LMFDB - Embedded newform 117.4.l.a.4.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([2, 1]))

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

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

chi := DirichletCharacter("117.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	117.l (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			4.2
Character	$\chi$	$=$	117.4
Dual form			117.4.l.a.88.39

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.36996i q^{2} +(-4.96560 + 1.53062i) q^{3} -20.8364 q^{4} +(-10.1662 - 5.86946i) q^{5} +(8.21934 + 26.6651i) q^{6} +(7.29194 + 4.21000i) q^{7} +68.9311i q^{8} +(22.3144 - 15.2009i) q^{9} +(-31.5187 + 54.5920i) q^{10} -64.0601i q^{11} +(103.465 - 31.8926i) q^{12} +(-3.50927 + 46.7406i) q^{13} +(22.6075 - 39.1574i) q^{14} +(59.4652 + 13.5848i) q^{15} +203.465 q^{16} +(30.6034 + 53.0066i) q^{17} +(-81.6280 - 119.828i) q^{18} +(-86.4378 + 49.9049i) q^{19} +(211.827 + 122.299i) q^{20} +(-42.6528 - 9.74404i) q^{21} -344.000 q^{22} +(53.0925 + 91.9588i) q^{23} +(-105.507 - 342.284i) 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} -144.612 q^{29} +(72.9500 - 319.325i) q^{30} +(94.2187 + 54.3972i) q^{31} -541.152i q^{32} +(98.0514 + 318.097i) q^{33} +(284.643 - 164.339i) q^{34} +(-49.4208 - 85.5994i) q^{35} +(-464.953 + 316.732i) q^{36} +(-4.75786 - 2.74695i) q^{37} +(267.987 + 464.167i) q^{38} +(-54.1163 - 237.467i) q^{39} +(404.588 - 700.767i) q^{40} +(57.7255 - 33.3278i) q^{41} +(-52.3251 + 229.043i) q^{42} +(-165.712 + 287.022i) q^{43} +1334.78i q^{44} +(-316.074 + 23.5614i) q^{45} +(493.815 - 285.104i) q^{46} +(181.062 - 104.536i) q^{47} +(-1010.33 + 311.428i) q^{48} +(-136.052 - 235.649i) q^{49} +(59.5365 - 34.3734i) q^{50} +(-233.097 - 216.368i) q^{51} +(73.1207 - 973.908i) q^{52} -303.187 q^{53} +(588.742 + 470.075i) q^{54} +(-375.998 + 651.247i) q^{55} +(-290.200 + 502.641i) q^{56} +(352.831 - 380.111i) q^{57} +776.561i q^{58} +665.165i q^{59} +(-1239.04 - 283.060i) q^{60} +(-318.154 + 551.059i) q^{61} +(292.110 - 505.950i) q^{62} +(226.711 - 16.9000i) q^{63} -1278.24 q^{64} +(310.018 - 454.577i) q^{65} +(1708.17 - 526.532i) q^{66} +(120.310 - 69.4610i) q^{67} +(-637.665 - 1104.47i) q^{68} +(-404.390 - 375.367i) q^{69} +(-459.665 + 265.388i) q^{70} +(-303.653 + 175.314i) q^{71} +(1047.81 + 1538.16i) q^{72} -497.163i q^{73} +(-14.7510 + 25.5495i) q^{74} +(-48.7550 - 45.2559i) q^{75} +(1801.06 - 1039.84i) q^{76} +(269.693 - 467.122i) q^{77} +(-1275.19 + 290.602i) q^{78} +(-1.08336 - 1.87643i) q^{79} +(-2068.47 - 1194.23i) q^{80} +(266.867 - 678.397i) q^{81} +(-178.969 - 309.983i) q^{82} +(-122.776 + 70.8847i) q^{83} +(888.731 + 203.031i) q^{84} -718.500i q^{85} +(1541.30 + 889.869i) q^{86} +(718.087 - 221.346i) q^{87} +4415.73 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} +(-551.114 - 125.902i) q^{93} +(-561.355 - 972.296i) q^{94} +1171.66 q^{95} +(828.296 + 2687.15i) q^{96} +(-442.042 - 255.213i) q^{97} +(-1265.42 + 730.592i) q^{98} +(-973.769 - 1429.46i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - q^{3} - 306 q^{4} + 42 q^{6} - 3 q^{7} - 17 q^{9} - 10 q^{10} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 63 q^{15} + 1102 q^{16} - 138 q^{17} - 168 q^{18} - 96 q^{19} - 387 q^{20} - 249 q^{21} + 62 q^{22}+ \cdots - 2331 q^{99}+O(q^{100}) $ 80 * q - q^3 - 306 * q^4 + 42 * q^6 - 3 * q^7 - 17 * q^9 - 10 * q^10 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 63 * q^15 + 1102 * q^16 - 138 * q^17 - 168 * q^18 - 96 * q^19 - 387 * q^20 - 249 * q^21 + 62 * q^22 - 327 * q^23 - 258 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 - 402 * q^29 + 450 * q^30 + 180 * q^31 + 369 * q^33 + 24 * q^34 + 297 * q^35 + 206 * q^36 + 246 * q^37 - 768 * q^38 - 983 * q^39 + 328 * q^40 + 381 * q^41 - 1113 * q^42 - 83 * q^43 - 1038 * q^45 - 6 * q^46 + 372 * q^47 + 1205 * q^48 + 1613 * q^49 - 708 * q^50 + 186 * q^51 + 402 * q^52 - 2568 * q^53 - 627 * q^54 - 127 * q^55 - 2298 * q^56 + 1332 * q^57 + 711 * q^60 - 419 * q^61 + 135 * q^62 + 1845 * q^63 - 3178 * q^64 + 363 * q^65 + 6228 * q^66 + 879 * q^67 + 1950 * q^68 - 3153 * q^69 - 1005 * q^70 - 2598 * q^71 + 1812 * q^72 + 471 * q^74 - 68 * q^75 + 1485 * q^76 - 1584 * q^77 - 60 * q^78 - 260 * q^79 - 1332 * q^80 + 1639 * q^81 - 1273 * q^82 + 1194 * q^83 + 1671 * q^84 - 2910 * q^86 - 1629 * q^87 - 1562 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 - 75 * q^93 + 539 * q^94 + 10584 * q^95 + 6777 * q^96 + 789 * q^97 - 6339 * q^98 - 2331 * q^99

Character values

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

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

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 $

$2$		−	5.36996i		−	1.89857i	−0.314422	−	0.949283i	$-0.601811\pi$
$2$		−	5.36996i		−	1.89857i	0.314422	−	0.949283i	$-0.398189\pi$
$3$	−4.96560	+	1.53062i	−0.955631	+	0.294567i
$3$	−4.96560	+	1.53062i	−0.955631	+	0.294567i
$4$	−20.8364			−2.60455
$5$	−10.1662	−	5.86946i	−0.909292	−	0.524980i	−0.0290890	−	0.999577i	$-0.509261\pi$
$5$	−10.1662	−	5.86946i	−0.909292	−	0.524980i	−0.880203	+	0.474597i	$0.842594\pi$
$6$	8.21934	+	26.6651i	0.559255	+	1.81433i
$7$	7.29194	+	4.21000i	0.393728	+	0.227319i	0.683774	−	0.729694i	$-0.260337\pi$
$7$	7.29194	+	4.21000i	0.393728	+	0.227319i	−0.290046	+	0.957013i	$0.593671\pi$
$8$			68.9311i			3.04635i
$9$	22.3144	−	15.2009i	0.826460	−	0.562995i
$10$	−31.5187	+	54.5920i	−0.996710	+	1.72635i
$11$		−	64.0601i		−	1.75589i	−0.478757	−	0.877947i	$-0.658913\pi$
$11$		−	64.0601i		−	1.75589i	0.478757	−	0.877947i	$-0.341087\pi$
$12$	103.465	−	31.8926i	2.48899	−	0.767216i
$13$	−3.50927	+	46.7406i	−0.0748690	+	0.997193i
$13$	−3.50927	+	46.7406i	−0.0748690	+	0.997193i
$14$	22.6075	−	39.1574i	0.431580	−	0.747518i
$15$	59.4652	+	13.5848i	1.02359	+	0.233839i
$16$	203.465			3.17915
$17$	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	$0.539193\pi$
$20$	211.827	+	122.299i	2.36830	+	1.36734i
$21$	−42.6528	−	9.74404i	−0.443219	−	0.101254i
$22$	−344.000			−3.33368
$23$	53.0925	+	91.9588i	0.481328	+	0.833684i	0.999770	−	0.0214281i	$-0.00682128\pi$
$23$	53.0925	+	91.9588i	0.481328	+	0.833684i	−0.518442	+	0.855113i	$0.673488\pi$
$24$	−105.507	−	342.284i	−0.897356	−	2.91119i
$25$	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
$29$	−144.612			−0.925994			−0.462997	−	0.886360i	$-0.653226\pi$
$29$	−144.612			−0.925994			−0.462997	+	0.886360i	$0.653226\pi$
$30$	72.9500	−	319.325i	0.443960	−	1.94335i
$31$	94.2187	+	54.3972i	0.545877	+	0.315162i	0.747457	−	0.664310i	$-0.231274\pi$
$31$	94.2187	+	54.3972i	0.545877	+	0.315162i	−0.201581	+	0.979472i	$0.564608\pi$
$32$		−	541.152i		−	2.98947i
$33$	98.0514	+	318.097i	0.517229	+	1.67799i
$34$	284.643	−	164.339i	1.43576	−	0.828937i
$35$	−49.4208	−	85.5994i	−0.238676	−	0.413398i
$36$	−464.953	+	316.732i	−2.15256	+	1.46635i
$37$	−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
$39$	−54.1163	−	237.467i	−0.222193	−	0.975003i
$40$	404.588	−	700.767i	1.59927	−	2.77003i
$41$	57.7255	−	33.3278i	0.219883	−	0.126950i	−0.386013	−	0.922493i	$-0.626148\pi$
$41$	57.7255	−	33.3278i	0.219883	−	0.126950i	0.605896	+	0.795544i	$0.292815\pi$
$42$	−52.3251	+	229.043i	−0.192236	+	0.841480i
$43$	−165.712	+	287.022i	−0.587696	+	1.01792i	0.406838	+	0.913500i	$0.366631\pi$
$43$	−165.712	+	287.022i	−0.587696	+	1.01792i	−0.994533	+	0.104418i	$0.966702\pi$
$44$			1334.78i			4.57332i
$45$	−316.074	+	23.5614i	−1.04706	+	0.0780518i
$46$	493.815	−	285.104i	1.58281	−	0.913833i
$47$	181.062	−	104.536i	0.561928	−	0.324429i	−0.191991	−	0.981397i	$-0.561494\pi$
$47$	181.062	−	104.536i	0.561928	−	0.324429i	0.753919	+	0.656967i	$0.228161\pi$
$48$	−1010.33	+	311.428i	−3.03809	+	0.936473i
$49$	−136.052	−	235.649i	−0.396652	−	0.687022i
$50$	59.5365	−	34.3734i	0.168395	−	0.0972227i
$51$	−233.097	−	216.368i	−0.640002	−	0.594069i
$52$	73.1207	−	973.908i	0.195000	−	2.59724i
$53$	−303.187			−0.785773			−0.392887	−	0.919587i	$-0.628524\pi$
$53$	−303.187			−0.785773			−0.392887	+	0.919587i	$0.628524\pi$
$54$	588.742	+	470.075i	1.48366	+	1.18461i
$55$	−375.998	+	651.247i	−0.921810	+	1.59662i
$56$	−290.200	+	502.641i	−0.692493	+	1.19943i
$57$	352.831	−	380.111i	0.819887	−	0.883280i
$58$			776.561i			1.75806i
$59$			665.165i			1.46775i	0.679286	+	0.733873i	$0.262289\pi$
$59$			665.165i			1.46775i	−0.679286	+	0.733873i	$0.737711\pi$
$60$	−1239.04	−	283.060i	−2.66599	−	0.609048i
$61$	−318.154	+	551.059i	−0.667795	+	1.15665i	0.310725	+	0.950500i	$0.399428\pi$
$61$	−318.154	+	551.059i	−0.667795	+	1.15665i	−0.978520	+	0.206154i	$0.933905\pi$
$62$	292.110	−	505.950i	0.598356	−	1.03638i
$63$	226.711	−	16.9000i	0.453379	−	0.0337968i
$64$	−1278.24			−2.49656
$65$	310.018	−	454.577i	0.591585	−	0.867436i
$66$	1708.17	−	526.532i	3.18577	−	0.981994i
$67$	120.310	−	69.4610i	0.219376	−	0.126657i	−0.386285	−	0.922379i	$-0.626242\pi$
$67$	120.310	−	69.4610i	0.219376	−	0.126657i	0.605661	+	0.795723i	$0.292909\pi$
$68$	−637.665	−	1104.47i	−1.13718	−	1.96965i
$69$	−404.390	−	375.367i	−0.705548	−	0.654911i
$70$	−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	$0.428001\pi$
$72$	1047.81	+	1538.16i	1.71508	+	2.51769i
$73$		−	497.163i		−	0.797104i	−0.917146	−	0.398552i	$-0.869513\pi$
$73$		−	497.163i		−	0.797104i	0.917146	−	0.398552i	$-0.130487\pi$
$74$	−14.7510	+	25.5495i	−0.0231726	+	0.0401361i
$75$	−48.7550	−	45.2559i	−0.0750632	−	0.0696760i
$76$	1801.06	−	1039.84i	2.71836	−	1.56945i
$77$	269.693	−	467.122i	0.399148	−	0.691344i
$78$	−1275.19	+	290.602i	−1.85111	+	0.421849i
$79$	−1.08336	−	1.87643i	−0.00154288	−	0.00267235i	0.865253	−	0.501336i	$-0.167158\pi$
$79$	−1.08336	−	1.87643i	−0.00154288	−	0.00267235i	−0.866796	+	0.498663i	$0.833824\pi$
$80$	−2068.47	−	1194.23i	−2.89078	−	1.66899i
$81$	266.867	−	678.397i	0.366073	−	0.930586i
$82$	−178.969	−	309.983i	−0.241022	−	0.417462i
$83$	−122.776	+	70.8847i	−0.162366	+	0.0937422i	−0.578981	−	0.815341i	$-0.696550\pi$
$83$	−122.776	+	70.8847i	−0.162366	+	0.0937422i	0.416615	+	0.909083i	$0.363216\pi$
$84$	888.731	+	203.031i	1.15439	+	0.263720i
$85$		−	718.500i		−	0.916851i
$86$	1541.30	+	889.869i	1.93259	+	1.11578i
$87$	718.087	−	221.346i	0.884908	−	0.272767i
$88$	4415.73			5.34907
$89$	−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
$93$	−551.114	−	125.902i	−0.614493	−	0.140381i
$94$	−561.355	−	972.296i	−0.615951	−	1.06686i
$95$	1171.66			1.26536
$96$	828.296	+	2687.15i	0.880600	+	2.85683i
$97$	−442.042	−	255.213i	−0.462707	−	0.267144i	0.250475	−	0.968123i	$-0.419413\pi$
$97$	−442.042	−	255.213i	−0.462707	−	0.267144i	−0.713182	+	0.700979i	$0.752747\pi$
$98$	−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
$101$	−1407.17			−1.38632			−0.693161	−	0.720783i	$-0.743782\pi$
$101$	−1407.17			−1.38632			−0.693161	+	0.720783i	$0.743782\pi$
$102$	−1161.88	+	1251.72i	−1.12788	+	1.21509i
$103$	−129.191	+	223.766i	−0.123588	+	0.214061i	−0.921180	−	0.389136i	$-0.872774\pi$
$103$	−129.191	+	223.766i	−0.123588	+	0.214061i	0.797592	+	0.603197i	$0.206107\pi$
$104$	−3221.88	−	241.898i	−3.03780	−	0.228077i
$105$	376.424	+	349.408i	0.349859	+	0.324750i
$106$			1628.10i			1.49184i
$107$	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	$-0.223140\pi$
$108$	1823.98	−	2284.43i	1.62511	−	2.03536i
$109$			1144.90i			1.00607i	0.864266	+	0.503035i	$0.167783\pi$
$109$			1144.90i			1.00607i	−0.864266	+	0.503035i	$0.832217\pi$
$110$	3497.17	+	2019.09i	3.03129	+	1.75012i
$111$	27.8302	+	6.35782i	0.0237975	+	0.00543655i
$112$	1483.66	+	856.590i	1.25172	+	0.722680i
$113$	−747.525			−0.622312			−0.311156	−	0.950359i	$-0.600716\pi$
$113$	−747.525			−0.622312			−0.311156	+	0.950359i	$0.600716\pi$
$114$	−2041.18	−	1894.69i	−1.67697	−	1.55661i
$115$		−	1246.50i		−	1.01075i
$116$	3013.20			2.41180
$117$	632.190	+	1096.33i	0.499539	+	0.866292i
$118$	3571.91			2.78661
$119$			515.361i			0.397000i
$120$	−936.418	+	4099.00i	−0.712357	+	3.11822i
$121$	−2772.69			−2.08317
$122$	2959.16	+	1708.47i	2.19598	+	1.26785i
$123$	−235.630	+	253.848i	−0.172732	+	0.186087i
$124$	−1963.18	−	1133.44i	−1.42176	−	0.820856i
$125$			1317.08i			0.942427i
$126$	−90.7522	−	1217.43i	−0.0641654	−	0.860771i
$127$	−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	$0.901155\pi$
$128$			2534.87i			1.75042i
$129$	383.541	−	1678.88i	0.261775	−	1.14587i
$130$	−2441.06	−	1664.78i	−1.64688	−	1.12316i
$131$	33.1785	−	57.4668i	0.0221284	−	0.0383274i	−0.854749	−	0.519041i	$-0.826289\pi$
$131$	33.1785	−	57.4668i	0.0221284	−	0.0383274i	0.876878	+	0.480714i	$0.159622\pi$
$132$	−2043.04	−	6628.01i	−1.34715	−	4.37041i
$133$	−840.399			−0.547908
$134$	−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
$137$	702.365	+	405.511i	0.438008	+	0.252884i	0.702752	−	0.711435i	$-0.251954\pi$
$137$	702.365	+	405.511i	0.438008	+	0.252884i	−0.264744	+	0.964319i	$0.585288\pi$
$138$	−2015.70	+	2171.56i	−1.24339	+	1.33953i
$139$	1047.37			0.639111			0.319555	−	0.947568i	$-0.396466\pi$
$139$	1047.37			0.639111			0.319555	+	0.947568i	$0.396466\pi$
$140$	1029.75	+	1783.59i	0.621644	+	1.07672i
$141$	−739.078	+	796.222i	−0.441430	+	0.475560i
$142$	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
$146$	−2669.75			−1.51335
$147$	1036.27	+	961.894i	0.581427	+	0.539699i
$148$	99.1369	+	57.2367i	0.0550608	+	0.0317894i
$149$		−	525.616i		−	0.288994i	−0.989505	−	0.144497i	$-0.953844\pi$
$149$		−	525.616i		−	0.288994i	0.989505	−	0.144497i	$-0.0461564\pi$
$150$	−243.022	+	261.812i	−0.132284	+	0.142513i
$151$	−9.76002	+	5.63495i	−0.00525999	+	0.00303686i	−0.502628	−	0.864503i	$-0.667633\pi$
$151$	−9.76002	+	5.63495i	−0.00525999	+	0.00303686i	0.497368	+	0.867540i	$0.334300\pi$
$152$	−3440.00	−	5958.25i	−1.83566	−	3.17946i
$153$	1488.64	+	717.614i	0.786599	+	0.379187i
$154$	−2508.42	−	1448.24i	−1.31256	−	0.757808i
$155$	−638.564	−	1106.02i	−0.330908	−	0.573149i
$156$	1127.59	+	4947.96i	0.578715	+	2.53945i
$157$	−775.103	+	1342.52i	−0.394012	+	0.682449i	−0.992975	−	0.118328i	$-0.962247\pi$
$157$	−775.103	+	1342.52i	−0.394012	+	0.682449i	0.598962	+	0.800777i	$0.295580\pi$
$158$	−10.0764	+	5.81759i	−0.00507362	+	0.00292926i
$159$	1505.51	−	464.064i	0.750909	−	0.231463i
$160$	−3176.27	+	5501.46i	−1.56941	+	2.71830i
$161$			894.077i			0.437659i
$162$	−3642.96	−	1433.07i	−1.76678	−	0.695014i
$163$	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
$165$	870.246	−	3809.34i	0.410597	−	1.79732i
$166$	380.648	+	659.301i	0.177976	+	0.308263i
$167$	736.874	−	425.434i	0.341443	−	0.197132i	−0.319467	−	0.947597i	$-0.603504\pi$
$167$	736.874	−	425.434i	0.341443	−	0.197132i	0.660910	+	0.750465i	$0.270171\pi$
$168$	671.667	−	2940.10i	0.308454	−	1.35020i
$169$	−2172.37	−	328.051i	−0.988789	−	0.149318i
$170$	−3858.32			−1.74070
$171$	−1170.21	+	2427.53i	−0.523324	+	1.08560i
$172$	3452.86	−	5980.52i	1.53069	−	2.65122i
$173$	336.827	−	583.402i	0.148026	−	0.256389i	−0.782472	−	0.622686i	$-0.786041\pi$
$173$	336.827	−	583.402i	0.148026	−	0.256389i	0.930498	+	0.366297i	$0.119375\pi$
$174$	−1188.62	−	3856.10i	−0.517867	−	1.68006i
$175$			107.794i			0.0465626i
$176$		−	13034.0i		−	5.58225i
$177$	−1018.11	−	3302.94i	−0.432350	−	1.40262i
$178$	−223.125	+	386.464i	−0.0939546	+	0.162734i
$179$	−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	$0.876360\pi$
$180$	6585.85	−	490.936i	2.72711	−	0.203290i
$181$	−2393.55			−0.982936			−0.491468	−	0.870896i	$-0.663540\pi$
$181$	−2393.55			−0.982936			−0.491468	+	0.870896i	$0.663540\pi$
$182$	1750.90	+	1194.10i	0.713108	+	0.486334i
$183$	736.367	−	3223.31i	0.297453	−	1.30204i
$184$	−6338.82	+	3659.72i	−2.53970	+	1.46629i
$185$	32.2463	+	55.8522i	0.0128151	+	0.0221964i
$186$	−676.089	+	2959.46i	−0.266523	+	1.16666i
$187$	3395.60	−	1960.45i	1.32787	−	0.766645i
$188$	−3772.69	+	2178.16i	−1.46357	+	0.844994i
$189$	−1099.89	+	430.926i	−0.423308	+	0.165848i
$190$		−	6291.76i		−	2.40238i
$191$	1517.89	−	2629.06i	0.575028	−	0.995978i	−0.421010	−	0.907056i	$-0.638324\pi$
$191$	1517.89	−	2629.06i	0.575028	−	0.995978i	0.996039	−	0.0889223i	$-0.0283423\pi$
$192$	6347.23	−	1956.49i	2.38579	−	0.735405i
$193$	−2227.05	+	1285.79i	−0.830603	+	0.479549i	−0.854059	−	0.520176i	$-0.825866\pi$
$193$	−2227.05	+	1285.79i	−0.830603	+	0.479549i	0.0234564	+	0.999725i	$0.492533\pi$
$194$	−1370.48	+	2373.75i	−0.507191	+	0.878480i
$195$	−843.644	+	2731.77i	−0.309818	+	1.00321i
$196$	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	$0.752287\pi$
$198$	−7676.16	+	5229.10i	−2.75516	+	1.87685i
$199$	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
$201$	−491.093	+	529.064i	−0.172334	+	0.185658i
$202$			7556.43i			2.63202i
$203$	−1054.50	−	608.818i	−0.364589	−	0.210496i
$204$	4856.91	+	4508.33i	1.66692	+	1.54728i
$205$	−782.465			−0.266584
$206$	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
$210$	1876.31	−	2021.38i	0.616560	−	0.664231i
$211$	2662.73	+	4611.98i	0.868766	+	1.50475i	0.863259	+	0.504762i	$0.168420\pi$
$211$	2662.73	+	4611.98i	0.868766	+	1.50475i	0.00550699	+	0.999985i	$0.498247\pi$
$212$	6317.34			2.04659
$213$	1239.48	−	1335.32i	0.398723	−	0.429552i
$214$	−9683.82	−	5590.96i	−3.09333	−	1.78593i
$215$	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
$218$	6148.07			1.91009
$219$	760.966	+	2468.72i	0.234801	+	0.761737i
$220$	7834.46	−	13569.7i	2.40090	−	4.15849i
$221$	−2584.95	+	1244.41i	−0.786800	+	0.378768i
$222$	34.1412	−	149.447i	0.0103217	−	0.0451812i
$223$			4111.48i			1.23464i	0.786712	+	0.617320i	$0.211782\pi$
$223$			4111.48i			1.23464i	−0.786712	+	0.617320i	$0.788218\pi$
$224$	2278.25	−	3946.05i	0.679563	−	1.17704i
$225$	311.367	+	150.097i	0.0922570	+	0.0444733i
$226$			4014.18i			1.18150i
$227$	−3234.19	−	1867.26i	−0.945641	−	0.545966i	−0.0539166	−	0.998545i	$-0.517171\pi$
$227$	−3234.19	−	1867.26i	−0.945641	−	0.545966i	−0.891724	+	0.452580i	$0.850504\pi$
$228$	−7351.73	+	7920.16i	−2.13544	+	2.30055i
$229$	2677.75	+	1546.00i	0.772711	+	0.446125i	0.833841	−	0.552005i	$-0.186137\pi$
$229$	2677.75	+	1546.00i	0.772711	+	0.446125i	−0.0611296	+	0.998130i	$0.519470\pi$
$230$	−6693.63			−1.91898
$231$	−624.204	+	2732.34i	−0.177790	+	0.778245i
$232$		−	9968.28i		−	2.82090i
$233$	−2795.27			−0.785941			−0.392970	−	0.919551i	$-0.628553\pi$
$233$	−2795.27			−0.785941			−0.392970	+	0.919551i	$0.628553\pi$
$234$	5887.27	−	3394.84i	1.64471	−	0.948407i
$235$	−2454.28			−0.681276
$236$		−	13859.7i		−	3.82283i
$237$	8.25163	+	7.65942i	0.00226161	+	0.00209929i
$238$	2767.46			0.753731
$239$	−2951.04	−	1703.78i	−0.798690	−	0.461124i	0.0443229	−	0.999017i	$-0.485887\pi$
$239$	−2951.04	−	1703.78i	−0.798690	−	0.461124i	−0.843013	+	0.537893i	$0.819220\pi$
$240$	12099.1	+	2764.05i	3.25414	+	0.743410i
$241$	−1938.89	−	1119.42i	−0.518236	−	0.299203i	0.217977	−	0.975954i	$-0.430054\pi$
$241$	−1938.89	−	1119.42i	−0.518236	−	0.299203i	−0.736212	+	0.676750i	$0.763388\pi$
$242$			14889.2i			3.95503i
$243$	−286.791	+	3777.12i	−0.0757106	+	0.997130i
$244$	6629.20	−	11482.1i	1.73931	−	3.01257i
$245$			3194.20i			0.832939i
$246$	1363.15	+	1265.32i	0.353299	+	0.327943i
$247$	−2029.25	−	4215.29i	−0.522746	−	1.08588i
$248$	−3749.66	+	6494.60i	−0.960094	+	1.66293i
$249$	501.159	−	539.908i	0.127549	−	0.137411i
$250$	7072.67			1.78926
$251$	−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
$254$	9860.20	+	5692.79i	2.43576	+	1.40629i
$255$	1099.75	+	3567.79i	0.270074	+	0.876171i
$256$	3386.24			0.826719
$257$	−1330.60	−	2304.66i	−0.322958	−	0.559380i	0.658139	−	0.752897i	$-0.271344\pi$
$257$	−1330.60	−	2304.66i	−0.322958	−	0.559380i	−0.981097	+	0.193516i	$0.938011\pi$
$258$	−9015.52	−	2059.60i	−2.17551	−	0.496996i
$259$	−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
$263$	−5541.11			−1.29916			−0.649581	−	0.760292i	$-0.725056\pi$
$263$	−5541.11			−1.29916			−0.649581	+	0.760292i	$0.725056\pi$
$264$	−21926.8	+	6758.79i	−5.11174	+	1.57566i
$265$	3082.26	+	1779.55i	0.714498	+	0.412515i
$266$			4512.91i			1.04024i
$267$	420.961	+	96.1688i	0.0964884	+	0.0220428i
$268$	−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	$0.936400\pi$
$270$	−3226.19	−	8234.47i	−0.727183	−	1.85605i
$271$	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
$273$	605.122	−	1959.42i	0.134153	−	0.434394i
$274$	2177.57	−	3771.67i	0.480117	−	0.831587i
$275$	710.231	−	410.052i	0.155740	−	0.0899167i
$276$	8426.04	+	7821.31i	1.83764	+	1.70575i
$277$	3519.80	−	6096.48i	0.763482	−	1.32239i	−0.177564	−	0.984109i	$-0.556822\pi$
$277$	3519.80	−	6096.48i	0.763482	−	1.32239i	0.941045	−	0.338280i	$-0.109845\pi$
$278$		−	5624.31i		−	1.21339i
$279$	2929.32	−	218.364i	0.628580	−	0.0468569i
$280$	5900.46	−	3406.63i	1.25936	−	0.727090i
$281$	2519.54	−	1454.66i	0.534886	−	0.308817i	−0.208118	−	0.978104i	$-0.566734\pi$
$281$	2519.54	−	1454.66i	0.534886	−	0.308817i	0.743004	+	0.669287i	$0.233400\pi$
$282$	4275.68	+	3968.81i	0.902883	+	0.838083i
$283$	−3080.02	−	5334.74i	−0.646954	−	1.12056i	−0.983847	−	0.179014i	$-0.942709\pi$
$283$	−3080.02	−	5334.74i	−0.646954	−	1.12056i	0.336893	−	0.941543i	$-0.390624\pi$
$284$	6327.05	−	3652.93i	1.32198	−	0.763244i
$285$	−5817.99	+	1793.36i	−1.20922	+	0.372735i
$286$	1207.19	−	16078.8i	0.249589	−	3.32433i
$287$	561.241			0.115432
$288$	−8225.98	−	12075.5i	−1.68306	−	2.47068i
$289$	583.369	−	1010.43i	0.118740	−	0.205664i
$290$	4557.99	−	7894.68i	0.922947	−	1.59859i
$291$	2585.64	+	590.690i	0.520869	+	0.118993i
$292$			10359.1i			2.07610i
$293$		−	6394.70i		−	1.27503i	−0.770440	−	0.637513i	$-0.779963\pi$
$293$		−	6394.70i		−	1.27503i	0.770440	−	0.637513i	$-0.220037\pi$
$294$	5165.33	−	5564.71i	1.02465	−	1.10388i
$295$	3904.16	−	6762.20i	0.770538	−	1.33461i
$296$	189.351	−	327.965i	0.0371817	−	0.0644006i
$297$	7023.31	+	5607.68i	1.37217	+	1.09559i
$298$	−2822.53			−0.548675
$299$	−4484.53	+	2158.87i	−0.867381	+	0.417560i
$300$	1015.88	+	942.971i	0.195506	+	0.181475i
$301$	−2416.73	+	1395.30i	−0.462784	+	0.267188i
$302$	30.2594	+	52.4109i	0.00576568	+	0.00998645i
$303$	6987.44	−	2153.84i	1.32481	−	0.408365i
$304$	−17587.1	+	10153.9i	−3.31806	+	1.91568i
$305$	6468.84	−	3734.78i	1.21444	−	0.701158i
$306$	3853.55	−	7993.94i	0.719912	−	1.49341i
$307$			6396.54i			1.18915i	0.804039	+	0.594576i	$0.202680\pi$
$307$			6396.54i			1.18915i	−0.804039	+	0.594576i	$0.797320\pi$
$308$	−5619.44	+	9733.16i	−1.03960	+	1.80064i
$309$	299.013	−	1308.87i	0.0550494	−	0.240969i
$310$	−5939.31	+	3429.06i	−1.08816	+	0.628250i
$311$	3896.83	−	6749.51i	0.710511	−	1.23064i	−0.254154	−	0.967164i	$-0.581797\pi$
$311$	3896.83	−	6749.51i	0.710511	−	1.23064i	0.964665	−	0.263478i	$-0.0848696\pi$
$312$	16368.8	−	3730.30i	2.97020	−	0.676879i
$313$	706.302	+	1223.35i	0.127548	+	0.220920i	0.922726	−	0.385456i	$-0.125956\pi$
$313$	706.302	+	1223.35i	0.127548	+	0.220920i	−0.795178	+	0.606376i	$0.792623\pi$
$314$	7209.26	+	4162.27i	1.29567	+	0.748058i
$315$	−2403.98	−	1158.86i	−0.429997	−	0.207284i
$316$	22.5733	+	39.0982i	0.00401851	+	0.00696027i
$317$	−4485.28	+	2589.58i	−0.794695	+	0.458818i	−0.841613	−	0.540081i	$-0.818393\pi$
$317$	−4485.28	+	2589.58i	−0.794695	+	0.458818i	0.0469177	+	0.998899i	$0.485060\pi$
$318$	−2492.00	−	8084.51i	−0.439448	−	1.42565i
$319$			9263.87i			1.62595i
$320$	12994.8	+	7502.57i	2.27010	+	1.31065i
$321$	−2409.75	+	10548.2i	−0.419000	+	1.83410i
$322$	4801.16			0.830925
$323$	−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
$327$	−1752.40	−	5685.12i	−0.296355	−	0.961431i
$328$	2297.32	+	3979.08i	0.386733	+	0.669841i
$329$	1760.39			0.294995
$330$	−20456.0	−	4673.18i	−3.41232	−	0.779547i
$331$	−6152.62	−	3552.22i	−1.02169	−	0.589872i	−0.107096	−	0.994249i	$-0.534155\pi$
$331$	−6152.62	−	3552.22i	−1.02169	−	0.589872i	−0.914592	+	0.404377i	$0.867488\pi$
$332$	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
$335$	−1630.79			−0.265969
$336$	−8678.36	−	1982.58i	−1.40906	−	0.321900i
$337$	−1016.32	+	1760.32i	−0.164281	+	0.284542i	−0.936400	−	0.350936i	$-0.885864\pi$
$337$	−1016.32	+	1760.32i	−0.164281	+	0.284542i	0.772119	+	0.635478i	$0.219197\pi$
$338$	−1761.62	+	11665.5i	−0.283490	+	1.87728i
$339$	3711.91	−	1144.17i	0.594700	−	0.183313i
$340$			14971.0i			2.38799i
$341$	3484.69	−	6035.66i	0.553391	−	0.958502i
$342$	13035.7	+	6283.99i	2.06109	+	0.993566i
$343$		−	5179.17i		−	0.815303i
$344$	−19784.8	−	11422.7i	−3.10094	−	1.79033i
$345$	1907.91	+	6189.60i	0.297734	+	0.965904i
$346$	−3132.84	−	1808.75i	−0.486771	−	0.281037i
$347$	5092.50			0.787837			0.393919	−	0.919145i	$-0.371119\pi$
$347$	5092.50			0.787837			0.393919	+	0.919145i	$0.371119\pi$
$348$	−14962.4	+	4612.06i	−2.30479	+	0.710437i
$349$		−	4348.27i		−	0.666927i	−0.942763	−	0.333463i	$-0.891783\pi$
$349$		−	4348.27i		−	0.666927i	0.942763	−	0.333463i	$-0.108217\pi$
$350$	578.848			0.0884021
$351$	−4817.27	−	4476.32i	−0.732556	−	0.680707i
$352$	−34666.2			−5.24920
$353$			8976.19i			1.35341i	0.736253	+	0.676706i	$0.236593\pi$
$353$			8976.19i			1.35341i	−0.736253	+	0.676706i	$0.763407\pi$
$354$	−17736.7	+	5467.22i	−2.66297	+	0.820845i
$355$	4116.00			0.615365
$356$	1499.55	+	865.766i	0.223247	+	0.128892i
$357$	−788.819	−	2559.08i	−0.116943	−	0.379386i
$358$	17613.6	+	10169.2i	2.60029	+	1.50128i
$359$			1660.55i			0.244124i	0.992523	+	0.122062i	$0.0389506\pi$
$359$			1660.55i			0.244124i	−0.992523	+	0.122062i	$0.961049\pi$
$360$	−1624.12	−	21787.3i	−0.237773	−	3.18970i
$361$	1551.50	−	2687.28i	0.226199	−	0.391788i
$362$			12853.3i			1.86617i
$363$	13768.1	−	4243.93i	1.99074	−	0.613632i
$364$	4633.34	−	6793.83i	0.667179	−	0.978279i
$365$	−2918.08	+	5054.26i	−0.418464	+	0.724800i
$366$	−17309.1	−	3954.26i	−2.47202	−	0.564733i
$367$	699.079			0.0994322			0.0497161	−	0.998763i	$-0.484168\pi$
$367$	699.079			0.0994322			0.0497161	+	0.998763i	$0.484168\pi$
$368$	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
$371$	−2210.82	−	1276.42i	−0.309381	−	0.178621i
$372$	11483.2	+	2623.35i	1.60048	+	0.365630i
$373$	−2680.87			−0.372145			−0.186073	−	0.982536i	$-0.559576\pi$
$373$	−2680.87			−0.372145			−0.186073	+	0.982536i	$0.559576\pi$
$374$	−10527.5	−	18234.3i	−1.45553	−	2.52104i
$375$	−2015.95	−	6540.10i	−0.277608	−	0.900612i
$376$	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	$0.565102\pi$
$380$	−24413.2			−3.29571
$381$	2453.64	−	10740.4i	0.329932	−	1.44422i
$382$	−14117.9	−	8150.98i	−1.89093	−	1.09173i
$383$			8757.77i			1.16841i	0.811606	+	0.584205i	$0.198594\pi$
$383$			8757.77i			1.16841i	−0.811606	+	0.584205i	$0.801406\pi$
$384$	−3879.92	−	12587.2i	−0.515615	−	1.67275i
$385$	−5483.51	+	3165.90i	−0.725884	+	0.419089i
$386$	6904.61	+	11959.1i	0.910455	+	1.57695i
$387$	665.211	+	8923.71i	0.0873761	+	1.17214i
$388$	9210.58	+	5317.73i	1.20515	+	0.695791i
$389$	−5694.49	−	9863.15i	−0.742216	−	1.28556i	−0.951484	−	0.307698i	$-0.900441\pi$
$389$	−5694.49	−	9863.15i	−0.742216	−	1.28556i	0.209268	−	0.977858i	$-0.432892\pi$
$390$	14669.5	+	4530.33i	1.90466	+	0.588211i
$391$	−3249.61	+	5628.50i	−0.420307	+	0.727993i
$392$	16243.5	−	9378.20i	2.09291	−	1.20834i
$393$	−76.7915	+	336.141i	−0.00985653	+	0.0431452i
$394$	−3945.92	+	6834.54i	−0.504550	+	0.873907i
$395$			25.4349i			0.00323992i
$396$	20289.9	+	29784.9i	2.57476	+	3.77967i
$397$	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
$399$	4173.09	−	1286.33i	0.523598	−	0.161396i
$400$	1302.39	+	2255.81i	0.162799	+	0.281977i
$401$	−10519.3	+	6073.31i	−1.30999	+	0.756325i	−0.982095	−	0.188388i	$-0.939674\pi$
$401$	−10519.3	+	6073.31i	−1.30999	+	0.756325i	−0.327899	+	0.944713i	$0.606341\pi$
$402$	2841.05	+	2637.15i	0.352484	+	0.327187i
$403$	−2873.20	+	4212.94i	−0.355147	+	0.520749i
$404$	29320.4			3.61075
$405$	−6694.85	+	5330.35i	−0.821407	+	0.653994i
$406$	−3269.32	+	5662.64i	−0.399640	+	0.692197i
$407$	−175.970	+	304.789i	−0.0214312	+	0.0371200i
$408$	14914.5	−	16067.6i	1.80974	−	1.94967i
$409$		−	4759.97i		−	0.575465i	−0.957711	−	0.287733i	$-0.907099\pi$
$409$		−	4759.97i		−	0.575465i	0.957711	−	0.287733i	$-0.0929014\pi$
$410$			4201.80i			0.506127i
$411$	−4108.35	−	938.553i	−0.493065	−	0.112641i
$412$	2691.89	−	4662.48i	0.321892	−	0.557534i
$413$	−2800.34	+	4850.34i	−0.333646	+	0.577892i
$414$	6685.37	−	13868.4i	0.793642	−	1.64636i
$415$	1664.22			0.196851
$416$	25293.8	+	1899.05i	2.98108	+	0.223819i
$417$	−5200.80	+	1603.11i	−0.610754	+	0.188261i
$418$	29734.6	−	17167.3i	3.47935	−	2.00880i
$419$	2297.80	+	3979.90i	0.267911	+	0.464036i	0.968322	−	0.249704i	$-0.0803333\pi$
$419$	2297.80	+	3979.90i	0.267911	+	0.464036i	−0.700411	+	0.713740i	$0.747000\pi$
$420$	−7843.34	−	7280.42i	−0.911228	−	0.845829i
$421$	5888.64	−	3399.81i	0.681698	−	0.393578i	−0.118797	−	0.992919i	$-0.537904\pi$
$421$	5888.64	−	3399.81i	0.681698	−	0.393578i	0.800494	+	0.599340i	$0.204570\pi$
$422$	24766.1	−	14298.7i	2.85686	−	1.64941i
$423$	2451.26	−	5084.97i	0.281759	−	0.584491i
$424$		−	20899.0i		−	2.39374i
$425$	−391.788	+	678.596i	−0.0447165	+	0.0774512i
$426$	−7170.60	−	6655.97i	−0.815532	−	0.757002i
$427$	−4639.92	+	2678.86i	−0.525858	+	0.303604i
$428$	−21694.0	+	37575.0i	−2.45004	+	4.24359i
$429$	−15212.1	+	3466.69i	−1.71200	+	0.390148i
$430$	−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	$0.692121\pi$
$432$	−17810.9	+	22307.2i	−1.98363	+	2.48439i
$433$	−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
$435$	−8599.39	−	1964.53i	−0.947838	−	0.216534i
$436$		−	23855.6i		−	2.62036i
$437$	−9178.39	−	5299.15i	−1.00472	−	0.580075i
$438$	13256.9	−	4086.36i	1.44621	−	0.445785i
$439$	7604.04			0.826700			0.413350	−	0.910572i	$-0.364359\pi$
$439$	7604.04			0.826700			0.413350	+	0.910572i	$0.364359\pi$
$440$	−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	0.994518	+	0.104564i	$0.0333448\pi$
$443$	5480.82	+	9493.06i	0.587814	+	1.01812i	−0.406704	+	0.913560i	$0.633322\pi$
$444$	−579.882	−	132.474i	−0.0619820	−	0.0141598i
$445$	487.759	+	844.823i	0.0519595	+	0.0899965i
$446$	22078.4			2.34405
$447$	804.516	+	2610.00i	0.0851282	+	0.276172i
$448$	−9320.84	−	5381.39i	−0.982965	−	0.567515i
$449$	−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
$452$	15575.7			1.62084
$453$	39.8394	−	42.9198i	0.00413205	−	0.00445154i
$454$	−10027.1	+	17367.4i	−1.03655	+	1.79536i
$455$	4174.40	−	2009.57i	0.430108	−	0.207055i
$456$	26201.5	+	24321.0i	2.69078	+	2.49767i
$457$		−	13148.4i		−	1.34586i	−0.739707	−	0.672929i	$-0.765036\pi$
$457$		−	13148.4i		−	1.34586i	0.739707	−	0.672929i	$-0.234964\pi$
$458$	8301.96	−	14379.4i	0.846998	−	1.46704i
$459$	−8490.40	−	1284.84i	−0.863394	−	0.130657i
$460$			25972.5i			2.63255i
$461$	−569.224	−	328.642i	−0.0575085	−	0.0332026i	0.470970	−	0.882149i	$-0.343904\pi$
$461$	−569.224	−	328.642i	−0.0575085	−	0.0332026i	−0.528479	+	0.848947i	$0.677237\pi$
$462$	14672.5	+	3351.95i	1.47755	+	0.337547i
$463$	5806.14	+	3352.18i	0.582795	+	0.336477i	0.762244	−	0.647290i	$-0.224098\pi$
$463$	5806.14	+	3352.18i	0.582795	+	0.336477i	−0.179448	+	0.983767i	$0.557431\pi$
$464$	−29423.6			−2.94387
$465$	4863.75	+	4514.68i	0.485056	+	0.450244i
$466$			15010.5i			1.49216i
$467$	−5159.32			−0.511231			−0.255616	−	0.966779i	$-0.582278\pi$
$467$	−5159.32			−0.511231			−0.255616	+	0.966779i	$0.582278\pi$
$468$	−13172.6	−	22843.7i	−1.30108	−	2.25630i
$469$	1169.72			0.115166
$470$			13179.4i			1.29345i
$471$	1793.97	−	7852.79i	0.175503	−	0.768232i
$472$	−45850.5			−4.47127
$473$	18386.7	+	10615.6i	1.78736	+	1.03193i
$474$	41.1307	−	44.3109i	0.00398565	−	0.00429381i
$475$	−1106.59	−	638.888i	−0.106892	−	0.0617141i
$476$		−	10738.3i		−	1.03401i
$477$	−6765.45	+	4608.71i	−0.649410	+	0.442387i
$478$	−9149.24	+	15847.0i	−0.875474	+	1.51637i
$479$			5030.03i			0.479808i	0.970797	+	0.239904i	$0.0771159\pi$
$479$			5030.03i			0.479808i	−0.970797	+	0.239904i	$0.922884\pi$
$480$	7351.47	−	32179.7i	0.699056	−	3.05999i
$481$	145.091	−	212.746i	0.0137538	−	0.0201671i
$482$	−6011.23	+	10411.7i	−0.568058	+	0.983905i
$483$	−1368.49	−	4439.63i	−0.128920	−	0.418241i
$484$	57773.0			5.42572
$485$	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	$0.505706\pi$
$488$	−37985.1	−	21930.7i	−3.52358	−	2.03434i
$489$	−8512.85	+	9171.05i	−0.787248	+	0.848117i
$490$	17152.7			1.58139
$491$	−4565.93	−	7908.43i	−0.419669	−	0.726889i	0.576237	−	0.817283i	$-0.304521\pi$
$491$	−4565.93	−	7908.43i	−0.419669	−	0.726889i	−0.995906	+	0.0903942i	$0.971187\pi$
$492$	4909.68	−	5289.29i	0.449889	−	0.484674i
$493$	−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
$497$	−2952.29			−0.266456
$498$	−2899.28	−	2691.20i	−0.260883	−	0.242160i
$499$	221.565	+	127.921i	0.0198770	+	0.0114760i	0.509906	−	0.860230i	$-0.329680\pi$
$499$	221.565	+	127.921i	0.0198770	+	0.0114760i	−0.490029	+	0.871706i	$0.663014\pi$
$500$		−	27443.3i		−	2.45460i
$501$	−3007.85	+	3240.41i	−0.268225	+	0.288964i
$502$	−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	$0.769202\pi$
$504$	1164.93	+	15627.4i	0.102957	+	1.38115i
$505$	14305.6	+	8259.32i	1.26057	+	0.727792i
$506$	−18263.8	−	31633.8i	−1.60459	−	2.77924i
$507$	11289.2	−	1696.09i	0.988902	−	0.148572i
$508$	22089.1	−	38259.4i	1.92922	−	3.34151i
$509$	8937.71	−	5160.19i	0.778305	−	0.449354i	−0.0575246	−	0.998344i	$-0.518321\pi$
$509$	8937.71	−	5160.19i	0.778305	−	0.449354i	0.835829	+	0.548990i	$0.184987\pi$
$510$	19158.9	−	5905.60i	1.66347	−	0.512754i
$511$	2093.06	−	3625.28i	0.181197	−	0.313842i
$512$			2095.01i			0.180834i
$513$	2095.20	−	13845.3i	0.180322	−	1.19159i
$514$	−12375.9	+	7145.24i	−1.06202	+	0.613158i
$515$	2626.77	−	1516.57i	0.224756	−	0.129763i
$516$	−7991.63	+	34981.9i	−0.681806	+	2.98448i
$517$	−6696.60	−	11598.9i	−0.569664	−	0.986687i
$518$	−215.127	+	124.204i	−0.0182474	+	0.0105351i
$519$	−779.586	+	3412.50i	−0.0659345	+	0.288616i
$520$	31334.5	+	21369.9i	2.64251	+	1.80218i
$521$	−17801.0			−1.49688			−0.748442	−	0.663200i	$-0.769198\pi$
$521$	−17801.0			−1.49688			−0.748442	+	0.663200i	$0.769198\pi$
$522$	11804.4	+	17328.5i	0.989779	+	1.45297i
$523$	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	$0.135138\pi$
$524$	−691.321	+	1197.40i	−0.0576345	+	0.0998259i
$525$	−164.991	−	535.262i	−0.0137158	−	0.0444966i
$526$			29755.5i			2.46655i
$527$			6658.94i			0.550414i
$528$	19950.1	+	64721.7i	1.64435	+	5.33457i
$529$	445.882	−	772.289i	0.0366468	−	0.0634741i
$530$	9556.08	−	16551.6i	0.783188	−	1.35652i
$531$	10111.1	+	14842.8i	0.826334	+	1.21303i
$532$	17510.9			1.42706
$533$	1355.19	+	2815.08i	0.110131	+	0.228770i
$534$	516.422	−	2260.54i	0.0418498	−	0.183190i
$535$	−21169.2	+	12222.0i	−1.71070	+	0.987672i
$536$	4788.02	+	8293.09i	0.385841	+	0.668297i
$537$	4383.01	−	19185.8i	0.352218	−	1.54177i
$538$	−13056.1	+	7537.96i	−1.04626	+	0.604060i
$539$	−15095.7	+	8715.49i	−1.20634	+	0.696480i
$540$	−31951.3	+	12518.2i	−2.54623	+	0.997588i
$541$			16139.3i			1.28259i	0.767294	+	0.641295i	$0.221603\pi$
$541$			16139.3i			1.28259i	−0.767294	+	0.641295i	$0.778397\pi$
$542$	3520.73	−	6098.07i	0.279019	−	0.483274i
$543$	11885.4	−	3663.61i	0.939324	−	0.289541i
$544$	28684.6	−	16561.1i	2.26074	−	1.30524i
$545$	6719.95	−	11639.3i	0.528167	−	0.914811i
$546$	−10522.0	−	3249.48i	−0.824726	−	0.254698i
$547$	3851.87	+	6671.63i	0.301086	+	0.521496i	0.976382	−	0.216050i	$-0.0693175\pi$
$547$	3851.87	+	6671.63i	0.301086	+	0.521496i	−0.675296	+	0.737547i	$0.735984\pi$
$548$	−14634.8	−	8449.39i	−1.14082	−	0.658650i
$549$	1277.15	+	17132.8i	0.0992849	+	1.33189i
$550$	−2201.96	−	3813.91i	−0.170713	−	0.295683i
$551$	12500.0	−	7216.86i	0.966455	−	0.557983i
$552$	25874.4	−	27875.0i	1.99509	−	2.14935i
$553$		−	18.2438i		−	0.00140290i
$554$	−32737.8	−	18901.2i	−2.51064	−	1.44952i
$555$	−245.610	−	227.983i	−0.0187848	−	0.0174367i
$556$	−21823.4			−1.66460
$557$	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
$561$	−13860.5	+	14932.2i	−1.04312	+	1.12378i
$562$	−7811.44	−	13529.8i	−0.586309	−	1.01552i
$563$	14995.5			1.12253			0.561265	−	0.827636i	$-0.310315\pi$
$563$	14995.5			1.12253			0.561265	+	0.827636i	$0.310315\pi$
$564$	15399.7	−	16590.4i	1.14973	−	1.23862i
$565$	7599.49	+	4387.56i	0.565863	+	0.326701i
$566$	−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
$569$	22982.6			1.69329			0.846643	−	0.532161i	$-0.178620\pi$
$569$	22982.6			1.69329			0.846643	+	0.532161i	$0.178620\pi$
$570$	9630.27	+	31242.4i	0.707662	+	2.29579i
$571$	3053.73	−	5289.21i	0.223808	−	0.387647i	−0.732153	−	0.681140i	$-0.761484\pi$
$571$	3053.73	−	5289.21i	0.223808	−	0.387647i	0.955961	+	0.293493i	$0.0948178\pi$
$572$	−62388.6	−	4684.12i	−4.56049	−	0.342400i
$573$	−3513.14	+	15378.1i	−0.256132	+	1.12117i
$574$		−	3013.84i		−	0.219155i
$575$	−679.696	+	1177.27i	−0.0492961	+	0.0853834i
$576$	−28523.2	+	19430.3i	−2.06331	+	1.40555i
$577$			6485.30i			0.467914i	0.972247	+	0.233957i	$0.0751676\pi$
$577$			6485.30i			0.467914i	−0.972247	+	0.233957i	$0.924832\pi$
$578$	−5425.94	−	3132.67i	−0.390466	−	0.225436i
$579$	9090.58	−	9793.45i	0.652490	−	0.702940i
$580$	−30632.8	−	17685.9i	−2.19303	−	1.26615i
$581$	−1193.70			−0.0852375
$582$	3171.98	−	13884.8i	0.225916	−	0.988904i
$583$			19422.2i			1.37974i
$584$	34270.0			2.42826
$585$	7.91227	−	14856.2i	0.000559200	−	1.04996i
$586$	−34339.3			−2.42072
$587$		−	18389.1i		−	1.29302i	−0.762907	−	0.646508i	$-0.776229\pi$
$587$		−	18389.1i		−	1.29302i	0.762907	−	0.646508i	$-0.223771\pi$
$588$	−21592.1	−	20042.4i	−1.51436	−	1.40567i
$589$	−10858.7			−0.759638
$590$	−36312.7	−	20965.1i	−2.53385	−	1.46292i
$591$	7444.62	+	1700.73i	0.518157	+	0.118373i
$592$	−968.061	−	558.910i	−0.0672079	−	0.0388025i
$593$		−	8897.54i		−	0.616152i	−0.951362	−	0.308076i	$-0.900315\pi$
$593$		−	8897.54i		−	0.616152i	0.951362	−	0.308076i	$-0.0996851\pi$
$594$	30113.0	−	37714.9i	2.08005	−	2.60515i
$595$	3024.89	−	5239.26i	0.208417	−	0.360989i
$596$			10952.0i			0.752701i
$597$	−18590.7	−	17256.4i	−1.27448	−	1.18301i
$598$	11593.0	+	24081.7i	0.792765	+	1.64678i
$599$	3417.69	−	5919.62i	0.233127	−	0.403788i	−0.725600	−	0.688117i	$-0.758437\pi$
$599$	3417.69	−	5919.62i	0.233127	−	0.403788i	0.958727	+	0.284329i	$0.0917708\pi$
$600$	3119.54	−	3360.73i	0.212258	−	0.228669i
$601$	−16844.9			−1.14329			−0.571644	−	0.820502i	$-0.693694\pi$
$601$	−16844.9			−1.14329			−0.571644	+	0.820502i	$0.693694\pi$
$602$	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
$605$	28187.8	+	16274.2i	1.89421	+	1.09362i
$606$	−11566.0	−	37522.3i	−0.775308	−	2.51524i
$607$	10593.7			0.708375			0.354187	−	0.935175i	$-0.384758\pi$
$607$	10593.7			0.708375			0.354187	+	0.935175i	$0.384758\pi$
$608$	27006.1	+	46776.0i	1.80139	+	3.12010i
$609$	6168.11	+	1409.11i	0.410418	+	0.0937601i
$610$	−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	$0.501573\pi$
$614$	34349.1			2.25768
$615$	3885.41	−	1197.65i	0.254756	−	0.0785269i
$616$	32199.2	+	18590.2i	2.10608	+	1.21594i
$617$			22615.3i			1.47562i	0.675009	+	0.737810i	$0.264140\pi$
$617$			22615.3i			1.47562i	−0.675009	+	0.737810i	$0.735860\pi$
$618$	−7028.60	−	1605.69i	−0.457495	−	0.104515i
$619$	−15814.0	+	9130.21i	−1.02685	+	0.592850i	−0.916080	−	0.400996i	$-0.868664\pi$
$619$	−15814.0	+	9130.21i	−1.02685	+	0.592850i	−0.110767	+	0.993846i	$0.535331\pi$
$620$	13305.4	+	23045.6i	0.861867	+	1.49280i
$621$	−14729.6	−	2229.02i	−0.951819	−	0.144038i
$622$	−36244.6	−	20925.8i	−2.33646	−	1.34895i
$623$	−349.856	−	605.969i	−0.0224987	−	0.0389689i
$624$	−11010.8	−	48316.3i	−0.706386	−	3.09968i
$625$	8530.69	−	14775.6i	0.545964	−	0.945637i
$626$	6569.34	−	3792.81i	0.419431	−	0.242158i
$627$	−24349.9	−	22602.4i	−1.55095	−	1.43964i
$628$	16150.4	−	27973.3i	1.02623	−	1.77748i
$629$		−	336.264i		−	0.0213159i
$630$	−6223.04	+	12909.3i	−0.393543	+	0.816378i
$631$	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
$633$	−20281.2	−	18825.6i	−1.27347	−	1.18207i
$634$	13905.9	+	24085.8i	0.871095	+	1.50878i
$635$	21554.8	−	12444.6i	1.34705	−	0.777717i
$636$	−31369.4	+	9669.43i	−1.95578	+	0.602858i
$637$	11491.8	−	5532.19i	0.714791	−	0.344103i
$638$	49746.6			3.08697
$639$	−4110.92	+	8527.83i	−0.254500	+	0.527944i
$640$	14878.3	−	25770.0i	0.918934	−	1.59164i
$641$	−15169.9	+	26275.0i	−0.934748	+	1.61903i	−0.159665	+	0.987171i	$0.551041\pi$
$641$	−15169.9	+	26275.0i	−0.934748	+	1.61903i	−0.775083	+	0.631860i	$0.782292\pi$
$642$	56643.6	+	12940.3i	3.48216	+	0.795500i
$643$		−	11875.9i		−	0.728366i	−0.931327	−	0.364183i	$-0.881348\pi$
$643$		−	11875.9i		−	0.728366i	0.931327	−	0.364183i	$-0.118652\pi$
$644$		−	18629.4i		−	1.13991i
$645$	−13753.3	+	14816.7i	−0.839589	+	0.904505i
$646$	−16402.6	+	28410.2i	−0.998997	+	1.73031i
$647$	−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	$0.296142\pi$
$648$	46762.7	+	18395.5i	2.83489	+	1.11519i
$649$	42610.5			2.57721
$650$	1397.70	+	2903.40i	0.0843423	+	0.175201i
$651$	−3488.64	−	3238.26i	−0.210031	−	0.194958i
$652$	−43454.6	+	25088.5i	−2.61014	+	1.50697i
$653$	5187.04	+	8984.22i	0.310849	+	0.538407i	0.978547	−	0.206026i	$-0.0660532\pi$
$653$	5187.04	+	8984.22i	0.310849	+	0.538407i	−0.667697	+	0.744433i	$0.732720\pi$
$654$	−30528.9	+	9410.33i	−1.82534	+	0.562650i
$655$	−674.598	+	389.479i	−0.0402423	+	0.0232339i
$656$	11745.1	−	6781.06i	0.699041	−	0.403591i
$657$	−7557.31	−	11093.9i	−0.448765	−	0.658775i
$658$		−	9453.22i		−	0.560068i
$659$	1295.81	−	2244.40i	0.0765971	−	0.132670i	−0.825183	−	0.564866i	$-0.808928\pi$
$659$	1295.81	−	2244.40i	0.0765971	−	0.132670i	0.901780	+	0.432196i	$0.142261\pi$
$660$	−18132.8	+	79373.2i	−1.06942	+	4.68121i
$661$	17856.5	−	10309.5i	1.05074	−	0.606645i	0.127884	−	0.991789i	$-0.459182\pi$
$661$	17856.5	−	10309.5i	1.05074	−	0.606645i	0.922856	+	0.385144i	$0.125848\pi$
$662$	−19075.3	+	33039.3i	−1.11991	+	1.93974i
$663$	10931.2	−	10135.8i	0.640318	−	0.593728i
$664$	−4886.16	−	8463.08i	−0.285572	−	0.494625i
$665$	8543.66	+	4932.69i	0.498209	+	0.287641i
$666$	59.2142	+	794.351i	0.00344520	+	0.0462170i
$667$	−7677.82	−	13298.4i	−0.445707	−	0.771987i
$668$	−15353.8	+	8864.53i	−0.889307	+	0.513442i
$669$	−6293.09	−	20416.0i	−0.363685	−	1.17986i
$670$			8757.29i			0.504960i
$671$	35300.9	+	20381.0i	2.03096	+	1.17258i
$672$	−5273.01	+	23081.6i	−0.302694	+	1.32499i
$673$	−17596.4			−1.00786			−0.503932	−	0.863744i	$-0.668114\pi$
$673$	−17596.4			−1.00786			−0.503932	+	0.863744i	$0.668114\pi$
$674$	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	0.847158	−	0.531341i	$-0.178312\pi$
$677$	−644.287	−	1115.94i	−0.0365760	−	0.0633515i	−0.883734	+	0.467990i	$0.844978\pi$
$678$	−6144.16	−	19932.8i	−0.348031	−	1.12908i
$679$	−2148.90	−	3722.00i	−0.121454	−	0.210364i
$680$	49527.0			2.79305
$681$	18917.7	+	4321.76i	1.06451	+	0.243187i
$682$	−32411.2	−	18712.6i	−1.81978	−	1.05065i
$683$	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
$686$	−27811.9			−1.54791
$687$	−15663.0	−	3578.22i	−0.869841	−	0.198715i
$688$	−33716.8	+	58399.2i	−1.86837	+	3.23611i
$689$	1063.97	−	14171.2i	0.0588301	−	0.783568i
$690$	33237.9	−	10245.4i	1.83383	−	0.565268i
$691$			15077.3i			0.830056i	0.909809	+	0.415028i	$0.136228\pi$
$691$			15077.3i			0.830056i	−0.909809	+	0.415028i	$0.863772\pi$
$692$	−7018.28	+	12156.0i	−0.385542	+	0.667778i
$693$	−1082.61	−	14523.1i	−0.0593436	−	0.796087i
$694$		−	27346.5i		−	1.49576i
$695$	−10647.7	−	6147.47i	−0.581138	−	0.335520i
$696$	15257.6	+	49498.5i	0.830946	+	2.69574i
$697$	3533.19	+	2039.89i	0.192007	+	0.110855i
$698$	−23350.0			−1.26620
$699$	13880.2	−	4278.49i	0.751069	−	0.231512i
$700$		−	2246.04i		−	0.121275i
$701$	9756.56			0.525678			0.262839	−	0.964840i	$-0.415341\pi$
$701$	9756.56			0.525678			0.262839	+	0.964840i	$0.415341\pi$
$702$	−24037.6	+	25868.5i	−1.29237	+	1.39081i
$703$	548.346			0.0294186
$704$			81884.1i			4.38370i
$705$	12187.0	−	3756.57i	0.651048	−	0.200682i
$706$	48201.8			2.56954
$707$	−10261.0	−	5924.18i	−0.545833	−	0.315137i
$708$	21213.8	+	68821.6i	1.12608	+	3.65321i
$709$	7601.62	+	4388.80i	0.402659	+	0.232475i	0.687630	−	0.726061i	$-0.258651\pi$
$709$	7601.62	+	4388.80i	0.402659	+	0.232475i	−0.284972	+	0.958536i	$0.591984\pi$
$710$		−	22102.7i		−	1.16831i
$711$	−52.6980	−	25.4035i	−0.00277965	−	0.00133995i
$712$	2864.13	−	4960.81i	0.150755	−	0.261116i
$713$			11552.3i			0.606785i
$714$	−13742.1	+	4235.93i	−0.720289	+	0.222025i
$715$	−29120.2	−	19859.8i	−1.52313	−	1.03876i
$716$	39458.4	−	68343.9i	2.05954	−	3.56722i
$717$	17261.5	+	3943.40i	0.899085	+	0.205396i
$718$	8917.07			0.463485
$719$	−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
$722$	−14430.6	−	8331.49i	−0.743836	−	0.429454i
$723$	11341.2	+	2590.89i	0.583377	+	0.133273i
$724$	49873.1			2.56011
$725$	−925.671	−	1603.31i	−0.0474187	−	0.0821316i
$726$	−22789.7	−	73934.1i	−1.16502	−	3.77955i
$727$	10788.1	+	18685.5i	0.550354	+	0.953242i	0.998249	+	0.0591553i	$0.0188407\pi$
$727$	10788.1	+	18685.5i	0.550354	+	0.953242i	−0.447894	+	0.894086i	$0.647826\pi$
$728$	−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
$731$	−20285.4			−1.02638
$732$	−15343.3	+	67162.4i	−0.774731	+	3.39125i
$733$	−10580.0	−	6108.38i	−0.533127	−	0.307801i	0.209162	−	0.977881i	$-0.432926\pi$
$733$	−10580.0	−	6108.38i	−0.533127	−	0.307801i	−0.742289	+	0.670080i	$0.766260\pi$
$734$		−	3754.02i		−	0.188779i
$735$	−4889.10	−	15861.1i	−0.245356	−	0.795982i
$736$	49763.7	−	28731.1i	2.49228	−	1.43892i
$737$	−4449.68	−	7707.06i	−0.222396	−	0.385201i
$738$	−8705.60	−	4196.62i	−0.434224	−	0.209322i
$739$	−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
$741$	16528.4	+	17825.4i	0.819417	+	0.883716i
$742$	−6854.32	+	11872.0i	−0.339124	+	0.587380i
$743$	−15838.7	+	9144.46i	−0.782052	+	0.451518i	−0.837157	−	0.546963i	$-0.815784\pi$
$743$	−15838.7	+	9144.46i	−0.782052	+	0.451518i	0.0551050	+	0.998481i	$0.482451\pi$
$744$	8678.57	−	37988.9i	0.427650	−	1.87196i
$745$	−3085.08	+	5343.51i	−0.151716	+	0.262780i
$746$			14396.2i			0.706542i
$747$	−1662.16	+	3448.05i	−0.0814129	+	0.168886i
$748$	−70752.3	+	40848.9i	−3.45850	+	1.99677i
$749$	15184.1	−	8766.53i	0.740739	−	0.427666i
$750$	−35120.1	+	10825.5i	−1.70987	+	0.527057i
$751$	1937.61	+	3356.04i	0.0941470	+	0.163067i	0.909252	−	0.416245i	$-0.136654\pi$
$751$	1937.61	+	3356.04i	0.0941470	+	0.163067i	−0.815105	+	0.579313i	$0.803321\pi$
$752$	36839.9	−	21269.5i	1.78645	−	1.03141i
$753$	21795.5	+	20231.3i	1.05481	+	0.979108i
$754$	−36297.0	−	2725.16i	−1.75313	−	0.131624i
$755$	132.296			0.00637716
$756$	22917.8	−	8978.97i	1.10253	−	0.431960i
$757$	−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	$0.173642\pi$
$758$	12428.7	−	21527.2i	0.595557	−	1.03154i
$759$	−24046.0	+	25905.2i	−1.14995	+	1.23887i
$760$			80763.7i			3.85475i
$761$			31894.5i			1.51929i	0.650341	+	0.759643i	$0.274626\pi$
$761$			31894.5i			1.51929i	−0.650341	+	0.759643i	$0.725374\pi$
$762$	−57675.3	−	13176.0i	−2.74194	−	0.626397i
$763$	−4820.03	+	8348.54i	−0.228698	+	0.396117i
$764$	−31627.3	+	54780.1i	−1.49769	+	2.59408i
$765$	−10921.8	−	16032.9i	−0.516182	−	0.757741i
$766$	47028.8			2.21830
$767$	−31090.2	−	2334.24i	−1.46363	−	0.109889i
$768$	−16814.7	+	5183.04i	−0.790038	+	0.243524i
$769$	7296.61	−	4212.70i	0.342162	−	0.197547i	−0.319066	−	0.947733i	$-0.603369\pi$
$769$	7296.61	−	4212.70i	0.342162	−	0.197547i	0.661228	+	0.750185i	$0.270036\pi$
$770$	17000.8	+	29446.2i	0.795669	+	1.37814i
$771$	10134.8	+	9407.39i	0.473404	+	0.439428i
$772$	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	$0.210915\pi$
$774$	47920.0	−	3572.15i	2.22538	−	0.165889i
$775$			1392.80i			0.0645558i
$776$	17592.1	−	30470.4i	0.813815	−	1.40957i
$777$	176.170	+	163.526i	0.00813391	+	0.00755014i
$778$	−52964.7	+	30579.2i	−2.44071	+	1.40915i
$779$	−3326.44	+	5761.57i	−0.152994	+	0.264993i
$780$	17578.5	−	56920.3i	0.806939	−	2.61291i
$781$	11230.7	+	19452.1i	0.514551	+	0.891228i
$782$	30224.8	+	17450.3i	1.38214	+	0.797981i
$783$	12659.0	−	15854.7i	0.577775	−	0.723630i
$784$	−27681.8	−	47946.4i	−1.26102	−	2.18415i
$785$	15759.7	−	9098.86i	0.716545	−	0.413697i
$786$	1805.06	+	412.367i	0.0819140	+	0.0187133i
$787$			27615.0i			1.25078i	0.780310	+	0.625392i	$0.215061\pi$
$787$			27615.0i			1.25078i	−0.780310	+	0.625392i	$0.784939\pi$
$788$	26519.3	+	15310.9i	1.19887	+	0.692169i
$789$	27515.0	−	8481.32i	1.24152	−	0.382691i
$790$	136.584			0.00615121
$791$	−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
$795$	−18029.1	−	4118.75i	−0.804310	−	0.183745i
$796$	−50857.1	−	88087.1i	−2.26455	−	3.92232i
$797$	11813.1			0.525019			0.262510	−	0.964929i	$-0.415450\pi$
$797$	11813.1			0.525019			0.262510	+	0.964929i	$0.415450\pi$
$798$	−6907.53	−	22409.3i	−0.306421	−	0.994086i
$799$	11082.2	+	6398.32i	0.490689	+	0.283299i
$800$	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
$803$	−31848.3			−1.39963
$804$	10232.6	−	11023.8i	0.448852	−	0.483557i
$805$	5247.75	−	9089.37i	0.229763	−	0.397960i
$806$	22623.3	+	15428.9i	0.988676	+	0.674269i
$807$	10691.8	+	9924.44i	0.466380	+	0.432908i
$808$		−	96997.7i		−	4.22323i
$809$	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	$0.0211478\pi$
$810$	28623.8	+	35951.1i	1.24165	+	1.55950i
$811$			3849.49i			0.166676i	0.996521	+	0.0833378i	$0.0265581\pi$
$811$			3849.49i			0.166676i	−0.996521	+	0.0833378i	$0.973442\pi$
$812$	21972.1	+	12685.6i	0.949592	+	0.548247i
$813$	−6642.42	−	1517.46i	−0.286543	−	0.0654609i
$814$	1636.70	+	944.952i	0.0704748	+	0.0406886i
$815$	−28269.0			−1.21499
$816$	−47427.2	−	44023.3i	−2.03466	−	1.88863i
$817$		−	33079.5i		−	1.41653i
$818$	−25560.8			−1.09256
$819$	−5.67525	+	10655.9i	−0.000242136	+	0.454637i
$820$	16303.8			0.694332
$821$			504.340i			0.0214392i	0.999943	+	0.0107196i	$0.00341222\pi$
$821$			504.340i			0.0214392i	−0.999943	+	0.0107196i	$0.996588\pi$
$822$	−5039.99	+	22061.6i	−0.213856	+	0.936117i
$823$	30422.7			1.28854			0.644270	−	0.764798i	$-0.277161\pi$
$823$	30422.7			1.28854			0.644270	+	0.764798i	$0.277161\pi$
$824$	−15424.4	−	8905.30i	−0.652106	−	0.376494i
$825$	−2899.09	+	3123.25i	−0.122344	+	0.131803i
$826$	26046.1	+	15037.7i	1.09717	+	0.633450i
$827$		−	7861.80i		−	0.330570i	−0.986246	−	0.165285i	$-0.947146\pi$
$827$		−	7861.80i		−	0.330570i	0.986246	−	0.165285i	$-0.0528544\pi$
$828$	−53811.8	−	25940.5i	−2.25856	−	1.08876i
$829$	−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	$0.937387\pi$
$830$		−	8936.78i		−	0.373735i
$831$	−8146.58	+	35660.2i	−0.340074	+	1.48861i
$832$	4485.69	−	59745.7i	0.186915	−	2.48955i
$833$	8327.28	−	14423.3i	0.346366	−	0.599924i
$834$	8608.66	+	27928.1i	0.357426	+	1.15956i
$835$	−9988.27			−0.413962
$836$	−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
$839$	28133.5	+	16242.9i	1.15766	+	0.668375i	0.950742	−	0.309984i	$-0.100324\pi$
$839$	28133.5	+	16242.9i	1.15766	+	0.668375i	0.206917	+	0.978358i	$0.433657\pi$
$840$	−24085.1	+	25947.3i	−0.989303	+	1.06580i
$841$	−3476.30			−0.142536
$842$	−18256.8	−	31621.7i	−0.747235	−	1.29425i
$843$	−10284.5	+	11079.7i	−0.420186	+	0.452675i
$844$	−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
$848$	−61688.2			−2.49809
$849$	23459.6	+	21775.9i	0.948328	+	0.880267i
$850$	3644.03	+	2103.88i	0.147046	+	0.0848972i
$851$		−	583.370i		−	0.0234990i
$852$	−25826.4	+	27823.3i	−1.03850	+	1.11879i
$853$	38754.7	−	22375.1i	1.55561	−	0.898133i	0.557944	−	0.829879i	$-0.311591\pi$
$853$	38754.7	−	22375.1i	1.55561	−	0.898133i	0.997668	−	0.0682538i	$-0.0217428\pi$
$854$	14385.4	+	24916.2i	0.576413	+	0.998377i
$855$	26144.9	−	17810.2i	1.04577	−	0.712394i
$856$	124306.	+	71767.9i	4.96341	+	2.86563i
$857$	459.332	+	795.586i	0.0183086	+	0.0317114i	0.875035	−	0.484060i	$-0.160839\pi$
$857$	459.332	+	795.586i	0.0183086	+	0.0317114i	−0.856726	+	0.515772i	$0.827505\pi$
$858$	18616.0	+	81688.5i	0.740722	+	3.25035i
$859$	−14789.9	+	25616.8i	−0.587455	+	1.01750i	0.407109	+	0.913379i	$0.366537\pi$
$859$	−14789.9	+	25616.8i	−0.587455	+	1.01750i	−0.994564	+	0.104123i	$0.966797\pi$
$860$	−70204.9	+	40532.8i	−2.78368	+	1.60716i
$861$	−2786.90	+	859.044i	−0.110310	+	0.0340025i
$862$	−3838.26	+	6648.06i	−0.151661	+	0.262684i
$863$		−	39382.6i		−	1.55342i	−0.629861	−	0.776708i	$-0.716888\pi$
$863$		−	39382.6i		−	1.55342i	0.629861	−	0.776708i	$-0.283112\pi$
$864$	59329.9	+	47371.3i	2.33616	+	1.86528i
$865$	−6848.50	+	3953.99i	−0.269198	+	0.155421i
$866$	−47165.8	+	27231.2i	−1.85076	+	1.06854i
$867$	−1350.21	+	5910.29i	−0.0528898	+	0.231515i
$868$	−9543.59	−	16530.0i	−0.373192	−	0.646388i
$869$	−120.204	+	69.4001i	−0.00469236	+	0.00270913i
$870$	−10549.5	+	46178.4i	−0.411104	+	1.79953i
$871$	2824.45	+	5867.12i	0.109877	+	0.228243i
$872$	−78919.2			−3.06484
$873$	−13743.4	+	1024.49i	−0.532810	+	0.0397178i
$874$	−28456.2	+	49287.6i	−1.10131	+	1.90753i
$875$	−5544.91	+	9604.07i	−0.214231	+	0.371059i
$876$	−15855.8	−	51439.2i	−0.611551	−	1.98398i
$877$		−	20348.5i		−	0.783488i	−0.920074	−	0.391744i	$-0.871872\pi$
$877$		−	20348.5i		−	0.783488i	0.920074	−	0.391744i	$-0.128128\pi$
$878$		−	40833.4i		−	1.56954i
$879$	9787.84	+	31753.6i	0.375581	+	1.21845i
$880$	−76502.6	+	132506.i	−2.93057	+	5.07590i
$881$	−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	$0.769282\pi$
$882$	−17131.5	+	35538.3i	−0.654024	+	1.35673i
$883$	18405.7			0.701475			0.350737	−	0.936474i	$-0.385931\pi$
$883$	18405.7			0.701475			0.350737	+	0.936474i	$0.385931\pi$
$884$	53861.2	−	25929.0i	2.04926	−	0.986522i
$885$	−9036.16	+	39554.1i	−0.343217	+	1.50237i
$886$	50977.3	−	29431.8i	1.93298	−	1.11600i
$887$	7683.33	+	13307.9i	0.290847	+	0.503761i	0.974010	−	0.226504i	$-0.0727297\pi$
$887$	7683.33	+	13307.9i	0.290847	+	0.503761i	−0.683163	+	0.730265i	$0.739396\pi$
$888$	−438.251	+	1918.37i	−0.0165617	+	0.0724957i
$889$	−15460.6	+	8926.20i	−0.583277	+	0.336755i
$890$	4536.66	−	2619.24i	0.170864	−	0.0986486i
$891$	−43458.2	−	17095.5i	−1.63401	−	0.642786i
$892$		−	85668.5i		−	3.21569i
$893$	−10433.7	+	18071.8i	−0.390988	+	0.677210i
$894$	14015.6	−	4320.22i	0.524330	−	0.161622i
$895$	38503.9	−	22230.2i	1.43804	−	0.830250i
$896$	−10671.8	+	18484.1i	−0.397902	+	0.689187i
$897$	18964.0	−	17584.2i	0.705897	−	0.654535i
$898$	11015.0	+	19078.6i	0.409328	+	0.708978i
$899$	−13625.2	−	7866.50i	−0.505478	−	0.291838i
$900$	−6487.78	−	3127.50i	−0.240288	−	0.115833i
$901$	−9278.55	−	16070.9i	−0.343078	−	0.594229i
$902$	−19857.6	+	11464.8i	−0.733020	+	0.423209i
$903$	9864.85	−	10627.6i	0.363546	−	0.391655i
$904$		−	51527.7i		−	1.89578i
$905$	24333.3	+	14048.9i	0.893776	+	0.516022i
$906$	−230.477	−	213.936i	−0.00845154	−	0.00784498i
$907$	11289.2			0.413286			0.206643	−	0.978416i	$-0.433746\pi$
$907$	11289.2			0.413286			0.206643	+	0.978416i	$0.433746\pi$
$908$	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	−0.999734	−	0.0230743i	$-0.992655\pi$
$911$	−14294.1	−	24758.0i	−0.519850	−	0.900406i	0.479884	−	0.877332i	$-0.340679\pi$
$912$	71788.9	−	77339.5i	2.60654	−	2.80808i
$913$	4540.88	+	7865.03i	0.164601	+	0.285098i
$914$	−70606.4			−2.55520
$915$	−26405.2	+	28446.8i	−0.954019	+	1.02778i
$916$	−55794.8	−	32213.2i	−2.01257	−	1.16196i
$917$	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	$-0.540865\pi$
$920$	85922.3			3.07910
$921$	−9790.65	−	31762.7i	−0.350285	−	1.13639i
$922$	−1764.79	+	3056.71i	−0.0630373	+	0.109184i
$923$	−7128.70	−	14808.2i	−0.254219	−	0.528079i
$924$	13006.2	−	56932.2i	0.463065	−	2.02698i
$925$		−	70.3337i		−	0.00250006i
$926$	18001.0	−	31178.7i	0.638824	−	1.10648i
$927$	518.606	+	6957.03i	0.0183746	+	0.246493i
$928$			78257.2i			2.76823i
$929$	−620.371	−	358.171i	−0.0219093	−	0.0126493i	0.489005	−	0.872281i	$-0.337360\pi$
$929$	−620.371	−	358.171i	−0.0219093	−	0.0126493i	−0.510915	+	0.859631i	$0.670693\pi$
$930$	24243.7	−	26118.1i	0.854818	−	0.920912i
$931$	23520.0	+	13579.3i	0.827968	+	0.478028i
$932$	58243.4			2.04703
$933$	−9019.21	+	39479.9i	−0.316480	+	1.38533i
$934$			27705.3i			0.970606i
$935$	−46027.2			−1.60989
$936$	−75571.5	+	43577.6i	−2.63903	+	1.52177i
$937$	10269.7			0.358053			0.179027	−	0.983844i	$-0.442705\pi$
$937$	10269.7			0.358053			0.179027	+	0.983844i	$0.442705\pi$
$938$		−	6281.36i		−	0.218650i
$939$	−5379.69	−	4993.60i	−0.186965	−	0.173546i
$940$	51138.5			1.77442
$941$	15117.0	+	8727.78i	0.523697	+	0.302357i	0.738446	−	0.674313i	$-0.235560\pi$
$941$	15117.0	+	8727.78i	0.523697	+	0.302357i	−0.214749	+	0.976669i	$0.568893\pi$
$942$	−42169.1	−	9633.56i	−1.45854	−	0.333204i
$943$	6129.57	+	3538.91i	0.211672	+	0.122209i
$944$			135338.i			4.66618i
$945$	13711.0	+	2074.87i	0.471978	+	0.0714240i
$946$	57005.1	−	98735.7i	1.95919	−	3.39342i
$947$			22499.0i			0.772038i	0.922491	+	0.386019i	$0.126150\pi$
$947$			22499.0i			0.772038i	−0.922491	+	0.386019i	$0.873850\pi$
$948$	−171.935	−	159.595i	−0.00589048	−	0.00546772i
$949$	23237.7	+	1744.68i	0.794867	+	0.0596784i
$950$	−3430.80	+	5942.33i	−0.117168	+	0.202942i
$951$	18308.5	−	19724.1i	0.624283	−	0.672551i
$952$	−35524.4			−1.20940
$953$	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
$956$	61489.1	+	35500.8i	2.08023	+	1.20102i
$957$	−14179.4	−	46000.7i	−0.478951	−	1.55381i
$958$	27011.0			0.910947
$959$	3414.40	+	5913.91i	0.114971	+	0.199135i
$960$	−76010.7	−	17364.7i	−2.55545	−	0.583795i
$961$	−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
$965$	30187.5			1.00701
$966$	−23840.6	+	7348.73i	−0.794058	+	0.244763i
$967$	−253.944	−	146.615i	−0.00844498	−	0.00487571i	0.495772	−	0.868453i	$-0.334885\pi$
$967$	−253.944	−	146.615i	−0.00844498	−	0.00487571i	−0.504217	+	0.863577i	$0.668219\pi$
$968$		−	191125.i		−	6.34606i
$969$	30946.2	+	7069.67i	1.02594	+	0.234376i
$970$	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	$0.862557\pi$
$972$	5975.71	−	78701.8i	0.197192	−	2.59708i
$973$	7637.32	+	4409.41i	0.251635	+	0.145282i
$974$	29747.1	+	51523.4i	0.978601	+	1.69499i
$975$	2286.38	−	2120.02i	0.0751003	−	0.0696360i
$976$	−64733.4	+	112122.i	−2.12302	+	3.67717i
$977$	−38408.3	+	22175.0i	−1.25772	+	0.726143i	−0.972630	−	0.232358i	$-0.925356\pi$
$977$	−38408.3	+	22175.0i	−1.25772	+	0.726143i	−0.285087	+	0.958502i	$0.592022\pi$
$978$	49248.1	+	45713.6i	1.61021	+	1.49464i
$979$	−2661.73	+	4610.26i	−0.0868942	+	0.150505i
$980$		−	66555.7i		−	2.16943i
$981$	17403.5	+	25547.8i	0.566412	+	0.831477i
$982$	−42467.9	+	24518.9i	−1.38005	+	0.796770i
$983$	7906.47	−	4564.80i	0.256538	−	0.148113i	−0.366216	−	0.930530i	$-0.619347\pi$
$983$	7906.47	−	4564.80i	0.256538	−	0.148113i	0.622754	+	0.782417i	$0.286014\pi$
$984$	−17498.0	−	16242.2i	−0.566887	−	0.526202i
$985$	8625.93	+	14940.5i	0.279030	+	0.483295i
$986$	−41162.9	+	23765.4i	−1.32951	+	0.767590i
$987$	−8741.40	+	2694.48i	−0.281907	+	0.0868960i
$988$	42282.4	+	87831.6i	1.36152	+	2.82823i
$989$	−35192.3			−1.13150
$990$	108729.	−	8105.13i	3.49055	−	0.260200i
$991$	−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	$0.891348\pi$
$992$	29437.1	−	50986.6i	0.942168	−	1.63188i
$993$	35988.6	+	8221.60i	1.15011	+	0.262744i
$994$			15853.7i			0.505884i
$995$		−	57304.2i		−	1.82579i
$996$	−10442.4	+	11249.8i	−0.332208	+	0.357894i
$997$	−12692.9	+	21984.7i	−0.403198	+	0.698359i	−0.994110	−	0.108377i	$-0.965435\pi$
$997$	−12692.9	+	21984.7i	−0.403198	+	0.698359i	0.590912	+	0.806736i	$0.298768\pi$
$998$	686.928	−	1189.79i	0.0217879	−	0.0377377i
$999$	717.659	−	281.172i	0.0227285	−	0.00890479i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.4.l.a.4.2	✓	80	1.1	even	1	trivial
117.4.l.a.88.39	yes	80	117.88	even	6	inner
117.4.r.a.43.2	yes	80	9.7	even	3
117.4.r.a.49.2	yes	80	13.10	even	6
351.4.l.a.127.2		80	117.101	odd	6
351.4.l.a.199.39		80	3.2	odd	2
351.4.r.a.10.39		80	39.23	odd	6
351.4.r.a.316.39		80	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-5.36996i q^{2} +(-4.96560 + 1.53062i) q^{3} -20.8364 q^{4} +(-10.1662 - 5.86946i) q^{5} +(8.21934 + 26.6651i) q^{6} +(7.29194 + 4.21000i) q^{7} +68.9311i q^{8} +(22.3144 - 15.2009i) q^{9} +(-31.5187 + 54.5920i) q^{10} -64.0601i q^{11} +(103.465 - 31.8926i) q^{12} +(-3.50927 + 46.7406i) q^{13} +(22.6075 - 39.1574i) q^{14} +(59.4652 + 13.5848i) q^{15} +203.465 q^{16} +(30.6034 + 53.0066i) q^{17} +(-81.6280 - 119.828i) q^{18} +(-86.4378 + 49.9049i) q^{19} +(211.827 + 122.299i) q^{20} +(-42.6528 - 9.74404i) q^{21} -344.000 q^{22} +(53.0925 + 91.9588i) q^{23} +(-105.507 - 342.284i) 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} -144.612 q^{29} +(72.9500 - 319.325i) q^{30} +(94.2187 + 54.3972i) q^{31} -541.152i q^{32} +(98.0514 + 318.097i) q^{33} +(284.643 - 164.339i) q^{34} +(-49.4208 - 85.5994i) q^{35} +(-464.953 + 316.732i) q^{36} +(-4.75786 - 2.74695i) q^{37} +(267.987 + 464.167i) q^{38} +(-54.1163 - 237.467i) q^{39} +(404.588 - 700.767i) q^{40} +(57.7255 - 33.3278i) q^{41} +(-52.3251 + 229.043i) q^{42} +(-165.712 + 287.022i) q^{43} +1334.78i q^{44} +(-316.074 + 23.5614i) q^{45} +(493.815 - 285.104i) q^{46} +(181.062 - 104.536i) q^{47} +(-1010.33 + 311.428i) q^{48} +(-136.052 - 235.649i) q^{49} +(59.5365 - 34.3734i) q^{50} +(-233.097 - 216.368i) q^{51} +(73.1207 - 973.908i) q^{52} -303.187 q^{53} +(588.742 + 470.075i) q^{54} +(-375.998 + 651.247i) q^{55} +(-290.200 + 502.641i) q^{56} +(352.831 - 380.111i) q^{57} +776.561i q^{58} +665.165i q^{59} +(-1239.04 - 283.060i) q^{60} +(-318.154 + 551.059i) q^{61} +(292.110 - 505.950i) q^{62} +(226.711 - 16.9000i) q^{63} -1278.24 q^{64} +(310.018 - 454.577i) q^{65} +(1708.17 - 526.532i) q^{66} +(120.310 - 69.4610i) q^{67} +(-637.665 - 1104.47i) q^{68} +(-404.390 - 375.367i) q^{69} +(-459.665 + 265.388i) q^{70} +(-303.653 + 175.314i) q^{71} +(1047.81 + 1538.16i) q^{72} -497.163i q^{73} +(-14.7510 + 25.5495i) q^{74} +(-48.7550 - 45.2559i) q^{75} +(1801.06 - 1039.84i) q^{76} +(269.693 - 467.122i) q^{77} +(-1275.19 + 290.602i) q^{78} +(-1.08336 - 1.87643i) q^{79} +(-2068.47 - 1194.23i) q^{80} +(266.867 - 678.397i) q^{81} +(-178.969 - 309.983i) q^{82} +(-122.776 + 70.8847i) q^{83} +(888.731 + 203.031i) q^{84} -718.500i q^{85} +(1541.30 + 889.869i) q^{86} +(718.087 - 221.346i) q^{87} +4415.73 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} +(-551.114 - 125.902i) q^{93} +(-561.355 - 972.296i) q^{94} +1171.66 q^{95} +(828.296 + 2687.15i) q^{96} +(-442.042 - 255.213i) q^{97} +(-1265.42 + 730.592i) q^{98} +(-973.769 - 1429.46i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - q^{3} - 306 q^{4} + 42 q^{6} - 3 q^{7} - 17 q^{9} - 10 q^{10} - 101 q^{12} - 13 q^{13} + 126 q^{14} - 63 q^{15} + 1102 q^{16} - 138 q^{17} - 168 q^{18} - 96 q^{19} - 387 q^{20} - 249 q^{21} + 62 q^{22}+ \cdots - 2331 q^{99}+O(q^{100}) \) 80 * q - q^3 - 306 * q^4 + 42 * q^6 - 3 * q^7 - 17 * q^9 - 10 * q^10 - 101 * q^12 - 13 * q^13 + 126 * q^14 - 63 * q^15 + 1102 * q^16 - 138 * q^17 - 168 * q^18 - 96 * q^19 - 387 * q^20 - 249 * q^21 + 62 * q^22 - 327 * q^23 - 258 * q^24 + 798 * q^25 + 510 * q^26 - 364 * q^27 + 18 * q^28 - 402 * q^29 + 450 * q^30 + 180 * q^31 + 369 * q^33 + 24 * q^34 + 297 * q^35 + 206 * q^36 + 246 * q^37 - 768 * q^38 - 983 * q^39 + 328 * q^40 + 381 * q^41 - 1113 * q^42 - 83 * q^43 - 1038 * q^45 - 6 * q^46 + 372 * q^47 + 1205 * q^48 + 1613 * q^49 - 708 * q^50 + 186 * q^51 + 402 * q^52 - 2568 * q^53 - 627 * q^54 - 127 * q^55 - 2298 * q^56 + 1332 * q^57 + 711 * q^60 - 419 * q^61 + 135 * q^62 + 1845 * q^63 - 3178 * q^64 + 363 * q^65 + 6228 * q^66 + 879 * q^67 + 1950 * q^68 - 3153 * q^69 - 1005 * q^70 - 2598 * q^71 + 1812 * q^72 + 471 * q^74 - 68 * q^75 + 1485 * q^76 - 1584 * q^77 - 60 * q^78 - 260 * q^79 - 1332 * q^80 + 1639 * q^81 - 1273 * q^82 + 1194 * q^83 + 1671 * q^84 - 2910 * q^86 - 1629 * q^87 - 1562 * q^88 - 1056 * q^89 + 2559 * q^90 + 537 * q^91 + 1056 * q^92 - 75 * q^93 + 539 * q^94 + 10584 * q^95 + 6777 * q^96 + 789 * q^97 - 6339 * q^98 - 2331 * q^99

Introduction

L-functions

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