29 + 87 * q^30 - 180 * q^31 + 117 * q^32 + 231 * q^33 - 24 * q^34 + 297 * q^35 + 251 * q^36 + 246 * q^37 - 768 * q^38 - 560 * q^39 + 328 * q^40 + 1212 * q^42 + 166 * q^43 - 603 * q^45 - 6 * q^46 - 372 * q^47 - 1288 * q^48 - 3226 * q^49 + 186 * q^51 + 186 * q^52 - 2568 * q^53 + 480 * q^54 - 127 * q^55 + 4596 * q^56 - 1332 * q^57 - 3 * q^58 - 531 * q^59 - 711 * q^60 + 838 * q^61 + 135 * q^62 + 2895 * q^63 - 3178 * q^64 - 2337 * q^65 + 6228 * q^66 - 3900 * q^68 + 591 * q^69 + 1005 * q^70 - 2598 * q^71 + 1821 * q^72 - 942 * q^74 - 494 * q^75 - 1584 * q^77 + 2631 * q^78 - 260 * q^79 - 1332 * q^80 - 2357 * q^81 - 1273 * q^82 - 1194 * q^83 + 8196 * q^84 + 3936 * q^85 + 2910 * q^86 - 363 * q^87 + 781 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 + 1830 * q^93 - 1078 * q^94 - 5292 * q^95 - 6777 * q^96 - 6339 * q^98 + 2331 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−4.65052	+	2.68498i	−1.64421	+	0.949283i	−0.664892	+	0.746939i	$0.731522\pi$
$2$	−4.65052	+	2.68498i	−1.64421	+	0.949283i	−0.979315	+	0.202344i	$0.935144\pi$
$3$	1.15725	+	5.06565i	0.222713	+	0.974884i
$3$	1.15725	+	5.06565i	0.222713	+	0.974884i
$4$	10.4182	−	18.0449i	1.30228	−	2.25561i
$5$	10.1662	−	5.86946i	0.909292	−	0.524980i	0.0290890	−	0.999577i	$-0.490739\pi$
$5$	10.1662	−	5.86946i	0.909292	−	0.524980i	0.880203	+	0.474597i	$0.157406\pi$
$6$	−18.9830	−	20.4507i	−1.29163	−	1.39149i
$7$		−	8.42000i		−	0.454637i	−0.973820	−	0.227319i	$-0.927004\pi$
$7$		−	8.42000i		−	0.454637i	0.973820	−	0.227319i	$-0.0729959\pi$
$8$			68.9311i			3.04635i
$9$	−24.3215	+	11.7244i	−0.900798	+	0.434238i
$10$	−31.5187	+	54.5920i	−0.996710	+	1.72635i
$11$	−55.4777	+	32.0300i	−1.52065	+	0.877947i	−0.520946	+	0.853590i	$0.674421\pi$
$11$	−55.4777	+	32.0300i	−1.52065	+	0.877947i	−0.999703	+	0.0243577i	$0.992246\pi$
$12$	103.465	+	31.8926i	2.48899	+	0.767216i
$13$	−38.7239	−	26.4094i	−0.826160	−	0.563435i
$13$	−38.7239	−	26.4094i	−0.826160	−	0.563435i
$14$	22.6075	+	39.1574i	0.431580	+	0.747518i
$15$	41.4974	+	44.7059i	0.714306	+	0.769535i
$16$	−101.733	−	176.206i	−1.58957	−	2.75322i
$17$	30.6034	+	53.0066i	0.436612	+	0.756234i	0.997426	−	0.0717079i	$-0.0228449\pi$
$17$	30.6034	+	53.0066i	0.436612	+	0.756234i	−0.560814	+	0.827942i	$0.689512\pi$
$18$	81.6280	−	119.828i	1.06888	−	1.56909i
$19$	−86.4378	+	49.9049i	−1.04369	+	0.602577i	−0.920878	−	0.389852i	$-0.872526\pi$
$19$	−86.4378	+	49.9049i	−1.04369	+	0.602577i	−0.122817	+	0.992429i	$0.539193\pi$
$20$		−	244.597i		−	2.73468i
$21$	42.6528	−	9.74404i	0.443219	−	0.101254i
$22$	172.000	−	297.913i	1.66684	−	2.88705i
$23$	−106.185			−0.962656			−0.481328	−	0.876541i	$-0.659845\pi$
$23$	−106.185			−0.962656			−0.481328	+	0.876541i	$0.659845\pi$
$24$	−349.181	+	79.7704i	−2.96984	+	0.678461i
$25$	6.40106	−	11.0870i	0.0512085	−	0.0886957i
$26$	250.995	+	18.8446i	1.89324	+	0.142144i
$27$	−87.5379	−	109.636i	−0.623951	−	0.781464i
$28$	−151.938	−	87.7214i	−1.02548	−	0.592064i
$29$	72.3061	+	125.238i	0.462997	+	0.801934i	0.999109	−	0.0422130i	$-0.0134408\pi$
$29$	72.3061	+	125.238i	0.462997	+	0.801934i	−0.536112	+	0.844147i	$0.680107\pi$
$30$	−313.019	−	96.4862i	−1.90497	−	0.587196i
$31$	−94.2187	+	54.3972i	−0.545877	+	0.315162i	−0.747457	−	0.664310i	$-0.768726\pi$
$31$	−94.2187	+	54.3972i	−0.545877	+	0.315162i	0.201581	+	0.979472i	$0.435392\pi$
$32$	468.651	+	270.576i	2.58896	+	1.49474i
$33$	−226.454	−	243.963i	−1.19456	−	1.28693i
$34$	−284.643	−	164.339i	−1.43576	−	0.828937i
$35$	−49.4208	−	85.5994i	−0.238676	−	0.413398i
$36$	−41.8213	+	561.027i	−0.193617	+	2.59735i
$37$	−4.75786	−	2.74695i	−0.0211402	−	0.0122053i	0.489393	−	0.872064i	$-0.337219\pi$
$37$	−4.75786	−	2.74695i	−0.0211402	−	0.0122053i	−0.510533	+	0.859858i	$0.670552\pi$
$38$	267.987	−	464.167i	1.14403	−	1.98152i
$39$	88.9676	−	226.724i	0.365288	−	0.930895i
$40$	404.588	+	700.767i	1.59927	+	2.77003i
$41$			66.6556i			0.253899i	0.991909	+	0.126950i	$0.0405186\pi$
$41$			66.6556i			0.253899i	−0.991909	+	0.126950i	$0.959481\pi$
$42$	−172.195	+	159.837i	−0.632625	+	0.587222i
$43$	331.425			1.17539			0.587696	−	0.809082i	$-0.300035\pi$
$43$	331.425			1.17539			0.587696	+	0.809082i	$0.300035\pi$
$44$			1334.78i			4.57332i
$45$	−178.442	+	261.947i	−0.591123	+	0.867751i
$46$	493.815	−	285.104i	1.58281	−	0.913833i
$47$	−181.062	−	104.536i	−0.561928	−	0.324429i	0.191991	−	0.981397i	$-0.438506\pi$
$47$	−181.062	−	104.536i	−0.561928	−	0.324429i	−0.753919	+	0.656967i	$0.771839\pi$
$48$	774.869	−	719.257i	2.33006	−	2.16283i
$49$	272.104			0.793305
$50$			68.7468i			0.194445i
$51$	−233.097	+	216.368i	−0.640002	+	0.594069i
$52$	−879.989	+	423.629i	−2.34678	+	1.12975i
$53$	−303.187			−0.785773			−0.392887	−	0.919587i	$-0.628524\pi$
$53$	−303.187			−0.785773			−0.392887	+	0.919587i	$0.628524\pi$
$54$	701.468	+	274.828i	1.76773	+	0.692581i
$55$	−375.998	+	651.247i	−0.921810	+	1.59662i
$56$	580.400			1.38499
$57$	−352.831	−	380.111i	−0.819887	−	0.883280i
$58$	−672.522	−	388.281i	−1.52252	−	0.879030i
$59$	−576.049	−	332.582i	−1.27111	−	0.733873i	−0.295910	−	0.955216i	$-0.595623\pi$
$59$	−576.049	−	332.582i	−1.27111	−	0.733873i	−0.975196	+	0.221342i	$0.928956\pi$
$60$	1239.04	−	283.060i	2.66599	−	0.609048i
$61$	636.308			1.33559			0.667795	−	0.744346i	$-0.267238\pi$
$61$	636.308			1.33559			0.667795	+	0.744346i	$0.267238\pi$
$62$	292.110	−	505.950i	0.598356	−	1.03638i
$63$	98.7197	+	204.788i	0.197421	+	0.409537i
$64$	−1278.24			−2.49656
$65$	−548.684	−	41.1950i	−1.04701	−	0.0786095i
$66$	1708.17	+	526.532i	3.18577	+	0.981994i
$67$			138.922i			0.253314i	0.991947	+	0.126657i	$0.0404247\pi$
$67$			138.922i			0.253314i	−0.991947	+	0.126657i	$0.959575\pi$
$68$	1275.33			2.27436
$69$	−122.882	−	537.895i	−0.214396	−	0.938478i
$70$	459.665	+	265.388i	0.784864	+	0.453142i
$71$	−303.653	+	175.314i	−0.507564	+	0.293042i	−0.731832	−	0.681485i	$-0.761334\pi$
$71$	−303.653	+	175.314i	−0.507564	+	0.293042i	0.224268	+	0.974528i	$0.428001\pi$
$72$	−808.178	−	1676.51i	−1.32284	−	2.74415i
$73$		−	497.163i		−	0.797104i	−0.917146	−	0.398552i	$-0.869513\pi$
$73$		−	497.163i		−	0.797104i	0.917146	−	0.398552i	$-0.130487\pi$
$74$	29.5021			0.0463452
$75$	63.5702	+	19.5951i	0.0978728	+	0.0301687i
$76$			2079.68i			3.13889i
$77$	269.693	+	467.122i	0.399148	+	0.691344i
$78$	195.003	+	1293.26i	0.283074	+	1.87734i
$79$	−1.08336	+	1.87643i	−0.00154288	+	0.00267235i	−0.866796	−	0.498663i	$-0.833824\pi$
$79$	−1.08336	+	1.87643i	−0.00154288	+	0.00267235i	0.865253	+	0.501336i	$0.167158\pi$
$80$	−2068.47	−	1194.23i	−2.89078	−	1.66899i
$81$	454.076	−	570.313i	0.622875	−	0.782322i
$82$	−178.969	−	309.983i	−0.241022	−	0.417462i
$83$	122.776	+	70.8847i	0.162366	+	0.0937422i	0.578981	−	0.815341i	$-0.303450\pi$
$83$	122.776	+	70.8847i	0.162366	+	0.0937422i	−0.416615	+	0.909083i	$0.636784\pi$
$84$	268.536	−	871.179i	0.348805	−	1.13159i
$85$	622.240	+	359.250i	0.794016	+	0.458425i
$86$	−1541.30	+	889.869i	−1.93259	+	1.11578i
$87$	−550.735	+	511.209i	−0.678678	+	0.629969i
$88$	−2207.87	−	3824.14i	−2.67454	−	4.63243i
$89$	−71.9677	−	41.5506i	−0.0857142	−	0.0494871i	0.456530	−	0.889708i	$-0.349092\pi$
$89$	−71.9677	−	41.5506i	−0.0857142	−	0.0494871i	−0.542244	+	0.840221i	$0.682425\pi$
$90$	126.524	−	1697.30i	0.148187	−	1.98790i
$91$	−222.367	+	326.056i	−0.256159	+	0.375603i
$92$	−1106.26	+	1916.09i	−1.25364	+	2.17138i
$93$	−384.591	−	414.327i	−0.428820	−	0.461976i
$94$	1122.71			1.23190
$95$	−585.829	+	1014.69i	−0.632682	+	1.09584i
$96$	−828.296	+	2687.15i	−0.880600	+	2.85683i
$97$			510.426i			0.534288i	0.963657	+	0.267144i	$0.0860799\pi$
$97$			510.426i			0.534288i	−0.963657	+	0.267144i	$0.913920\pi$
$98$	−1265.42	+	730.592i	−1.30436	+	0.753071i
$99$	973.769	−	1429.46i	0.988560	−	1.45118i
$100$	−133.375	−	231.013i	−0.133375	−	0.231013i
$101$	703.584	+	1218.64i	0.693161	+	1.20059i	0.970797	+	0.239904i	$0.0771158\pi$
$101$	703.584	+	1218.64i	0.693161	+	1.20059i	−0.277636	+	0.960686i	$0.589551\pi$
$102$	503.079	−	1632.08i	0.488355	−	1.58432i
$103$	−129.191	−	223.766i	−0.123588	−	0.214061i	0.797592	−	0.603197i	$-0.206107\pi$
$103$	−129.191	−	223.766i	−0.123588	−	0.214061i	−0.921180	+	0.389136i	$0.872774\pi$
$104$	1820.43	−	2669.28i	1.71642	−	2.51678i
$105$	376.424	−	349.408i	0.349859	−	0.324750i
$106$	1409.98	−	814.051i	1.29197	−	0.745921i
$107$	1041.15	−	1803.33i	0.940675	−	1.62930i	0.176487	−	0.984303i	$-0.443527\pi$
$107$	1041.15	−	1803.33i	0.940675	−	1.62930i	0.764188	−	0.644994i	$-0.223140\pi$
$108$	−2890.36	+	437.396i	−2.57523	+	0.389708i
$109$			1144.90i			1.00607i	0.864266	+	0.503035i	$0.167783\pi$
$109$			1144.90i			1.00607i	−0.864266	+	0.503035i	$0.832217\pi$
$110$		−	4038.18i		−	3.50023i
$111$	8.40907	−	27.2806i	0.00719057	−	0.0233275i
$112$	−1483.66	+	856.590i	−1.25172	+	0.722680i
$113$	373.762	−	647.375i	0.311156	−	0.538938i	−0.667457	−	0.744648i	$-0.732617\pi$
$113$	373.762	−	647.375i	0.311156	−	0.538938i	0.978613	+	0.205711i	$0.0659506\pi$
$114$	2661.44	+	820.371i	2.18655	+	0.673989i
$115$	−1079.50	+	623.248i	−0.875336	+	0.505375i
$116$	3013.20			2.41180
$117$	1251.46	+	188.302i	0.988869	+	0.148791i
$118$	3571.91			2.78661
$119$	446.315	−	257.680i	0.343812	−	0.198500i
$120$	−3081.63	+	2860.46i	−2.34427	+	2.17603i
$121$	1386.35	−	2401.22i	1.04158	−	1.80407i
$122$	−2959.16	+	1708.47i	−2.19598	+	1.26785i
$123$	−337.654	+	77.1372i	−0.247522	+	0.0565465i
$124$			2266.89i			1.64171i
$125$			1317.08i			0.942427i
$126$	−1008.95	−	687.308i	−0.713367	−	0.485954i
$127$	−1060.12	+	1836.18i	−0.740711	+	1.28295i	0.211461	+	0.977387i	$0.432178\pi$
$127$	−1060.12	+	1836.18i	−0.740711	+	1.28295i	−0.952172	+	0.305563i	$0.901155\pi$
$128$	2195.26	−	1267.44i	1.51590	−	0.875208i
$129$	383.541	+	1678.88i	0.261775	+	1.14587i
$130$	2662.27	−	1281.63i	1.79613	−	0.864662i
$131$	33.1785	+	57.4668i	0.0221284	+	0.0383274i	0.876878	−	0.480714i	$-0.159622\pi$
$131$	33.1785	+	57.4668i	0.0221284	+	0.0383274i	−0.854749	+	0.519041i	$0.826289\pi$
$132$	−6761.54	+	1544.68i	−4.45846	+	1.01854i
$133$	420.199	+	727.807i	0.273954	+	0.474503i
$134$	−373.002	−	646.059i	−0.240466	−	0.416500i
$135$	−1533.43	−	600.784i	−0.977607	−	0.383017i
$136$	−3653.80	+	2109.52i	−2.30376	+	1.33007i
$137$		−	811.021i		−	0.505768i	−0.967497	−	0.252884i	$-0.918621\pi$
$137$		−	811.021i		−	0.505768i	0.967497	−	0.252884i	$-0.0813791\pi$
$138$	2015.70	+	2171.56i	1.24339	+	1.33953i
$139$	−523.683	+	907.045i	−0.319555	+	0.553486i	−0.980395	−	0.197041i	$-0.936867\pi$
$139$	−523.683	+	907.045i	−0.319555	+	0.553486i	0.660840	+	0.750527i	$0.270200\pi$
$140$	−2059.51			−1.24329
$141$	320.010	−	1038.17i	0.191133	−	0.620069i
$142$	941.431	−	1630.61i	0.556360	−	0.963643i
$143$	2994.21	+	224.804i	1.75097	+	0.131462i
$144$	4540.22	+	3092.85i	2.62744	+	1.78984i
$145$	1470.16	+	848.795i	0.841999	+	0.486128i
$146$	1334.87	+	2312.07i	0.756677	+	1.31060i
$147$	314.892	+	1378.38i	0.176679	+	0.773380i
$148$	−99.1369	+	57.2367i	−0.0550608	+	0.0317894i
$149$	455.197	+	262.808i	0.250276	+	0.144497i	0.619891	−	0.784688i	$-0.287177\pi$
$149$	455.197	+	262.808i	0.250276	+	0.144497i	−0.369614	+	0.929185i	$0.620510\pi$
$150$	−348.247	+	79.5572i	−0.189562	+	0.0433054i
$151$	9.76002	+	5.63495i	0.00525999	+	0.00303686i	0.502628	−	0.864503i	$-0.332367\pi$
$151$	9.76002	+	5.63495i	0.00525999	+	0.00303686i	−0.497368	+	0.867540i	$0.665700\pi$
$152$	−3440.00	−	5958.25i	−1.83566	−	3.17946i
$153$	−1365.79	−	930.395i	−0.721685	−	0.491621i
$154$	−2508.42	−	1448.24i	−1.31256	−	0.757808i
$155$	−638.564	+	1106.02i	−0.330908	+	0.573149i
$156$	−3164.32	−	3967.47i	−1.62403	−	2.03623i
$157$	−775.103	−	1342.52i	−0.394012	−	0.682449i	0.598962	−	0.800777i	$-0.295580\pi$
$157$	−775.103	−	1342.52i	−0.394012	−	0.682449i	−0.992975	+	0.118328i	$0.962247\pi$
$158$		−	11.6352i		−	0.00585852i
$159$	−350.863	−	1535.84i	−0.175002	−	0.766038i
$160$	6352.54			3.13883
$161$			894.077i			0.437659i
$162$	−580.410	+	3871.43i	−0.281490	+	1.87758i
$163$	2085.51	−	1204.07i	1.00215	−	0.578589i	0.0932635	−	0.995641i	$-0.470270\pi$
$163$	2085.51	−	1204.07i	1.00215	−	0.578589i	0.908883	+	0.417052i	$0.136937\pi$
$164$	1202.79	+	694.433i	0.572697	+	0.330647i
$165$	−3734.11	−	1151.02i	−1.76182	−	0.543070i
$166$	−761.295			−0.355952
$167$			850.868i			0.394264i	0.980377	+	0.197132i	$0.0631628\pi$
$167$			850.868i			0.394264i	−0.980377	+	0.197132i	$0.936837\pi$
$168$	671.667	+	2940.10i	0.308454	+	1.35020i
$169$	802.084	+	2045.35i	0.365082	+	0.930975i
$170$	−3858.32			−1.74070
$171$	1517.20	−	2227.20i	0.678496	−	0.996013i
$172$	3452.86	−	5980.52i	1.53069	−	2.65122i
$173$	−673.654			−0.296052			−0.148026	−	0.988983i	$-0.547292\pi$
$173$	−673.654			−0.296052			−0.148026	+	0.988983i	$0.547292\pi$
$174$	1188.62	−	3856.10i	0.517867	−	1.68006i
$175$	−93.3522	−	53.8969i	−0.0403244	−	0.0232813i
$176$	11287.8	+	6517.01i	4.83437	+	2.79112i
$177$	1018.11	−	3302.94i	0.432350	−	1.40262i
$178$	446.250			0.187909
$179$	−1893.72	+	3280.02i	−0.790744	+	1.36961i	0.134762	+	0.990878i	$0.456973\pi$
$179$	−1893.72	+	3280.02i	−0.790744	+	1.36961i	−0.925507	+	0.378732i	$0.876360\pi$
$180$	2867.76	+	5948.98i	1.18750	+	2.46339i
$181$	−2393.55			−0.982936			−0.491468	−	0.870896i	$-0.663540\pi$
$181$	−2393.55			−0.982936			−0.491468	+	0.870896i	$0.663540\pi$
$182$	158.672	−	2113.38i	0.0646239	−	0.860737i
$183$	736.367	+	3223.31i	0.297453	+	1.30204i
$184$		−	7319.44i		−	2.93259i
$185$	−64.4925			−0.0256302
$186$	2901.01	+	894.218i	1.14361	+	0.352512i
$187$	−3395.60	−	1960.45i	−1.32787	−	0.766645i
$188$	−3772.69	+	2178.16i	−1.46357	+	0.844994i
$189$	−923.138	+	737.069i	−0.355283	+	0.283671i
$190$		−	6291.76i		−	2.40238i
$191$	−3035.77			−1.15006			−0.575028	−	0.818134i	$-0.695009\pi$
$191$	−3035.77			−1.15006			−0.575028	+	0.818134i	$0.695009\pi$
$192$	−1479.24	−	6475.11i	−0.556016	−	2.43386i
$193$		−	2571.57i		−	0.959097i	−0.877515	−	0.479549i	$-0.840800\pi$
$193$		−	2571.57i		−	0.959097i	0.877515	−	0.479549i	$-0.159200\pi$
$194$	−1370.48	−	2373.75i	−0.507191	−	0.878480i
$195$	−426.285	−	2827.11i	−0.156548	−	1.03822i
$196$	2834.83	−	4910.08i	1.03310	−	1.78939i
$197$	−1272.74	−	734.815i	−0.460298	−	0.265753i	0.251871	−	0.967761i	$-0.418954\pi$
$197$	−1272.74	−	734.815i	−0.460298	−	0.265753i	−0.712170	+	0.702007i	$0.752287\pi$
$198$	−690.450	+	9262.30i	−0.247819	+	3.32446i
$199$	2440.78	+	4227.55i	0.869458	+	1.50595i	0.862551	+	0.505970i	$0.168865\pi$
$199$	2440.78	+	4227.55i	0.869458	+	1.50595i	0.00690693	+	0.999976i	$0.497801\pi$
$200$	764.236	+	441.232i	0.270198	+	0.155999i
$201$	−703.729	+	160.767i	−0.246951	+	0.0564162i
$202$	−6544.06	−	3778.22i	−2.27940	−	1.31601i
$203$	1054.50	−	608.818i	0.364589	−	0.210496i
$204$	1475.87	+	6460.37i	0.506529	+	2.21724i
$205$	391.232	+	677.634i	0.133292	+	0.230868i
$206$	1201.61	+	693.752i	0.406409	+	0.234641i
$207$	2582.58	−	1244.96i	0.867159	−	0.418022i
$208$	−714.016	+	9510.10i	−0.238020	+	3.17023i
$209$	3196.91	−	5537.21i	1.05806	−	1.83262i
$210$	−812.414	+	2635.62i	−0.266961	+	0.866072i
$211$	−5325.45			−1.73753			−0.868766	−	0.495223i	$-0.835086\pi$
$211$	−5325.45			−1.73753			−0.868766	+	0.495223i	$0.835086\pi$
$212$	−3158.67	+	5470.98i	−1.02329	+	1.77240i
$213$	−1239.48	−	1335.32i	−0.398723	−	0.429552i
$214$			11181.9i			3.57187i
$215$	3369.33	−	1945.28i	1.06877	−	0.617057i
$216$	7557.35	−	6034.08i	2.38061	−	1.90077i
$217$	458.024	+	793.321i	0.143284	+	0.248176i
$218$	−3074.03	−	5324.38i	−0.955045	−	1.65419i
$219$	2518.45	−	575.342i	0.777084	−	0.177525i
$220$	7834.46	+	13569.7i	2.40090	+	4.15849i
$221$	214.791	−	2860.84i	0.0653774	−	0.870773i
$222$	34.1412	+	149.447i	0.0103217	+	0.0451812i
$223$	3560.64	−	2055.74i	1.06923	−	0.617320i	0.141259	−	0.989973i	$-0.454885\pi$
$223$	3560.64	−	2055.74i	1.06923	−	0.617320i	0.927971	+	0.372653i	$0.121552\pi$
$224$	2278.25	−	3946.05i	0.679563	−	1.17704i
$225$	−25.6954	+	344.701i	−0.00761346	+	0.102134i
$226$			4014.18i			1.18150i
$227$			3734.52i			1.09193i	0.837807	+	0.545966i	$0.183837\pi$
$227$			3734.52i			1.09193i	−0.837807	+	0.545966i	$0.816163\pi$
$228$	−10534.9	+	2406.71i	−3.06006	+	0.699071i
$229$	−2677.75	+	1546.00i	−0.772711	+	0.446125i	−0.833841	−	0.552005i	$-0.813863\pi$
$229$	−2677.75	+	1546.00i	−0.772711	+	0.446125i	0.0611296	+	0.998130i	$0.480530\pi$
$230$	3346.81	−	5796.85i	0.959489	−	1.66188i
$231$	−2054.17	+	1906.75i	−0.585085	+	0.543094i
$232$	−8632.78	+	4984.14i	−2.44297	+	1.41045i
$233$	−2795.27			−0.785941			−0.392970	−	0.919551i	$-0.628553\pi$
$233$	−2795.27			−0.785941			−0.392970	+	0.919551i	$0.628553\pi$
$234$	−6325.53	+	2484.44i	−1.76715	+	0.694073i
$235$	−2454.28			−0.681276
$236$	−12002.8	+	6929.83i	−3.31066	+	1.91141i
$237$	−10.7591	−	3.31642i	−0.00294885	−	0.000908963i
$238$	−1383.73	+	2396.69i	−0.376866	+	0.652751i
$239$	2951.04	−	1703.78i	0.798690	−	0.461124i	−0.0443229	−	0.999017i	$-0.514113\pi$
$239$	2951.04	−	1703.78i	0.798690	−	0.461124i	0.843013	+	0.537893i	$0.180780\pi$
$240$	3655.82	−	11860.2i	0.983260	−	3.18988i
$241$			2238.84i			0.598407i	0.954189	+	0.299203i	$0.0967209\pi$
$241$			2238.84i			0.598407i	−0.954189	+	0.299203i	$0.903279\pi$
$242$			14889.2i			3.95503i
$243$	3414.48	+	1640.19i	0.901395	+	0.432998i
$244$	6629.20	−	11482.1i	1.73931	−	3.01257i
$245$	2766.26	−	1597.10i	0.721346	−	0.416469i
$246$	1363.15	−	1265.32i	0.353299	−	0.327943i
$247$	4665.17	+	350.260i	1.20177	+	0.0902287i
$248$	−3749.66	−	6494.60i	−0.960094	−	1.66293i
$249$	−216.995	+	703.971i	−0.0552268	+	0.179166i
$250$	−3536.33	−	6125.11i	−0.894630	−	1.54954i
$251$	−2861.54	−	4956.33i	−0.719597	−	1.24638i	−0.961160	−	0.275993i	$-0.910993\pi$
$251$	−2861.54	−	4956.33i	−0.719597	−	1.24638i	0.241563	−	0.970385i	$-0.422340\pi$
$252$	4723.85	+	352.135i	1.18085	+	0.0880255i
$253$	5890.89	−	3401.11i	1.46386	−	0.845161i
$254$		−	11385.6i		−	2.81258i
$255$	−1099.75	+	3567.79i	−0.270074	+	0.876171i
$256$	−1693.12	+	2932.57i	−0.413360	+	0.715960i
$257$	2661.19			0.645917			0.322958	−	0.946413i	$-0.395323\pi$
$257$	2661.19			0.645917			0.322958	+	0.946413i	$0.395323\pi$
$258$	−6291.43	−	6777.87i	−1.51817	−	1.63555i
$259$	−23.1294	+	40.0612i	−0.00554899	+	0.00961113i
$260$	−6459.67	+	9471.76i	−1.54081	+	2.25928i
$261$	−3226.94	−	2198.23i	−0.765297	−	0.521330i
$262$	−308.594	−	178.167i	−0.0727672	−	0.0420122i
$263$	2770.56	+	4798.74i	0.649581	+	1.12511i	0.983223	+	0.182407i	$0.0583890\pi$
$263$	2770.56	+	4798.74i	0.649581	+	1.12511i	−0.333642	+	0.942700i	$0.608278\pi$
$264$	16816.7	−	15609.7i	3.92043	−	3.63907i
$265$	−3082.26	+	1779.55i	−0.714498	+	0.412515i
$266$	−3908.29	−	2256.45i	−0.900875	−	0.520120i
$267$	127.196	−	412.648i	0.0291546	−	0.0945828i
$268$	2506.83	+	1447.32i	0.571377	+	0.329885i
$269$	−1403.73	−	2431.33i	−0.318166	−	0.551080i	0.661939	−	0.749558i	$-0.269734\pi$
$269$	−1403.73	−	2431.33i	−0.318166	−	0.551080i	−0.980106	+	0.198477i	$0.936400\pi$
$270$	8744.35	−	1323.28i	1.97098	−	0.298267i
$271$	1135.59	+	655.634i	0.254547	+	0.146963i	0.621845	−	0.783141i	$-0.286384\pi$
$271$	1135.59	+	655.634i	0.254547	+	0.146963i	−0.367297	+	0.930104i	$0.619717\pi$
$272$	6226.73	−	10785.0i	1.38805	−	2.40418i
$273$	−1909.02	−	749.107i	−0.423220	−	0.166073i
$274$	2177.57	+	3771.67i	0.480117	+	0.831587i
$275$			820.105i			0.179833i
$276$	−10986.5	−	3386.51i	−2.39604	−	0.738565i
$277$	−7039.61			−1.52696			−0.763482	−	0.645829i	$-0.776512\pi$
$277$	−7039.61			−1.52696			−0.763482	+	0.645829i	$0.776512\pi$
$278$		−	5624.31i		−	1.21339i
$279$	1653.77	−	2427.68i	0.354869	−	0.520938i
$280$	5900.46	−	3406.63i	1.25936	−	0.727090i
$281$	−2519.54	−	1454.66i	−0.534886	−	0.308817i	0.208118	−	0.978104i	$-0.433266\pi$
$281$	−2519.54	−	1454.66i	−0.534886	−	0.308817i	−0.743004	+	0.669287i	$0.766600\pi$
$282$	1299.26	+	5687.25i	0.274360	+	1.20096i
$283$	6160.03			1.29391			0.646954	−	0.762529i	$-0.276043\pi$
$283$	6160.03			1.29391			0.646954	+	0.762529i	$0.276043\pi$
$284$			7305.85i			1.52649i
$285$	−5817.99	−	1793.36i	−1.20922	−	0.372735i
$286$	−14528.2	+	6993.93i	−3.00375	+	1.44601i
$287$	561.241			0.115432
$288$	−14570.7	−	1086.16i	−2.98120	−	0.222231i
$289$	583.369	−	1010.43i	0.118740	−	0.205664i
$290$	−9115.99			−1.84589
$291$	−2585.64	+	590.690i	−0.520869	+	0.118993i
$292$	−8971.25	−	5179.56i	−1.79796	−	1.03805i
$293$	5537.97	+	3197.35i	1.10420	+	0.637513i	0.937322	−	0.348464i	$-0.113297\pi$
$293$	5537.97	+	3197.35i	1.10420	+	0.637513i	0.166882	+	0.985977i	$0.446630\pi$
$294$	−5165.33	−	5564.71i	−1.02465	−	1.10388i
$295$	−7808.31			−1.54108
$296$	189.351	−	327.965i	0.0371817	−	0.0644006i
$297$	8368.05	+	3278.52i	1.63489	+	0.640536i
$298$	−2822.53			−0.548675
$299$	4111.90	+	2804.28i	0.795308	+	0.542394i
$300$	1015.88	−	942.971i	0.195506	−	0.181475i
$301$		−	2790.60i		−	0.534377i
$302$	−60.5189			−0.0115314
$303$	−5359.00	+	4974.38i	−1.01606	+	0.943138i
$304$	17587.1	+	10153.9i	3.31806	+	1.91568i
$305$	6468.84	−	3734.78i	1.21444	−	0.701158i
$306$	8849.73	+	659.696i	1.65329	+	0.123243i
$307$			6396.54i			1.18915i	0.804039	+	0.594576i	$0.202680\pi$
$307$			6396.54i			1.18915i	−0.804039	+	0.594576i	$0.797320\pi$
$308$	11238.9			2.07920
$309$	984.012	−	913.390i	0.181160	−	0.168158i
$310$		−	6858.12i		−	1.25650i
$311$	3896.83	+	6749.51i	0.710511	+	1.23064i	0.964665	+	0.263478i	$0.0848696\pi$
$311$	3896.83	+	6749.51i	0.710511	+	1.23064i	−0.254154	+	0.967164i	$0.581797\pi$
$312$	15628.3	+	6132.63i	2.83583	+	1.11279i
$313$	706.302	−	1223.35i	0.127548	−	0.220920i	−0.795178	−	0.606376i	$-0.792623\pi$
$313$	706.302	−	1223.35i	0.127548	−	0.220920i	0.922726	+	0.385456i	$0.125956\pi$
$314$	7209.26	+	4162.27i	1.29567	+	0.748058i
$315$	2205.60	+	1502.48i	0.394512	+	0.268746i
$316$	22.5733	+	39.0982i	0.00401851	+	0.00696027i
$317$	4485.28	+	2589.58i	0.794695	+	0.458818i	0.841613	−	0.540081i	$-0.181607\pi$
$317$	4485.28	+	2589.58i	0.794695	+	0.458818i	−0.0469177	+	0.998899i	$0.514940\pi$
$318$	5755.39	+	6200.39i	1.01493	+	1.09340i
$319$	−8022.75	−	4631.94i	−1.40811	−	0.812974i
$320$	−12994.8	+	7502.57i	−2.27010	+	1.31065i
$321$	10339.9	+	3187.22i	1.79788	+	0.554184i
$322$	−2400.58	−	4157.92i	−0.415463	−	0.719603i
$323$	−5290.58	−	3054.52i	−0.911379	−	0.526185i
$324$	−5560.56	−	14135.4i	−0.953457	−	2.42376i
$325$	−540.674	+	260.282i	−0.0922807	+	0.0444242i
$326$	−6465.80	+	11199.1i	−1.09849	+	1.90264i
$327$	−5799.66	+	1324.93i	−0.980801	+	0.224064i
$328$	−4594.64			−0.773466
$329$	−880.196	+	1524.54i	−0.147498	+	0.255474i
$330$	20456.0	−	4673.18i	3.41232	−	0.779547i
$331$			7104.44i			1.17974i	0.807497	+	0.589872i	$0.200822\pi$
$331$			7104.44i			1.17974i	−0.807497	+	0.589872i	$0.799178\pi$
$332$	2558.21	−	1476.98i	0.422892	−	0.244157i
$333$	147.925	+	11.0269i	0.0243431	+	0.00181463i
$334$	−2284.56	−	3956.98i	−0.374269	−	0.648252i
$335$	815.396	+	1412.31i	0.132985	+	0.230336i
$336$	−6056.14	−	6524.40i	−0.983303	−	1.05933i
$337$	−1016.32	−	1760.32i	−0.164281	−	0.284542i	0.772119	−	0.635478i	$-0.219197\pi$
$337$	−1016.32	−	1760.32i	−0.164281	−	0.284542i	−0.936400	+	0.350936i	$0.885864\pi$
$338$	−9221.84	−	7358.37i	−1.48403	−	1.18415i
$339$	3711.91	+	1144.17i	0.594700	+	0.183313i
$340$	12965.3	−	7485.49i	2.06806	−	1.19399i
$341$	3484.69	−	6035.66i	0.553391	−	0.958502i
$342$	−1075.77	+	14431.3i	−0.170090	+	2.28174i
$343$		−	5179.17i		−	0.815303i
$344$			22845.5i			3.58066i
$345$	−4406.40	−	4747.10i	−0.687631	−	0.740797i
$346$	3132.84	−	1808.75i	0.486771	−	0.281037i
$347$	−2546.25	+	4410.23i	−0.393919	+	0.682287i	−0.992963	−	0.118429i	$-0.962214\pi$
$347$	−2546.25	+	4410.23i	−0.393919	+	0.682287i	0.599044	+	0.800716i	$0.295547\pi$
$348$	3487.03	+	15263.8i	0.537139	+	2.35123i
$349$	−3765.71	+	2174.13i	−0.577576	+	0.333463i	−0.760169	−	0.649725i	$-0.774884\pi$
$349$	−3765.71	+	2174.13i	−0.577576	+	0.333463i	0.182594	+	0.983188i	$0.441551\pi$
$350$	578.848			0.0884021
$351$	494.379	+	6557.37i	0.0751795	+	0.997170i
$352$	−34666.2			−5.24920
$353$	7773.61	−	4488.10i	1.17209	−	0.676706i	0.217918	−	0.975967i	$-0.430073\pi$
$353$	7773.61	−	4488.10i	1.17209	−	0.676706i	0.954171	+	0.299261i	$0.0967400\pi$
$354$	4133.58	+	18094.0i	0.620614	+	2.71663i
$355$	−2058.00	+	3564.56i	−0.307683	+	0.532922i
$356$	−1499.55	+	865.766i	−0.223247	+	0.128892i
$357$	1821.82	+	1962.68i	0.270086	+	0.290969i
$358$		−	20338.4i		−	3.00256i
$359$			1660.55i			0.244124i	0.992523	+	0.122062i	$0.0389506\pi$
$359$			1660.55i			0.244124i	−0.992523	+	0.122062i	$0.961049\pi$
$360$	−18056.3	−	12300.2i	−2.64347	−	1.80077i
$361$	1551.50	−	2687.28i	0.226199	−	0.391788i
$362$	11131.3	−	6426.64i	1.61615	−	0.933084i
$363$	13768.1	+	4243.93i	1.99074	+	0.613632i
$364$	3566.96	+	7409.51i	0.513625	+	1.06693i
$365$	−2918.08	−	5054.26i	−0.418464	−	0.724800i
$366$	−12079.0	−	13012.9i	−1.72508	−	1.85846i
$367$	−349.539	−	605.420i	−0.0497161	−	0.0861108i	0.840096	−	0.542437i	$-0.182498\pi$
$367$	−349.539	−	605.420i	−0.0497161	−	0.0861108i	−0.889813	+	0.456326i	$0.849165\pi$
$368$	10802.5	+	18710.4i	1.53021	+	2.65041i
$369$	−781.499	−	1621.17i	−0.110253	−	0.228712i
$370$	299.924	−	173.161i	0.0421413	−	0.0243303i
$371$			2552.84i			0.357242i
$372$	−11483.2	+	2623.35i	−1.60048	+	0.365630i
$373$	1340.43	−	2321.70i	0.186073	−	0.322287i	−0.757865	−	0.652412i	$-0.773757\pi$
$373$	1340.43	−	2321.70i	0.186073	−	0.322287i	0.943937	+	0.330124i	$0.107091\pi$
$374$	21055.1			2.91105
$375$	−6671.87	+	1524.19i	−0.918757	+	0.209890i
$376$	7205.80	−	12480.8i	0.988326	−	1.71183i
$377$	507.484	−	6759.26i	0.0693282	−	0.923395i
$378$	2314.06	−	5906.36i	0.314873	−	0.803678i
$379$	4008.82	+	2314.50i	0.543323	+	0.313688i	0.746425	−	0.665470i	$-0.231769\pi$
$379$	4008.82	+	2314.50i	0.543323	+	0.313688i	−0.203101	+	0.979158i	$0.565102\pi$
$380$	12206.6	+	21142.4i	1.64786	+	2.85417i
$381$	−10528.3	−	3245.27i	−1.41569	−	0.436379i
$382$	14117.9	−	8150.98i	1.89093	−	1.09173i
$383$	−7584.45	−	4378.88i	−1.01187	−	0.584205i	−0.100133	−	0.994974i	$-0.531927\pi$
$383$	−7584.45	−	4378.88i	−1.01187	−	0.584205i	−0.911739	+	0.410769i	$0.865260\pi$
$384$	8960.85	+	9653.69i	1.19084	+	1.28291i
$385$	5483.51	+	3165.90i	0.725884	+	0.419089i
$386$	6904.61	+	11959.1i	0.910455	+	1.57695i
$387$	−8060.77	+	3885.77i	−1.05879	+	0.510400i
$388$	9210.58	+	5317.73i	1.20515	+	0.695791i
$389$	−5694.49	+	9863.15i	−0.742216	+	1.28556i	0.209268	+	0.977858i	$0.432892\pi$
$389$	−5694.49	+	9863.15i	−0.742216	+	1.28556i	−0.951484	+	0.307698i	$0.900441\pi$
$390$	9573.18	+	12003.0i	1.24297	+	1.55845i
$391$	−3249.61	−	5628.50i	−0.420307	−	0.727993i
$392$			18756.4i			2.41669i
$393$	−252.711	+	234.574i	−0.0324366	+	0.0301086i
$394$	7891.85			1.00910
$395$			25.4349i			0.00323992i
$396$	−15649.6	−	32464.0i	−1.98591	−	4.11964i
$397$	339.920	−	196.253i	0.0429725	−	0.0248102i	−0.478360	−	0.878164i	$-0.658769\pi$
$397$	339.920	−	196.253i	0.0429725	−	0.0248102i	0.521332	+	0.853354i	$0.325435\pi$
$398$	−22701.8	−	13106.9i	−2.85914	−	1.65072i
$399$	−3200.54	+	2970.84i	−0.401572	+	0.372751i
$400$	−2604.79			−0.325599
$401$		−	12146.6i		−	1.51265i	−0.654196	−	0.756325i	$-0.726993\pi$
$401$		−	12146.6i		−	1.51265i	0.654196	−	0.756325i	$-0.273007\pi$
$402$	2841.05	−	2637.15i	0.352484	−	0.327187i
$403$	5085.11	+	381.789i	0.628555	+	0.0471917i
$404$	29320.4			3.61075
$405$	1268.80	−	8463.09i	0.155672	−	1.03836i
$406$	−3269.32	+	5662.64i	−0.399640	+	0.692197i
$407$	351.940			0.0428625
$408$	−14914.5	−	16067.6i	−1.80974	−	1.94967i
$409$	4122.25	+	2379.98i	0.498367	+	0.287733i	0.728039	−	0.685536i	$-0.240432\pi$
$409$	4122.25	+	2379.98i	0.498367	+	0.287733i	−0.229672	+	0.973268i	$0.573765\pi$
$410$	−3638.87	−	2100.90i	−0.438319	−	0.253064i
$411$	4108.35	−	938.553i	0.493065	−	0.112641i
$412$	−5383.77			−0.643785
$413$	−2800.34	+	4850.34i	−0.333646	+	0.577892i
$414$	−8667.66	+	12723.9i	−1.02897	+	1.51049i
$415$	1664.22			0.196851
$416$	−11002.3	−	22854.6i	−1.29671	−	2.69360i
$417$	−5200.80	−	1603.11i	−0.610754	−	0.188261i
$418$			34334.6i			4.01760i
$419$	−4595.60			−0.535822			−0.267911	−	0.963444i	$-0.586333\pi$
$419$	−4595.60			−0.535822			−0.267911	+	0.963444i	$0.586333\pi$
$420$	−2383.36	−	10432.7i	−0.276896	−	1.21206i
$421$	−5888.64	−	3399.81i	−0.681698	−	0.393578i	0.118797	−	0.992919i	$-0.462096\pi$
$421$	−5888.64	−	3399.81i	−0.681698	−	0.393578i	−0.800494	+	0.599340i	$0.795430\pi$
$422$	24766.1	−	14298.7i	2.85686	−	1.64941i
$423$	5629.34	+	419.634i	0.647063	+	0.0482348i
$424$		−	20899.0i		−	2.39374i
$425$	783.575			0.0894329
$426$	9349.54	+	2881.94i	1.06335	+	0.327771i
$427$		−	5357.72i		−	0.607209i
$428$	−21694.0	−	37575.0i	−2.45004	−	4.24359i
$429$	2326.26	+	15427.8i	0.261802	+	1.73627i
$430$	−10446.1	+	18093.2i	−1.17152	+	2.02914i
$431$	−1238.01	−	714.766i	−0.138359	−	0.0798818i	0.429223	−	0.903199i	$-0.358788\pi$
$431$	−1238.01	−	714.766i	−0.138359	−	0.0798818i	−0.567582	+	0.823317i	$0.692121\pi$
$432$	−10413.1	+	26578.3i	−1.15973	+	2.96007i
$433$	−5071.03	−	8783.28i	−0.562813	−	0.974821i	−0.997249	−	0.0741185i	$-0.976386\pi$
$433$	−5071.03	−	8783.28i	−0.562813	−	0.974821i	0.434436	−	0.900703i	$-0.356948\pi$
$434$	−4260.10	−	2459.57i	−0.471178	−	0.272035i
$435$	−2598.36	+	8429.56i	−0.286395	+	0.929118i
$436$	20659.6	+	11927.8i	2.26930	+	1.31018i
$437$	9178.39	−	5299.15i	1.00472	−	0.580075i
$438$	−10167.3	+	9437.63i	−1.10916	+	1.02956i
$439$	−3802.02	−	6585.30i	−0.413350	−	0.715943i	0.581904	−	0.813258i	$-0.302308\pi$
$439$	−3802.02	−	6585.30i	−0.413350	−	0.715943i	−0.995254	+	0.0973146i	$0.968975\pi$
$440$	−44891.2	−	25917.9i	−4.86387	−	2.80816i
$441$	−6617.98	+	3190.26i	−0.714608	+	0.344483i
$442$	6682.40	+	13881.1i	0.719116	+	1.49379i
$443$	5480.82	−	9493.06i	0.587814	−	1.01812i	−0.406704	−	0.913560i	$-0.633322\pi$
$443$	5480.82	−	9493.06i	0.587814	−	1.01812i	0.994518	−	0.104564i	$-0.0333448\pi$
$444$	−404.667	−	435.956i	−0.0432537	−	0.0465980i
$445$	−975.518			−0.103919
$446$	−11039.2	+	19120.5i	−1.17202	+	2.03000i
$447$	−804.516	+	2610.00i	−0.0851282	+	0.276172i
$448$			10762.8i			1.13503i
$449$	−3552.85	+	2051.24i	−0.373428	+	0.215599i	−0.674955	−	0.737859i	$-0.735837\pi$
$449$	−3552.85	+	2051.24i	−0.373428	+	0.215599i	0.301527	+	0.953458i	$0.402504\pi$
$450$	−806.017	−	1672.03i	−0.0844356	−	0.175156i
$451$	−2134.98	−	3697.90i	−0.222910	−	0.386091i
$452$	−7787.87	−	13489.0i	−0.810422	−	1.40369i
$453$	−17.2499	+	55.9618i	−0.00178912	+	0.00580423i
$454$	−10027.1	−	17367.4i	−1.03655	−	1.79536i
$455$	−346.862	+	4619.92i	−0.0357388	+	0.476012i
$456$	26201.5	−	24321.0i	2.69078	−	2.49767i
$457$	−11386.9	+	6574.21i	−1.16555	+	0.672929i	−0.952627	−	0.304141i	$-0.901631\pi$
$457$	−11386.9	+	6574.21i	−1.16555	+	0.672929i	−0.212920	+	0.977070i	$0.568297\pi$
$458$	8301.96	−	14379.4i	0.846998	−	1.46704i
$459$	3132.49	−	7995.32i	0.318545	−	0.813049i
$460$			25972.5i			2.63255i
$461$			657.284i			0.0664051i	0.999449	+	0.0332026i	$0.0105706\pi$
$461$			657.284i			0.0664051i	−0.999449	+	0.0332026i	$0.989429\pi$
$462$	4433.40	−	14382.8i	0.446451	−	1.44837i
$463$	−5806.14	+	3352.18i	−0.582795	+	0.336477i	−0.762244	−	0.647290i	$-0.775902\pi$
$463$	−5806.14	+	3352.18i	−0.582795	+	0.336477i	0.179448	+	0.983767i	$0.442569\pi$
$464$	14711.8	−	25481.6i	1.47194	−	2.54947i
$465$	−6341.71	−	1954.79i	−0.632451	−	0.194949i
$466$	12999.5	−	7505.24i	1.29225	−	0.746080i
$467$	−5159.32			−0.511231			−0.255616	−	0.966779i	$-0.582278\pi$
$467$	−5159.32			−0.511231			−0.255616	+	0.966779i	$0.582278\pi$
$468$	16435.9	−	20620.7i	1.62340	−	2.03673i
$469$	1169.72			0.115166
$470$	11413.7	−	6589.70i	1.12016	−	0.646724i
$471$	5903.73	−	5480.02i	0.577557	−	0.536106i
$472$	22925.3	−	39707.7i	2.23564	−	3.87224i
$473$	−18386.7	+	10615.6i	−1.78736	+	1.03193i
$474$	58.9397	−	13.4648i	0.00571138	−	0.00130477i
$475$			1277.78i			0.123428i
$476$		−	10738.3i		−	1.03401i
$477$	7373.99	−	3554.70i	0.707823	−	0.341213i
$478$	−9149.24	+	15847.0i	−0.875474	+	1.51637i
$479$	4356.13	−	2515.01i	0.415526	−	0.239904i	−0.277636	−	0.960686i	$-0.589551\pi$
$479$	4356.13	−	2515.01i	0.415526	−	0.239904i	0.693161	+	0.720783i	$0.256217\pi$
$480$	7351.47	+	32179.7i	0.699056	+	3.05999i
$481$	111.698	+	232.025i	0.0105883	+	0.0219947i
$482$	−6011.23	−	10411.7i	−0.568058	−	0.983905i
$483$	−4529.08	+	1034.67i	−0.426667	+	0.0974723i
$484$	−28886.5	−	50032.9i	−2.71286	−	4.69881i
$485$	2995.92	+	5189.09i	0.280491	+	0.485824i
$486$	−20283.0	+	1540.06i	−1.89312	+	0.143742i
$487$	−9594.76	+	5539.54i	−0.892772	+	0.515442i	−0.874848	−	0.484397i	$-0.839039\pi$
$487$	−9594.76	+	5539.54i	−0.892772	+	0.515442i	−0.0179238	+	0.999839i	$0.505706\pi$
$488$			43861.4i			4.06868i
$489$	8512.85	+	9171.05i	0.787248	+	0.848117i
$490$	−8576.36	+	14854.7i	−0.790695	+	1.36952i
$491$	9131.87			0.839339			0.419669	−	0.907677i	$-0.362146\pi$
$491$	9131.87			0.839339			0.419669	+	0.907677i	$0.362146\pi$
$492$	−2125.82	+	6896.55i	−0.194795	+	0.631953i
$493$	−4425.62	+	7665.40i	−0.404300	+	0.700268i
$494$	−22635.9	+	10897.0i	−2.06161	+	0.992468i
$495$	1509.35	−	20247.7i	0.137051	−	1.83852i
$496$	19170.2	+	11067.9i	1.73542	+	1.00195i
$497$	1476.15	+	2556.76i	0.133228	+	0.230757i
$498$	−881.008	−	3856.45i	−0.0792750	−	0.347012i
$499$	−221.565	+	127.921i	−0.0198770	+	0.0114760i	−0.509906	−	0.860230i	$-0.670320\pi$
$499$	−221.565	+	127.921i	−0.0198770	+	0.0114760i	0.490029	+	0.871706i	$0.336986\pi$
$500$	23766.6	+	13721.6i	2.12575	+	1.22730i
$501$	−4310.20	+	984.666i	−0.384362	+	0.0878077i
$502$	26615.3	+	15366.3i	2.36633	+	1.36620i
$503$	2257.49	+	3910.09i	0.200113	+	0.346605i	0.948565	−	0.316584i	$-0.102536\pi$
$503$	2257.49	+	3910.09i	0.200113	+	0.346605i	−0.748452	+	0.663189i	$0.769202\pi$
$504$	−14116.2	+	6804.86i	−1.24759	+	0.601414i
$505$	14305.6	+	8259.32i	1.26057	+	0.727792i
$506$	−18263.8	+	31633.8i	−1.60459	+	2.77924i
$507$	−9432.82	+	6430.06i	−0.826285	+	0.563252i
$508$	22089.1	+	38259.4i	1.92922	+	3.34151i
$509$			10320.4i			0.898709i	0.893354	+	0.449354i	$0.148346\pi$
$509$			10320.4i			0.898709i	−0.893354	+	0.449354i	$0.851654\pi$
$510$	−4465.03	−	19544.9i	−0.387676	−	1.69698i
$511$	−4186.12			−0.362393
$512$			2095.01i			0.180834i
$513$	13038.0	+	5108.15i	1.12211	+	0.439631i
$514$	−12375.9	+	7145.24i	−1.06202	+	0.613158i
$515$	−2626.77	−	1516.57i	−0.224756	−	0.129763i
$516$	34291.0	+	10570.0i	2.92554	+	0.901780i
$517$	13393.2			1.13933
$518$		−	248.407i		−	0.0210703i
$519$	−779.586	−	3412.50i	−0.0659345	−	0.288616i
$520$	2839.62	−	37821.4i	0.239472	−	3.18957i
$521$	−17801.0			−1.49688			−0.748442	−	0.663200i	$-0.769198\pi$
$521$	−17801.0			−1.49688			−0.748442	+	0.663200i	$0.769198\pi$
$522$	20909.1	+	1558.65i	1.75320	+	0.130690i
$523$	1182.75	−	2048.59i	0.0988874	−	0.171278i	−0.812337	−	0.583188i	$-0.801805\pi$
$523$	1182.75	−	2048.59i	0.0988874	−	0.171278i	0.911224	+	0.411910i	$0.135138\pi$
$524$	1382.64			0.115269
$525$	164.991	−	535.262i	0.0137158	−	0.0444966i
$526$	−25769.0	−	14877.8i	−2.13609	−	1.23327i
$527$	−5766.81	−	3329.47i	−0.476672	−	0.275207i
$528$	−19950.1	+	64721.7i	−1.64435	+	5.33457i
$529$	−891.763			−0.0732936
$530$	9556.08	−	16551.6i	0.783188	−	1.35652i
$531$	17909.8	+	1335.07i	1.46369	+	0.109109i
$532$	17510.9			1.42706
$533$	1760.34	−	2581.17i	0.143056	−	0.209761i
$534$	516.422	+	2260.54i	0.0418498	+	0.183190i
$535$		−	24444.1i		−	1.97534i
$536$	−9576.04			−0.771683
$537$	−18806.9	−	5797.12i	−1.51132	−	0.465855i
$538$	13056.1	+	7537.96i	1.04626	+	0.604060i
$539$	−15095.7	+	8715.49i	−1.20634	+	0.696480i
$540$	−26816.7	+	21411.5i	−2.13705	+	1.70631i
$541$			16139.3i			1.28259i	0.767294	+	0.641295i	$0.221603\pi$
$541$			16139.3i			1.28259i	−0.767294	+	0.641295i	$0.778397\pi$
$542$	−7041.45			−0.558037
$543$	−2769.94	−	12124.9i	−0.218912	−	0.958249i
$544$			33122.1i			2.61048i
$545$	6719.95	+	11639.3i	0.528167	+	0.914811i
$546$	10889.3	−	1641.93i	0.853511	−	0.128696i
$547$	3851.87	−	6671.63i	0.301086	−	0.521496i	−0.675296	−	0.737547i	$-0.735984\pi$
$547$	3851.87	−	6671.63i	0.301086	−	0.521496i	0.976382	+	0.216050i	$0.0693175\pi$
$548$	−14634.8	−	8449.39i	−1.14082	−	0.658650i
$549$	−15476.0	+	7460.35i	−1.20310	+	0.579964i
$550$	−2201.96	−	3813.91i	−0.170713	−	0.295683i
$551$	−12500.0	−	7216.86i	−0.966455	−	0.557983i
$552$	37077.7	−	8470.42i	2.85893	−	0.653125i
$553$	15.7996	+	9.12189i	0.00121495	+	0.000701451i
$554$	32737.8	−	18901.2i	2.51064	−	1.44952i
$555$	−74.6339	−	326.696i	−0.00570817	−	0.0249865i
$556$	10911.7	+	18899.6i	0.832299	+	1.44158i
$557$	7014.78	+	4049.98i	0.533619	+	0.308085i	0.742489	−	0.669858i	$-0.233645\pi$
$557$	7014.78	+	4049.98i	0.533619	+	0.308085i	−0.208870	+	0.977943i	$0.566979\pi$
$558$	−1172.60	+	15730.3i	−0.0889610	+	1.19340i
$559$	−12834.1	−	8752.74i	−0.971062	−	0.662257i
$560$	−10055.4	+	17416.5i	−0.758785	+	1.31425i
$561$	6001.40	−	19469.7i	0.451657	−	1.46526i
$562$	15622.9			1.17262
$563$	−7497.74	+	12986.5i	−0.561265	+	0.972139i	0.436122	+	0.899888i	$0.356352\pi$
$563$	−7497.74	+	12986.5i	−0.561265	+	0.972139i	−0.997386	+	0.0722513i	$0.976982\pi$
$564$	−15399.7	−	16590.4i	−1.14973	−	1.23862i
$565$		−	8775.13i		−	0.653403i
$566$	−28647.3	+	16539.5i	−2.12745	+	1.22828i
$567$	−4802.03	−	3823.32i	−0.355673	−	0.283182i
$568$	−12084.6	−	20931.2i	−0.892709	−	1.54622i
$569$	−11491.3	−	19903.5i	−0.846643	−	1.46643i	−0.884186	−	0.467134i	$-0.845286\pi$
$569$	−11491.3	−	19903.5i	−0.846643	−	1.46643i	0.0375429	−	0.999295i	$-0.488047\pi$
$570$	31871.8	−	7281.13i	2.34204	−	0.535040i
$571$	3053.73	+	5289.21i	0.223808	+	0.387647i	0.955961	−	0.293493i	$-0.0948178\pi$
$571$	3053.73	+	5289.21i	0.223808	+	0.387647i	−0.732153	+	0.681140i	$0.761484\pi$
$572$	35250.9	−	51688.1i	2.57677	−	3.77830i
$573$	−3513.14	−	15378.1i	−0.256132	−	1.12117i
$574$	−2610.06	+	1506.92i	−0.189794	+	0.109578i
$575$	−679.696	+	1177.27i	−0.0492961	+	0.0853834i
$576$	31088.8	−	14986.6i	2.24890	−	1.08410i
$577$			6485.30i			0.467914i	0.972247	+	0.233957i	$0.0751676\pi$
$577$			6485.30i			0.467914i	−0.972247	+	0.233957i	$0.924832\pi$
$578$			6265.34i			0.450871i
$579$	13026.7	−	2975.95i	0.935009	−	0.213603i
$580$	30632.8	−	17685.9i	2.19303	−	1.26615i
$581$	596.849	−	1033.77i	0.0426187	−	0.0738178i
$582$	10438.6	−	9689.40i	0.743458	−	0.690101i
$583$	16820.1	−	9711.10i	1.19489	−	0.689868i
$584$	34270.0			2.42826
$585$	13827.8	−	5431.08i	0.977283	−	0.383842i
$586$	−34339.3			−2.42072
$587$	−15925.4	+	9194.56i	−1.11978	+	0.646508i	−0.941346	−	0.337443i	$-0.890438\pi$
$587$	−15925.4	+	9194.56i	−1.11978	+	0.646508i	−0.178439	+	0.983951i	$0.557105\pi$
$588$	28153.3	+	8678.09i	1.97453	+	0.608636i
$589$	5429.37	−	9403.95i	0.379819	−	0.657866i
$590$	36312.7	−	20965.1i	2.53385	−	1.46292i
$591$	2249.44	−	7297.60i	0.156564	−	0.507924i
$592$			1117.82i			0.0776050i
$593$		−	8897.54i		−	0.616152i	−0.951362	−	0.308076i	$-0.900315\pi$
$593$		−	8897.54i		−	0.616152i	0.951362	−	0.308076i	$-0.0996851\pi$
$594$	−47718.5	+	7221.21i	−3.29615	+	0.498804i
$595$	3024.89	−	5239.26i	0.208417	−	0.360989i
$596$	9484.67	−	5475.98i	0.651858	−	0.376350i
$597$	−18590.7	+	17256.4i	−1.27448	+	1.18301i
$598$	−26651.9	−	2001.02i	−1.82254	−	0.136836i
$599$	3417.69	+	5919.62i	0.233127	+	0.403788i	0.958727	−	0.284329i	$-0.0917708\pi$
$599$	3417.69	+	5919.62i	0.233127	+	0.403788i	−0.725600	+	0.688117i	$0.758437\pi$
$600$	−1350.71	+	4381.97i	−0.0919044	+	0.298155i
$601$	8422.43	+	14588.1i	0.571644	+	0.990116i	0.996397	+	0.0848072i	$0.0270274\pi$
$601$	8422.43	+	14588.1i	0.571644	+	0.990116i	−0.424753	+	0.905309i	$0.639639\pi$
$602$	7492.70	+	12977.7i	0.507275	+	0.878626i
$603$	−1628.78	−	3378.80i	−0.109998	−	0.228184i
$604$	203.364	−	117.412i	0.0136999	−	0.00790966i
$605$		−	32548.4i		−	2.18724i
$606$	11566.0	−	37522.3i	0.775308	−	2.51524i
$607$	−5296.83	+	9174.38i	−0.354187	+	0.613470i	−0.986979	−	0.160852i	$-0.948576\pi$
$607$	−5296.83	+	9174.38i	−0.354187	+	0.613470i	0.632791	+	0.774322i	$0.281909\pi$
$608$	−54012.3			−3.60278
$609$	4304.38	+	4637.19i	0.286408	+	0.308552i
$610$	−20055.6	+	34737.4i	−1.33119	+	2.30570i
$611$	4250.69	+	8829.80i	0.281448	+	0.584641i
$612$	−31018.0	+	14952.5i	−2.04874	+	0.987613i
$613$	13031.2	+	7523.54i	0.858603	+	0.495715i	0.863544	−	0.504273i	$-0.168240\pi$
$613$	13031.2	+	7523.54i	0.858603	+	0.495715i	−0.00494128	+	0.999988i	$0.501573\pi$
$614$	−17174.6	−	29747.2i	−1.12884	−	1.95521i
$615$	−2979.90	+	2766.04i	−0.195384	+	0.181362i
$616$	−32199.2	+	18590.2i	−2.10608	+	1.21594i
$617$	−19585.4	−	11307.6i	−1.27792	−	0.737810i	−0.301458	−	0.953480i	$-0.597473\pi$
$617$	−19585.4	−	11307.6i	−1.27792	−	0.737810i	−0.976466	+	0.215670i	$0.930806\pi$
$618$	−2123.74	+	6889.79i	−0.138235	+	0.448460i
$619$	15814.0	+	9130.21i	1.02685	+	0.592850i	0.916080	−	0.400996i	$-0.131336\pi$
$619$	15814.0	+	9130.21i	1.02685	+	0.592850i	0.110767	+	0.993846i	$0.464669\pi$
$620$	13305.4	+	23045.6i	0.861867	+	1.49280i
$621$	9295.20	+	11641.7i	0.600650	+	0.752280i
$622$	−36244.6	−	20925.8i	−2.33646	−	1.34895i
$623$	−349.856	+	605.969i	−0.0224987	+	0.0389689i
$624$	−49001.1	+	7388.60i	−3.14361	+	0.474008i
$625$	8530.69	+	14775.6i	0.545964	+	0.945637i
$626$			7585.62i			0.484317i
$627$	31749.2	+	9786.49i	2.02223	+	0.623341i
$628$	−32300.7			−2.05245
$629$		−	336.264i		−	0.0213159i
$630$	−14291.3	−	1065.33i	−0.903776	−	0.0673712i
$631$	12091.5	−	6981.04i	0.762846	−	0.440429i	−0.0674708	−	0.997721i	$-0.521493\pi$
$631$	12091.5	−	6981.04i	0.762846	−	0.440429i	0.830317	+	0.557292i	$0.188160\pi$
$632$	−129.345	−	74.6771i	−0.00814091	−	0.00470015i
$633$	−6162.87	−	26976.9i	−0.386970	−	1.69389i
$634$	−27811.8			−1.74219
$635$			24889.3i			1.55543i
$636$	−31369.4	−	9669.43i	−1.95578	−	0.602858i
$637$	−10536.9	−	7186.10i	−0.655397	−	0.446976i
$638$	49746.6			3.08697
$639$	5329.86	−	7824.08i	0.329962	−	0.484375i
$640$	14878.3	−	25770.0i	0.918934	−	1.59164i
$641$	30339.7			1.86950			0.934748	−	0.355312i	$-0.115625\pi$
$641$	30339.7			1.86950			0.934748	+	0.355312i	$0.115625\pi$
$642$	−56643.6	+	12940.3i	−3.48216	+	0.795500i
$643$	10284.8	+	5937.94i	0.630783	+	0.364183i	0.781055	−	0.624462i	$-0.214682\pi$
$643$	10284.8	+	5937.94i	0.630783	+	0.364183i	−0.150272	+	0.988645i	$0.548015\pi$
$644$	16133.5	+	9314.69i	0.987189	+	0.569954i
$645$	13753.3	+	14816.7i	0.839589	+	0.904505i
$646$	32805.2			1.99799
$647$	−6511.05	+	11277.5i	−0.395635	+	0.685260i	−0.993182	−	0.116574i	$-0.962809\pi$
$647$	−6511.05	+	11277.5i	−0.395635	+	0.685260i	0.597547	+	0.801834i	$0.296142\pi$
$648$	39312.3	+	31299.9i	2.38323	+	1.89750i
$649$	42610.5			2.57721
$650$	1815.56	−	2662.15i	0.109557	−	0.160643i
$651$	−3488.64	+	3238.26i	−0.210031	+	0.194958i
$652$		−	50177.1i		−	3.01393i
$653$	−10374.1			−0.621699			−0.310849	−	0.950459i	$-0.600614\pi$
$653$	−10374.1			−0.621699			−0.310849	+	0.950459i	$0.600614\pi$
$654$	23414.0	−	21733.6i	1.39994	−	1.29947i
$655$	674.598	+	389.479i	0.0402423	+	0.0232339i
$656$	11745.1	−	6781.06i	0.699041	−	0.403591i
$657$	5828.96	+	12091.8i	0.346133	+	0.718030i
$658$		−	9453.22i		−	0.560068i
$659$	−2591.61			−0.153194			−0.0765971	−	0.997062i	$-0.524406\pi$
$659$	−2591.61			−0.153194			−0.0765971	+	0.997062i	$0.524406\pi$
$660$	−59672.8	+	55390.1i	−3.51933	+	3.26675i
$661$			20619.0i			1.21329i	0.794973	+	0.606645i	$0.207485\pi$
$661$			20619.0i			1.21329i	−0.794973	+	0.606645i	$0.792515\pi$
$662$	−19075.3	−	33039.3i	−1.11991	−	1.93974i
$663$	14740.6	−	2222.65i	0.863463	−	0.130197i
$664$	−4886.16	+	8463.08i	−0.285572	+	0.494625i
$665$	8543.66	+	4932.69i	0.498209	+	0.287641i
$666$	−717.536	+	345.895i	−0.0417477	+	0.0201248i
$667$	−7677.82	−	13298.4i	−0.445707	−	0.771987i
$668$	15353.8	+	8864.53i	0.889307	+	0.513442i
$669$	14534.2	+	15658.0i	0.839946	+	0.904890i
$670$	−7584.03	−	4378.64i	−0.437309	−	0.252480i
$671$	−35300.9	+	20381.0i	−2.03096	+	1.17258i
$672$	22625.8	+	6974.26i	1.29882	+	0.400354i
$673$	8798.21	+	15238.9i	0.503932	+	0.872835i	0.999990	+	0.00454578i	$0.00144697\pi$
$673$	8798.21	+	15238.9i	0.503932	+	0.872835i	−0.496058	+	0.868289i	$0.665220\pi$
$674$	9452.84	+	5457.60i	0.540222	+	0.311897i
$675$	−1775.87	+	268.741i	−0.101264	+	0.0153242i
$676$	45264.4	+	6835.41i	2.57536	+	0.388906i
$677$	−644.287	+	1115.94i	−0.0365760	+	0.0633515i	−0.883734	−	0.467990i	$-0.844978\pi$
$677$	−644.287	+	1115.94i	−0.0365760	+	0.0633515i	0.847158	+	0.531341i	$0.178312\pi$
$678$	−20334.4	+	4645.40i	−1.15183	+	0.263135i
$679$	4297.79			0.242907
$680$	−24763.5	+	42891.6i	−1.39653	+	2.41885i
$681$	−18917.7	+	4321.76i	−1.06451	+	0.243187i
$682$			37425.2i			2.10130i
$683$	11888.3	−	6863.70i	0.666021	−	0.384527i	−0.128546	−	0.991704i	$-0.541031\pi$
$683$	11888.3	−	6863.70i	0.666021	−	0.384527i	0.794567	+	0.607176i	$0.207698\pi$
$684$	−24383.1	−	50581.1i	−1.36303	−	2.82751i
$685$	−4760.25	−	8245.00i	−0.265518	−	0.459891i
$686$	13906.0	+	24085.8i	0.773954	+	1.34053i
$687$	−10930.3	−	11775.4i	−0.607013	−	0.653946i
$688$	−33716.8	−	58399.2i	−1.86837	−	3.23611i
$689$	11740.6	+	8007.00i	0.649175	+	0.442732i
$690$	33237.9	+	10245.4i	1.83383	+	0.565268i
$691$	13057.4	−	7538.67i	0.718850	−	0.415028i	−0.0954795	−	0.995431i	$-0.530438\pi$
$691$	13057.4	−	7538.67i	0.718850	−	0.415028i	0.814329	+	0.580403i	$0.197105\pi$
$692$	−7018.28	+	12156.0i	−0.385542	+	0.667778i
$693$	−12036.1	−	8199.14i	−0.659759	−	0.449436i
$694$		−	27346.5i		−	1.49576i
$695$			12294.9i			0.671041i
$696$	−35238.2	−	37962.7i	−1.91911	−	2.06749i
$697$	−3533.19	+	2039.89i	−0.192007	+	0.110855i
$698$	11675.0	−	20221.7i	0.633102	−	1.09657i
$699$	−3234.82	−	14159.8i	−0.175039	−	0.766201i
$700$	−1945.13	+	1123.02i	−0.105027	+	0.0606374i
$701$	9756.56			0.525678			0.262839	−	0.964840i	$-0.415341\pi$
$701$	9756.56			0.525678			0.262839	+	0.964840i	$0.415341\pi$
$702$	−19905.5	−	29167.8i	−1.07021	−	1.56819i
$703$	548.346			0.0294186
$704$	70913.7	−	40942.1i	3.79639	−	2.19185i
$705$	−2840.22	−	12432.5i	−0.151729	−	0.664165i
$706$	−24100.9	+	41744.0i	−1.28477	+	2.22529i
$707$	10261.0	−	5924.18i	0.545833	−	0.315137i
$708$	−48994.3	−	52782.5i	−2.60073	−	2.80182i
$709$		−	8777.60i		−	0.464950i	−0.972602	−	0.232475i	$-0.925318\pi$
$709$		−	8777.60i		−	0.464950i	0.972602	−	0.232475i	$-0.0746824\pi$
$710$		−	22102.7i		−	1.16831i
$711$	4.34887	−	58.3395i	0.000229389	−	0.00307722i
$712$	2864.13	−	4960.81i	0.150755	−	0.261116i
$713$	10004.6	−	5776.16i	0.525491	−	0.303393i
$714$	−13742.1	−	4235.93i	−0.720289	−	0.222025i
$715$	31759.2	−	15289.0i	1.66116	−	0.799685i
$716$	39458.4	+	68343.9i	2.05954	+	3.56722i
$717$	12045.9	+	12977.2i	0.627421	+	0.675932i
$718$	−4458.53	−	7722.41i	−0.231742	−	0.401390i
$719$	−14737.9	−	25526.8i	−0.764439	−	1.32405i	−0.940542	−	0.339676i	$-0.889683\pi$
$719$	−14737.9	−	25526.8i	−0.764439	−	1.32405i	0.176103	−	0.984372i	$-0.443651\pi$
$720$	64310.1	+	4793.94i	3.32874	+	0.248138i
$721$	−1884.11	+	1087.79i	−0.0973203	+	0.0561879i
$722$			16663.0i			0.858908i
$723$	−11341.2	+	2590.89i	−0.583377	+	0.133273i
$724$	−24936.6	+	43191.4i	−1.28005	+	2.21712i
$725$	1851.34			0.0948374
$726$	−75423.7	+	17230.6i	−3.85569	+	0.880835i
$727$	10788.1	−	18685.5i	0.550354	−	0.953242i	−0.447894	−	0.894086i	$-0.647826\pi$
$727$	10788.1	−	18685.5i	0.550354	−	0.953242i	0.998249	−	0.0591553i	$-0.0188407\pi$
$728$	−22475.4	−	15328.0i	−1.14422	−	0.780350i
$729$	−4357.23	+	19194.7i	−0.221370	+	0.975190i
$730$	27141.2	+	15670.0i	1.37608	+	0.794481i
$731$	10142.7	+	17567.7i	0.513190	+	0.888871i
$732$	65835.9	+	20293.5i	3.32427	+	1.02469i
$733$	10580.0	−	6108.38i	0.533127	−	0.307801i	−0.209162	−	0.977881i	$-0.567074\pi$
$733$	10580.0	−	6108.38i	0.533127	−	0.307801i	0.742289	+	0.670080i	$0.233740\pi$
$734$	3251.08	+	1877.01i	0.163487	+	0.0943893i
$735$	11291.6	+	12164.6i	0.566662	+	0.610476i
$736$	−49763.7	−	28731.1i	−2.49228	−	1.43892i
$737$	−4449.68	−	7707.06i	−0.222396	−	0.385201i
$738$	7987.18	+	5440.96i	0.398390	+	0.271388i
$739$	−31979.8	−	18463.5i	−1.59187	−	0.919068i	−0.992986	−	0.118235i	$-0.962276\pi$
$739$	−31979.8	−	18463.5i	−1.59187	−	0.919068i	−0.598888	−	0.800833i	$-0.704390\pi$
$740$	−671.897	+	1163.76i	−0.0333776	+	0.0578117i
$741$	3624.47	+	24037.5i	0.179687	+	1.19168i
$742$	−6854.32	−	11872.0i	−0.339124	−	0.587380i
$743$		−	18288.9i		−	0.903036i	−0.892262	−	0.451518i	$-0.850883\pi$
$743$		−	18288.9i		−	0.903036i	0.892262	−	0.451518i	$-0.149117\pi$
$744$	28560.0	−	26510.3i	1.40734	−	1.30634i
$745$	6170.16			0.303432
$746$			14396.2i			0.706542i
$747$	−3817.18	−	284.549i	−0.186966	−	0.0139372i
$748$	−70752.3	+	40848.9i	−3.45850	+	1.99677i
$749$	−15184.1	−	8766.53i	−0.740739	−	0.427666i
$750$	26935.2	−	25002.1i	1.31138	−	1.21726i
$751$	−3875.22			−0.188294			−0.0941470	−	0.995558i	$-0.530012\pi$
$751$	−3875.22			−0.188294			−0.0941470	+	0.995558i	$0.530012\pi$
$752$			42539.0i			2.06282i
$753$	21795.5	−	20231.3i	1.05481	−	0.979108i
$754$	15788.4	+	32796.7i	0.762573	+	1.58406i
$755$	132.296			0.00637716
$756$	3682.88	+	24336.9i	0.177176	+	1.17080i
$757$	−456.389	+	790.489i	−0.0219125	+	0.0379535i	−0.876774	−	0.480903i	$-0.840309\pi$
$757$	−456.389	+	790.489i	−0.0219125	+	0.0379535i	0.854861	+	0.518857i	$0.173642\pi$
$758$	−24857.5			−1.19111
$759$	24046.0	+	25905.2i	1.14995	+	1.23887i
$760$	−69943.4	−	40381.9i	−3.33831	−	1.92737i
$761$	−27621.5	−	15947.3i	−1.31574	−	0.759643i	−0.332699	−	0.943033i	$-0.607959\pi$
$761$	−27621.5	−	15947.3i	−1.31574	−	0.759643i	−0.983040	+	0.183390i	$0.941293\pi$
$762$	57675.3	−	13176.0i	2.74194	−	0.626397i
$763$	9640.07			0.457397
$764$	−31627.3	+	54780.1i	−1.49769	+	2.59408i
$765$	−19345.8	−	1442.12i	−0.914314	−	0.0681567i
$766$	47028.8			2.21830
$767$	13523.6	+	28092.0i	0.636647	+	1.32248i
$768$	−16814.7	−	5183.04i	−0.790038	−	0.243524i
$769$			8425.40i			0.395094i	0.980293	+	0.197547i	$0.0632976\pi$
$769$			8425.40i			0.395094i	−0.980293	+	0.197547i	$0.936702\pi$
$770$	−34001.5			−1.59134
$771$	3079.66	+	13480.7i	0.143854	+	0.629694i
$772$	−46403.7	−	26791.2i	−2.16335	−	1.24901i
$773$	13965.8	−	8063.17i	0.649826	−	0.375177i	−0.138563	−	0.990354i	$-0.544248\pi$
$773$	13965.8	−	8063.17i	0.649826	−	0.375177i	0.788390	+	0.615176i	$0.210915\pi$
$774$	27053.6	−	39713.8i	1.25636	−	1.84429i
$775$			1392.80i			0.0645558i
$776$	−35184.2			−1.62763
$777$	−229.702	−	70.8044i	−0.0106056	−	0.00326910i
$778$		−	61158.3i		−	2.81829i
$779$	−3326.44	−	5761.57i	−0.152994	−	0.264993i
$780$	−55456.0	−	21761.2i	−2.54570	−	0.998944i
$781$	11230.7	−	19452.1i	0.514551	−	0.891228i
$782$	30224.8	+	17450.3i	1.38214	+	0.797981i
$783$	7401.09	−	18890.4i	0.337795	−	0.862183i
$784$	−27681.8	−	47946.4i	−1.26102	−	2.18415i
$785$	−15759.7	−	9098.86i	−0.716545	−	0.413697i
$786$	545.410	−	1769.41i	0.0247508	−	0.0802962i
$787$	−23915.3	−	13807.5i	−1.08321	−	0.625392i	−0.151451	−	0.988465i	$-0.548394\pi$
$787$	−23915.3	−	13807.5i	−1.08321	−	0.625392i	−0.931761	+	0.363072i	$0.881728\pi$
$788$	−26519.3	+	15310.9i	−1.19887	+	0.692169i
$789$	−21102.5	+	19588.0i	−0.952179	+	0.883842i
$790$	−68.2922	−	118.286i	−0.00307561	−	0.00532711i
$791$	−5450.90	−	3147.08i	−0.245021	−	0.141463i
$792$	98534.5	+	67122.9i	4.42080	+	3.01150i
$793$	−24640.4	−	16804.5i	−1.10341	−	0.752518i
$794$	−1053.87	+	1825.35i	−0.0471038	+	0.0815861i
$795$	−12581.5	−	13554.3i	−0.561282	−	0.604680i
$796$	101714.			4.52910
$797$	−5906.53	+	10230.4i	−0.262510	+	0.454680i	−0.966908	−	0.255125i	$-0.917883\pi$
$797$	−5906.53	+	10230.4i	−0.262510	+	0.454680i	0.704399	+	0.709805i	$0.251217\pi$
$798$	6907.53	−	22409.3i	0.306421	−	0.994086i
$799$		−	12796.6i		−	0.566599i
$800$	5999.73	−	3463.95i	0.265153	−	0.153086i
$801$	2237.52	+	166.794i	0.0987004	+	0.00735754i
$802$	32613.4	+	56488.0i	1.43593	+	2.48711i
$803$	15924.2	+	27581.5i	0.699815	+	1.21212i
$804$	−4430.58	+	14373.6i	−0.194346	+	0.630496i
$805$	5247.75	+	9089.37i	0.229763	+	0.397960i
$806$	−24673.5	+	11877.9i	−1.07827	+	0.519084i
$807$	10691.8	−	9924.44i	0.466380	−	0.432908i
$808$	−84002.4	+	48498.8i	−3.65742	+	2.11161i
$809$	10156.8	−	17592.1i	0.441402	−	0.764532i	−0.556391	−	0.830920i	$-0.687814\pi$
$809$	10156.8	−	17592.1i	0.441402	−	0.764532i	0.997794	+	0.0663888i	$0.0211478\pi$
$810$	16822.6	+	42764.4i	0.729737	+	1.85505i
$811$			3849.49i			0.166676i	0.996521	+	0.0833378i	$0.0265581\pi$
$811$			3849.49i			0.166676i	−0.996521	+	0.0833378i	$0.973442\pi$
$812$		−	25371.2i		−	1.09649i
$813$	−2007.05	+	6511.23i	−0.0865809	+	0.280884i
$814$	−1636.70	+	944.952i	−0.0704748	+	0.0406886i
$815$	14134.5	−	24481.6i	0.607496	−	1.05221i
$816$	61838.9	+	19061.5i	2.65293	+	0.817751i
$817$	−28647.7	+	16539.7i	−1.22675	+	0.708264i
$818$	−25560.8			−1.09256
$819$	1585.51	−	10537.3i	0.0676460	−	0.449577i
$820$	16303.8			0.694332
$821$	436.772	−	252.170i	0.0185669	−	0.0107196i	−0.490688	−	0.871335i	$-0.663254\pi$
$821$	436.772	−	252.170i	0.0185669	−	0.0107196i	0.509255	+	0.860616i	$0.329921\pi$
$822$	−16585.9	+	15395.6i	−0.703773	+	0.653263i
$823$	−15211.3	+	26346.8i	−0.644270	+	1.11591i	0.340200	+	0.940353i	$0.389505\pi$
$823$	−15211.3	+	26346.8i	−0.644270	+	1.11591i	−0.984470	+	0.175555i	$0.943828\pi$
$824$	15424.4	−	8905.30i	0.652106	−	0.376494i
$825$	−4154.36	+	949.065i	−0.175317	+	0.0400512i
$826$		−	30075.5i		−	1.26690i
$827$		−	7861.80i		−	0.330570i	−0.986246	−	0.165285i	$-0.947146\pi$
$827$		−	7861.80i		−	0.330570i	0.986246	−	0.165285i	$-0.0528544\pi$
$828$	4440.79	−	59572.6i	0.186387	−	2.50035i
$829$	−15744.2	+	27269.8i	−0.659613	+	1.14248i	0.321103	+	0.947044i	$0.395946\pi$
$829$	−15744.2	+	27269.8i	−0.659613	+	1.14248i	−0.980716	+	0.195439i	$0.937387\pi$
$830$	−7739.48	+	4468.39i	−0.323664	+	0.186868i
$831$	−8146.58	−	35660.2i	−0.340074	−	1.48861i
$832$	49498.4	+	33757.6i	2.06256	+	1.40665i
$833$	8327.28	+	14423.3i	0.346366	+	0.599924i
$834$	28490.8	−	6508.72i	1.18292	−	0.270238i
$835$	4994.14	+	8650.10i	0.206981	+	0.358502i
$836$	−66612.3	−	115376.i	−2.75578	−	4.77315i
$837$	14211.6	+	5567.97i	0.586888	+	0.229937i
$838$	21371.9	−	12339.1i	0.881003	−	0.508647i
$839$		−	32485.8i		−	1.33675i	−0.743825	−	0.668375i	$-0.766990\pi$
$839$		−	32485.8i		−	1.33675i	0.743825	−	0.668375i	$-0.233010\pi$
$840$	24085.1	+	25947.3i	0.989303	+	1.06580i
$841$	1738.15	−	3010.57i	0.0712679	−	0.123440i
$842$	36513.6			1.49447
$843$	4453.04	−	14446.5i	0.181935	−	0.590229i
$844$	−55481.7	+	96097.1i	−2.26275	+	3.91919i
$845$	20159.3	+	16085.7i	0.820710	+	0.654868i
$846$	−27306.1	+	13163.1i	−1.10969	+	0.534938i
$847$	−20218.3	−	11673.0i	−0.820200	−	0.473543i
$848$	30844.1	+	53423.5i	1.24904	+	2.16341i
$849$	7128.69	+	31204.5i	0.288170	+	1.26141i
$850$	−3644.03	+	2103.88i	−0.147046	+	0.0848972i
$851$	505.213	+	291.685i	0.0203508	+	0.0117495i
$852$	−37008.9	+	8454.69i	−1.48815	+	0.339968i
$853$	−38754.7	−	22375.1i	−1.55561	−	0.898133i	−0.997668	−	0.0682538i	$-0.978257\pi$
$853$	−38754.7	−	22375.1i	−1.55561	−	0.898133i	−0.557944	−	0.829879i	$-0.688409\pi$
$854$	14385.4	+	24916.2i	0.576413	+	0.998377i
$855$	2351.66	−	31547.3i	0.0940645	−	1.26186i
$856$	124306.	+	71767.9i	4.96341	+	2.86563i
$857$	459.332	−	795.586i	0.0183086	−	0.0317114i	−0.856726	−	0.515772i	$-0.827505\pi$
$857$	459.332	−	795.586i	0.0183086	−	0.0317114i	0.875035	+	0.484060i	$0.160839\pi$
$858$	−52241.5	−	65501.1i	−2.07867	−	2.60626i
$859$	−14789.9	−	25616.8i	−0.587455	−	1.01750i	−0.994564	−	0.104123i	$-0.966797\pi$
$859$	−14789.9	−	25616.8i	−0.587455	−	1.01750i	0.407109	−	0.913379i	$-0.366537\pi$
$860$		−	81065.6i		−	3.21432i
$861$	649.495	+	2843.05i	0.0257082	+	0.112533i
$862$	7676.52			0.303322
$863$		−	39382.6i		−	1.55342i	−0.629861	−	0.776708i	$-0.716888\pi$
$863$		−	39382.6i		−	1.55342i	0.629861	−	0.776708i	$-0.283112\pi$
$864$	−11359.8	−	75066.9i	−0.447301	−	2.95582i
$865$	−6848.50	+	3953.99i	−0.269198	+	0.155421i
$866$	47165.8	+	27231.2i	1.85076	+	1.06854i
$867$	5793.56	+	1785.83i	0.226943	+	0.0699538i
$868$	19087.2			0.746384
$869$		−	138.800i		−	0.00541827i
$870$	−10549.5	−	46178.4i	−0.411104	−	1.79953i
$871$	3668.85	−	5379.60i	0.142726	−	0.209278i
$872$	−78919.2			−3.06484
$873$	−5984.46	−	12414.4i	−0.232008	−	0.481286i
$874$	−28456.2	+	49287.6i	−1.10131	+	1.90753i
$875$	11089.8			0.428462
$876$	15855.8	−	51439.2i	0.611551	−	1.98398i
$877$	17622.3	+	10174.2i	0.678520	+	0.391744i	0.799297	−	0.600936i	$-0.205205\pi$
$877$	17622.3	+	10174.2i	0.678520	+	0.391744i	−0.120777	+	0.992680i	$0.538539\pi$
$878$	35362.7	+	20416.7i	1.35927	+	0.784772i
$879$	−9787.84	+	31753.6i	−0.375581	+	1.21845i
$880$	153005.			5.86114
$881$	−24802.5	+	42959.1i	−0.948486	+	1.64283i	−0.199868	+	0.979823i	$0.564051\pi$
$881$	−24802.5	+	42959.1i	−0.948486	+	1.64283i	−0.748617	+	0.663002i	$0.769282\pi$
$882$	22211.3	−	32605.5i	0.847950	−	1.24477i
$883$	18405.7			0.701475			0.350737	−	0.936474i	$-0.385931\pi$
$883$	18405.7			0.701475			0.350737	+	0.936474i	$0.385931\pi$
$884$	−49385.8	−	33680.7i	−1.87899	−	1.28145i
$885$	−9036.16	−	39554.1i	−0.343217	−	1.50237i
$886$			58863.6i			2.23201i
$887$	−15366.7			−0.581693			−0.290847	−	0.956770i	$-0.593937\pi$
$887$	−15366.7			−0.581693			−0.290847	+	0.956770i	$0.593937\pi$
$888$	1880.48	+	579.646i	0.0710639	+	0.0219050i
$889$	15460.6	+	8926.20i	0.583277	+	0.336755i
$890$	4536.66	−	2619.24i	0.170864	−	0.0986486i
$891$	−6923.92	+	46183.7i	−0.260337	+	1.73649i
$892$		−	85668.5i		−	3.21569i
$893$	20867.5			0.781975
$894$	−3266.37	−	14298.0i	−0.122197	−	0.534894i
$895$			44460.4i			1.66050i
$896$	−10671.8	−	18484.1i	−0.397902	−	0.689187i
$897$	−9447.02	+	24074.7i	−0.351646	+	0.896131i
$898$	11015.0	−	19078.6i	0.409328	−	0.708978i
$899$	−13625.2	−	7866.50i	−0.505478	−	0.291838i
$900$	5952.38	+	4054.84i	0.220459	+	0.150179i
$901$	−9278.55	−	16070.9i	−0.343078	−	0.594229i
$902$	19857.6	+	11464.8i	0.733020	+	0.423209i
$903$	14136.2	−	3229.42i	0.520956	−	0.119013i
$904$	44624.3	+	25763.8i	1.64179	+	0.947890i
$905$	−24333.3	+	14048.9i	−0.893776	+	0.516022i
$906$	−70.0354	−	306.567i	−0.00256818	−	0.0112417i
$907$	−5644.58	−	9776.69i	−0.206643	−	0.357916i	0.744012	−	0.668166i	$-0.232920\pi$
$907$	−5644.58	−	9776.69i	−0.206643	−	0.357916i	−0.950655	+	0.310250i	$0.899587\pi$
$908$	67388.9	+	38907.0i	2.46297	+	1.42200i
$909$	−31400.2	−	21390.2i	−1.14574	−	0.780492i
$910$	−10791.3	−	22416.3i	−0.393108	−	0.816588i
$911$	−14294.1	+	24758.0i	−0.519850	+	0.900406i	0.479884	+	0.877332i	$0.340679\pi$
$911$	−14294.1	+	24758.0i	−0.519850	+	0.900406i	−0.999734	+	0.0230743i	$0.992655\pi$
$912$	−31083.5	+	100841.i	−1.12859	+	3.66137i
$913$	−9081.76			−0.329203
$914$	35303.2	−	61146.9i	1.27760	−	2.21287i
$915$	26405.2	+	28446.8i	0.954019	+	1.02778i
$916$			64426.3i			2.32391i
$917$	483.870	−	279.363i	0.0174251	−	0.0100604i
$918$	6899.56	+	45593.1i	0.248060	+	1.63921i
$919$	−25711.9	−	44534.3i	−0.922913	−	1.59853i	−0.794883	−	0.606763i	$-0.792468\pi$
$919$	−25711.9	−	44534.3i	−0.922913	−	1.59853i	−0.128030	−	0.991770i	$-0.540865\pi$
$920$	−42961.2	−	74410.9i	−1.53955	−	2.66658i
$921$	−32402.6	+	7402.39i	−1.15929	+	0.264839i
$922$	−1764.79	−	3056.71i	−0.0630373	−	0.109184i
$923$	16388.6	+	1230.45i	0.584439	+	0.0438795i
$924$	13006.2	+	56932.2i	0.463065	+	2.02698i
$925$	−60.9107	+	35.1668i	−0.00216512	+	0.00125003i
$926$	18001.0	−	31178.7i	0.638824	−	1.10648i
$927$	5765.66	+	3927.64i	0.204282	+	0.139159i
$928$			78257.2i			2.76823i
$929$			716.343i			0.0252986i	0.999920	+	0.0126493i	$0.00402651\pi$
$929$			716.343i			0.0252986i	−0.999920	+	0.0126493i	$0.995973\pi$
$930$	34740.8	−	7936.55i	1.22494	−	0.279838i
$931$	−23520.0	+	13579.3i	−0.827968	+	0.478028i
$932$	−29121.7	+	50440.3i	−1.02351	+	1.77278i
$933$	−29681.0	+	27550.8i	−1.04149	+	0.966746i
$934$	23993.5	−	13852.7i	0.840570	−	0.485303i
$935$	−46027.2			−1.60989
$936$	−12979.9	+	86264.6i	−0.453270	+	3.01244i
$937$	10269.7			0.358053			0.179027	−	0.983844i	$-0.442705\pi$
$937$	10269.7			0.358053			0.179027	+	0.983844i	$0.442705\pi$
$938$	−5439.82	+	3140.68i	−0.189356	+	0.109325i
$939$	7014.43	+	2162.15i	0.243778	+	0.0751430i
$940$	−25569.3	+	44287.3i	−0.887210	+	1.53669i
$941$	−15117.0	+	8727.78i	−0.523697	+	0.302357i	−0.738446	−	0.674313i	$-0.764440\pi$
$941$	−15117.0	+	8727.78i	−0.523697	+	0.302357i	0.214749	+	0.976669i	$0.431107\pi$
$942$	−12741.7	+	41336.3i	−0.440707	+	1.42974i
$943$		−	7077.82i		−	0.244417i
$944$			135338.i			4.66618i
$945$	−5058.61	+	12911.5i	−0.174134	+	0.444457i
$946$	57005.1	−	98735.7i	1.95919	−	3.39342i
$947$	19484.7	−	11249.5i	0.668604	−	0.386019i	−0.126943	−	0.991910i	$-0.540517\pi$
$947$	19484.7	−	11249.5i	0.668604	−	0.386019i	0.795548	+	0.605891i	$0.207183\pi$
$948$	−171.935	+	159.595i	−0.00589048	+	0.00546772i
$949$	−13129.8	+	19252.1i	−0.449116	+	0.658536i
$950$	−3430.80	−	5942.33i	−0.117168	−	0.202942i
$951$	−7927.30	+	25717.6i	−0.270305	+	0.876920i
$952$	17762.2	+	30765.0i	0.604701	+	1.04737i
$953$	17997.1	+	31171.9i	0.611734	+	1.05955i	0.990948	+	0.134246i	$0.0428611\pi$
$953$	17997.1	+	31171.9i	0.611734	+	1.05955i	−0.379214	+	0.925309i	$0.623806\pi$
$954$	−24748.6	+	36330.2i	−0.839900	+	1.23295i
$955$	−30862.3	+	17818.3i	−1.04574	+	0.603757i
$956$		−	71001.6i		−	2.40204i
$957$	14179.4	−	46000.7i	0.478951	−	1.55381i
$958$	−13505.5	+	23392.2i	−0.455473	+	0.788903i
$959$	−6828.80			−0.229941
$960$	−53043.6	−	57144.9i	−1.78331	−	1.92119i
$961$	−8977.39	+	15549.3i	−0.301346	+	0.521946i
$962$	−1142.44	−	779.132i	−0.0382886	−	0.0261125i
$963$	−4179.45	+	56066.8i	−0.139856	+	1.87614i
$964$	40399.5	+	23324.7i	1.34977	+	0.779292i
$965$	−15093.7	−	26143.1i	−0.503507	−	0.872100i
$966$	18284.5	−	16972.2i	0.609000	−	0.565293i
$967$	253.944	−	146.615i	0.00844498	−	0.00487571i	−0.495772	−	0.868453i	$-0.665115\pi$
$967$	253.944	−	146.615i	0.00844498	−	0.00487571i	0.504217	+	0.863577i	$0.331781\pi$
$968$	165519.	+	95562.4i	5.49585	+	3.17303i
$969$	9350.58	−	30335.0i	0.309994	−	1.00568i
$970$	−27865.2	−	16088.0i	−0.922369	−	0.532530i
$971$	−2773.93	−	4804.59i	−0.0916784	−	0.158792i	0.816539	−	0.577290i	$-0.195890\pi$
$971$	−2773.93	−	4804.59i	−0.0916784	−	0.158792i	−0.908217	+	0.418498i	$0.862557\pi$
$972$	65169.9	−	44526.0i	2.15054	−	1.46931i
$973$	7637.32	+	4409.41i	0.251635	+	0.145282i
$974$	29747.1	−	51523.4i	0.978601	−	1.69499i
$975$	−1944.19	−	2437.65i	−0.0638605	−	0.0800691i
$976$	−64733.4	−	112122.i	−2.12302	−	3.67717i
$977$		−	44350.1i		−	1.45229i	−0.687543	−	0.726143i	$-0.741311\pi$
$977$		−	44350.1i		−	1.45229i	0.687543	−	0.726143i	$-0.258689\pi$
$978$	−64213.2	−	19793.3i	−2.09950	−	0.647158i
$979$	5323.47			0.173788
$980$		−	66555.7i		−	2.16943i
$981$	−13423.3	−	27845.8i	−0.436874	−	0.906266i
$982$	−42467.9	+	24518.9i	−1.38005	+	0.796770i
$983$	−7906.47	−	4564.80i	−0.256538	−	0.148113i	0.366216	−	0.930530i	$-0.380653\pi$
$983$	−7906.47	−	4564.80i	−0.256538	−	0.148113i	−0.622754	+	0.782417i	$0.713986\pi$
$984$	−5317.15	−	23274.8i	−0.172261	−	0.754040i
$985$	−17251.9			−0.558061
$986$		−	47530.8i		−	1.53518i
$987$	−8741.40	−	2694.48i	−0.281907	−	0.0868960i
$988$	54923.2	−	80533.4i	1.76856	−	2.59323i
$989$	−35192.3			−1.13150
$990$	47345.4	+	98214.9i	1.51994	+	3.15300i
$991$	−23742.5	+	41123.3i	−0.761056	+	1.31819i	0.181251	+	0.983437i	$0.441985\pi$
$991$	−23742.5	+	41123.3i	−0.761056	+	1.31819i	−0.942307	+	0.334751i	$0.891348\pi$
$992$	−58874.3			−1.88434
$993$	−35988.6	+	8221.60i	−1.15011	+	0.262744i
$994$	−13729.7	−	7926.85i	−0.438108	−	0.252942i
$995$	49626.9	+	28652.1i	1.58118	+	0.912897i
$996$	10442.4	+	11249.8i	0.332208	+	0.357894i
$997$	25385.8			0.806395			0.403198	−	0.915113i	$-0.367899\pi$
$997$	25385.8			0.806395			0.403198	+	0.915113i	$0.367899\pi$
$998$	686.928	−	1189.79i	0.0217879	−	0.0377377i
$999$	115.328	+	762.097i	0.00365245	+	0.0241358i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.4.r.a.43.2	yes	80
3.2	odd	2		351.4.r.a.316.39		80
9.4	even	3		117.4.l.a.4.2	✓	80
9.5	odd	6		351.4.l.a.199.39		80
13.10	even	6		117.4.l.a.88.39	yes	80
39.23	odd	6		351.4.l.a.127.2		80
117.23	odd	6		351.4.r.a.10.39		80
117.49	even	6	inner	117.4.r.a.49.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.2	✓	80	9.4	even	3
117.4.l.a.88.39	yes	80	13.10	even	6
117.4.r.a.43.2	yes	80	1.1	even	1	trivial
117.4.r.a.49.2	yes	80	117.49	even	6	inner
351.4.l.a.127.2		80	39.23	odd	6
351.4.l.a.199.39		80	9.5	odd	6
351.4.r.a.10.39		80	117.23	odd	6
351.4.r.a.316.39		80	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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	117.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.65052 + 2.68498i) q^{2} +(1.15725 + 5.06565i) q^{3} +(10.4182 - 18.0449i) q^{4} +(10.1662 - 5.86946i) q^{5} +(-18.9830 - 20.4507i) q^{6} -8.42000i q^{7} +68.9311i q^{8} +(-24.3215 + 11.7244i) q^{9} +(-31.5187 + 54.5920i) q^{10} +(-55.4777 + 32.0300i) q^{11} +(103.465 + 31.8926i) q^{12} +(-38.7239 - 26.4094i) q^{13} +(22.6075 + 39.1574i) q^{14} +(41.4974 + 44.7059i) q^{15} +(-101.733 - 176.206i) q^{16} +(30.6034 + 53.0066i) q^{17} +(81.6280 - 119.828i) q^{18} +(-86.4378 + 49.9049i) q^{19} -244.597i q^{20} +(42.6528 - 9.74404i) q^{21} +(172.000 - 297.913i) q^{22} -106.185 q^{23} +(-349.181 + 79.7704i) q^{24} +(6.40106 - 11.0870i) q^{25} +(250.995 + 18.8446i) q^{26} +(-87.5379 - 109.636i) q^{27} +(-151.938 - 87.7214i) q^{28} +(72.3061 + 125.238i) q^{29} +(-313.019 - 96.4862i) q^{30} +(-94.2187 + 54.3972i) q^{31} +(468.651 + 270.576i) q^{32} +(-226.454 - 243.963i) q^{33} +(-284.643 - 164.339i) q^{34} +(-49.4208 - 85.5994i) q^{35} +(-41.8213 + 561.027i) q^{36} +(-4.75786 - 2.74695i) q^{37} +(267.987 - 464.167i) q^{38} +(88.9676 - 226.724i) q^{39} +(404.588 + 700.767i) q^{40} +66.6556i q^{41} +(-172.195 + 159.837i) q^{42} +331.425 q^{43} +1334.78i q^{44} +(-178.442 + 261.947i) q^{45} +(493.815 - 285.104i) q^{46} +(-181.062 - 104.536i) q^{47} +(774.869 - 719.257i) q^{48} +272.104 q^{49} +68.7468i q^{50} +(-233.097 + 216.368i) q^{51} +(-879.989 + 423.629i) q^{52} -303.187 q^{53} +(701.468 + 274.828i) q^{54} +(-375.998 + 651.247i) q^{55} +580.400 q^{56} +(-352.831 - 380.111i) q^{57} +(-672.522 - 388.281i) q^{58} +(-576.049 - 332.582i) q^{59} +(1239.04 - 283.060i) q^{60} +636.308 q^{61} +(292.110 - 505.950i) q^{62} +(98.7197 + 204.788i) q^{63} -1278.24 q^{64} +(-548.684 - 41.1950i) q^{65} +(1708.17 + 526.532i) q^{66} +138.922i q^{67} +1275.33 q^{68} +(-122.882 - 537.895i) q^{69} +(459.665 + 265.388i) q^{70} +(-303.653 + 175.314i) q^{71} +(-808.178 - 1676.51i) q^{72} -497.163i q^{73} +29.5021 q^{74} +(63.5702 + 19.5951i) q^{75} +2079.68i q^{76} +(269.693 + 467.122i) q^{77} +(195.003 + 1293.26i) q^{78} +(-1.08336 + 1.87643i) q^{79} +(-2068.47 - 1194.23i) q^{80} +(454.076 - 570.313i) q^{81} +(-178.969 - 309.983i) q^{82} +(122.776 + 70.8847i) q^{83} +(268.536 - 871.179i) q^{84} +(622.240 + 359.250i) q^{85} +(-1541.30 + 889.869i) q^{86} +(-550.735 + 511.209i) q^{87} +(-2207.87 - 3824.14i) q^{88} +(-71.9677 - 41.5506i) q^{89} +(126.524 - 1697.30i) q^{90} +(-222.367 + 326.056i) q^{91} +(-1106.26 + 1916.09i) q^{92} +(-384.591 - 414.327i) q^{93} +1122.71 q^{94} +(-585.829 + 1014.69i) q^{95} +(-828.296 + 2687.15i) q^{96} +510.426i q^{97} +(-1265.42 + 730.592i) q^{98} +(973.769 - 1429.46i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 3 q^{2} - q^{3} + 153 q^{4} - 3 q^{6} - 17 q^{9} - 10 q^{10} - 3 q^{11} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 84 q^{15} - 551 q^{16} - 138 q^{17} + 168 q^{18} - 96 q^{19} + 249 q^{21} - 31 q^{22}+ \cdots + 2331 q^{99}+O(q^{100}) \) 80 * q - 3 * q^2 - q^3 + 153 * q^4 - 3 * q^6 - 17 * q^9 - 10 * q^10 - 3 * q^11 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 84 * q^15 - 551 * q^16 - 138 * q^17 + 168 * q^18 - 96 * q^19 + 249 * q^21 - 31 * q^22 + 654 * q^23 - 834 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 + 201 * q^29 + 87 * q^30 - 180 * q^31 + 117 * q^32 + 231 * q^33 - 24 * q^34 + 297 * q^35 + 251 * q^36 + 246 * q^37 - 768 * q^38 - 560 * q^39 + 328 * q^40 + 1212 * q^42 + 166 * q^43 - 603 * q^45 - 6 * q^46 - 372 * q^47 - 1288 * q^48 - 3226 * q^49 + 186 * q^51 + 186 * q^52 - 2568 * q^53 + 480 * q^54 - 127 * q^55 + 4596 * q^56 - 1332 * q^57 - 3 * q^58 - 531 * q^59 - 711 * q^60 + 838 * q^61 + 135 * q^62 + 2895 * q^63 - 3178 * q^64 - 2337 * q^65 + 6228 * q^66 - 3900 * q^68 + 591 * q^69 + 1005 * q^70 - 2598 * q^71 + 1821 * q^72 - 942 * q^74 - 494 * q^75 - 1584 * q^77 + 2631 * q^78 - 260 * q^79 - 1332 * q^80 - 2357 * q^81 - 1273 * q^82 - 1194 * q^83 + 8196 * q^84 + 3936 * q^85 + 2910 * q^86 - 363 * q^87 + 781 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 + 1830 * q^93 - 1078 * q^94 - 5292 * q^95 - 6777 * q^96 - 6339 * q^98 + 2331 * q^99

Introduction

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